User manual | Heft 189 Pawan Kumar Thapa Physically

Heft 189
Pawan Kumar Thapa
Physically-based spatially distributed
rainfall runoff modelling
for soil erosion estimation
Physically-based spatially distributed rainfall runoff
modelling for soil erosion estimation
Von der Fakultät Bau- und Umweltingenieurwissenschaften der
Universität Stuttgart zur Erlangung der Würde eines
Doktor-Ingenieurs (Dr.-Ing.) genehmigte Abhandlung
Vorgelegt von
Pawan Kumar Thapa
aus Kathmandu / Nepal
Hauptberichter:
Mitberichter:
Prof. Dr. rer. nat. Dr.-Ing. habil. András Bárdossy
Prof. Dr. Erwin Zehe
Tag der mündlichen Prüfung:
22. Dezember 2009
Institut für Wasserbau der Universität Stuttgart
2010
Heft 189
Physically-based spatially
distributed rainfall runoff
modelling for soil erosion
estimation
von
Dr.-Ing.
Pawan Kumar Thapa
Eigenverlag des Instituts für Wasserbau der Universität Stuttgart
D93
Physically-based spatially distributed rainfall runoff modelling for soil
erosion estimation
Bibliografische Information der Deutschen Nationalbibliothek
Die Deutsche Nationalbibliothek verzeichnet diese Publikation in der Deutschen
Nationalbibliografie; detaillierte bibliografische Daten sind im Internet über
http://www.d-nb.de abrufbar
Thapa, Pawan, Kumar:
Physically-based spatially distributed rainfall runoff modelling for soil erosion
estimation / von Pawan Kumar Thapa. Institut für
Wasserbau, Universität Stuttgart. - Stuttgart: Inst. für Wasserbau, 2010
(Mitteilungen / Institut für Wasserbau, Universität Stuttgart: H. 189)
Zugl.: Stuttgart, Univ., Diss., 2010
ISBN 978-3-933761-93-4
NE: Institut für Wasserbau <Stuttgart>: Mitteilungen
Gegen Vervielfältigung und Übersetzung bestehen keine Einwände, es wird lediglich
um Quellenangabe gebeten.
Gedruckt mit Unterstützung des Deutschen Akademischen Austauschdienstes
Herausgegeben 2010 vom Eigenverlag des Instituts für Wasserbau
Druck: Document Center S. Kästl, Ostfildern
Acknowledgement
This research work was carried out as a doctoral student in the department of ‘Hydrology and Geohydrology’ of ‘Institute of Hydraulics (IWS)’ in ‘Stuttgart University’ within the academic framework of ‘ENWAT International Doctoral Program’
and was financially supported by a scholarship program (DAAD) provided by the
‘Deutscher Akademischer Austauschdienst’, which I gratefully acknowledge and feel
honored for.
My first and foremost thanks go to my eminent supervisor Prof. Dr. rer. nat.
Dr.-Ing. András Bárdossy for providing me this precious opportunity to work with
him. I cannot explain how greatly indebted I am to him, who helped in attaining my
childhood dream of once becoming a PhD doctor to a close reality. His acceptance
for supervising me helped me to win the DAAD scholarship from the beginning.
His continuous support, valuable suggestions, constructive criticisms, fruitful discussions and enlightening guidance through the years have brought me to the point of
successfully completing this thesis. Thank you very much for teaching me the ever
optimistic attitude, which not only helped me during this work but will be an asset
in my future too. I am fortunate to be your student.
My sincere and deepest gratitude goes also to Prof. Dr. Erwin Zehe for his willingness and acceptance to co-supervise my work. His helpful and friendly nature always
makes me feel comfortable to ask for any support and guidance anytime.
I would also like to thank all my colleagues and friends at the institute for the wonderful atmosphere, several fruitful discussions and the continuous support. Thank
you Dr.-Ing. Arne Färber, Dr.-Ing. Tapash Das, Dr.-Ing. Wei Yang, Dr.-Ing Yi He,
Osorio Haydee and Dr.-Ing. Sachin Patil for the motivating tips and encouragement
during the hard days in the beginning of my research period. Frequent discussions
with Abror Gafurov, Jing Li, Mahboob Alam, Min Liu, Shailesh Singh, Alehandro
Chamorro, Mahyar Mehdizadeh and Bukimchandra Oinam helped me to feel better
several times during the hard times of the research period. I am heartedly grateful
to Dr.-Ing Jürgen Brommundt and Steffan Schönau who were always there to help
me and whose continuous support and encouragement through the years values a
lot during my research work. I owe a lot to them for my knowledge in German
language too. Cooperation, help and suggestions received from Christian Ebert,
Claus Haslauer, Ferdinand Beck, Henning Lebrenz, Jan Bliefernicht, Dr.-Ing. Jens
Götzinger, Dr.-Ing. Jochen Seidel and Thomas Pfaff are also duely acknowledged
and I am always obliged to them. I wish to mention deep sense of gratitude towards
Mr. Ferdinand Beck for his very kind help to write the summary of my work in
German language and towards Mr. Bikash Sherchan for his never tiring help during
the write-up in Latex. I would also like to thank Dr.-Ing. Edwin Ayros to provide his
i
Acknowledgement
valuable comments on my thesis write-up. My sincere thanks also go to Mrs Krista
Uhrmann (IWS), Dr. Ing. Gabriele Hartmann (ENWAT) and Mr. Benedikt von
Romberg (DAAD) for always being cooperative and helpful to me.
Finally, I am extremely grateful to my beloved parents and brothers for supporting
me unconditionally in all my choices. My heartfelt thanks to my wife Sapana Sapkota Thapa for always being there for me with enormous love and patience. Thanks
for being a source of constant support and encouragement.
I am thankful to all those who I might have inadvertently failed to mention here,
but have made positive contribution in successful completion of this work. Thank
you all for all the academic and non-academic issues that we shared for years. I
feel privileged to have your company and learned a lot from you all. Of course, this
endeavour would not have been possible without the direct and indirect help from
you all.
ii
Contents
Acknowledgement
i
List of Figures
vi
List of Tables
ix
List of Abbreviations
xii
Abstract
xv
Kurzfassung
1 General Background
1.1 Introduction . . . . . . . . . . . . . . . . . . . . . .
1.2 Hydrology and soil erosion: The Literature Review
1.2.1 Surface Runoff in a catchment . . . . . . .
1.2.2 Erosion, Sediment Yield and their effects .
1.2.3 Distributed watershed modeling . . . . . .
1.2.4 Spatial erosion assessment . . . . . . . . . .
1.3 Problem Statement and Motivation . . . . . . . . .
1.4 Aim, Objectives and Research Questions . . . . . .
xxiii
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2 Joint Hydrological - Soil Erosion Modeling
2.1 Background . . . . . . . . . . . . . . . . . . . . . . . . . . . .
2.2 Universal Soil Loss Equation (USLE) and its modification . .
2.2.1 Introduction . . . . . . . . . . . . . . . . . . . . . . .
2.2.2 Rainfall - Runoff erosivity factor (R) . . . . . . . . . .
2.2.3 Soil erodibility factor (K) . . . . . . . . . . . . . . . .
2.2.4 Topographic factor (LS) . . . . . . . . . . . . . . . . .
2.2.5 Cover management factor (C) . . . . . . . . . . . . . .
2.2.6 Support practice factor (P) . . . . . . . . . . . . . . .
2.3 Sediment Delivery Ratio and Sediment Yield . . . . . . . . .
2.4 Rainfall-Runoff modeling . . . . . . . . . . . . . . . . . . . . .
2.4.1 SCS-CN model and its modifications . . . . . . . . . .
2.4.2 Water Flow Balance Simulation Model - WaSiM-ETH
2.5 Application of remote sensing and GIS in the modeling . . . .
3 The
3.1
3.2
3.3
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study area and available data: An overview
33
Background . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 33
Ganspoel catchment in Central Belgium . . . . . . . . . . . . . . . . . 33
Rems catchment in Southern Germany . . . . . . . . . . . . . . . . . . 37
iii
Contents
4 Spatially Distributed Soil Erosion estimation: A case study
4.1 Relevancy of the case study . . . . . . . . . . . . . . . . . . . . . .
4.2 Methodology, model formulation, application and results . . . . . .
4.2.1 Selection of events and data preprocessing . . . . . . . . . .
4.2.2 Rainfall-runoff modeling . . . . . . . . . . . . . . . . . . . .
4.2.2.1 Using SCS-CN model with different modifications
4.2.2.2 Using WaSiM-ETH model . . . . . . . . . . . . .
4.2.2.3 Results and comparisons . . . . . . . . . . . . . .
4.2.3 Estimation of factors influencing erosion . . . . . . . . . . .
4.2.4 Sediment Delivery Ratio and Sediment Yield estimation . .
4.3 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
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5 Physically based distributed hydrological modeling for HSA estimation
5.1 Background . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
5.2 Distributed watershed modeling of surface runoff with WaSiM-ETH
5.2.1 Soil model for WaSiM-ETH version using extended Top model
approach . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
5.3 Setup of WaSiM-ETH for Rems catchment . . . . . . . . . . . . . .
5.4 Calibration and Simulation: Procedures, Results and Discussions . .
5.4.1 Free model parameters and their influences . . . . . . . . . .
5.4.2 Multi-criteria assessment of model performance . . . . . . . .
5.4.3 Calibration procedures and Simulation . . . . . . . . . . . . .
5.4.3.1 Gauss-Marquardt-Levenberg method . . . . . . . .
5.4.3.2 Shuffled-Complex-Evolution method (SCE-UA) . . .
5.4.3.3 Robust Parameter Estimation (ROPE) - a new Algorithm . . . . . . . . . . . . . . . . . . . . . . . . . .
5.5 Surface runoff estimation through baseflow separation . . . . . . . .
5.5.1 Parameters identification based on surface runoff and other
criteria . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
5.6 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
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6 Spatially Distributed and Temporally varying soil erosion risk estimation 132
6.1 Background . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 132
6.2 Estimation of rainfall-runoff erosivity factor . . . . . . . . . . . . . . . 132
6.2.1 Daily Runoff erosivity factor using WaSiM-ETH results . . . . 132
6.2.2 Rainfall erosivity factor using NiedSiM results . . . . . . . . . 134
6.3 Estimation of topographic factor . . . . . . . . . . . . . . . . . . . . . 139
6.4 Temporal dynamics of spatially distributed crop cover factor . . . . . 140
6.4.1 MODIS NDVI series for Rems catchment . . . . . . . . . . . . 142
6.4.2 Monthly cover factor estimation using NDVI . . . . . . . . . . 144
6.5 Distribution and dynamics of soil erosion risk in Rems catchment . . . 146
6.6 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 152
7 Overall summary and Outlook
156
7.1 Overall summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 156
7.2 Outlook . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 166
iv
Contents
Bibliography
168
v
List of Figures
1.1
HSAs-ESAs-CSAs concept for erosion risk estimation . . . . . . . . . .
2.1
2.2
An introduction to USLE model . . . . . . . . . . . . . . . . . . . . . 15
Model structure of WaSiM-ETH (Schulla & Jasper 1999, 2006) . . . . 30
3.1
3.2
3.3
3.4
3.5
Location of Ganspoel catchment . . . . . . . . . . . . . . . . . . . .
Topography of Ganspoel catchment . . . . . . . . . . . . . . . . . . .
Location of Rems catchment . . . . . . . . . . . . . . . . . . . . . .
Topography of Rems catchment . . . . . . . . . . . . . . . . . . . . .
Land use of Rems catchment (classified from LANDSAT 1993) (left)
and Major land use coverage area in 1975, 1993 and 2000 (right) . .
3.6 Soil texture of Rems catchment (left) and Area coverage percentage
by each type of soil texture (right) . . . . . . . . . . . . . . . . . . .
3.7 Locations of meteorological stations in and around Rems catchment
3.8 Intra-annual (left) and inter-annual (right) variability of rainfall in
Rems catchment . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
3.9 Discharge gauges and subcatchments of the Rems catchment . . . .
3.10 Intra-annual (left) and inter-annual (right) variability of runoff in
Rems catchment . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
4.1
4.2
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Methodology to estimate spatial distribution of erosion source areas .
Measured catchment outlet data. The May 19, 1997 event (Event No.
1) in Ganspoel . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
4.3 Adopted methodology for estimating runoff using SCS-CN models . .
4.4 Adopted methodology for estimating runoff using WaSiM-ETH model
4.5 Comparison of simulated against the observed runoff volumes from
different models . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
4.6 Maps of runoff simulated by modified SCS-CN Model 6 (left) and
WaSiM-ETH (right) for event number 7 . . . . . . . . . . . . . . . . .
4.7 Spatially distributed LS factor estimated following 1-D (left) and 2-D
(right) approaches . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
4.8 Spatial patterns of erosion as observed and simulated by different models for May 1997 events . . . . . . . . . . . . . . . . . . . . . . . . . .
4.9 Modeled percentage of erosion volume (left) and modeled erosion rate
(right) with respect to distance from the observed erosion area for May
1997 event . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
4.10 Observed and simulated hydrographs with WaSiM-ETH for event no.
7 (left) and event no. 6 (right) . . . . . . . . . . . . . . . . . . . . . .
4.11 Spatially distributed surface runoff for the event no. 7 simulated by
WaSiM-ETH . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
vi
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73
LIST OF FIGURES
5.1
5.2
5.3
5.4
5.5
5.6
5.7
5.8
5.9
5.10
5.11
5.12
5.13
5.14
5.15
5.16
5.17
5.18
5.19
5.20
5.21
5.22
6.1
6.2
6.3
6.4
Topographic analysis of a DEM by TANALYS (Schulla & Jasper, 2006) 84
Flow travel time grid for the river gauge network of Rems catchment . 85
Spatially distributed topographic wetness index calculated for Rems
catchment . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 85
Spatial average annual precipitation in Rems catchment . . . . . . . . 89
Objective function approaching its optimum in steepest gradient method 96
Check for homoscedasticity (top) and independency (bottom) of residuals of calibration with PEST . . . . . . . . . . . . . . . . . . . . . . . 98
Simulated and observed hydrographs at the gauges for the calibration
year 1993 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 99
Monthly variation of daily precipitation (left) and temperature (right)
in Rems catchment during the year 1996 and average of simulation
period (1990-2005) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 103
Comparisons of yearly NS efficiencies with the parameters calibrated
with PEST for the year 1993, 1996 and 2000 . . . . . . . . . . . . . . 103
Surface runoff generation probabilities (HSAs) for the month January
with the three sets of parameters calibrated with PEST . . . . . . . . 104
Illustration of Shuffled Complex Evolution (SCE-UA) method (Duan
et al. 1994) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 107
Objective function reduction during calibration with PEST . . . . . . 109
Relation between inflow at Schorndorf and outflow at Neustadt . . . . 109
Surface runoff generation probabilities (HSAs) for the month January
with the parameters calibrated with SCE-UA . . . . . . . . . . . . . . 110
Steps of ROPE algorithm for robust parameter vectors estimation . . 112
Surface runoff simulated by six robust parameter sets of each subcatchment separately . . . . . . . . . . . . . . . . . . . . . . . . . . . . 113
Distributed Surface runoff simulated by different good parameter sets
identical for all subcatchments . . . . . . . . . . . . . . . . . . . . . . 116
Statistics of distributed surface runoff (1993) simulated by different
good parameter sets identical for all subcatchments . . . . . . . . . . . 118
Surface runoff-baseflow separation of observed discharge series (1993)
in Gauge 1 using digital filter . . . . . . . . . . . . . . . . . . . . . . . 119
Distribution of the geometrical depth of the parameter sets deep and
non-deep on the basis of the surface runoff volume error . . . . . . . . 120
Performance analysis of 1955 good parameter sets (step-3) based on
different criteria . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 122
Performance analysis of 3007 good parameter sets (step-2) based on
different criteria . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 124
Spatially distributed MUSLE-based erosivity for day 30/03/2000 with
the four different parameter sets . . . . . . . . . . . . . . . . . . . . .
Regression estimated annual R factor against observed for calibration
(left) and validation (right) . . . . . . . . . . . . . . . . . . . . . . . .
Spatial variation of the topographic factor (LS factor) in Rems catchment . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Spatial variation and temporal dynamics of NDVI in Rems catchment
134
138
141
144
vii
LIST OF FIGURES
6.5
6.6
6.7
6.8
6.9
6.10
6.11
6.12
6.13
viii
Temporal variation of spatially averaged NDVI and R-factor in Rems
catchment . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 144
Temporal variation of spatially averaged R and C factor (left) and
precipitation and product of R and C factor (right) in Rems catchment146
Spatial distribution of soil erodibility (K factor) in Rems catchment . 147
Annual sediment yield with different good parameter sets in Rems
catchment . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 148
Monthly sediment yield with different good parameter sets in Rems
catchment . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 148
Annual average sediment yield and area under high erosion risk with
different good parameter sets in Rems catchment . . . . . . . . . . . . 149
Spatial distribution of annual sediment yield with different good parameter sets in Rems catchment . . . . . . . . . . . . . . . . . . . . . 149
Spatial distribution of annual sediment yield frequency averaged over
different good parameter sets in Rems catchment . . . . . . . . . . . . 151
Spatial distribution of monthly sediment yield frequency averaged over
different good parameter sets in Rems catchment . . . . . . . . . . . . 151
List of Tables
2.1
2.2
2.3
Values of K factor [ton.ha.h./(MJ.ha.mm)] based on soil texture . . . 20
NRCS soil groups based on infiltration rate and soil properties . . . . 27
AMC classes for SCS-CN method (SCS 1972) . . . . . . . . . . . . . . 27
3.1
3.2
Main characteristics of Ganspoel catchment . . . . . . . . . . . . . . . 35
Monthly precipitation coefficients in the representative stations of
Rems catchment . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 40
4.1
4.2
4.3
Events selected for the case study in Ganspoel catchment . . . . . . .
Observed land use in Ganspoel catchment during the selected events .
Observed soil surface parameters in Ganspoel catchment during the
selected events . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Infiltration capacity (mm/hr) based on soil surface parameters (Cerdan et al. 2002) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Runoff volume simulated by the six SCS-CN models at catchment outlet
Data requirement for the WaSiM-ETH with TOPMODEL version . .
Modules of WaSiM-ETH used in the case study . . . . . . . . . . . . .
Adjustable parameters in TOPMODEL version of WaSiM-ETH . . . .
Measured saturated hydraulic conductivity as per land use in Ganspoel catchment . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Runoff volume simulated by WaSiM-ETH and its performance measures
Comparison of runoff volume simulated by WaSiM-ETH, SCS-CN and
MEFIDIS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Statistical comparisons of runoff volumes simulated at outlet by different models . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Summary of distributed S factor estimated from different approaches .
Summary of flow accumulation estimated from three different routing
algorithms . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Summary of LS factor estimated from different approaches using three
different routing algorithms . . . . . . . . . . . . . . . . . . . . . . . .
Gross erosion simulated by different models for the event on May 1997
Statistical analysis of the results of better performing approaches /
combinations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
4.4
4.5
4.6
4.7
4.8
4.9
4.10
4.11
4.12
4.13
4.14
4.15
4.16
4.17
5.1
5.2
5.3
5.4
5.5
Necessary input data and derivatives for WaSiM-ETH version 1 . . . .
Basic characteristics of Rems catchment and its subcatchments . . . .
Input parameters to derive land use dependent secondary grids for Rems
Input parameters to derive soil type dependent secondary grids for Rems
Input data from Rems catchment for the parameterization of WaSiMETH . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
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ix
LIST OF TABLES
5.6
5.7
5.8
5.9
5.10
5.11
5.12
5.13
5.14
5.15
5.16
5.17
5.18
5.19
5.20
5.21
5.22
5.23
5.24
5.25
5.26
6.1
6.2
6.3
6.4
6.5
x
Modules of WaSiM-ETH used in the Rems catchment . . . . . . . .
Free model parameters to be estimated from calibration . . . . . . .
Model performance ratings based on NS, PBIAS and RSR . . . . . .
The parameter values calibrated with PEST for the year 1993 . . . .
The yearly model performance with parameter values calibrated with
PEST for the year 1993 with land use of 1993 . . . . . . . . . . . . .
The parameter values calibrated with PEST for the year 1993, 1996
and 2000 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
The yearly model performance with parameter values calibrated with
PEST for the year 1996 with land use of 1993 . . . . . . . . . . . . .
The yearly model performance with parameter values calibrated with
PEST for the year 2000 with land use of 2000 . . . . . . . . . . . . .
Annual total precipitation and annual average daily temperature in
the Rems catchment during the simulation period (1990-2005) . . . .
The obtained best regression models to estimate surface runoff generation probabilities . . . . . . . . . . . . . . . . . . . . . . . . . . . .
The parameter values calibrated with PEST for the year 1993, 1996
and 2000 and with SCE-UA for the year 1993 . . . . . . . . . . . . .
The yearly model performance with parameter values calibrated with
SCE-UA . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
The comparison of model performance with parameter values calibrated with PEST and SCE-UA . . . . . . . . . . . . . . . . . . . .
Assessment of the application of depth function (ROPE algorithm) in
estimation of ‘good parameter vectors’ . . . . . . . . . . . . . . . . .
Different parameter sets same for all subcatchments estimated with
SCE-UA and ROPE and their performance . . . . . . . . . . . . . .
Spatial correlation (values and rank) of the distributed surface runoff
simulated by different good parameter sets identical for all subcatchments . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Twenty deepest parameters and the rank of their depth based on different criteria . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Rank of depth of deepest parameter sets based on different criteria .
Performance measures of selected 21 different parameter sets for the
year 1993 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Performance measures of selected 21 different parameter sets for 19931997 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Performance ranking of the selected 21 different parameter sets . . .
Surface runoff amount simulated by the selected 21 different parameter
sets for the year 1993 . . . . . . . . . . . . . . . . . . . . . . . . . . .
Different models to estimate rainfall erosivity factor, R . . . . . . . .
Annual rainfall erosivity factor, R[M Jmmha−1 h−1 yr−1 ], estimated
by different models . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Monthly rainfall erosivity factor, R[M Jmmha−1 h−1 mo−1 ], estimated
by two different models . . . . . . . . . . . . . . . . . . . . . . . . .
Annual and monthly average rainfall simulated by NiedSim as compared to observed ones . . . . . . . . . . . . . . . . . . . . . . . . . .
.
.
.
.
89
91
95
97
. 99
. 100
. 101
. 102
. 102
. 105
. 108
. 108
. 109
. 114
. 115
. 117
. 121
. 121
. 125
. 125
. 126
. 133
. 135
. 135
. 136
. 137
LIST OF TABLES
6.6
6.7
Annual and monthly rainfall erosivity from NiedSim generated rainfall
Rainfall parameters considered initially for the multiple non-linear regression . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
6.8 Non-linear regression models for monthly erosivity factors . . . . . . .
6.9 Summary of S factor estimated from different approaches . . . . . . .
6.10 Summary of flow accumulation estimated from three different routing
algorithms . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
6.11 Summary of LS factor estimated from different approaches using three
different routing algorithms . . . . . . . . . . . . . . . . . . . . . . . .
6.12 Spatial correlation matrix of the distributed annual sediment yield
values (top) and their rank (bottom) simulated by different good parameter sets in Rems catchment . . . . . . . . . . . . . . . . . . . . .
137
138
139
140
140
141
150
xi
List of Abbreviations
ADR
AGNPS
AMC
ANSWERS
ARS
ASCGRID
ASCII
ASCE
BMP
CC
CCE
CGM
CMA
CMZ
CN
CORINE
CPU
CREAMS
CSA
DA
DEM
DTM
DWD
EOS
EPIC
EROS
ESA
ESRI
EUROSEM
EVI
FAO
FD
FORTRAN
GCTE
GIS
GLEAMS
GLUE
xii
Altitude Dependent Regression
Agricultural Non Point Source Pollution
Antecedent Moisture Conditions
Areal Non-point Source Watershed Environment Response Simulation
Agricultural Resources Services
ASCII to Grid
American Standard Code for Information Interchange
American Society of Civil Engineering
Best Management Practices
Canopy-Cover
Competitive Complex Evolution
Conjugate Gradient Method
Critical Management Areas
Critical Management Zones
Curve Number
COoRdinated INformation on the Environment in the European Community
Central Processing Unit
Chemicals, Runoff, and Erosion from Agricultural Management Systems
Critical Source Areas
Drainage Area
Digital Elevation Model
Digital Terrain Model
Deutscher Wetterdienst
Earth Observing System
Erosion/Productivity Impact Calculator
Earth Resources Observation and Science centre
Erosion Susceptible/Sensitive Areas
Environmental Systems Research Institute
European Soil Erosion Model
Enhanced Vegetation Index
Food and Agricultural Organization
Flux Decomposition
FORmula TRANslation
Global Change of Terrestrial Ecosystems
Geographic Information System
Groundwater Loading Effects of Agricultural Management Systems
Generalized Likelihood Uncertainity Estimation
List of Abbreviations
GPS
GRIDASCI
GWLF
HAA
HSA
IAHS
IDW
INDEROSI
ISCO
KINEROS2
LAI
LANDSAT
LISEM
LP DAAC
LUBW
MEFIDIS
MF
MIKE-SHE
MMF
MODIS
MRT
MUSLE
NASA
NDVI
NEH
NiedSiM
NIR
NRCS
NS
PBIAS
PEST
PLU
RMSE
ROPE
RSR
RUSLE
SC
SCE-UA
SCS
SDR
SEDD
SEDEM
SF
SLESMA
SLR
SM
Global Positioning System
Grid to ASCII
Generalized Watershed Loading Functions
Hydrologically Active Areas
Hydrologically Sensitive Areas
International Association of Hydrological Sciences
Inverse Distance Weighting
Indonesian Model for Estimating Soil Loss
International Soil Conservation Organization
KINematic EROsion Simulation
Leaf Area Index
Land Satellite
LImburg Soil Erosion Model
Land Processes Distributed Active Archieve Center
Landesanstalt fuer Umwelt, Messungen und Naturschtuz BadenWuerttemberg
Portuguese acronym for Physically Based Distributed Erosion Model
Multiple Flow
MIKE - System Hydrologique European
Morgan, Morgan and Finney
Moderate Resolution Imaging Spectroradiometer
MODIS Reprojection Tool
Modified Universal Soil Loss Equation
National Aeronautics and Space Administration
Normalized Difference Vegetation Index
National Engineering Handbook
Niederschlag SiMulator
Near InfraRed
Natural Resources Conservation Services
Nash-Sutcliffe
Percentage BIAS
Parameter ESTimation tool
Prior Land Use
Root Mean Square Error
Robust Parameter Estimation
RMSE-observations Standard deviation Ratio
Revised Universal Soil Loss Equation
Surface-Cover
Shuffled-Complex-Evolution method
Soil Conservation Service
Sediment Delivery Ratio
SEdiment Delivery Distribution model
Soil Erosion and sediment DElivery Model
Single Flow
Soil Loss Estimation Method for South Africa
Soil Loss Ratio
Soil-Moisture
xiii
List of Abbreviations
SOILOSS
SONNEREL
SR
SWAT
SY
TANALYS
TIN
TOPMODEL
TOPOFACT
USDA
USGS
USLE
VSA
WaSiM-ETH
WaTEM
WEPP
xiv
The computer program SOILOSS is a DOS application that enables
the prediction of soil erosion by rainfall in New South Wales, Australia.
Relative Sunshine Duration
Surface-Roughness
Soil and Water Assessment Tool
Sediment Yield
Terrain Analysis
Triangulated Irregular Model
TOPography-based hydrological MODEL
TOPOgraphic Wettness FACTor
United States Department of Agriculture
United States Geological Survey
Universal Soil Loss Equation
Variable Source Areas
Water Flow and Balance Simulation Model
Water and Tillage Erosion Model
Water Erosion Prediction Project
Abstract
Predictions of spatial patterns are fundamental to many areas including rainfallrunoff and erosion-sediment yield process. Patterns and dynamics are everywhere
in hydrology and soil erosion. The rainfall and consequent runoff is the primary
driving force for erosion and sedimentation process. Addressing several issues like
sedimentation, water quality, conservation measures, environmental and geomorphologic studies etc require not only the quantity and quality of the water and sediment
in a stream, but also the source areas from where the runoff along with the sediments
and contaminants originate. Even if the quantitative estimates are contestable, qualitative results concerning the spatial heterogeneity and temporal dynamics are of
value. So the results of not only "how much" but also "where f rom" is equally or
even more needed to best invest scarce financial resources to minimize the problem.
Several modeling alternatives exist, all with certain potential and limitations. The
use of a distributed rainfall-runoff model is basis for identification of such areas. Distributed models should be able to explicitly represent the spatial variability of some,
if not most, of the important land surface and climatic characteristics. Such models have important applications to estimate spatially distributed surface runoff that
enable further to calculate spatially distributed soil erosion. However, such models,
even in case of physically-based, need prior calibration of some or many parameters.
The optimization and prediction capability of those distributed models is generally
assessed based on their ability to correctly predict lumped hydrograph at watershed
outlet.
The quality and quantity of normally available observed data even in developed countries, at the moment, is simply not enough for the use of a completely physically-based
erosion model. In addition, owing to the problems like, large spatial and temporal
variability of soil erosion phenomena and the uncertainty associated with the input
parameter it is clear that accurate erosion prediction is still difficult and the problem
will not be solved by constructing even more complete and complex models. However,
the available data conditions are normally good enough to try out better hydrological modeling. This directs to an interesting area of research- what improvement in
the modeling of soil erosion and sediment yield can be achieved by improving the
hydrological component of the process? The improvement on the hydrological representation can be best thought by using a physically-based distributed rainfall-runoff
model. Based on this, the general goal of this research is formulated as- investigate
the use of physically-based rainfall-runoff modeling as the hydrological component
with a computationally simple and low data demanding erosion model to estimate
spatially distributed and temporally varying erosion/sediment yield in a catchment.
The USLE model (Wischmeier & Smith 1978) and its variants/modifications is
the simple erosion model used in this research work. It is integrated within GIS
xv
Abstract
framework in this study to account for the spatial heterogeneity of erosion relevant
watershed characteristics. The WaSiM-ETH (Schulla & Jasper 1999, 2006) is the
physically-based distributed hydrological model that is used here for the better hydrological representation in the simple erosion model.
A case study was carried out, at first, in Ganspoel catchment- a small data-rich agricultural catchment located in central Belgium. The study is intended, at first step,
to investigate the use of a less data intensive simple rainfall-runoff model coupled
with the simple but still widely used soil erosion model (i.e. USLE and its variants)
in distributed manner using GIS capabilities to predict the spatial pattern of surface
runoff and sediment source areas within the catchment in addition to the lumped
predictions of runoff and sediment yield at outlet. The next intention of the case
study is to investigate if the better hydrology representation will enhance capability
of the simple erosion model to predict spatial erosion patterns or erosion source areas.
Seven rainfall-runoff-erosion-sediment yield events with varying characteristics and
with different landuse conditions are selected. Using the available data for those
events, the several factors of USLE and its modifications, i.e. crop cover factor C,
soil erodibility factor K, topographical factor LS, management practice factor P ,
and rainfall/runoff erosivity factor R are calculated in GIS environment. Two existing sediment delivery ratio (SDR) estimation methods and one ‘proposed-one’ is
also been tested. In depth work is done to estimate LS-factor examining several algorithms (single flow, multiple flow and flux decomposition) focusing specially on the
difference between and importance of 1-D and 2-D consideration. For R-factor also,
numbers of possible methods are explored. Those methods need runoff volume and
peak flow and this makes the link of soil erosion model with the hydrologic model.
On one hand the simplest runoff estimation method requiring minimal data- the SCS
curve number method has been used in distributed manner. The original form and
its several modified forms mainly, modifications for slope incorporation, continuous
antecedent moisture condition, antecedent moisture dependent initial abstraction,
varying initial abstraction ratio etc are tested. It is noteworthy to mention that
several erosion and water quality models like- SWAT, EPIC, AGNPS, ANSWERS,
CREAMS, GLEAMS, GWLF etc use SCS-CN method for runoff estimation. On
the other hand more complicated but more physically based or process-oriented spatially distributed rainfall-runoff model- the WaSiM-ETH, is used to estimate runoff
volume, peak flow and also the runoff generating areas. The results of runoff, gross
erosion, sediment yield and spatial distribution of erosion producing areas are compared with observed ones and also with that of a physically based soil erosion model
(MEFIDIS). Through the comparison of several forms of erosivity factor, it is found
that the combination of both rainfall and runoff in erosivity representation as proposed by Onstad and Foster simulates erosion better than considering either of them
alone. It is also shown that, unlike the normally followed procedure of considering
the topographic effects on erosion using the flow path length in one dimensional way,
the two dimensional consideration which uses the upslope contributing area, captures
the topographic effects in more realistic way as it ensures more erosion in the hollow
due to the flow convergence. In addition, it is also observed instead of the steepest
descent algorithm, which is followed by almost all the USLE-based models for the
xvi
Abstract
estimation of the upslope contributing area, the flux decomposition algorithm which
considers multi-directional flow from a grid gives better results when simulated and
observed gross erosion and sediment yield are compared. Also from the different
sediment delivery ratio (SDR) models used, it is found that the proposed new one
which is based on more number of relevant factors produces better results at least
for the considered events in the case study. Most importantly, it is observed that
the SCS-CN method with USLE, despite several modifications, could improve the
runoff volume estimation, but could not simulate the spatial distribution of runoff
generating and erosion producing areas well. The spatial distribution resembles the
land use map of the watershed. However, encouraging results were obtained when
WaSiM-ETH is used even with the simple, empirical erosion models- USLE (and its
families). The spatial distribution of runoff generating and erosion producing areas
are very well simulated, reasonably close to the observed ones and comparable to
or sometimes even better than that simulated by the more data-intensive physically
based soil erosion model. This depicts that the simplest and still widely used erosion
model (USLE and its families) requiring minimum input data compared to other
erosion models, can predict the spatial distribution of erosive areas in a catchment
reasonably well when they are coupled with better rainfall runoff model for better
hydrological processes representation in the catchment.
However, an important unreasonable consequence was encountered as a random result while calibrating and applying the WaSiM-ETH model in the Ganspoel catchment. As is the trend, the calibration was done with objective function of minimizing
hydrograph prediction errors in the catchment outlet. Very nice results were obtained
with closely matching hydrographs and high Nash-Sutcliffe efficiencies (0.97 in calibration and 0.81 in validation) thus verifying the calibrated parameters and model
results for further use. But when the corresponding simulated distributed runoff
source areas within the catchment were investigated, a very much unrealistic patterns were observed with almost all the runoff coming from a small isolated patch in
the catchment and no runoff from the areas where erosion and sediment transport
were observed during the events, which is unrealistic. This brings an alarming situation to notice that a very good model performance can be associated with completely
unrealistic process representation within the catchment.
Erosion control strategies or best management practices (BMPs) should focus especially on surface runoff and their spatial and temporal variation within the catchment. In this research work, the influence of surface runoff is defined or captured
through the identification of Hydrologically Sensitive Area (HSA) in the catchment.
The term "HSA" is used to refer to areas in a watershed especially prone to generating runoff that are, therefore, potentially susceptible to transporting sediment and
contaminants to perennial surface water bodies. HSAs, thus, describe the risk of
runoff generation and determine the potential erosion source areas. In addition, the
spatial extent of the runoff-generating areas, the HSAs, changes throughout the year
making some portions of a watershed more prone to runoff in one month than at
another. Recognizing the spatial and temporal variation of HSAs within the catchment limits the scope of watershed scale soil erosion problems to only those sensitive
areas and only for the required period of time. Thus, some erosion conservation
xvii
Abstract
measures or potentially polluting activities might only need to be restricted from an
area for part of each year, and such measures would be more readily accepted and
adopted by the farmers in their agricultural lands. Either direct or remotely sensed
data would provide the most accurate measures of such areas, but these data are
generally not available for large enough areas or long enough periods to calculate
probability of runoff generation. Therefore, HSAs are best determined based on long
term simulations using a physically based hydrological model. The case study is
therefore followed by a detailed investigation in the application of the physicallybased distributed rainfall-runoff model, the WaSiM-ETH, in identifying the spatially
distributed and temporally varying Hydrologically Sensitive Areas (HSAs) within a
catchment.
The identification of distribution and dynamics of the HSAs with WaSiM-ETH is
carried out in the meso-scale Rems catchment of southern Germany. The model,
set up for the Rems catchment (with four subcatchments/gauges), is run in the
WaSiM-ETH runoff generation mode- the combined extended/modified Topmodel
(saturated overland flow) and Green and Ampt (infiltration excess) runoff approach
for the simulation of runoff generating areas. The year 1993 is chosen for calibration
with 1992 as warmup period and the land use used in the modeling is also from the
satellite map of the year 1993. For the CPU intensive WaSiM-ETH, the parameters
estimation is carried out with comparatively faster Gauss-Marquardt-Levenberg algorithm using PEST tool and the daily simulation is done continuously for sixteen
years (1990-2005). The parameter sets are calibrated for each subcatchment independently using their observed discharge series at the respective outlets. The observed
discharge series in the gauges, not the simulated one, are passed to the downstream
subcatchment in each time step to avoid propagation of the error associated with the
simulated series.
The performance measures showed quite good simulation for non-headwater subcatchments 3 and 4 (Schorndorf and Neustadt) but not so good for the headwater
subcatchments 1 and 2 (Schwäbisch Gmünd and Haubersbronn). Aiming for the better overall model performance several further tries are made. Calibration was redone
using the same method but for different time period, the year 1996 (the worst performing year), with the same land use grid (1993). It is also redone for the year 2000
but then using the land use grid of the year 2000. It is observed that, the optimized
values of the parameters vary widely and randomly with the change in calibration
period and/or land use, although the method of estimation is same. However the
trend of model performances remains similar. The year 1996, an extreme case in
the lower side (low precipitation and temperature), could not be simulated properly
except for the calibration is done for this year itself. The WaSiM-ETH model may
be incapable of simulating such low events. However, it is noticed that the calibrated parameter set from the year 1996, which represent events of low magnitude
(say unusual events of the simulation period), have performed better throughout the
simulation period than that from 1993 and 2000 which represent medium events of
the simulation period. This result shows the necessity of the inclusion of or giving
priority to unusual events during calibration for achieving good model performance
overall. Calibrating only the unusual events of a period is not only necessary but,
xviii
Abstract
may also be sufficient; this remains an interesting area for further research. The
spatially distributed monthly HSAs are also estimated from the daily simulated spatially distributed surface runoff grids for all the three sets of the calibrated parameter
sets. They are calculated as the percentage of number of days that any pixel generates surface runoff in that month during the sixteen years of simulation period
(1990-2005). Attempts made to relate these monthly probabilities of surface runoff
generation to the easily measurable relevant proxy parameters (distributed values of
precipitation, topographic wetness index and runoff curve number) shows surprising
and unacceptable results. So the general relationships applicable to identify HSAs
through easily obtainable parameters cannot be devised.
The patterns of spatially distributed surface runoff are found to vary not only among
the different parameter sets with which they were simulated but they also vary
abruptly and unrealistically among the subcatchments. The optimization method
is doubted and then the parameters estimation is redone using a more acceptable
global optimization technique, the SCE-UA (Shuffled Complex Evolution) which requires huge computation time The calibrated values are found to vary widely with the
change in the optimization method too, however the model performances could not be
improved than what was obtained earlier from the considerably quicker method. The
low extreme events as in 1996 are simulated still poorly with the globally optimized
parameters too thus confirming the deficiency of WaSiM-ETH model in simulating
the low events and necessity of using unusual events in calibration. Also the simulated surface runoff patterns are quite different for differently calibrated parameter
sets thus raising question of reliability to use particular pattern for calculating soil
erosion. Further questionable is the unrealistic behaviour that the surface runoff
patterns are still totally different from one subcatchment to another.
In the further attempt to address the problem, a new and completely different approach of parameters estimation, the multidimensional data-depth based "Robust
Parameter Estimation (ROPE)" algorithm, has been applied. The algorithm is based
on the fact that robust parameter sets are geometrically well-structured and lie in the
interior of the parameters cloud in multi-dimensional space. With this, it is aimed
to estimate a set of robust parameter vectors instead of a single set of optimized
parameters like earlier and analyze them with their distributed results to find the
best set for the intended purpose, i.e. to achieve acceptable surface runoff patterns,
the HSAs. The different robust parameter vectors are estimated independently for
each of the four subcatchments based on their respective observed discharge series
and using observed discharges to flow downstream from the upstream catchments.
Again, it is observed that despite the good model performance the simulated surface
runoff pattern are still unrealistic as, besides among the different good parameter
sets, it varies widely among the subcatchments. Then parameter estimation is redone now by not allowing the parameter set to vary among the subcatchments. The
good parameter sets are defined not as the best in the sum of the squared errors of
whole catchment but are defined compromisingly best in sum of the squared errors of
each subcatchment independently. 1955 acceptably good performing robust parameter sets are obtained using the ROPE algorithm. It is finally observed that there are
no more unacceptable random variations of patterns among the subcatchments and
xix
Abstract
seems to be reasonable then. The unacceptable variations of the distributed patterns
among the subcatchments could be thus avoided by assigning same parameter set for
all the subcatchments. Further, the high values of spatial correlation and the rank
correlation among the surface runoff from different good parameter sets prove that
the patterns are uniform and reasonable. But when a simple quantitative analysis
of these distributed results from the good parameter sets was made, once again another unacceptable result came in front. In spite of the good model performances
and reasonable surface runoff patterns within the catchment, the mean surface runoff
and its total amount varies highly, as much as four times, among the different good
parameter sets thus creating doubt to use a particular distributed result quantitatively. They will give unacceptably different results, at least quantitatively in this
case, when they are used further in estimating soil erosion by the surface runoff.
Which prediction, although all from the equally good model performances, should
we believe for further use? These results once again show the very good predictions
by the rainfall runoff model but for all wrong reasons. This indicates that simply the
better hydrograph prediction by a physically-based distributed rainfall runoff model
does not guarantee better hydrology representation by it thus making the reliability
of the distributed results in doubt to be accepted.
The 1955 good parameter sets obtained with the ROPE algorithm are based on
minimum sum of squared error. Then further attempt is made in identifying the
good parameter sets by calculating their depth based on other performance criteria
mainly, the surface runoff volume error among others. The digital filter technique
is used to separate observed surface runoff from the respective hydrographs at the
gauges. It is seen that there are hardly any parameter sets that were good in surface
runoff estimation too at the same time. So compromising with the small loss in other
performance criteria, the good parameter sets are searched in the 3007 parameter
sets which are generated one step back, at the second last step (lower performance
than the last step) of the ROPE algorithm. Here, several good parameters based
on the surface runoff estimation too are found. Twenty different good and robust
parameter sets (from the 3007 sets) based on all performance criteria including the
amount of surface runoff are selected for the further use. Daily surface runoff grids
for the sixteen years are generated with the 21 parameter sets (including the SCE-UA
optimized set) and supplied to the simple modified USLE erosion model (MUSLE)
for spatially distributed and temporally varying erosion risk estimation.
MUSLE based daily erosivity factor (R-factor) is calculated using WaSiM-ETH and
CREAMS model for the sixteen years (1990-2005) with all the 21 different parameter
sets. As a small secondary part of research, an attempt was made to develop new
relationships applicable to calculate the erosivity (R-factor) based on more readily
available daily rainfall data/parameters in the Rems catchment. The 5 minutes’
precipitation time series from 1958 to 2004 were generated for three representative
locations in the Rems catchment using a stochastic simulator called "NiedSim". The
erosivity was calculated from the erosive events in the generated series, independently for the three stations. Then the seven different statistical parameters based
on the daily series were considered as independent variables for the multiple nonlinear regressions which are carried out for each month and each year (1958-2004)
xx
Abstract
to estimate the R-factor. Although the attempt made here is quite a preliminary
one, covering the detail investigation being outside the scope of this thesis work, the
high correlation coefficients for the yearly and monthly models in both calibration
and validation pointed out the applicability of the NiedSim-generated precipitation
series in calculating rainfall erosivity factors and possibilities of obtaining those erosivities acceptably through the use of more easily available daily rainfall parameters
in the region. However in this thesis work, the MUSLE erosivity model based runoff
erosivity factor is used whose spatial heterogeneity and temporal variation identifies
the Hydrologically Sensitive Areas (HSAs), from the erosion point of view, in the
Rems catchment.
On the other hand, the topographic factor (LS-factor), crop cover factor (C-factor)
and the soil erodibility factor (K-factor) are calculated to estimate the spatially
distributed and temporally varying Erosion Susceptible Areas (ESAs) in the Rems
catchment. Several spatially distributed 1-D (considering flow path length) and 2D (considering upstream contributing area) approaches are investigated to estimate
the topographic LS-factor. It is again shown that the 2-D approach incorporates
flow convergence in the estimation of the LS-factor. The upslope contributing areas
are calculated using the single flow, multiple flow and flow decomposition algorithm.
The 2-D approach with flux decomposition routing algorithm along with the Nearing’s slope factor was used to define the effect of topography in identification of the
Erosion Susceptible Areas (ESAs) in the Rems catchment. Unlike to the normal
practices of adopting temporally static C-factor based on a land use map, in this
research work, their temporal dynamics have been captured by utilizing the development and advancement in the field of remote sensing and satellite imagery. The
Normalized Difference Vegetation Index (NDVI), a widely used spectral indicator
of vegetation growth, are extracted (through LPDAAC data archive center) for the
Rems catchment for the period of 2000 to 2008. Those NDVI time series are acquired
from the Terra platform of MODIS satellite and available as 16 days composite. The
prepared NDVI series are transformed to the spatially distributed monthly C-factor
for the Rems catchment by employing a scaling approach proposed by a study led
by European Soil Bureau (van der Knijff et al. 2000). Consequently, it is seen that
the higher erosivity is normally associated with higher crop resistance factor and so
the net effect on the soil erosion, as determined by the magnitude of their product,
would be governed by either of the two. Both of these factors vary considerably
within a year and therefore they constitute an important aspect of soil erosion risk
estimation and their dynamics. The spatial distribution of soil erodibility factor (Kfactor), another important aspect to identify Erosion Susceptible Areas (ESAs) in a
catchment, is calculated by assigning corresponding erodibility value to each pixel
based on the soil texture classification of that pixel. The Erosion Susceptible Areas
(ESAs) on every month in the Rems catchment is then obtained by intersecting the
prepared distributed data sets of the topographic, soil erodibility and monthly crop
cover factors.
The monthly ESAs when intersected with the Hydrologically Sensitive Areas (HSAs),
described by the erosivities calculated with the selected 21 different good parameter
sets, results the 21 sets of monthly varying spatially distributed sediment yield. Very
xxi
Abstract
high differences, as high as more than four times, in the quantitative estimation of
the total sediment yield at the catchment outlet is observed among the good performing parameter sets. The spatial extent of erosion risky areas and distributed
erosion amount within the catchment is also found to vary considerably (as high as
three times) among them. So it is uncertain and unreliable in deciding or choosing
any of the estimated results to define the soil erosion risk quantitatively because none
of the results could be fully believed or all should be equally believed. However, the
spatial correlations of the value and rank of the distributed sediment yield estimated
by the different good performing parameter sets were found to be quite high which
suggests that the spatial distribution within the catchment simulated by the different
good parameter sets are identical. So the spatial distribution of the sediment yield
frequency, averaged over the results from the 21 good parameter sets, was calculated
on monthly and yearly basis (1990-2005) as the percentage of days that each pixel
yields the sediment. They describe the location of Critical Source Areas (CSAs).
Hence, the temporal variability captured through HSAs and ESAs yields dynamics
of the erosion risk areas through CSAs. Such areas give guidance during planning
process that where the soil conservation measures can be designed to prevent the
problem from occurring or to minimize the runoff. Such understanding helps in
identifying priority areas that require urgent management interventions in controlling soil erosion or in determining the priority for implementing the needed BMPs
(Best Management Practices). The temporal dynamics of the critical source areas in
Rems catchment could be observed such that the parts of areas risky at a time are
not always risky throughout the year. So, unlike the existing practices of having temporally static erosion risk maps which would declare certain portion of the catchment
to be permanently under high risk and therefore to be prevented from being used
for agriculture; the consideration of temporal variation, like in this research work,
will not force the farmers or the land users to permanently abandon their land. The
identification of the Critical Source Areas (CSAs) or the Critical Management Zones
(CMZs) for the prioritization of urgent anti-erosion measures within the catchment
in this way would be more effective, fruitful, convincing and acceptable to farmers more so in the developing countries where agricultural land-dependence and erosion
problem is more severe. No erosion models or BMPs (Best Management Practices)
currently account for this type of dynamic behavior in hydrological sensitivity and
erosion risk in such a simple approach.
xxii
Kurzfassung
In vielen Bereichen der Hydrologie, wie zum Beispiel der Niederschlags-AbflussSimulation oder der Modellierung von Sedimentaufkommen, ist eine korrekte Abschätzung der räumlichen Variabilität hydrologischer Variablen von fundamentaler
Bedeutung. Räumliche Strukturen und deren Dynamik finden sich in allen Bereichen
der Hydrologie und der Bodenerosion. Regen und der daraus resultierende Abfluss
sind die Hauptantriebe für Erosions- und Sedimentationsprozesse. In vielen Untersuchungsbereichen, wie dem Sedimenttransport, der Wasserqualität, geeigneten Bodenschutzmaßnahmen, ökologischen und geomorphologischen Fragestellungen, muss
nicht nur die Menge und die Qualität von Wasser und Sediment bekannt sein, sondern auch von welchen Flächen der Abfluss stammt und damit das mitgeführte
Sediment sowie mögliche Schadstoffe. Selbst wenn quantitative Abschätzungen anfechtbar sind, so sind qualitative Aussagen über die räumliche Heterogenität und
die zeitliche Dynamik von großem Nutzen. Bei vielen hydrologischen Aufgaben ist
das "von wo" genauso wichtig oder sogar wichtiger als das "wie viel", um begrenzte finanzielle Mittel (z.B. zum Erosionsschutz) möglichst effizient einzusetzen. Es
gibt verschiedene Ansätze, um solche Problemstellungen zu modellieren; alle haben
ihre typischen Einsatzmöglichkeiten und Beschränkungen. Die Suche nach den erosionsgenerierenden Flächen in einem Einzugsgebiet erfolgt in der Regel durch den
Einsatz von flächendetaillierten (räumliche verteilt) Niederschlags-Abfluss-Modellen.
Flächendetaillierte Modelle sollten in der Lage sein, die räumliche Variabilität einiger,
wenn nicht der meisten, Landnutzungs- und Klimaeigenschaften des Einzugsgebiets
explizit abzubilden. Darum werden solche Modelle dafür eingesetzt, die räumliche
Verteilung der Abflussentstehung zu simulieren, um anschließend die Bodenerosion
in ihrer räumlichen Variabilität zu berechnen. Allerdings müssen die Modelle, selbst
physikalisch basierte Modelle, vor dem Einsatz in einigen Parametern kalibriert werden. Die optimale Kalibrierung und Vorhersagefähigkeit wird dabei zumeist daran
gemessen, wie gut der Hydrograph am Auslass des gesamten modellierten Einzugsgebiets vorhergesagt wird.
Selbst in entwickelten Ländern reicht derzeit die Qualität und Quantität der für
die meisten Einzugsgebiete zur Verfügung stehenden Beobachtungsdaten für ein rein
physikalisch basiertes Erosionsmodell nicht aus. Zieht man zusätzlich weitere Probleme wie die groß- räumige und zeitliche Variabilität von Bodenerosionsprozessen
und die Unsicherheit der Eingangsparameter in Betracht, so wird deutlich, dass eine
präzise Erosionsvorhersage noch immer schwierig ist und die bestehenden Probleme
sich nicht damit lösen lassen, dass noch vollständigere und komplexere Modelle erstellt werden. Die Datenlage ist in der Regel jedoch gut genug für einen Versuch,
die hydrologische Modellierung zu verbessern. Daraus ergibt sich ein sehr interessantes Forschungsfeld: Welche Verbesserungen in der Modellierung von Bodenerosion und Sedimentaufkommen lassen sich erzielen, wenn der hydrologische Teil
xxiii
Kurzfassung
der Prozesse besser simuliert wird? Die besten Möglichkeiten für eine Verbesserung
der hydrologischen Repräsentation bietet ein physikalisch basiertes, flächendetailliertes Niederschlags-Abfluss-Modell. Basierend auf diesem Modell wird das allgemeine Ziel dieser Untersuchung formuliert: Welchen Nutzen bietet eine Kombination aus einem physikalisch basiertes hydrologischen Modell mit einem einfachen,
wenig rechenaufwändigen und wenig Eingangsdaten erfordernden Erosionsmodell,
um die räumliche Verteilung und zeitliche Dynamik der Erosions- und Sedimentationsprozesse in einem Einzugsgebiet zu bestimmen?
In dieser Forschungsarbeit werden verschiedene Varianten des Erosionsmodells USLE
verwendet (Wischmeier & Smith 1978). Es ist in eine GIS-Umgebung integriert,
um räumliche Variabilität der erosionsrelevanten Eigenschaften des Einzugsgebiets
abzubilden. Als hydrologisches Modell wird das physikalisch basierte, flächendetaillierte Modell WaSim-ETH ((Schulla & Jasper 1999, 2006) verwendet für eine bessere
Repräsentation der hydrologischen Bedingungen.
Zuerst wurde eine Fallstudie für das Ganspoel Einzugsgebiet durchgeführt, einem
kleinen, von Messungen gut erfassten, landwirtschaftlich geprägten Einzugsgebiet
in Belgien. In dieser Fallstudie wurde das einfache, aber immer noch weit verbreitete USLE-Model mit einem einfachen und wenig datenintensiven NiederschlagsAbflussmodell kombiniert. Die Erosionsanalyse dieser Fallstudie wurde flächendetailliert durchgeführt, in dem die Möglichkeiten des GIS genutzt wurden, um die
räumliche Struktur des Oberflächenabflusses vorauszusagen. Gleichzeitig wurden
der Gesamtabfluss und die Sedimentfracht am Gebietsauslass vorhergesagt. Die Intention war zu untersuchen, ob nun eine bessere hydrologische Repräsentierung des
Einzugsgebiets die Vorhersagequalität des einfachen Erosionsmodell in Bezug auf die
räumliche Struktur der Bodenerosion und die Quellflächen des Erosionsaufkommens
zu verbessern vermag.
Es wurden sieben Niederschlags-Abfluss-Ereignisse mit ausgeprägter Erosionsverfrachtung und unterschiedlicher Charakteristik in Bezug auf die Landnutzung ausgewählt. Mit den verfügbaren Daten für diese Ereignisse, wurden die Parameter
des USLE-basierten Erosionsmodells (wie z.B. der Bedeckungs- und Bearbeitungsfaktor C, den Bodenerodierbarkeitsfaktor K, den topographischen oder HanglängenHangneigungsfaktor LS, den Erosionsschutzfaktor P und der Niederschlags- und
Oberflächenabfluß-Errosivitätsfaktor R) in der GIS-Umgebung berechnet. Zwei existierende Methoden zur Abschätzung des Sedimentanlieferungsverhältnisses (Sediment Delivery Ratio SDR) wurden ebenso getestet, sowie eine hier vorgeschlagene
Methode.
Eine Fundamentalanalyse mit verschiedenen Algorithmen (‚single f low’, ‚multiple
f low’ und ‚f lux decomposition’) wurde durchgeführt, um den LS-Faktor zu bestimmen. Der Fokus lag auf den Unterschieden zwischen einer 1-D und 2-D Betrachtung. Ebenso wurden verschiedene Methoden zur Bestimmung des R-Faktors
untersucht. Diese Methoden benötigen eine Abschätzung des Abflussvolumens und
des Spitzenabflusses und stellen damit die Verbindung vom Erosionsmodell zum hydrologischen Modell her. Auf der einen Seite wurde das denkbar einfachste Ver-
xxiv
Kurzfassung
fahren mit minimalem Datenaufwand, das SCS-Curve-Verfahren, in flächendetaillierter Weise (räumliche verteilt) verwendet. Die ursprüngliche Form und verschiede
modifizierte Formen, wurden getestet. Die Modifikationen betrafen dabei die z.B.
die Integration der Steigung, der kontinuierlichen Vorfeuchte, veränderlicher Initialer
Verlust usw. Es ist erwähnenswert, dass die SCS-CN Methode für die Abflussaschätzung in einigen Erosions- und Wasserqualitätsmodellen wie SWAT, EPIC, AGNPS, ANSWERS, CREAMS, GLEAMS, GWLF verwendet werden. Andererseits
wurde ein komplexeres, aber eher physikalisch basiertes / prozessorientiertes flächendetailliertes Abflussmodel, das WaSiM-ETH Model eingesetzt, um das Abflussvolumen, den Spitzenabfluss und die abflusserzeugenden Flächen zu bestimmen. Der
resultierende Abfluss, die Brutto-Erosion, die Sedimentfracht und die räumliche
Verteilung der erodierten Flächen beider Modellansätze wurden dann mit beobachteten
Werten verglichen, sowie mit den Ergebnissen des physikalisch basierten Erosionsmodell, MEFDIS. Über diesen Vergleich wird deutlich, dass mit der Kombination
von beidem, Regen und Abfluss, in der Erosivitätsabbildung - wie dies von Onstad
und Foster vorgestellt wurde - die Erosion besser simuliert werden kann als mit je
nur einer der Größen allein. In Bezug auf die Abbildung der Topographie konnte
gezeigt werden, dass der zweidimensionale Ansatz, die gesamte zum Abfluss beitragende Hangfläche oberhalb einzubeziehen, zu realistischeren Ergebnissen führt als der
eindimensionale Ansatz der Fließweglänge, welcher normalerweise bei der Erosionsmodellierung verfolgt wird. Beim zweidimensionalen Ansatz wird berücksichtigt,
dass es in Senken durch konvergenten Abfluss zu hoher Erosion kommen kann, was
beim Verfahren über die Fließweglänge vernachlässigt wird. Bei der Berücksichtigung
der zum Abfluss beitragenden Hangfläche erzielt der f lux decomposition Algrorithmus bessere Ergebnisse in Bezug auf die Brutto-Erosion und die Sedimentfracht
als der Algorithmus des steilsten Abfalls, wie er in den meisten USLE-basierten
Modellen verwendet wird. Von den verschiedenen verwendeten Sedimentanlieferungsverhältnisses (SDR) Modellen liefert das hier vorgestellte neue Modell, welches
auf mehr relevanten Faktoren basiert, bessere Ergebnisse, zumindest für die in der
Fallstudie untersuchten Niederschlags-Ereignisse. Das wichtigste Ergebnis der Fallstudie war, dass die SCS-CN Methode, wenn sie mit USLE verwendet wird, zwar die
Abschätzung des Abflussvolumens verbessern konnte, aber trotz mehrerer Modifikationen nicht in der Lage war, die räumliche Verteilung der abfluss- und erosionsgenerierenden Flächen plausibel zu simulieren, die räumliche Verteilung ähnelnd lediglich
der Landnutzungskarte des Einzugsgebiets. Dagegen wurden selbst mit einem einfachen, empirischen Erosionsmodell der USLE-Familie vielversprechende Ergebnisse
erzielt, wenn WaSiM-ETH als hydrologisches Modell eingesetzt wurde. Die räumliche Verteilung der abfluss- und erosionserzeugenden Flächen wird sehr gut simuliert,
kommt nah an die beobachtete Verteilung heran und ist zum Teil sogar besser als bei
der Simulation mit datenintensiveren, physikalisch basierten Erosionsmodellen. Dies
zeigt anschaulich, dass ein simples Erosionsmodell mit minimal erforderlichem Datenaufwand die räumliche Verteilung erosiver Flächen in einem Einzugsgebiet relativ
genau abbilden kann, wenn es mit einem besseren hydrologischen Modell angetrieben
wird, das die hydrologischen Prozesse im Einzugsgebiet genauer darzustellen vermag.
Es wurde jedoch, als ein zufälliges Ergebnis, eine unplausible Folge der Kalibrierung
des WaSiM-ETH Models auf das Ganspoel catschment entdeckt. Die Kalibrierung
xxv
Kurzfassung
wurde durchgeführt, in dem man die Vorhersagefehler des Abflusses am Einzugsgebietsauslass minimiert. Es wurden sehr gute Ergebnisse erzielt, der Hydrograph wurde
sehr gut getroffen. Die Nash-Sutcliffe Koeffizienten sind mit 0.97 in der Kalibrierung
und 0.81 in der Validierung entsprechend hoch. Die Parameterwerte der Kalibrierung
wurden also bestätigt und der mögliche weitere Einsatz des Models schein gesichert.
Aber als die vom Modell simulierten abflusserzeugenden Flächen betrachtet wurden, zeigten sich sehr unrealistische Strukturen. Fast der gesamte Abfluss kam von
einem kleinen, isolierten Stück des Einzugsgebiets und die Flächen, auf denen in
der Realität starke Erosion und Sedimentverfrachtung beobachtet wurde, trugen im
Modell praktisch nicht zum Abfluss bei. Damit wurde der alarmierende Sachverhalt aufgedeckt, dass eine sehr gute Vorhersagegüte erzielt werden kann, obwohl das
Modell das Einzugsgebiet völlig unrealistisch abbildet.
Strategien zur Erosionskontrolle oder zur nachhaltigen Landbearbeitungen sollten
sich ganz besonders auf den Oberflächenabfluss konzentrieren und auf dessen räumliche und zeitliche Variabilität im Einzugsgebiet. In dieser Arbeit wird der Einfluss
des Oberflächenabflusses über die Identifizierung hydrologisch wirksamer Flächen
(Hydrologically Sensitive Areas - HSAs) erfasst. Der Term "HSA" wird für Flächen
verwendet, die besonders dazu veranlagt sind, Abfluss zu erzeugen und dadurch potentiell dazu beitragen, Sedimente und Schadstoffe in mehrjährige Oberflächengewässer
einzutragen. HSAs beschreiben also das Risiko der Abflusserzeugung und legen
die potentiellen Quellflächen für Erosion fest. Die räumliche Ausdehnung der HSA
schwankt im Laufe des Jahres, so dass manche Teile des Einzugsgebiets in einem
Monat mehr zur Erosion beitragen, als in einem anderen. Erkennt man die die
räumliche und zeitliche Variabilität der HSA im Einzugsgebiet, limitiert sich das
Erosionsproblem des Einzugsgebiets auf die relevanten Flächen und Zeiträume. Folglich müssen Beschränkungen zum Erosionsschutz oder zur Verhinderung potentiell verschmutzender Aktivität nur auf einem Teil der Einzugsgebietsfläche und nur
während eines Teils des Jahres durchgeführt werden, was die Akzeptanz der Maßnahmen und die Handlungsbereitschaft der Landwirte im Einzugsgebiet fördern kann.
Die genaueste Bestimmung der HSAs wäre mit direkten Messungen oder mit Daten
aus der Fernerkundung möglich. Aber in der Regel sind solche Daten nicht flächendeckend und für ausreichend lange Zeiträume verfügbar, um die Wahrscheinlichkeit
der Generierung von Oberflächenabfluss zu berechnen. Darum werden HSAs am
besten über Langzeitsimulationen mit einem physikalisch basierten hydrologischen
Modell definiert. Dafür folgte der Fallstudie eine detaillierte Untersuchung der Einsatzmöglichkeit des WaSiM-ETH Modells zur Identifizierung der HSA innerhalb eines
Einzugsgebiets.
Die Identifizierung von HSAs, deren Verteilung und deren Dynamik mit WaSiM-ETH
wurde für das mittelgroße Einzugsgebiet der Rems in Süddeutschland durchgeführt.
Das Modell für die Rems wurde mit vier Untereinzugsgebieten und vier Pegeln aufgesetzt. Es wird in der WaSiM-ETH Abflussgenierungs-Konfiguration betrieben, mit
einem modifizierten Topmodel Ansatz für den gesättigten Oberflächenabfluss und
dem Infiltrationsüberschuss-Ansatz von Green und Ampt für die Simulierung der
abflussgenierenden Flächen. Das Jahr 1993 wurde zur Kalibrierung herangezogen
mit 1992 als Anlaufzeitraum; die Landnutzung wurde anhand von Sattelitendaten
xxvi
Kurzfassung
aus dem Jahr 1993 bestimmt. Für das CPU intensive WaSiM-ETH wurde die Parameterkalibrierung mit dem relativ schnellen Gauss-Marquardt-Levenberg Algorithmus
durchgeführt, unter Verwendung des PEST-Tools. Die tägliche Simulierung wird kontinuierlich für 16 Jahre von 1990 bis 2005 durchgeführt. Die Parametersets werden
mit den Abflusszeitreihen des jeweils zugehörigen Pegels für jedes Untereinzugsgebiet
einzeln bestimmt. Für den Beitrag der jeweils oberstrom liegenden Einzugsgebiete
werden die beobachteten Hydrographen angesetzt und nicht etwa die simulierten, um
eine Fehlerfortpflanzung zu vermeiden.
Die Messung der Modellgüte zeigt eine recht gute Simulierung der Abflüsse von den
Nicht-Quelleinzugsgebieten Schorndorf und Neustadt, sind aber für die Quelleinzugsgebiete (Schwäbisch-Gmünd und Haubersbronn) schlechter. Um eine bessere Gesamtleistung zu erzielen, wurden verschiedene weitere Versuche durchgeführt. Es wurde
neu kalibriert, aber für einen anderen Zeitraum, dem Jahr 1996, welches bisher
am schlechtesten simuliert wurde (weiterhin mit den Landnutzungsdaten von 1993).
Außerdem wurde für das Jahr 2000 kalibriert mit Landnutzungsdaten von 2000. Die
Parameterwerte für die verschiedenen Kalibrierungen schwanken in einem weiten
Bereich und sehr willkürlich, obwohl sich die Kalibriermethode nicht ändert. Es
zeigt sich jedoch eine ähnliche Tendenz in der Modellgüte wie bisher. Das Jahr
1996, ein extrem kühles und trockenes Jahr, konnte nicht gut simuliert werden, es
sei denn, die Kalibrierung wurde mit den Daten dieses Jahres durchgeführt. WaSiMETH scheint ansonsten nicht in der Lage zu sein, solche Bedingungen entsprechend
abzubilden. Bemerkenswert ist jedoch, dass das Parameterset von der Kalibrierung
für das Jahr 1996, das eher kleine Ereignisse repräsentiert (und damit für den Simulationszeitraum eher untypisch ist) über die gesamten Simulationszeitraum eine bessere
Modellgüte liefert als die Parametersets der 1993er und 2000er Kalibrierungen, die
eher durchschnittliche hydrologische Verhältnisse widerspiegeln. Das Ergebnis zeigt,
dass es notwendig ist, bei der Kalibrierung unübliche Ereignisse mit einzubeziehen
oder ihnen sogar eine Priorität zu geben, um eine leistungsfähige Modellanpassung zu
erhalten. Die Kalibrierung auf unübliche Ereignisse ist nicht nur notwendig, sie mag
sogar hinreichend sein bezüglich des Gesamtzeitraums. Diese Fragestellung bleibt
ein interessantes Thema für weitere Untersuchungen.
Die räumliche Verteilung der HSA in jedem Monat wird über den simulierten täglichen
Oberflächenabfluss aller drei Kalibrierungen festgelegt. Definiert werden sie über
den Anteil an Tagen, an denen ein Rasterpunkt des Feldes während der Simulationsperiode von 1990 bis 2005 Oberflächenabfluss im jeweiligen Monat erzeugt hat.
Es wurde der Versuch unternommen, die so berechneten monatlichen Wahrscheinlichkeiten mit einfach messbaren relevanten Proxi-Parametern wie Niederschlagsfeldern, Topographischer Feuchtigkeitsindex und der Curve-Number zu assoziieren.
Die Ergebnisse waren überraschend und letztlich nicht plausibel. Somit konnte keine
allgemeine Beziehung zwischen einfach zu messenden Parametern und den zu bestimmenden HSAs erstellt werden.
Die Struktur der räumlichen Verteilung des Oberflächenabflusses variieren nicht nur
über die verschiedenen Parametersets, mit denen simuliert wurde, sondern auch über
die Teileinzugsgebiete auf unrealistische Weise. Deshalb wurde die Optimierungsmeth-
xxvii
Kurzfassung
ode in Zweifel gezogen und die Parameterschätzung erneut durchgeführt, mit einer
globalen Optimierungstechnik, dem SCE-UA (Shuf f led Complex Evolution), die
allerdings sehr viel Rechenzeit beansprucht. Die kalibrierten Werte der Parameter variieren auch bei dieser Methode in einem weiten Bereich, jedoch konnte die
Modellgüte gegenüber der schnelleren Kalibrierungsmethode nicht verbessert werden. Auch hier wird das Jahr 1996 als abflussarmes Extrem sehr schlecht simuliert,
was die Defizite des WaSiM-ETH Modells in Bezug auf die Repräsentierung extrem kleiner Ereignisse bestätigt und noch einmal zeigt, dass auf jeden Fall untypische Ereignisse mit zur Kalibrierung herangezogen werden müssen. Außerdem ist
für unterschiedlich kalibrierte Parametersets, die simulierte räumliche Struktur des
Oberflächenabflusses ziemlich verschieden. Das wirft die Frage auf, wie verlässlich
die gefundenen Strukturen sind, wenn man mit ihnen Bodenerosion simulieren will.
Fragwürdig ist außerdem, dass die modellierte räumliche Struktur des Oberflächenabflusses in den Teileinzugsgebieten völlig unterschiedlich ist.
Ein weiterer Versuch, diese Problem anzugehen, war ein völlig anderer ParameteranpassungsAlgorithmus, der multidimensionale Data-Depth Algorithmus ROPE ("Robust P arameter
Estimation"). Der Algorithmus basiert auf der Tatsache, dass ein robustes Parameterset klar strukturiert ist in der Mitte der Parameterwolke liegen muss im mehrdimensionalen Raum aller Parameter. Mit diesem Algorithmus wird versucht, ein
ganzes Set robuster Parameter Vektoren zu finden, im Gegensatz zu einem einzigen
optimiertes Parameterset wie in den vorherigen Analysen und dieses Set anhand der
Verteilung der Simulationsergebnisse zu untersuchen, um daraus das beste Parameterset für die gedachte Anwendung zu finden, z.B die Struktur des Oberflächenabflusses oder die HSAs. Die robusten Parameter Vektoren werden für die vier
Teileinzugsgebiete unabhängig voneinander bestimmt, basierend auf deren jeweiliger
beobachteter Abflusszeitreihe (und den beobachteten Zeitreihen der Teileinzugsgebiete flussaufwärts). Auch hierbei zeigt sich wieder eine unrealistische räumliche
Verteilung der Oberflächenabflüsse, obwohl das Modell eine hohe Simulationsgüte
liefert. Dazu variieren die Ergebnisse der guten Parametersets sehr stark über die
Teileinzugsgebiete. Nun wird die Parameterschätzung wiederholt, mit der Nebenbedingung, dass die Parameter der einzelnen Untereinzugsgebiete nicht voneinander
abweichen dürfen. Die guten Parametersets werden nicht daran definiert, dass sie
bezogen auf das Gesamteinzugsgebiet die geringsten quadratischen Abweichungen
zum beobachteten Abfluss liefern, sondern für jedes Teileinzugsgebiet einzeln. Mit
dem ROPE Algorithmus werden 1955 akzeptierbar gute Parametersets identifiziert.
Nun wurden letztlich keine unrealistischen Unterschiede in der räumlichen Verteilung
zwischen den Teileinzugsgebieten festgestellt. Die nicht akzeptierbaren Unterschiede
zwischen den Teileinzugsgebieten konnten also dadurch vermieden werden, dass allen
Teileinzugsgebieten das gleiche Parameterset zugewiesen wurde. Darüber hinaus beweisen die hohen Werte der räumlichen Korrelation und der Rangkorrelation über
den mit den verschiedenen Parametersets berechneten Oberflächenabfluss, dass die
nun gefundenen räumlichen Strukturen beständig und realistisch sind. Aber als
eine quantitative Analyse der Verteilung der Simulationsergebnisse der guten Parametersets durchgeführt wurde, kamen wiederum nicht akzeptable Ergebnisse zu
Tage. Trotz der guten Modellgüte und der realistischen räumlichen Verteilung des
Oberflächenabflusses, variiert der Mittelwert des Oberflächenabflusses und dessen
xxviii
Kurzfassung
Gesamtvolumen sehr stark über die Parametervektoren, d.h. bis zum Vierfachen. Es
ist zweifelhaft, ob ein ausgewähltes Parametersets somit für die quantitative Erosionsmodellierung eingesetzt werden kann. Die einzelnen Parametersets würden extrem
unterschiedliche Ergebnisse liefern, wenn sie zur Abschätzung der Bodenerosion über
den Obeflächenabfluss weiter verwendet würden. Welche Vorhersage sollen wir also
weiterverwenden, da ja alle eine gleich gute Modellgüte liefern? Die Ergebnisse zeigen
wieder ein Mal eine sehr gute Vorhersage durch das Niederschlags-Abfluss Modell,
aber aus den völlig falschen Gründen. Eine bessere Vorhersage der Abflusszeitreihe
durch das physikalisch-basierte Niederschlags-Abflussmodell garantiert noch keine
bessere Abbildung der hydrologischen Verhältnisse, darum sollte die Zuverlässigkeit
der verteilten Ergebnisse im Zweifel akzeptiert werden.
Die 1955 guten Parametersets, die mit dem ROPE-Algorithmus identifiziert wurden, basieren auf dem minimierten quadratischen Fehler. Für einen weiteren Anpassungsversuch wurde die Data-Depth anhand von anderen Kriterien berechnet, unter
anderem den Gesamtabflussvolumen. Mit einer digitalen Filtertechnik wurde der
beobachtete Oberflächenabfluss vom jeweiligen Hydrographen am Pegel abgetrennt.
Es zeigte sich, dass fast keine Parametersets, die das Volumen gut reproduzieren
gleichzeitig den Oberflächenabfluss gut abzuschätzen vermögen. Darum wurde das
Modellgüte-Kriterium aufgeweicht und ein passendes Parameterset unter den 3007
Parametervektoren des vorletzten Schritt im ROPE-Algorithmus gesucht. Hier wurden mehrere Parametersets gefunden, die auch bei der Abschätzung des Oberflächenabflusses funktionieren. 20 gute und robuste Parametersets (von den 3007) basierend
auf allen Gütekriterien, inklusive dem Oberflächenabfluss, wurden ausgewählt für die
folgenden Analysen. Mit diesen 20 Sets und einem SCE-UA optimierten Set als Referenz wurden tägliche Rasterfelder des Oberflächenabflusses erzeugt und dem USLEErosionsmodell weiter gegeben. Damit wurde eine flächendetaillierte und zeitliche
variable Erosionsabschätzung durchgeführt.
Der MUSLE basierte tägliche Erossivitätsfaktor (R-Faktor) wird mit dem WaSiMETH und dem CREAMS Modell für die 16 Jahre (1990-2005) mit allen 21 verschiedenen Parametersets berechnet. Als eine kleine Nebenstudie wurde versucht,
einen neue Beziehung zwischen dem R-Faktor und besser zugänglichen Daten und
Parametern des Rems-Einzugsgebiets zu finden. Mit einem Niederschlagsgenerator
namens "NiedSim" wurde eine Regenreihe von 1958 bis 2004 für drei unabhängige
Stationen im Remseinzugsgebiet berechnet. Dann wurden sieben verschiedene statistische Parameter basierend auf der Zeitreihe berechnet und als unabhängige Variablen für eine nicht-lineare Multiple Regression verwendet, mit der für jeden Monat
von 1958 bis 2004 der R-Faktor berechnet wurde. Obwohl der gemachte Versuch
eher einer Vorstudie gleicht, eine detaillierte Untersuchung lag außerhalb des Fokus
dieser Dissertation, so zeigen die hohen Korrelationskoeffizienten sowohl in der Kalibrierung der jährlichen und monatlichen Modelle die grundsätzliche Anwendbarkeit
von NiedSim-generierten Zeitreihen in bei der Berechnung von Erosivitätsfaktoren
und die Möglichkeit, akzeptable Werte für diese Errosivitäten mit einfacheren Regenparametern der Region zu erhalten. In dieser Arbeit wurde trotzdem der Erosivitätsfaktor aus MUSLE gewählt, dessen räumliche Heterogenität und zeitliche Variabilität
die HSAs im Rems-Einzugsgebiet bestimmt.
xxix
Kurzfassung
Auf der anderen Seite werden der topographische Faktor (LS-Faktor), der Bedeckungsund Bearbeitungsfaktor (C-Faktor) und der Boden-Erodierbarkeitsfaktor (K-Faktor)
berechnet, um die räumliche Verteilung und zeitliche Variabilität der erosionsanfälligen Flächen (Erosion Susceptible Areas- ESAs) im Rems Einzugsgebiet zu berechnen. Mehrere flächendetaillierte 1D-Ansätze (nach Fließweglänge) und 2D-Ansätze
(nach abflussbeitragender Fläche) werden verfolgt, um den LS-Faktor abzuschätzen.
Es zeigt sich wiederum, dass nur der 2-D Ansatz, konvergenten Abfluss bei der Parameterabschätzung miteinbeziehen kann. Die zum Abfluss beitragenden oberhalb
liegenden Flächen werden einmal mit dem Single F low Algorithmus berechnet, einmal mit M utliple F low Algorithmus und einmal mit F lux Decomposition Algorithmus. Der 2-D Ansatz mit dem F lux Decomposition Algorithmus und dem NearingHangneigungsfaktor wurde dazu verwendet, die topographischen Effekte der ESAs
im Rems-Einzugsgebiet zu definieren. Entgegen der gängigen Praxis zeitlich unveränderliche C-Faktoren auf Basis der Bodennutzungskarte anzusetzen, wurde in dieser
Arbeit die Fortschritte der Satelliten- und Fernerkundungstechnik genutzt, um die
Dynamik der C-Faktoren zu bestimmen. Der N ormalized Dif f erence V egetation
Index (NDVI), ein häufig angewandter Spektralindikator für Pflanzenwachstum wird
(über das LPDAAC Daten-Archivierungs-Center) für die Jahre 2000 bis 2008 für
das Rems Einzugsgebiet extrahiert. Diese NDVI Zeitreihen wurden von der TERRA
Plattform des MODIS Satteliten bezogen und sind als 16 Tages-Komposite erhältich.
Die NDVI Zeitreihen werden mit einem Skalierungsansatz nach dem European Soil
Bureau (van der Knijff et al. 2000) in den flächendetaillieren, monatsweisen C-Faktor
überführt. Daraus resultierend sind höhere Erosivitäten in der Regel mit einem
höheren Pflanzen-Widerstands-Faktor verbunden und damit würde der resultierende
Effekt auf die Bodenerosion, als deren Produkt , von einem der beiden bestimmt werden. Beide Faktoren variieren innerhalb eines Jahres beträchtlich und spielen daher
eine wichtige Rolle in der Abschätzung des Erosionsrisikos und in dessen Dynamik.
Die räumliche Verteilung des Boden-Erodierbarkeitsfaktors (K-Faktor), ebenfalls ein
wichtiger Aspekt, um die ESA in einem Einzugsgebiet zu bestimmen, wird berechnet,
in dem der entsprechende Erodierbarkeitswert zu jeden Pixel aus der Bodenstruktur Klassifizierung ausgelesen wird. Die ESA-Verteilung für jeden Monat in Rems
Einzugsgebiet erhält man nun, indem man das die Verteilung des topographischen
Faktors, der Bodenerodierbarkeit und der monatlichen Pflanzenbedeckungsfaktoren
verschneidet.
Werden die monatlichen ESAs mit den hydrologisch wirksamen Flächen (HSAs) verschnitten, die über die Erosivitäten aus den 21 robusten Parametersets beschrieben
werden, erhält man 21 Sets an monatlich variierenden, flächendetailliertem Sedimentaufkommen. Zwischen den Berechnungen mit den 21 Parametersets des Sedimentaufkommens am Auslass des Gesamteinzugsgebiets ergeben sich sehr große
Unterschiede bis zum Vierfachen. Die räumliche Ausdehnung der erosionsanfälligen Flächen und die Verteilung der Erosionsmenge innerhalb des Einzugsgebietes
schwanken ebenfalls beträchtlich, bis zum Dreifachen. Damit ist es unsicher und
wenig verlässlich, wenn man das quantitative Erosionsrisiko anhand eines Einzelergebnisses abschätzen möchte. Keinem der Ergebnisse kann voll vertraut werden
und alle müssen als gleich richtig oder gleich falsch angesehen werden. Allerdings sind
xxx
Kurzfassung
die Werte der räumlichen Korrelation und der räumlichen Rangkorrelation der Sedimenaufkommensverteilung, wie sie von den verschiedenen Sets robuster Parameter
berechnet werden, recht hoch, was darauf schließen lässt, dass simulierte räumliche
Verteilung der einzelnen Parametersets sehr ähnlich sind. So wurde die durchschnittliche monatliche und jährliche Frequenz des Sedimentaufkommens aus den Ergebnissen der 21 Parametersets in der Periode von 1990 bis 2005 gemittelt. Dies dient zur
Beschreibung der Kritischen Erosions-Quellflächen (Critical Source Areas - CSAs).
Die Festlegung solcher Flächen gibt Orientierung in Planungsprozessen, wenn die
Maßnahmen zum Erosionsschutz festgelegt werden. Ein solches Verständnis des Systems hilft dabei, prioritäre Gebiete festzulegen, in denen dringend schützend eingegriffen werden muss oder in denen eine nachhaltige Bodenbewirtschaftung durchgesetzt werden sollte. Durch die zeitliche Dynamik der kritischen Quellflächen für
Erosion im Rems Einzugsgebiet sind Flächen, die zu einem Zeitpunkt erosionsgefährdet sind, dies nicht über das ganze Jahr hinweg. Im Gegensatz zu statischen
Erosionsrisiko-Karten, die Teile des Einzugsgebiets permanent in Hochrisikogebiete
einteilen und dadurch von der Agrarnutzung ausschließen, kann mit der Berücksichtigung der zeitlichen Dynamik verhindert werden, dass Landwirte manche Flächen
endgültig aufgeben müssen. Die Identifizierung von CSAs oder sog. CMZs (Critical
M anagement Zones) für eine Piorisierung dringender Erosionsschutzmaßnahmen
wären in dieser Hinsicht effizienter und für die betroffenen Landwirte einleuchtender und einfacher zu akzeptieren. Das gilt vor allem in den Entwicklungsländern,
wo die Abhängigkeit von geeignetem Ackerland und die Erosionsprobleme besonders
gravierend sind. Bisher existiert weder ein Erosionsmodell noch eine Konzeption
für nachhaltige Bodenbearbeitung, welche die zeitliche Dynamik der hydrologischen
Sensitivität und des Erosionsrisikos in so einem einfachen Ansatz berücksichtigt.
xxxi
1 General Background
1.1 Introduction
Hydrological models try to replicate the natural phenomenon explaining the complex
behavior associated with the management of environmental systems on the basis of
available geo-hydrological information and theoretical knowledge of the hydrological
processes underneath. They are essential tools of any hydrologist to address the
problems or issues of predictions of rainfall-runoff process. There are innumerable
varying reasons or goals for why we need to model the rainfall-runoff process. One
commonly employed aspect of this is to achieve reasonable prediction of surface runoff
that can be used to estimate soil erosion reasonably.
Soil erosion occurs when the forces of water/overland flow (and also wind) move
soil particles at very small spatial scales. It is a natural geomorphic process, but is
being accelerated under improper land use and management practices. Accelerated
erosion and associated soil degradation currently represent a serious global problem.
Problems caused by soil erosion and sediment yield include loss of soil productivitycrop yield reduction, water quality degradation, and less channel capacity to prevent
natural disasters such as floods. Apart from reducing the water storage capacity, sediment delivered into water bodies may also be a source of contamination, adversely
impacting the aquatic biota (Novotny & Olem 1994). Soil erosion and sediment
transport are spatially distributed processes, and their evaluation can be realized by
means of the use of Geographic Information Systems (GIS). The greater availability
of digital and geo-lithological data managed and stored inside GIS has implied the
development of techniques and procedures aimed at the definition of the spatial prediction of erosion and deposition rates across a catchment.
Prediction equations and simulation models to estimate soil erosion by water have
been developed over the past 50 years. Hydrological model/module has to be either
linked externally or is integrated internally in the soil erosion models for computing the surface runoff, the triggering force for soil erosion. As considered by several
lumped models, the generation and spatial distribution of the surface runoff, in reality, is never constant or uniform across a catchment. It is rather governed by the
spatially varying catchment characteristics like topography, soil, land use etc, for the
given rainfall event/series. This means, there will be regions within a watershed that
are more susceptible to producing runoff than other regions. According to the explanation of Walter et al. (2000), these areas can be considered Hydrologically Active
Areas (HAA). Runoff from most of these areas quickly moves downhill to perennial
waterways thus providing a potential direct hydrological link between the landscape
and primary surface water bodies. When this linkage exists, an HAA can be said to
be a Hydrologically Sensitive Area (HSA) and the eroded sediments and water-born
1
1. General Background
constituents in these areas are likely to be readily transported to surface waters.
Though a distinction between HAAs and HSAs is specifically defined, practically
speaking, there has been little evidence that HSAs are ever hydrologically insensitive. These terminologies had been used by Walter et al. (2000), who identified HSAs
with reference to Variable Source Area (VSA) hydrology, i.e. for saturation excess
overland flow. However, the definition is equally applicable also for the catchment
experiencing infiltration excess overland flow or both.
HSAs describe the risk of runoff
generation and hence determine
the potential erosion source areas. A quantifiable description
of HSAs is, therefore, very useful as it provides a basis for
water erosion risk assessment
in a basin and developing soil
and water conservation practices against erosion and water
pollution. Recognizing the existence of HSAs limits the scope
of watershed-scale soil erosion
problems to only those areas
where HSAs coincide with Erosion Susceptible/Sensitive Ar- Figure 1.1: HSAs-ESAs-CSAs concept for erosion risk estimation
eas (ESAs). ESAs can be identified through the spatially distributed erosive aspects of soil type, topography, land use or land cover conditions
and existing management practices. The intersection of HSAs and ESAs can be
referred as Critical Source Areas, CSAs (problem zones) or Critical Management
Areas, CMAs (target zones). Such areas give guidance during planning process that
where the soil conservation measures can be designed to prevent the problem from
occurring or to minimize the runoff. This understanding, thus, help in identifying priority areas that require urgent management interventions in controlling soil erosion
or determine the priority for implementing the BMPs (Best Management Practices)
needed. Fig 1.1 summarizes this concept.
1.2 Hydrology and soil erosion: The Literature Review
Erosion and sedimentation by water embodies the processes of detachment, transportation and deposition of soil particles (sediment) by the erosive and transport
agents of raindrop impact and runoff over the soil surface (ASCE 1975). The erosion
and sedimentation can be major problems causing on-site and off-site effects. Erosion
reduces productivity of cropland. Sediment degrades water quality and may carry
soil with absorbed polluting chemicals. Deposition in irrigation canals, stream channels, reservoirs, estuaries, harbours and other water conveyance structures reduces
the capacity.
2
1.2. Hydrology and soil erosion: The Literature Review
The hydrologic processes of rainfall and runoff drive erosion sedimentation processes.
Factors that affect either rainfall or runoff directly affect erosion and sedimentation.
Thus, any analysis of erosion, sediment transport or sediment yield must consider
hydrology. Therefore, a hydrologic model is required to drive the erosion-sediment
yield model. Hydrologically, a watershed may be conceptualized as having overland
flow, channel flow and subsurface flow components, with overland flow and channel
areas being major ones so far as erosion and sedimentation are concerned. Although
overland flow is usually analyzed as a broad sheet flow, often it concentrates in many
small definable channels (Foster 1971). Any erosion caused by flow in these small
channels (rills) is rill erosion. Erosion on areas between the rills is interrill erosion
(Meyer et al. 1975). Both interrill and rill erosion are overland flow rated processes,
generally called- upland erosion. Where surface flow cannot be hydrologically or
hydraulically treated as overland flow, it is considered as channel flow. Erosion
occurring in channel flow is defined and analyzed as gully and stream channel (bed
and bank) erosion. It is also the flow path of rainwater that triggers the process of
soil erosion (Morgan 1995).The soil erosion, in its several stages, is thus, governed
by the surface runoff in the catchment.
1.2.1 Surface Runoff in a catchment
Surface runoff refers to the portion of rainwater that is not lost to interception, infiltration, evapotranspiration or surface storage and flows over the surface of land to
a stream channel.
The surface runoff in a catchment may be generated in three ways:
(i) When the rate of rainfall on a surface exceeds the rate at which water can
infiltrate the ground, and the depression storage has been filled. This is called
infiltration excess overland flow, Hortonian overland flow (after Robert E. Horton), or unsaturated overland flow. This more commonly occurs in arid and
semi-arid regions, where rainfall intensities are high and the soil infiltration
capacity is reduced because of surface sealing, or in paved areas.
(ii) When the soil is saturated and the depression storage filled, and rain continues
to fall, the rainfall will immediately produce surface runoff. This is saturation
excess overland flow or saturated overland flow.
(iii) After water infiltres the soil on an up-slope portion of a hill, the water may
flow laterally through the soil, and exfiltrate (flow out of the soil) closer to a
channel. This is called subsurface return flow or interflow.
Overland flow or the surface runoff is the main flow path of runoff that can largely be
influenced by human activities through catchment management practices. It is also
the flow path of rainwater that triggers the process of soil erosion (Morgan 1995).
During a rainstorm, a certain portion of rainfall is intercepted by vegetation canopy.
What is left over falls directly onto the soil as throughfall. Intercepted rainwater
either evaporates or in cases of heavy and continuous rainfall events, when canopy
storage capacity is exceeded, it falls to the ground as leaf drainage or stemflow. The
3
1. General Background
amount of rainwater that is lost due to interception depends on the vegetation cover
and the rainfall pattern. Rainwater retained in vegetation canopy that ultimately
evaporates is referred to as interception loss. Rainfall that is not lost to interception and reaches the soil surface either infiltrates into the soil, is stored in surface
depressions or evapo-transpires. The remaining excess rainwater travels over land as
surface runoff.
Runoff is not in itself a form of land degradation but it is one of the major causes of
land degradation problems, of which the main ones are erosion and flooding. In turn,
the rate at which runoff is generated can be increased because of land degradation
problems. Runoff on the one hand is an essential process in that it maintains water
level in lakes and rivers preventing them from drying out and providing fresh water
on which many living beings including humans largely depend. On the other hand,
if the rate of runoff is increased as a result of catchment management practices it
can result in severe land degradation problems (Dunne & Leopold 1978, Maidment
1993, Schwab et al. 1981).
Areas having shallow and compact soils ensuing from a combination of poor farming
techniques, exploitation of marginal lands, deforestation and excessive erosion are
susceptible to higher rates of runoff. High runoff rate leads to an increase in soil
erosion by running water. On the other hand, areas with deeper, more porous soil
structures that are densely vegetated contribute to a reduction in the amount of
water available for runoff which results in reduced rates of erosion (Schwab et al.
1981, White 1997). Land use/ cover changes that increase runoff rates therefore
ultimately influence the rate at which soil loss occurs. Soil loss brings about problems
of soil degradation which in turn further aggravates problems of runoff.
1.2.2 Erosion, Sediment Yield and their effects
Erosion is a physical phenomenon that results in the removal of soil and rock particles by water, wind, ice and gravity. Soil erosion processes by water comprise: splash
erosion, which occurs when soil particles are detached and transported as a result of
the impact of falling raindrops; sheet or interrill erosion, which removes soil in thin
layers and is caused by the combined effects of splash erosion and surface runoff;
rill erosion, which is the disappearance of soil particles caused by concentrations of
flowing water; and gully erosion, that occurs when the flow concentration becomes
large and the incision deeper and wider than with rills (Morgan 2005). Biophysical
factors that regulate erosion processes include climate, soil, terrain and ground cover
(Lal 2001). The importance of each individual factor is not always the same, but
depends on regional characteristics, the specific erosion process under consideration,
and the spatial and temporal scale studied.
The total amount of erosion in a watershed is the gross erosion (E) and sediment
is the end product of erosion. However, all the eroded material does not enter the
stream systems. Some of it is deposited at natural or man-made barriers within the
watershed, and some is deposited within the channels and their flood plains. The
portion of the eroded material that does travel through the drainage network and
4
1.2. Hydrology and soil erosion: The Literature Review
reaches downstream measuring or control point (for eg. a reservoir) is referred as the
sediment yield (SY ) at that point. It is generally estimated as ton/km2 /yr (specific
sediment yield) and sometimes as kg/s (sediment load).
Most present-day concerns about soil erosion, leading to its perception as a process
of degradation, are related to accelerated erosion, where the natural rate has been
significantly increased by human activities. Such activities are quite pronounced in
the watershed that makes the water erosion a serious and continuous environmental problem in many parts of the world and has been recognized as a global threat
against the sustainability of natural ecosystem. Inadequate moisture and periodic
droughts reduce the periods when growing plants provide good soil cover and limit
the quantities of plant residue produced. Erosive rainstorms are not uncommon and
they are usually concentrated within the season when cropland is least protected
(Wischmeier & Smith 1978). Water, as rainfall and runoff, is the active agent for the
basic process of water erosion (Cook 1936). The energy available for erosion takes
two forms: potential and kinetic (Morgan 1979). PPotential energy results from the
difference in height of one body with respect to another. This energy in the form
of rainfall causes splash erosion. The potential energy for erosion is converted into
kinetic energy, the energy of motion of the running water. This kind of energy in
running water (surface runoff) causes interrill, rill, gully, and riverbank erosion. Considering the slope of rain fed farms in most areas which are usually much more than
FAO recommendations, applying Alberts & Neibling (1994) improved agricultural
practices could decrease the volume of surface runoff and use rainwater at dropping
point. Refahi (1996) points out to some of lands which could be under cultivation
and have more crop yield by removing some restrictions. He indicates the role of
slope on concentration of runoff and explains that doubling runoff velocity, removes
particles with 64 times bigger in diameter. Karimzadeh et al. (1996) show significant effects of land-use, land management, and soil physico-chemical characteristics
on soil erodibility. Alberts & Neibling (1994) found that surface runoff and soil loss
exponentially decrease with increasing vegetal residue and reducing soil preparation
practices. They indicate the role of canopy cover on reducing destructive effect of
rain drops on soil, increasing infiltration, and reducing surface runoff.
The main on-site impact of water erosion is reduction in soil quality that results
from the loss of the nutrient-rich upper layers of the soil, and the reduced waterholding-capacity of many eroded soils. The eroded soil becomes sediment that covers bottomlands and man-made structures. Gullies, sand dunes, and other obvious
signs of erosion are examples of using the lands without proper management. Proper
management implies long-term usefulness as well as satisfying current needs. Deterioration in the quality of cropping and grazing land as a result of erosion reduces
productivity and increases expenditure on fertilizers to maintain fertility. In extreme
cases yields become so poor that land has to be taken out of cultivation (Morgan
1986). Many researchers have observed declining crop yields with decreasing topsoil
depth (Segarra 1992). Erosion adds to the cost of producing food and other soil
products and thereby increases the cost of living. Taking ruined land out of production places a greater load on the remaining land and drives up production costs.
Implementing expensive erosion control practices also adds to production costs.
5
1. General Background
Water erosion’s main offsite effect is the movement of sediment and agricultural pollutants into watercourses. Perhaps the most costly result of soil erosion is related to
damage done by the dislodged soil particles that moved downstream. Sedimentation
raises streambeds, reducing the depth and capacity of the channels. This causes
navigation problems and can lead to severe flooding. Sedimentation of lakes and
reservoirs reduces their capacity, value, and life expectancy (Frederick et al. 1991).
Soil particles adsorb pollutants such as pesticides, fertilizers, and different industrial
and municipal chemicals that should be best kept out of water by keeping the soil
on the land (Glymph 1972, Foster 1988, Singh 1992, Wanielista & Yousef 1993).
Keeping sediment out of water lowers the supply of plant nutrients in the water and
thereby reduces unwanted growth of algae and other vegetation, which is an important problem in most rivers, reservoirs and lakes. Changing the aquatic environment
of streams and lakes reduces their value for home and industrial use, recreation, and
fish and wildlife (Frederick et al. 1991). Thus disrupting the ecosystems of water
bodies and contaminating the drinking water the erosion has become an environmental problem that must be remedied for the sake of clean water. Controlling soil
erosion keeps streams, ponds, and lakes from filling rapidly with sediment. Reservoir
capacities are thus maintained for recreation, flood control, power generation, and
irrigation.
1.2.3 Distributed watershed modeling
Observation and interpretation of spatial patterns are fundamental to many areas of
the earth sciences such as geology and geomorphology, yet in catchment hydrology,
our historic interest has been more related to temporal patterns and in particular,
that of stream-flow. But, the fact that patterns are everywhere in hydrology hardly
needs explanation and the spatial patterns in hydrology draws the researchers’ interest since last few decades. People now want to know not only about the quantity and
quality of the water in a stream, but also from where the sediments and contaminants
came and where best to invest scarce financial resources to minimize the problem
(Grayson & Blöschl 2000). So the results of not only “how much” but also “where
from” is equally or even more needed. This rise in the environmental awareness of
the broader community demands for the spatially distributed watershed modeling.
The distributed parameter hydrologic models are those which simulate runoff by
considering the spatial variability of watershed characteristics. Today, spatiallydistributed hydrological models are increasingly applied to account for spatial variability of the main forcing variables within the catchment (e.g., precipitation); landscape characteristics (e.g., soil, land use) and detailed process calculation (Götzinger
& Bárdossy 2005). Usually, to perform the spatially-distributed modeling, a watershed is discretized into a group of unit elements, with the hydrological response of
each element computed over a proper time and spatial sequence. For many years,
the application of distributed parameter hydrologic models was hampered by limitation in describing watershed spatial characteristics. This is no more the scenario
due to the ever decreasing cost of computing power and availability of Geographic
Information System (GIS) software. Nowadays, one can easily use a proliferation of
6
1.2. Hydrology and soil erosion: The Literature Review
advanced equipment, geographical information systems (GIS) which remove many of
the earlier technical bottlenecks. Especially, with the advent of triangulated irregular
network (TIN), digital elevation model (DEM) based on GIS raster data structure has
become a profusion of watershed topographic analysis. In addition, DEM and TIN
have received significant attention in recent years, while grid cell models continue to
be popular because they can be easily coupled to remotely-sensed data structures.
On the other hand, hydrologically significant parameters require the use of large
databases and computers with high memory capacity and fast processing speed. Recent advances in computer workstation technologies have facilitated higher processing
speeds and operating systems. Therefore, distributed parameter hydrologic models
are now being used in the workstation computer environment in connection with GIS.
As explained by Grayson & Blöschl (2000), there are many distributed parameter
hydrological models available today and they should provide us with the tools to
undertake the detailed spatial analyses that should occur. Algorithms that were developed for the various processes to convert precipitation to runoff, infiltration and
evaporation, now have a framework within which they can be linked. We have a variety of methods for representing terrain, we can choose from an array of sub-process
representations for evapotranspiration, infiltration and surface ponding, vertical and
lateral flow through porous media, overland and channelized flow and so on. But
how well do the process descriptions represent the spatial reality? There are few
examples of explicit comparisons of spatial reality with spatial simulated response.
There have, of course, been innumerable applications of these models, using other
methods of testing. It is quite common that the model performance evaluation is
done by the good fitting of hydrograph. How well have we really exploited the spatial
capabilities of distributed hydrological models is still a question mark.
1.2.4 Spatial erosion assessment
The approaches for spatial erosion assessment presented here are based on the explanation given by Vrieling 2007. Spatial assessment of soil erosion can basically
be done in three different ways. The first way is the use of some measuring device
or erosion plots to measure soil erosion rates at different locations (Hudson 1993,
Loughran 1989). However, standard equipment is hardly available and the accurate
measurements are generally expensive and time-consuming (Stroosnijder 2005). In
addition, measurement results may be highly variable under similar circumstances
(Nearing et al. 1999). Field measurements are mostly used for assessing the role
of a specific erosion factor, model development, or validation purposes, but not for
spatial evaluation of erosion.
The execution of erosion field surveys is the second approach in which, features that
are formed due to erosion processes are identified, such as pedestals or rills (Herweg
1996). The repeated measurement of feature dimensions may give the quantitative
information. But surveys are often performed in a qualitative sense thus classifying
the amount of erosion based on the features encountered. Survey timing is important, because features may not be visible throughout the year for example, due to
management practices like ploughing. Surveys may allow spatial erosion mapping
7
1. General Background
for small catchments of about 2-km2 (Vigiak et al. 2005), but for larger regions it
becomes difficult. However, systematic visual identification of certain features from
aerial photographs would be another form of erosion survey that could be performed
for larger areas up to 50-km2 (Bergsma 1974).
The third and most common method for spatial erosion assessment, which is employed in this research work also, is the distributed erosion modeling by integrating
spatial data on erosion factors. The most widely-used model is the Universal Soil
Loss Equation (USLE: Wischmeier & Smith 1978; to be discussed in Chapter 2)
and its several variants, although many other erosion models exist that allow spatial
mapping of erosion (Merritt et al. 2003). Spatial data are needed for the application
of the erosion models. The relevant spatial data may be derived from a variety of
sources like e.g. existing soil, land use, and topographic maps, weather stations,
field measurements and surveys, aerial photographs, and satellite imagery. However,
many erosion models require a large amount of detailed data on a wide variety of
rainfall, soil, vegetation, and topography parameters. In data-poor environments like
e.g. developing countries, these data are often not readily available, or only at very
coarse scales.
1.3 Problem Statement and Motivation
Development of improved spatially distributed and temporally varying soil erosion
and sediment yield prediction approach is required to provide catchment stakeholders with the tools they need to evaluate the impact of various management strategies
on soil loss and sediment yield in order to plan for the optimal use of the land. Localization of erosion-prone areas and quantitative estimation of soil loss rates with
sufficient accuracy are of extreme importance for designing and implementing appropriate erosion control or soil and water conservation practices (Shi et al. 2004).
Overland flow, or surface runoff, is a primary hydrological vector for potential soil
erosion, however the implementation of current management practices does not utilize up-to-date scientific understanding of how and where runoff is generated and
erosion occurs.
Current soil erosion and water quality protection decisions are often made based on
results from models like CREAMS (Knisel 1980), GLEAMS (Leonard et al. 1987),
GWLF (Haith & Shoemaker 1987), AGNPS (Young et al. 1989), EPIC (Sharpley &
Williams 1990), SWAT (Arnold et al. 1995), etc., which use the SCS-Curve Number
method (e.g. USDA-SCS 1972) as their runoff estimating component and mostly
the USLE (Wischmeier & Smith 1965, 1978) and its several offspring like RUSLE
(Renard et al. 1991, 1997), MUSLE (Williams 1975) etc. as erosion estimating
component. Other sophisticated erosion and water quality models, also in practice,
include ANSWERS (Beasley et al. 1980), KINEROS2 (Smith et al. 1995), MIKESHE (Refsgaard & Storm 1995), LISEM (Roo 1996, Jetten & Roo 2001), (Morgan
et al. 1998) EUROSEM (Morgan et al. 1998), EROSION3D (Schmidt et al. 1999),
TOPMODEL (Beven & Freer 2001), WEPP (Flanagan et al. 2001), etc., which are
based on water and sediment balance and are more physically-based.
8
1.3. Problem Statement and Motivation
In recent years, several efforts have been made to assess the predictive quality of
erosion models, varying from continuous hillslope models to event based catchment
models. Meetings at Oxford (1995) and Utrecht (1997) of the Global Change of Terrestrial Ecosystems Programme (GCTE-Focus 3), and the Franqui Chair workshop
in Leuven (2000) focused on the comparison of simulation results using the same
input data set and on techniques for model improvements. Results indicated that
the predictive quality is moderate at best for all models, with slightly better results
obtained only when the model was calibrated for a particular situation and when
the modeler knew the area well (Boardman & Favis-Mortlock 1998, Jetten et al.
1999). Several methods for uncertainty assessment have been suggested (e.g. the
GLUE method of Beven & Binley 1992), but studies from Nearing (2000), Wendt
et al. (1986), Risse et al. (1993), and Nearing (2000) indicate that the coefficient of
variance of the predictions will always be from 10% for very large events to more
than 200% for small events. Perhaps the most severe shortcoming of these model
applications is that they are evaluated based on their ability to correctly predict
lumped discharge and soil loss or hydrographs and sedigraphs at watershed outlet.
No attention is given to the locations of runoff and sediment producing areas, although this may arguably be just as important in the sense of designing anti-erosion
measures and determining source and sink areas. While outlet data is the only data
available generally, the outlet alone is a poor integrator of the dynamics of runoff
and erosion in a catchment (Jetten 1996, Favis-Mortlock 1998).
However, the aspect of distributed models that makes them very interesting for environmental analysis is their ability to produce spatial patterns of the runoff and,
erosion and deposition. This enables us to change our focus from ‘how much’ runoff
and sediment a catchment produces to ‘from where’ it is produced. While quantifying the net output is important to design conservation measures, they are usually
over-dimensioned to be on the safer side. Moreover, the available modeling capabilities hardly produce satisfactory quantitative results for soil erosion and sediment
yield, in general. However, the runoff routing inside the catchment and the location
of sinks and sources of water and sediment are equally important. But to be careful here is that we may make very good predictions for all the wrong reasons, i.e.
the prediction of acceptable soil loss and discharge with an incorrect pattern of the
source and sink areas (e.g. Jetten et al. 1996, Takken et al. 1999, Favis-Mortlock
et al. 2001. If a conservation measure is given in a wrong location, it is of course
very cost-ineffective. Moreover many conservation measures are taken at a field or
hill-slope level (e.g. buffer strips, contour ploughing) and their effect can be important locally while not being perceptible at the outlet. This immediately raises the
question: how good are we in predicting spatial patterns?
The accuracy of the predicted soil loss rates depends on how exactly the erosion
parameters are quantified, but will never be absolute (Brazier et al. 2000). The more
simple models seem to perform equally well as the more complex distributed models.
The large spatial and temporal variability of soil erosion phenomena and the uncertainty associated with the input parameter values used in models to predict these
processes, is probably the most important reason why more complex physically based
9
1. General Background
erosion models, in general, do not perform better than simpler, lumped, regressionbased models. More complex models with better process descriptions (physicallybased) should, in principle, be capable of better output predictions; but, they also
require more input data, with which there is always an (often unknown) amount of
uncertainty and error associated that will propagate through the model calculations
and ultimately deteriorate the quality of the final results. (Zhang et al. 1996) tested
the WEPP model and showed that, even for optimized values of saturated hydraulic
conductivity of soil, prediction was moderate. Barthrust et al. (1998) tested the SHE
model in the Draix area (France) and got, for several events, one to two orders of
magnitude difference between observed and predicted values. However, for the same
data, Barthrust et al. (1998) obtained good results using a simple regression model
based on precipitation amount and intensity only. Roo (1993) compared the lumped
USLE and MMF (Morgan 2001) models with the spatially distributed ANSWERS
and KINEROS models and concluded that they performed equally well when the
models were tested for the same types of result. Risse et al. (1993) tested the USLE
for over 1700 years of erosion on 208 plots and got good results which are even somewhat better than those obtained by Zhang et al. (1996) for the much more complex
and physically based WEPP model. The comparison of these results suggests that
the additional error resulting from introducing additional parameters often outweighs
the potential improvement in prediction due to a better process description.
Far more limiting constraints face the modeler in terms of the presence or absence of
available data. The availability of data determines ultimately which type of model
can be selected. Rompaey et al. (2003, 2005) state that it is difficult to validate the
soil erosion rates at catchment scale for a number of reasons: (i) there is a lack of
direct soil erosion field measurements, (ii) the time frame of field measurements is
often short and does not correspond to that of the model, and (iii) measuring soil
erosion rates are fraught with methodological and practical problems, and different
techniques of measurement of the same erosion processes give quite different results.
The hydrologic processes of rainfall and runoff drive erosion and sedimentation process. Mainly in developing countries and even in developed ones, it is extremely
difficult to obtain all the required data for complete physically based soil erosion
modeling; however, required data for physically based hydrological model are more
or less readily available. This fact motivates to do a research on an interesting area,
mainly on- what improvement in the estimation of soil erosion can be achieved by
improving the hydrological component of the process? Improvement on the hydrological representation can be best thought by using the physically-based distributed
rainfall-runoff model. But, it is a well-understood fact that some of the model parameters need calibration against observed data, even if the model is physically-based.
Further, several parameter sets exist that yield equally good model performance
(equifinality), but how do the distributed results (spatial pattern) behave with those
equally good model parameters? With the constraints of the available data which
are mainly observed at a point (gauge/outlet), how believable the distributed results
of a distributed model are, even if they are physically-based? Those several issues
have motivated this research work.
10
1.4. Aim, Objectives and Research Questions
1.4 Aim, Objectives and Research Questions
Owing to the problems discussed above, it is clear that accurate erosion prediction
is still difficult and the problem will not be solved by constructing even more complete, and therefore more complex, models. Even if the quantitative estimates are
contestable, qualitative results concerning the spatial heterogeneity and temporal dynamics are of value. The quality and quantity of normally available observed data,
at the moment, is not enough for the use of a completely physically-based erosion
model but they are normally good enough to try out better hydrological modeling.
The general aim of this research is, therefore, to investigate the use of physicallybased rainfall-runoff modeling as the hydrological component with a computationally
simple and low data demanding erosion model to estimate spatially distributed and
temporally varying erosion/sediment yield in a catchment.
In this context, following specific objectives were addressed and each of them has
been achieved by trying to answer several research questions as mentioned below:
1. To investigate the use of the less data intensive rainfall-runoff model and soil
erosion model in distributed manner using GIS capabilities to predict spatial
pattern of surface runoff and sediment source areas within a catchment along
with the predictions of lumped predictions of runoff and sediment yield at
outlet.
p How good the simple rainfall-runoff model, used in several erosion models,
can predict runoff with its most recent modifications?
p How well does this modified/improved simple rainfall-runoff model coupled with a simple erosion model perform in predicting spatial patterns?
2. To compare the performance in the predictions when the simple rainfall-runoff
model is replaced by a more complex physically-based fully distributed rainfallrunoff model and then coupled with the same low data demanding soil erosion
model.
p Does the improvement in hydrology leads to a better estimation of erosion
and sediment yield at the catchment scale?
p Does perfectly matching hydrograph means better representation of hydrological process in the catchment?
3. To evaluate the distributed performance of the better performing rainfall-runoff
model in identifying the spatially distributed and temporally varying Hydrologically Sensitive Areas (HSAs).
p How do the surface runoff patterns differ in different subcatchments when
subcatchments are calibrated independently and how do they look like
when calibrated for same parameter set in all subcatchments?
p How do the distributed results obtained from parameters calibrated with
different calibration techniques differ?
p Are the calibrated parameters, performing good in hydrograph simulation,
good enough in predicting spatially distributed surface runoff too? How
11
1. General Background
to find the parameters that are good in all aspects or what would be a
robust parameter estimation technique?
4. To implement the simple modeling approach to identify spatially heterogeneous
and temporally dynamic Erosion Susceptible Areas (ESAs).
p What are the important factors that affect erosion and sediment yield in
the catchment?
p How does 2-D representation of topographical effects on erosion differ from
the normally followed 1-D representation?
p How to capture the effects of spatially distributed and temporally varying
vegetation cover on erosion and sediment yield in a catchment?
5. To carry out erosion risk modeling for identifying spatially distributed and temporally varying Critical Management Zones (CMZs) for anti-erosion measures.
p What are the effects of different good performing parameter sets on distribution and dynamics of erosion risk modeling?
p Can we reach to an overall applicable general conclusion?
After describing the models in Chapter 2 and study area in Chapter 3; the first and
second objectives are investigated with a case study which is described in Chapter
4. The investigation of the third objective is described in Chapter 5. The Chapter 6
deals with the fourth and fifth objectives. At the end, the Chapter 7 concludes this
thesis work by presenting the summary and outlook of the work in brief.
The objectives set up here is aimed to achieve finally a practical approach, scientifically justified and simple enough to be implemented to identify the timing and
location of areas in a basin that is prone to generate runoff and has the potential to
cause erosion thereby transporting sediment and pollutants downstream.
12
2 Joint Hydrological - Soil Erosion
Modeling
2.1 Background
Soil erosion models are simplified replica of the actual soil erosion process which
describes the effects of controlling parameters in the erosion process. These models
play an important role both in meeting practical needs of soil conservation goals
and in advancing the scientific understanding of soil erosion processes (Nearing et al.
2005). They help land managers in choosing practices to reduce erosion rates and
engineers for predicting rates of sediment loading to artificial reservoirs. The results
of soil erosion modeling form a basis for regulating conservation programs. Therefore
the central support in soil conservational decision making arises from the soil erosion
modeling. But it, in turn, depends on the hydrological input as the impacting rainfall
and dragging runoff is the primary governing forces of soil erosion by water. This
necessitates the joint hydrological-soil erosion modeling. The modeling of these two
aspects has their own complexities. From the point of view of data requirements, it
is almost impossible to use complex soil erosion model in data poor regions as compare to complex hydrological model. Moreover, the better performance capability of
complex erosion models, as compared to simpler ones, is yet to be proved with the
limitation of current data availability conditions.
It is noteworthy to mention here that several erosion and water quality models likeSWAT, EPIC, AGNPS, ANSWERS, CREAMS, GLEAMS, GWLF etc use the simplest runoff estimation method requiring minimal data. They use the SCS curve
number (CN) method as the hydrological component on one hand and the USLE
based models for soil erosion estimation on the other hand. In this context, it’s
worthy to investigate the capabilities of the simple USLE-based erosion model that
would be enhanced when its hydrological component is augmented by the more complex physically based distributed rainfall runoff model. This investigation forms the
basis or starting point of this research work. The joint modeling of USLE-based
erosion models with the recent modifications of simple hydrological model SCS-CN
and with more complex physically-based hydrological model WaSiM-ETH has been
attempted in this research. The description of these three models is presented in this
Chapter.
13
2. Joint Hydrological - Soil Erosion Modeling
2.2 Universal Soil Loss Equation (USLE) and its
modification
2.2.1 Introduction
Soil erosion by water had begun from the very beginning of the formation of the earth.
Though it is a natural process, human activities accelerate soil erosion process. According to Baver (1939), the first scientific investigation of erosion was carried out
by the German soil scientist Wollny, between 1877 and 1895 (Hudson 1995). The
first mathematical expression of erosion was established by Zingg (1940) to evaluate
the effect of the length and steepness of slope in erosion. Smith (1941) introduced
the concept of permissible soil loss and evaluated the effect of crop factor and mechanical protection over erosion. Browning and his co-workers worked in Iowa to
find soil erodibility and evaluated the effect of crop rotation and management in
erosion around the same time (Hudson 1995). Musgrave and co-worker developed
an empirical equation in 1947 known as Musgrave equation or Slope Practice equation. This equation was exclusively implemented for nearly ten years before it was
replaced with more realistic Purdue product, Universal Soil Loss Equation (USLE),
in 1958. Wischmeier & Smith (1965) published the Agricultural Handbook 282 to
use it as erosion planning tool for farmers and conservation planners. Continuous
experimentation and research extended the scope of its application and the Agricultural Handbook 537 was subsequently published with more experimental results and
improvement in the existing parameter estimation methods (Wischmeier & Smith
1978). A large number of erosion models are based on the USLE (e.g., Agricultural
Non Point Source Pollution (AGNPS) (Young et al. 1989), ANSWERS (Beasley et al.
1980, Dabral & Cohen 2001), the Erosion Productivity Impact Calculator (EPIC)
(Sharpley & Williams 1990) and SWAT (Arnold 1996)). Different models have been
developed further based on USLE in different countries to suit their particular requirements between late 1980s and early 1990s. The Soil Loss Estimation Model
for Southern Africa, SLEMSA (Elwell 1981) developed in South Africa, INDEROSI
(Gnagey 1991) developed in Indonesia and SOILOSS (Rosewell 1993) developed in
Australia are some of the examples of such models. Thus, although the USLE was
developed in the USA, it has been used throughout the world (Pilesjo 1992, Mellerowicz et al. 1994, Kinnell & Risse 1998, Bartsch et al. 2002) because it seemed to meet
the needs of researchers better than any other available tool (Summer et al. 1998).
It is hailed as one of the most significant developments in soil and water conservation.
USLE is an index method with factors that represent how climate, soil, topography,
and land use affect rill and inter-rill soil erosion caused by raindrop impact and
surface runoff. In general, erosion depends on the erosivity, caused by the amount
and intensity of rainfall and runoff, and the resistance of soil surface or the degree
of erodibility caused by intrinsic soil properties, adopted land use practices and the
topography of the landscape as described by slope length and steepness. USLE
captures these erosion influencing parameters into six factors whose product forms
the simple structure of the model. This basic explanation of USLE is depicted in
Fig. 2.1.
14
2.2. Universal Soil Loss Equation (USLE) and its modification
Figure 2.1: An introduction to USLE model
The basic form of USLE is hence given as;
E = R × K × LS × C × P
(2.1)
where
E
= Soil loss rate expressed as weight (in unit selected for K) per unit area
(in unit selected for R) over a period selected for R.
R = Rainfall-runoff erosivity factor [MJ mm/ha h].
K = The soil erodibility factor [t h/MJ mm]. It equals the soil loss rate per
erosion index unit for a specified soil as measured on a unit plot, which
is defined as a 72.6 ft (22.1 m) length of uniform 9% slope continuously
in clean-tilted fallow.
L
= Slope length factor [ - ]. It is equal to the ratio of soil loss from the field
slope length to soil loss from a 72.6-ft length under identical conditions.
S
= Slope steepness factor [ - ]. It represents the ratio of soil loss from the
field slope gradient to soil loss from a 9% slope under, otherwise, identical
conditions.
C
= Cover and management factor [ - ]. It equals the ratio of soil loss from
an area with the specified cover and management to soil loss from an
identical area in tilled continuous fallow.
P
= Conservation support practice factor [ - ]. It represents the ratio of soil
loss with a support practice like contouring, strip cropping, or terracing
to soil loss with straight-row farming up and down the slope.
After the research and experience gained in this field using USLE equation since
1970s; it has provided insights to develop improved technology that has led to the
15
2. Joint Hydrological - Soil Erosion Modeling
designing of Revised USLE (Renard et al. 1991). The project to revise and update
the USLE strengthened the technology. The update is based on an extensive review
of the USLE and its database, analysis of data not previously included in the USLE,
and theory describing fundamental hydrologic and erosion processes. This result of
this update of the USLE is referred to as RUSLE – the Revised USLE.
The RUSLE has some significant improvement over the various factors, which can
be briefly summarized as below:
p
p
p
p
Minor changes in R factors.
Expanded information on soil erodibility.
A slope length factor that varies with soil susceptibility to rill erosion.
A nearly linear slope steepness relationship that reduces computed soil loss
values for very steep slopes.
p A sub-factor method for computing values for the cover-management factor.
p Improved factor values for the effects of contouring, terracing, strip cropping,
and management practices for rangeland.
Another version, which is known as The Modified Universal Soil Loss Equation - the
MUSLE (Williams 1975) follows the structure of the USLE, with the exception that
the rainfall factor is replaced with the runoff factor. The model calculates sediment
yield for a storm instead of gross erosion.
The basics and the estimation procedure of the six factors of USLE and its variants
are discusses in the subsequent sections.
2.2.2 Rainfall - Runoff erosivity factor (R)
All the rain that falls on the earth’s surface does not contribute to surface runoff
and soil erosion. Therefore, only the part of the rain that really cause erosion is
considered for predicting soil loss due to water and that part of the erosive rainfall
is represented by this factor called rainfall erosivity factor or simply R-Factor. The
kinetic energy of the raindrops disintegrate the soil particles and the lighter materials
like very fine sand, silt, clay and organic matter are then easily removed by the runoff
water. When the raindrop energy and runoff amount increases, even larger soil particles are detached from the surface and transported and the problem becomes more
severe. Although the energy is significantly less, the low intensity rainfall extended
over a long duration also produce significant erosion which depends of several properties of underlying soil for example soil saturation, infiltration, permeability and so on.
The R factor [MJ mm/(ha h)] represents the erosive potential of rainfall. Estimating
this parameter involves analysis of rainfall events that are separated by temporal
interval of 6 or more hours of dry period (Johnson et al. 2001). FFor these rainfall
events to be erosive enough to consider for R factor estimation, either the rainfall
amount should be greater than 12 mm or 15 minute intensity should be greater than
12 mm/hr. The product of the total energy (E) and the maximum 30 minute intensity
(I30 ) is the erosivity for that particular event and all those erosivity terms summed
16
2.2. Universal Soil Loss Equation (USLE) and its modification
over a particular period of time represents erosivity for that period. Mathematically,
R factor for a period j consisting n number of events is computed as:
Rj =
X
EI30
(2.2)
n
where
I30 = Max. 30 minutes rainfall intensity [mm/hr]
E = Total kinetic energy of the storm/event [MJ/ha]
For an event having M number of periods such that the rainfall intensity can be
considered constant for each period k, then the total kinetic energy E for the event
is computed as:
E=
M
X
e k · vk
(2.3)
k=1
e = 0.29 [1 − 0.72 · exp(−0.082i)]
(2.4)
where
vk = Rainfall amount in k th period [mm]
ek = Unit energy of rainfall in k th period [MJ/ha.mm]
i = Rainfall intensity during k th period [mm/hr]
The estimation of R factor, as described above, requires a long series of rainfall intensity data which is not available in many cases. So, different measures of rainfall
erosivity that uses more easily available rainfall parameters have been proposed as alternatives to estimate the R factor. These include, for example, the Fournier’s index
(Fournier 1960) and the modified Fournier index (Arnoldus 1977), Lal’s AIm index
(Lal 1976), Hudson’s KE > 25 index (Hudson 1971), Onchev’s universal erosivity
index (Onchev 1985). Investigation of some of these methods along with a newly
proposed/developed method is presented in Chapter 4.
Further, the original R factor which considers only rainfall but not runoff has been
replaced by runoff erosivity factor differently by different researchers. Those models
are presented and investigated in a case study described in Chapter 4 (Equation
4.18).
2.2.3 Soil erodibility factor (K)
Soil erodibility reflects the ability of soil to resist erosion, based on the physical
characteristics of the soil. It depends on soil structure, texture, content of organic
matter, permeability, and other inherent soil properties like cohesion and particle
size distribution. Generally soil with faster infiltration rates, higher levels of organic
matter and improved soil structure have a greater resistance to erosion. Sand, sandy
loam and loam textured soils tend to be less erodible than silt, very fine sand, and
certain clay textured soils. Soil with higher clay content will have smaller K value
due to high cohesion where as sandy soil will again have less K value due to higher
17
2. Joint Hydrological - Soil Erosion Modeling
infiltration rate resulting in less surface runoff. Organic soils such as loam will have
moderate value of K as they are moderately susceptible to detachment. Soils with
high silt content will have high erodibility factor as they possess less cohesion and
allow more runoff. Soil erodibility is increased with tillage and cropping practices
which lower soil organic matter levels, as it causes poorer soil structure. On the
compacted surface infiltration is decreased and runoff increases thereby increasing
the rill erosion.
In USLE, this property of soil is captured through the soil erodibility factor or K
factor and is an experimentally determined value on a unit plot. A unit plot is a
standard plot of length 22.1m and uniform slope of 9% and is continuously in cleantilled fallow condition with tillage-performed upslope and down slope (Wischmeier
& Smith 1978). Minimum width of plot is recommended to be 1.83 m to minimize
the effect of boundary in soil loss and flow. For a particular soil, soil erodibility is
the rate of soil loss per erosion index unit (ton.ha.h./(MJ.ha.mm)) measured on the
unit plot (Wischmeier & Smith 1978).
Susceptibility to erosion also depends on erosion events in the past, because the exposed surfaces due to erosion can be readily eroded than the original surface. Such
surfaces have poor structure and lower organic content which are associated to the
lower level of nutrient contents responsible for the lower crop yield. This results in
reduced vegetation cover which means to less protection for the soil against erosion.
The physical, chemical and mineralogical soil properties and their interactions that
affect K values are many and varied. Wischmeier & Smith (1978) developed a soil
erodibility nomogram which associates different properties of soil like the effect of
particle size distribution, classes of structure and permeability of soil. If the total
percentage of silt and very fine sand is less than 70, this nomograph can be approximated as (Renard et al. 1997):
K = 2.77 × 10−7 M 1.14 + 4.28 × 10−3 (s − 2) + 3.29 × 10−3 (p − 3)
where
K
S
P
OM
M
=
=
=
=
=
(2.5)
Soil erodibility factor (ton.ha.h./(MJ.ha.mm))
Classes of structure (1-4)
Soil permeability class (1-6)
Percentage organic matter content
Product of primary particle size fraction and given as (Rosewell 1993);
M = (si + 0.7F s) (si + F s + Cs)
(2.6)
where
si = Percentage silt
F s = Percentage fine sand
Cs = Percentage coarse sand
Classes of structure and soil permeability class are the functions of particle size and
permeability of soil.
18
2.2. Universal Soil Loss Equation (USLE) and its modification
For application in European soils another approach was proposed by Römkens et al.
(1986) based on regression analysis of a world-wide dataset of all the measured Kvalues, which yielded the following equation, revised in Renard et al. 1997 (van der
Knijff et al. 2000):
"
K = 0.0034 + 0.0405 × exp −0.5 ×
log Dg + 1.659
0.7101
2 #
(2.7)
where
K = Soil erodibility factor (ton.ha.h./(MJ.ha.mm))
Dg = Geometric mean weight diameter of the primary soil particles [mm]. It
is the function of surface texture, and can be calculated using:
"
Dg = exp
X
fi · ln
di + di−1
2
!#
(2.8)
where, for each particle size class (clay, silt, sand):
di
= Maximum diameter [mm]
di−1 = Minimum diameter [mm]
fi
= Corresponding mass fraction
As several formulas are available to estimate K factor based on the intrinsic properties of the soil, the required detailed soil data is not available in many cases. In such
cases, according to the fact that the soil texture is the principal affecting factor, the
tabulated K values based on the soil texture shall be directly used. A commonly
used K factor list is shown in Table 2.1.
2.2.4 Topographic factor (LS)
Topography is an important factor affecting soil erosion. It is significant to quantitatively evaluate the effect of topography on erosion for predicting soil loss. These
effects include slope length and steepness in terms of soil-loss estimation. Naturally,
the steeper the slope of a field, the greater is the amount of soil loss from erosion
by water. Soil erosion by water also increases as the slope length increases due to
the greater accumulation of runoff. Consolidation of small fields into larger ones often results in longer slope lengths with increased erosion potential, due to increased
velocity of water which permits a greater degree of scouring, i.e., carrying capacity
of sediment (Shelton 2003). In USLE based models, those factors of slope length
and steepness are cited with dimensionless values L and S, and together called as
topographic factor.
L is the slope length factor and represents the effect of slope length on erosion.
Slope length is defined as the horizontal distance from the origin of overland flow to
the point where either the slope gradient decreases enough that deposition begins
or runoff becomes concentrated in a defined channel (Wischmeier & Smith 1978).
19
2. Joint Hydrological - Soil Erosion Modeling
Table 2.1: Values of K factor [ton.ha.h./(MJ.ha.mm)] based on soil texture
(Organic Matter Content)
Textural Class
Clay
Clay Loam
Coarse Sandy Loam
Fine Sand
Fine Sandy Loam
Heavy Clay
Loam
Loamy Fine Sand
Loamy Sand
Loamy Very Fine Sand
Sand
Sandy Clay Loam
Sandy Loam
Silt Loam
Silty Clay
Silty Clay Loam
Very Fine Sand
Very Fine Sandy Loam
Less than 2%
More than 2%
0.032
0.044
0.012
0.029
0.025
0.045
0.02
0.007
0.058
0.001
0.018
0.054
0.036
0.046
0.061
0.054
0.028
0.037
0.009
0.008
0.022
0.02
0.038
0.012
0.005
0.033
0.003
0.026
0.016
0.049
0.034
0.04
0.049
0.044
Average
0.029
0.04
0.009
0.011
0.024
0.022
0.04
0.015
0.005
0.051
0.001
0.026
0.017
0.05
0.034
0.042
0.057
0.046
Quantitatively, L is the ratio of soil loss from the field slope length to that from
22.1m long plot of same soil and gradient. If λ is the horizontal projection of the
slope length (in meter), then L factor is given as;
L=
λ
22.1
m
(2.9)
where, m is the slope-length exponent. In USLE (1978), the exponent m is recommended as 0.2, 0.3, 0.4 and 0.5 for slope gradients less than 1%, 1-3.5%, 3.5-5%, and
5% or greater, respectively. This means that when slope gradient is greater than 5%,
the slope length factor does not change with slope steepness. However in RUSLE,
m continues to increase with the slope steepness according to Eqs. 2.10 and 2.11
(McCool et al. 1989).
β
1+β
(2.10)
sinθi,j /0.0896
3 · (sinθi,j )0.8 + 0.56
(2.11)
m=
β=
where θ is the slope angle (degrees) and β is the ratio of rill erosion (caused by flow)
to interrill erosion (principally caused by raindrop impact). The value for m is to be
adjusted by multiplying the value of β by 0.5 for lower ratio of rill to interrill erosion
or 2.0 for larger ratio of rill to interrill erosion (McCool et al. 1989).
20
2.2. Universal Soil Loss Equation (USLE) and its modification
S is slope steepness factor and represents the effect of slope steepness on erosion.
Quantitatively, it is again the ratio of soil loss from the field gradient to that from
a 9% slope with other condition remaining the same. Soil loss increase more rapidly
with slope steepness than it does with slope length. The slope gradient factor for
USLE is expressed as follows:
S = 65.41sin2 θ + 4.56sinθ + 0.065
(2.12)
where θ is the angle to horizontal. The following equations stand for RUSLE (McCool
et al. 1987):



10.0sinθ + 0.03,
for θ < 9%;
for θ >= 9%;
for shorter slopes (< 4m)
S = 16.8sinθ − 0.50,


3.0sin0.8 θ + 0.56,
(2.13)
Further, Nearing (1997) proposed a more general, single, continuous function for
slope steepness:
S = −1.5 +
17
1+
e(2.3−6.1sinθ)
(2.14)
The equations presented above are the basics for the estimation of the topographical factor. However, the LS factor is one of the most variable factors discussed in
erosion scientific literature. With the advent of GIS, the approach of estimating the
topographical factor has been improved with two dimensional consideration which
uses upslope contributing area instead of the one dimensional flow length. It, hence,
capture the effect of the landscape on erosion in more realistic way. Several modified methods based on this approach are presented and investigated in a case study
described in Chapter 4 (see equations 4.25-4.29).
R and K factors are generally uncontrollable factors and cannot be adjusted to
reduce erosion. The LS factor may be modified in some cases to reduce erosion, for
eg. landscaping, but it is usually prohibitively expensive. C and P factors, which
are described in subsequent sub-sections, are the only controllable factors that can
be managed for the control of erosion.
2.2.5 Cover management factor (C)
The potential soil loss i.e., soil loss from a barren land (land without vegetation
cover) is substantially higher in comparison to the actual soil loss. This difference
in particular is governed by the presence of vegetation cover, crop sequence, and
management practices (Wischmeier & Smith 1978). Cover management factor C,
used in the USLE-based models is the measure of the effect of such cropping and
management practices on erosion rate. The C factor is defined as the ratio of the
soil loss from land cropped under specified conditions to the corresponding loss from
21
2. Joint Hydrological - Soil Erosion Modeling
continuously fallow and tilled land. It varies from 0.01 to 1.0 with 1.0 applied to
continuously fallow, tilled land.
The USLE was developed for use on agricultural fields. It is adapted to use in nonagricultural conditions by appropriate selection of the C factor. This is often done
by relating the land use conditions to some agricultural situation. For example, a
firing range with a grass cover might be assumed to be similar to a pasture land use.
So, in the simplest form, as in the USLE, the C factor is estimated based on the
land use categorization of the concerned area. But in RUSLE, this factor is greatly
revised and is estimated with the soil-loss ratio (SLR) algorithm which incorporates
several sub factors like prior-land-use (PLU), canopy-cover (CC), surface-cover (SC),
surface-roughness (SR), and soil-moisture (SM) (Renard et al. 1997).
However, in a catchment scale, such a detail data as required by RUSLE is hardly
available or is impractical and the C factor estimation is normally based on the land
use classification/map of the catchment. So knowing the land use, its value can be
simply obtained from published tables. But the ground-cover or canopy-cover which
comes under the agriculture, grassland/pasture or forest classification in the land
use is not static over time. To capture this dynamics, the C factor at a time has
been either linked directly with the crop cover percentage of that time, as used in
the case study described in Chapter 4 (see equation 4.20), or indirectly through the
vegetation parameters like NDVI (Normalized Difference Vegetation Index) or LAI
(Leaf Area Index) as used and described in Chapter 6.
2.2.6 Support practice factor (P)
Support/conservation practice factor, P , accounts for the variations in agricultural
management practices. It is defined as the ratio of soil loss with given support conservation practice to the corresponding loss with up and down slope tillage. Specific
support practices affect erosion by modifying the flow pattern, grade and direction
of surface runoff and by reducing the amount of runoff (Renard & Foster 1983). The
principle behind this is that the erosion potential of the runoff water is reduced by
altering the drainage pattern which ultimately reduces runoff concentration, runoff
velocity and the hydraulic forces from the runoff water (Kim & Julien 2006).
For cultivated land, the support practices include contouring, strip cropping, terracing and subsurface drainage. On dryland or rangeland areas, soil-disturbing practices oriented on or near the contours that result in storage moisture and reduction
of runoff are also termed as support practices. The support practice factor for individual support practice associated with the land of interest is to be calculated and
incorporated to compute overall P factor. Details of calculation procedures are described in the Agricultural Handbook 703 (Renard et al. 1997). But practically the
data of the adopted erosion control practices in the agricultural area are, in general,
not available and are also not so significant in case of large catchment. So, its value
can be safely taken as 1 assuming that no conservation measures are implemented in
the catchment.
22
2.3. Sediment Delivery Ratio and Sediment Yield
2.3 Sediment Delivery Ratio and Sediment Yield
The USLE model discussed above (except the variants using runoff erosivity factor
instead of rainfall erosivity) predicts the amount of soil lost from the considered area
(gross erosion), however all the soil lost do not reach to the stream or gage station
or to the outlet of the catchment. This is because some portion of the soil that is
eroded from the overland region of the catchment is deposited back at several places
downstream where the slope is more gentle or at plains or in depressions. However, it is the interest of environmentalists, civil engineers and others to quantify
the amount of sediment that actually reaches to the point of interest; for example,
to the catchment outlet, river confluence, reservoir/dam location, flow gauge etc.;
and this portion of the eroded soil is called the Sediment Yield (SY ) at that point.
Sediment yield, therefore, involves erosion processes as well as sediment deposition
and delivery to the point of concern, the catchment outlet in our case.
The sediment yield at the catchment outlet can be quantified using the Sediment
Delivery Ratio (SDR) along with the gross erosion as estimated by the USLE model.
The SDR, sometimes also called transmission coefficient, is the ratio of sediment
delivered to a particular location in the stream system (catchment outlet) to the
gross erosion within the drainage area above that location. Hence it is defined as;
SDR =
SY
Sediment Yield
=
E
Gross Erosion
(2.15)
SDR may range from a few percent to nearly 100 percent with larger delivery ratios
generally applying to smaller watersheds with steeper slopes, finer grained material
and with extensive and well-defined channel network. It is affected by numerous
factors including soil texture, sediment source, proximity to the streams, channel
density, basin area, slope, land use/cover and other rainfall-runoff factors. There
is no general procedure available for computing the sediment delivery ratio for a
particular watershed. General relationships have been developed relating sediment
delivery ratios to the increased opportunity for sediment deposition to occur before
reaching the watershed outlet. Some of such relationships are;
Based on drainage area
SDR
= 0.5656 · A−0.11
log SDR
= 1.7935 − 0.14191 · log (A)
SDR
= 0.375 · A−0.2382
(Boyce 1975)
SDR
= 0.4724 · A
−0.125
(V anoni 1975)
SDR
= 0.475 · A−0.134958 − 0.127097
(U SDA 1972)
(Renf ro 1975)
(2.16)
(U SDA − N RCS 1983)
where
A = drainage area in sq. km
The SDR model developed by Vanoni (1975) is more generalized than other areabased models given above because it was derived from larger number of watersheds.
23
2. Joint Hydrological - Soil Erosion Modeling
Based on topography
(i) Williams & Berndt (1972) used slope of the main stream channel to predict
sediment delivery ratio. The model is written as:
SDR = 0.627 · SLP 0.403
SLP
where
(2.17)
= % slope of main stream channel.
(ii) Maner’s studies (1958) suggested that SDR was better correlated with relief
and maximum length of a watershed expressed as relief-length ratio (R/L) than
with other factors. Renfro (1975) modified the model as follows:
R
log (SDR) = 2.94259 + 0.82362 · log
L
(2.18)
R = Relief of a watershed, defined as the difference in elevation
between the average elevation of the watershed divide and
the watershed outlet
L = Maximum length of a watershed, measured approximately
parallel to mainstream drainage
where
(iii) Williams (1977) found that the sediment delivery ratio is correlated with drainage
area, relief-length ratio, and runoff curve numbers. He developed a model based
on the sediment yield data for 15 Texas basins. The model is expressed as follows:
SDR = 1.366 × 1011 · (DA)−0.0998 · (ZL)0.3629 · (CN )5.444
DA
ZL
CN
where
(2.19)
= the drainage area in km2
= the relief-length ratio in m/km
= the long-term average SCS curve number
Based on rainfall-runoff
A SDR model which is used in the Soil and Water Assessment Tool (SWAT) (Arnold
et al. 1996) takes rainfall-runoff factor into account. The primary form of the SDR
model is:
SDR =
where
24
qp
PI
P
Q
=
=
=
=
qp
PI
Q
· (0.78285 + 0.21716) ·
P
Peak flow [mm/h]
Maximum rainfall intensity in mm/h
Precipitation in mm
Runoff in mm
0.56
(2.20)
2.4. Rainfall-Runoff modeling
Recently Mishra & Singh (2006) made a hypothesis for the estimation of SDR as;
SDR = ψ
where
ψ = runoff coefficient =
(2.21)
Runoff
Rainfall
Besides, there are some GIS-based models like WATEM/SEDEM, SEDD etc that can
be used for estimating spatially distributed SDR, but they need observed sediment
yield for calibration, which is rarely available. A couple of simple SDR equations
along with a new proposed one (see equations 4.30 - 4.32) have been investigated in
a case study as described in Chapter 4.
Once the SDR is estimated, the Sediment Yield (SY ) from a watershed can be computed simply by multiplying the gross erosion within the watershed (results from
USLE) by the sediment delivery ratio.
2.4 Rainfall-Runoff modeling
The rainfall-runoff modeling to be done in this research work is basically aimed to
simulate the spatially distributed surface runoff that couples with or deliver input
to the erosion model for the estimation of spatially distributed erosion risk. As set
in the objectives, two types of model are to be dealt with. The first one is a simple
rainfall-runoff model to investigate its capability in predicting the spatial patterns
of erosion risk when coupled with another simple erosion model. The next one is a
more complex rainfall-runoff model to investigate the improvement in the prediction
of the simple erosion model that can be achieved when its hydrological component
is replaced by this more detailed complex rainfall-runoff model. The SCS-CN model
which is the core component of many erosion models and the WaSiM-ETH model
have been chosen for the purpose respectively. The description of the basics of these
two models is presented in this section.
2.4.1 SCS-CN model and its modifications
The Soil Conservation Service Curve Number (SCS-CN) method was developed by
originally the U.S. Department of Agriculture Soil Conservation Service (USDASCS), now Natural Resources, documented in detail in the National Engineering
Handbook, Sect. 4: Hydrology (NEH-4) (SCS, 1956, 1964, 1971, 1985, 1993). Due
to its simplicity, it soon evolved well beyond its original objectives and becomes one of
the most popular techniques among the engineers and the practitioners. Accordingly,
the applicability of the SCS-CN method and the runoff generation mechanism have
been thoroughly analysed throughout the world. The main reasons for its success
is that it accounts for many of the factors affecting runoff generation including soil
type, land use and treatment, surface condition, and antecedent moisture condition,
incorporating them in a single parameter- CN, the Curve Number.
25
2. Joint Hydrological - Soil Erosion Modeling
The future of the SCS-CN method shall be projected from the quote in the paper of
Melesse & Graham (2004) which states that; "Dingman (2001) concluded that the
NRCS(SCS)-CN approach will continue to be used since (1) it is computationally
simple, (2) it uses readily available watershed information, (3) it has been packaged in readily available tables, graphs, and computer programs, (4) it appears to
give reasonable results under many conditions, and (5) there are few other practicable
methodologies for obtaining a priori estimates of runoff that are known to be better."
The hypothesis of the USDA-SCS CN method is that the ratio of actual direct runoff
to the potential maximum runoff (effective rainfall) is the same as the ratio of actual
retention in the watershed to the potential maximum retention (USDA-SCS 1985,
Chow et al. 1988), as indicated by;
Q
F
=
(P − Ia )
S
where
Q
P
Ia
F
S
=
=
=
=
=
(2.22)
Direct runoff [mm],
Total rainfall [mm],
Initial abstraction [mm],
Cumulative infiltration excluding Ia and
Potential maximum retention [mm]
Further, the water balance principle gives;
P = Ia + F + Q
(2.23)
The combination of Eqs. 2.22 and 2.23 yields the basic form of the SCS-CN method,
given as;
(P − Ia )2
, if P > Ia ;
Q = (P − Ia + S)


0,
if P ≤ Ia



(2.24)
The initial abstraction (Ia ) includes all losses before runoff begins. It includes water
retained in surface depressions, water intercepted by vegetation, and water lost to
evaporation and infiltration. Ia is highly variable but is generally correlated with
soil and cover parameters. Through studies of many small watersheds the second
hypothesis was made to approximate Ia by:
Ia = λS
where
(2.25)
λ = Initial abstraction coefficient [ - ]
In original SCS-CN, the λ is set to a constant value of 0.2 which makes S to be the
only parameter of the method. Furthermore, the potential retention S is expressed
in terms of the dimensionless curve number (CN) through the relationship;
S=
26
25400
− 254
CN
(2.26)
2.4. Rainfall-Runoff modeling
The Curve Number (CN) ranges between 0 and 100 and is an index of hydrologic soil
group, soil condition, land cover and antecedent conditions of the concerned area.
Its values can be found in widely published tables and can be picked up based on
these four factors.
For the estimation of CN, the soil is divided into four groups hydrologically as shown
and described in Table 2.2 (Roberson et al. 1988).
Table 2.2: NRCS soil groups based on infiltration rate and soil properties
Group
Minimum
Infiltration
Rate
Soil Description
(in/hr)
(mm/hr)
A
0.30-0.45
7.60-11.4
Soils having a high filtration rate. They are chiefly deep, well
drained sands or gravels, deep loess or aggregated silts. Thy
have low runoff potential
B
0.15-0.30
3.80-7.60
Soils having a moderate infiltration rate when thoroughly wet.
They are chiefly moderately deep, well drained soils of moderately fine to moderately coarse texture such as shallow loess and
sandy loam.
C
0.05-0.15
1.20-3.80
Soils having a slow infiltration rate when wet. They are soils
with a layer that impedes downward movement of water and
soils of moderately fine to fine texture such as clay loams, shallow
sandy loam, soils low in organic content and soils high in clay
content
D
0.00-0.05
0.00-1.20
Soils having a very low infiltration rate. They are chiefly clay
soils with a high swelling potential, soils with a permanent high
water table, soils with a clay pan at or near the surface, shallow
soils over nearly impervious material, heavy plastic clays and
certain saline soils. They have high runoff potential.
Furthermore, three initial watershed conditions are described Table 2.3: AMC classes for SCS-CN method (SCS 1972)
by the Antecedent Moisture
AMC
5-day antecedent rainfall [mm]
Condition (AMC) based on preclass
Dormant Season Growing Season Average
vious five days’ rainfall amount.
I
< 13
< 36
< 23
AMC I, II and III is applied reII
13-28
36-53
23-40
spectively to dry, wet and avIII
> 28
> 53
> 40
erage moisture conditions. The
CN values picked up from the
published table represents the average condition (CN II) and has to be modified
based on the existing AMC. The original SCS-CN method has proposed the Table
2.3 for employing these modifications.
In the course of continuous use of the SCS-CN model word-wide, several modifications
for its better performance have been proposed. Some of the notable ones, that have
been applied in the case study described in Chapter 4 (Eqns. 4.4 - 4.13), are;
27
2. Joint Hydrological - Soil Erosion Modeling
p
p
p
p
p
Incorporation of the effect of slope
Improvement in initial abstraction ratio, λ
Incorporation of continuous antecedent moisture
Improvement in estimation of initial abstraction, Ia
Incorporation of depression storage
2.4.2 Water Flow Balance Simulation Model - WaSiM-ETH
The WaSiM-ETH has been chosen here, for better hydrological representation to be
used for erosion risk estimation, because it includes most of the processes relevant for
runoff generation. Also, it considers the spatial distribution of catchment characteristics and is based on spatial and temporal dynamics of climate variables. Moreover,
the model has been successively used to model different problems in different temporal resolutions, covering wide range of catchment sizes from 12.5 ha to 40,000 km2 .
The Water Flow and Balance Simulation Model (WASIM-ETH) is a deterministic,
process-based fully distributed hydrological catchment model. The spatial resolution
is given by a grid and the time resolution can vary from minutes to days. The modular architecture provides spatial information about all the hydrological aspects of a
catchment. It considers different processes of runoff generation, for example Hortontype overland flow or runoff generation from saturated areas. The main processes of
the water flux- the result of surface runoff, percolation, soil moisture, deep percolation, the storage and the phase transition of water are simulated by physically-based
simplified process descriptions (Schulla & Jasper 1999, 2006).
Primary model input data grid includes a digital elevation map (DEM), soil and
land use map. While some data is mandatory, other secondary data is derived from
the primary data either within the model during the model run or is estimated
through preprocessing. The WASIM-ETH suite includes the terrain analysis program
called TANALYS, which performs a complex analysis of the Digital Terrain Model
(DTM/DEM), calculating secondary grids like local slope and aspect. Furthermore,
it determines the automatic derivation of flow directions, sub-basin boundaries, flow
accumulation, the river network and flow time grids. The flow directions are calculated by the steepest slope of neighboring grid cells. Artifacts like sinks in the
elevation map are filled interactively. After the flow directions are determined the
flow accumulation is calculated. The flow accumulation represents the catchment
area for each grid cell. The river network is then extracted by setting a threshold of
grid cells for the flow accumulation. The flow orders identified according to Strahler
are essential to outline artifacts like parallel rivers. Flow time zones are zones of
equal flow times for surface runoff to reach the sub-basin outlet, where all grid cells
belonging to the same zone have the same flow time (rounded up to the next integer
number of time steps). It is calculated using Manning-Strickler formula. The land
use and soil type’s grids are parameterized with a land-use and a soil type table that
describes each grid cell with a parameter data set (like albedo, LAI, root depth, field
capacity, porosity etc.) according to the grid classification.
Observed temperature, precipitation, wind speed, sunshine duration, air humidity
28
2.5. Application of remote sensing and GIS in the modeling
and vapour pressure are the driving input time series for the model. Since meteorological data is usually provided as station data the input to each grid cell is
generated by interpolation. WaSiM-ETH provides some of the common interpolation techniques like altitude dependent regression, inverse distance weighting or a
combination of both methods where different weightage can be given to each method.
Besides, a systematic correction can be performed to allow for the impact of wind
on precipitation. Also shadowing and exposition grids are taken to adjust radiation
and temperature distribution with the approach taken from (Oke 1987).
The interpolation and correction of input data is followed by the simulation of the
main hydrological processes like evapotranspiration, interception, infiltration and the
separation of discharge into direct flow, interflow and base flow. Direct runoff and
interflow are routed to the subcatchment outlet by subdividing the catchment into
flow-time zones calculated with the preprocessor- TANALYS. Discharge routing in
the river bed channel is performed by a kinematic wave approach using different flow
velocities for different water levels in the channel. After the translation of the wave,
a single linear storage is applied accounting for diffusion and retention. Finally, discharges from different sub-basins are superposed.
The complete simulation using WaSiM-ETH is governed by a “control file” which is
gateway to the model. All necessary input-output filenames, directory-path, modeling parameters, derived secondary parameters, module initializations, definitions
and calibration parameters are defined in the control file. For most processes, different approaches can be chosen depending on the available data, the scope of the
simulation and the necessary spatial and temporal resolution. These calculations are
modularly built and can be adapted to the physical characteristic of the catchments
area. The modular scheme of WaSiM-ETH is shown in Fig. 2.2. A detailed description can be found in the WaSiM-ETH model description handbook (Schulla &
Jasper 1999, 2006). The different modules and the calibration aspect relevant to this
research work is described later in the respective chapters.
2.5 Application of remote sensing and GIS in the modeling
Often the predictive hydrologic and soil erosion models do not examine the problem
in a spatial context. However the processes in hydrology and soil erosion are greatly
influenced by the spatial heterogeneity in hydrometeorology, topography, vegetation,
soil properties and land use, among other factors. So the concern for resource management and environmental quality requires application of the distributed models to
capture this heterogeneity. The Soil erosion prediction along with the hydrological
components is relevant at a wide range of spatial scales; from the plot scale to the
catchment scale, from the regional scale up to the continental and global scales. At
the larger scales, the variability of the hydro-meteorological and geomorphological
characteristics within the basin becomes much more important. This is where the
remote sensing and GIS (Geographic Information Systems) become valuable tools.
The Geographic Information Systems are becoming a popular and effective tool when
29
2. Joint Hydrological - Soil Erosion Modeling
Figure 2.2: Model structure of WaSiM-ETH (Schulla & Jasper 1999, 2006)
seeking solutions to issues which are spread over large spatial extents like surface hydrology and soil erosion. It is a useful tool for storing the spatially distributed data
derived from a soil map, a digital elevation map, a land cover map or a land use
map. Further, the possibility of catchment discretization into smaller units in the
GIS environment provides the platform for the detail spatial representation of the hy-
30
2.5. Application of remote sensing and GIS in the modeling
drometeorological variables. With the advent of GIS and improved computer power,
the constraints on handling and computing vast spatial data sets have been significantly reduced. GIS offers the important spatial and analytical function, performing
time-consuming georeferencing and spatial overlays to extracts necessary information
for the hydrological and soil erosion modeling in a time-efficient manner at different spatial scales. Furthermore, the GIS capability in coupling with remotely sensed
data allows the models to reflect the nature of physical characteristics of a basin more
realistically. Several examples of the application of GIS and remote sensing in the
field of hydrology and soil erosion can be found in the literature (Wallis 1988, Zhang
et al. 1990, Shih & Jordan 1993, DeVantier & Feldman 1993, Dwivedi & Tewari 1997,
Hill & Schütt 2000, Martínez-Casasnovas & Sánchez-Bosch 2000, Vaidyanathan &
Dikshit 2002, Vrieling et al. 2002).
Depending on its intended use, GIS can be adapted to model any feature related to
spatial location. The models that lack spatial component have no use for GIS. As
stated earlier, the SCS CN, WaSiM-ETH and USLE based models have been used
in this research work. Further, as the title of this thesis suggests, all the modeling
has to be carried out in distributed manner to estimate the erosion risk within a
catchment and the GIS has to be used throughout the work.
The SCS-CN method has been long recognized as a representative lumped parameter
model that applies an averaged single value to each hydrologic computation unit being modeled. Stuebe and Johnston’s work (1990) shows that the GIS-based SCS-CN
method is much more advantageous to the manual SCS-CN method, especially when
the study area is large and different scenarios are explored. It is understood that
the SCS-CN method using lumped parameters cannot effectively reflect the spatial
variability of the physical characteristics of a basin. Therefore, in this research efforts have been made to integrate the SCS-CN method into a spatially distributed
modeling process, so that the SCS-CN method reflects the spatial variability of basin
characteristics which affect the surface runoff.
The WaSiM-ETH is the distributed model that operates with the discretized grids.
Therefore it requires several of its input in the form of grids. They are prepared
with the application of GIS by deriving different secondary input grids from the primary grid (e.g. DEM). GIS is also used with WaSiM-ETH to display and analyze
its distributed results, especially the results of distributed surface runoff required for
erosion modeling in this research.
Erosion modeling within GIS generally focuses on describing the spatial distributions. Predicting the location of high risk areas with the highest possible accuracy,
which is core objective of this research, is extremely important for erosion prevention
as it allows for identification of the proper location and type of erosion prevention
measures needed. Wilson & Gallant (2000) argue that the ability to represent elevation in terms of topographical surfaces in GIS is central to geomorphological analyses
and erosion studies.
With USLE-based model the soil erosion can be calculated in spatially distributed
31
2. Joint Hydrological - Soil Erosion Modeling
manner by using a grid cell representation of the landscape in the GIS environment
and assuming that each cell is internally uniform with respect to rainfall-runoff, soil,
land use, aspect and slope gradient. The effects of land curvature, flow divergence
and convergence can be captured easily in GIS to take into account the spatial variability of the topography factors (slope length - L and slope inclination - S) in two
dimensional ways. Similarly rapid growth in the field of remote sensing, temporally
varying data like vegetation cover (in terms of NDVI or LAI) can be easily acquired
which can be integrated into GIS without any hassle to see the temporal changes in
erosion processes during various time of a year.
Several attempts have been made to combine this model with GIS and generate regional soil loss assessments. Although USLE was developed originally in plot scale,
the study of Lufafa et al. (2003) shows that GIS - USLE approach has the ability to
predict soil loss over large areas. With the assistance of GIS and remote sensing, the
USLE and adapted versions have been applied to various spatial scales in different
environments worldwide. USLE applications in which satellite imagery accounted for
the vegetation component have been performed for a small hydrological catchment
of about 2.5 km2 in size (Jürgens & Fander 1993), areas between 10 to 100 km2
(Fenton 1982, Fraser et al. 1995, Lee 2004, Millward & Mersey 1999, Reusing et al.
2000), between 100 and 500 km2 (Anys et al. 1994, Baban & Yusuf 2001, Bonn et al.
1997, Cihlar 1987), large watersheds of more than 10,000 km2 (Cerri et al. 2001, Ma
et al. 2003, Mati et al. 2000), the country scale for Morocco (Gay et al., 2002) and
to the European scale (CORINE, 1992; van der Knijff et al. 2000). In this research,
the USLE-GIS is used in the catchment scale. In addition, a remote sensing data
for capturing the effects of seasonal variation of crop cover on erosion have been used.
There are different strategies for linking the hydrological and soil erosion models with
GIS. Pullar & Springer (2000) categorize three levels of integration as follows:
Loose coupling : the GIS system and the model are separated, and the files
must be transferred back and forth externally between GIS
and the model.
Tight coupling : the GIS (typically) provide the shared interface to move the
spatial data between the GIS and the separated modeling
program.
Embedded :
the model is fully integrated as a component in the host GIS
application.
Most of the current integrations of the models with GIS are examples of the first two
approaches. In the third approach, the linkages are problematic owing to the lack of
a temporal dimension in most GIS systems. The integration in this research work
follows the tight coupling for the SCS CN and the USLE based models and loose
coupling for the WaSiM-ETH with GIS. Several comprehensive GIS packages are
becoming available that are capable of managing and processing massive quantities
of data. The GIS utilized throughout this research work is ArcView 3.3 system
developed by ESRI.
32
3 The study area and available data: An
overview
3.1 Background
The spatial assessment of soil erosion through the use of simple erosion model, with
better hydrological representation, is one of the initial objectives of this research
work. For this, we need a catchment that essentially has both spatially distributed
and outlet-lumped observed erosion/sediment data along with others. The Ganspoel
catchment in Belgium has such rarely measured data and hence chosen for the investigation. Then, for the subsequent steps to investigate the use, challenges and
complexities of the spatially distributed physically-based rainfall runoff model in
estimating spatially distributed erosion, a larger catchment (Rems) in Baden Württemberg (Germany) is chosen. An overview to those chosen study areas and the
available data are discussed in this Chapter.
3.2 Ganspoel catchment in Central Belgium
Soil erosion by water on cultivated land is causing a number of environmental problems in the Loess Belt of central Belgium. After intense rain events, mainly in late
spring – early summer, many villages in central Belgium are confronted with muddy
floods originating from intensively cultivated fields. Apart from the damage to local and public property, soil erosion by water is also responsible for high sediment
loads in Flemish rivers. This results in silting of rivers at some locations leading to
increased risk as discharge capacity of the rivers decreases. For the larger rivers in
the northern part of Belgium, sediment deposition is hindering navigation as well,
especially in the vicinity of locks (Rompaey et al. 2003).
Location
The Ganspoel catchment located in central Belgium about 15 km west of Leuven (Fig. 3.2), is representative of a temperate agricultural area over the European loess belt. The landscape is typical for large parts of northwest Europe
that were covered with Loess deposits
in the late Pleistocene. Soil in this region is very prone to crusting; a condition which leads to decreased permeability and increased runoff and erosion
Figure 3.1: Location of Ganspoel catchment
33
3. The study area and available data: An overview
(Cerdan et al. 2002). The precise location of the catchment is 50◦ 48’N, 4◦ 35’E.
Topography
The Ganspoel catchment has drainage area of about 111 ha. The catchment is
characterized by a dense network of dry valleys resulting in a rolling topography.
The elevation ranges from 60m to 100m, the mean being around 90m. A digital
elevation model (DEM) of the area with resolution of 5m × 5m is shown in Figure
3.2. The maximum slope in the catchment, as calculated from the DEM is about
22◦ in the dry valleys; however majority of the areas are with lesser slope resulting
the mean slope of the catchment to be about 3.4◦ .
Figure 3.2: Topography of Ganspoel catchment
Climate
The area has a temperate oceanic climate with an average annual temperature around
10◦ C (average max. 18◦ C in July; average min. 2◦ C in January (Fu et al. 1994).
The annual precipitation varies between 700-800mm, and high-intensity rainfall occurs mostly in summer. July is usually the wettest month (Bollinne 1978), and is
also the period with maximum soil erosion (Kwaad & Mulligun 1991).
Soil
A loess sheet covers Tertiary sandy deposits and at some places in the catchment,
sandy outcrops occur. However, soils are fairly homogeneous and fertile. Ninety per
cent of the soil is loamy with varying degrees of truncation. Soil physical parameters are much more related to land use than to soil texture. Topsoils have high silt
content (70-80%) and moderate clay content (7-15%) and are mainly classified as
Haplic Luvisols. Organic carbon content of the soil ranges between 0.6% and 1.5%
(Oost et al. 2005). The main drainage channels are covered by several metres thick
colluvial deposits.
34
3.2. Ganspoel catchment in Central Belgium
Land use
The natural vegetation was mainly deciduous forests, which were cleared and the
area was brought under agriculture in the 11th to 13th centuries. The current land
use is chiefly farmland, with small patches of woodland and grassland. The catchment is being used for high-input, mechanized agriculture and the most important
crops are winter wheat and barley, maize, sugar beets and potatoes. The general
crop rotation is one of the winter cereals followed by a root crop such as beet or
potatoes, or by maize. The winter cereals are sown in late autumn and harvested the
next summer (July-August). The summer crops are sown in early spring and harvested at the end of the summer (cereals, maize) or in late autumn (root crops) (Oost
et al. 2005). High intensity rainfall events in spring and summer combined with this
cropping cycle means that the erosion risk is highest in early spring when the crop
cover is low and sedimentary crusts may have formed or in late autumn after harvest.
Small patches of woodland and pastures exist on steeper slopes and in some of the
thalwegs. In the northwest corner of the catchment, there is a relatively large built
up area too that drains into the catchment. The land use in Ganspoel, hence, consists of intensive arable farming with some roads, buildings, grassland, and forest.
The main characteristics of Ganspoel catchment are presented in Table 3.1.
Table 3.1: Main characteristics of Ganspoel catchment
Area
Elevation
:
:
Slope
:
Mean annual precipitation
Mean annual temperature
Perennial surface water bodies
Soil
Top soil composition
:
:
:
:
:
Landuse
:
111 ha
min.- 61.66 m, max.- 100 m, mean- 89.63 m, std. dev.7.94 m
min.-0◦ , max.- 21.62◦ (39.6%), mean- 3.39◦ (6%), std.
dev.- 3.17◦
740 mm
10◦ C
none
loess (Haplic Luvisols)
7-14% clay, 75-80% silt, 9-17% sand, 0.6-1.5% organic
carbon
farmed land with scarce constructed areas
Available data
The data of the Ganspoel catchment is described in detail by Oost et al. 2005 and
is summarized below. Database is available online on “http://www.kuleuven.be/
geography/frg”.
A high precision digital elevation model (DEM) of Ganspoel catchment (5m resolution) was created using aerial photographs. Field boundaries, roads and built-up
areas were mapped using a GPS.
The catchment is continuously monitored for rainfall, runoff and soil erosion dynam-
35
3. The study area and available data: An overview
ics for the period of 3 years (March 1997 - March 1999). Measurement stations,
consisting of a San Dimas flume equipped with a flowmeter (ISCO-4220, ISCO, Lincoln, NE, USA) and an automatic sampler (ISCO-6700) were installed at the outlet
of the Ganspoel catchment. Within the catchment, a tipping-bucket rain gauge (logging interval=1 min; 1 tip=0.5 mm) measured the rainfall depth and intensity.
Monitoring of soil erosion dynamics was carried out on two levels: runoff and sediment export were continuously monitored at the catchment outlets while internal
dynamics were assessed by collecting spatially referenced data on soil status, crop
cover and erosion and deposition features.
Water discharge is continuously measured with a time interval of 2 minutes and an
accuracy of 2 mm. Most of the rainfall-runoff events that occurred during the observation period were adequately sampled. During the observation period, 30 rainfallrunoff events were recorded in the catchment. Many minor events occur while a
few extreme events are responsible for most of the sediment export during the observation period: two events account for more than 50% of the total sediment export.
During the monitoring period, 19 monthly field surveys were conducted which involve
the data collection of land use and soil surface parameters. This collection basically
includes the following observations:
p Description of land use,
p Random and oriented soil surface roughness - in five classes; 0: 0-1 cm, 1: 1-2
cm, 2: 2-5 cm, 3: 5-10 cm, 4: > 10 cm,
p Soil surface crusting stage in four stages:
(i) Non sealed: initial fragmentary structure with all fragments clearly distinguishable;
(ii) Structural seal: altered fragmentary state with local structural seal;
(iii) Transitional seal: generalized structural seal with local appearance of
depositional seal;
(iv) Sedimentary seal: continuous state with depositional seal,
p Crop cover (exact % of coverage leaves, litter and debris; or notation in three
classes- C1: 0-20%, C2: 21-60%, C3: 61-100%) for every field within the catchments.
At the end of one or a series of rainfall-runoff events, volumes of rills and gullies
in the catchment were measured and the extent and thickness of sediment deposits
were mapped. On three occasions in Ganspoel, erosion and deposition features were
mapped within the catchments. The data is stored in Idrisi32 raster maps format.
The measured volumes of erosion and deposition are stored in Idrisi32 values files
and can be geo-referenced by using the identifier.
Volumetric estimates of rill and gully erosion were converted into erosion rates by
assuming a constant dry bulk density of 1350 kg m−3 and sediment volumes were
converted into deposition rates by assuming a dry bulk density of 1400 kg m−3 for
36
3.3. Rems catchment in Southern Germany
deposits. Interrill erosion is difficult to measure at the catchment scale and therefore
was assumed to be 10% of total rill and gully erosion volumes.
3.3 Rems catchment in Southern Germany
The river Rems originates underneath Lutenburg near the
city Aalen in district Ostalbkreis.
It then flows approximately 80 km towards
west forming Rems valley before discharging finally into
Ne
Neckar river as its right tribck a
utary (at 203 m asl) near the
city of Stuttgart in BadenWürttemberg, the south-western
state of Germany. The Rems is
the fifth biggest tributary of the
river Neckar. The catchment of
Figure 3.3: Location of Rems catchment
river Rems has an area of about
580 km2 and is spread over five districts of Baden-Württemberg namely; Ostalbkreis
in the east, Rems-Murr Kreis in the north, Göppingen in the south, Ludwigsburg in
the north-west and Esslingen in the south-west (Fig. 3.3).
µ
Ludwigsburg
Rems-Murr-Kreis
Re
Ostalbkreis
ms
Stuttgart
r
Esslingen
0
4.5
9
18
Scale
27
36
Kilometers
Göppingen
Neckar River
REMS River
Rems Catchment
District Boundary
The grid based data set for
Rems catchment available from
different sources (LUBW, DWD
etc.)
mainly consists of
DEM (1:30 000), soil grid
(1:200 000) and three land
use grids classified from the
satellite images of LANDSAT
1975, 1993 and 2000 (1:75
000).
The available DEM (Fig. 3.4)
shows that the Rems catchment has the elevation ranging
Figure 3.4: Topography of Rems catchment
from about 195 m to 795 m
above mean sea level. The slope
within the catchment varies from flat or zero degrees to the steep slope as high as 42
degrees. The average elevation and slope in the catchment is 400 m and 8.7 degree
respectively. The only important tributary of Rems, the Wieslauf, is also shown in
the figure.
37
3. The study area and available data: An overview
Forests and grasslands in high areas and agriculture and settlement along the river in
the valleys are the basic land use within the Rems catchment. Land use distribution
as observed with LANDSAT 1993 in the catchment is shown in Fig. 3.5 (left).
Major land use categorization for the year 1975, 1993 and 2000 from the respective
LANDSAT images shows increment in the settlement area at the cost of agricultural
area in the Rems catchment. This change is depicted in Fig. 3.5 (right).
50
Landuse 1975
Water bodies
Mixed forest
Agriculture
Bushes
Dense settlement
Grassland
Loose settlement
Naked soil
Horticulture
Plantations
Pine forest
Wetland
Decidious forest
4
0
4
Kilometers
Coverage area [%]
Landuse
N
40
Landuse 1993
Landuse 2000
30
20
10
0
Agriculture &
Horticulture
Settlements
Forest
Bushes &
Grassland
Figure 3.5: Land use of Rems catchment (classified from LANDSAT 1993) (left) and Major land
use coverage area in 1975, 1993 and 2000 (right)
The geology of the catchment is governed by marls, clays and sandstones of the
Triassic Keuper formation, accompanied by Jurassic limestones in the eastern part
and loess cover in the western part of the catchment. Accordingly, eutric, vertic and
stagnic cambisols as well as haplic and luvic chernozems are found in the catchment.
The soil texture on the ground surface includes mainly light sandy soils on high areas
and loam and clay on lows. The spatial distribution of the soil texture within the
Rems catchment is shown in Fig. 3.6 (left). The percentage of area covered by each
category of the soil texture in the catchment is shown in Fig. 3.6 (right). It can be
seen that the sandy clay loam (42%) followed by clay loam (30%) and then the loam
(13%) are the major soil texture in the Rems catchment.
50
N
Soil
silty loam [SIL]
loamy sand [LS]
clay [C]
clay loam [CL]
sandy clay loam [SCL]
settlements/rocks [R]
4
0
4
Kilometers
Coverage area [%]
loam [L]
40
30
20
10
0
Silty
loam
Loam
Loamy
sand
Clay
Clay
loam
Sandy
clay
loam
Settlements/ro
ck
Figure 3.6: Soil texture of Rems catchment (left) and Area coverage percentage by each type of
soil texture (right)
The available meteorological and hydrological data series includes discharges and
precipitation along with temperature (air and soil), vapor pressure, humidity, wind
speed, cloud cover, sunshine duration, snow depth etc. in daily resolution. For
the research work with Rems, the data series from 1990 to 2005 in daily resolution
have been used. Altogether 37 relevant precipitation measuring stations (see Fig.
3.7), out of which 10 stations (with red tick in the figure) have records for other
meteorological data too, have been used in the work. As can be seen in the figure, 8
38
3.3. Rems catchment in Southern Germany
stations are inside the Rems catchment and rests are within 40 km from the center
of the catchment.
$Z
N
ò$Z
4
ò$Z
$Z
17
$Z
32
5
$Z
10
$Z
#
·
22
ò$Z
$Z
12
33
ò$Z
$Z
13
Z$
$Z
37
9
#
·
$Z
21
23
6
$Z
ò$Z
29
$Z
Discharge gauges
$Z
19
$Z
35
ò$Z
ò$Z
24
#
·
$Z
#
·
25
ò$Z
26
$Z
ò
$Z
14
$Z
8
15
$Z
$Z
#
·
$Z
11
1
ò$Z
16
$Z
36
18
$Z
34
$Z
28
$Z
2
30
$Z
$Z
27
ò$Z
$Z
31
20
3
7
Elevation [m amsl]
Climatestns.shp
Meteorological stns.
190 - 257
392 - 459
594 - 661
257 - 325
459 - 526
661 - 728
325 - 392
526 - 594
728 - 796
5
0
5
10
Kilometers
Figure 3.7: Locations of meteorological stations in and around Rems catchment
As observed in those stations, the mean annual temperature in the Rems catchment
is 9.5◦ C and the average annual precipitation is 900 mm. The mean temperature
varies from about 0◦ C in January to above 18◦ C in July-August. A simple assessment
of the observed rainfall (primary hydrological input) in two representative stations
of the catchment (Heubach and Lorch) shows the intra-annual (monthly) and interannual (1990-2005) variability of rainfall as shown in Fig. 3.8. Furthermore, the
precipitation coefficients, which is calculated for each month as the ratio of the
monthly precipitation to one twelfth of mean annual precipitation, is also shown
in Table 3.2. It can be observed that summer precipitation (June-August) is, in
general, higher than that in winter. Specifically, July shows the highest precipitation
coefficient and April shows the minimum. The inter-annual comparison shows that
the dry year, during the considered period, can go as low as to about 800 mm and
the wet year as high as to 1350 mm.
1400
125
Heubach
Lorch
1200
100
Summer
Winter
Year
Precipitation [mm]
Precipitation [mm]
1000
75
50
800
600
400
25
200
0
Jan
Feb
Mar
Apr
May
Jun
Jul
Aug
Sep
Oct
Nov
Dec
0
1991 1992 1993 1994 1995 1996 1997 1998 1999 2000 2001 2002 2003 2004 2005
Figure 3.8: Intra-annual (left) and inter-annual (right) variability of rainfall in Rems catchment
39
3. The study area and available data: An overview
Table 3.2: Monthly precipitation coefficients in the representative stations of Rems catchment
Month
Jan
Feb
Mar
Apr
May
Jun
Jul
Aug
Sep
Oct
Nov
Dec
Precipitataion [mm]
(Heubach+Lorch)
65
70
78
64
88
99
103
79
80
86
83
86
Precipitation coeff.
0.80
0.86
0.96
0.78
1.07
1.21
1.26
0.97
0.97
1.05
1.01
1.05
Similarly, 12 gauges including an outlet-gauge at Neustadt (little upstream to the
confluence with Neckar) recorded the discharge data at daily time step. But the
available time series for the gauges in smaller subcatchments is not for an adequate
period of time. So the four gauges, as shown in Fig. 3.9, are considered for this
research work. The area of the individual subcatchments as delineated by these
gauges are calculated to be 92 km2 , 76 km2 , 246 km2 and 150 km2 for SchwäbischGmüund, Haubersbronn, Schorndorf and Neustadt respectively.
Schwäbisch-Gmünd
Ta
n
nb
ac
h
auf
ach
pfelb
Wiesl
Strüm
Neustadt
Bären
ep
h
ac
h
rb
ze
bac
Jo
s
Klotzbach
h
ac
ch
hen
nb
#
Y
ba
Eic
ei
Ha
lde
ers
ch
a
w
ch
S
#
Y
alk
#
Y
b
Rem
s
W
rn
o
ch
S
#
Y
bach
Haubersbronn
hs
ba
ch
Schorndorf
Figure 3.9: Discharge gauges and subcatchments of the Rems catchment
The inter-annual (1990-2005) and intra-annual (monthly) variation of discharges in
the considered four gauges is shown in Fig. 3.10. It can be seen that higher discharges
at outlet occurred during November to March and lowest during August-September.
12
12
Neustadt
Schorndorf
Schw.-Gmünd
Haubersbronn
10
6
4
6
4
2
2
D
ec
ov
N
O
ct
Se
p
Ju
l
Au
g
Ju
n
M
ay
Ap
r
Fe
b
M
ar
0
Ja
n
Neustadt
Schorndorf
Schw.-Gmünd
Haubersbronn
8
8
Dischrage [m³/s]
Discharge [m³/s]
10
0
90 991 992 993 994 995 996 997 998 999 000 001 002 003 004 005
19
1
1
1
1
1
1
1
1
1
2
2
2
2
2
2
Figure 3.10: Intra-annual (left) and inter-annual (right) variability of runoff in Rems catchment
40
3.3. Rems catchment in Southern Germany
Besides those available data, eight years series (2000-2007) of 16 days’ composite
spatially distributed NDVI data for Rems have been gathered from MODIS satellite data and 40 years of 5 minutes precipitation series have been generated in the
three stations inside Rems catchment using “NiedSim” package that had been developed in the department of Hydrology and Geohydrology of Institute of Hydraulic
Engineering, Stuttgart University. These data are described further along with their
application in Chapter 6.
41
4 Spatially Distributed Soil Erosion
estimation: A case study
4.1 Relevancy of the case study
The case study presented in this Chapter is in lieu with the fulfillment of the first two
objectives stated under Section 1.4 in Chapter 1. Those objectives were motivated by
the fact that- it is extremely difficult to obtain all the required data for a completely
physically based soil erosion modeling mainly in developing countries and even in
developed ones; however, required data for physically based hydrological model are
comparatively readily available. Accordingly, this case study has two aspects as explained below.
First attempt is to investigate the use of the less data intensive rainfall-runoff model
and soil erosion model in distributed manner using GIS capabilities to predict spatial
pattern of surface runoff and sediment source areas within a catchment along with
the lumped predictions of runoff and sediment yield at outlet. This investigation
seeks answers to the following two questions:
p How good the simple rainfall-runoff model, used in several erosion models, can
predict runoff with its most recent modifications?
p How well does this modified/improved simple rainfall-runoff model coupled
with a simple erosion model perform in predicting spatial patterns?
Then the next aspect is to compare the performance in the predictions when the
simple rainfall-runoff model is replaced by a more complex physically-based fully
distributed rainfall-runoff model and then coupled with the same low data demanding
soil erosion model. This modification seeks answers to the following two questions:
p Does the improvement in hydrology lead to a better estimation of erosion and
sediment yield at the catchment scale?
p Does the perfectly matching hydrographs mean better representation of hydrological process in the catchment?
The simple rainfall-runoff model chosen here, for the case study, is the SCS-CN
model and its several current modifications are investigated. Similarly the erosion
model undertaken is the simplest and still widely-used-USLE model and its several
derivatives are also investigated. For the better hydrological representation, the more
complex physically-based fully distributed WaSiM-ETH model is used. All of these
three models are described in detail in Chapter 2.
42
4.2. Methodology, model formulation, application and results
4.2 Methodology, model formulation, application and results
The study area chosen here is the Ganspoel catchment whose characteristics and
the data availability are discussed in detail in Chapter 3. The reason behind choosing this catchment is that- very detailed data in finer resolution, both temporally
and spatially, including, rarely measured, observed erosion patterns for some events
within the catchment is available freely. Moreover the objective of examining predicted soil erosion patterns by using physically based rainfall-runoff model results
with simple erosion model-USLE and its extensions is more purpose-oriented than
site-specific. In addition, the results of spatially-distributed physically-based soil erosion model (“MEFIDIS”- the Portuguese acronym for Physically Based Distributed
Erosion Model, Nunes et al. 2005) for some of the selected events in this catchment
are available from literature. So, there would be the opportunity to compare the results not only with the observed ones but also to that with the completely physically
based erosion model. The basic sequence of actions followed to carry out this case
study is presented in Fig 4.1.
Figure 4.1: Methodology to estimate spatial distribution of erosion source areas
4.2.1 Selection of events and data preprocessing
As discussed in Chapter 3, Ganspoel catchment is continuously monitored for rainfall,
runoff and soil erosion dynamics for the period of 3 years (March 1997 - March
1999). During the observation period, 30 rainfall–runoff events were recorded in the
catchment. Among them, seven events as shown in Table 4.1 are selected for this
study. The selected events are with varying characteristics in terms of rainfall-runoff
amount, intensity and antecedent moisture conditions and those events occurred with
different land use and soil surface conditions. The data measured at catchment outlet
43
4. Spatially Distributed Soil Erosion estimation: A case study
for the event number 1 (Table 4.1) is shown in Fig. 4.2 as an example.
Table 4.1: Events selected for the case study in Ganspoel catchment
Event
No.
Field
Survey
Precipitation
Runoff
Start
End
Ptotal
(mm)
5/19/'97
21:30
5/19/'97
21:54
10
25
2
5/21/'97
9:17
5/21/'97
17:39
3
3
7/11/'97
16:20
7/11/'97
16:55
7/14/'97
6:17
5
6
1
5/16/1997
4
7/22/1997
9/18/1998
7
I30
P5
(mm/h) (mm)
Start
End
Vol. (m3)
11
5/19/'97
21:54
5/20/'97
1:00
252.1
6
28.5
5/21/'97
17:32
5/21/'97
20:36
178
19.5
36
0
7/11/'97
16:20
7/11/'97
19:46
2307
7/14/'97
6:54
6.5
12
15.5
7/14/'97
6:18
7/14/'97
10:16
427.8
7/17/'97
17:34
7/17/'97
21:54
17.5
12
9
7/17/'97
17:34
7/18/'97
2:50
404.3
9/9/'98
18:23
9/9/'98
19:27
10.5
23
30
9/9/'98
18:24
9/10/'98
2:46
343
9/13/'98
17:00
9/14/'98
12:06
41
15
51.5
9/13/'98
18:12
9/14/'98
17:20
10325
Figure 4.2: Measured catchment outlet data. The May 19, 1997 event (Event No. 1) in Ganspoel
The selected seven events are associated with three different field survey dates; May
’97, July ’97 and September ’98 (Table 4.1). The field survey involves the data collection of land use and soil surface parameters (e.g. vegetation cover, soil surface
crusting and roughness).
The land use observations during these surveys are loaded in ArcView GIS and the
spatial coverage of each land use type are estimated. The results are shown in Table
4.2. Land use in May 1997 is dominated by beet, winter cereals and summer cereals
44
4.2. Methodology, model formulation, application and results
and in July 1997 is the same occupation as in May but with the crops in later stage
of development. The September 1998 land use is dominated by beet, potatoes and
the winter cereals are harvested (Table 4.2).
Table 4.2: Observed land use in Ganspoel catchment during
the selected events
Area (%)
Landuse
Path
Paved road
Ditch/brooklet
Institute
Farm
Garden
Grass
Ploughed field
Meadow/pasture
Wood
Cereal/wheat
Sugar beet
Maize
Potatoes
Barley
Tomato
Cabbages
Oat
No data
5/16/1997
7/22/1997
9/18/1998
1.5
1.0
0.5
4.3
0.6
0.2
1.0
9.6
6.0
53.9
15.6
1.2
1.9
0.1
2.6
1.5
1.0
0.5
4.3
0.6
0.2
3.3
8.9
6.0
48.5
15.9
0.8
2.8
2.0
0.1
0.1
0.7
2.8
1.5
1.0
0.5
4.3
0.6
0.1
18.4
3.1
8.9
6.0
6.9
13.9
18.1
18.1
10.1
2.8
The observed soil surface parameters during the field survey include vegetation cover,
soil surface crusting and roughness. The observed vegetation cover are expressed as
percentage of coverage leaves, litter and debris for every field within the catchments
and grouped into the three classes; C1: 0-20%, C2: 21-60%, C3: 61-100%.
The observed soil surface crusting stage is grouped into the following four categories:
non-sealed
: initial fragmentary structure with all fragments clearly
distinguishable,
structural seal
: altered fragmentary state with local structural seal,
transitional seal : generalized structural seal with local appearance of
depositional seal,
sedimentary seal : continuous state with depositional seal.
The observed random and oriented soil surface roughness is categorized into the five
classes; 0: 0-1 cm, 1: 1-2 cm, 2: 2-5 cm, 3: 5-10 cm, 4: > 10 cm.
These observed soil surface parameters are loaded on ArcView GIS and their spatial
coverage are calculated. The results are shown in Table 4.3. Cerdan et al. (2002),
combine the surface state, roughness and crop cover to represent their degree of
influence in terms of infiltration capacity. For each combination of the parameters,
an average potential value of infiltration capacity is assigned as shown in Table 4.4.
45
4. Spatially Distributed Soil Erosion estimation: A case study
Table 4.3: Observed soil surface parameters in Ganspoel catchment during the selected events
Parameters
Area(%)
Values
5/16/1997
7/22/1997
9/18/1998
Vegetation Cover
0 to 20 %
21 to 60 %
61 to 100 %
19.7
18.3
51.3
7.1
26.3
55.9
26.2
26.3
37.0
Soil surface crusting
Fragmented seal
Structural seal
Sedimentary seal
Transitional crust
17.8
25.1
0.1
46.2
18.3
0
54.6
16.4
14.9
22.1
4.6
47.8
Roughness
0 to 1 cm.
1 to 2 cm.
2 to 5 cm.
5 to 10 cm.
> 10 cm.
45.9
35.9
7.5
0.0
0.0
62.4
22.2
4.7
0.0
0.0
59.8
21.7
7.8
0.0
0.0
All
No data
10.7
10.7
10.7
Table 4.4: Infiltration capacity (mm/hr) based on soil surface parameters (Cerdan et al. 2002)
Crusting stage
46
Roughness
Vegetation cover
> 10 cm
Fragmented
seal
Structural
seal
Ssedimentary
seal
Transitional
seal
61 - 100%
21 - 60%
0 - 20%
50
50
50
50
50
20
50
20
20
10
10
10
5 - 10 cm
61 - 100%
21 - 60%
0 - 20%
50
50
50
50
50
20
50
20
10
10
10
5
2 - 5 cm
61 - 100%
21 - 60%
0 - 20%
50
50
50
50
20
20
20
10
10
10
5
5
1 - 2 cm
61 - 100%
21 - 60%
0 - 20%
50
50
20
20
20
10
10
10
5
5
5
2
0 - 1 cm
61 - 100%
21 - 60%
0 - 20%
50
20
10
20
10
10
10
5
5
5
2
2
4.2. Methodology, model formulation, application and results
Based on these infiltration potential, the catchment is divided into four hydrological
soil groups as follows:
Group A: Infiltration rate > 7.6 mm/hr - high infiltration (low runoff) - corresponds to sand, loamy sand, or sandy loam.
Group B: Infiltration rate 3.8 to 7.6 mm/hr - moderate infiltration (moderate
runoff) - corresponds to silt loam or loam.
Group C: Infiltration rate 1.2 to 3.8 mm/hr - low infiltration (moderate to high
runoff) - corresponds to sandy clay loam.
Group D: Infiltration rate 0 to 1.2 mm/hr - very low infiltration (high runoff) corresponds to clay loam, silty clay loam, sandy clay, silty clay or clay.
For the application of models in spatially distributed manner, the Ganspoel catchment is represented by the regular grids of 5m × 5m resolution (the resolution of
available DEM) in GIS environment. Then all the discussed parameters relevant for
the modeling are estimated for each grid, and that completes the data pre-processing.
4.2.2 Rainfall-runoff modeling
Rainfall-Runoff modeling constitutes an important part of soil erosion and sediment
yield estimationis as it is the primary vector or driving force for soil erosion. Guided
by the objectives as stated earlier, two different types of rainfall-runoff modeling have
to be adopted. The simple rainfall-runoff model chosen here, for the case study, is the
SCS-CN model with its several current modifications. Then, for the better hydrological representation the more complex physically-based fully distributed WaSiM-ETH
model is used. Both of these models are described in detail in Chapter 2 and their
application in the Ganspoel catchment is discussed below.
4.2.2.1 Using SCS-CN model with different modifications
The detail of this SCS-CN model which is core component of many hydrologic and
erosion models is described in Chapter 2. Some basics are restated here while describing the methodology adopted in using this model. It is based on land use-soils
index, the Curve Number (CN), developed from real-world data by the United States
Department of Agriculture, Soil Conservation Service (USDA 1986).
According to the model in its original form:
(P − Ia )2
, if P > Ia ;
Q = (P − Ia + S)


0,
if P < Ia
(4.1)
Ia = λS = 0.2S
(4.2)



S=
25400
− 254
CN
(4.3)
47
4. Spatially Distributed Soil Erosion estimation: A case study
where
Q
P
Ia
λ
S
CN
=
=
=
=
=
=
Runoff [mm]
Precipitation [mm]
Initial abstraction [mm]
Initial abstraction coefficient [ - ]
Potential maximum retention [mm]
Curve Number
The general form of the relation (4.1) is ‘well established by both theory and observation’ (Maidment 1993). No runoff occurs until rainfall (P ) equals an initial
abstraction Ia. After allowing for Ia , the depth of runoff Q is the residual after
subtracting F , the infiltration of water retained in the drainage basin (excluding Ia )
from the rainfall P . The potential retention S is the value that (F + Ia ) would reach
in a very long storm.
The curve number (CN) on which the method relies, varies as a function of four
major runoff-producing watershed properties:
(i) Hydrologic soil group: A, B, C and D
(ii) Land use and treatment classes: agricultural, range, forest and urban
(iii) Hydrologic surface condition of native pasture: poor, fair and good
(iv) Soil moisture condition
Following the discussion in Section 4.2.1, the hydrological soil group for each 5m
grid of the Ganspoel catchment is calculated in GIS environment, based on the available data of soil surface parameters (vegetation cover, crusting stage and roughness)
and their corresponding infiltration capacity (after Cerdan et al. 2002) for the given
events. This soil group combined with the available land use data enable to assign
CN value for each grid during each event following curve number table provided in
NEH-4, SCS 1985. The CN value so assigned represents the average antecedent soil
moisture condition, i.e. CN2.
The effect of soil moisture condition is incorporated by considering three Antecedent
Moisture Condition classes- AMC 1 (dry), 2 (average) and 3 (wet) which statistically
correspond respectively to 90, 50 and 10% cumulative probability of exceedance of
runoff depth for a given rainfall (Hjelmfelt et al. 1982). These classes are based on
the 5-day antecedent rainfall (i.e. the accumulated 5 days’total rainfall preceding the
runoff/event under consideration) as shown in Table 2.3.
Once the AMC class for each event is determined, the correspondingly adjusted CN
value can be directly read from the NEH-4 tables or by using the equations given by
Hawkins et al. 1985.
CN 2
2.281 − 0.01281CN 2
CN 2
CN 3 =
0.427 + 0.00573CN 2
CN 1 =
48
(4.4)
4.2. Methodology, model formulation, application and results
Since the advent and with continuing use, the SCS-CN method has been undergone
several modifications and improvements, which has been discussed in detail in Chapter 2. The modifications investigated in this case study are restated here.
Modifications of SCS-CN model
Incorporation of the effect of Slope
The original curve number table considers only soil, land use, and management
assuming that the tabulated CN value (CN2) is appropriate for a 5 % land slope.
Although effect of the slope on runoff volume has been clearly established, very few
attempts have been made to include a slope factor into the CN method. One of
these is that of Sharpley & Williams (1990), incorporated in EPIC-model, for which
a slope-adjusted CN2 for moisture condition II (average), named CN2s, is obtained
by;
CN 2s =
i
h
1
(CN 3 − CN 2) 1 − 2e13.86S + CN 2
3
(4.5)
where, CN2s is the tabulated CN2 value adjusted for slope, S [mm−1 ] is the slope
and CN3 is the curve number for moisture condition III (wet) and is calculated as:
CN 3 = CN 2 × e0.00673(100−CN 2)
(4.6)
Improvement in initial abstraction ratio, λ
The constant initial abstraction coefficient (λ) in the SCS-CN methodology, which
largely depends on climatic conditions (Ponce & Hawkins 1996), is an ambiguous
assumption and requires considerable refinement. It was assumed in its original
development to have a value of 0.20. Using event rainfall-runoff data from several
hundred plots this assumption was investigated (ARS/NRCS CN working group
1997), and λ values were determined by two different methods. In general, the
results showed that assumption of λ = 0.20 is unusually high. Results indicate a λ
value of about 0.05 gives a better fit to the data and would be more appropriate for
use in runoff calculations. Moreover, the S value is also suggested to be changed
according to the change of λ from 0.2 to 0.05.
1.15
S0.05 = 1.33 S0.2
(with λ = 0.05)
(4.7)
Incorporation of continuous antecedent moisture, M
The incorporation of antecedent moisture in the original SCS-CN method in terms
of three AMC levels permits unreasonable sudden jumps in the CN-variation. To circumvent these problems, Mishra & Singh (2002) suggested an SCS-CN-based equation, later modified with variable λ by Mishra & Singh (2004), to compute the
antecedent moisture from 5 days antecedent precipitation for computation of runoff;
49
4. Spatially Distributed Soil Erosion estimation: A case study
Q=


 (P − Ia ) (P − Ia + M ),
if P > Ia ;


if P ≤ Ia
(P − Ia + M + S)
M = 0.5 − (1 + λ) S +
0,
q
(1 − λ)2 S 2 + 4P5 S
(4.8)
if P5 > λS
(4.9)
M vs. S plot for above equation shows that for a given P5 , M increases first with
increasing S, reaches a maximum value and then decreases. The increasing trend is
consistent with the fact that, for a given P5 , a watershed with larger retention capacity would retain greater amount of moisture. This increasing trend was incorporated
and proposed in the following general relation.
M = α (P5 × S)0.5
(4.10)
where α is a non-dimensional coefficient and equal to 0.72 (mean of the optimized
α-values) and λ is proposed to be equal to 0.08 (median of the optimized λ-values).
Improvement in estimation of initial abstraction, Ia
Original SCS-CN method treats the initial abstraction Ia , to be independent of antecedent moisture, M . However, in reality, the initial abstraction, which represents
losses due to interception, surface storage, evaporation, and infiltration, varies inversely with the antecedent moisture. The higher the antecedent moisture, the lower
will be the initial abstraction, and vice-versa. On this ground, Mishra & Singh (2004)
suggests following non-linear Ia -S relation, which incorporates M , for inclusion in the
SCS-CN methodology.
Ia =
λS 2
(S + M )
(4.11)
Incorporation of depression storage ϕ
In general, the runoff as computed from SCS-CN method resulted into over-estimation.
A further analysis of these deviations revealed that the deviations are of small magnitude when the field conditions are smooth, but large deviations were observed
when the field conditions are rough. This is probably due to the limitation of the
parameterization of surface roughness in the SCS CN method. In order to handle
this problem, the depression storage ϕ calculated after Onstad, 1984 as a function
of random surface parameter, R, was introduced as provided in LISEM model (Roo
1996). Thus the runoff can be computed as:
50
4.2. Methodology, model formulation, application and results
Q=


 (P − Ia ) (P − Ia + M ) − ϕ,
if P > Ia − ϕ;


if P ≤ Ia − ϕ
(P − Ia + M + S)
0,
M = 0.5 − (1 + λ) S +
q
(1 − λ)2 S 2 + 4P5 S
(4.12)
ϕ = 0.112 × R + 0.031 × R2 × S
if P5 > λS
(4.13)
(4.14)
Based on these several modifications, the following six different forms of SCS-CN
models are formulated.
Model 1: Original SCS CN method with AMC tables/equations
Model 2: Incorporation of slope, continuous AMC, improved Ia with λ = 0.2
and S = original S
Model 3: Model 2 but with λ = 0.05 and S = original S
Model 4: Model 2 but with λ = 0.05 and S = modified S (S0.05 )
Model 5: Model 2 but with general relation of AMC, P5 and S taking α = 0.72,
λ = 0.08 and S = original S
Model 6: Model 2 with incorporation of depression storage
The parameters necessary for each of these six models are prepared or calculated in
the distributed manner for each grid of the catchment using the available data in the
GIS environment. Then the models are computed for all the selected events. The
methodology is presented in Fig. 4.3.
The runoff volumes, at the catchment outlet, simulated by the formulated six SCSCN models are shown in Table 4.5. Further discussions on results are made together
after describing the runoff estimation with WaSiM-ETH.
4.2.2.2 Using WaSiM-ETH model
The WaSiM-ETH model is used here to investigate the improvement in the prediction
of a simple soil erosion model when its simple rainfall-runoff component (using SCSCN) is replaced by the more complex physically-based distributed model. WaSiMETH, the Water flow and balance Simulation Model (Schulla & Jasper 1999, 2006), is
a fully distributed grid based catchment model using physically based algorithms and
parameters (except a few) for the simulation of the different hydrological processes.
The modified TOPMODEL version of WaSiM-ETH is used in this case study. It
considers runoff generation by both mechanisms: saturated overland flow as well as
Horton overland flow. For this it uses the combined extended Topmodel (saturated
overland flow) and Green and Ampt (infiltration excess) approaches. The detail of
51
4. Spatially Distributed Soil Erosion estimation: A case study
Figure 4.3: Adopted methodology for estimating runoff using SCS-CN models
Table 4.5: Runoff volume simulated by the six SCS-CN models at catchment outlet
Rainfall Events
Simulated RO (m3)
Obs. Original
RO SCS CN
Modified SCS CN method
Event Ptotal I30 (mm/ P5
(m3) method
No. (mm)
h)
(mm)
Model 1 Model 2 Model 3 Model 4 Model 5 Model 6
1
10
25
11
252.1
194.6
449.9
1166
703.1
1427.8
449.8
2
3
6
28.5
178
35
118
179.8
133.8
136.8
118
3
19.5
36
0
2307
658.5
1458
3590
2445.5
3022
1154.7
4
6.5
12
22
427.8
182.1
288.1
970.7
549.4
968.9
286.8
5
17.5
12
10
404.3
551.9
1196.4
3679
2396.3
4451.2
980.8
6
10.5
23
30
342.9
429.2
635
2279
1432
2421
601.6
7
41
15
12877
18355
14045
19114.8
11966
51.5 10325 18128.9
this model is described in Chapter 2. Their applications in this case study along with
some basics on the model are presented here. The basic model components include
the followings (Gurtz et al. 2003):
p Temporal and spatial interpolation of meteorological input data (Schulla, 1999)
p Correction of the precipitation measurement error for rain and snow (Sevruk
1986)
p Shading and topography-dependent adjustment for radiation and temperature
p Interception storage and evaporation (Menzel 1997)
p Potential and real evapotranspiration (Monteith 1975)
p Snow accumulation and snowmelt (Anderson 1973, Braun 1985)
p Glacier melt (Hock 1999, Klok et al. 2001)
52
4.2. Methodology, model formulation, application and results
p Infiltration and surface runoff generation (Green & Ampt 1911, Peschke 1987;
extended Topmodel)
p Soil water storage, percolation, interflow generation
p Soil moisture extraction by transpiration
p Groundwater recharge and storage
p Groundwater runoff generation (baseflow)
p Runoff concentration, discharge, and flood-routing.
Data requirement for the WaSiM-ETH with TOPMODEL version is presented in
Table 4.6.
Table 4.6: Data requirement for the WaSiM-ETH with TOPMODEL version
Spatial data
Topography/DEM:
Landuse
:
Soil texture
:
Slope, exposition, watersheds, streams-links-orders, flow direction, flow accumulation, flow times, routing parameters etc.
Albedo, LAI-Leaf Area Index, vegetation coverage degree, root
depth
Available FC - Field Capacity, saturated hydraulic conductivity,
fillable porosity, soil-topographic index, suction head.
Temporal data
Meteorogical
:
Hydrologic
:
Precipitation, temperature, global radiation, relative sunshine duration, wind speed, relative humidity.
Sub-basins and/or basin runoff (for calibration and performance
evaluation
Starting with the available 5m × 5m DEM of the Ganspoel catchment, the several
topographical inputs to the model (Table 4.6) are prepared using the preprocessing
tools like TANALYS (Terrain Analysis), TOPOFACT (Topographic wetness factor),
ASCIGRID, GRIDASCI and ArcView-GIS. Then, land use maps are prepared from
the field survey data at different dates and supplied to the model. The land use
related parameters required for the modeling (Table 4.6) were provided through a
control file that governs the model- set up and run. The soil texture of the catchment
is classified as silty clay and the corresponding parameters (Table 4.6) are also supplied through the control file. Besides precipitation, none other meteorological data
is available or used for modeling the events. The precipitation corresponding to the
selected events measured at single station with 2 minutes temporal resolution in the
catchment is distributed equally to each grid cell. The runoff measured at the outlet
with 2 minutes interval during the events is used for model calibration and validation.
Depending on the aim of application of model and on amount and quality of available
input data, some or many modules of the model shall be turned off. For example, if
WaSiM is run with the groundwater module, spatial raster data of aquifer properties
(storage coefficient, hydraulic conductivity in x- and y-directions, and thickness of
the aquifer) as well as the definition of boundary conditions are also required. Also,
if it is run with Richard equation version many additional data are required. In our
53
4. Spatially Distributed Soil Erosion estimation: A case study
case study, the catchment is quite small (111 ha) and has only one rainfall station.
So, interpolation module is basically not required, but nevertheless it is used just
to distribute the station data into all the grids. Based on the data availability and
the aim of our case study, some modules are turned off during modeling as stated in
Table 4.7.
Table 4.7: Modules of WaSiM-ETH used in the case study
Precipitation correction
Radiation correction
Evaporation model
Interception model
Soil model
Discharge routing
:
:
:
:
:
:
no
no
no
no
yes
yes
Input data interpolation
Temperature modification
Snow melt and glacier model
Infiltration model
Groundwater model
:
:
:
:
:
yes
no
no
yes
no
After preparing all the required inputs, the model is to be run for calibration to
indentify some of the free parameters. The adjustable parameters that practically
need calibration, in the Topmodel version of WaSiM-ETH are listed in Table 4.8.
Table 4.8: Adjustable parameters in TOPMODEL version of WaSiM-ETH
Symbol
Name of Parameter
Tgrz
co
hSH
xf
m
Tkorr
Kkorr
kD
SHmax
kH
Pgrenz
Threshold temperature snow/rain
Melt/degree-day factor
Maximum water layer thickness at leaf surfaces
Fraction of re-infiltrating water
Recession parameter for base flow
Correction factor for the transmissivity of the soil
Correction factor for vertical percolation
Single reservoir recession constant for surface runoff
Maximum storage capacity of the interflow storage
Single reservoir recession constant for interflow
Precipitation intensity threshold for generating preferential
flow into saturated zone
Scaling of capillary rise/refilling of soil storage from interflow
Fraction of snowmelt which is surface runoff
Initial content of the unsaturated zone
Initial saturation deficit
rk
cmelt
SU Z0
SD0
Unit
[◦ C]
[mm/◦ C/d]
[-]
[-]
[m]
[-]
[-]
[h]
[mm]
[h]
[mm h−1 ]
[0. . . 1]
[0. . . 1]
[mm]
[-]
Further, in general the saturated hydraulic conductivity (ksat ) is the soil-texture
dependent parameter and is supposed to be used accordingly with one value for each
soil type. But the Loess derived soils, as in Ganspoel catchment, are very prone to
crusting which causes more or less exponential decline of the permeability. The soil
physical parameters like ksat are much more related to land use than to soil texture
although soils are fairly homogeneous in texture. As minimum and maximum ksat
are provided as per land use (Table 4.9), they also need to be calibrated within that
54
4.2. Methodology, model formulation, application and results
range, instead of using single ksat value for whole catchment (one soil type for whole
catchment).
Table 4.9: Measured saturated hydraulic conductivity as per land use in Ganspoel catchment
Measured saturated hydraulic
conductivity −ksat (m/s)
Landuse
1997 (crusted)
Min.
Beet
Forest
Meadow
Fallow
Maize
Potatoes
Summer cereals
Winter cereals
1.16E-06
9.44E-07
7.50E-07
3.05E-07
1.16E-06
3.05E-07
5.27E-07
5.27E-07
1998
Max.
Min.
Max.
8.91E-06
9.07E-05
4.19E-05
2.04E-05
8.91E-06
7.02E-06
8.88E-05
8.88E-05
1.04E-05
9.44E-07
7.50E-07
3.05E-07
4.80E-06
1.04E-05
5.27E-07
5.27E-07
1.50E-04
9.07E-05
4.19E-05
2.04E-05
3.33E-05
1.50E-04
8.88E-05
8.88E-05
A short event of 1997 occurred for 4hrs on 5/19/’97 (the event no. 1) and another
relatively longer event of 1998 occurred for 25hrs on 9/14/’98 (the event no. 7) are
used for calibration. The calibration is carried out according to the following steps.
1st Step: Appropriate initial values are set for the parameters using hydrographs
analysis, literature review, and previous model applications.
2nd Step: Trial and error calibration of the parameters is carried out with several
runs of model and the better parameter values and parameters’ domain are obtained,
evaluating the model performances through linear and logarithmic NS efficiencies
(Nash & Sutcliffe 1970) in these runs.
3rd Step: Using the manually calibrated values and the parameter space obtained
in step 2 as the initial values, an automated technique is adopted utilizing PEST
(Parameter ESTimation) (Doherty 2002, 2007) tool. PEST is a calibration tool
which is supposed to substitute the method of trial and error for an automated,
more objective means of estimating parameters. The purpose of PEST is to realize
a quasi-objective, automized calibration process based on a gradient-based complex
mathematical theory, called Gauss-Marquardt-Levenberg method which minimizes
the sum of square of differences between observed and simulated output for the nonlinear problems. The strength of this method is said to be lying in the fact that it can
generally estimate parameters using fewer model runs than many other estimation
methods, and that it can be used model-independently. The detail of this calibration
technique is presented in Chapter 5, where it is more relevant.
Once the optimum parameters are obtained yielding highest model performance and
closest graphical match of the results with observations, they are then, used to simulate remaining five events for validation as well as simulation. All the results and
their comparison with that from SCS-CN models are discussed later in following section. The summary of the adopted methodology is shown in Fig. 4.4.
55
4. Spatially Distributed Soil Erosion estimation: A case study
Figure 4.4: Adopted methodology for estimating runoff using WaSiM-ETH model
4.2.2.3 Results and comparisons
Unlike with SCS-CN models where only the total runoff volume for the event is
calculated, with WaSiM-ETH the complete hydrograph for the event is estimated
i.e. the runoff is estimated in each time step of the event which is two minutes here.
This enables to test the model performance during each event too. The linear and
logarithmic Nash Sutcliffe coefficient- lin. NS and log NS (Nash & Sutcliffe 1970),
and unsigned/absolute volume error, as estimated below, are used to investigate the
model performance to simulate runoff for each event.
 n 2 
X
obs
sim
Yi − Yi


 i=1



ln N S = 1 −  n 2 
X


obs
mean
Yi
(4.15)
−Y
i=1
 n 2 
X
obs
sim
log
Y
−
log
Y


i
i
 i=1



log N S = 1 −  n 2 
X


obs
mean
log Yi
(4.16)
− log Y
i=1
unsigned vol. error =
V olobs − V olsim
× 100
V olobs
(4.17)
where Yiobs and Yisim are the observed and simulated flow respectively in ith time
step of the event and V olobs and V olsim are the observed and simulated runoff vol-
56
4.2. Methodology, model formulation, application and results
ume respectively for the event. Y mean is the average observed flow and n is the total
records in the series/event.
The runoff volumes simulated by the calibrated WaSiM-ETH for the seven selected
events along with the model performances for each event is shown in Table 4.10.
Table 4.10: Runoff volume simulated by WaSiM-ETH and its performance measures
Runoff (m3 )
Events
WaSiM-ETH Model efficiency
Event
No.
Ptotal
(mm)
I30
(mm/h)
P5
(mm)
Obs.
RO
Simulated
RO
lin. NS
[-]
log NS
[-]
unsigned volume
error (%)
1
2
3
4
5
6
7
10
3
19.5
6.5
17.5
10.5
41
25.0
6.0
36.0
12.0
12.0
23.0
15
11.0
28.5
0.0
15.5
9.0
30.0
51.5
252.1
178
2307
427.8
404.3
342.9
10325
288.3
210.7
1530.4
454.7
421.4
321.6
13463
0.62
0.44
0.28
0.05
0.77
0.71
0.31
0.35
0.01
0.57
0.09
0.1
0.54
0.10
13.0
18.7
31.0
7.9
5.5
6.5
30.0
The runoff volumes simulated by the WaSiM-ETH and the formulated six SCS-CN
models are compared. Moreover, for five out of the seven events, the runoff volumes
simulated by a physically-based spatially distributed erosion model, MEFIDIS published elsewhere (Nunes et al. 2005) are also listed in Table 4.11 for comparisons.
Table 4.11: Comparison of runoff volume simulated by WaSiM-ETH, SCS-CN and MEFIDIS
Rainfall Events
Simulated RO (m3)
Obs. Original
Modified SCS CN method
RO SCS CN
I30
P5
Event Ptotal
WaSiMMEFIDIS
3
No. (mm) (mm/h) (mm) (m ) method
ETH
Model 1 Model 2 Model 3 Model 4 Model 5 Model 6
1
10
25
11
252.1
194.6
449.9
1166
703.1
1427.8
449.8
288.3
321.9
2
3
6
28.5
178
35
118
179.8
133.8
136.8
118
210.7
122.1
3
19.5
36
0
2307
658.5
1458
3590
2445.5
3022
1154.7
1530.4
2220
4
6.5
12
22
427.8
182.1
288.1
970.7
549.4
968.9
286.8
454.7
NA
5
17.5
12
10
404.3
551.9
1196.4
3679
2396.3 4451.2
980.8
421.4
NA
6
10.5
23
30
342.9
429.2
635
2279
1432
601.6
321.6
521.7
7
41
15
12877
18355
14045 19114.8 11966
13463
4551
51.5 10325 18128.9
2421
The statistical comparison of the results of runoff volumes from different models has
been performed by calculating the correlation, linear NS, log NS, averaged unsigned
error and root mean square error (RMSE) of the results against the observed ones.
The comparison is shown in Table 4.12. Among the six formulated SCS-CN models, the comparison of runoff volume estimation at catchment outlet (Table 4.11 and
4.12) shows that the performance of Model 1 which is the original SCS-CN model is
greatly improved by the incorporation of modifications in Model 2; namely incorporation of effect of slope, consideration of continuous antecedent moisture condition
57
4. Spatially Distributed Soil Erosion estimation: A case study
(AMC) and the use of modified relationship for initial abstraction. The further
modifications like in initial abstraction ratio, surface retention parameter and use
of optimized relationship for AMC as incorporated in Model 3, 4 and 5 does not
bring any improvement in performance; instead it decreases in some cases. However,
incorporation of depression storage in estimation as represented by Model 6 further
improves the performance. Hence the results of SCS-CN Model 6 are further used
for erosion modeling.
Table 4.12: Statistical comparisons of runoff volumes simulated at outlet by different models
Statistical
measures
Original
SCS CN
method
Modified SCS CN method
WaSiM
-ETH
MEFIDIS
Model
1
Model
2
Model
3
Model
4
Model
5
Model
6
Correlation
0.98
0.99
0.98
0.99
0.97
0.99
0.99
0.97
Linear NS coeff.
0.28
0.91
0.32
0.79
0.21
0.95
0.88
0.6
Log NS coeff.
0.6
0.81
0.42
0.58
0.34
0.82
0.98
0.91
Avg. unsigned error (%)
52.76
69.63
285.49
154.92
334.16
61.28
16.22
34.19
RMSE (in mm)
2.72
0.96
3.08
1.49
3.41
0.72
1.1
2.28
Logarithm of Simulated RO volume [m3]
Linear NS coefficient of the SCS4.5
CN Model 6 is better even than the
physically based models WaSiM-ETH
4
and MEFIDIS. But it is only be3.5
cause the event number seven, which
is by far the largest among the
3
seven events, is better estimated by
SCS-CN
the SCS-CN Model 6 and the linWaSiM-ETH
2.5
MEFIDIS
ear NS coefficient is highly influenced
1:1 Line
by the larger values.
Otherwise,
2
2
2.5
3
3.5
4
4.5
the overall performance as shown by
Logarithm of Observed RO volume [m3]
the other measures (except RMSE)
is better with the WaSiM-ETH and
MEFIDIS. This is further verified by Figure 4.5: Comparison of simulated against the
observed runoff volumes from differFig. 4.5.
ent models
Further, when the spatially distributed runoff maps simulated by the modified SCSCN method are compared with that from WaSiM-ETH, remarkably different patterns
can be observed. Despite the fact that the runoff volume is quite similar, the modeled
spatial distribution of runoff contributing areas differs. While the results of WaSiMETH show the combined effect of topography and land use, the soil type being same
overall, that from SCS-CN method strongly follow the land use category which seems
to be lesser realistic. The spatial distribution of surface runoff simulated for event
no. 7 can be seen in Fig. 4.6 as an example.
58
4.2. Methodology, model formulation, application and results
Figure 4.6: Maps of runoff simulated by modified SCS-CN Model 6 (left) and WaSiM-ETH (right)
for event number 7
4.2.3 Estimation of factors influencing erosion
The land use or vegetation cover, persistent management practices, soil’s resistance,
topography and the rainfall-runoff are the basic factors that govern the erosion. The
simple but most popular and widely used erosion model, the Universal Soil Loss
Equation (USLE) (Wischmeier & Smith 1960, 1965, 1978) and its revised or modified forms, which is chosen for this case study, capture those erosion affecting factors
in terms of six parameters. The erosion is estimate as the product of those six factors, so simple is the form of model. The detail of the model is presented in Chapter 2.
Following the basic form of USLE, the soil detachment (gross erosion) per unit area
can be expressed as;
E = λ × K × LS × C × P
(4.18)
where E is the soil loss in t/ha over a period selected for λ; λ is the rainfall-runoff
erosivity factor in MJ mm/ha h; K is the soil erodibility factor (t h/MJ mm); L is
the slope length factor; S is the slope steepness factor; C is the cover and management factor; and P is the conservation support-practices factor. The L, S, C, and
P values are dimensionless.
Within a raster-based ArcView GIS, the six factors are calculated in each grid /cell
for each of the selected events in order to predict erosion potential on a cell-by-cell
basis. The estimation procedures of these factors adopted in this case study is discussed below.
Rainfall-runoff erosivity factor (λ)
Rainfall-runoff erosivity was determined by calculating the erosivity value for each
59
4. Spatially Distributed Soil Erosion estimation: A case study
storm/event using the different USLE-based methods as shown below.


EI30 ,




0.56


,

11.8 × (Q × Qp )
(R)USLE
MUSLE
MUST
MUSS
i


 0.646 × (EI30 ) + 0.45 × (Q × Qp )0.33 × A,
Onstad and Foster
λ = 2.5 × (Q × Qp )0.5 ,




0.79 × (Q × Qp )0.65 × A0.009 ,

h
(4.19)
where
E
e
i
v
I30
Q
Qp
A
=
=
=
=
=
=
=
=
=
=
e·v
Total kinetic energy of storm
0.29 1 − 0.72 · e−0.082i
Unit energy [MJ/ha.mm]
Rainfall intensity [mm/hr]
Rainfall amount [mm]
Max. 30 minutes rainfall intensity [mm/hr]
Surface runoff [m3 ]
Peak runoff rate [m3 /s]
Area of catchment/grid cell [ha]
P
The parameters Q and Qp link or couple the erosion model with the rainfall-runoff
model; the SCS-CN and WaSiM-ETH in our case. The spatially distributed results
of surface runoff (Q) from these SCS-CN and WaSiM-ETH models are used along
with the grid-wise interpolated rainfall for each of the selected events. The cell-wise
peak runoff rate, Qp [m3 /s] is estimated as described in CREAMS Model (Young
et al. 1989):
Qp = 3.79 × A
0.7
×S
0.16
×
Q
25.4
0.903A0.017
× LW −0.19
(4.20)
where A = Area of the cell [km2 ], S = slope [m/km], Q = Runoff depth [mm], LW
= Length to width ratio of the cell.
Then, the spatially distributed erosivity factor is estimated by using all the five versions (Eqn. 4.14) for each of the selected events. The results are presented and
discussed in Section 4.3.
Soil erodibility factor (K)
K, the soil erodibility factor, is the measure of the intrinsic susceptibility of given soil
to soil erosion which depends on a complex interaction between several soil properties.
Basically, it depends on the organic matter and texture of the soil, its permeability
and profile structure. So knowing the soil texture, this can be simply obtained from
published tables. The soil texture of the entire catchment, which is quite small (1.11
km2 ), is classified as silty clay. However in the Belgian loam belt area, an erosion
plot study was carried out by Bollinne 1985 (Oost et al. 1999). The soil erodibility
60
4.2. Methodology, model formulation, application and results
factor was estimated as 40 kg.m2 hm−2 M J −1 mm−1 (i.e., 0.04 t.ha.hr/ha.M J.mm)
and this value of K is adopted in this study, which remains constant for all the events.
Cover and management factor (C)
C, the plant cover factor, is a simple relation between erosion on bare soil and erosion
observed under a cropping system. It reflects the effect of cropping and management
practices on soil erosion rates (Renard et al. 1997). The C factor combines plant
cover, its production level and the associated cropping techniques. It varies from 1
on bare soil to 1/1000 under forest, 1/100 under grasslands and cover plants, and 1
to 9/10 under root and tuber crops. Knowing the land use, its value can be simply
obtained from published tables. But the spatially distributed crop cover percentage
is available in our area which varies for the selected events. So it would be more
appropriate and realistic to make use of this rarely available data in estimation of
C factor rather than assigning directly from the land use category. Knowing the
vegetation cover c (%), the crop cover factor, C, is estimated here, following Yang &
Shi (1994) given by Cai (1998), as:



1,
for c = 0
C = 0.6508 − 0.343 × log (c) , for 0 < c < 78.3%


0,
for c ≥ 78.3%
(4.21)
The results are presented and discussed in Section 4.3.
Conservation support practice factor (P )
The support practice factor (P ) is the soil-loss ratio with a specific support practice
to the corresponding soil loss with up-and-down slope tillage (Renard et al. 1997). It
takes account of specific erosion control practices such as contour tilling or mounding,
or contour ridging. It varies from 1 on bare soil with no erosion control to about 1/10
with tied ridging on a gentle slope. Practically, the data in erosion control practices
are, in general, not available and are also not so significant in case of large catchment.
So its value has been safely taken as 1 in our study area for all the events. Bollinne
1985, from his erosion-plot study carried out in this area also suggest its value to be
unity (Oost et al. 1999).
Topographic factor (LS)
L is a slope length factor and S is a slope steepness factor. These factors are often
combined into one LS factor (product of slope length L and steepness S) and referred
to as the topographic factor. It accounts for the increased quantity of runoff that
occurs as distance from the top of the slope increases and for the increased velocity of
runoff with slope steepness Soil erosion is very sensitive to the topographical factor
LS and better estimation of this factor is thus important.
The LS factor estimation approach has continuously undergone improvements with
the consideration of the influence of profile convexity/concavity by segmenting of ir-
61
4. Spatially Distributed Soil Erosion estimation: A case study
regular slopes and improving the equation (Foster & Wischmeier 1974, Renard et al.
1991). In this case study, using the available 5m × 5m DEM of the study area,
the spatially distributed LS factor is calculated in GIS environment and thereby,
different approaches for the estimation have been investigated. The basics of the
approaches mainly differ in the consideration of slope length, L, either as one dimensional using flow-path length or using upslope contributing area instead, making it
two dimensional.
1-D consideration (upslope flow-path length)
The slope length factor , in the original form, is defined as:
L=
λ
22.12
m
(4.22)
where λ is the projected horizontal distance in metres between the onset of runoff
and the point where runoff enters a channel larger than a rill or deposition occurs.
In USLE (1978), the slope length exponent m is recommended as 0.2, 0.3, 0.4 and
0.5 for slope gradients less than 1%, 1-3.5%, 3.5-5%, and 5% or greater, respectively.
But in RUSLE, the exponent m is estimated based on ratio of rill to interrill erosion
β as:
β
1+β
sinθ/0.0896
β=
3sin0.8 θ + 0.056
m=
(4.23)
The value for m is adjusted by multiplying the value of β by 0.5 for lower ratio of rill
to interrill erosion or 2.0 for larger ratio of rill to interrill erosion (McCool et al. 1989).
And the slope steepness factor is estimated as:
(i) In USLE (Wischmeier & Smith 1978),
S = 65.4sin2 θ + 4.56sinθ + 0.0654
(4.24)
where, θ = the angle to horizontal
(ii) But in the RUSLE (McCool et al. 1987, 1989),


10.0sinθ + 0.03,

slopes < 9%
S = 16.8sinθ − 0.50, slopes ≥ 9%


3.0sin0.8 + 0.56, shorter slopes (<4m)
(iii) Nearing (1997) proposed a single, continuous function for slope steepness:
S = −1.5 +
62
17
1+
e2.3−6.1sinθ
(4.25)
4.2. Methodology, model formulation, application and results
In modeling erosion in GIS with DEM, several grid based LS computing equations
are developed. These techniques requires a flow accumulation map for the area.
Flow accumulation, which represents the number of upstream cells and hence the
upstream area contributing to the flow to that cell, can be computed in GIS from
the DEM using the hydrologic extension. The LS factor, for each cell, can be then
computed according to Moore & Burch 1986 as:
LS =
Flow accumulation × Cell size
22.13
×
sinθ
0.0896
1.3
(4.26)
with upper bound of slope length set as approximately 100 m. But the LS value
generated by this GIS equation considers L factor value for the hillslope above any
given cell, not the L factor for the cell. Therefore, the slope length factor for segment
or cell ‘i’ as described by Renard et al. (1997) gives:
Li =
λm+1
− λm+1
i
i−1
(λi − λi−1 ) · 22.13m
(4.27)
As pointed out by Kinnell, the Moore and Burch equation can be modified to compute
L factor for the cell, instead for the hillslope above the cell, based on equation 4.26,
as:
λi−1
λi
= Flow accumulation × Cell size
= λi−1 + Cell size
Li
=
1.4
λ1.4
i − λi−1
Cell size × 22.130.4
!0.3
LS
= Li ×
sinθ
0.0896
2-D consideration (upslope contributing area)
For two-dimensional applications, the slope length is to be replaced by unit contributing area. The unit contributing area can be defined as the contributing area
per unit of width of contour.
In order to adapt the USLE-based models to a two-dimensional landscape i.e. to
incorporate the impact of flow convergence and divergence, the hillslope length factor should be replaced by upslope contributing area (Moore & Wilson 1992, Mitsova
et al. 1995, 1996, Desmet & Govers 1996). The two 2-D approaches that have been
investigated in this case study are:
According to Moore & Wilson (1992):
LS = 1.6 ×
unit contributing area
22.13
0.6
×
sinθ
0.0896
1.3
(4.28)
63
4. Spatially Distributed Soil Erosion estimation: A case study
Further, a modified equation for computation of LS factor in finite difference form
in grid cell representing a hillslope segment was derived by Desmet & Govers (1996):
m+1
Li,j
Ai,j−in + D2
− Am+1
i,j−in
=
m
m+2
m
D
· xi,j · 22.13
Si,j =
tanθ
0.09
1.45
(4.29)
where
Li,j = The slope length factor for the grid cell with coordinates (i, j) [ - ]
Ai,j−in = The contributing area at the inlet of a grid cell with coordinates (i, j)
[m2 ]
D
= The grid cell side length [m]
xi,j
= sinαi.j + cosαi,j
αi,j
= Aspect direction for the grid cell with coordinates (i, j)
m
= Slope length exponent [ - ] (≈ 0.755 - based on field data by Govers,
1991)
Si,j
= The slope steepness factor for the grid cell with coordinates (i, j) [ - ]
θ
= The angle to horizontal
Routing algorithms
Computation of LS factor in GIS environment, as indicated above, requires flow accumulation or contributing area for each cell. Steepest descent algorithm is the most
commonly followed routing algorithm in GIS for estimating the flow accumulation.
However, the overland flow over a hillslope cannot be strictly uni-directional as represented by the steepest descent algorithm. Therefore two more algorithms, which
consider this fact as described below, have also been investigated in this study for
the estimation of the topographical factor, LS.
p Single Flow Algorithm (SF) by O’Callaghan & Mark 1984: It is the steepest
descent algorithm in which the flow in a cell is completely directed into a
neighboring cell corresponding to the highest slope gradient.
p Multiple Flow Algorithm (MF) by Quinn et al. 1991: With this algorithm,
the flow in a cell is directed to all neighboring cell downslope such that the
receiving fraction transferred to each of them is proportional to the product of
the distance-weighted drop and a geometric weight factor, which depends on
the direction.
p Flux Decomposition Algorithm (FD) by Desmet & Govers 1995, 1996:
This algorithm is based on decomposition of the flux vector in which a vector
having a magnitude equal to the upslope area to be distributed, increased with
the area of the grid cell itself, and directed according to the aspect direction,
is split into its two ordinal components. The magnitude of each component is
proportional to the sine or cosine of the aspect value, normalized so that the
sum of the two components equals the magnitude of the vector
64
4.2. Methodology, model formulation, application and results
Using the spatial analyst of ArcView GIS with 5m × 5m DEM, at first the slope of
the catchment is calculated which is then used to estimate S factor following different
approaches discussed above. The summary of the spatially distributed S factor is
shown in Table 4.13.
Table 4.13: Summary of distributed S factor estimated from different approaches
Measures
Wischmeir & Smith,
USLE (1978)
Moore & Burch
(1986)
McCool et al.
(1987, 1989),
RUSLE (1993)
Govers,
(1996)
Nearing,
(1997)
Min.
Max.
Mean
Std.dev.
0.0654
10.63
0.76
1.03
0
6.28
0.67
0.8
0.03
5.69
0.72
0.77
0
8.58
0.69
0.95
0.05
6.78
0.72
0.77
DEM often contains local depressions or pits which act as a sink for the flow. So
the hydrologic correction of the available DEM is done using “demfill” avenue script
in ArcView GIS which fills such sinks so that the continuous flow till the catchment
outlet is ensured. Then using the hydro-tools extension (Schäuble 2003) with spatial
analyst in ArcView GIS, the flow accumulation maps for the study area based on single flow and multiple flow algorithms is calculated from the hydrologically corrected
DEM. However, the flow accumulation map with flux decomposition algorithm is imported into ArcView GIS after calculating using “USLE 2D” software developed in
Katholieke Universiteit, Leuven by Oost & Govers 2000. This software works with
Idrisi GIS GIS format. The summary of the flow accumulation estimated by the
three different routing algorithms is shown in Table 4.14. Mean flow accumulation
value is lowest with SF and highest with FD but the maximum value is lowest with
MF algorithm.
Using this flow accumulation maps with
Table 4.14: Summary of flow accumulation
different algorithms, the topographical facestimated from three different
tor LS is then calculated following differrouting algorithms
ent approaches based on upstream flow-path
Measures
SF
MF
FD
length (1-D) and upstream contributing area
(2-D). The summary of the spatially disMin.
0
0
0
Max.
11137 9938 11380
tributed results is shown in Table 4.15. In
Mean
59
72
86
general, the LS factor estimated by using FD
S.D.
484.6
390.2
508
routing algorithm gives highest mean value
than with SF and MF algorithms but the
maximum value is highest with SF algorithm. Moreover, 2-D approach estimated
higher LS values than the 1-D approach. Further, the values differ among the different methods of 2-D approach where the Govers method gives the results comparatively on higher side. Above all, the most important investigation here is difference
in spatial distribution of LS factor estimated with the use of upstream flow-path
length (1-D) and upstream contributing area (2-D). This is depicted in Figure 4.7 in
a sloping portion of the catchment.
65
4. Spatially Distributed Soil Erosion estimation: A case study
Table 4.15: Summary of LS factor estimated from different approaches using three different routing
algorithms
Approach/Method
1-D consideration
(flow accumulation)
2-D consideration
(unit contributing
area)
LS factor
Measures
SF
MF
FD
Moore & Burch, 1986
(with upper bound=100m)
(L for slope)
Min:
Max:
Mean:
Std. dev:
0
36.59
1.45
1.26
0
21.62
1.84
1.37
0
23.03
1.93
1.39
Moore & Burch
modified by Kinnell
(L for cell)
Mmin:
Max:
Mean:
Std. dev:
0
11.04
0.88
2.24
0
10.9
1.06
2.44
0
10.9
1.08
2.58
Wischmeir & Smith (1978)
Min:
Max:
Mean:
Std. dev:
0
87.49
1.76
3.63
0
42.5
2.29
3.7
0
46.07
2.42
3.99
McCool (1987,1989)
(rill=interrill)
Min:
Max:
Mean:
Std. dev:
0
119.66
1.86
4.01
0
39.76
2.4
3.78
0
47.93
2.55
4.15
Govers (1991)
Min:
Max:
Mean:
Std. dev:
0
284.01
3.37
11.64
0
164.63
4.49
8.74
0
273.04
4.94
10.04
Nearing (1997)
(‘m’ from McCool,
rill=interrill)
Min:
Max:
Mean:
Std. dev:
0
132.01
1.78
4.05
0
46.22
2.32
3.8
0
51.46
2.48
4.17
Figure 4.7: Spatially distributed LS factor estimated following 1-D (left) and 2-D (right) approaches
66
4.2. Methodology, model formulation, application and results
As can be seen in Fig. 4.7, the difference between the two approaches is obvious. The
1-D approach which considers the flow-path length predicts high LS values only on
steeper slopes but very low or zero values in the hollows where the slope gradient is
low. However, the 2-D approach which considers the contributing area instead of flow
path length yields higher values in hollows too although the slope is small. Hence,
it is found that the 2-D approach takes into account the flow convergence which is
a major factor explaining the enhanced erosion risk in hillslope hollows. Therefore
the incapability of original USLE-based model in predicting adequate erosion in the
hollows can be corrected by implementing the 2-D topographical factor estimation
instead of using the normally followed flow-path length.
4.2.4 Sediment Delivery Ratio and Sediment Yield estimation
The USLE-based models which involve rainfall erosivity, but not the runoff erosivity
only, like (R)USLE and Onstad and Foster (equation 4.18) determine gross erosion
rates in the catchment and not the amount of eroded material that is actually delivered to a downstream point (Sediment Yield). In addition to the sediment delivered
at catchment outlet, the location and amount of gross erosion within the catchment
(such data is rarely available), has also been observed in three different occasions in
our study area. Out of them, one occasion is on May 1997 which consists of the two
(event No. 1 and 2) out of our seven selected events (Table 4.1). MUSLE, MUST
and MUSS (equation 4.18) uses totally the runoff erosivity and hence give directly
the sediment yield. While USLE incorporates totally the rainfall erosivity, Onstad
and Foster uses combination of both and therefore requires rainfall runoff modeling
too. The gross erosion for the available May 1997 event in the study area as simulated by the Onstad and Foster along with runoff components from SCS-CN Model 6
(best performing in runoff simulation) and WaSiM-ETH, and the standalone USLE
is shown in Table 4.16. The comparison of the results as obtained by adopting the
three different flow routing algorithms (SF, MF and FD) for 2-D topographical factor
estimation have also been made.
Table 4.16: Gross erosion simulated by different models for the event on May 1997
Modelled gross erosion [ t ]
Event
May 1997
Observed
gross erosion [ t ]
76.30
Flow
algorithm
USLE
SF
Onstad and Foster
SCS CN (Model 6)
WaSiM-ETH
82.43
53.65
53.72
MF
109.84
71.49
71.57
FD
119.75
77.93
78.03
It is observed that the Onstad and Foster that incorporates both rainfall and runoff in
the erosivity factor can predict gross erosion better than the USLE that incorporates
only the rainfall erosivity factor. Moreover, the topographical factor consideration
with flux decomposition (FD) as routing algorithm, instead of commonly used single
flow (SF) algorithm gives better results. The runoff components supplied by both the
67
4. Spatially Distributed Soil Erosion estimation: A case study
simple but modified SCS-CN model and the more complex physically based WaSiMETH model seems to perform equally well so far as the result of lumped gross erosion
is concerned. The sediment yield and the spatially distributed results are yet to be
analyzed.
To obtain the sediment yield from the gross erosion, estimation of the Sediment
Delivery Ratio (SDR) becomes necessary. The SDR represents the fraction of the
material eroded from a watershed which reaches a downstream point where sediment
yield is to be estimated. Its values may range from a few percent to nearly 100 percent with larger delivery ratios generally applying to smaller watersheds with steeper
slopes and finer grained material.
Determining the SDR is a critical step in converting estimates of soil erosion within
a basin into a quantifiable value of sediment yield. It is affected by numerous factors
including sediment source, texture, nearness to the stream, channel density, basin
area, slope, land use/cover, and rainfall-runoff factors. There is no generally accepted
procedure to estimate the SDR; however, several empirical formulas exist. Here, in
this case study the following three models for SDR calculation have been considered:
Model 1: Based on area as proposed by Vanoni 1975,
SDR = 0.4724 × A−0.125
where
(4.30)
A= Area in km2 .
Model 2: Based on rainfall-runoff as hypothesized by Mishra et al. 2005,
SDR = ψ
where
ψ= Runoff coefficient =
(4.31)
Runoff
Rainfall
Model 3: Based on area, land use and topography (a new formulation),
SDR = C1 × C2 × C3
where
C1 =
=
C2 =
=
C3 =
=
(4.32)
factor of area;
e−0.02A , a modified form of Maidment 1993
USLE C factor
factor of land use;
factor of topography;
ratio of elevation of the area (cell) to elevation of its upstream
connected area (cell).
Then the sediment yield, that can be compared with the observed sediment lumped
at outlet, is estimated by simply multiplying the estimated gross erosion with the
SDR. In this case study, the erosion modeling is done for all the seven events and the
68
4.2. Methodology, model formulation, application and results
results are investigated with the possible combinations of all the approaches discussed
above. That is basically, the five different models for rainfall-runoff erosivity factor
(Equation 4.18), several approaches for both one-dimensional and two dimensional
consideration of topographical factor (Equations 4.21 - 4.29) with three different flow
routing algorithms, and the three different SDR models (Equations 4.30 – 4.32) are
combined. Moreover, the required runoff component is provided through the rainfallrunoff modeling results of the formulated six SCS-CN models and the WaSiM-ETH.
It is not worthy and not possible or it is rather irrelevant to present all the results
here. However, the statistical analysis of the results of approaches/combinations that
were performing better is shown in Table 4.17. The expression of Govers for twodimensional LS factor estimation with flux decomposition flow routing algorithm is
used in the presented results. In addition, the analysis of the results of physically
based soil erosion model- MEFIDIS is also listed along for the comparison.
Table 4.17: Statistical analysis of the results of better performing approaches / combinations
SCS CN (Model 6)
USLE
Measures
WASIM-ETH
Onstad & Foster
Onstad & Foster
MEFIDIS
SDR
SDR
SDR MUSLE SDR
SDR
SDR MUSLE SDR
SDR
SDR
Model 1 Model 2 Model 3
Model 1 Model 2 Model 3
Model 1 Model 2 Model 3
Correlation [-]
0.81
0.82
0.52
0.83
0.89
0.85
0.79
0.83
0.9
0.83
0.81
0.93
Linear NS coeff.
[-]
0.26
0.57
0.25
-1.26
0.57
0.59
0.58
-3.87
0.23
-0.73
0.65
0.78
Avg. Unsigned
error [%]
614.25
77.77
301.26
90.6
381.82
79.02
205.47
104.09
389.9
92.9
202.7
281.48
RMSE [mm]
25.81
15.78
19.96
34.78
16.63
15.16
15.13
58.17
24.01
30.07
13.53
11.57
The results of the simulated sediment yield lumped at catchment outlet with the
combination of several approaches, in general, vary a lot among the approaches and
none of the combination can be singled out as better performing. However, the
consideration of both rainfall and runoff in erosivity factor, two dimensional consideration of topographical factor and routing algorithm with multiple flow directions
have certainly enhanced the results.
Further, it can be seen that, as far as the sediment yield lumped at outlet is concerned, the least data demanding simple erosion model (eg. USLE-based) can perform equally well as a data-intensive complex physically-based soil erosion model (eg.
MEFIDIS). The use of a complex (WaSiM-ETH) hydrological model in comparison
to a simple (SCS-CN) model to supply runoff component to the USLE-based model
also does not bring considerable improvement when the sediment yield at catchment
outlet is concerned.
If it is so, then it is interesting to investigate the difference in the spatial patterns
of erosion or source-area of erosion as simulated by the simple and complex models.
The spatial distribution of erosion for the event in May, 1997 (i.e. event no. 1 and
2) as simulated by the MUSLE with SCS-CN and with WaSiM-ETH is shown in
the Fig. 4.8. Also shown in the figure, for the comparison, is the observed erosion
pattern and the pattern simulated elsewhere by the physically based complex erosion
model – MEFIDIS (Nunes et al. 2005) for the same event.
69
4. Spatially Distributed Soil Erosion estimation: A case study
Figure 4.8: Spatial patterns of erosion as observed and simulated by different models for May 1997
events
For the spatial location of the erosion source areas within the catchment, the simulated erosion patterns shows that all the three models capture the observed area of
erosion, but the MUSLE with SCS-CN simulates the whole block of land according
to the land use as erosive area although the erosion is observed in a small part of
it. This yields unnecessarily optimistic erosion source areas. However, when the
runoff component of MUSLE is improved by coupling it with WaSiM-ETH, it yields
erosion source areas reasonably matching with the observed ones. More importantly,
the result of simple MUSLE model with WaSiM-ETH is equally good as that of the
complex erosion model –MEFIDIS.
Further, the percentage of simulated erosion volume and modeled erosion rate with
respect to the distance from the observed erosion area for the May 1997 event as
resulted by the MUSLE with SCS-CN and WaSiM-ETH is shown in Fig. 4.9.
The figure indicates that 75% of the mass of eroded soil is simulated by MUSLE-SCS
CN and MUSLE-WaSiM-ETH within 100m and 68m respectively from the observed
erosion regions. However, that from MEFIDIS is 65m (Nunes et al. 2005); not so
better than with MUSLE-WaSiM-ETH. Moreover, there is sharp decrease in the
modeled erosion rate as we move away from the observed erosion regions in case of
MUSLE-WaSiM-ETH (also with MEFIDIS) but this does not occur strictly in case of
MUSLE-SCS CN. This means, the location of severe erosion is also better captured
by MUSLE-WaSiM-ETH; but not by MUSLE-SCS CN which is the basis of several
erosion and water quality models even in the distributed form.
70
4.3. Conclusions
20
100
SCS-CN
WaSiM-ETH
SCS-CN
18
80
16
70
14
Erosion rate (t/ha)
Erosion volume (%)
90
60
50
40
30
20
WaSiM-ETH
12
10
8
6
4
2
10
0
0
0
20
40
60
80
100
120
140
Distance from observed area (m)
160
180
200
0
20
40
60
80
100
120
140
160
180
200
Distance from observed area (m)
Figure 4.9: Modeled percentage of erosion volume (left) and modeled erosion rate (right) with
respect to distance from the observed erosion area for May 1997 event
4.3 Conclusions
The presented case study was carried out to investigate basically the two research
objectives. The first one was to find out how well the simplest and still widely used
erosion model (USLE and its families) requiring minimum input data compared to
other erosion models, can predict the spatial distribution of erosive areas in a catchment when they are coupled with another low data demanding SCS-CN rainfall
runoff model. This combination is the core of several soil erosion and water quality
models. In this study, several improvements suggested for the SCS-CN model have
been incorporated and coupled with USLE and its derivatives in the grid-based GIS
environment to capture the spatial distribution.
The second one was to investigate if the capability of the simple erosion model, to
predict spatial erosion patterns or erosion source areas, would be enhanced when
its hydrological component is improved. That is to see if the better hydrology representation improves the simple erosion model. In this part of the research work,
the SCS-CN component of the USLE based model was replaced by the more process oriented fully distributed hydrologic model, WaSiM-ETH. This investigation is
motivated by the fact that the fully physically based complex erosion model is practically unusable in most of the real cases due to its very intensive data requirements
where as the use of physically based complex hydrological model is more commonly
usable in today’s data availability scenarios. In this work the results of joint USLE
-WaSiM-ETH modeling have also been compared with that from a completely physically based complex erosion model – MEFIDIS.
During the course of this case study, some other secondary investigations have also
been made. The totally rainfall-based, runoff-based and the rainfall-runoff combination based erosivity factors were investigated. It is found that the combination
of rainfall and runoff in erosivity representation as proposed by Onstad and Foster
simulates better than considering either of them alone. Similarly, the differences in
spatial response by considering the topographic effects on erosion in one dimensional
way which uses flow path length and in two dimensional way which uses the ups-
71
4. Spatially Distributed Soil Erosion estimation: A case study
lope contributing area have been investigated. It has been observed that the two
dimensional consideration captures the topographic effects in more realistic way as
it ensures more erosion in the hollow which is realistic as more erosion occurs in the
hollows due to flow convergence. For the estimation of the upslope contributing area
three different flow routing algorithms namely; single flow or the steepest descent,
multiple flow and the flux decomposition; have been investigated. Unlike the steepest descent algorithm, which is followed by almost all the USLE-based models, the
flux decomposition algorithm gives better results when simulated and observed gross
erosion and sediment yield are compared. Similarly the different sediment delivery
ratio models along with a proposed one were investigated and found that the proposed one which is based on more number of relevant factors produced better results
at least for the considered events in this case study.
From the results of runoff, gross erosion, sediment yield and spatial distribution of
erosion producing areas for the selected events with the different model coupling, it
can be concluded that the SCS-CN method with USLE (and its families), despite
several modifications which improves the runoff volume estimation, could not simulate the spatial distribution of runoff generating and erosion producing areas well.
The distribution resembles the landuse map of the watershed. However, encouraging results were obtained when WaSiM-ETH is used even with the simple, empirical
erosion models- USLE (and its families). The spatial distribution of runoff generating and erosion producing areas are very well simulated, reasonably close to the
observed ones and comparable to or sometimes even better than that simulated by
the more data-intensive physically based complex soil erosion model – the MEFIDIS.
Although not in the direction of targeted objectives, but a very important conclusion
has been encountered from an intermediate result during the course of this case study.
This is related to the parameters estimation of the distributed hydrologic model or
the application of the results. To apply WaSiM-ETH for the selected events in
the catchment, its 11 parameters were calibrated using Gauss-Marquardt-Levenberg
algorithm. As is the trend, the calibration was done with objective function of
minimizing runoff prediction errors in the catchment outlet. Very nice results were
obtained with closely matching hydrographs as shown in Fig. 4.10. The calculated
Nash-Sutcliffe efficiency was as high as 0.97 in calibration (event no. 7) and 0.81 in
validation (event no. 6).
But when the corresponding simulated runoff source areas within the catchment
were investigated, a very much unrealistic patterns were observed with almost all
the runoff coming from a small isolated patch in the catchment as shown in Fig.
4.11. The areas bounded by the dotted polygons in the figure are the areas where
erosion and sediment transport were observed during the event, but no runoff was
simulated in those areas.
It simply indicates the very good predictions by the distributed rainfall runoff model
but for all wrong reasons. This shows that simply the better hydrograph prediction
by a physically-based distributed rainfall runoff model does not guarantee better hydrology representation by it within the catchment. Thus it makes the reliability of
72
4.3. Conclusions
Figure 4.10: Observed and simulated hydrographs with WaSiM-ETH for event no. 7 (left) and
event no. 6 (right)
Wood
Ditch/Brooklet
Sugarbeets
Meadow/Pasture
Institute
Path
cereals
Farm
Grass
Paved Road
Potatoes
Maize
Overland flow (mm)
Cabbages
0 - 10
N
10 - 20
20 - 30
30 - 40
Ploughed Field
40 - 50
Cereals
Garden
50 - 100
200
0
200
Meters
Figure 4.11: Spatially distributed surface runoff for the event no. 7 simulated by WaSiM-ETH
distributed results, which is the main aim of using distributed model, in doubt to be
accepted if its parameterization is verified only with lumped observed data at outlet.
To proceed the case study further, this problem was overcome by re-calibrating
the whole catchment with single set of parameter; but the intermediate negative
results of this case study raises the question or demand for robust parameterization
of distributed model when only the lumped observed data at outlet is available, as
it is generally the case. This forms the basis of further investigation in this research
work and it is carried out as described in the next chapter.
73
5 Physically based distributed
hydrological modeling for HSA
estimation
5.1 Background
Erosion control strategies should focus especially on surface runoff and their spatial and temporal variation within the catchment. Surface runoff is that portion
of precipitation which, during and immediately following a storm event, ultimately
appears as flowing water in the drainage network of a watershed. Such flow may
result from direct movement of water over the ground surface, precipitation in excess
of abstraction demand, or it may result from emergence of soil water into drainage
way. Surface runoff can be occurred, thus, as either infiltration excess or saturation
excess or subsurface return flow; as discussed already in Chapter 1.
The surface runoff is one of the prime cause of erosion and sediment yield on earth’s
surface and it is therefore of great concern to land managers. It carries, along with
it, the soil particles detached by the impact of rainfall as splash erosion. The kinetic
energy associated with the surface runoff, as it flows as overland flow is responsible
for further erosion as spreaded sheet erosion, a bit concentrated rill erosion or highly
concentrated gully erosion. Hence, the surface runoff is the core part of erosion and
sediment yield.
According to the approach adopted in this research work for addressing the erosion
problem in a catchment, as discussed in Chapter 1, the influence of surface runoff
is defined or captured through the identification of Hydrologically Sensitive Area
(HSA) in the catchment. The term “HSA” is used to refer to areas in a watershed
especially prone to generating runoff that are, therefore, potentially susceptible to
transporting sediment and contaminants to perennial surface water bodies. HSAs,
thus, describe the risk of runoff generation and determine the potential erosion source
areas. Recognizing the existence of such HSAs limits the scope of watershed-scale
erosion and sediment yield (also the water quality) problems to only those sensitive areas. In addition, the spatial extent of the runoff-generating areas, the HSAs,
changes throughout the year making some portions of a watershed more prone to
runoff in one month than in another. Therefore it is possible for a specific location
to be hydrologically sensitive at one time of the year and insensitive at another.
Thus, some erosion conservation measures or potentially polluting activities might
only need to be restricted in an area only for a part of each year, and such measures
would be more readily accepted and adopted by the farmers in their agricultural
lands.
74
5.2. Distributed watershed modeling of surface runoff with WaSiM-ETH
Therefore, the reasonable estimation of spatial patterns of soil erosion or its risk
requires predicting, at first, the temporal variation of spatially distributed surface
runoff within the catchment or the HSAs with adequate accuracy. A direct measurement of such areas in the field is hardly possible and therefore the modeling is
required. Several alternatives for distributed watershed modeling of surface runoff
exist. The WaSiM-ETH, the Water flow and balance Simulation Model (Schulla &
Jasper 1999, 2006) has been chosen here for the purpose. The brief description of
the model is presented in Chapter 2.
So this Chapter deals with the third objective set-up in chapter1; i.e. to evaluate
the distributed performance of the better performing rainfall-runoff model from the
case study in Chapter 4 (i.e. WaSiM-ETH model here) in identifying the spatially
distributed and temporally varying Hydrologically Sensitive Areas (HSAs). During
this investigation, the following specific questions are encountered and are researched;
p How do the surface runoff patterns differ in different subcatchments when subcatchments are calibrated independently and how do they look like when calibrated for same parameter set in all subcatchments?
p How do the distributed results obtained from parameters calibrated with different calibration techniques differ?
p Are the calibrated parameters, performing good in hydrograph simulation, good
enough in predicting spatially distributed surface runoff too? How to find the
parameters that are good in all aspects or what would be a robust parameter
estimation technique?
The investigation here with WaSiM-ETH is carried out in Rems catchment of southern Germany. The brief description of this study area is given in Chapter 3.
5.2 Distributed watershed modeling of surface runoff with
WaSiM-ETH
A watershed model typical of distributed philosophy was originally outlined by Huggins & Monke (1966) and then expanded to incorporate non-point pollution process
as described in Lake & Morrison (1977). A truly physically-based distributed hydrologic model would require the development and solution of a comprehensive set
of partial differential hydrodynamic and porous media flow equations. The solution
of such equations is highly boundary value dependent. A detailed description of the
infinite variety of boundary conditions present in a natural watershed is currently
not feasible (Huggins, 1982). Therefore, those models that are currently classified
as distributed models only approximate this approach. Models can be classified as
distributed when they utilize data concerning the spatial distribution of controlling
parameter variations in conjunction with computational algorithms to evaluate the
influence of this distribution on simulated behavior. The distributed models, normally, conceptualize a watershed to be modeled as being made up of a collection of
75
5. Physically based distributed hydrological modeling for HSA estimation
square elements or regular grids. While parameter values must be assumed uniform
within each element, they are allowed to vary in an unrestricted manner between
elements. Thus, any degree of spatial variability within a watershed is easily represented.
The chosen model, WaSiM-ETH, is a deterministic, fully distributed grid based
catchment model for the simulation of the hydrologically important parts of the
water balance and uses physically based algorithms for most of the hydrological processes. The basics of this model are described in Chapter 2. It provides several
alternative approaches to compute the different hydrological components like evapotranspiration, snow accumulation, snow melt, infiltration and generation of surface
and subsurface flow components. For example, the evapotranspiration can be simulated using either of the Penman-Monteith, Hamon, Wendling or Haude method.
Similarly, the modeling of snow accumulation and snowmelt can be performed using
a temperature-index approach, a temperature-wind-index-approach, a combination
approach after Anderson (1973) or an extended combination approach after Braun
(1985). The version 1 of WaSiM-ETH follows the Topmodel approach of Beven &
Kirkby (1979) while the version 2 uses Richard’s equation for describing the water
flow within the unsaturated soil zone. The version 1 is used in this research work
whose soil model, responsible for generating surface runoff and hence relevant in this
research work, is described below. Detailed description of other modules and the
underlying mathematics can be found in Schulla & Jasper (1999, 2006).
5.2.1 Soil model for WaSiM-ETH version using extended Top model
approach
This version of WaSiM-ETH (version 1) is able to consider runoff generation by both
mechanisms: the saturated overland flow as well as Horton overland flow. For this,
it uses the combination of extended Topmodel (saturated overland flow) and Green
and Ampt (infiltration excess) approaches.
Infiltration excess- Surface Runoff
The infiltration model is an integrated part of the soil model in the WaSiM-ETH. The
model uses the approach after Peschke (1977, 1987) which is based on the approach
of Green & Ampt (1911). The Green and Ampt equation calculates infiltration based
upon soil moisture conditions and surface runoff occurs when soil infiltration capacity has been exceeded. The matrix flow is assumed to dominate in the soil and the
wetting front is approximated as a step function. The soil is assumed to be homogeneous and unlayered and the precipitation intensity is assumed to be constant over
each time step.
The calculation of the infiltration excess surface runoff is realized in two phases.
Within the first phase the time to saturation, ts , is calculated as:
ψf
P I/Ks − 1
ts =
PI
76
(5.1)
5.2. Distributed watershed modeling of surface runoff with WaSiM-ETH
where
ts
ψf
PI
Ks
=
=
=
=
saturation time from the beginning of the time step [h]
suction at wetting front [mm]
precipitation intensity [mm/h]
saturated hydraulic conductivity [mm/h]
The saturation occurs only when P I > Ks . With the increase in the saturated hydraulic conductivity and suction, saturation time rises. On the other hand, a higher
intensity of precipitation leads to a decrease in saturation time.
Within the second phase, the cumulated infiltration until the end of the time step is
calculated. At first, the infiltrated amount of water up to the saturation time, Fs , is
computed as:
Fs = P I × ts
(5.2)
Then, the cumulated amount of infiltration (F ) after saturation until the end of the
time step t, is calculated as:
A
F = +
2
A2
+ AB + Fs2
4
!1/2
with, A = Ks (t − ts )
B = Fs + 2 · na · ψf
(5.3)
where na is the fillable porosity. Evidently, the cumulated amount of infiltration
increases with the increase in precipitation, saturated hydraulic conductivity and
suction. The exceeding (not infiltrated) amount of precipitation is the infiltration
excess surface runoff (Qsurf,I ) and hence computed as:
Qsurf,I = P I · (t − ts ) − F − Fs
(5.4)
In the WaSiM-ETH the amount of re-infiltrating water can be controlled using a
parameter xf [0-1]. This is important to consider heterogeneity of the soil properties
if using larger grid cells.
Saturation excess- Surface Runoff
The modeling of the soil water balance within the vadose zone and saturation excess
runoff generation is done in WaSiM-ETH version 1 by using a modified variable saturated area approach (Beven & Kirkby 1979) extended by capillary rise and interflow.
The soil zone is divided in three active storages which interact with each other.
The spatial distribution of the topographic index, Ti , is the base for this modeling
and this index is defined as:
Ti = ln
at
T0 tan β
(5.5)
77
5. Physically based distributed hydrological modeling for HSA estimation
where Ti
at
T0
β
=
=
=
=
Topographic index [ - ]
Specific catchment area per unit length of a grid cell [m2 /m]
Saturated local hydraulic transmissivity [m2 /s]
Local slope angle [m/m]
Using this index, the potential extent of saturation areas can be estimated depending
on the mean saturation deficit within the basin. As opposed to modeling of classes
of similar indices like in the original Topmodel, the calculation is done separately for
each of the grid cells.
The Topmodel is a conceptual variable contributing area approach based upon the
distribution of saturation deficit. In this concept, it is assumed that: (i) the groundwater table is parallel to the topographic slope, (ii) the dynamic of the saturated
zone can be approximated by subsequent quasi stationary states, and (iii) the local
hydraulic transmissivity Th is an exponential function of the saturation deficit S:
Th = T0 e−S/m
(5.6)
The distribution of the saturation deficit or, in other words the spatial distribution
of saturated areas, can be found by:
Si = Sm − m (Ti − γ)
(5.7)
where Si = Local saturation deficit [mm]
Sm = Mean saturation deficit of the basin (arithmetic average of all
Si ) [mm]
m = Recession parameter [mm]
Ti = Local topographic index [ - ]
γ
= Mean topographic index of the (sub-) catchment [ - ]
At places where Si ≤ 0, any further liquid precipitation (or snowmelt) generates
surface runoff immediately. The mean saturation deficit is then newly calculated in
each time step as average value of all local saturation deficits from the previous time
step after balancing all inflows into and outflows out of the basin. After estimating
all runoff components for the entire sub-basin, the new mean saturation deficit is
calculated by:
Sm,t = SM,t−1 + QB + Qrück − QSU Z
(5.8)
where Sm,t
Sm,t−1
QB
Qrück
QSU Z
78
= Spatially averaged saturation deficit in the actual time step
[mm]
= Spatially averaged saturation deficit in the previous time step
[mm]
= Base flow in actual time step (a mean value for the subcatchment) [mm]
= Capillary rise in actual time step (a mean value for the subcatchment [mm]
= Groundwater recharge from the unsaturated zone (a mean value
for the subcatchment) [mm]
5.2. Distributed watershed modeling of surface runoff with WaSiM-ETH
Surface runoff from snow melt
In the case when there is a sufficient snow cover on the ground (>10 mm water
equivalent), a specified fraction of snow melt is taken as surface runoff directly from
this melt as:
Qsurf,S = Qsnow,out × QDSnow
(5.9)
where Qsurf,S
= Surface runoff (fraction from snow melt) [mm]
Qsnow,out = Snow melt [mm]
QDSnow = Factor defining fraction of surface runoff on the snow melt [ - ]
This melt is not given to the infiltration module.
Partitioning of water reaching soil
Based on the precipitation intensity, a greater or lesser fraction of precipitation can
flow directly into deeper soil region without going into the root zone storage. In
WaSiM-ETH this fraction is specified by a threshold value for the precipitation intensity such that all exceeding precipitation is routed into the deep soil by macro
pores so that rise in base flow would occur even if soil is only partly saturated. This
threshold intensity is calculated as:
Pgrenz = Pgrenz,1h × ∆tav
where Pgrenz
Pgrenz,1h
∆t
ap
=
=
=
=
(5.10)
Threshold precipitation intensity [mm/∆t]
Threshold precipitation intensity for time step ∆t = 1h [mm/h]
Time step [h]
Empirical value describing the decrease of the variance of the
precipitation intensity with larger time steps (≈ 0.6) [ - ]
All precipitation below the threshold value Pgrenz flows into the root zone storage,
also called soil storage, from where it can be withdrawn by evaporation. The exceeding fraction flows into deeper soil region immediately which is computed as:
qv = Kkorr · Ks · e−Si ·m
(5.11)
where qv
= Vertical flow rate (percolation) [mm]
Kkorr = Scaling parameter for considering unsaturated soils and preferred flow paths [ - ]
Si
= Local saturation deficit [mm]
m
= Recession parameter [mm]
Ks
= Saturated hydraulic conductivity [mm/h]
In the original Topmodel, the parameter Kkorr is used for considering the unsaturated conditions, while in WaSiM-ETH it is used for considering preferential flow
79
5. Physically based distributed hydrological modeling for HSA estimation
paths too. Thus, this parameter can be within a wide range of values and should be
calibrated. Its value should be much greater for soils with high macro pores than for
compact soils; otherwise the water will not go down fast enough within the model
(Schulla & Jasper 1999, 2006).
Generation of interflow and surface runoff from saturated areas
Interflow is generated between soil layers of different hydraulic conductivities or
porosities. However, there must be a sufficient slope, otherwise no interflow but
water logging will occur. In the version 1 of WaSiM-ETH, interflow is simulated
using a conceptual approach. As with the surface runoff, the interflow storage is
filled depending upon the local saturation deficit as:
QSH,in = (Si − SU Z) − SHmax
(5.12)
where QSH,in = Inflow into the interflow storage (for each grid cell one storage)
[mm]
Si
= Actual local saturation deficit [mm]
SU Z
= Storage content of the unsaturated zone (pore volume, which is
not accessible by plant roots down to the saturated zone) [mm]
SHmax = Maximum content of the interflow storage [mm], (a model parameter)
When the interflow storage is completely filled which means also that the unsaturated zone is filled too, and hence there is no unsaturated zone at all, only then
the saturation excess-surface runoff, Qsurf,sat , is generated. The original Topmodel
which has only one fast runoff component is obtained when SHmax = 0 mm.
The total surface runoff, Qsurf , is then the sum of all the possible three components:
Qsurf,I from infiltration excess, Qsurf,S from snow melt and Qsurf,sat from saturated
areas.
Qsurf = Qsurf,I + Qsurf,S + Qsurf,sat
(5.13)
Estimation of capillary rise from the saturated zone
The deficit in soil storage (root zone storage) caused by evaporation can be replaced
by water from the saturated zone and/or from the interflow storage, in order to allow
evaporation with potential rates at places with high groundwater. The first re-flow
is taken from the interflow storage proportional to its filling, Qrück , and then the
capillary rise, Qkap , will take water from the saturated zone until the evaporation
losses are refilled. A hydraulic contact between the root zone and the saturated zone
is required for this flow to take place. Two assumptions are made here;
(i) there is no capillary fringe above the groundwater and whether the capillary
rise will take place depends only on the saturation deficit compared to the root
zone capacity.
80
5.2. Distributed watershed modeling of surface runoff with WaSiM-ETH
(ii) the extraction of water by evaporation is done using an unique intensity for the
entire soil profile, thus avoiding a subdivision of the soil into layers.
A parameter rk is used to scale the saturation deficit to root zone depth while quantifying the re-flow into the soil storage. This accounts to the fact that modeled
groundwater table as given by the saturation deficit doesn’t fit well with the real
groundwater table as observed in the catchment. The reflows are estimated as:
Qrück = (ET R − Qkap ) ·
Si
= 1−
rk · ne · zw
Qkap
where Qrück
Qkap
ET R
SH
SHmax
S
rk
ne
zw
=
=
=
=
=
=
=
=
=
SH
· rk
SHmax
(5.14)
· ET R
(5.15)
Re-flow from the interflow storage into the soil storage [mm]
Capillary rise from groundwater [mm]
Evaporation withdrawal from the soil [mm]
Content of the interflow storage [mm]
Maximum content of the interflow storage [mm]
Local saturation deficit [mm]
Scaling parameter [ - ]
Drainable porosity [ - ]
Root depth [mm]
There will be no capillary rise for cells with Si > rk · ne · zw
Estimating baseflow
Based on the assumption that transmissivity profile is an exponential function of
saturation deficit, the base flow to the stream is calculated as:
QB = Tkorr · e−r · e−Sm /m
(5.16)
where QB
= Base flow [mm/time step]
Tkorr = Scaling factor for transmissivities as well as for scale dependent
shifts in the distribution function of the topographic index [ - ]
γ
= Mean topographic index of the (sub-) catchment [ - ]
Sm
= Mean saturation deficit of the (sub-) basin [mm]
m
= Recession parameter [mm]
Flow concentration within the sub-basin and discharge routing
The base flow is generated as an average value for an entire sub-basin. However,
the interflow and surface runoff generated for each grid cell is routed to sub-basin
outlet using subdivision of the basin into flow time zones (zones of equal flow times for
surface runoff to reach the sub-basin outlet), which is calculated using a preprocessor,
TANALYS. For considering retention, a single linear storage approach is applied to
the surface runoff in the last flow time zone, using a storage constant kD :
81
5. Physically based distributed hydrological modeling for HSA estimation
0
Qsurf,t = Qsurf,t−1 · e−∆t/kD + Qsurf,t · 1 − e−∆t/kD
(5.17)
where Qsurf,t
= Transformed surface runoff in the time step t [mm]
Qsurf,t−1 = Transformed surface runoff in the time step t−1 [mm]
0
Qsurf,t
= Surface runoff in time step t within the lowest flow time zone
[mm]
∆t
= Time step [h]
kD
= Recession constant for surface runoff single linear storage [h]
Translation and retention of interflow is treated accordingly using the single linear
storage concept with the recession constant kH .
WaSiM-ETH does the discharge routing based on a hydraulic calculation of the of
the flow velocities. Discharge routing in the river bed channel is performed by a
kinematic wave approach using different flow velocities for different water levels in
the channel. After the translation of the wave, a single linear storage is applied to the
routed discharge accounting for diffusion and retention. Then the discharges from
different subbasins are superposed.
5.3 Setup of WaSiM-ETH for Rems catchment
As WaSiM-ETH has modular structure, it allows choosing different modeling approaches for the single hydrological processes according to the available amount and
quality of data and the modeling purpose. The modeling purpose here is to obtain
the temporally varying spatially distributed Hydrological Sensitive Areas (HSAs) in
the selected catchment (Rems) and this is identified by the continuous simulation of
spatially distributed surface runoff using the WaSiM-ETH model. The setting up of
WaSiM-ETH for Rems catchment depends on the data required by the model and
the data available for the catchment. The needed input data to run WaSiM- ETH
can be divided into two categories as shown in Table 5.1.
Table 5.1: Necessary input data and derivatives for WaSiM-ETH version 1
Input Data
Spatial Data [Grids]
Temporal Data [Time series]
Primary data
DEM
Land use
Soil texture
Meteorological
Hydrological
Derivatives
▪ Slope
▪ Albedo
▪ Available field
▪ Precipitation
▪ (Sub-) basins
▪ Exposition
▪ Leaf Area Index
▪ Watersheds
(LAI)
▪ Stream links_ ▪ Vegetation
orders
▪ Flow times
▪ Routing
parameters
82
capacity
▪ Saturated hydraulic
conductivity
coverage degree ▪ Fillable porosity
▪ Root depth
▪ Temperature
▪ Global radiation
▪ Relative sunshine
duration
▪ Soil topographic index ▪ Wind speed
▪ Suction head
▪ Relative humidity
runoff
5.3. Setup of WaSiM-ETH for Rems catchment
Several secondary data grids as required for the modeling are derived from the primary data grids: the digital elevation model (DEM), land use information and soil
type information. The grids derived from topography (DEM) and soil are time invariant while that from land use are in respect to yearly phenology and hence are
time variants. Time series of the meteorological data are required as station data
for whole simulation period. However, the discharge data are required not as input
to the model but for calibration and performance evaluation of the model. For the
application of WaSiM-ETH in Rems catchment, the available data is described in
Chapter 3. The setting up of the model is described below.
Spatial and temporal resolution
Modeling with WaSiM-ETH challenges the available computing power with increasing spatial and temporal resolution. Therefore the chosen resolution should be fine
enough to deliver reasonable results and coarse enough to allow for large number of
runs. For the distributed hydrological modeling here, the Rems catchment domain
is spatially discretized into regularly spaced horizontal grids of 100 × 100 m size. As
restricted to the available meteorological and hydrological data, which are only in
daily resolution, the simulation is carried out in the daily time step for the period
of 1990 to 2005. Further, based on the available flow gauges, the catchment is subdivided into four subcathments (Fig. 3.9). The DEM, land use (1993) and soil grid
for the Rems catchment in 100 m spatial resolution is shown in Fig. 3.3, 3.5 (left)
and 3.7 (left) respectively.
Pre-processing of spatial data grids
The DEM is one of the most important data set required for the modeling. It is used
with a preprocessing tool, TANALYS (Terrain Analysis) to derive number of data
sets of hydrologic interests (Table 5.1). The tool TANALYS performs a complex
analysis of the DEM and in a series of steps, the data sets as shown in Fig. 5.1 are
generated. At first, artifacts like sinks in DEM are filled interactively. Then, besides
generating the secondary grids like local slope and aspect, it determines automatic
delineation of flow directions, sub-basin structure, flow accumulation, and the river
network. Flow directions are calculated by the steepest slope of neighboring grid
cells and then flow accumulation is calculated which represents the catchment area
for each grid cell. River network is then extracted by setting a threshold of the flow
accumulation. The flow orders identified according to Strahler are essential to outline artifacts like parallel rivers.
The topographic analysis with TANALYS is governed by a control file which uses all
features of the WaSiM control file. Besides the DEM as input, the global parameter of
roughness, M [m1/3 /s], specific discharge, q [liter/(s.km2 )] and threshold for streams
extraction also have to be specified in this control file. They are used to calculate
drainage structure, geometry of cross sections and discharge routing parameters. For
terrain analysis of Rems catchment, the M value of 25 m1/3 /s, q of 200 liter/s.km2
(in the range of specific medium flood discharge) and stream extraction threshold of
15 is provided. The pre-defined pour points as shown in Fig. 3.9 are also provided
83
5. Physically based distributed hydrological modeling for HSA estimation
to make TANALYS delineate the sub-basins such that each of them is observed by
a flow gauging station at the outlet. The TANALYS is then run.
Figure 5.1: Topographic analysis of a DEM by TANALYS (Schulla & Jasper, 2006)
Only the shaded data sets in Fig. 5.1 are actually needed by the WaSiM-ETH. The
grid containing the (sub-)catchments and the text file containing the routing descriptions are required for the infiltration- and soil module and for the runoff routing. The
slope and aspect are required for the radiation correction and temperature modification. The flow time sums are used for routing surface runoff and interflow. Table 5.2
below shows the basic characteristics of the Rems catchment and its subcatchments
as delineated by TANALYS and Fig. 5.2 shows the flow travel time grid as calculated
for the Rems catchment with the four subcatchments.
Another use of DEM here is to calculate the spatially distributed topographic index
which is the basis of soil module in WaSiM-ETH version 1. The flow accumulation
calculated by TANALYS from DEM is supplied along with the local transmissivity
(based on soil data) to another preprocessing tool, TOPOFACT, which calculates
the topographic index based on Equation 5.5. The result which describes the spatial
variability of the building of saturated areas in the Rems catchment is shown in Fig.
5.3 which shows the variation from 10 to 24. The locations with higher topographic
index tend to saturate quickly which is either caused by a larger draining area and/or
a larger gradient of the gravitational force.
With the another primary grid- the land use grid, regular grids of tabulated parameters like albedo, surface resistance, LAI, effective vegetation height, and vegetation
coverage degree, as well as root depth values are generated. The tabulated parameters are obtained from Schulla & Jasper (1999, 2006). Except for albedo, WaSiM-
84
5.3. Setup of WaSiM-ETH for Rems catchment
Table 5.2: Basic characteristics of Rems catchment and its subcatchments
Catch/Gauge
1
Catch/Gauge
2
Catch/Gauge
3
Catch/Gauge
4
Whole
catch.
SchwäbischGmünd
Haubersbronn
Schorndorf
Neustadt
Rems
Basin size [km2 ]
Drainage area [km2 ]
Min. basin elevation [m]
Max. basin elevation [m]
Mean basin elevation [m]
Max slope [deg.]
Mean slope [deg.]
Flow length [km]
92
92
331
768
494
31.34
6.37
23.7
76
76
258
578
410
26.61
7.61
23.5
246
414
246
796
401
34.37
7.27
52.3
149
563
231
531
334
24.56
6.26
71.5
563
563
231
796
400
34.37
6.92
71.5
Mean annual rainfall [mm]
Mean annual temperature [◦ C]
Mean annual flow [m3 /s]
1117
8.6
1.15
1050
9.3
0.91
1076
9.4
5.14
913
10.2
6.54
1036
9.5
6.54
Characteristics
Name
N
5
0
5
km
#
Y
#
Y
#
Y
1h
#
Y
2h
3h
4h
5h
6h
7h
8h
9h
10h
11h
Figure 5.2: Flow travel time grid for the river gauge network of Rems catchment
Topographic Wetness index [TWI]
10 - 12
N
12 - 13
13 - 15
15 - 16
16 - 18
18 - 20
20 - 21
21 - 23
4
0
4
Kilometers
23 - 24
Figure 5.3: Spatially distributed topographic wetness index calculated for Rems catchment
85
5. Physically based distributed hydrological modeling for HSA estimation
ETH allows to consider the phenological development within a year by introducing
seasons. The tabulated parameters corresponding to the land use category of the
Rems catchment is shown in Table 5.3 which is supplied to the WaSiM control file.
The four seasons of the Europe is categorized by the Julian days as shown in the table.
Similarly, the soil texture grids are parameterized with a soil type table that describes
each grid cell with a parameter data set according to the grid classification. With
the soil grid, regular grids of tabulated parameters, as required by the WaSiM-ETH
version 1, namely; available field capacity, maximum available water content, saturated hydraulic conductivity and suction head at the wetting front are generated.
The tabulated parameters (Schulla & Jasper 1999, 2006) corresponding to the soil
type category of the Rems catchment which is supplied to the WaSiM control file is
shown in Table 5.4.
Pre-processing of temporal data series
The temporal data series include the meteorological and hydrological data (Table
5.1), whose availability in Rems catchment is described in Chapter 3. Temporal data
at a daily time step consisting of following five meteorological inputs is used in this
study for the modeling.
p
p
p
p
p
Precipitation [mm]
Temperature [◦ C]
Vapor pressure [mbar]
Relative sunshine duration [hr/hr]
Wind speed [m/s]
The spatial distribution of the gauging stations measuring these variables in the
Rems catchment is shown in Fig. 3.6 (left). The well representative network of 37
precipitation measuring stations has been used in this study out of which 10 stations
have the records for other meteorological data. In total, 8 stations are inside catchment and rests are not farther than 40 km from the centre of catchment (Fig. 3.6
(left)). This dense representation has avoided the use of anisotropy during interpolation of the meteorological variables in WaSiM-ETH. Pecipitation, temperature and
vapor pressure time series are used as they are observed. The required relative sunshine duration is calculated from the observed absolute sunshine duration by using a
pre-processing tool, SONNEREL which requires, in addition, the parameters for geographic location of the catchment, time steps and for time shift for the calculation.
After validation of all the data, the time series of each meteorological input data are
tabulated following the WaSiM-input format on a daily basis for the period of 1990
to 2005. The interpolation of point meteorological data from the gauging stations
to spatial grids is to be carried out within WaSiM-ETH. For the use of ’Altitude
Dependent Regression (ADR)’ in the interpolation of the observed meteorological
variables, the regression parameters (altitude dependent gradients) changing at each
time step also have to be supplied to the model. This time series is prepared by using
another pre-processing tool, REGR, which produces the binary output file directly
useable by WaSiM-ETH.
86
Landuse
Water
Agriculture
Dense_settlements
Loose_settlements
Horticulture
Pine_forest
Decidious_forest
Mixed_forest
Bushes
Grass
Naked_soil
Loose_forest
Wetland
Code
1
2
3
4
5
6
7
8
9
10
11
12
13
0.07
0.15
0.12
0.25
0.2
0.1
0.13
0.08
0.25
0.2
0.23
0.25
0.07
Albedo
[−]
80
20
2
3
75
20
80
75
90
80
90
75
70
85
4
65
70
70
75
65
70
85
90
75
20
5
50
50
60
65
55
60
65
75
65
20
55
50
60
65
55
60
65
75
65
20
6
55
50
60
65
55
60
65
75
65
20
7
55
55
60
65
55
60
65
80
65
20
8
60
55
60
65
55
60
75
80
65
20
9
10
70
70
80
85
75
80
85
90
75
20
11
12
110
110
1
100 110
100 110
90
20
80
110
90
80
90
90
80
90
110
110
110
100 100 110
80
100 100 110
95
95
90
20
20
90
20
90
20
85
20
70
20
60
20
60
20
60
20
60
20
60
20
80
20
90
20
90
110
110
250 250 250 250 250 250 250 250 250 250 250 250 110
90
80
90
100 100 95
80
100 100 90
100 100 95
100 100 95
80
20
1
Monthly surface resistance [s/m]
150
150
150
150
150
150
150
150
150
150
150
150
150
2
250
250
250
250
250
250
250
250
250
250
250
250
250
3
Julian days
4
280
280
280
280
280
280
280
280
280
280
280
255
280
1
4
1
2
3
2
0.5
8
0.5
1
1
1
1
1
1
6
1
4
5
10
8
12
5
1
1
5
1
2
1
6
1
4
5
10
8
12
5
1
1
3
1
3
LAI [−]
1
4
1
2
3
2
0.5
8
0.5
1
1
1
1
4
0.01
4
0.05
0.15
1.5
3
0.3
10
0.4
10
10
0.05
0.01
1
0.01
6
0.05
0.4
2.5
10
10
10
3
10
10
0.5
0.01
2
0.01
6
0.05
0.3
2.5
10
10
10
3
10
10
0.2
0.01
3
Eff. veg. ht.
(m2 /m2 )
Table 5.3: Input parameters to derive land use dependent secondary grids for Rems
0.01
4
0.05
0.15
1.5
3
0.3
10
0.4
10
10
0.05
0.01
4
0.8
0.7
0.8
0.1
2
0.8
0.7
0.7
0.1
3
0.5
0.4
0.3
0.1
4
0.95 0.95 0.9
0.95 0.95 0.6
0.95 0.95 0.8
0.8
0.8
0.8
0.1
0.1
0.1
0.1
0.85 0.85 0.85 0.85
0.8
0.95 0.95 0.95 0.95
0.9
0.6
0.8
0.95 0.95 0.95 0.95
0.75 0.75 0.75 0.75
0.5
0.4
0.3
0.1
1
Veg. coverage
(m2 /m2 )
2
3
4
0.3
0.05
1
0.1
0.4
0.5
1.2
1.3
1.1
0.8
0.4
1
0.1
0.4
0.5
1.2
1.3
1.1
0.8
0.4
1
0.1
0.4
0.5
1.2
1.3
1.1
0.8
0.4
0.01 0.01 0.01 0.01
1
0.1
0.4
0.5
1.2
1.3
1.1
0.8
0.4
0.25 0.25 0.25 0.25
0.05 0.4
0.01 0.01 0.01 0.01
1
Root depth [m]
5.3. Setup of WaSiM-ETH for Rems catchment
87
5. Physically based distributed hydrological modeling for HSA estimation
Table 5.4: Input parameters to derive soil type dependent secondary grids for Rems
Code
1
2
3
4
5
6
7
Soil type
Available
Field capacity
Max. available
water content
Sat. hydraulic
conductivity
Suction at
wetting front
[Vol. %]
[Vol. %]
[m/s]
[mm]
22.58
12.90
10.91
29.12
21.24
13.35
14 .00
38.3
35.2
37.3
31.2
31.5
29.0
15.0
1.25E-06
2.89E-06
4.05E-05
5.56E-07
7.22E-07
3.64E-06
1.00E-09
383
352
373
312
315
290
50
Silty loam
Loam
Loamy sand
Clay
Clay loam
Sandy clay loam
Settlements rock
Further input time series include the observed discharges at river gauges. These data
are required in order to calibrate the model and to estimate the model efficiency. Observed daily discharge series (m3 /s) for the four gauges in the Rems catchment (Fig.
3.9) are checked and tabulated in the WaSiM-input format for the same period of
1990 to 2005. It is then converted to mm/day, as required by WaSiM, by using
another pre-processing tool, QtoSPEND.
The Table 5.5 below summarizes the data of Rems catchment that have been used
in the pre-processing for the parameterization of WaSiM-ETH.
Table 5.5: Input data from Rems catchment for the parameterization of WaSiM-ETH
Data
Meteorological
Data
Precipitation [mm]
Temperature [◦ C]
Vapor pressure [m bar]
Relative sunshine
duration [hr/hr]
Wind Speed [m/s]
Geographical
Data
Digital Elevation
model [m]
Land use [-]
Soil Type [-]
Hydrological
Data
Discharge [m3 /s]
Temporal
Resolution
Spatial
Resolution
1 day
1 day
1 day
-
1 day
-
1 day
-
-
100 m
-
100 m
100 m
1 day
-
Acquisition
Number of
Gauges/ Scale
Stations
measurement
37
10
10
4
10
Satellite image and
maps analysis
Gauge
measurements
1:30,000
1:75,000
1:200,000
4
Processing
WASIM-ETH, when run with all the sub-modules, provides lots of output data in
different format. Possible output data format are binary grids, ASCII tables or stacks
showing modeled soil moisture, precipitation, the groundwater level, evapotranspiration, runoff, the volume of a reservoir (if applied) etc. The input and output data
are stored in two different directories which are defined in the WaSiM Control File.
The modules used in our application in Rems catchment is shown in Table 5.6.
88
5.3. Setup of WaSiM-ETH for Rems catchment
Table 5.6: Modules of WaSiM-ETH used in the Rems catchment
Precipitation correction
Temperature modification
Evaporation model
Interception model
Soil model
Unsaturated zone model
Solute transport model
:
:
:
:
:
:
:
yes
yes
yes
yes
yes
no
no
Radiation correction
Input data interpolation
Snow and glacier model
Infiltration model
Groundwater model
Irrigation model
Discharge routing
:
:
:
:
:
:
:
yes
yes
yes
yes
no
no
yes
Governed by the prepared control file, the WaSiM-ETH is run with the pre-processed
input data. The altitude dependent regression (ADR) method combined with an inverse distance weighting (IDW) routine is used for the spatial interpolation of the five
meteorological input data. The weightage given for IDW are 85% for precipitation,
30% for temperature and wind speed and 50% for relative sunshine duration and
vapor pressure. The catchment average of interpolated precipitation as compared to
stations averaged observed precipitation is shown on annual basis in Fig. 5.4.
1400
Average of Rain Gauges
Precipitation [mm]
1200
Average of Interpolation
(IDW + ADR)
1000
800
600
400
200
19
90
19
91
19
92
19
93
19
94
19
95
19
96
19
97
19
98
19
99
20
00
20
01
20
02
20
03
20
04
20
05
0
Year
Figure 5.4: Spatial average annual precipitation in Rems catchment
Precipitation correction is carried out separately for rain and snow (with threshold
temperature) using the wind speed as a parameter. Topography dependent adjustment of radiation and temperature is done to account for shadowing effect. The
potential evapotranspiration is calculated using Penman-Monteith approach (Monteith 1975, Brutsaert 1982) approach. The real evapotranspiration is calculated using
a reduction function of potential evapotranspiration such that the real evaporation is
reduced to below the potential evaporation if the content of the soil moisture storage
drops below a specified level (0.6 after Menzel 1997). Modeling of snow accumula-
89
5. Physically based distributed hydrological modeling for HSA estimation
tion and snowmelt is done by using a temperature-index-approach. A simple bucket
approach is used for interception calculation, with a capacity depending on the leaf
area index, the vegetation coverage degree, and the maximum height of water at the
leaves. The interception is calculated after the snow model, so that snow melt also
flows into interception storage along with the rain water. The simulation of runoff
generation from infiltration excess (Green and Ampt) and saturated areas (TOPMODEL), the soil water balance within the vadose zone (extended TOPMODEL)
and the routing of generated discharges (flow times and Kinematic wave) are accomplished by the infiltration and soil modules which follow the approaches as described
in Section 5.2.
5.4 Calibration and Simulation: Procedures, Results and
Discussions
Although the WaSiM-ETH claims to be the physically based, there are certain free
model parameters which have only a low physical background or which cannot be
easily obtained by measurements. Therefore, the WaSiM-ETH needs calibration for
the estimation of those parameters before their results can be used for the intended
purpose. The reliability of model results depends on the robustness of the model
parameters estimated through calibration. The adjustable parameters of the WaSiMETH, adopted calibration techniques in this study, the encountered challenges and
the simulation are described in this section along with the results.
5.4.1 Free model parameters and their influences
In the pre-processing stage, strong emphasis was made on the parameters for the soil
model. The most important component of WaSiM-ETH for the model behaviour is
the soil module which plays the central role. Therefore all the free model parameters
related to the soil model need be accurately calibrated as far as possible. The other
adjustable parameters, for example, maximum water layer thickness on leaves etc.,
can be safely taken from literature, previous studies and knowledge of study area.
The soil model of the WaSiM-ETH version 1 has nine parameters and two initial
conditions that practically need calibration. These eleven adjustable parameters are
listed in Table 5.7. The use of these parameters in the model can be seen through
the Equations 5.1 to 5.17 presented above in Section 5.2.
To understand the effect of these parameters in the modeling and to know the feasible space within which they can vary is quite necessary before they are used for
calibration.
m and Tkorr
The first two parameters- the recession parameter m and transmissivity correction
factor Tkorr have been identified as the most sensitive (Schulla & Jasper 1999, 2006)
and are strongly dependent on each other (Equation 5.16). Due to the interaction
90
5.4. Calibration and Simulation: Procedures, Results and Discussions
Table 5.7: Free model parameters to be estimated from calibration
Symbol
m
Tkorr
Kkorr
kD
SHmax
kH
Pgrenz
:
:
:
:
:
:
:
rk
Cmelt
SU Z0
SD0
:
:
:
:
Name of Parameter
Unit
Recession parameter for base flow
Correction factor for the transmissivity of the soil
Correction factor for vertical percolation
Single reservoir recession constant for surface runoff
Maximum storage capacity of the interflow storage
Single reservoir recession constant for interflow
Precipitation intensity threshold for generating preferential
flow into saturated zone
Scaling of capillary rise/refillig of soil storage from interflow
Fraction of snomelt which is surface runoff
Initial content of the unsaturated zone
Initial saturation deficit
[m]
[-]
[-]
[h]
[mm]
[h]
[mmh−1 ]
[0...1]
[0...1]
[mm]
[-]
it is difficult to interpret. The smaller the m, the more water leaves the soil and
saturation deficit increases fast. But the larger saturation deficit decreases the outflow from the saturated zone. This along with higher recharge rates in winter and
higher evaporation losses in summer leads to high base flow rates in the winter and
low base flow rates in summer. This means, the long term storage effect is small and
the base flow has a larger dynamics. On the other hand, the larger m will result
in considerably more temporal storage of water in the saturated zone by transferring water from the winter into the summer. For estimating the parameter m, it is
recommended to fit some appropriate recession periods (unaffected by high evaporation, snow melt and frozen soils) in an inverted graph (days/mm) of the observed
discharge by a linear regression. The tangent of the slope of this invertedly plotted discharge recession periods gives an estimate of parameter m. However with
modeling interflow too (SHmax > 0), the parameter m usually has to be two to
three times larger and needs calibration, because then the fast runoff components
are handled by the interflow storage and m is responsible for the slower components
(base flow) only. The value of m generally, but not strictly, varies within 0.001 to 0.8.
Tkorr is the scaling factor that affects the base flow generation linearly but it affects
the location of the topographic index distribution function logarithmically (Equations 5.7 & 5.16). So the value for Tkorr varies widely as 10−5 ≤ Tkorr ≤ 10+5 . A
large transmissivity of the soil means considerable base flow even at low groundwater
tables (high deficit) and this leads to a more evenly distributed regime temporally
than a small transmissivity. On the other side, this also leads to a high dynamic of
the groundwater table (or the saturated zone) resulting relatively small floods even
after the heavy precipitation events due to higher recharge. So the Tkorr needs to be
carefully estimated in conjunction with m.
Kkorr
The correction factor Kkorr scales the drainage from the unsaturated zone into the
saturated zone (Equation 5.11). It also allows taking macro pores and other prefer-
91
5. Physically based distributed hydrological modeling for HSA estimation
ential flow paths into account since the hydraulic conductivity of the soil is given for
vertical matrix flow only. It is important in the areas with deep soils having deep
groundwater table where, often a first flood peak is followed by a second flood which
is usually much slower rising and falling but may be even higher than the first peak.
It’s value may vary widely from 1 to 10000 but in most basins, it should be sufficiently
large (eg. 1000) in order to avoid the breakdown of the hydraulic interconnection
between unsaturated and saturated zone. If Kkorr would be too small and Tkorr too
large, the saturation deficit becomes larger and larger whereas the percolation from
the unsaturated zone becomes very, very small due to the exponential recession of
the soil conductivities with increasing saturation deficit. In such cases the water will
fill up the soil and the unsaturated zone and all rain will become surface runoff.
kD and kH
kD is the single reservoir constant for surface runoff and kH is the single reservoir
constant for interflow. They determine water travel times and effects of retardation
of both components. The smaller the values, the narrower and steeper is the flood
peak. While kD applies to the earlier segment of the run-off curve produced by direct
run-off, the interflow storage coefficient kH applies to the later and flatter part of the
falling run-off curve. The approximate or starting value of recession constants for
surface runoff and interflow can be estimated using observed hydrographs. They can
be derived from a semi-logarithmic plot of measured discharge against time as the
negative inverse slope of the falling branch of a flood peak. As the slope of the run-off
curve is less steep for the part contributed by interflow, kD is always smaller than kH .
SHmax
SHmax helps to balance the components between surface runoff, interflow and base
flow (Equation 5.12). Setting the parameter SHmax to values greater than zero activates the interflow and this increases the value of m which then account only for base
flow. A large value of SHmax leads to an increased interflow. The value of SHmax
can be estimated either by analyzing observed hydrographs or by taking values from
similar basins. Current model applications show, that an interflow storage of 10 to
40 mm may be appropriate (Schulla & Jasper 1999, 2006).
Pgrenz and rk
Both parameters Pgrenz and rk influence the filling and emptying of the plant available soil water storage, the saturated zone and the interflow storage. However, they
have opposite effects on soil storage (Equations 5.10, 5.14 and 5.15). A moist basin
will allow high reflow and capillary rise rates whereas a dry basin will virtually not
allow any recharge at all. Therefore these parameters are quite sensitive if the model
is applied to a rather dry catchment with much higher evaporation than runoff. The
starting value of Pgrenz should be large enough (around 10 mm/h) in order to avoid
any fast macro pore drainage otherwise all precipitation infiltrates into the root zone
soil storage. The parameter rk , which scales the rate of capillary rise, varies between
0 and 1.
92
5.4. Calibration and Simulation: Procedures, Results and Discussions
cmelt
The parameter cmelt affects especially the peaks of melt floods. A large cmelt value
means high surface runoff fractions on snow melt and thus large peak flows in the
melt season, but it means also a smaller storage effect of melt water in the soil in
winter and spring. It is, thus, useful to influence the annual storage behavior. The
optimum value for cmelt must be between 0 and 1, often it can be set to 0.1-0.2 in
flat regions or to 0.2-0.35 in mountainous regions (Schulla & Jasper 1999, 2006).
SU Z0 and SD0
The initial conditions SU Z0 and SD0 give information about the system status at
the beginning of the calibration period. Large initial saturation deficit SD0 with
large Kkorr will lead to a kind of hydraulic “stop bar” as a result of the exponential
function (Equation 5.11). No water will be able to percolate and all precipitation
will leave the cell as either evaporation or surface runoff. It is therefore safe to set
Kkorr at the beginning to a large number (e.g. 1000) and to set SD0 to a rather
small number (≥ 0). However a sufficient long time offset before the calibration
period helps to stabilize the model and provides reasonable initial conditions for the
calibration.
5.4.2 Multi-criteria assessment of model performance
Incorporation of observed runoff in the modeling process enables evaluation of the
quality of the model performance. For the performance evaluation of the watershed
models, Leagates & McCabe (1999) recommended to include at least one dimensionless statistic and one absolute error index statistic with additional information such
as the standard deviation of measured data, and to include at least one graphical
technique as well. An extensive review on published literature related to calibration,
validation and application of watershed models conducted recently by Moriasi et al.
(2007) suggest that three quantitative statistics, Nash-Sutcliffe efficiency (NS), percent bias (PBIAS), and ratio of the root mean square error to the standard deviation
of measured data (RSR), in addition to the graphical techniques (matching hydrographs), be used in model evaluation.
If n is the total records (time steps) in the series, Yiobs and Yisim are the observed
and simulated flow respectively in ith time step and Y mean is the average observed
flow of the series, then the three performance statistics can be defined as follows.
Nash-Sutcliffe efficiency (NS): NS is a normalized statistic that determines relative magnitude of residual variance (“noise”) compared to the measured data variance
(“information”) (Nash & Sutcliffe 1970). It varies from ∞ to 1 (best) and is computed
as:
 n

X
Yiobs − Yisim
2


 i=1



NS = 1 −  n 2 
X
obs
mean 
Yi − Y
(5.18)
i=1
93
5. Physically based distributed hydrological modeling for HSA estimation
This statistic is greatly influenced by the peak values. Therefore, to account for the
simulation of low flows the NS should be calculated also in logarithmic form as:

n X

 i=1
log N S = 1 − 
n X

2 



2 
mean 
log Yiobs − log Yisim
log Yiobs
− log Y
(5.19)
i=1
Percent bias (PBIAS): PBIAS measures the average tendency of the simulated
data to be larger or smaller than their observed counterparts (Gupta et al. 1999).
The optimal value of PBIAS is 0.0, with low-magnitude values indicating accurate
model simulation. Positive values indicate model underestimation bias, and negative
values indicate model overestimation bias. It is computed as:
 n 
X
obs
sim
Yi − Yi
× 100

 i=1


P BIAS = 
n


X


obs
(5.20)
Yi
i=1
RMSE-observations standard deviation ratio (RSR): Singh et al. (2004) have
published a guideline to qualify what is considered a low RMSE based on the standard deviation of observations. Based on this recommendation, a model evaluation
statistic, named the RMSE-observations standard deviation ratio (RSR), was developed. RSR standardizes RMSE using the observations standard deviation, and
it combines both an error index and the additional information recommended by
Leagates & McCabe (1999). RSR is calculated as the ratio of the RMSE and standard deviation of measured data and it varies from the optimal value of 0 to a large
positive value.
 v

uX
2
u n obs
 t
Yi − Yisim 




RM SE
i=1


P SR =
= v
n ST DVobs  u
2 

X
u
t
Y obs − Y mean 
i
(5.21)
i
i=1
The general performance ratings for these recommended statistics for monthly time
step (lesser strict for lesser time step) is given by Moriasi et al. (2007) and adopted
in this study as shown in Table 5.8.
5.4.3 Calibration procedures and Simulation
The simulation period considered for this study to determine hydrologically sensitive
area (HSA) is from 1990 to 2005. After the careful data analysis the year 1993 is
94
5.4. Calibration and Simulation: Procedures, Results and Discussions
Table 5.8: Model performance ratings based on NS, PBIAS and RSR
Performance Rating
NS [ - ]
PBIAS [%]
RSR [ - ]
Very good
0.75 < N S ≤ 1.00
P BIAS < ±10
0.00 ≤ RSR ≤ 0.50
Good
0.65 < N S ≤ 0.75
±10 ≤ P BIAS < ±15
0.50 < RSR ≤ 0.60
Satisfactory
0.50 < N S ≤ 0.65
±15P BIAS < ±25
0.60 < RSR ≤ 0.70
N S ≤ 0.50
P BIAS ≥ ±25
RSR > 0.70
Unsatisfactory
found to be representative for this period. Also the land use grid (Fig. 3.5 - left)
available is from the LANDSAT satellite image of the year 1993. So 1993 is considered as the calibration year with the year 1992 as spin-up period to stabilize the
initial conditions. All the input data required for the calibration and simulation with
the WaSiM-ETH in Rems catchment is described in section 5.3 and used accordingly.
The estimation of the model parameters can be done within a plausible parameter
space using the manual trial and error procedure, but this can be very time consuming and quite tedious; more so when the number of parameters to be calibrated is
quite high and will be more complicated when the inter-dependency between the parameters exist. The parameter estimation approaches using regionalization concepts
(for e.g. as presented by Hundecha & Bárdossy 2004) can not be applied here due
to the comparatively small number of subcatchments in this study. However, when
discharge measurements for a sufficient time period exist, as is in our case, an inverse
modeling approach can be used for an objective estimation of the parameters in more
promising way. Inverse hydrological modeling means that a set of model parameters is estimated for which the model generated river runoff is as close as possible
to the observed runoff. This approach use the model-independent algorithms based
on mathematical optimization theory. In our work the three different non-linear
optimization algorithms are used. It was not prior intention to use the different
algorithms and compare them, but the deficiencies and the challenges encountered
while using a widely used algorithm prompt to research for another algorithm and
finally land up trying with a newly developed algorithm. The three algorithms are
described below briefly in the respective order of their use in this work. The obtained
results are also presented along with.
5.4.3.1 Gauss-Marquardt-Levenberg method
The Gauss-Marquardt-Levenberg optimization method has the advantage that it
can generally estimate parameters using fewer model runs than any other estimation
method for nonlinear models. This algorithm is employed in a parameter estimation
tool, commonly called as PEST (Doherty 2002, 2007), which is used in this study for
the parameters estimation.
PEST is a model independent nonlinear parameter estimation tool which aims to
match the model simulation with an observed set of data by minimizing the weighted
sum of squared differences between the two. For linear models, parameter estimation
can be achieved in one step but for non-linear problems like with WaSiM-ETH, the
95
5. Physically based distributed hydrological modeling for HSA estimation
Parameter 2
optimization problem is iteratively solved by linearizing the relationship between a
model’s output and its parameters. At the beginning of each iteration the relationship
between model parameters and observations is linearized by formulating it as a Taylor
expansion about the currently best parameter set; hence the partial derivatives of
each model output with respect to every parameter is calculated at every iteration.
The central difference operator is used in our case for calculating the derivatives.
This linearized problem is then solved
for a better parameter set (by using a
weighted least square method). The
updated parameter vector is tested by
Initial parameter
yet another model-run, hopefully resultestimates
ing in better model-output which then
can be compared to that of the previous time step and matched to the observations again. Thus, PEST uses a
”hill-climbing” technique following the
Contours of
steepest gradient of the objective funcequal objective
function value
tion starting at a specified initial point
in the parameter space. An optimum
Parameter 1
value is reached, when the gradient becomes small enough with respect to a Figure 5.5: Objective function approaching
certain tolerance limit. The method is
its optimum in steepest gradient
schematically shown in Fig. 5.5 considmethod
ering two parameters as an example.
The Gauss-Marquardt-Levenberg method is computationally efficient and the success
of the algorithm depends largely upon initial parameter values supplied as a priori
information. The initial parameter values and the feasible ranges of the parameters
are provided as discussed in Section 5.4.1. Then as said earlier; with the year 1992
as warm-up period for stabilization, the iterative optimization is carried out for the
year 1993 using the input data as described in Section 5.3. The land use used is
also of the year 1993. The four subcatchments (Fig. 3.9), which are gauged at their
outlet, are calibrated with their independent parameter sets simultaneously. To avoid
propagation of errors from a sub-catchment to its downstream sub-catchment (Fig.
3.9), observed flows instead of modeled flows at upstream gauge(s) are used as inflow
to the downstream sub-catchment(s). The optimization here basically solves the
following minimization problem.
min ·
n h
X
i2
Yiobs − Yisim (xt ; P )
(5.22)
i=1
where n is total number of time steps in the series (here 366), Yiobs and Yisim are
observed and simulated flow respectively in it h time step (the difference of which
is the model residual error t ), xt is a vector of inputs (such as rainfall and any
exogenous variables such as evaporation, snow, etc.) and P is a parameter vector
about which inference is sought. The use of this objective function, which is to be
minimized for parameter estimation, implies certain assumptions about the residuals
96
5.4. Calibration and Simulation: Procedures, Results and Discussions
t (Clarke 1973, Xu 2001) that need to be tested and verified:
(i) that t have zero mean and constant variance σ2 (Homoscedasticity):
E(t ) = 0
and
E(2t ) = σ2
(5.23)
(ii) that the t are mutually uncorrelated (Independence):
E(t , t−k ) = 0
for all k 6= 0
(5.24)
The results of the calibration of year 1993 with Gauss-Marquardt-Levenberg method
and then simulation of the 16 years (1990-2005) are described below. The optimized
parameter values are shown in Table 5.9.
Table 5.9: The parameter values calibrated with PEST for the year 1993
Subbasin codes
Recession parameter m [m]
Scaling factor Tkorr [ - ]
Scaling facor Kkorr [ - ]
Recession constant surf. Runoff KD [h]
Maximum interflow storage SHmax [mm]
Recession constant interflow KH [h]
Initial content of unsaturated zone SU Z0 [mm]
Initial saturation deficit SD0 [n*nFK]
Macro pore flow Pgrenz [mm/h]
Scaling of capillary rise rk [0...1]
Fraction on snow melt going into surface runoff cmelt [m]
1
2
3
4
0.017
0.003
3200.1
18.7
43.4
1000.0
0.01
0.51
10.0
0.00
0.92
0.062
0.000
1000.0
28.0
24.7
54.0
0.01
2.25
10.0
0.42
0.04
0.027
0.016
998.8
48.1
20.0
123.6
0.01
0.34
9.6
1.00
0.77
0.014
0.211
1000.0
26.7
20.0
32.9
0.00
0.51
10.0
0.30
0.15
The residuals (difference between simulated and observed discharges) during the
calibration are analyzed and checked for the homoscedasticity and independency as
shown in Fig. 5.6. It can be seen that magnitude of the residuals does not depend
upon magnitude of the flows and that the residuals are not auto-correlated.
The model performance measures (Section 5.4.2) for the simulation period (19902005) are shown on yearly basis in Table 5.10 along with the calibration year 1993.
The figures in red shows very good performance and the blue shows unsatisfactory performance while that in black indicates good/satisfactory performance by the
model based on the ratings given in Table 5.8. This convention of font colour is used
throughout this thesis. The observed and simulated hydrographs at the four gauges
in the calibration year 1993 are compared in Fig. 5.7.
As can be seen, the optimization is completed with very good model performance
ratings (year 1993). The simulated hydrographs are also nicely matching with the observed hydrographs. The performance in subcatchment 3 (Schorndorf) and subcatchment 4 (Neustadt) is quite good throughout the sixteen years, that in subcatchment
2 (Haubersbronn) is acceptable but that of subcatchment 1 (Schwäbisch-Gmünd) is
quite low for most of the years although it is highest during calibration.
97
5. Physically based distributed hydrological modeling for HSA estimation
5
Residual [m3/s]
Gauge 1
Gauge 2
0
-5
0
10
20
30
40
0
10
20
30
40
40
Gauge 4
Gauge 3
Residual [m3/s]
20
0
-20
-40
0
20
40
60
80
100 0
20
40
Sim. flow [m3/s]
60
80
100
Sim. flow [m3/s]
Autocorrelation coeff.
1.2
Gauge 1
Gauge 2
Gauge 3
Gauge 4
0.8
0.4
0.0
-0.4
Autocorrelation coeff.
1.2
0.8
0.4
0.0
-0.4
0.00
2.00
4.00
6.00
Time lags [days]
8.00
10.00
12.00 0.00
2.00
4.00
6.00
8.00
10.00
12.00
Time lags [days]
Figure 5.6: Check for homoscedasticity (top) and independency (bottom) of residuals of calibration
with PEST
98
5.4. Calibration and Simulation: Procedures, Results and Discussions
Table 5.10: The yearly model performance with parameter values calibrated with PEST for the
year 1993 with land use of 1993
Linear NS
Year
Log NS
PBIAS
RSR
Gauge Gauge Gauge Gauge Gauge Gauge Gauge Gauge Gauge Gauge Gauge Gauge Gauge Gauge Gauge Gauge
1
2
3
4
1
2
3
4
1
2
3
4
1
2
3
4
1990
0.66
0.39
0.78
0.84
0.47
0.22
-0.02
0.68 -40.02 -25.31 26.78 11.64
0.59
0.77
0.46
0.40
1991
0.40
0.50
0.65
0.68
0.65
0.60
0.12
0.60
-6.84 10.74 10.85
0.78
0.70
0.59
0.57
1992
0.40
0.57
0.54
0.74
0.67
0.57
0.56
0.71 -39.20 5.07 -13.28 -1.63
0.78
0.66
0.68
0.51
1993
(calib.)
0.90
0.77
0.85
0.85
0.69
0.56
0.50
0.77
0.32
0.48
0.39
0.39
1994
0.64
0.73
0.80
0.94
0.57
0.71
0.60
0.74 -41.56 -18.18 3.98
6.32
0.60
0.51
0.45
0.25
1995
-0.44
0.67
0.63
0.74
0.44
0.62
0.52
0.73 -60.70 4.00 -10.87 -1.37
1.20
0.57
0.61
0.50
1996
-0.08
0.33
0.76
0.88
0.40
0.01
0.38
0.60 -30.15 30.54
2.86
4.83
1.04
0.82
0.49
0.34
1997
0.14
0.63
0.65
0.79
0.60
0.16
0.24
0.60 -37.13 19.58
3.58
4.92
0.93
0.61
0.59
0.46
1998
0.26
0.57
0.58
0.84
0.58
0.71
0.37
0.73 -64.88 8.41 -11.15 -6.40
0.86
0.66
0.65
0.40
1999
0.31
0.63
0.80
0.90
0.59
0.65
0.60
0.81 -39.73 1.33
-3.46
-2.77
0.84
0.61
0.45
0.31
2000
0.54
0.79
0.86
0.88
0.64
0.57
0.47
0.75 -38.64 4.85
2.19
0.07
0.68
0.45
0.38
0.34
2001
0.31
0.64
0.83
0.80
0.64
0.79
0.46
0.78 -49.61 7.81
-8.24 -13.06 0.81
0.59
0.39
0.43
2002
0.50
0.67
0.90
0.91
0.34
0.56
0.61
0.88 -37.45 7.40
0.84
-4.83
0.71
0.57
0.32
0.30
2003
0.77
0.86
0.75
0.89
0.81
0.85
-0.02
0.62 -16.87 -3.48
9.18
9.07
0.49
0.38
0.50
0.34
2004 (till
0.29
Nov.)
0.47
0.70
0.80
0.68
0.41
0.50
0.68 -26.02 26.94
0.94
-4.47
0.85
0.73
0.55
0.45
2005 (till
May)
NA
NA
NA
0.89
NA
NA
NA
0.78
NA
NA
-7.86
NA
NA
NA
0.33
Average
0.37
0.61
0.74
0.84
0.58
0.53
0.39
0.72 -34.83 4.76
2.32
1.24
0.77
0.61
0.50
0.40
Discharge [m3/s]
Observed
Simulated
lin. NS: 0.90
log NS: 0.69
NA
9.31
20.72 14.50
Observed
Simulated
lin. NS: 0.77
log NS: 0.56
12
10
20
8
15
6
10
4
5
2
0
0
120
140
100
Discharge [m3/s]
-6.30
14
30
25
5.75
Observed
Simulated
lin. NS: 0.85
log NS: 0.50
Observed
Simulated
lin. NS: 0.85
log NS: 0.77
120
100
80
80
60
60
40
40
20
20
0
1/1/1993
0
2/20/1993
4/11/1993
5/31/1993
7/20/1993
Time [d]
9/8/1993
10/28/1993
12/17/1993
1/1/1993
2/20/1993
4/11/1993
5/31/1993
7/20/1993
9/8/1993
10/28/1993
12/17/1993
Time [d]
Figure 5.7: Simulated and observed hydrographs at the gauges for the calibration year 1993
99
5. Physically based distributed hydrological modeling for HSA estimation
So, before proceeding for calculating HSAs through spatially distributed surface
runoff in the catchment, it is aimed to try for achieving better overall model performance. With that hope, the calibration is redone using the same Gauss-MarquardtLevenberg method now for the year 1996 (the worst performing year) with the same
land use of 1993 and also for the year 2000 but this time using the land use grids of
the year 2000. The change in land use from 1993 to 2000 can be seen in Fig. 3.6.
The re-optimized parameter values in comparison with that achieved before with the
year 1993 is shown in Table 5.11.
Table 5.11: The parameter values calibrated with PEST for the year 1993, 1996 and 2000
Calibration year- 1993
[LU 93]
Subbasin codes
Calibration year- 1996
[LU 93]
Calibration year- 2000
[LU 2000]
1
2
3
4
1
2
3
4
1
2
3
4
0.017
0.062
0.027
0.014
0.128
0.069
0.039
0.027
0.019
0.077
0.035
0.012
Scaling factor Tkorr[-]
0.003
0.000
0.016
0.211
0.000
0.000
0.030
0.059
0.001
0.000
0.000
0.622
Scaling factor Kkorr[-]
3200.1 1000.0 998.8 1000.0
0.6
1000.0
21.3
88.8
7613.3 1010.0 3027.2 1000.0
Recession parameter m [m]
Recession constant surf. Runoff KD[h]
18.7
28.0
48.1
26.7
1.6
32.1
30.6
32.2
34.4
7.2
39.2
Maximum interflow storage SHmax[mm]
43.4
24.7
20.0
20.0
35.3
27.7
22.8
25.0
68.3
56.5
28.0
20.1
Recession constant interflow KH[h]
1000.0
54.0
123.6
32.9
98.6
140.2
173.7
22.5
4226.4
56.1
92.3
169.2
Init. content unsat. Zone SUZo[mm]
0.01
0.01
0.01
0.00
0.00
0.01
0.00
0.00
0.03
0.01
0.01
0.00
Init. satur. deficit SDo[n*nFK]
0.51
2.25
0.34
0.51
5.45
0.02
2.66
3.16
1.07
3.14
0.49
0.65
Macro pore flow Pgrenz[mm/h]
10.0
10.0
9.6
10.0
10.0
10.0
10.0
10.0
10.0
10.0
9.6
10.0
Scaling of capillary rise rk[0...1]
0.00
0.42
1.00
0.30
0.61
0.10
0.51
0.10
0.00
1.00
1.00
0.10
Fraction on snow melt in surface runoff cmelt[0...1]
0.92
0.04
0.77
0.15
0.08
0.30
0.12
0.06
1.00
0.00
1.00
0.15
27.3
It can be seen that the optimized values of the parameters vary widely and randomly
with the change in calibration period and/or land use, although the method is same.
The yearly model performance during the simulation period is shown in Table 5.12
with 1996 calibration (land use 1993) and in Table 5.13 with 2000 calibration (land
use 2000). The yearly model performance exhibit the similar trend despite the different parameter sets. For example, the year 1996 cannot be simulated properly unless
calibration is done for this year itself. This creates interest to analyze, at least briefly,
the 1996 event as compared with others. Table 5.14 lists the annual precipitation
and annual average daily temperature, the main hydrological variables, during the
simulation period (1990-2005). It can be noticed that the total precipitation in 1996
is in the lower region and the mean temperature is the lowest. Further, Fig. 5.8
shows the monthly variation of the daily precipitation and temperature. It shows
that the maximum daily precipitation and temperature of 1996 is lower in every
month than the average of maximum daily precipitation and temperature during
the simulation period (1990-2005). This means the year 1996 represents an extreme
case in the lower side. It gives an indication that the physically-based distributed
WaSiM-ETH model is incapable of simulating such low event. However, as the erosion is affected by the higher extreme events and lesser bothered with the low extreme
events, and also that the use of other different physically-based distributed model
is beyond the scope of this research work, the use of WaSiM-ETH is taken up further.
Further, yearly model performances with the three sets of calibrated parameters are
compared (see Table 5.10, 5.12 and 5.13). The comparison at outlet (Neustadt) with
linear and log NS coefficients is shown in Fig. 5.9. Surprisingly it can be seen that
100
5.4. Calibration and Simulation: Procedures, Results and Discussions
Table 5.12: The yearly model performance with parameter values calibrated with PEST for the
year 1996 with land use of 1993
Linear NS
Year
Log NS
PBIAS
RSR
Gauge Gauge Gauge Gauge Gauge Gauge Gauge Gauge Gauge Gauge Gauge Gauge Gauge Gauge Gauge Gauge
1
2
3
4
1
2
3
4
1
2
3
4
1
2
3
4
1990
0.41
0.35
0.88
0.85
0.32
0.08
0.87
0.83
27.30 -33.20
2.16
-1.26
0.78
0.79
0.37
0.39
1991
0.49
0.51
0.84
0.72
0.36
0.69
0.87
0.83
-13.62 -4.53
0.12
1.34
0.72
0.70
0.40
0.53
1992
0.56
0.55
0.63
0.80
0.41
0.67
0.85
0.88
-7.08
6.49
-14.65 -1.77
0.66
0.67
0.61
0.44
1993
0.55
0.73
0.83
0.85
-0.48
0.63
0.87
0.88
34.37
6.76
1.72
4.59
0.68
0.52
0.41
0.39
1994
0.55
0.76
0.81
0.95
0.23
0.75
0.90
0.86
-51.58 -19.36 -1.85
-4.27
0.67
0.49
0.44
0.23
1995
0.51
0.67
0.78
0.83
0.26
0.71
0.87
0.88
-44.09
4.63
-8.00
1.49
0.70
0.58
0.47
0.41
1996
(calib.)
0.80
0.35
0.86
0.94
0.57
0.23
0.88
0.87
-2.11
29.36
7.32
3.50
0.45
0.81
0.38
0.25
1997
0.16
0.60
0.77
0.92
-0.02
0.43
0.85
0.88
-69.15 19.94
4.76
2.21
0.92
0.64
0.48
0.29
1998
0.21
0.55
0.58
0.95
0.40
0.72
0.81
0.90
-18.55 10.09
-7.34
-1.46
0.89
0.67
0.65
0.23
1999
0.54
0.64
0.84
0.96
0.18
0.74
0.92
0.92
-48.65
0.07
-4.01
-4.14
0.68
0.60
0.40
0.20
2000
0.52
0.78
0.86
0.94
0.20
0.67
0.89
0.91
-45.05
5.72
-0.79
-3.40
0.69
0.47
0.37
0.25
2001
0.62
0.66
0.90
0.96
0.37
0.80
0.90
0.94
-22.56
7.18
-5.75
-8.51
0.63
0.58
0.30
0.21
2002
0.69
0.63
0.93
0.96
0.25
0.64
0.89
0.94
-29.77 10.24
0.51
-4.45
0.56
0.61
0.27
0.20
2003
2004
(till
Nov.)
2005
(till
May)
Average
0.69
0.84
0.81
0.93
0.10
0.87
0.94
0.87
-64.62 -7.73
-1.09
-1.46
0.56
0.40
0.44
0.26
0.39
0.43
0.76
0.96
0.43
0.53
0.90
0.91
-7.87
26.86
4.49
-0.73
0.78
0.76
0.49
0.20
NA
NA
NA
0.94
NA
NA
NA
0.88
NA
NA
NA
-6.24
NA
NA
0.18
0.24
0.51
0.60
0.81
0.90
0.24
0.61
0.88
0.89
-24.20
4.17
-1.49
-1.54
0.69
0.62
0.42
0.29
instead of the calibrated parameter set from the year 1993, which is more representative being the medium event year of the simulation period, that from the year
1996, which has events of low magnitude, performed better throughout the period.
The performance of 1996 parameter set is better than that of the year 2000 although
its corresponding land use map of year 2000 have been used. This suggests to give
priority to extreme lows too while choosing the calibration period.
Then the hydrologically sensitive areas (HSAs) are estimated from the daily simulated spatially distributed surface runoff grids for all the three sets of the calibrated
parameter sets. The temporal variation of HSAs is captured on monthly basis. The
HSAs are quantified as the probability of generating the surface runoff, which is calculated as the percentage of number of days that any pixel generates surface runoff in
that month during the sixteen years of simulation period (1990-2005). As an example
of results, the surface runoff generation probabilities maps or HSAs in the month of
January with the three parameter sets is shown in Fig. 5.10. The similar pattern is
observed in the other months but with different magnitudes/probabilities.
Then an attempt has been made to relate the monthly probabilities of surface runoff
generation with the easily measurable relevant proxy parameters so that the complicated modeling could be avoided to locate the HSAs equally well. For this, the surface
runoff generation can be easily thought of being function of topography, climate, soil
and land use. So the topographic wetness index and precipitation is considered as
proxy parameters representing the topography and climate and the effect of land use
101
5. Physically based distributed hydrological modeling for HSA estimation
Table 5.13: The yearly model performance with parameter values calibrated with PEST for the
year 2000 with land use of 2000
Linear NS
Year
Log NS
PBIAS
RSR
Gauge Gauge Gauge Gauge Gauge Gauge Gauge Gauge Gauge Gauge Gauge Gauge Gauge Gauge Gauge Gauge
1
2
3
4
1
2
3
4
1
2
3
4
1
2
3
4
1990
0.63
0.37
0.86
0.84
0.48
0.44
0.61
0.71 -33.57 -18.41 -11.33 7.11
0.62
0.78
0.37
0.40
1991
0.48
0.55
0.79
0.65
0.69
0.66
0.73
0.63
6.06
0.72
0.67
0.46
0.59
1992
0.62
0.62
0.80
0.73
0.69
0.69
0.85
0.73 -30.68 2.50
-6.78
0.61
0.62
0.45
0.52
1993
0.84
0.78
0.84
0.84
0.72
0.65
0.81
0.80
-2.43 14.43 -6.80 10.74
0.41
0.48
0.40
0.40
1994
0.62
0.78
0.82
0.92
0.59
0.79
0.85
0.74 -41.15 -20.73 -4.15
1.58
0.62
0.47
0.42
0.28
1995
-0.08
0.71
0.84
0.77
0.46
0.72
0.85
0.77 -56.52 -0.39
-4.76
-3.86
0.81
0.59
0.41
0.34
1996
0.11
0.41
0.78
0.91
0.47
0.26
0.79
0.66 -27.75 30.09
0.97
9.68
0.94
0.77
0.47
0.29
1997
0.35
0.65
0.83
0.89
0.54
0.46
0.75
0.67 -35.67 15.83
2.08
6.46
0.81
0.59
0.41
0.34
1998
0.29
0.56
0.70
0.86
0.60
0.76
0.82
0.78 -52.60 5.80
-4.72
-7.94
0.84
0.67
0.55
0.38
1999
0.44
0.63
0.86
0.92
0.59
0.76
0.86
0.83 -40.29 -3.15
-1.73
-3.65
0.75
0.61
0.38
0.29
2000
(calib.)
0.62
0.81
0.88
0.93
0.71
0.71
0.78
0.80
0.38
-1.62
0.62
0.45
0.35
0.30
2001
0.55
0.64
0.87
0.84
0.65
0.85
0.81
0.81 -43.44 5.24
-4.56 -14.19 0.66
0.60
0.35
0.39
2002
0.65
0.69
0.89
0.93
0.39
0.68
0.84
0.91 -32.87 4.83
3.66
-5.84
0.59
0.55
0.34
0.27
2003
0.87
0.88
0.88
0.90
0.79
0.88
0.66
0.66 -21.78 -8.83
2.26
7.24
0.36
0.34
0.35
0.32
2004 (till
Nov.)
0.55
0.52
0.75
0.79
0.71
0.60
0.82
0.72 -19.91 22.46
7.67
-6.39
0.67
0.69
0.50
0.46
2005 (till
May)
NA
NA
NA
0.91
NA
NA
NA
0.81
NA
NA
NA
1.64
NA
NA
0.18
0.30
Average
0.50
0.64
0.83
0.85
0.61
0.66
0.79
0.75
-31.10
2.51
-1.71
0.02
0.67
0.59
0.40
0.37
7.84 -13.72 4.62
-35.75
1.70
-9.26
Table 5.14: Annual total precipitation and annual average daily temperature in the Rems catchment during the simulation period (1990-2005)
Year
1991
1992
1993
1994
1995
1996
1997
1998
1999
2000
2001
2002
2003
2004
2005
Average
Precipitation
1027
[mm]
1990
758
1033
1122
1127
1157
928
883
1116
1178
1026
1217
1346
707
957
995
1036
Temperature
[◦ C]
8.7
9.6
9.0
10.4
9.3
7.8
9.4
9.6
9.7
10.3
9.6
10.0
9.8
9.1
9.3
9.5
9.6
and soil type is captured through the estimation of Curve Number-CN (see Chapter
2) for the Rems catchment. Then the spatially distributed multiple linear regressions
are carried out between those proxy parameters and the surface runoff generation
probabilities simulated with each of the three parameter sets for each month. The
obtained best regression models in each subcatchment for four representative months
are shown in Table 5.15 along with the performance measure of the respective regression.
During the regressions, surprising and unacceptable results are obtained which show
that the surface runoff generation probabilities are negatively correlated with the topography wetness index and curve number in several cases. Even the best regression
models show negative coefficients of topographic wetness index in subcatchment 4
for January and March (Table 5.15). Moreover the regression coefficients as well as
the main influencing proxy parameter vary widely and randomly between subcatchments and between the set of the calibrated parameters. So the general applicable
relationships to identify HSAs through easily obtainable parameters cannot be found
102
5.4. Calibration and Simulation: Procedures, Results and Discussions
30
Temperature [degree C]
Precipitation [mm]
100
10
1
0
Jan
Feb
Mar
Apr
May Jun
Jul
Aug
Sep
Oct
Nov
Dec
20
10
0
-10
-20
Jan
Feb Mar
Apr May Jun
Jul
Aug
Sep
Oct
Nov
Min. [1996-2005]
Max. [1996-2005]
Avg. [1996-2005]
Min. [1996-2005]
Max. [1996-2005]
Avg. [1996-2005]
Min. [1996]
Max. [1996]
Avg. [1996]
Min. [1996]
Max. [1996]
Avg. [1996]
Dec
Figure 5.8: Monthly variation of daily precipitation (left) and temperature (right) in Rems catchment during the year 1996 and average of simulation period (1990-2005)
Calib. 1996 [LU 1993]
Calib. 2000 [LU 2000]
Calib. 1993 [LU 1993]
1
0.8
0.8
0.6
0.6
log. NS coeff.
0.4
0.2
0
Calib. 1996 [LU 1993]
Calib. 2000 [LU 2000]
0.4
0.2
Year
20
04
Av
er
ag
e
20
02
20
00
19
98
19
96
19
94
19
92
04
ve
ra
ge
A
20
02
20
00
20
98
19
96
19
94
19
92
19
19
90
0
19
90
lin. NS coeff.
Calib. 1993 [LU 1993]
1
Year
Figure 5.9: Comparisons of yearly NS efficiencies with the parameters calibrated with PEST for
the year 1993, 1996 and 2000
out. In the similar context, the pattern of spatially distributed surface runoff varies
not only among the different parameter sets with which they are simulated but also
varies abruptly and unrealistically between the subcatchments (Fig. 5.10).
These issues then force to raise the question on the parameters optimization method
adopted here. The Gauss-Marquardt-Levenberg method have been used for its advantage that it estimates parameters using considerably fewer model runs than any
other estimation method for nonlinear models and hence best suited practically for
the CPU intensive distributed model like the WaSiM-ETH. But it has the disadvantage that it is only a local search automatic parameter estimation tool and their
results depend on the closeness of the initial values of the search to the global optimum. So with this method there is always chance of being trapped in the local
optima. Further the optimization method is gradient-based and uses the linearization
of relationship between the model’s output and the parameters by formulating the
Taylor expansion. But the hydrological model contains threshold and the derivatives
with respect to the parameter in the Taylor expansion will not change smoothly at
any threshold. Hence it adversely impacts the calibration process by creating the
discontinuities in the derivatives of the objective function response surface. These
deficiencies of method are investigated and reported in literatures.
103
5. Physically based distributed hydrological modeling for HSA estimation
N
Psat_jan. [1993 parameters]
0 - 4
22 - 25
5 - 8
26 - 30
9 - 12
31 - 34
13 - 17
35 - 38
18 - 21
39 - 43
4
0
4
Kilometers
4
0
4
Kilometers
N
Psat_jan. [1996 parameters]
0 - 4
22 - 25
5 - 8
26 - 29
9 - 12
30 - 33
13 - 16
34 - 37
17 - 21
38 - 42
Prunoff_jan. [2000 parameters]
0 - 4
22 - 25
5 - 8
26 - 29
9 - 12
30 - 33
13 - 16
34 - 37
17 - 21
38 - 42
4
0
4
Kilometers
Figure 5.10: Surface runoff generation probabilities (HSAs) for the month January with the three
sets of parameters calibrated with PEST
104
5.4. Calibration and Simulation: Procedures, Results and Discussions
Table 5.15: The obtained best regression models to estimate surface runoff generation probabilities
Catchment 1
Multiple regression equation
R2
Std.
error
Jan.
3.80*TWI + 0.66*ppt + 0.09*CN - 92.03
0.70
Mar.
4.77*TWI + 0.66*ppt + 0.12*CN - 119.42
Jul.
Oct.
Month
Independent R2 analysis
TWI
ppt.
CN
5.38
61.1%
0.2%
0.4%
0.75
6.02
65.5%
0.0%
0.4%
2.98*TWI + 0.01*ppt - 0.08*CN - 33.48
0.60
7.28
57.0%
3.9%
3.1%
3.48*TWI + 0.12*ppt + 0.03*CN - 56.70
0.78
4.45
78.2%
4.9%
0.9%
Catchment 2
Jan.
0.59*TWI + 0.32*ppt - 0.01*CN - 22.46
0.65
1.76
11.9%
46.3%
7.3%
Mar.
0.91*TWI + 0.13*ppt + 0.00*CN - 18.97
0.50
2.05
40.3%
2.7%
0.2%
Jul.
0.98*TWI + 0.01*ppt + 0.02*CN - 13.34
0.70
1.65
68.2%
3.4%
2.5%
Oct.
1.07*TWI + 0.05*ppt + 0.01*CN - 17.80
0.73
1.56
72.2%
0.6%
0.9%
Catchment 3
Jan.
0.20*TWI + 0.39*ppt - 0.03*CN - 22.18
0.76
1.92
2.4%
75.8%
0.5%
Mar.
0.23*TWI + 0.20*ppt + 0.01*CN - 17.51
0.67
2.45
8.9%
62.7%
5.3%
Jul.
0.55*TWI + 0.02*ppt + 0.02*CN - 10.81
0.66
1.05
63.7%
0.6%
0.0%
Oct.
0.57*TWI + 0.04*ppt + 0.01*CN - 11.52
0.75
0.88
72.8%
0.2%
0.4%
Catchment 4
Jan.
- 0.07*TWI + 0.24*ppt + 0.00*CN - 10.24
0.59
0.77
8.4%
56.5%
0.1%
Mar.
- 0.06*TWI + 0.22*ppt + 0.03*CN - 10.31
0.42
1.25
5.2%
37.5%
1.2%
Jul.
0.05*TWI + 0.00*ppt + 0.00*CN - 0.77
0.21
0.25
21.2%
0.5%
0.0%
Oct.
0.06*TWI + 0.16*ppt + 0.11*CN - 17.95
0.12
2.79
0.1%
1.8%
8.8%
So with the aim of achieving the reasonable HSAs, the calibration of the parameters
are redone now with a more acceptable global optimization technique compromising
with large number of required model runs, that too of the computation-intensive
WaSiM-ETH. The optimization technique and the results are described in the following section.
5.4.3.2 Shuffled-Complex-Evolution method (SCE-UA)
A globally based search method known as Shuffled-Complex-Evolution (SCE-UA)
was developed by Duan et al. (1994) at the University of Arizona. Unlike the GaussMarquardt-Levenberg method, SCE-UA does not require computation of derivatives
of model outputs with respect to adjustable parameters. This method was formulated combining the strengths of already existing Genetic Algorithm (Holland 1975),
a global random search procedure based on evolutionary principles, and the Simplex method (Nelder & Mead 1965), a local direct search procedure. In addition
the concepts of complex partition and complex shuffling have been introduced. The
105
5. Physically based distributed hydrological modeling for HSA estimation
SCE-UA method is based on a synthesis of four concepts (Duan et al. 1994) which
include: a) combination of deterministic and probabilistic approaches; b) systematic
evolution of a ’complex’ of points spanning the parameter space, in the direction of
global improvement; c) competitive evolution; and d) complex shuffling. Numerous
researchers have investigated the use of SCE-UA for calibration of hydrological models and found to be consistently more efficient and robust when compared against a
variety of search methods. The method has also been used in other areas of hydrology like soil erosion, subsurface hydrology, remote sensing and land surface modeling.
The SCE-UA algorithm requires in the first step (zero-loop) the generation of a “population” of points, for parameters to be optimized, distributed randomly throughout
the feasible parameter space. A criterion value is calculated at each point and the
points are then ranked in order of increasing criterion value. The population is then
partitioned into number of “complexes” say p, each containing say m points. Each
complex then evolves independently according to a “reproduction” process following
Competitive Complex Evolution (CCE) algorithm which is key component of the
SCE-UA method. The CCE algorithm is based on Simplex downhill search scheme
of Nelder & Mead 1965 in which formation of sub-complex (with say q number of
points) and generation of potential offspring (say α number of points) takes place.
The points in the evolved complexes are then combined into a single sample population and ranking is done similarly based on increasing criterion value. The entire
population is then shuffled or re-partitioned by re-assigning the points into new complexes formed so that information gained by the previous complexes is shared. The
evolution and the shuffling steps continue until pre-specified convergence criteria are
reached. The SCE-UA method is pictorially explained in Fig. 5.11, by the use of a
two-dimensional example (parameters X and Y ) as given by Duan et al. 1994.
As can be noticed in the description above, the SCE-UA method contains some algorithmic parameters that control several probabilistic and deterministic components
of the method. They are: m− the number of points in a complex; q− the number of
points in a sub-complex; p− the number of complexes; pmin − the minimum number
of complexes required in the population; α− the number of consecutive offspring generated by each sub-complex; and, β− the number of evolution steps taken by each
complex. These parameters should be chosen carefully for the method to perform
optimally. Duan et al. (1994) conducted a detailed study on the identification of
those SCE-UA algorithmic parameters and provide some suggestions based on the
numbers of parameters to be optimized. In our study the 11 (say n) parameters need
to be optimized (Table 5.7) and based on the recommendations, the algorithmic parameters of the SCE-UA are used as: p = 5 (compromised choice between 2 to 20),
m = 2n + 1 = 23, q = n + 1 = 12, pmin = p = 5, α = 1 and β = 2n + 1 = 23.
With these algorithmic parameters, the SCE-UA algorithm is applied for calibration
of the eleven parameters (Table 5.7) in Rems catchment. Like earlier with PEST,
the year 1993 with input data as described in section 5.3 including land use map
of 1993 is considered for the calibration where 1992 is run as warm-up period in
every iteration for the stabilization of initial conditions. Here also, the objective
function to be minimized is selected as the sum of square error between observed
runoff and simulated one. The calibration is terminated if the objective function is
106
5.4. Calibration and Simulation: Procedures, Results and Discussions
Independently Evolved Complexes
(End of the First Cycle)
Initial population
(Start of the First Cycle)
Y
0
1
2
3
4
5
0
2
3
4
5
Independently Evolved Complexes
(End of the Second Cycle)
Shuffled Population
(Start of the Second Cycle)
Y
1
6
6
5
5
4
4
3
3
2
2
1
1
0
0
0
1
2
3
X
4
5
0
1
2
3
4
5
X
Figure 5.11: Illustration of Shuffled Complex Evolution (SCE-UA) method (Duan et al. 1994)
not reduced by more than one percent over five successive iterations (i.e. evolution
loops), or if the maximum 10,000 model runs have been carried out. Unlike the
earlier Gauss-Marquardt-Levenberg algorithm which takes couple of days for optimization, the SCE-UA method takes some weeks to more than a month, that too
using four PCs for the four subcatchments, for optimizing the eleven parameters
of the WaSiM-ETH. This is a huge disadvantage of using such global optimization
method for CPU intensive model like WaSiM-ETH.
The finally obtained calibrated parameters with the SCE-UA are shown in Table
5.16 along with the earlier calibrated values with PEST. The calibrated values are
found to vary widely with the change in the optimization method too.
The model is run for whole sixteen years (1990-2005) with the SCE-UA estimated
parameters and the respective yearly model performance is shown in Table 5.17. The
comparison of the performance measures with that from the application of PEST is
shown in Table 5.18.
107
5. Physically based distributed hydrological modeling for HSA estimation
Table 5.16: The parameter values calibrated with PEST for the year 1993, 1996 and 2000 and with
SCE-UA for the year 1993
Calibration year- 1993
[LU 93]
Subbasin codes
Calibration year- 1996
[LU 93]
1
2
3
4
1
2
0.017
0.062
0.027
0.014
0.128
0.069
0.039 0.027
Scaling factor Tkorr[-]
0.003
0.000
0.016
0.211
0.000
0.000
Scaling factor Kkorr[-]
3200.1 1000.0 998.8 1000.0
0.6
1000.0
Recession parameter m [m]
3
4
Calibration year- 2000
[LU 2000]
Calibration year- 1993 using SCEUA [LU 93]
1
2
3
4
1
2
3
4
0.019
0.077
0.035
0.012
0.026
0.030
0.027
0.011
0.030 0.059
0.001
0.000
0.000
0.622
4.755
6.184
21.3
88.8
7613.3 1010.0 3027.2 1000.0 7813.1 9470.2
2025.61 2506.31
4425.9
2657.1
Recession constant surf. Runoff
KD [h]
18.7
28.0
48.1
26.7
1.6
32.1
30.6
32.2
34.4
7.2
39.2
27.3
43.6
33.7
55.9
57.5
Maximum interflow storage
Shmax [mm]
43.4
24.7
20.0
20.0
35.3
27.7
22.8
25.0
68.3
56.5
28.0
20.1
55.4
13.2
23.2
65.2
54.0
123.6
32.9
98.6
140.2
173.7
22.5
4226.4
56.1
92.3
169.2
982.4
45.1
119.0
354.8
Recession constant interflow KH
1000.0
[h]
Init. content unsat. Zone SUZo
0.01
[mm]
0.01
0.01
0.00
0.00
0.01
0.00
0.00
0.03
0.01
0.01
0.00
0.34
2.01
6.95
8.03
Init. satur. deficit SDo[n*nFK]
0.51
2.25
0.34
0.51
5.45
0.02
2.66
3.16
1.07
3.14
0.49
0.65
2.39
3.94
3.79
5.15
Macro pore flow Pgrenz[mm/h]
10.0
10.0
9.6
10.0
10.0
10.0
10.0
10.0
10.0
10.0
9.6
10.0
1.6
16.0
8.8
0.2
Scaling of capillary rise rk [0...1]
0.00
0.42
1.00
0.30
0.61
0.10
0.51
0.10
0.00
1.00
1.00
0.10
0.11
0.53
0.56
0.21
Fraction on snow melt in
surface runoff cmelt[0...1]
0.92
0.04
0.77
0.15
0.08
0.30
0.12
0.06
1.00
0.00
1.00
0.15
0.98
0.08
0.22
0.42
Table 5.17: The yearly model performance with parameter values calibrated with SCE-UA
Linear NS
Year
Log NS
PBIAS
RSR
Gauge Gauge Gauge Gauge Gauge Gauge Gauge Gauge Gauge Gauge Gauge Gauge Gauge Gauge Gauge Gauge
1
2
3
4
1
2
3
4
1
2
3
4
1
2
3
4
1990
0.60
0.30
0.81
0.85
0.33
0.05
0.46
0.72 -17.72 -20.11 21.02 -12.17 0.61
0.84
0.44
0.39
1991
0.51
0.46
0.67
0.72
0.35
0.48
0.40
0.75 -10.15 -11.54 12.39 -7.08
0.79
0.88
0.43
0.65
1992
0.63
0.25
0.57
0.79
0.36
0.54
0.64
0.81 -39.93 -10.45 -15.30 -14.39 0.61
0.87
0.66
0.46
1993
(calib.)
0.84
0.77
0.86
0.87
0.63
0.62
0.69
0.84
0.58
0.75
0.53
0.64
1994
0.50
0.60
0.80
0.95
0.21
0.66
0.70
0.83 -56.63 -23.26 3.64
-8.27
0.71
0.63
0.45
0.22
1995
0.06
0.60
0.68
0.81
0.25
0.62
0.59
0.81 -51.85 1.82
-7.88
-8.58
0.98
0.67
0.55
0.46
1996
0.27
0.16
0.78
0.91
0.25
-0.01
0.48
0.81 -30.68 29.10
2.30
-8.16
0.85
0.92
0.47
0.31
1997
0.18
0.53
0.71
0.91
0.18
0.42
0.36
0.84 -51.12 9.51
6.96
-5.98
0.91
0.67
0.54
0.30
1998
0.08
0.54
0.61
0.93
0.44
0.62
0.46
0.85 -51.09 -1.94
-9.12 -14.03 0.95
0.90
0.63
0.27
1999
0.50
0.56
0.82
0.96
0.45
0.55
0.65
0.91 -36.33 -6.07
3.47
0.72
0.67
0.40
0.20
2000
0.61
0.72
0.87
0.93
0.38
0.51
0.53
0.84
-1.90
1.76 -10.80 0.62
0.53
0.36
0.27
2001
0.61
0.71
0.87
0.95
0.40
0.71
0.53
0.87 -38.51 -0.60
-6.55 -12.99 0.63
0.60
0.41
0.25
2002
0.68
0.57
0.90
0.96
0.21
0.45
0.67
0.90 -38.93 4.13
1.51
-9.71
0.56
0.66
0.31
0.20
2003
0.80
0.62
0.77
0.93
0.47
0.73
0.11
0.84 -41.46 -12.85 11.21 -7.82
0.45
0.61
0.47
0.26
0.40
0.72
0.92
0.45
0.37
0.56
0.80 -25.19 18.13
0.74 -17.97 0.62
0.78
0.53
0.28
NA
NA
0.94
NA
NA
NA
0.86
NA
NA
NA
2.45
NA
NA
NA
0.31
0.52
0.76
0.90
0.36
0.49
0.52
0.83
-35.91
-1.02
2.71
-9.26
0.71
0.73
0.48
0.34
2004 (till
0.61
Nov.)
2005 (till
NA
May)
Average
0.50
-3.09 10.78 14.55 -4.44
-45.99
-8.20
It is seen that despite the use of the global optimization method- SCE-UA compromising with huge computation time, the model performances cannot be improved
than what was obtained from the considerably quicker Gauss-Marquardt-Levenberg
method (PEST). Or probably the chosen initial values for the PEST were such that
the method also converges to the same global optimum region as that estimated
by the global method SCE-UA. The low extreme events as in 1996 are simulated
poorly with the globally optimized parameters too thus confirming the deficiency of
WaSiM-ETH model in simulating the low events.
108
5.4. Calibration and Simulation: Procedures, Results and Discussions
Table 5.18: The comparison of model performance with parameter values calibrated with PEST
and SCE-UA
Gauge 1
log.
PBIAS RSR
NS
Gauge 2
lin.
NS
Gauge 3
log.
PBIAS RSR
NS
With observed inflows
Calib.1993 [LU 1993]
0.90 0.69 -6.30 0.32
0.77 0.56
0.85 0.50 20.72 0.39
0.85 0.77 14.50 0.39
Calib.1996 [LU 1993]
0.80 0.57 -2.11 0.45
0.35 0.23 29.36 0.81
0.86 0.88
7.32
0.38
0.94 0.87
Calib. 2000 [LU 2000]
0.62 0.71 -35.75 0.62
0.81 0.71
0.88 0.78
0.38
0.35
0.93 0.80 -1.62 0.30
SCEUA_Calib.1993 [LU 1993]
0.84 0.63 -3.09 0.58
0.77 0.62 10.78 0.75
0.86 0.69 14.55 0.53
0.87 0.84 -4.44 0.64
Calib.1993 [LU 1993]
0.37 0.58 -34.83 0.77
0.61 0.53
4.76
0.61
0.74 0.46
2.32
0.50
0.84 0.72
Calib.1996 [LU 1993]
0.51 0.24 -24.20 0.69
0.60 0.61
4.17
0.62
0.81 0.84
1.49
0.42
0.90 0.89 -1.54 0.29
Calib. 2000 [LU 2000]
0.50 0.61 -31.10 0.67
0.64 0.66
2.51
0.59
0.83 0.79 -1.71 0.40
0.85 0.75
SCEUA_Calib.1993 [LU 1993]
0.50 0.36 -35.91 0.71
0.52 0.49 -1.02
0.73
0.76 0.52
0.90 0.83 -9.26 0.34
9.31
1.70
lin.
NS
Gauge 4
lin.
NS
0.48
0.45
log.
PBIAS RSR
NS
lin.
NS
log.
PBIAS RSR
NS
3.50
0.25
Avgerage [1990 - 2005] with
2.71
0.48
1.24
0.02
0.40
0.37
Further, analyzing the model performances (Tables 5.12, 5.13, 5.17, 5.18), it can be
seen that the subcatchments 3 and 4 which are not-headwater basins
are simulated quite perfectly with
very high values of performance
measures every year with all the
four parameter sets. It seems that
these subcatchments are not sensitive to the model calibration and
simulation. For the purpose, the
number of iterations required to calibrate each of the subcatchments
Interation no.
with PEST is analyzed. As is the
advantage of the PEST method, the
Figure 5.12: Objective function reduction during caloptimization is achieved with conibration with PEST
siderably few model runs but as can
be seen in Fig. 5.12, surprisingly the non-headwater subcatchments 3 and 4 are optimized almost immediately.
100
90
Schwäbis ch Gm ünd (Gauge 1)
Haubers bronn (Gauge 3)
Schorndorf (Gauge 3)
Neus tadt (Gauge 4)
Relative residuals
80
70
60
50
40
30
20
10
0
0
2
4
6
8
10
12
14
16
18
20
22
24
26
28
30
Outflow at Neustadt [mm/d]
What has happened here actually is
10
that- as obviously followed in the
calibration procedure in order to
8 f(x) = 0.82x + 0.11
avoid propagation of errors downR² = 0.97
6
stream, the observed flows at upstream gauge(s) are used as inflows
4
to the downstream subcatchment
(Fig. 5.11), instead of allowing sim2
ulated discharges to flow to downstream subcatchment. But in our
0
0
1
2
3
4
5
6
7
8
9
10
case, as shown in Fig. 5.13, a simInflow at Schorndorf [mm/d]
ple linear regression of inflows and
outflows, for example from gauge Figure 5.13: Relation between inflow at Schorndorf
at Schorndorf to that at Neustadt
and outflow at Neustadt
109
5. Physically based distributed hydrological modeling for HSA estimation
(outlet) shows that the outflow is almost fully governed by the inflows thereby providing little room for calibrating and evaluating the model performance. So here the
high model performances values for subcatchments 3 and 4 are misleading.
Then, like earlier, the monthly hydrologically sensitive areas (HSAs), which are quantified as the probability of generating the surface runoff, are estimated from the daily
simulated spatially distributed surface runoff grids with the parameter sets from SCEUA. As an example of the results, the surface runoff generation probabilities maps
or HSAs in the month of January is shown in Fig. 5.14 which shall be compared to
that from PEST in Fig. 5.10.
Prunoff_jan. [1993 para. SCE-UA]
0 - 4
22 - 25
5 - 8
26 - 29
9 - 12
30 - 33
13 - 16
34 - 37
17 - 21
38 - 42
4
0
4
Kilometers
Figure 5.14: Surface runoff generation probabilities (HSAs) for the month January with the parameters calibrated with SCE-UA
Comparing Fig. 5.14 and 5.10 it can be observed that the simulated surface runoff
patterns are quite different for differently calibrated parameter sets. Then question
arises that which one should be considered reliable to proceed further for using them
to calculate soil erosion. More questionable is the unrealistic behaviour that the surface runoff patterns are totally different from one subcatchment to another. This is
obviously linked to the different subcatchments having the different parameter sets
which are calibrated independently with the observed flows at their corresponding
gauges. This means, unlike the general trend and understandings of calibration,
should we have to calibrate the different subcatchments simultaneously with same
single set of parameters for all the subcatchments although they have their own observed outflows.
In lieu with this, a new and completely different approach of parameters estimation
have been investigated, which does not produce a single set of optimized parameter
set like earlier but instead produce several sets of good performing parameters. This
gives opportunity to analyze and search the parameter set from the group of the
good performing parameters that would satisfy our purpose, i.e. reasonable spatial
patterns of surface runoff, the HSAs. The method, its application in our Rems catchment and the results are described in the following section.
110
5.4. Calibration and Simulation: Procedures, Results and Discussions
5.4.3.3 Robust Parameter Estimation (ROPE) - a new Algorithm
Despite the use of complex optimization algorithm, the best and unique parameter
set cannot be obtained. The quality of input data, which is always uncertain, or
the erroneous observed data lead to very different optimal parameter vectors, which
could be seen in our case with the use of different calibration year, different land
use and different optimization method. They may perform equally well when evaluated at catchment outlet but produce entirely different distributed results within
the catchment. To address this problem, it is aimed to estimate several sets of robust parameter vectors instead of a single set of optimized parameters and analyze
them with their distributed results to find the best set for the intended purpose, for
example, to achieve acceptable surface runoff patterns (HSAs) as in our case. Such
robust parameter sets may not be necessarily the best parameter set during calibration but they should represent the hydrological processes reasonably, they should
be transferrable to other time period and they should not be sensitive which means
small changes of the parameters should not lead to very different results For this, a
completely new algorithm successfully tested for the estimation of so defined robust
parameter vectors (Bárdossy & Singh 2008) has been used.
This new algorithm is a geometrical approach based on convex sets and half-space
depth. It is founded on the fact proven by Bárdossy (2007) that the set of good
performing parameters are well-structured in multi-dimension which cannot be visualized through the scatter plots when number of parameters is greater than two. The
Tukey’s half-space depth function (Tukey 1975) is used as the location estimator to
indentify those well-structured good performing parameters. The depth function was
first introduced by Tukey (1975) to identify the center (a kind of generalized median)
of a multivariate dataset. Following (Bárdossy & Singh 2008), the half-space depth
of a point p with respect to the finite set X in the d dimensional space Rd is defined
as the minimum number of points of the set X lying on one side of a hyperplane
among all possible hyperplanes through the point p. Mathematically, the half-space
depth of the point p with respect to set X is given as:
Dx (p) = min {min (|{x ∈ X hnh , x − pi > 0}|) , (|{x ∈ X hnh , x − pi < 0}|)} (5.25)
where hx, yi is the scalar product of the d dimensional vectors, and nh is an arbitrary
unit vector in the d dimensional space representing the normal vector of a selected
hyperplane. If the point p is outside the convex hull of X then its depth is zero.
While points on and near the boundary have low depth, points deeply inside have
high depth. This depth function is invariant to affine transformations of the space.
This means that the different ranges of the parameters have no influence on their
depth. The calculation of the halfspace depth is computationally very expensive
when the number of points in X is large or the dimension is high and in this study
the approximate calculation suggested in Rousseeuw & Struyf (1998) was used (Bárdossy & Singh 2008).
In order to estimate good performing parameter vectors in our Rems catchment using
this new concept (ROPE), the following steps are followed.
111
5. Physically based distributed hydrological modeling for HSA estimation
1. N number of uniformly distributed random parameter sets forming the set XN
are generated in the d(= 11) dimensional space bounded by the limits defined
by feasible parameter space as described in Section 5.4.1.
2. Using the input data described in section 5.3 including landuse of 1993, the
model WaSiM-ETH is run with each parameter vector in XN for the year
1992-1993. Like earlier the 1992 run is for the stabilization of initial conditions
and the objective function (sum of square error) is calculated for the year 1993
with each parameter set.
∗ (about 10% of X ) of best performing parameters, based on
3. The subset XN
N
objective function evaluated at step ii, is identified.
4. M number of new uniformly distributed random parameter sets forming the
set YM are generated within the plausible parameter space such that for each
∗ is greater than
parameter vector the depth calculated with respect to set XN
∗
zero (i.e. inside the convex hull formed by XN ). To avoid the unnecessary
model runs (important for time consuming WaSiM-ETH) the set YM is refined
by eliminating those generated sets which have zero depth i.e. being in the
geometrical boundary of the generated data clouds. This is based on the proven
fact that all points with high depth lead to good model performance.
5. The refined set YM is considered as XN and steps ii-v are repeated until the
performance corresponding to XN and YM do not differ much.
These methodological steps are pictorially presented in Fig. 5.15.
NN
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Generate random parameter
sets in feasible space, XN
→ Model runs
NNN N N NNN N N N NNN N N
N
N N N NNN N
NN NN NNN NNN
N
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N N N
N N NN
NN N NN
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NN N N N
N
N
NN
N N NNNN
N NNN NN
NN
N NN NNNN N
NNNNN
NN NN N
N
N
NN
NN
N N
N N N NN N
N
NN NN
N N N N N NN
N
NN
N NN N
N NN N N NN N N N
N
N NN
N
N NN N NNNN
NNN
NN
N N NNNN N N N N NN NN N
N N
NN N N
NN N
NN
N
NN
NN NNN N NNNNN
NN
NN N
N N N NNN
N
N
N
N
N
N
N
N N NNNN
NNN N N N
N N NNN N N
NN
NN
NNNN NN
N
N N NN N NNN N
NN
NN NN
N
Good candidates
(YM = XN ) for next cycle
→ Model runs
NN
N
N
N
N N
N
N
NN NN
N N
N
N
N
N
N
N
NN
N
N
N NN N
N N
N N
N
N
N NN
N
N
N N
N
N
N
N
N
N
N
N N NN N
N
N
N NN
NN
NN N N N
N
N
N
N
N
N N NN N
N
N NN
N N N NNN
NN
N
NN N
NN
N
N NN N N
N
N
N
NN N
NN
NN
N
N
N
N
N N
N
NN N
N
N N
N
N N N
N
N
N
N
N
N
N
N
N
N
N
N
N N
N
NN
N
N
N NN N
N N N N NNNN N N
N
NN
N N
N
N
N
N
N N
N
N N
N
N
N
N
N
N
N
N
N
N
N
N
N N
N N
N
N
N NN N N NN
N
N
NN
N N
N
N NNN
NN N
N
N
N
N
N
N
N
N
N
N
N
N
N
N
NN
N N
N
NN
N
N
N
N N
N
N
N
N
N
N
N
N
N
N N
N
NN N N N
NNâ Nâ
NâNâ Nâ NN
N
N
N N
N NN
N
Nâ Nâ
N
N N
âN N
NâNââN
N
Nâ
N
N
N
NN
NN N
Nâ
N
NN
Nâ
N
N
N
âN N N
Nâ
NâNâ
N
N
NN N N
â
N
NN
N
Nâ
Nâ
N
Nâ Nâ Nâ
NN
N
Nâ
N
NâNâ
NN
N
N N N N N
N N
Nâ
Nâ Nâ
Nâ
Nâ Nâ
N
NN
NN
N
Nâ NâNâ
NâNâ Nâ N
Nâ Nâ
N N
N N N N N
N
Nâ
Nâ
N
Nâ âN Nâ
NN N
âN
Nâ
N
NN NN
N âN Nâ
Nâ Nâ
âN
N
N
N N NN
N N N
Nâ
Nâ Nâ
N
Nâ
N
N
N
N
Nâ
N
N
NâNâ
Nâ
âN
N
N
âN
N
N
N
Nâ Nâ
N
âN
NN N
N NN N NN
Nâ NâNâ Nâ
N
N
Nâ Nâ
N
Nâ
N NNNNN
N
NâNâ Nâ âN Nâ
Nââ
Nâ
N
N
N
N
Nâ
âNN
N NN NN
N
N N NN NN
N
Nâ
N
N
âN
NN N
N NN
âN
N
NN
Nâ Nâ
Nâ âNNâ
N NN
N
NN
N N
N
N
N
N
Nâ âN
N
N
N
NN
N
N
NN
Nâ
âN
âN
âN
N N
N N NN
N
N
N N
N
Nâ
Nâ âN
NNN
Nâ
N
NN
Nâ
âN
NN N
NNN
Nâ Nâ
N N
N
N
N
â
N
â
N
N
N N
N
N
N
N
NN
N
Nâ Nâ
Nâ
Nâ
N
Nâ Nâ
Nâ
N N
N N N
NN NN
N N N
N N
NâNâ Nâ
N
Nâ
Nâ
NN N N
NN
Nâ Nâ Nâ Nâ Nâ
Nâ
NN N
N
NN
Nâ
NâNâ Nâ
NN N N
NN
N
NN
N
Nâ
N N
N N
Nâ
N N
N NN
N NN
Nâ
N
NâNâ Nâ
N N
â
NââNNâ
âN
NN
N
N
NN
âN N
N
â
N
N
N
Nâ
âN N
Nâ Nâ Nâ
N
N
N
NNN
NN
N Nâ
Nâ
Nâ
Nââ âNNâ
Nâ Nâ
N N
âN
N N
Nâ
Nâ
N
N
Nâ
N
N
NN
Nâ âN
NâNâ Nâ N
N
N
N
Nâ
NN N
N
N N
NN
N âN
N
N N NN N
N
N
NN
N
N
N
N NN
N
NNNNN N
N
N N N
NN
N N
N
N NN NN
N
N
N
N
N N
N
N
N
N
N N
N
N
N
N N
N
NN
N
N N
N
N
N
N
N
N
N
N
N N NN
N
N
N
N
N
N
N
N
N
N
N
N
N
N
N
N
N
N
N N NN N
N
N
N
N
N
N
NNNN
NN
N NN
N
N
N N
N NN N
NN N N
N
N
N N
N
NN
N
NN
NN N
NNN
N NN
N
N N
N
N
N
N NN
N
N
N N
N
NN N N
N N
NN N NN
NN
N
NN
N
N
N
N
N N
N
N
NN
N
N NN
N
N
NN
N
NN N
N
N N
N
N
N NN
N
N
N
N
N NN
N
N NN
N
N
N
NN
N
N
N
N
NN
N NN N N
N
N
N
N N
N
N N
N
N N
N
NN
N
N N
N
N
NN
N
N
N
N N
N
N
N
N
N
N
N
N
∗
Identify good sets, XN
NNN N N NNN N N N NNN N N
N
N N N NNN N
NN NN NNN NNN
N
N
N N N
N N NN
NN N NN
N
N
N NN N N N
N NN N N N
N N NN
N
N
NN
N
N
N NN N NN
N NN N N N
N
NN N
N N NN N NN NN
N N NNNN N
NN
NN
N N NN N
N
N
N
N N
NN N
N N
NN NN N
N NN N N NâN NâN
âNN N NN N N N
N N NN
âN
N N N
N
â
N
N
N
â
N
N N
N
âN N NN
NN NN âN âN
âN
âN
NN
âN âN N
N NNN N NâN
âN
N
âNâN âNâN
N N
N NN N NâN âNâN âN âNâN âNâN âN
âN
N âNâN âN
âN âN
âNâN NNN NN N
âN
âNâNâN
N
N
âNâNâN âN âN âNâN
N
N
NNN
âN N
âNâNâN
N âNâNâN âNâN
âNâN
N N NNN NNNN N
NNNNN
N âN N N âN
N
N
NN
NN
N N
N N N NN N
N
NN NN
N N N N N NN
N
NN
N NN N
N NN N N NN N N N
N
N NN
N
N NN N NNNN
NNN
NN
N N NNNN N N N N NN NN N
N N
NN N N
NN N
NN
N
NN
NN NNN N NNNNN
NN
NN N
N N N NNN
N
N
N
N
N
N
N
N N NNNN
NNN N N N
N N NNN N N
NN
NN
NNNN NN
N
N N NN N NNN N
NN
NN NN
N
∗
Identify good sets, XN
NNN N N NNN N N N NNN N N
N
N N N NNN N
NN NN NNN NNN
N
N
N N N
N N NN
NN N NN
N
N
N NN N N N
N NN N N N
N N NN
N
N
NN
N
N
N NN N NN
N NN N N N
N
NN N
N N NN N NN NN
N N NNNN N
NN
NN
N N NN N
N
N
N
N N
NN N
N N
NN NN N
N NN N N NN NN
NN N NN N N N
N N NN
N
N N N
N
N
N
N
N N NN
N
NN
NN NNNN N N
NN NN N N
N
N N NNNN N
N
N N N NNN N NNN
NN
N N
N NN N N N N N NN NN N NN NN N
NN
NN NNNN NN N
N
N N N
N NN
N
N
NNN N N N N NNN NNN N N NN
N NN
NN N N
N
NNN
N N
NNN
N N NNNN N NN N
N
NN
N N NNN NNNN N
N
N NN N
N
N
NNN
N
NN
NN
N N
N N N NN N
N
NN NN
N NN N N N N N N NN
N
N
N NN N
N NN N N NN N N N
N
N NN
N
N NN N NNNN
NNN
NN
N N NNNN N N N N NN NN N
N N
NN N N
NN N
NN
N
NN
NN NNN N NNNNN
N
NN
NN N
N
N
N
N
N
N
N
N
N
N
N
N N NNNN
NNN N N N
N NNNNN N N
NN
NN
NNNN NN
N
N N NN N NNN N
NN
NN NN
N
Generate random sets, YM
but deep based on good sets
(i.e. inside convex hull)
NN N N
NN
N NN
N N N NNN N N N N NNN N N
N
NN N
NN N NNNNN N
N NN NN
N N
N
NN
NN
#
N# N#N NN N N N N N N
N#N# N# NN N N N NNN NNNNNN N
N#N#N# NNN
N NN
N N NN NN N N N
Generate random sets, YM
but deep based on good sets
(i.e. inside convex hull) &
identify bad in good ones
NNN N N NNN N N N NNN N N
N
N N N NNN N
NN NN NNN NNN
N
N
N N N
N N NN
NN N NN
N
N
N NN N N N
N NN N N N
N N NN
N
N
NN
N
N
N NN N NN
N NN N N N
N
NN N
N N NN N NN NN
N N NNNN N
NN
NN
N N NN N
N
N
N
N N
NN N
N N
NN NN N
N NN N N NN NN
NN N NN N N N
N N NN
N
N N N
N
N
N
N
N N N# N#
N
NN
NN NNN N N
NN NN N N
N#
N N NNNN N
N NNN N NN
N
N#
N
NN
N#
N
N N
N# N#N# N# N# N N N NN NN N NN NN N
NN
NN
N N
N# N#N# N# N# N#
N NN NN NN N N N
NNN NNNN
N# N#N# N#
NN N N N
N
N NN
N#N# N# N#
N
NN
N N NNNN
N# N# NNNN N NN N
N#
NN
N NN NNNN N
N
N NN N
N
N
N#N#N##
N#
NN
NN
N N
N N N NN N
N
NN NN
N# N#N# N N N N N N NN
N
N
N NN N
N NN N N NN N N N
N
N NN
N
N NN N NNNN
NNN
NN
N N NNNN N N N N NN NN N
N N
NN N N
NN N
NN
N
NN
NN NNN N NNNNN
N
NN
NN N
N
N
N
N
N
N
N
N
N
N
N
N N NNNN
NNN N N N
N NNNNN N N
NN
NN
NNNN NN
N
N N NN N NNN N
NN
NN NN
N
Identify bad sets in the good
(deep) and throw them out
NN N N
NN
N NN
N N N NNN N N N N NNN N N
N
NN N
NN N NNNNN N
N N NN
N N
N
N NN N NN NN
NN
N
NN NN NNN NNN NNNNNN N
NN
N NN
N
NN
N NN NN N N
Good candidates
(YM = XN ) for next cycle
→ Model runs
Figure 5.15: Steps of ROPE algorithm for robust parameter vectors estimation
The parameter sets YM at the end are already good performing parameters. The
final set of robust parameter vectors can be chosen from YM by calculating the
112
5.4. Calibration and Simulation: Procedures, Results and Discussions
depth of each of the parameter vectors based on the data cloud of YM itself. It has
been shown (Bárdossy & Singh 2008) that the chosen deep parameter sets in this way
have low sensitivity and perform well when transferred to a different time period too.
Here also, at first, the attempt has been made to estimate the different robust parameter vectors for each of the four subcatchments based on their respective observed discharge series and allowing observed discharges to flow downstream from
the upstream catchments- the normally followed calibration strategy. But like earlier, despite the good model performance the simulated surface runoff patterns are
unrealistic as it varies widely among the subcatchments and also among the different
good parameter sets. An example of such unacceptable variations can be seen in Fig.
5.16 which shows the spatially distributed surface runoff for the month of December
1993 simulated by six sets of robust parameters estimated using the ROPE algorithm.
Set1
Set3
Set5
Surface runoff [mm] sum1293
Set2
N
Surface runoff [mm] sum1293
0 - 20
120 - 140
0 - 20
120 - 140
20 - 40
140 - 160
20 - 40
140 - 160
40 - 60
160 - 180
40 - 60
160 - 180
60 - 80
180 - 200
60 - 80
180 - 200
80 - 100
200 - 220
80 - 100
200 - 220
100 - 120
> 220
100 - 120
> 220
4
Surface runoff [mm] sum1293
0 - 20
120 - 140
20 - 40
140 - 160
40 - 60
160 - 180
60 - 80
180 - 200
80 - 100
200 - 220
100 - 120
> 220
0
4
Kilometers
Set4
N
4
Surface runoff [mm] sum1293
0
4
Kilometers
Set6
N
0 - 20
120 - 140
20 - 40
140 - 160
40 - 60
160 - 180
60 - 80
180 - 200
80 - 100
200 - 220
100 - 120
> 220
120 - 140
0 - 20
120 - 140
140 - 160
20 - 40
140 - 160
40 - 60
160 - 180
40 - 60
160 - 180
60 - 80
180 - 200
60 - 80
180 - 200
200 - 220
> 220
4
0
4
Kilometers
80 - 100
200 - 220
100 - 120
> 220
0
4
Kilometers
4
Kilometers
4
Kilometers
N
4
Surface runoff [mm] sum1293
0 - 20
80 - 100
4
Surface runoff [mm] sum1293
20 - 40
100 - 120
N
0
N
4
0
Figure 5.16: Surface runoff simulated by six robust parameter sets of each subcatchment separately
Then to avoid the inter-subcatchments random variation of surface runoff patterns,
the parameter set is not allowed to vary among the subcatchments which means
same sets of robust parameter vectors are estimated for whole Rems catchment.
However, the observed discharges at all the four gauges are considered for the objective function (sum of square of errors) evaluation. The simulated discharge is
allowed to flow from upstream subcatchment to downstream subcatchment; i.e from
Schwäbisch Gmünd (Gauge 1) and Haubersbronn (Gauge 2) to Schorndorf (Gauge
3) and from Schorndorf to Neustadt (Gauge 4). The good parameter sets are defined
not as the best in the sum of square errors of all the subcatchments but are defined
compromisingly best in sum of square errors of each subcatchment independently.
113
5. Physically based distributed hydrological modeling for HSA estimation
Further as the two initial storage parameters, SU Z0 and SD0 , have almost no effect when sufficient model warm-up period (1992) is used before calibration starts,
these two parameters are held fixed to 0.01 and 1.5 respectively. This brings down
the number of parameters to be optimized to nine that helps for faster convergence
of the algorithm. And also as the parameter Tkorr is quite sensitive and can vary
over large range, the generation of values for Tkorr is done in logarithmic space and
the model is run taking its antilog values. Then the ROPE algorithm is re-applied
for the year 1992-1993 to estimate the robust parameter sets for the Rems catchment.
A simple assessment of the application of ROPE algorithm in estimation of good
parameter vectors is presented in Table 5.19. It lists the percentage of good parameter
sets based on the corresponding thresholds of sum of square of errors in successive
steps. It shows how the new parameter sets after every step are being rapidly better
when they are generated based on the depth function, i.e. deep/interior based on
good parameter sets of previous step.
Table 5.19: Assessment of the application of depth function (ROPE algorithm) in estimation of
‘good parameter vectors’
Threshold
(sum of square
of residuals)
Monte Carlo
simulations
(11211 paras.)
After Step 1
(7041 paras.)
After Step 2
(3007 paras.)
After Step 3
(1955 paras.)
Whole catch.
3000
2500
2000
1500
1100
36.5 %
23.5 %
10.0 %
1.50 %
0.1 %
86.0 %
46.0 %
22.0 %
9.50 %
2.0 %
100.0 %
99.9 %
94.0 %
71.0 %
25.0 %
100.0 %
100.0 %
100.0 %
98.0 %
65.0 %
Catch. 1
800
600
400
21.0 %
11.0 %
3.0 %
42.0 %
21.0 %
6.0 %
99.7 %
94.0 %
54.0 %
100.0 %
100.0 %
99.0 %
Catch. 2
800
600
400
45.0 %
37.0 %
24.0 %
92.0 %
80.0 %
29.0 %
100.0 %
99.7 %
89.0 %
100.0 %
100.0 %
100.0 %
Catch. 3
800
600
400
43.0 %
25.0 %
8.0 %
92.0 %
50.0 %
15.0 %
100.0 %
99.1 %
75.0 %
100.0 %
100.0 %
98.0 %
Catch. 4
800
600
400
50.0 %
36.0 %
5.5 %
95.0 %
76.0 %
17.0 %
100.0 %
99.9 %
78.0 %
100.0 %
100.0 %
98.0 %
Catchment
The parameter generation is stopped after the step 3 when almost all the generated
parameter sets performed well based on the considered threshold. This means we
have now 1955 acceptably good performing parameter sets. The depth of these 1955
parameter sets are then calculated based on the combined (in all subcatchments)
best performing 320 parameters from them. Altogether 11 good parameter sets
which include- the deepest parameter set, sets with best objective function value
(minimum sum of square of errors) and some diametrically opposite sets- are shown
in Table 5.20. Also shown are the corresponding Nash Sutcliffe (NS) efficiencies for
114
5.4. Calibration and Simulation: Procedures, Results and Discussions
each subcatchment for the optimization year 1993. Further for the comparison, the
SCE-UA algorithm is once again applied in the Rems catchment but this time with
same parameter set for all subcatchments and allowing simulated discharges to flow
across subcatchments. The optimized single set of parameter and the corresponding
NS coefficients are also shown in Table 5.20.
Table 5.20: Different parameter sets same for all subcatchments estimated with SCE-UA and
ROPE and their performance
Parameters
SCE- Para. Para. Para. Para. Para. Para. Para. Para. Para. Para. Para.
UA set 1 set 2 set 3 set 4 set 5 set 6 set 7 set 8 set 9 set 10 set 11
Recession parameter m [m]
0.053
0.047
0.041
0.028
0.037
0.025
0.034
0.024
0.035
0.029
0.027
0.044
Scaling factor Tkorr[-]
0.002
0.068
0.109
0.492
0.152
0.563
0.252
0.417
0.086
0.544
0.629
0.120
Scaling factor Kkorr[-]
3.5
125.3
171.9
652.5
203.3
871.0
364.2
704.0
113.3
765.4
712.9
176.3
Recession constant surf. Runoff
KD[h]
40.1
27.4
36.9
44.7
37.2
46.2
48.6
38.8
33.5
32.4
38.0
51.3
Maximum interflow storage
SHmax[mm]
26.3
23.9
50.0
13.7
23.2
35.8
30.7
18.8
13.6
37.5
15.4
47.5
Recession constant interflow KH[h] 113.3
107.7
52.9
213.5
182.0
91.6
274.5
47.7
123.5
204.0
127.2
189.4
Init. content unsat. Zone
SUZo[mm]
0.25
0.01
0.01
0.01
0.01
0.01
0.01
0.01
0.01
0.01
0.01
0.01
Init. satur. deficit Sdo
1.6
1.5
1.5
1.5
1.5
1.5
1.5
1.5
1.5
1.5
1.5
1.5
Macro pore flow Pgrenz[mm/h]
1.5
7.2
1.3
7.8
1.6
6.4
3.7
6.7
2.0
8.7
6.9
2.9
Scaling of capillary rise rk[0...1]
0.02
0.23
0.24
0.70
0.70
0.28
0.87
0.37
0.78
0.13
0.50
0.95
Fraction on snow melt in surface
runoff cmelt[0...1]
0.75
0.33
0.58
0.86
0.98
0.27
0.02
0.75
0.32
0.53
0.96
0.24
catch 1
0.84
0.79
0.82
0.81
0.83
0.83
0.84
0.80
0.78
0.83
0.77
0.80
catch 2
0.78
0.36
0.80
0.74
0.75
0.68
0.70
0.70
0.73
0.72
0.65
0.65
catch 3
0.79
0.64
0.79
0.79
0.79
0.78
0.77
0.78
0.78
0.76
0.76
0.74
catch 4
0.71
0.56
0.72
0.70
0.70
0.67
0.66
0.69
0.70
0.66
0.67
0.63
catch 1
0.67
0.62
0.62
0.72
0.70
0.73
0.71
0.69
0.70
0.70
0.69
0.68
catch 2
0.71
0.43
0.69
0.50
0.68
0.42
0.49
0.35
0.67
0.47
0.47
0.55
catch 3
0.73
0.67
0.70
0.81
0.76
0.77
0.74
0.74
0.80
0.74
0.82
0.74
catch 4
0.73
0.66
0.71
0.77
0.73
0.68
0.70
0.66
0.78
0.69
0.75
0.67
Model performance
linear NS coeff.
log NS coeff.
Note:
Para. set 1 is the deepest parameter set i.e. Depth = 12
All parameter sets except set 1 are in the boundaries i.e. Depth = 1
Para. set 2 is with min. sum of sum of square of residuals of all subcatchments
Para. set 4 is combined best when sum of square of residuals of each subcatchment is treated individually
The spatially distributed surface runoff for the year 1993 simulated by the good parameters listed in Table 5.20 are shown in Fig. 5.17.
It can be observed that now there are not unacceptable variations of patterns among
the subcatchments. The random variations of the distributed patterns among the
subcatchments could be avoided by assigning same parameter set for all the subcatchments. The high spatial correlation (values and rank) of the distributed surface
runoff simulated by the different good parameter sets as presented in Table 5.21
115
5. Physically based distributed hydrological modeling for HSA estimation
N
SCE-UA
N
Set 1
Surface runoff [mm] sum93
Surface runoff [mm] sum93
0 - 5
200 - 300
0 - 5
200 - 300
5 - 10
300 - 400
5 - 10
300 - 400
10 - 20
400 - 500
10 - 20
400 - 500
20 - 50
500 - 700
50 - 100
700 - 900
100 - 200
>900
4
0
4
Kilometers
20 - 50
500 - 700
50 - 100
700 - 900
100 - 200
>900
4
0
N
Set 2
200 - 300
5 - 10
300 - 400
0 - 5
200 - 300
5 - 10
300 - 400
400 - 500
10 - 20
400 - 500
500 - 700
20 - 50
500 - 700
50 - 100
700 - 900
50 - 100
700 - 900
100 - 200
>900
100 - 200
>900
0
4
Kilometers
4
0
N
Set 4
200 - 300
5 - 10
300 - 400
10 - 20
400 - 500
20 - 50
500 - 700
50 - 100
700 - 900
100 - 200
>900
4
0
4
Kilometers
0 - 5
200 - 300
5 - 10
300 - 400
10 - 20
400 - 500
20 - 50
500 - 700
50 - 100
700 - 900
100 - 200
>900
4
0
200 - 300
0 - 5
5 - 10
300 - 400
10 - 20
400 - 500
20 - 50
500 - 700
20 - 50
500 - 700
50 - 100
700 - 900
50 - 100
700 - 900
100 - 200
>900
100 - 200
>900
4
Kilometers
4
0
N
Set 8
200 - 300
0 - 5
200 - 300
300 - 400
5 - 10
300 - 400
10 - 20
400 - 500
10 - 20
400 - 500
20 - 50
500 - 700
20 - 50
500 - 700
700 - 900
>900
4
0
4
Kilometers
50 - 100
700 - 900
100 - 200
>900
4
0
N
Set 10
200 - 300
0 - 5
200 - 300
300 - 400
5 - 10
300 - 400
10 - 20
400 - 500
10 - 20
400 - 500
20 - 50
500 - 700
20 - 50
500 - 700
700 - 900
>900
4
0
Kilometers
Surface runoff [mm] sum93
0 - 5
5 - 10
50 - 100
4
N
Set 11
Surface runoff [mm] sum93
100 - 200
Kilometers
Surface runoff [mm] sum93
0 - 5
5 - 10
50 - 100
4
N
Set 9
Surface runoff [mm] sum93
100 - 200
Kilometers
200 - 300
300 - 400
400 - 500
0
4
Surface runoff [mm] sum93
5 - 10
10 - 20
4
Kilometers
N
Set 7
Surface runoff [mm] sum93
0 - 5
4
Surface runoff [mm] sum93
N
Set 6
Kilometers
N
Set 5
Surface runoff [mm] sum93
0 - 5
4
Surface runoff [mm] sum93
10 - 20
20 - 50
4
Kilometers
N
Set 3
Surface runoff [mm] sum93
0 - 5
4
4
Kilometers
50 - 100
700 - 900
100 - 200
>900
4
0
Figure 5.17: Distributed Surface runoff simulated by different good parameter sets identical for all
subcatchments
indicate that the simulated patterns are quite similar with the different parameter
sets. So now we have estimated parameters yielding good model performances with
acceptable surface runoff patterns within the catchment. However the quantity or
116
5.4. Calibration and Simulation: Procedures, Results and Discussions
amount of surface runoff simulated by them seems to vary a lot. The total surface
runoff and the statistics of its spatial distribution in the year 1993 modeled by these
good parameter sets are shown in Fig. 5.18. It can be seen that despite the good
model performances and reasonable surface runoff patterns within the catchment,
the total amount and the spatial average of the surface runoff varies as much as
about four times among the different good parameter sets thus creating doubt to use
the results quantitatively.
Table 5.21: Spatial correlation (values and rank) of the distributed surface runoff simulated by
different good parameter sets identical for all subcatchments
Correlation of spatially distributed surface runoff
SCEUA
Para.
set 1
Para.
set 2
Para.
set 3
Para.
set 4
Para.
set 5
Para.
set 6
Para.
set 7
Para.
set 8
Para.
set 9
Para.
set 10
Para.
set 11
1
0.97
0.96
0.87
0.97
0.98
0.97
0.99
0.93
0.99
0.92
0.98
Para. set 1
0.97
1
0.96
0.86
0.95
0.97
0.96
0.98
0.91
0.97
0.91
0.98
Para. set 2
0.96
0.96
1
0.75
0.89
0.99
0.91
0.97
0.83
0.97
0.83
0.98
Para. set 3
0.87
0.86
0.75
1
0.96
0.82
0.96
0.88
0.98
0.89
0.98
0.84
Para. set 4
0.97
0.95
0.89
0.96
1
0.94
0.99
0.97
0.99
0.97
0.98
0.94
Para. set 5
0.98
0.97
0.99
0.82
0.94
1
0.95
0.99
0.89
0.99
0.89
1.00
Para. set 6
0.97
0.96
0.91
0.96
0.99
0.95
1
0.98
0.98
0.98
0.97
0.96
Para. set 7
0.99
0.98
0.97
0.88
0.97
0.99
0.98
1
0.93
0.99
0.93
0.99
Para. set 8
0.93
0.91
0.83
0.98
0.99
0.89
0.98
0.93
1
0.93
0.98
0.89
Para. set 9
0.99
0.97
0.97
0.89
0.97
0.99
0.98
0.99
0.93
1
0.94
0.99
Para. set 10
0.92
0.91
0.83
0.98
0.98
0.89
0.97
0.93
0.98
0.94
1
0.90
Para. set 11
0.98
0.98
0.98
0.84
0.94
1.00
0.96
0.99
0.89
0.99
0.90
1
SCE-UA
Rank correlation of spatially distributed surface runoff
SCE-UA
SCEUA
Para.
set 1
Para.
set 2
Para.
set 3
Para.
set 4
Para.
set 5
Para.
set 6
Para.
set 7
Para.
set 8
Para.
set 9
Para.
set 10
Para.
set 11
1
0.65
0.92
0.89
0.93
0.94
0.91
0.95
0.92
0.90
0.86
0.84
Para. set 1
0.65
1
0.68
0.65
0.63
0.64
0.69
0.66
0.64
0.65
0.62
0.72
Para. set 2
0.92
0.68
1
0.87
0.90
0.92
0.92
0.94
0.89
0.89
0.84
0.87
Para. set 3
0.89
0.65
0.87
1
0.97
0.94
0.93
0.94
0.97
0.94
0.97
0.87
Para. set 4
0.93
0.63
0.90
0.97
1
0.96
0.94
0.96
0.98
0.94
0.94
0.86
Para. set 5
0.94
0.64
0.92
0.94
0.96
1
0.95
0.99
0.95
0.96
0.92
0.87
Para. set 6
0.91
0.69
0.92
0.93
0.94
0.95
1
0.96
0.92
0.97
0.90
0.93
Para. set 7
0.95
0.66
0.94
0.94
0.96
0.99
0.96
1
0.95
0.95
0.91
0.87
Para. set 8
0.92
0.64
0.89
0.97
0.98
0.95
0.92
0.95
1
0.93
0.95
0.85
Para. set 9
0.90
0.65
0.89
0.94
0.94
0.96
0.97
0.95
0.93
1
0.92
0.93
Para. set 10
0.86
0.62
0.84
0.97
0.94
0.92
0.90
0.91
0.95
0.92
1
0.85
Para. set 11
0.84
0.72
0.87
0.87
0.86
0.87
0.93
0.87
0.85
0.93
0.85
1
Then it is noteworthy to investigate further identifying the good parameter sets by
calculating their depth based on other performance criteria. Besides others, the ideal
117
5. Physically based distributed hydrological modeling for HSA estimation
SCEUA
Para.
set 1
Para.
set 2
Para.
set 3
Para.
set 4
Para.
set 5
Para.
set 6
Para.
set 7
Para.
set 8
Para.
set 9
Para.
set 10
Para.
set 11
Min. [mm]
0
0
0
0
0
0
0
0
0
0
0
0
Max. [mm]
918
917
917
917
917
918
917
918
917
917
917
917
Mean [mm]
77
60
44
144
106
61
98
72
122
80
134
65
Std. dev [mm]
155
158
153
190
165
152
163
155
177
154
171
152
Sum [mi. m3]
43.417
34.011
24.581
80.973
59.470
34.353
55.176
40.300
68.987
45.332
75.470
36.470
Sum of surface runoff [mi. m3]
90
80
70
60
50
40
30
20
10
1
a.
se
t1
0
t1
Pa
r
se
a.
a.
se
t9
Pa
r
t8
Pa
r
a.
se
t7
Pa
r
a.
se
t6
Pa
r
Pa
r
a.
se
t5
Pa
r
a.
se
t4
Pa
r
a.
se
t3
se
a.
Pa
r
Pa
r
a.
se
t1
se
a.
-U
A
Pa
r
E
SC
t2
0
Parameters
Figure 5.18: Statistics of distributed surface runoff (1993) simulated by different good parameter
sets identical for all subcatchments
criteria in our case would be the observed surface runoff in the catchment which is
the basis of locating HSAs; but such observations are hardly available. However,
base-flow separation of observed and simulated hydrographs at gauges can be done
using some existing algorithm and so obtained surface runoff and its simulation error
can be used to evaluate the depth for identifying good parameters. It is described in
following section.
5.5 Surface runoff estimation through baseflow separation
The exact separation of the different flow components is often arbitrary and based
on either the use of chemical or isotopic tracers on the field and mass balance approaches or the use of standard methodologies cited in the literature. Several hydrograph analysis methods for river discharge time-series are very often applied when
the quantification of the effective groundwater recharge and discharge, or of the
interflow, is needed. All methods separate the hydrograph into at least two components: a direct discharge, identified as surface runoff, and a baseflow, identified
as groundwater discharge or as the sum of groundwater discharge and interflow. In
our case here, it is not intended to use the separated flow components further in
the modeling/simulation; instead it is intended to have the separated surface runoff
for the observed and simulated (with different parameter sets) hydrographs and use
118
5.5. Surface runoff estimation through baseflow separation
the simulation performance to identify the good parameter sets based on the ROPE
algorithm. In this context, an automated baseflow separation technique based on a
recursive digital filter (Arnold et al. 1995) is used in this study. The filtering technique is analogous to that in signal analysis and processing in which high frequency
signals (surface runoff) is filtered from low frequency signals (baseflow). The equation of the single parameter recursive filter which is followed here as used in SWAT
model (Arnold et al. 1995) is:
Qsurf,t = β · Qsurf,t−1 + (1 + β) /2 · (Qtot,t − Qtot,t−1 )
then, Qbase,t = Qtot,t − Qsurf,t
(5.26)
(5.27)
Flo w [mm]
where Qsurf,t , Qtot,t , and Qbase,t , are respectively the filtered surface runoff (quick
response), total stream flow and the separated base flow (slow response) at t time step
and β is the filter parameter (= 0.925; Nathan & McMahon 1990).
The filter can be passed through
20
the stream flows for three times;
Total Flow
forward, backward and forward.
Base Flow – Filter
16
pass1
Each pass, in general, results
Base Flow – Filter
pass2
12
lesser baseflow in percentage of
Base Flow – Filter
pass3
total flow. This option provides
8
some added flexibility to adjust
the separation to approximate
4
site conditions more accurately.
0
As an example, the baseflow1/1/1993
2/20/1993 4/11/1993 5/31/1993 7/20/1993
9/8/1993 10/28/1993 12/17/1993
Time [d ]
surface runoff separated from
the observed discharge series of
1993 in Gauge 1 of the Rems Figure 5.19: Surface runoff-baseflow separation of observed discharge series (1993) in Gauge 1 uscatchment by using this digital
ing digital filter
filter with the three passes is
shown in Fig. 5.19.
In the absence of observed on-site conditions of baseflow or surface runoff it is recommended to use one pass filter (Arnold et al. 1995) and same is followed in our
further analysis.
5.5.1 Parameters identification based on surface runoff and other criteria
The parameters estimated up to now were based on sum of squared error of discharge
series. The main criteria considered here further is the accuracy in simulating surface
runoff by different parameter sets compared to the observed surface runoff; which
is separated from the respective hydrographs using same method (the digital filter)
for the both. Along with the surface runoff volume error, other considered criteria
are 90% non-exceeding surface runoff value error, linear and log NS coefficients, root
mean square error (RMSE) of peaks, sum of squared error of biggest 10% flow values
(top 10% of flow duration curve) and baseflow volume error.
119
5. Physically based distributed hydrological modeling for HSA estimation
The final 1955 good parameter sets obtained using the ROPE algorithm (Section
5.4.3.3 and Table 5.19) are numbered serially according to the ascending order of the
sum of squared error of the discharge series (equally weighted for the four subcatchments) which they simulated for the year 1993. This means the parameter set 1 is
with minimum sum of squared error of the discharge series while parameter set 1955
is with maximum sum of the squared error. The surface runoff and baseflow volume
error are calculated for each parameter set by employing the hydrograph separation
technique using the digital filter as discussed above. The flows above 2mm/d in each
gauge are considered to calculate RMSE of peaks. The observed and simulated discharge series are arranged in descending order and the sum of squared error for the
top 10% discharge values are calculated for each parameter set. And the linear and
log NS coefficients are calculated (Equations 5.18 and 5.19) for each set of simulated
series. These calculations are carried out for each of the four gauges.
Then using the half-space depth
function (Equation 5.25), depth of
each parameter set is calculated, at
first based on the 1955 parameter
sets itself (own geometry) and then
based on about 500 best parameter
sets in each of the criteria mentioned
above. When the deep parameter
sets based on the different criteria are compared with their depth
based on the whole 1955 parameter
sets itself, it is found that the sets in
the interior of the geometry (higher
depth) are deep in the other criteria
too. For example, based on the surface runoff volume error, it is found
that 1345 parameter sets lie outside
the convex hull and have zero depth
while 610 parameter sets are found
Figure 5.20: Distribution of the geometrical depth of
to be deep based on this criterion.
the parameter sets deep and non-deep
The depth distribution of these 610
on the basis of the surface runoff volume
error
and 1345 parameter sets based on
the whole 1955 parameter sets (position in the geometry) is shown in Fig. 5.20,
which indicates that majority of the 610 parameters deep on the basis of surface
runoff volume criteria are deep sets in the clouds of the 1955 parameter sets. Table 5.22 lists the twenty deepest parameter sets and the rank of their depth based
on the different criteria and Table 5.23 lists the rank of the depth of the deepest
parameter set in each of the criteria and the rank of the combined depth of all criteria. They also show that the high depth parameter sets are generally deep in all
other criteria too. This verifies the basis of the concept that the good performing
parameter sets have certain well defined structure/geometry in the parameter clouds.
The performance (for the calibration year 1993) of each of the 1955 parameter sets
120
5.5. Surface runoff estimation through baseflow separation
Table 5.22: Twenty deepest parameters and the rank of their depth based on different criteria
Parameter
set No.
Itself
Sum sq.
Error
lin. NS
log NS
Peaks
RMSE
10% flow
dur.
sro vol.
Error
Baseflow
vol. Error
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
8
36
1
2
4
58
9
1007
1260
34
1507
5
12
1701
3
19
1487
6
1000
60
3
22
1
4
2
25
7
574
59
30
600
6
11
602
5
18
67
9
40
123
1
45
3
7
113
24
2
6
1264
40
1507
4
32
1701
49
1001
565
22
535
122
11
39
2
3
1
119
18
547
49
23
572
5
24
574
8
14
1490
10
47
85
8
41
2
1
3
29
7
23
100
32
602
27
53
603
10
569
1489
22
34
600
2
19
1
3
6
47
5
37
68
32
1509
8
44
1702
27
28
1489
56
57
1472
2
1370
10
11
825
23
1
4
1304
40
1520
8
449
1702
719
1064
544
42
1096
1487
1178
1333
288
632
561
1245
529
986
1253
660
1507
544
899
1701
380
933
1487
877
978
1470
Table 5.23: Rank of depth of deepest parameter sets based on different criteria
Parameter
set No.
Itself
Sum sq.
Error
lin. NS
log NS
Peaks
RMSE
10% flow
dur.
sro vol.
Error
Baseflow
vol. Error
Threshold
(basis set)
all
800 (321
paras)
930 (522
paras)
830 (505
paras)
880 (505
paras)
750 (502
paras)
750 (511
paras)
780 (501
paras)
paras D>0
all (605
D>1)
366
paras
602
paras
565
paras
574
paras
603
paras
610
paras
557
paras
288
529
3rd
7th
1st
7th
1st
7th
3rd
2nd
2nd
14th
2nd
6th
1st
5th
561
5th
4th
2nd
96th
1st
3rd
5th
576th
632
1178
4th
1st
1st
6th
4th
3rd
7th
1st
3rd
10th
1st
7th
3rd
2nd
8th
1st
558th
(D=0)
8th
2nd
544
12th
5th
6th
4th
5th
27th
8th
8th
2nd
Combined
ranking
1st
4th
1st
3rd
based on six different criteria namely, linear and log NS coefficients, root mean square
error (RMSE) of peaks, sum of squared error of biggest 10% flow values (top 10%
of flow duration curve), surface runoff volume and 90% non-exceeding surface runoff
values are plotted as shown in Fig. 5.21 for all the four subcatchments respectively.
The corresponding performance measures due to the parameter sets obtained by
PEST and SCE-UA with different parameter set for different subcatchments and
again with SCE-UA with same parameter set for all subcatchments are also plotted
as parameter number 500, 1000 and 1500 respectively in the Fig. 5.21.
The 1955 good parameter sets analyzed here are obtained based on minimum sum
of squared error. In Fig. 5.21 it can be seen that they are good for all the subcatchments in many of the mentioned criteria, but there are not any parameter sets that
121
5. Physically based distributed hydrological modeling for HSA estimation
Catchment 1
Catchment 2
0.95
0.90
Catchment 3
Catchment 4
0.9
0.9
0.9
0.8
0.8
0.8
lin NS
0.7
0.85
0.6
0.5
0.80
0.3
0.70
0.2
log NS
0
RMSE of peaks [mm/d]
500
1000
1500 2000
0
500
1000
0.5
0.5
0.4
0.4
0
1500 2000
500
1000
1500
2000
0.8
0.9
1.0
0.8
0.6
0.8
0.8
0.6
0.7
0.4
0.7
0.6
0.2
0.6
0.5
0.0
0.5
0.4
0.2
0.4
500
1000
1500 2000
3.0
0
500
1000
2.5
500
1000
1500
2000
3.5
3.5
3.0
2.5
2.5
2.5
1.5
2.0
2.0
2.0
1.0
1.5
1.5
300
0
500
1000
200
150
500
1000
1500
2000
300
250
250
200
200
200
150
150
150
100
100
100
50
50
50
50
0
0
0
500
1000
1500 2000
250
200
0
500
1000
1500 2000
200
120
180
100
40
f or obs. series
20
50
0
500
2.0
1.8
1.6
1.4
1.2
1.0
0.8
0.6
0.4
1000
f or obs. series
0
500
1000
Parameter Set
1500
2000
80
f or obs. ser ies
60
0
1500 2000
1500 2000
120
60
f or obs. series
1000
140
80
100
500
160
100
150
500
1000
1500 2000
0
500
1000
1500
f or obs. series
0
500
1000
1500 2000
Parameter Set
1000
1500
2000
0
500
1000
1500
2000
0
500
1000
1500 2000
0
500
1000
0
500
1000
200
180
160
140
120
100
80
60
40
2000
1.2
1.1
1.0
0.9
0.8
0.9
0.8
0.7
0.6
0.5
0.4
0.3
0.2
0.1
500
0
0
140
0
300
250
100
0
2000
1.5
0
1500 2000
300
250
1500
0.0
3.0
1500 2000
1000
-0.2
3.0
1000
500
0.2
2.0
500
0
0.4
0
1500 2000
3.5
0
Sq. Error- biggest 10%
0.6
0.9
0
Total SRO vol [mm]
0.7
0.6
0.4
0.75
90% < SRO value [mm]
0.7
f or obs. series
1500 2000
1.2
1.0
0.8
0.6
0.7
0.6
0.5
0.4
0.4
f or obs. series
f or obs. ser ies
0.2
0
500
1000
1500 2000
Parameter Set
1500
2000
Parameter Set
Figure 5.21: Performance analysis of 1955 good parameter sets (step-3) based on different criteria
are good in surface runoff criteria too at the same time. Probably we have reached
quite far in the direction of minimum sum of squared error by reaching the third step
of the ROPE algorithm in which we obtained the good performing 1955 parameter
sets (Table 5.19). So compromising with some loss in other performance criteria,
we move to one step back where 3007 parameters were generated (Table 5.19). The
parameter sets were searched from the 3007 parameter sets that are, besides others,
good in the surface runoff criteria also. Like earlier with 1955 parameter sets, the
122
5.5. Surface runoff estimation through baseflow separation
3007 parameter sets are numbered according to ascending sum of squared error of
equally weighted discharge series of the four subcatchments and performance of each
of them based on already mentioned different criteria are plotted as shown in Fig.
5.22. The corresponding performance measures with the parameter sets obtained
by PEST and SCE-UA with different parameter set for different subcatchments and
again with SCE-UA with same parameter set for all subcatchments are also plotted
in Fig. 5.22 as parameter number 500, 1000 and 1500 respectively. Comparing it
to Fig. 5.21 it can be seen that unlike with the 1955 parameter sets of last step of
ROPE algorithm, the 3007 parameter sets of one step earlier consist of several good
parameter vectors that are good based on the surface runoff estimation too.
Due to the large variability in the total amount of the simulated distributed surface
runoff despite the similar spatial patterns and equally well model performance of
different parameter sets, a single parameter set to be used in further analysis could
not be finalized with acceptable reliability. Therefore twenty different parameter sets
performing well on all performance criteria including the surface runoff simulation
are selected from the evaluated 3007 parameter sets. The ten of them are with higher
depth (D>2) and another ten are the boundary sets (D=1). The SCE-UA optimized
parameter set is also taken up for the further analysis. The performance measures
of these selected 21 parameter sets for the calibration year are shown in Table 5.24.
The transferability of these parameter sets to other time period is investigated by
evaluating their performance measures in the period of 1993-1997. The obtained
performance measures are shown in Table 5.25 which shows that the selected parameters perform equally well in other time period too.
The ranking of these 21 parameter sets based on the mentioned performance criteria
is shown in Table 5.26. It can be seen that the globally optimized parameter set
(with SCE-UA) is best in linear NS efficiency but is almost worst in surface runoff
volume estimation among the selected 21 parameter sets.
The WaSiM-ETH model is run with these 21 parameter sets for the period of 19902005. The simulated daily surface runoff grids (HSAs) with each parameter set for
the sixteen years are then supplied to the erosion model for spatially distributed and
temporally varying erosion risk estimation, which is described, along with further
research works, in Chapter 6.
123
5. Physically based distributed hydrological modeling for HSA estimation
Catchment 1
Catchment 2
0.95
0.90
lin NS
0.85
0.80
log NS
RMSE of peaks [mm/d]
0.8
0.8
0.6
0.5
0.7
0.7
0.6
0.6
0.75
0.5
0.5
0.2
0.4
0.4
1000
2000
0
3000
1000
2000
3000
0
1000
2000
3000
0.9
0.8
0.9
1.0
0.8
0.6
0.8
0.8
0.7
0.4
0.7
0.6
0.2
0.6
0.5
0.0
0.5
0.0
0.4
-0.2
0.4
-0.2
0
1000
2000
3000
0
1000
2000
3000
0.6
0.4
1000
2000
3000
0
1000
2000
3000
0.2
0
1000
2000
3000
3.0
3.5
3.5
3.5
2.5
3.0
3.0
3.0
2.0
2.5
2.5
2.5
1.5
2.0
2.0
2.0
1.0
1.5
1.5
0
Sq. Error- biggest 10%
0.9
0.70
0
1000
2000
3000
0
1000
2000
3000
1.5
0
1000
2000
3000
300
300
300
250
250
250
250
200
200
200
200
150
150
150
150
100
100
100
50
50
50
50
0
0
0
1000
2000
3000
0
1000
2000
3000
120
f or obs. ser i es
2.0
1.8
1.6
1.4
1.2
1.0
0.8
0.6
0.4
2000
3000
1000
2000
Parameter Set
1000
0.9
0.8
0.7
0.6
0.5
0.4
0.3
0.2
0.1
f or obs. series
0
0
3000
2000
f or obs. series
0
1000
2000
Parameter Set
80
3000
f or obs. ser i es
60
0
3000
2000
3000
0
1000
2000
3000
0
1000
0
1000
200
180
160
140
120
100
80
60
40
100
40
20
1000
3000
120
60
0
2000
140
80
f or obs. series
1000
160
100
1000
0
0
200
180
140
250
225
200
175
150
125
100
75
50
0
300
100
0
Total SRO vol [mm]
Catchment 4
0.9
0.4
0.3
0
90% < SRO value [mm]
Catchment 3
0.9
0.8
0.7
1000
1.2
1.1
1.0
0.9
0.8
0.7
0.6
0.5
0.4
2000
3000
f or obs. ser ies
0
1000
2000
Parameter Set
3000
f or obs. ser ies
1.2
1.1
1.0
0.9
0.8
0.7
0.6
0.5
0.4
0.3
0.2
2000
3000
f or obs. series
2000
3000
Parameter Set
Figure 5.22: Performance analysis of 3007 good parameter sets (step-2) based on different criteria
124
5.5. Surface runoff estimation through baseflow separation
Table 5.24: Performance measures of selected 21 different parameter sets for the year 1993
Best performing parameters but not deep
Measures
Best performing parameters and deep
Para.
Set
from
SCEUA
Catchments
Para. Para. Para. Para. Para. Para. Para. Para. Para. Para. Para.
Set
Set
Set
Set
Set
Set
Set
Set
Set
Set Set
695
628
876
877 1132 1302 1307 1378 1405 1641 15
Para. Para. Para. Para. Para. Para. Para. Para. Para.
Set
Set
Set
Set
Set
Set
Set
Set
Set
295
501
895
921 1199 1243 1245 1299 1581
catch. 1
0.82 0.82
0.78
0.81
0.81
0.81
0.82
0.80
0.80
0.81 0.84
0.81
0.82
0.81
0.82
0.77
0.77
0.81
0.81 0.79
0.83
catch. 2
0.60 0.59
0.60
0.55
0.52
0.45
0.42
0.49
0.50
0.38 0.73
0.66
0.64
0.54
0.64
0.56
0.62
0.45
0.46 0.54
0.78
catch. 3
0.76 0.76
0.76
0.76
0.73
0.71
0.71
0.70
0.70
0.67 0.79
0.78
0.76
0.74
0.71
0.73
0.72
0.72
0.71 0.66
0.79
catch. 4
0.66 0.65
0.69
0.65
0.63
0.63
0.63
0.63
0.60
0.60 0.68
0.68
0.66
0.66
0.62
0.67
0.63
0.64
0.63 0.60
0.70
catch. 1
0.72 0.71
0.64
0.72
0.69
0.69
0.66
0.64
0.71
0.62 0.73
0.73
0.69
0.69
0.68
0.70
0.70
0.71
0.68 0.71
0.66
catch. 2
0.50 0.44
0.54
0.42
0.40
0.40
0.65
0.68
0.43
0.63 0.48
0.49
0.40
0.47
0.49
0.59
0.45
0.38
0.33 0.52
0.71
catch. 3
0.81 0.80
0.79
0.80
0.77
0.75
0.75
0.77
0.78
0.73 0.78
0.82
0.76
0.80
0.53
0.81
0.79
0.79
0.72 0.74
0.74
catch. 4
0.74 0.71
0.73
0.71
0.65
0.64
0.72
0.72
0.63
0.70 0.71
0.74
0.64
0.72
0.08
0.76
0.60
0.69
0.58 0.49
0.73
catch. 1
2.1
2.1
2.2
2.2
2.2
2.2
2.1
2.3
2.3
2.2
2.1
2.2
2.2
2.2
2.2
2.4
2.4
2.2
2.2
2.3
2.0
catch. 2
2.4
2.4
2.4
2.5
2.6
2.8
2.9
2.7
2.7
3.0
1.9
2.1
2.2
2.5
2.2
2.5
2.3
2.8
2.8
2.6
1.7
catch. 3
2.4
2.4
2.3
2.4
2.5
2.6
2.6
2.7
2.7
2.8
2.3
2.3
2.4
2.5
2.6
2.5
2.6
2.6
2.6
2.8
2.2
catch. 4
2.6
2.6
2.5
2.6
2.7
2.7
2.7
2.7
2.8
2.8
2.5
2.5
2.6
2.6
2.7
2.6
2.7
2.7
2.7
2.8
2.4
catch. 1
sum of sq.
catch. 2
error for
biggest
catch. 3
10%
catch. 4
60
54
94
74
55
64
53
66
64
60
42
69
52
70
46
92
97
71
71
91
48
71
68
75
92
93
135
163
121
102
169
18
45
48
98
50
83
60
128
130
101
19
22
28
34
34
35
46
51
51
39
60
29
23
28
32
45
28
37
38
50
77
38
13
17
16
15
18
15
22
18
19
26
41
19
22
13
19
10
12
14
18
21
55
59.1
17.6
22.4
18.5
25.8
20.7
2.7
11.0
-5.7
16.6
7.9
34.8
6.6
13.3
9.9
7.4
8.4
23.4
18.5
-20.9 -21.1 -5.9 -25.9 -7.2
-4.1
11.0 -16.8 -23.2 -5.8 -47.2 -40.2 -42.8 -12.2 -32.4 -40.9 -37.2 -17.2 -20.7 -25.1
-43.4
-9.5 -13.7 24.8
-4.3
20.0
19.7
-11.0
-23.1 -23.0 -13.8 -27.3 -19.7 -22.3 -10.1 -12.8 -31.2 -15.4 -42.5 -31.2 -30.9 -16.6 -26.1 -22.5 -12.4 -32.7 -23.9 -1.2
-31.9
lin. NS
log NS
RMSE of
peaks
[mm/d]
catch. 1
90% nonexceedence catch. 2
value error catch. 3
[%]
catch. 4
catch. 1
Surface
catch. 2
runoff vol.
error [%] catch. 3
catch. 4
Baseflow
vol. error
[%]
24.4 22.2
3.8
1.4
18.4
-3.2
0.8
-6.6
3.0
3.0
4.3
-21.4 -21.3 -13.9 -18.2 -15.3 -11.3
3.7
-5.6
6.0
-7.3
5.5
-6.5
-1.9
-0.1
3.9
2.9
-16.0
-4.1
5.6
0.9
-25.3 -8.1 -11.0 -0.7
-11.7
0.0
-2.8
9.1
-1.0
-4.0
-6.6
3.6
6.5
-9.7
5.9
-5.4
-1.0
1.7
6.1
-3.3
-11.1 -21.0 -1.5 -42.6 -27.8 -29.2 -15.0 -27.2 -20.4 -24.9 -15.7 -13.1 -16.1
3.7
-7.0
4.7
-24.9 -11.6 -11.1
0.3
-0.4
-4.6
-0.5
-5.8
-1.5
-38.3
11.0
-19.6
-18.7 -18.3 -11.2 -18.8 -14.9 -15.8 -8.4 -10.4 -17.6 -9.7 -35.2 -24.3 -24.6 -15.4 -16.9 -19.5 -12.5 -20.2 -17.1 -4.7
-31.2
catch. 1
8.1
10.5
-2.3
11.1
8.9
9.0
16.1
1.2
11.0
10.4 15.0
8.6
5.1
1.7
2.6
1.1
12.1
7.1
5.0
14.9
catch. 2
-0.7
0.4
-5.9
0.2
-3.3
-4.3
16.6
1.5
-2.9
5.0
-1.5 -12.6 -3.5
-8.8
-3.7
-8.8
-0.8
-9.6
-0.3
18.4
catch. 3
9.7
12.4
-0.3
12.0
7.8
5.7
22.7
5.3
9.7
12.0 16.4
10.1
-0.6
5.2
-9.9
3.3
1.5
10.4
1.5
3.9
24.4
catch. 4
6.2
7.5
-3.8
7.9
2.7
0.4
19.5
-0.8
1.6
7.0
6.8
-5.4
1.0
-21.8 -0.4
-9.8
5.8
-4.0
-9.5
22.5
2.2
13.5
3.9
Table 5.25: Performance measures of selected 21 different parameter sets for 1993-1997
Best performing parameters but not deep
Measures
lin. NS
log NS
Best performing parameters and deep
Para.
Set
from
SCEUA
Catchments
Para. Para. Para. Para. Para. Para. Para. Para. Para. Para.
Para. Para. Para. Para. Para. Para. Para. Para. Para.
Para.
Set
Set
Set
Set
Set
Set
Set
Set
Set
Set
Set
Set
Set
Set
Set
Set
Set
Set
Set
Set 15
628
695
876
877 1132 1302 1307 1378 1405 1641
295
501
895
921 1199 1243 1245 1299 1581
catch. 1
0.50 0.51 0.39 0.49 0.51 0.48 0.51 0.41 0.49 0.49 0.56 0.49 0.47 0.48 0.49 0.38 0.41 0.49 0.46 0.44
0.53
catch. 2
0.49 0.48 0.44 0.47 0.47 0.47 0.50 0.43 0.48 0.48 0.50 0.49 0.47 0.47 0.49 0.41 0.44 0.47 0.44 0.46
0.56
catch. 3
0.69 0.68 0.64 0.68 0.67 0.66 0.67 0.62 0.68 0.65 0.70 0.69 0.66 0.68 0.66 0.63 0.66 0.68 0.64 0.67
0.71
catch. 4
0.65 0.64 0.59 0.64 0.61 0.60 0.62 0.56 0.63 0.58 0.67 0.66 0.59 0.63 0.60 0.57 0.61 0.64 0.56 0.61
0.69
catch. 1
0.66 0.66 0.63 0.68 0.66 0.66 0.58 0.61 0.67 0.57 0.63 0.67 0.66 0.66 0.66 0.66 0.69 0.68 0.66 0.67
0.53
catch. 2
0.58 0.55 0.61 0.55 0.51 0.53 0.63 0.66 0.55 0.63 0.54 0.59 0.55 0.57 0.59 0.64 0.57 0.51 0.50 0.60
0.62
catch. 3
0.81 0.80 0.80 0.81 0.79 0.77 0.75 0.77 0.79 0.73 0.77 0.82 0.79 0.81 0.79 0.82 0.82 0.80 0.74 0.82
0.69
catch. 4
0.74 0.72 0.73 0.73 0.67 0.63 0.68 0.70 0.70 0.61 0.71 0.75 0.65 0.72 0.63 0.75 0.73 0.71 0.55 0.73
0.69
catch. 1
3.2
3.2
3.5
3.4
3.1
3.3
3.1
3.6
3.4
3.2
3.1
3.4
3.4
3.3
3.3
3.8
3.7
3.4
3.4
3.5
3.1
2.5
2.5
2.6
2.5
2.4
2.5
2.4
2.6
2.4
2.4
2.4
2.5
2.5
2.5
2.5
2.7
2.6
2.5
2.6
2.6
2.3
2.4
2.4
2.5
2.4
2.4
2.4
2.4
2.6
2.4
2.4
2.3
2.4
2.5
2.4
2.5
2.6
2.5
2.4
2.5
2.4
2.3
2.1
2.1
2.3
2.2
2.2
2.2
2.1
2.4
2.2
2.2
2.1
2.1
2.3
2.2
2.3
2.4
2.3
2.2
2.4
2.3
RMSE of catch. 2
peaks [mm/
catch. 3
d]
catch. 4
2.0
catch. 1
sum of sq.
catch. 2
error for
biggest
catch. 3
10%
catch. 4
1997 1974 3624 2588 1927 2032 1975 2840 1690 1743 1520 2562 2334 2403 2102 3475 3271 2123 2616 3005
2044
482
515 1003 647
549
564
640
390
582
288
544
611
646
539 1037 805
535
787
275
692
819 1263 899
826
762
857 1054 493
731
755
826
892
822
855 1084 884
638 1022 899
686
336
375
426
468
480
511
298
384
523
464
468
342
593
281
catch. 1
90% nonexceedence catch. 2
value error catch. 3
[%]
catch. 4
57.8 51.9 113.3 43.0 56.5 49.5 62.5 79.7 30.2 64.8 15.0 42.7 49.4 71.5 57.8 63.6 54.2 29.6 47.4 52.3
64.7
-12.2 -15.4 19.8 -24.4 -6.1
-20.2
catch. 1
Surface
catch. 2
runoff vol.
error [%] catch. 3
catch. 4
Baseflow
vol. error
[%]
816
447
-4.3
8.8
973
805
275
16.7 -18.8 18.4 -41.6 -28.4 -6.4
6.3
2.0
43.2
-4.8
9.3
10.1 19.6 34.0
1.7
-3.4
36.9 -10.7
6.4
7.3
-7.2
3.3
790
591
799
698
-4.2 -12.0 -18.1 -20.2 -5.5 -12.0
30.0 -22.5 -5.7
9.6
18.5 11.1 12.0
6.6
-7.3
11.5
7.7
3.6
16.0 32.9 -10.2 28.5 -27.2 -11.3
6.0
13.0 11.3 10.7
4.4
-11.3
8.1
7.9
-1.8
28.3 23.7 59.2 26.0 25.3 29.0 32.3 50.6 20.1 35.7
8.4
27.0 30.4 37.7 29.7 44.3 40.1 23.3 33.0 38.7
-17.8 -20.2
5.1
-18.3 -15.4 -11.0 -4.4
7.9
-19.7
2.9
-2.3
-6.5
23.8
-4.2
-1.1
4.5
7.3
23.4
-5.2
15.2 -21.4 -5.1
4.2
7.2
3.2
-4.8
-9.1
21.5
-7.1
-3.2
2.9
5.7
22.4
-7.0
15.1 -24.2 -8.2
2.2
4.6
3.3
34.1
-9.7 -18.3 -6.0
-9.4
-21.6
14.4
8.1
-4.2
9.2
7.1
-4.4
11.8
5.8
-7.0
7.5
7.0
-7.1
catch. 1
42.6 44.8 25.1 42.9 41.8 40.1 50.1 35.4 44.9 47.1 51.5 41.5 37.4 35.8 38.8 34.0 31.2 42.9 35.7 35.5
49.9
catch. 2
12.4 12.2
3.8
12.3
9.4
26.3
catch. 3
22.5 23.8
9.8
22.9 18.9 16.7 30.1 18.2 22.2 24.4 29.6 22.8 14.9 16.1 16.8 16.3 13.1 20.9 12.4 18.1
35.3
catch. 4
21.8 23.0
9.6
22.4 17.6 15.2 30.0 18.1 20.9 23.6 28.3 22.4 13.6 15.5 13.9 16.2 12.1 19.9 11.0 15.7
35.3
8.0
7.5
-35.9 -20.5 -11.6 -8.9 -13.7 -2.3
21.9 13.0 11.7 16.8 16.7 12.7
5.5
7.2
8.1
9.6
4.4
10.2
3.7
125
5. Physically based distributed hydrological modeling for HSA estimation
Table 5.26: Performance ranking of the selected 21 different parameter sets
Parameter
Set No.
Surface
Runoff
90% non
exceedence
value
lin. NS
log NS
Combined
Boundary
parameter
sets
(Depths = 1)
628
695
876
877
1132
1302
1307
1378
1405
1641
5
15
19
13
1
4
2
20
7
16
11
13
20
16
3
4
6
18
15
14
4
6
17
8
12
14
5
16
10
11
3
7
8
6
15
19
10
12
14
17
2
5
16
8
5
14
1
16
5
9
Deep
parameter
sets
(Depths >2)
15
295
501
895
921
1199
1243
1245
1299
1581
21
17
8
3
12
14
9
11
6
10
21
19
9
5
10
7
2
17
8
1
2
3
15
9
19
13
18
7
21
20
4
1
18
11
21
2
9
13
20
16
19
14
11
2
19
4
11
9
19
16
SCE-UA
18
12
1
5
11
5.6 Conclusions
Erosion control strategies should focus especially on surface runoff and their spatial
and temporal variation within the catchment. Therefore the models should consider
variable hydrological active source areas; called as Hydrologically Sensitive Areas
(HSAs) in this study. These models should also be able to consider runoff generation
by saturated overland flow as well as Horton overland flow. Here the model was
run in the WaSiM-ETH runoff generation mode- the combined extended/modified
Topmodel (saturated overland flow) and Green and Ampt (infiltration excess) runoff
approach for the simulation of runoff generating areas. The possibility of predicting
spatial patterns of catchment erosion reasonably well by the use of WaSiM-ETH with
USLE-based models is already shown through a case study described in Chapter 4.
So, the research work presented in this Chapter was basically aimed to identify the
spatially distributed and temporally varying HSAs through the use of the physically
based distributed rainfall-runoff modeling (with WaSiM-ETH) and evaluate the distributed performance of the model. In the course, attempts have been made to seek
the answers to the following research questions:
p How do the surface runoff patterns differ in different subcatchments when subcatchments are calibrated independently and how do they look like when calibrated for same parameter set in all subcatchments?
126
5.6. Conclusions
p How do the distributed results obtained from parameters calibrated with different calibration techniques differ?
p Are the calibrated parameters, performing good in hydrographs simulation,
good enough in predicting spatially distributed surface runoff too? How to
find the parameters that are good in all aspects or what would be a robust
parameter estimation technique?
At first, the thorough review of the soil module of WaSiM-ETH version 1 (modified
Topmodel version) was made which is responsible for generating surface runoff and
hence relevant in this research work. Based on the data requirements and available
data, the model was then set-up for the Rems catchment consisting of four subcatchments/gauges. The spatial discretization was done with 100m x 100m regular grids
and the temporal resolution adopted was 1 day. The eleven free model parameters
that need model-calibration for their estimation have been reviewed. The year 1993
was chosen for calibration with 1992 as warm-up period. The parameters estimation
was carried out, at first, with quite efficient Gauss-Marquardt-Levenberg algorithm
using PEST tool and the simulation is done continuously for sixteen years (19902005). This algorithm was first choice for its advantage that it estimates parameters
using considerably fewer model runs than any other estimation method for nonlinear
models and hence best suited practically for the CPU intensive distributed model
like the WaSiM-ETH. The parameter sets were calibrated for each subcatchment
independently using their observed discharge series at the respective outlets. The
observed discharge series in the gauges are passed to downstream subcatchment in
each time step during calibration/simulation to avoid propagation of the error associated with the simulated series. The calibration and over all model performances
evaluated through yearly linear and log NS efficiency, PBIAS and RSR showed quite
good simulation for subcatchment 3 (Schorndorf) and subcatchment 4 (Neustadt),
acceptable performance for subcatchment 2 (Haubersbronn) but that of subcatchment 1 (Schwäbisch-Gmünd) is quite low for most of the years although it was highest
during calibration (1993).
With the hope of achieving better overall model performance, the calibration is redone using the same Gauss-Marquardt-Levenberg method now for the year 1996 (the
worst performing year) with the same land use of 1993 and also for the year 2000 but
this time using the land use grid of the year 2000. It was found that the optimized
values of the parameters vary widely and randomly with the change in calibration
period and/or land use, although the method is same. The yearly model performance exhibit the similar trend despite the different parameter sets. The year 1996,
which represents an extreme case in the lower side (low precipitation and temperature, cannot be simulated properly unless calibration is done for this year itself. It
gives an indication that the physically-based distributed WaSiM-ETH model may be
incapable of simulating such low events. Further it was seen that the calibrated parameter set from the year 1996, which has events of low magnitude, have performed
better throughout the simulation period than that from 1993 and 2000 representing
medium events of the simulation period. It implies that the inclusion of or giving
priority to unusual events for calibration is necessary for achieving good model performance overall.
127
5. Physically based distributed hydrological modeling for HSA estimation
Then the monthly HSAs were estimated from the daily simulated spatially distributed
surface runoff grids for all the three sets of the calibrated parameter sets. They were
calculated as the percentage of number of days that any pixel generates surface runoff
in that month during the sixteen years of simulation period (1990-2005). Attempt
has been made to relate these monthly probabilities of surface runoff generation with
the easily measurable relevant proxy parameters so that the complicated modeling
could be avoided to locate the HSAs equally well. The surface runoff generation
can be easily thought of being a function of topography, climate, soil and land use
and accordingly the distributed values of precipitation, topographic wetness index
and curve number (CN) were used as those proxy parameters. The spatially distributed multiple linear regressions carried out between those proxy parameters and
the surface runoff generation probabilities for each month yielded surprising and
unacceptable results. The surface runoff generation probabilities were found to be
negatively correlated with the topography wetness index and curve number in several cases. Moreover the regression coefficients as well as the main influencing proxy
parameter vary widely and randomly between subcatchments and between the set
of the calibrated parameters. So the applicable relationships, in general, to identify
HSAs through easily obtainable parameters cannot be devised. In the similar context, it was also found that the pattern of spatially distributed surface runoff varies
not only among the different parameter sets with which they are simulated but also
varies abruptly and unrealistically between the subcatchments.
Immediate doubt for these issues went to the parameter optimization method adopted
here. The Gauss-Marquardt-Levenberg method have been used for its faster convergence but it has the disadvantage that it is only a local search technique; their results
depend on the closeness of the selected initial values of the search to the global optimum and so there is always chance of being trapped in the local optima. Further
the method is gradient-based and uses the linearization of relationship between the
model’s output and the parameters by formulating the Taylor expansion. But the
hydrological model contains threshold and the derivatives with respect to the parameter in the Taylor expansion will not change smoothly at any threshold. Hence
it adversely impacts the calibration process by creating the discontinuities in the
derivatives of the objective function response surface. So with the aim of achieving
the reasonable HSAs, the parameters estimation was redone using year 1993 as before
but then with a more acceptable global optimization technique - SCE-UA (Scuffled
Complex Evolution. The calibrated values were found to vary widely with the change
in the optimization method too. The yearly model performances evaluated as before
showed that despite the use of the global optimization method- SCE-UA compromising with huge computation time, the model performances cannot be improved
than what was obtained from the considerably quicker Gauss-Marquardt-Levenberg
method (PEST). The low extreme events as in 1996 were simulated still poorly with
the globally optimized parameters too thus confirming the deficiency of WaSiM-ETH
model in simulating the low events and necessity of using unusual events in calibration.
128
5.6. Conclusions
Noticeably the subcatchments 3 and 4 which are not-headwater basins were simulated
with very high performance values consistently every year for all the four parameter
sets. Upon further investigation it was found that these subcatchments were calibrated almost immediately by PEST and that outflows from them are almost totally
governed by inflows to them from upstream subcatchment. On the other hand, as
already mentioned, the observed flows at upstream gauge(s), instead of simulated
discharges, were used as inflows to the downstream subcatchment during modeling
to avoid propagation of errors. So here the high model performances values for subcatchments 3 and 4 are misleading.
With the SCE-UA generated parameters also, the monthly hydrologically sensitive
areas (HSAs), which are quantified as the probability of generating the surface runoff,
are estimated from the daily simulated spatially distributed surface runoff grids
(1990-2005). It was observed that the simulated surface runoff patterns are quite
different for differently calibrated parameter sets thus raising question of reliability
to use particular pattern calculating soil erosion. Further questionable is the unrealistic behaviour that the surface runoff patterns were still totally different from
one subcatchment to another. This is obviously linked to the different subcatchments having the different parameter sets which are calibrated independently with
the observed discharges at their corresponding gauges. Then this directed further investigation to calibrate the different subcatchments simultaneously with same single
set of parameters for all the subcatchments although they have their own observed
outflows.
In lieu with this, then, a new and completely different approach of parameters estimation, the multidimensional data-depth based ROPE algorithm has been investigated.
The algorithm is based on the proven fact that robust parameter sets are geometrically well-structured in multidimensional space. This approach does not produce
a single set of optimized parameter set like earlier but instead produce several sets
of good performing parameters. This gives opportunity to analyze and search the
parameter set from the group of the good performing parameters that would satisfy
our purpose, i.e. reasonable spatial patterns of surface runoff, the HSAs. Besides the
advantage of obtaining several number of robust parameter sets, another beauty of
this parameter estimation algorithm (ROPE), that have been noticed during their
use, is that every iteration/model run is independent of previous run. This means
unlike with other optimization methods, several computers can be used to compute
the required number of model runs/iteration independently and the results can be
brought together to analyze after every loop. This is huge advantage particularly
for the CPU-intensive process-based models like WaSiM-ETH. For example, in our
work while the global optimization method SCE-UA required more than a month for
optimization, the ROPE algorithm was completed in few days using five computers,
even if number of model runs were much more than with SCE-UA. Thus, the ROPE
algorithm has the computational efficiency comparable to the fast gradient-based
method like PEST (Gauss-Marquardt-Levenberg algorithm) without having danger
of being trapped in local optima which PEST etc does have.
129
5. Physically based distributed hydrological modeling for HSA estimation
Then algorithm was applied in our Rems catchment with 1993 as calibration year,
with one preceding year as the spin-up period. At first normal calibration strategy
like earlier was followed. This means the different robust parameter vectors were estimated independently for each of the four subcatchments based on their respective
observed discharge series and using observed discharges to flow downstream from the
upstream catchments. But like earlier, it was found that despite the good model performance the simulated surface runoff pattern are still unrealistic as it varies widely
among the subcatchments and also among the different good parameter sets. Then
the same parameters’ values were considered for all four subcatchments (whole Rems
catchment) to avoid the inter-subcatchments random variation of the surface runoff
patterns. Equally weighted combinations of the observed discharges at all the four
gauges were considered for the objective function (sum of square of errors) evaluation and the simulated discharges at the gauges are allowed to flow downstream
subcatchment without replacing it with the observed series. Then using the ROPE
algorithm for three loops, 1955 acceptably good performing parameter sets were obtained. In addition, the single parameter set for whole catchment was also obtained
using SCE-UA for the comparison. Despite the similarly good model performances,
the obtained good/optimized parameters sets vary considerably (equifinality). However, it was observed that then there were not unacceptable variations of patterns
among the subcatchments. The unacceptable variations of the distributed patterns
among the subcatchments could be avoided by assigning same parameter set for all
the subcatchments. The spatial correlation of the distributed surface runoff values
and their rank simulated by the different good parameter sets were found to be quite
high indicating that the simulated patterns are quite similar for the different parameter sets. However, in spite of the good model performances and reasonable surface
runoff patterns within the catchment, the amount of the surface runoff varies more
than four times among the different good parameter sets thus creating doubt to use
a particular distributed result quantitatively.
Then further attempt was made in identifying the good parameter sets by calculating their depth based on other performance criteria besides the sum of squared
error. The main criteria considered was accuracy in simulating surface runoff by different parameter sets compared to the observed surface runoff for which the surface
runoff was separated from the respective hydrographs using the digital filter technique. Along with the surface runoff volume error, other considered criteria are 90%
non-exceeding surface runoff value error, linear and log NS coefficients, root mean
square error (RMSE) of peaks, sum of squared error of biggest 10% flow values (top
10% of flow duration curve) and baseflow volume error. When the depth of each
of the 1955 parameter sets calculated based on itself were compared to their depth
based on those different criteria, it was observed that high depth parameter sets are
generally deep in all other criteria too. This also verifies the basis of the concept that
the good performing parameter sets have certain well defined structure/geometry in
the parameter clouds.
The 1955 good parameter sets were obtained based on minimum sum of squared
error. So although they were good in many of the mentioned criteria, but it was observed that there are hardly any parameter sets that are also good in surface runoff
130
5.6. Conclusions
estimation at the same time. So compromising with the small loss in other performance criteria, the good parameter sets were searched in the 3007 parameter sets
which were generated at the second last step of the ROPE algorithm. Several good
parameters based on the surface runoff estimation could be found.
Owing to the large variability in the total amount of the simulated distributed results
with different good performing parameter sets, a single parameter set could not be
finalized with reliability. Therefore 20 different good parameter sets (from the 3007
sets) based on all performance criteria focusing mainly on the surface runoff and also
the SCE-UA optimized set were selected for the further analysis. The daily surface
runoff grids (HSAs) for the sixteen years were generated with those 21 parameter sets
and supplied to the erosion model for spatially distributed and temporally varying
erosion risk estimation, which is described in next chapter.
131
6 Spatially Distributed and Temporally
varying soil erosion risk estimation
6.1 Background
A case study conducted as described in Chapter 4 already shows the possibility of
predicting spatial patterns of soil erosion within a catchment reasonably well even
with the simple USLE-based erosion models, but only after augmented with better
hydrological input (surface runoff) as provided by the WaSiM-ETH model. However, the application of the WaSiM-ETH model to estimate spatially distributed and
temporally varying surface runoff (HSAs) in the Rems catchment, as described in
Chapter 5, highlights the fact of existing several good parameter sets which could
finally produce similar spatial patterns but are quite different in amount. So, although the amount of soil erosion cannot be reliable, the HSAs patterns (sources) in
the catchment can be used to identify the spatial variation and temporal dynamics
of the soil erosion risk. For this, besides the variations of driving force-the HSAs,
the variations (spatial and temporal) of other resisting forces like that of topography,
soil landuse and vegetation cover, which define the Erosion Susceptible Areas (ESAs)
in the catchment should also be identified. The intersection of the HSAs and ESAs
yields the spatially and temporally varying soil erosion risk areas, defined as Critical Source Areas/Critical Management Zones (CSAs or CMZs), that needs attention
of required management practices with anti-erosion measures. The identification of
such areas in the Rems catchment is presented in this chapter.
6.2 Estimation of rainfall-runoff erosivity factor
The basics of rainfall-runoff erosivity factor R [MJ mm/ (ha h)], as used in the
USLE-based models, which represents the erosive potential of rainfall and surface
runoff and requires high resolution rainfall data (rainfall intensity) is described in
Chapter 2. Some commonly used alternative models to estimate the R-factor have
been investigated during the case study and are presented in the Chapter 4 (Equation
4.18). Widely used MUSLE model (Williams 1975, Williams & Berndt 1977), which
is purely runoff based model, is used here to estimate the erosivity. In addition, an
attempt is made to develop a new relationship applicable to calculate the erosivity
based on rainfall data of more readily available resolution (eg. daily). It is described
in the following sections.
6.2.1 Daily Runoff erosivity factor using WaSiM-ETH results
Williams (1975) and Williams & Berndt (1977) developed a modified version of
the USLE (MUSLE) to derive a sediment yield estimation model based on runoff
132
6.2. Estimation of rainfall-runoff erosivity factor
characteristics, as the best single indicator for sediment yield prediction (Hrissanthou
2005). If Q is surface runoff [m3 ] and Qp is peak runoff rate [m3 /s] then, runoff
erosivity factor of the MUSLE used in this study can be expressed as;
R = 11.8 × (Q × Qp )0.56
(6.1)
The surface runoff Q is calculated for each day of the sixteen years of simulation
period (1990-2005) in each 100 m by 100 m grid cell of the Rems catchment by applying the WaSiM-ETH model as described in detail in Chapter 5. As stated earlier,
due to the non-uniqueness and non-reliability of the simulated amount, the spatially
distributed daily surface runoff grids simulated by the selected 21 different good parameter sets for the 16 years period are considered for the erosion risk estimation.
The performances of these different parameter sets evaluated through different measures are shown in Tables 5.24, 5.25 and 5.26 in Chapter 5. The differences in the
simulation of the surface runoff amount, which are relevant for the soil erosion and
are estimated using a digital filter for hydrograph separation, can also be seen in the
Tables 5.24 and 5.25 through the surface runoff volume error. The differences in the
surface runoff amount for the year 1993, as an example, are shown in Table 6.1.
Table 6.1: Surface runoff amount simulated by the selected 21 different parameter sets for the year
1993
Parameter Set No.
Surface Runoff amount [mm]
catch. 1
catch. 2
catch. 3
catch. 4
Boundary
parameter
sets
(Depths = 1)
628
695
876
877
1132
1302
1307
1378
1405
1641
211
206
240
205
209
209
212
209
195
205
92
92
101
96
99
104
121
104
92
115
143
141
160
142
149
152
161
158
141
159
120
121
131
120
126
125
136
133
122
134
Deep
parameter
sets
(Depths >2)
15
295
501
895
921
1199
1243
1245
1299
1581
179
203
197
222
195
210
215
201
206
215
67
84
83
99
85
93
88
99
102
98
114
134
135
152
151
145
151
143
150
169
96
112
112
125
123
119
129
118
123
141
SCE-UA
196
72
122
102
203
117
152
148
From Observed Hydrographs
The required peak runoff rate, Qp , is estimated for each day in each grid cell by
using the area, slope and the simulated runoff depth for that cell on that day and as
133
6. Spatially Distributed and Temporally varying soil erosion risk estimation
described in CREAMS Model (Young et al. 1989), which is given as;
Qp = 3.79 × A
0.7
×S
0.16
×
Q
25.4
0.903×A0.017
× LW −0.19
(6.2)
where A = Area of the cell [km2 ], S = slope [m/km], Q = Runoff depth [mm], LW
= Length to width ratio of the cell.
Then following the MUSLE erosivity model (Equation 6.1), the spatially distributed
runoff erosivity is calculated for each day of the simulated sixteen years (1990-2005)
with each of the selected twenty one parameter sets. As an example of the results, the
estimated spatially distributed erosivity for the day 30/03/2000 with four parameter
sets are shown in Fig. 6.1.
Paraset 628
Paraset 15
Paraset 1199
Paraset SCE-UA
0
0.05
0.10
0.15
0.20
0.25
0.30
0.35
0.40
0.45
0.60
Figure 6.1: Spatially distributed MUSLE-based erosivity for day 30/03/2000 with the four different
parameter sets
6.2.2 Rainfall erosivity factor using NiedSiM results
In the original form or by definition, the erosivity factor- R, is calculated as described
in Section 2.2.2 of Chapter 2. The calculation includes basically the estimation of
kinetic energy and maximum 30 minutes intensity of the sufficiently erosive events
and summing them up. This requires rainfall intensity data spanning over a long
period of time which is often not available, even in developed countries. So, based on
several independent research, different alternative methods for the estimation of rainfall erosivity (R factor) have been proposed that uses more easily available rainfall
parameters. Some of these commonly used alternative methods that are investigated
here for estimating the R factor for the Rems catchment are listed in Table 6.2 where
P is annual rainfall, Psummer is summer rainfall and pi is the rainfall of month i.
134
6.2. Estimation of rainfall-runoff erosivity factor
Table 6.2: Different models to estimate rainfall erosivity factor, R
Renard & Freimund (1994)
:
R = 0.07397 × Fi1.847
when Fi < 55 mm
R = 95.77 − 6.081 × Fi + 0.477 ×
Fi =
p2i
12
X
Fi2
when Fi ≥ 55 mm
= modified Fournier Index
pi
i=1
12
van der Knijff et al. (1999, 2002):
R = 1.3 × P
Yu & Rosewell (1996)
:
R = 3.82 × F 1.41
Lo et al. (1996)
:
R = 38.46 + 3.48 × P
Rogler and Schwertman (1987) :
R = 0.083 × P − 1.77
R = 0.141 × Psummer − 1.48
The simple statistics of the spatially distributed long term annual R factor estimated using these listed models with grid wise interpolated rainfall (P ), for the
Rems catchment, is shown in Table 6.3. The daily distributed rainfall grids for the
Rems catchment (1990-2005) are obtained using weighted combination of inverse
distance weighting (IDW) and altitude dependent regression (ADR) as used by the
interpolation module of WaSiM-ETH. While other listed methods for R factor estimation are developed from different parts of the world, the Rogler & Schwertman
model was developed for the state of Bayern and can be used in its neighboring state
of Baden Württemberg too, in which our Rems catchment is located. The daily
proportion of the annual R factor is also provided by Schwertmann et al. (1987)
based on which the monthly R factor for the Rems catchment is estimated as shown
in Table 6.4. The monthly R factor estimated by the Renard & Freimund method
is also shown in the table for comparison. It can be observed that the values of R
factor estimated by the Schwertman method are quite low as compared to others. It
is because all the methods include only the rainfall amount and it has been stated
that the similar amount of rainfall in Bayern region is comparatively less intense and
hence less erosive than in other parts of the world.
Table 6.3: Annual rainfall erosivity factor, R[M Jmmha−1 h−1 yr−1 ], estimated by different models
Min.
Max.
Mean
Std. dev.
Renard &
Freimund
1994
van der
Kniff et al.,
1999, 2002
Yu & Rosswell,
1996
Lo et al.,
1985
Rogler &
Schwertmann,
1981
2122
5233
3306
544
1062
1692
1347
118
159
2900
2124
237
2880
4567
3644
317
660
1062
842
76
In this context it seems worthy to make an attempt to devise a new relationship, if
possible, to calculate the R factor using easily available rainfall parameters in the
135
6. Spatially Distributed and Temporally varying soil erosion risk estimation
Table 6.4: Monthly rainfall erosivity factor, R[M Jmmha−1 h−1 mo−1 ], estimated by two different
models
Precipitation [mm]
R Factor
[M Jmmha−1 h−1 mo−1 ]
R Factor
[M Jmmha−1 h−1 mo−1 ]
min.
max.
mean
min.
max.
mean
min.
max.
mean
Jan
Feb
Mar
Apr
May
Jun
Jul
Aug
Sep
Oct
Nov
Dec
46
49
59
51
85
93
96
68
66
73
69
60
94
102
110
84
106
121
140
109
109
111
115
118
68
73
84
68
93
104
111
82
85
91
88
90
31
39
83
46
298
437
597
151
142
212
165
89
248
364
488
146
464
786
1232
434
439
498
540
666
100
138
236
95
359
574
744
214
245
321
292
325
1
4
5
20
68
185
138
136
65
21
11
7
1
6
8
32
109
297
222
219
104
34
17
12
1
5
6
23
87
236
176
174
83
27
13
9
Annual
817
1301
1036
2122
5233
3306
660
1062
842
Rems catchment. As the required long time series of observed rainfall intensity is not
available, the series of synthetic rainfall simulated in quite high temporal resolution
(5 minutes) by a simulator called NiedSim (‘Niederschlag Simulator’) is used. The
stochastic precipitation time series generator NiedSim is an operational system based
on a non-parametric approach developed in the Institute of Hydraulic Engineering
(IWS), University of Stuttgart. NiedSim produces rainfall time series in five-minute
resolution in the state of Baden-Württemberg. The system generates a time series
on the basis of statistical properties of the natural rainfall and takes following two
steps for doing so (Brommundt & Bárdossy 2005);
(i) Hourly values are generated taking local statistics into account. An objective
function is formulated from statistical properties of the generated time series
and local statistics. The function is then minimized using simulated annealing
technique.
(ii) The time series is disaggregated to five minutes values applying simulated annealing using a similar objective function keeping the hourly sum unchanged.
NiedSim can generate 5 minutes’ time series with maximum duration of 44 years
for any arbitrarily selected point(s) within 70,000 km2 system area (Brommundt
2008). The Rems catchment lies within its system area and hence generation of the
time series is possible at any location within the catchment. Accordingly, the precipitation time series with temporal resolution of 5 minutes are generated for three
representative locations, situated at upstream, middle and downstream region of the
catchment. These selected locations coincide with existing rainfall stations namelyHeubach, Alfdorf and Winterbach which can be seen as station number 25, 37 and
11 respectively in Fig. 3.9. The annual and monthly average (1990-2005) of the
NiedSim generated rainfall in comparison with observed ones are shown in Table 6.5.
136
6.2. Estimation of rainfall-runoff erosivity factor
Table 6.5: Annual and monthly average rainfall simulated by NiedSim as compared to observed
ones
NiedSim generated rainfall [mm]
Observed rainfall [mm]
Station 25
Station 11
Station 37
Station 25
Station 11
Station 37
Jan
Feb
Mar
Apr
May
Jun
Jul
Aug
Sep
Oct
Nov
Dec
72
47
49
51
60
88
108
113
100
104
103
97
76
51
52
55
69
91
105
113
97
98
119
108
56
38
45
49
66
83
93
98
80
79
76
78
68
72
85
62
90
103
111
145
144
86
85
91
65
77
92
67
83
107
106
68
86
92
97
100
41
56
67
61
76
95
94
67
68
65
67
67
Annual
991
1036
841
1038
1040
827
At first the R factor is calculated following its basic definition as described in section
2.2.2 for each of the three selected locations/stations. The erosive rainfall events,
i.e. events isolated by greater than six hours of dry period and comprising of either
rainfall amount greater than 12 mm or 15 minutes intensity greater than 12 mm/hr,
are identified from the NiedSim generated 5 minutes rainfall series independently for
the three stations spanning from 1958 to 2004. The R factor is calculated for these
erosive events following the basic methodology (Equations 2.2 - 2.4). The calculated
mean monthly and annual average R factor are shown in Table 6.6.
Table 6.6: Annual and monthly rainfall erosivity
from NiedSim generated rainfall
The rainfall erosivity calculated from
the NiedSim rainfall are considered as
−1 −1
−1
the observed erosivity and attempt is
R Factor [M Jmmha h mo ]
made to find relationships, consisting
Station 25 Station 11 Station 37
more easily available rainfall parameJan
32
34
84
ters, for estimating those erosivity. It is
Feb
30
53
106
assumed that, at minimum, daily rainMar
40
93
178
fall data will be generally available and,
Apr
51
60
100
May
64
39
61
therefore, the parameters considered are
Jun
27
41
31
based on the daily rainfall data series.
Jul
54
46
95
The considered parameters are listed in
Aug
42
47
51
Table 6.7, which are obtained from the
Sep
63
62
59
Oct
39
71
42
daily rainfall series of the period for
Nov
37
29
57
which the R factor is being calculated.
Dec
52
60
50
The multiple non-linear regression using
Annual
919
990
1101
a multiple power function of the form;
R = a · V1b · V2c · V3d .....; is carried out
for each month and each year (1958-2004), where V1 , V2 etc are the independent
variables/parameters listed in the Table 6.7 and a, b, c etc are regression coefficients
137
6. Spatially Distributed and Temporally varying soil erosion risk estimation
which are determined by using Conjugate Gradient Method (CGM). Data from stations 25 and 37 are combined and used for the development of the regression models
and the station 11 is used for the validation of the developed relationships.
Table 6.7: Rainfall parameters considered initially for the multiple non-linear regression
Mean Daily rainfall [mm]
Maximum daily rainfall [mm]
Number of rainy days [ - ]
Standard Deviation [mm]
Skewness [ - ]
Number of days with rainfall exceeding 12 mm per day
Rainfall amount exceeding 12 mm/day [mm]
Total rainfall [mm]
:
:
:
:
:
:
:
:
PDmean
PDmax
Dn
PDstdev
PDskw
Dp > 12 mm/d
PT > 12 mm/d
PT
While investigating for the annual erosivity factor, the following model is obtained
which shows that only three out of the selected eight parameters are significant.
1.1048
R = 0.00822 · PDmax
· PT >12mm/d · Dn0.4322
(6.3)
The observed annual R factor (NiedSim: 1948-2004) and that estimated with the regression model during calibration and validation are plotted in Fig. 6.2. Correlation
coefficient is found to be 0.86 and 0.83 for calibration and validation respectively.
3000
Estimated R factor [Regression]
Estimated R factor [Regression]
3000
2500
2000
1500
1000
500
0
2500
2000
1500
1000
500
0
0
500
1000
1500
2000
Observed R factor [NiedSim]
2500
3000
0
500
1000
1500
2000
2500
3000
Observed R factor [NiedSim]
Figure 6.2: Regression estimated annual R factor against observed for calibration (left) and validation (right)
Similarly the regression models for each month’s erosivity factor are found to be as
shown in Table 6.8. The R2 performance measure over the years (1948-2004) is also
listed in the table for the calibration and validation. The estimated monthly and
annual R factors lie within the expected range. The attempt made here is quite a
preliminary one and detail investigation is not covered in the scope of this thesis.
However the preliminary results already show the applicability of the NiedSim generated precipitation series in calculating rainfall erosivity factors and possibilities of
obtaining those erosivities reasonably through the parameters of more easily available daily rainfall series. In this thesis work, the erosivity factor based on runoff as
described in Section 6.2.1 is used further.
138
6.3. Estimation of topographic factor
Table 6.8: Non-linear regression models for monthly erosivity factors
R2
Exponents to
Month
Multiplier
PT
PDmax
PDmean
PDstdev
PDskw
DP >12mm/d
Pt>12mm/d
Dn
Calibration
Validation
Jan
1.2592574
×
×
×
2.1568
×
×
×
×
0.73
0.68
Feb
0.0017360
×
3.1380
×
×
×
×
×
×
0.79
0.40
Mar
0.0029803
×
×
0.6393
3.1857
1.6482
×
×
0.1938
0.97
0.92
Apr
0.0000214
×
3.7529
×
×
×
×
×
1.3534
0.91
0.86
May
0.6260694
×
×
×
2.5856
×
×
×
×
0.84
0.94
Jun
0.0000378
×
1.7766
×
1.3196
×
×
×
1.8742
0.86
0.71
Jul
0.0405408
×
0.9292
×
2.2575
×
×
×
×
0.93
0.73
Aug
0.2622204
×
×
×
1.8146
×
×
×
0.9313
0.80
0.88
Sep
0.2023905
×
0.9644
×
1.5430
×
×
×
×
0.82
0.76
Oct
0.0125844
×
0.8712
×
×
×
×
1.0793
0.6747
0.85
0.65
Nov
0.4032923
×
×
×
2.5030
×
×
×
×
0.70
0.84
Dec
0.0000821
×
2.9664
×
×
×
×
×
1.0091
0.86
0.84
6.3 Estimation of topographic factor
The effect of topography is an important factor to identify the Erosion Susceptible
Areas (ESAs) in a catchment. When using the USLE based models, the effects of
topography on soil erosion are estimated by the slope length (L) and slope steepness
(S) constituents of the dimensionless topographic factor, called LS factor. The LS
factor is calculated as product of the slope length and steepness converging onto a
point of interest (e.g., a farm field or a raster cell on a GIS grid). The basics of
this factor and its estimation methods (Equations 2.9-2.14) are already described
in Section 2.2.4 (Chapter 2). The estimation of LS factor is proved to be more
problematic than any other USLE factors, particularly if the model is to be applied
at a catchment scale (Wilson & Lorang 2000, Renard et al. 1991) where labourintensive field measurements are obviously not feasible in the complex landscape. It
has undergone continuous improvement with consideration of the influence of profile
convexity/concavity by segmenting of irregular slopes and improving the equation
(Foster & Wischmeier 1974, Renard et al. 1991). Accordingly various approaches
and algorithms for quantifying the topographic factor have been developed in recent
years. Several spatially distributed approaches investigated in this research work basically differ in the consideration of slope length, L, either using flow-path length (one
dimensional) or using upslope contributing area instead, making it two dimensional.
The considered different approaches are already described in section 4.2.2.3 (Chapter
4, Equations 4.21-4.29) and are not repeated here; only the results are presented.
The basic input for calculating LS factor grid in GIS is a DEM dataset of the catchment or watershed. Here, the available 100m × 100m DEM of the Rems catchment
with its extent little bit extended to avoid edge effects, is at first hydrologically
corrected by filling up the existing sinks/pits in the DEM so that the continuous
flow till the catchment outlet is ensured. This DEM is then used in ArcView GIS
with hydro-tools and spatial analyst to calculate the spatially distributed LS factor
following the considered approaches (Equations 4.22-4.29). The summary of the spa-
139
6. Spatially Distributed and Temporally varying soil erosion risk estimation
tially distributed S factor estimated with different approaches is shown in Table 6.9.
Similarly, summary of the flow accumulation estimated by three different routing
algorithms is shown in Table 6.10. Mean flow accumulation value is lowest with SF
and highest with FD but the maximum value is lowest with MF algorithm.
Table 6.9: Summary of S factor estimated from different approaches
Measures
Wischmeir & Smith,
USLE (1978)
Moore & Burch
(1986)
McCool et al.
(1987, 1989),
RUSLE (1993)
Govers,
(1996)
Nearing,
(1997)
Min.
Max.
Mean
Std.dev.
0.0654
23.48
2.01
2.25
0
10.94
1.59
1.43
0.03
8.98
1.60
1.33
0
18.93
1.81
1.88
0.05
11.39
1.62
1.46
The topographical factor LS is then calculated following different approaches based on upstream flow-path Table 6.10: Summary of flow
length (1-D) and upstream contributing area (2-D). The
accumulation estimated from three
spatially averaged summary of the obtained distributed
different routing
results is shown in Table 6.11. In general, the LS factor
algorithms
estimated by using F D routing algorithm gives highest
mean value than with SF and M F algorithms. More- Measures SF MF FD
over, 2-D approach estimated higher LS values than the Min.
0
0
0
1-D approach. The values differ among the different Max.
195 184 238
4
5
7
methods of 2-D approach where Govers method gives Mean
Std.dev.
10
9
13
the results comparatively on higher side. The most important observation here also, as already shown in the
case study (Chapter 4) in Fig. 4.7, is the difference in spatial distribution of LS
factor estimated with the use of upstream flow-path length (1-D) and upstream contributing area (2-D). It is found that the 2-D approach estimates high LS values
in hollows too; hence it takes into account the flow convergence which is a major
factor explaining the enhanced erosion risk in hillslope hollows. The spatially distributed topographic factor grid of the Rems catchment estimated following the 2-D
approach with flux decomposition routing algorithm along with the Nearing’s slope
factor (Eqns. 2.14 or 4.25)is shown in Fig. 6.3. This grid is used here further to
define the Erosion Susceptible Areas (ESAs) in the Rems catchment.
6.4 Temporal dynamics of spatially distributed crop cover
factor
Another quite important factor to identify the Erosion Susceptible Areas (ESAs) in
a catchment is the land use and vegetation cover which are, in general, the major
input in defining actual soil erosion risk. In the USLE-based models, the crop cover
management factor, C-factor, incorporates the combined effect of all interrelated
cropping and management practices in the area. It is defined as the ratio of soil loss
under a given cropping conditions to that from bare soil. Generally the C-factor in
140
6.4. Temporal dynamics of spatially distributed crop cover factor
Table 6.11: Summary of LS factor estimated from different approaches using three different routing
algorithms
Approach/Method
1-D consideration
(flow accumulation)
2-D consideration
(unit contributing
area)
SF
MF
FD
Moore & Burch, 1986
(with upper bound=100m)
(L for slope)
Min:
Max:
Mean:
Std. dev:
0
29.18
3.17
3.2
0
29.18
3.35
3.32
0
29.18
3.36
3.53
Moore & Burch
modified by Kinnell
(L for cell)
Min:
Max:
Mean:
Std. dev:
0
360.25
6.50
8.24
0
56.94
5.56
5.14
0
63.48
7.37
6.87
Wischmeir & Smith (1978)
Min:
Max:
Mean:
Std. dev:
0.1
187.20
10.47
13.07
0.1
176.07
12.40
14.32
0.1
208.44
13.31
15.56
McCool (1987,1989)
(rill=interrill)
Min:
Max:
Mean:
Std. dev:
0.03
311.33
11.43
15.37
0.03
322.95
13.87
16.34
0.03
330.52
15.14
18.51
Govers (1991)
mmin:
Max:
Mean:
Std. dev:
0
806.29
22.76
34.57
0
841.56
28.11
34.89
0
864.63
31.78
41.47
Nearing (1997)
(‘m’ from McCool,
rill=interrill)
Min:
Max:
Mean:
Std. dev:
0.05
328.20
11.62
16.41
0.05
340.46
14.12
17.67
0.05
362.68
15.40
19.94
N
5
LS factor
Measures
LS Factor [-]
0
5
km
0 - 5
25 - 30
5 - 10
30 - 35
10 - 15
35 - 40
15 - 20
40 - 50
20 - 25
> 50
Figure 6.3: Spatial variation of the topographic factor (LS factor) in Rems catchment
a catchment ranges between 1 and almost 0. The C value of 1 means no cover effect
and represents a soil loss comparable to that from a tilled bare fallow and the value
of 0 means a very strong cover effect resulting in no erosion.
141
6. Spatially Distributed and Temporally varying soil erosion risk estimation
Accurate information about the spatial distribution and temporal variation of the
vegetation-related parameters, which account for the protection given by the canopy
cover and ground cover, is of utmost importance when attempting to model erosion
risk at the catchment or regional scale. In practices, for the USLE-based distributed
erosion modeling in GIS, C-factor is normally calculated from the available land use
map of the concerned area by assigning an individual value for each land use/cover
class. So the calculated C-factor map for the catchment remains temporally constant.
But, though there are certain land use types (for e.g. water bodies, settlements etc)
for which this factor remains constant throughout the year, there are other types
of land use like agricultural land and forest which experience monthly or seasonal
variations. Due to this seasonal variability of the vegetation coverage, the amount
of erosion that may occur in a place is different in different season even for similar
type of rainfall event. Development and advancement in the fields of remote sensing
and satellite imagery has made it possible to capture such temporal dynamics of spatially distributed cover and management factor in terms of certain vegetation indices.
The vegetation index is an alternative measure of vegetation amount and condition,
which being specific class of spectral band ratios, often exploit the fact that green
vegetation has high reflectance in the NIR (near infra-red) and low reflectance in the
red part of the spectrum. A common index is the normalized difference vegetation
index (NDVI), which has been used within erosion studies directly as an indication
of the protective cover of vegetation (Liu et al. 2000, Gay et al. 2002, Jain & Goel
2002, Thiam 2003) or was related to vegetation cover with regression analysis (Zhang
1999, Bhuyan et al. 2002, Symeonakis & Drake 2004). The NDVI time series can
be easily derived from data acquired by a variety of satellites operating at different
spatial and temporal resolutions.
6.4.1 MODIS NDVI series for Rems catchment
The Normalized Difference Vegetation Index (NDVI) is the most widely used remotesensing derived indicator of vegetation growth. It is a non-linear transformation of
the visible red and near-infrared bands of satellite information and is defined as:
N DV I =
N IR − RED
N IR + RED
(6.4)
where NIR and RED are the spectral reflectance acquired in red and near-infrared
regions respectively. The index is found to be sensitive indicators of the condition
of green vegetation. Healthy vegetation will have a high NDVI value. Bare soil and
rock reflect similar levels of near-infrared and red and so will have NDVI values near
to zero. The intermediate values give an indication for differences in coverage with
green vegetation. Clouds, water, and snow are the opposite of vegetation in that they
reflect more visible energy than infrared energy, and so they yield negative NDVI
values. The NDVI values hence range from -1 to +1.
NDVI being the spectral ratio between near infrared and red reflectance, can be derived from various satellite imageries which has the ‘Red Reflectance’ and ‘Near In-
142
6.4. Temporal dynamics of spatially distributed crop cover factor
frared Band’. In this study, the products of MODerate resolution Imaging Spectroradiometer (MODIS), the space-borne remote sensing system, for the NDVI-imageries
(NDVI, MOD13Q1) are imported to derive monthly vegetation cover that defines vegetation resistance to soil erosion. MODIS is the key instrument mounted on polar orbiting Terra and Aqua satellites, a part of NASA’s Earth Observing Systems (EOS),
which is viewing the entire Earth’s surface every 1 to 2 days. It is acquiring data in
36 spectral bands ranging from the visible to the thermal infrared with near-nadir
spatial resolutions of 250, 500, and 1000 meters (http://modis.gsfc.nasa.gov/).
The Terra was first launched in February 1999 and started to deliver data from
February 2000, whereas Aqua delivers data starting only from July 2002.
MODIS NDVI time series acquired from its Terra platform are extracted (through
LPDAAC data archive center) for our Rems catchment for the period of 2000 to
2008. Since the catchment is completely contained within a single tile (h18v04)
of the standard MODIS grid, the downloading and merging of different tiles is not
required. The series is available at the temporal resolution of 16 days and spatial resolution of 250 m in Hierarchical Data Format (*.hdf). The MODIS gridded outputs
are in Integerized Sinusoidal Projection (ISIN). Because most of the conventional
software packages used for image processing and spatial data analysis do not accommodate the ISIN projection, the ‘MODIS Reprojection Tool, MRT’ (USGS-EROS,
2003) is used to perform geographical transformation to the coordinate system and
cartographic projection matching to that of other GIS data sets in the modeling system (i.e. Gauss Krüger 3 coordinate system). The MRT tool is used also to convert
the hdf format to Geotiff readable by GIS and to resample the grid to the common
100 m size. Further, clipping for the catchment boundary from the big MODIS tile is
done with each of the NDVI data set. The time series being long, these processes of
format conversion, geographical transformation, the clipping and resampling is automatized with a computer program written in FORTRAN. It was aimed to capture
the effect of temporal dynamics of vegetation cover in erosion on monthly basis. So
the prepared 200 NDVI files for the Rems catchment at 16 days interval, starting
from Julian day 49 of the year 2000 to day 273 of the year 2008, are temporally
aggregated and averaged to determine the spatially distributed monthly NDVI maps
for the catchment. The estimated variations, as an example for four selected months,
are shown in Fig. 6.4.
Besides the spatial variation of the vegetation cover within the catchment, their
temporal variation within a year is also clearly visible. The monthly variation of the
spatially averaged NDVI in the Rems catchment is shown in Fig. 6.5. For the relevant comparison, the spatially averaged monthly rainfall erosivity factor (R-factor)
as calculated following Rogler and Schwertmann, 1981, (Table 6.4), is also plotted in
the same figure. It can be seen that the months of high rainfall erosivity (Jun-Aug)
is in fact associated with the period of high NDVI which means higher vegetation
coverage. Hence here resistance to soil erosion by vegetation coverage also increases
with increase in the climatic erosivity.
The consideration of such dynamics in erosion risk estimation yields more realistic
results as compared to normal practices of using static land use grid for capturing
143
6. Spatially Distributed and Temporally varying soil erosion risk estimation
January
March
July
October
0.2
0.5
0.6
0.7
0.9
Figure 6.4: Spatial variation and temporal dynamics of NDVI in Rems catchment
0.9
250
NDVI
200
R Factor
0.7
150
0.6
100
0.5
50
0.4
R Factor [MJ mm/ha/mo]
NDVI [-]
0.8
0
Jan
Feb
Mar
Apr
May
Jun
Jul
Aug
Sep
Oct
Nov
Dec
Figure 6.5: Temporal variation of spatially averaged NDVI and R-factor in Rems catchment
the effects of existing vegetation cover on soil erosion and sediment yield estimation.
To employ it with the USLE-based models, the spatially distributed and temporally
varying C-factor has to be estimated from the extracted NDVI series and this is done
for the Rems catchment as described below.
6.4.2 Monthly cover factor estimation using NDVI
The most common procedure for estimating C-factor using the NDVI involves the
use of regression model derived from the correlation analysis between the C-factor
values measured in the field and the satellite-derived NDVI series. Jong (1994), in
his PhD thesis, describes the use of vegetation indices in order to extract vegetation
144
6.4. Temporal dynamics of spatially distributed crop cover factor
parameters for erosion models and derived the following linear function for estimating
USLE-C from NDVI (revised in Jong et al. 1998):
C = 0.431 − 0.805 × N DV I
(6.5)
The function has a correlation coefficient of –0.64, which is modest. The function
was tested on several NDVI profiles. In general, estimated C-values were found to
be rather low. Furthermore, De Jong’s equation is unable to predict C-values over
0.431. Also, the function was obtained for (semi-)natural vegetation types only, using
Landsat TM imagery.
On another separate study, led by European Soil Bureau (van der Knijff et al. 2000),
investigation was made whether the NDVI-images could be ‘scaled’ to approximate
USLE-C values in some alternative way. After some experimentation, they come up
with the following provisional equation that seemed adequate:
−α
C=e
N DV I
β − N DV I
!
(6.6)
where α and β are unitless parameters that determine the shape of the curve relating
NDVI and the C-factor. van der Knijff et al. (1999, 2000) found that this scaling
approach gave better results than assuming the linear relationship. Prior application
using MODIS data showed that an α of 2.5 and a β of 1 gave reasonable results (van
Leeuwen & Sammons 2003, 2005).
Accordingly, this scaling approach is followed here to generate monthly C-factor surfaces from the prepared monthly NDVI values for the Rems catchment. A minimum
NDVI threshold of 0.05 is set, below which it is assumed that the vegetation is absent
(a C-factor of 1, or no ground cover). It is important to note that the C-factor values are a relative measure based on NDVI values and have not been calibrated. The
spatial distribution of the estimated C-factor for the Rems catchment is identical to
that of NDVI as already shown in Fig. 6.3. The monthly variation of the spatially
averaged C−factor along with the corresponding erosivity factor (R) is shown in Fig.
6.6 (left) and their combined effect as the product of R− and C− factor along with
the corresponding monthly precipitation amount is shown in Fig 6.6 (right).
It can be seen that the higher erosivity is normally associated with higher crop resistance factor and the net effect on the soil erosion, as determined by the magnitude
of their product, may be governed by either of the two. Both of these factors vary
considerably within a year and constitute an important aspect of soil erosion risk
estimation and their variation. The temporally static R and C factor as calculated
from the annual rainfall and the land use map respectively, which is the common
practice in erosion risk modelling with USLE-based models, is also shown in the figure. Such practice obviously cannot capture the temporal variations in the erosion
risk.
145
6. Spatially Distributed and Temporally varying soil erosion risk estimation
0.18
250
150
0.10
0.08
100
0.06
0.04
50
Rx C
1.5
100
90
1.0
80
70
RxC
0.12
Static C Factor
Precipitation [mm]
200
Static R Factor
110
R Factor [MJ mm/ha/h/mo]
C Factor [-]
2.0
Precipitation
R Factor
0.14
0.5
60
0.02
0.00
Jan
120
C Factor
0.16
0
Feb
Mar
Apr
May
Jun
Jul
Aug
Sep
Oct
Nov
Dec
50
0.0
Jan
Feb
Mar
Apr
May Jun
Jul
Aug
Sep
Oct
Nov
Dec
Figure 6.6: Temporal variation of spatially averaged R and C factor (left) and precipitation and
product of R and C factor (right) in Rems catchment
6.5 Distribution and dynamics of soil erosion risk in Rems
catchment
The soil erosion risk estimation based on USLE-based models requires calculation
of the five different influencing factors (Section 2.2). Estimation of these factors
for the Rems catchment is done in spatially distributed (100m × 100m grid) and
temporally varying (monthly) manner. The spatial distribution of monthly erosivity
factor (R) which defines the Hydrologically Sensitive Areas (HSAs) is calculated with
the application of WaSiM-ETH model as described in Chapter 5 and Section 6.2.1.
Similar distribution and dynamics of crop cover management factor (C) is calculated
through MODIS-NDVI series as described in Section 6.4. The spatially distributed
but time invariant topographic factor (LS) is calculated as described in Section 6.3.
Now, similar distribution of soil erodibility factor (K-factor) which also constitutes
an important aspect to identify Erosion Susceptible Areas (ESAs) in a catchment, is
calculated by assigning corresponding erodibility value to each pixel based on the soil
texture class of that pixel. The soil texture map of the Rems catchment is already
shown in Fig. 3.6 (left) and the resulting K-factor distribution is shown in Fig. 6.7.
The area percentage of the Rems catchment under each class can be seen in Fig.
3.6 (right). The remaining factor i.e. the conservation support practice factor (P factor), is considered as unity throughout the catchment due to non-availability of
field data on the support practices adopted by the farmers on their agricultural land.
Such data are rarely available for erosion modeling in the meso-scale catchment or
in regional scale. So the erosion susceptibility or actual erosion risk could be a bit
lower than the estimated one, if considerable support practices are adopted in reality
in the catchment.
Then using the prepared data sets of topographic factor, soil erodibility and monthly
crop cover factor, the spatial distribution of Erosion Susceptible Areas (ESAs) in every month in the Rems catchment are calculated. The monthly ESAs are then intersected spatially with the Hydrologically Sensitive Areas (HSAs) defined by the erosivity of the corresponding month in the Rems catchment. The intersection produces the
spatially distributed and temporally varying (monthly) soil erosion/sediment yield
risk which locates the Critical Management Zones (CMZs) for providing the required
anti-erosion measures in the Rems catchment.
146
6.5. Distribution and dynamics of soil erosion risk in Rems catchment
N
K-factor [-]
0.005
0.026
0.04
0.05
5
0
5
Km
Figure 6.7: Spatial distribution of soil erodibility (K factor) in Rems catchment
However, due to uncertainty in defining a single set of best parameter with WaSiMETH modelling (Chapter 5), the 21 different good performing parameter sets were
chosen (Tables 5.24-5.26, 6.1) and accordingly 21 different sets of sediment yield risk
maps have been estimated. The parameter set numbers in the tables are serially
named here as Set 1- Set 21, where the Setset 21 is from SCE-UA and others are
from ROPE algorithm of parameters estimation. The sediment yield at the catchment outlet estimated by these different good performing parameter sets are shown
in Fig. 6.8 in yearly basis and in Fig. 6.9 in monthly average basis. Very large
differences in the quantitative estimation, as high as more than four times, can be
observed among the good performing parameter sets although the dynamics are similar among them. Percentage of the catchment area under the threat of high erosion
rate/sediment yield annually is shown in Fig. 6.10 along with the corresponding
annual average sediment yield from the catchment. It has been observed that not
only the quantity of the sediment yield but also the areal extent of erosion risk areas
within the catchment varies considerably (as high as three times) among the chosen
good parameter sets.
Further, the spatial distributions of the annual sediment yield from the different good
performing parameter sets are also compared. The selected four of them (same sets
as shown earlier in Fig. 6.1) are shown as an example in Fig. 6.11 where it can be
seen that they differ considerably in the magnitude. This brings total uncertainty
and unreliability for using or choosing any of the estimated results to define the soil
erosion risk quantitatively as none of the results can be fully believed or all should
be equally believed.
The spatial distribution patterns simulated by the different parameter sets, however,
looks identical. To check this, the spatial correlation of the distributed annual sediment yield rate as simulated by the different parameter sets and the correlation of
their rank are calculated. The correlations are found to be quite high as shown in
Table 6.12.
147
6. Spatially Distributed and Temporally varying soil erosion risk estimation
160
Paraset 1
Paraset 2
140
Paraset 3
Paraset 4
Paraset 5
120
Paraset 6
Paraset 7
Paraset 8
100
Paraset 9
Paraset 10
80
Paraset 11
Paraset 12
Paraset 13
60
Paraset 14
Paraset 15
Paraset 16
40
Paraset 17
Paraset 18
20
Paraset 19
Paraset 20
SCE-UA
0
1990
1991
1992
1993
1994
1995
1996
1997
1998
1999
2000
2001
2002
2003
Figure 6.8: Annual sediment yield with different good parameter sets in Rems catchment
1400
Paraset 1
Paraset 2
Paraset 3
1200
Paraset 4
Sedimen t Yield [ x 1000 t]
Paraset 5
Paraset 6
1000
Paraset 7
Paraset 8
Paraset 9
800
Paraset 10
Paraset 11
Paraset 12
600
Paraset 13
Paraset 14
Paraset 15
400
Paraset 16
Paraset 17
Paraset 18
200
Paraset 19
Paraset 20
0
Jan
SCE-UA
Feb
Mar
Apr
May
Jun
Jul
Aug
Sep
Oct
Nov
Dec
Figure 6.9: Monthly sediment yield with different good parameter sets in Rems catchment
The high spatial correlations of the value and rank of the distributed sediment yield
estimated by the different good performing parameter sets suggest that although the
total quantitative estimates from the catchment differ a lot, the spatial distribution
within the catchment simulated by the different good parameter sets are similar and
therefore can be considered reliable to identify the distributed soil erosion risk or the
Critical Management Zones (CMZs) relatively within a catchment, along with their
temporal variation. So, the number of times (days) that each pixel produces some
sediment (yield) are estimated during the simulation period of 16 years (1990-2005).
Then the spatial distribution of the sediment yield frequency is calculated on monthly
as well as yearly basis and averaged over the results from the 21 good parameter
148
6.5. Distribution and dynamics of soil erosion risk in Rems catchment
Sediment Yield [t/ha/yr] & Area under high erosion [%]
100
Annual Average SY [t/ha/yr]
Area under high erosion [%]
81.69
80.51
80
73.84
72.68
69.43
64.02
60
54.87
54.08
52.63
50.65
47.0
40.0
36.65 36.79
40
35.92
35.0
30.85 30.48
27.08
24.49
24.0
6
7
25.5
40.0
34.0 35.13
42.5
33.0
29.0
28.0
26.0
23.0
22.0
20.0
19.5
20
24.0
41.29
40.0
39.04
49.36
45.5
16.5
16.0
0
1
2
3
4
5
8
9
10
11
12
13
14
15
16
17
18
19
20
21
Parameter set No.
Figure 6.10: Annual average sediment yield and area under high erosion risk with different good
parameter sets in Rems catchment
Set 1
5
Set 16
0
5
1
5
10
0
Mean SY = 50.65 t/ha/y
Area under severe erosion = 28%
N
5 Km
5
Set 21
Mean SY = 81.69 t/ha/y
Area under severe erosion = 47%
N
0
Set 11
Mean SY = 24.49 t/ha/y
Area under severe erosion = 16%
N
5
25
50
5 Km
Mean SY = 49.36 t/ha/y
Area under severe erosion = 29%
N
5 Km
15
0
75
100
0
5 Km
> 500 t/ha/y
Figure 6.11: Spatial distribution of annual sediment yield with different good parameter sets in
Rems catchment
sets. The resulting distribution of soil erosion risk or the Critical Management Zones
(CMZs) in terms of the sediment yield frequency per year is shown in Fig. 6.12.
The higher risk zone or critical erosion source areas demanding for the preventive
measures can be seen as the darker areas distributed within the catchment. To show
the temporal dynamics of such critical areas, the monthly sediment yield frequency
149
6. Spatially Distributed and Temporally varying soil erosion risk estimation
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
1
0.99
0.99
0.99
0.97
0.98
0.99
0.97
0.99
0.96
0.98
0.99
0.98
0.98
0.97
0.99
0.99
0.99
0.97
0.98
0.96
1.00
1
1.00
0.99
1.00
1.00
1.00
1.00
1.00
1.00
1.00
0.99
1.00
1.00
1.00
0.99
1.00
1.00
1.00
1.00
1.00
0.99
1
0.99
0.97
0.99
0.99
0.99
0.98
0.99
0.98
0.99
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0.99
1.00
0.99
0.98
0.98
0.99
0.98
0.98
0.98
1.00
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1
0.99
1.00
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0.99
1.00
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1.00
0.99
1.00
1.00
1.00
1.00
1.00
0.99
0.99
1
0.97
0.99
1.00
1.00
0.99
1.00
0.99
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0.97
1.00
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0.99
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1.00
0.99
0.99
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0.99
0.99
1
0.99
0.99
0.99
0.99
1.00
0.99
1.00
1.00
0.99
0.99
0.99
1.00
1.00
1.00
0.99
1.00
0.99
0.99
0.97
0.97
1
0.94
0.96
0.97
0.96
0.98
0.94
0.97
1.00
0.97
0.96
0.95
0.99
0.99
0.99
0.96
0.98
0.94
0.99
1.00
1.00
0.99
1
1.00
1.00
1.00
1.00
1.00
0.99
0.99
1.00
1.00
1.00
0.99
0.99
1.00
0.99
0.99
1.00
0.97
0.99
0.99
0.94
1
0.99
0.99
0.98
0.99
0.99
0.96
0.94
0.98
1.00
0.99
0.96
0.97
0.98
0.98
0.97
0.97
1.00
1.00
1.00
0.99
1.00
1
1.00
1.00
1.00
1.00
0.99
0.99
1.00
1.00
1.00
1.00
1.00
1.00
1.00
1.00
1.00
0.98
0.99
1.00
0.96
0.99
1
1.00
1.00
0.99
0.99
0.97
0.96
1.00
0.99
0.99
0.99
0.99
0.99
0.99
0.98
0.96
1.00
1.00
1.00
0.99
1.00
1.00
1
1.00
1.00
1.00
0.99
0.99
1.00
1.00
1.00
1.00
1.00
1.00
1.00
1.00
1.00
0.99
0.99
1.00
0.97
0.99
1.00
1
0.99
1.00
0.99
0.97
0.97
1.00
1.00
0.99
0.99
0.99
0.99
0.99
0.98
0.97
0.99
1.00
1.00
0.99
1.00
1.00
1.00
1
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1.00
0.99
0.99
1.00
1.00
1.00
1.00
1.00
1.00
1.00
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1.00
0.97
0.98
0.99
0.96
0.98
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1
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0.99
0.96
0.95
1.00
0.99
0.99
0.99
0.98
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1.00
0.98
0.95
1.00
1.00
1.00
1.00
1.00
1.00
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1
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1.00
1.00
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1.00
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1.00
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1.00
1.00
0.99
0.99
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0.98
0.99
0.99
1.00
0.99
1
0.98
0.98
0.98
1.00
0.99
0.99
0.99
0.99
1.00
0.99
0.99
0.96
0.99
1.00
1.00
0.99
1.00
1.00
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1
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0.99
1.00
1.00
1.00
0.99
0.99
0.99
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0.99
1.00
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0.98
0.99
0.94
0.99
0.99
0.99
0.99
0.98
1
0.95
0.93
0.99
0.99
0.99
0.97
0.97
0.98
0.99
0.97
0.95
1.00
1.00
0.99
1.00
0.99
0.99
0.99
0.99
1.00
0.99
1
1.00
0.99
0.99
0.99
0.99
0.99
1.00
0.99
1.00
1.00
0.98
0.99
0.97
0.97
0.96
0.97
0.97
0.96
0.98
0.95
1
0.98
0.96
0.97
0.96
0.96
0.97
0.98
0.95
0.97
0.98
1.00
0.99
0.99
1.00
0.99
0.99
0.99
0.99
1.00
0.99
1.00
1
0.99
0.99
0.99
1.00
1.00
1.00
0.99
1.00
0.99
0.99
0.97
0.97
1.00
0.94
0.96
0.97
0.95
0.98
0.93
0.98
1
0.96
0.96
0.95
0.98
0.99
0.98
0.95
0.98
0.95
1.00
1.00
1.00
0.99
1.00
1.00
1.00
1.00
1.00
1.00
0.99
0.99
1
1.00
1.00
1.00
1.00
1.00
1.00
1.00
1.00
0.98
0.99
1.00
0.97
0.98
1.00
1.00
1.00
1.00
0.99
0.96
0.96
1
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0.99
0.99
0.99
0.99
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0.99
0.95
1.00
1.00
1.00
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1.00
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0.99
0.99
1.00
1
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1.00
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1.00
1.00
0.98
1.00
1.00
0.96
1.00
0.99
1.00
0.99
0.99
0.99
0.97
0.96
0.99
1
1.00
0.98
0.98
0.99
0.98
0.98
0.97
1.00
1.00
1.00
0.99
1.00
1.00
1.00
1.00
1.00
1.00
0.99
0.99
1.00
1.00
1
0.99
0.99
1.00
1.00
1.00
1.00
0.97
0.99
0.99
0.95
0.99
0.99
0.99
0.99
0.99
0.99
0.96
0.95
0.99
1.00
1
0.98
0.98
0.99
0.99
0.99
0.96
0.99
0.99
0.99
1.00
0.99
1.00
1.00
1.00
1.00
0.99
0.99
1.00
1.00
0.99
0.99
1
1.00
1.00
1.00
1.00
0.99
0.99
0.98
0.99
0.99
0.96
0.99
0.99
0.99
0.99
0.97
0.96
0.98
0.99
0.98
0.98
1
1.00
0.99
0.99
0.99
0.94
1.00
1.00
1.00
1.00
0.99
1.00
1.00
1.00
1.00
0.99
0.99
1.00
1.00
0.99
0.99
1.00
1
1.00
1.00
1.00
0.99
0.99
0.98
0.99
0.99
0.97
0.99
0.99
0.98
0.99
0.97
0.97
0.99
0.99
0.98
0.98
1.00
1
1.00
0.98
1.00
0.95
1.00
1.00
1.00
1.00
1.00
1.00
1.00
1.00
1.00
0.99
1.00
1.00
1.00
1.00
1.00
1.00
1.00
1
1.00
1.00
1.00
0.99
0.99
1.00
0.99
0.98
0.99
0.99
0.99
1.00
0.98
0.98
0.98
0.99
0.99
0.99
0.99
1.00
1
0.98
0.99
0.97
0.99
1.00
1.00
0.99
0.99
1.00
1.00
1.00
1.00
1.00
0.99
0.99
1.00
1.00
1.00
1.00
1.00
1.00
1
1.00
0.99
0.97
0.98
0.99
0.96
0.98
0.99
0.99
1.00
0.99
0.99
0.95
0.95
1.00
0.98
0.99
0.99
0.98
0.98
1
0.98
0.94
1.00
1.00
1.00
1.00
0.99
1.00
1.00
1.00
1.00
0.99
1.00
1.00
1.00
1.00
1.00
1.00
1.00
1.00
1.00
1
0.99
0.98
0.98
0.99
0.98
0.97
0.98
0.98
0.98
0.99
0.97
0.97
0.98
0.99
0.98
0.99
0.99
1.00
0.99
0.98
1
0.95
1.00
1.00
1.00
0.99
1.00
1.00
1.00
1.00
1.00
1.00
1.00
0.99
1.00
1.00
1.00
0.99
0.99
1.00
0.99
0.99
1
0.96
0.98
0.97
0.94
0.97
0.96
0.97
0.95
0.96
0.95
0.98
0.95
0.95
0.97
0.96
0.94
0.95
0.97
0.94
0.95
1
Paraset Paraset Paraset Paraset Paraset Paraset Paraset Paraset Paraset Paraset Paraset Paraset Paraset Paraset Paraset Paraset Paraset Paraset Paraset Paraset Paraset
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
1
1.00
1.00
1.00
0.99
1.00
1.00
0.99
1.00
0.99
1.00
1.00
1.00
1.00
1.00
0.99
1.00
1.00
0.99
1.00
1.00
Paraset Paraset Paraset Paraset Paraset Paraset Paraset Paraset Paraset Paraset Paraset Paraset Paraset Paraset Paraset Paraset Paraset Paraset Paraset Paraset Paraset
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
Table 6.12: Spatial correlation matrix of the distributed annual sediment yield values (top) and their rank (bottom) simulated by different good parameter
sets in Rems catchment
Paraset
Paraset
Paraset
Paraset
Paraset
Paraset
Paraset
Paraset
Paraset
Paraset
Paraset
Paraset
Paraset
Paraset
Paraset
Paraset
Paraset
Paraset
Paraset
Paraset
Paraset
Paraset
Paraset
Paraset
Paraset
Paraset
Paraset
Paraset
Paraset
Paraset
Paraset
Paraset
Paraset
Paraset
Paraset
Paraset
Paraset
Paraset
Paraset
Paraset
Paraset
Paraset
150
6.5. Distribution and dynamics of soil erosion risk in Rems catchment
distributions are shown in Fig. 6.13 for the months of January, March, July and
October. Unlike the common practice of calculating temporally static erosion risk
maps which would declare the certain portion of the catchment to be permanently
prevented or abandoned from agriculture for being under high risk, here it can be
noticed that the risky areas are temporally varying and are not always risky throughout the year, hence not forcing the farmers or land users to permanently abandon
their land. This can be more effective, acceptable and fruitful practices- more so in
the developing countries where erosion problem is more severe.
N
Yearly SY frequency [%]
5
0
5
km
0 .00 - 0.01
0.07 - 0.08
0.01 - 0.03
0.08 - 0.10
0.03 - 0.04
0.10 - 0.11
0.04 - 0.06
0.11 - 0.12
0.06 - 0.07
0.12 - 0.14
Figure 6.12: Spatial distribution of annual sediment yield frequency averaged over different good
parameter sets in Rems catchment
January
March
July
October
0.00
0.01
0.02
0.05
0.07
0.09
0.11
0.14
0.18
0.24
0.27
Figure 6.13: Spatial distribution of monthly sediment yield frequency averaged over different good
parameter sets in Rems catchment
151
6. Spatially Distributed and Temporally varying soil erosion risk estimation
6.6 Conclusions
The final work presented in this Chapter is in accordance with the fulfillment of the
last two objectives stated under Section 1.4 in Chapter 1. The aim was basically
to implement the simple modeling approach to identify spatially heterogeneous and
temporally dynamic Erosion Susceptible Areas (ESAs) in the Rems catchment and to
carry out the erosion risk modeling (USLE-based) for identifying spatially distributed
and temporally varying Critical Source Areas (CSAs) or the Critical Management
Zones (CMZs) for anti-erosion measures.
At first the spatially distributed daily erosivity (R-factor) in the Rems catchment
was calculated. The purely runoff based, widely used MUSLE model (Williams 1975,
Williams & Berndt 1977) was used for the estimation. The required surface runoff Q
was supplied by the surface runoff calculated for each day of the sixteen years of simulation period (1990-2005) in each 100 m by 100 m grid cell of the Rems catchment
by applying the WaSiM-ETH model as described in Chapter 5. Similarly, the required peak runoff rate, Qp , was estimated for each day in each grid cell by using the
area, slope and the simulated runoff depth for that cell on that day as described in
CREAMS Model (Young et al. 1989). Due to the non-uniqueness and non-reliability
of the simulated total surface runoff amount, the spatially distributed daily surface
runoff grids simulated by all the selected 21 different good parameter sets for the 16
years period were considered.
In addition, an attempt has been made to develop a new relationship, if possible, applicable to calculate the erosivity (R-factor) based on easily available rainfall
data/parameters in the Rems catchment. The required long time series of observed
rainfall intensity was not available and so the series of synthetic rainfall with 5 minutes resolution simulated by a simulator called “NiedSim” was used. The stochastic
precipitation time series generator “NiedSim” is an operational system based on a
non-parametric approach developed in the Institute of Hydraulic Engineering (IWS),
Stuttgart University. The 5 minutes’ precipitation time series (1958 to 2004) were
generated for three representative locations coinciding with the location of existing
rainfall stations, situated at upstream, mid- and downstream region of the Rems
catchment. The erosive rainfall events were identified, following the standard definition, from the rainfall series independently for the three stations. The R-factor
was then calculated for those erosive events following the basic definition of R-factor.
Then assuming that, at least, the daily rainfall data will be generally available, the
seven different statistical parameters based on the daily series were considered as
proxy parameters to estimate the R-factor. The multiple non-linear regressions were
carried out for each month and each year (1958-2004). The regression coefficients
were determined by using Conjugate Gradient Method (CGM). Two of the stations
were combined and used for the development of the regression models and that from
third station was used for the validation of the developed relationships. The correlation coefficient for the yearly model was found to be 0.86 and 0.83 for calibration
and validation respectively. Similarly regression models for each month’s erosivity
factor showed the R2 performance measure in the range of 0.70 to 0.97 in calibration
and 0.54 to 0.94 in validation. The attempt made here was quite a preliminary one
152
6.6. Conclusions
and covering the detail investigation is not within the scope of this thesis. However
the preliminary results hinted the applicability of the NiedSim-generated precipitation series in calculating rainfall erosivity factors and possibilities of obtaining those
erosivities reasonably through the use of parameters of more easily available daily
rainfall series in the region. However in this thesis work, the runoff erosivity factor
based on MUSLE erosivity model as described above was used to identify the Hydrologically Sensitive Areas (HSAs).
On the other hand, the spatially distributed and temporally varying Erosion Susceptible Areas (ESAs) in the Rems catchment were calculated based on the topographic factor (LS-factor), crop cover factor (C-factor) and the soil erodibility
factor (K-factor). Several spatially distributed approaches- categorically, the 1-D
approach considering flow path length and 2-D approach considering upstream contributing area were investigated to estimate the topographic i.e. slope length and
slope steepness LS-factor. The hydrologically corrected 100m × 100m DEM of the
Rems catchment, with its extent little bit extended to avoid edge effects, was used
in ArcView GIS with hydro-tools and spatial analyst to calculate the spatially distributed LS factor following the considered approaches. It was found that the 2-D
approach estimates high LS values in hollows too thus ensuring the consideration of
flow convergence in the estimation of the LS factor which is a major factor causing
the enhanced erosion risk in hillslope hollows. The single flow, multiple flow and flow
decomposition algorithm were investigated while calculating the upslope contributing area. The spatially distributed LS-factor grid of the Rems catchment calculated
following the 2-D approach with flux decomposition routing algorithm along with the
Nearing’s slope factor was used further in the research work to define the Erosion
Susceptible Areas (ESAs) in the Rems catchment.
The crop cover management factor or the C-factor, which incorporates the combined
effect of all interrelated cropping and management practices in the catchment, is
the only factor that causes the temporal variability of the Erosion Susceptible Areas (ESAs). However, the USLE-based common practices uses the temporally static
C-factor based on a land use map. The land use category like agricultural land and
forest experiences monthly or seasonal variations due to which the amount of erosion that may occur in a place is different in different season even for similar type
of rainfall event. Development and advancement in the fields of remote sensing and
satellite imagery has been utilized in this research work to capture such temporal dynamics of spatially distributed cover and management factor in terms of Normalized
Difference Vegetation Index (NDVI), the most widely used remote-sensing derived
indicator of vegetation growth. Sixteen days composite MODIS NDVI time series
acquired from its Terra platform were extracted (through LPDAAC data archive
center) for the Rems catchment for the period of 2000 to 2008. The MODIS Reprojection Tool (MRT) was used to convert the projection system from sinusoidal ISN
to Gauss-Krüger III and the hdf format to Geotiff readable by GIS and to resample
the grid to the common 100m size. The clipping for the catchment boundary from
the big MODIS tile was done in Arc GIS with each of the NDVI data set. The time
series being long, these processes of geographical transformation, format conversion,
the clipping and resampling was automatized with a computer program written in
153
6. Spatially Distributed and Temporally varying soil erosion risk estimation
FORTRAN. The obtained NDVI files for the Rems catchment at 16 days interval,
starting from the year 2000 to 2008, were temporally aggregated and averaged to
determine the spatially distributed monthly NDVI maps for the catchment. It was
observed that the months of high rainfall erosivity (Jun-Aug) was in fact associated
with the period of high NDVI, which means higher vegetation coverage, hence indicating the increasing resistance to soil erosion with increase in the climatic erosivity.
To employ the USLE-based models in the Rems catchment, spatially distributed
monthly C-factor was estimated from the extracted NDVI following the scaling approach proposed by a study led by European Soil Bureau (van der Knijff et al. 2000).
The estimated C-factor values were a relative measure based on NDVI values and
have not been calibrated. It was observed that the higher erosivity was normally
associated with higher crop resistance factor and the net effect on the soil erosion,
as determined by the magnitude of their product, would be governed by either of
the two. Both of these factors vary considerably within a year and constitute an
important aspect of soil erosion risk estimation and their dynamics.
The spatial distribution of soil erodibility factor (K-factor), which also is an important aspect to identify Erosion Susceptible Areas (ESAs) in a catchment, was
calculated by assigning corresponding erodibility value to each pixel based on the
soil texture classification of that pixel. The conservation support practice factor
(P -factor) was considered as unity assuming no anti-erosion practices were adopted
throughout the catchment as no field data on the support practices adopted by the
farmers on their agricultural land were available.
The prepared data sets of topographic factor, soil erodibility and monthly crop cover
factor were then used to determine the spatial distribution of the Erosion Susceptible
Areas (ESAs) on every month in the Rems catchment. The monthly ESAs on one
hand and the HSAs, described by the erosivities calculated with the selected twenty
one different good parameter sets, on the other hand, when intersected, produces the
twenty one sets of monthly variation of spatially distributed sediment yield. Quite
large differences in the quantitative estimation of the sediment yield at the catchment
outlet, as high as more than four times, were observed among the good performing
parameter sets. Also, the areal extent of erosion risky areas within the catchment was
found to vary considerably (as high as three times) among the chosen good parameter
sets. The spatial distributions of the annual sediment yield from the different good
performing parameter sets were also found to differ considerably in the magnitude.
These all create total uncertainty and unreliability of using or choosing any of the
estimated results to define the soil erosion risk quantitatively because none of the
results could be fully believed or all should be equally believed.
However, high values of the calculated spatial correlations of the value and rank of
the distributed sediment yield estimated by the different good performing parameter
sets proved that, although total quantitative estimates from the catchment differ a
lot, spatial patterns within the catchment simulated by the different good parameter
sets are identical. Therefore, they can be considered reliable and reasonable to locate
the soil erosion risk along with their temporal dynamics.
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6.6. Conclusions
So the spatial distribution of the sediment yield frequency (percentage of days that
each pixel yields the sediment) was calculated on monthly as well as yearly basis
(1990-2005) and averaged over the results from the twenty one good parameter sets.
It was observed that the erosion risk or sediment source areas are temporally dynamics and are not always risky throughout the year. So unlike the common practice
which provides temporally static erosion risk maps that would decide certain portion
of the catchment to be permanently under high risk and therefore to be prevented
from being used for agriculture, the consideration of temporal variation will not force
the farmers or the land users to permanently abandon their land. The identification
of the Critical Source Areas (CSAs) or the Critical Management Zones (CMZs) for
the prioritization of anti-erosion measures within the catchment in this way would be
more effective, fruitful, convincing and acceptable to farmers - more so in the developing countries where agricultural land-dependence and erosion problem is more severe.
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7 Overall summary and Outlook
This chapter briefly summarizes the overall conclusions and gives some general comments. Detailed conclusions and discussions are already presented in the corresponding chapters. Here, a brief outlook of possible future work is also presented.
7.1 Overall summary
As discussed in the introductory chapter, predictions of spatial patterns are fundamental to many areas including rainfall-runoff and erosion-sediment yield process.
Addressing several issues like sedimentation, water quality, conservation measures,
environmental and geomorphologic studies etc, require the prediction of erosion patterns and source areas within the catchment. Erosion and sedimentation process is
driven by the hydrologic processes of rainfall and runoff. The general interest in
catchment hydrology has been more related to temporal patterns and in particular,
that of stream-flow. In the other hand, the erosion and sediment yield has been
more related to long term annual average without considering temporal/seasonal dynamics. But, the fact that patterns and dynamics are everywhere in hydrology and
soil erosion hardly needs explanation. It’s now necessity to know not only about
the quantity and quality of the water in a stream, but also from where the runoff
loaded with the sediments and contaminants come and where it is best to invest
scarce financial resources to minimize the problem. So the results of not only “how
much” but also “where from” is equally or even more needed. This demand for the
spatially distributed rainfall-runoff and erosion-sediment yield modeling. For the use
of a completely physically-based erosion model the quality and quantity of normally
available observed data even in developed countries, at the moment, is simply not
enough and development or use of more complex erosion models would not improve
the predictions. However, the available data conditions are normally good enough to
try out better hydrological modeling. This suggests an interesting area/direction to
research- what improvement in the modeling of soil erosion and sediment yield can be
achieved by improving the hydrological component of the process? The improvement
on the hydrological representation can be best thought by using the physically-based
distributed rainfall-runoff model. Based on this, the general goal of this research was
formulated to investigate the use of physically-based rainfall-runoff modeling as the
hydrological component with a computationally simple and low data demanding erosion model to estimate spatially distributed and temporally varying erosion/sediment
yield in a catchment. The specific objectives and research questions set for this thesis
are presented in Chapter 1.
The USLE model (Wischmeier & Smith 1978) along with its variants/modifications
is the simple erosion model used in this work. The USLE is integrated within GIS
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7.1. Overall summary
framework in this study to account for the spatial heterogeneity of erosion relevant
watershed characteristics like topography, soil type, land use and land cover etc.
The WaSiM-ETH (Schulla & Jasper 1999, 2006) is the physically-based distributed
hydrological model that is used here for the better hydrological representation in the
simple erosion model. These chosen models are described in detail in Chapter 2.
At first, a case study was carried out in Ganspoel catchment, a small data-rich agricultural catchment located in central Belgium. The details of this study area along
with the wide varieties of available data in high resolution are discussed in Chapter
3. The study was intended to investigate, at first step, the use of a less data intensive
simple rainfall-runoff model coupled with the simple but still widely used soil erosion model (i.e. USLE and its variants) in distributed manner using GIS capabilities
to predict the spatial pattern of surface runoff and sediment source areas within a
catchment along with the lumped predictions of runoff and sediment yield at outlet.
The simple rainfall-runoff model chosen for the case study was the Soil Conservation
Service Curve Number (SCS-CN) method (SCS, 1956, 1964, 1971, 1985, 1993) and
its several current modifications/improvements as discussed in Chapter 2 and 4. The
combination of SCS-CN and USLE-families is the core of several soil erosion and water quality models being used in practice. Six different improvised forms of SCS-CN
model were coupled with several variants of USLE-based erosion model in distributed
manner and applied for seven selected rainfall-runoff-erosion-sediment yield events
in the Ganspoel catchment. The selected events were with varying characteristics
in terms of rainfall-runoff amount, intensity and antecedent moisture conditions and
those events occurred with different land use and soil surface conditions. The results
of a spatially-distributed physically-based soil erosion model (“MEFIDIS”- the Portuguese acronym for Physically Based Distributed Erosion Model, Nunes et al. 2005)
for some of the selected events in this catchment were also available from literature
providing the opportunity to compare our results not only with the observed ones
but also to that with the completely physically based erosion model. The modeling
was carried out in 5m × 5m spatial resolution with 2 minutes temporal resolution.
It was concluded from the results of runoff, gross erosion, sediment yield and spatial
distribution of erosion producing areas that the SCS-CN method with USLE (and
its families), despite several modifications, could improve the runoff volume estimation, but could not simulate the spatial distribution of runoff generating and erosion
producing areas well. The distribution resembles the land use map of the watershed.
This then followed the second intention of the case study which was to investigate if
the capability of the simple erosion model, to predict spatial erosion patterns or erosion source areas, would be enhanced when its hydrological component is improved.
That is to see if the better hydrology representation can improve the simple erosion
model. In this part of research work, the modeling of the events was redone by replacing the SCS-CN component of the USLE based model by the more process oriented
fully distributed hydrologic model, the WaSiM-ETH. The basics of this model are described in Chapter 2 and the application in Chapter 4. The model parameters for the
WaSiM-ETH were calibrated here using the Gauss-Marquardt-Levenberg algorithm
as employed in the PEST (Parameter Estimation Tool). Encouraging results were
obtained with the WaSiM-ETH – USLE coupling. The location of severe erosion was
better captured. The spatial distribution of runoff generating and erosion producing
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7. Overall summary and Outlook
areas are also very well simulated, reasonably close to the observed ones and comparable to or sometimes even better than that simulated by the more data-intensive
physically based complex soil erosion model – the MEFIDIS. This summarizes that
the simplest and still widely used erosion model (USLE and its families) requiring
minimum input data compared to other erosion models, can predict the spatial distribution of erosive areas in a catchment reasonably well when they are coupled with
better rainfall-runoff model for better hydrological processes representation in the
catchment.
While calibrating and applying the physically-based distributed rainfall runoff modelthe WaSiM-ETH- in the Ganspoel catchment, an important unreasonable consequence had been encountered as a random result. The calibration was done with
objective function of minimizing hydrograph prediction errors in the catchment outlet. This is the normal procedure of calibrating any hydrological model, including the
distributed ones as no distributed results are normally available for the calibration.
Very nice results were obtained with closely matching hydrographs and high NashSutcliffe efficiencies (0.97 in calibration and 0.81 in validation) thus verifying the
calibrated parameters and model results for further use. But when the corresponding simulated distributed runoff source areas within the catchment were investigated,
a very much unrealistic patterns were observed with almost all the runoff coming from
a small isolated patch in the catchment and no runoff from areas where erosion and
sediment transport were observed during the events. This shows an alarming situation to notice that a very good model performance can be associated with completely
unrealistic process representation within the catchment.
During the course of the case study, some other secondary conclusions were also
drawn. Through the comparison of several forms of erosivity factor, it was found
that the combination of both rainfall and runoff in erosivity representation as proposed by Onstad and Foster simulates erosion better than considering either of them
alone. Similarly it was also shown that, in comparison to the normally followed procedure of considering the topographic effects on erosion using the flow path length
in one dimensional way, the two dimensional consideration which uses the upslope
contributing area captures the topographic effects in more realistic way as it ensures
more erosion in the hollow due to flow convergence. In addition, it was also observed that unlike the steepest descent algorithm, which is followed by almost all the
USLE-based models for the estimation of the upslope contributing area, the flux decomposition algorithm which considers multi-directional flow from a grid gives better
results when simulated and observed gross erosion and sediment yield are compared.
Also the different sediment delivery ratio (SDR) models along with a new proposed
one were used and it was found that the proposed one which is based on more number
of relevant factors produced better results at least for the considered events in the
case study.
The erosion control strategies or best management practices (BMPs) in a catchment
should focus especially on surface runoff- the primary hydrological vector for the
erosion. However, the generation and spatial distribution of surface runoff, in reality,
is never constant or uniform across a catchment and over the time. There exist re-
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7.1. Overall summary
gions within the watershed that are more susceptible to producing runoff than other
regions. Eroded sediments and water-born constituents in these areas are likely to
be readily transported to surface waters. Such areas can be defined as the Hydrologically Sensitive Areas (HSAs) which describe the risk of runoff generation and hence
determine the potential erosion source areas. Recognizing the spatial and temporal
variation of HSAs within the catchment limits the scope of watershed-scale soil erosion problems to only those sensitive areas and for the required period of time. A
direct measurement of such areas in the field is hardly possible and therefore modeling is required. The case study was therefore followed by a detailed investigation in
the application of the physically-based distributed rainfall-runoff model, the WaSiMETH, in identifying the spatially distributed and temporally varying Hydrologically
Sensitive Areas (HSAs) within a bigger catchment.
The identification of distribution and dynamics of the HSAs with WaSiM-ETH was
carried out in the meso-scale Rems catchment of southern Germany. The details
of this study area along with the available data are discussed in Chapter 3. While
the basics of the model is described in Chapter 2, the application along with the
modules responsible for the surface runoff generation, input data requirement and
preparation, adjustable model parameters (eleven in numbers) and their effects, several parameters estimation techniques are described in Chapter 5. The model, set up
for the Rems catchment (with four subcatchments/gauges), was run in the WaSiMETH runoff generation mode which uses the combined extended/modified Topmodel
(saturated overland flow) & Green and Ampt (infiltration excess) runoff approach
for the simulation of runoff generating areas. The spatial discretization was done
with 100m x 100m regular grids and the modeled temporal resolution was 1 day.
The year 1993 was chosen for calibration with year 1992 as warm-up period. The land
use data used in the modeling was also from the satellite map of the year 1993. For the
CPU intensive WaSiM-ETH, the parameters estimation was carried out with quite
rapid Gauss-Marquardt-Levenberg algorithm using PEST tool and the daily simulation was done continuously for sixteen years (1990-2005). The parameter sets were
calibrated for each subcatchment independently using their observed discharge series
at the respective outlets. The observed discharge series in the gauges, not the simulated one, were passed to the downstream subcatchment in each time step to avoid
propagation of possible error associated with the simulated series. Following the recommendation by Moriasi et al. 2007, the calibration and over all model performances
were evaluated through yearly linear and log Nash-Sutcliffe (NS) efficiency, percent
bias (PBIAS) and RMSE-observations standard deviation ratio (RSR). The performance measures showed quite good simulation for non-headwater subcatchments 3
and 4 (Schorndorf and Neustadt) but not so good for the headwater subcatchments 1
and 2 (Schwäbisch-Gmünd and Haubersbronn). Aiming for the better overall model
performance, the calibration was redone using the same Gauss-Marquardt-Levenberg
method but for the year 1996 (the worst performing year) with the same land use grid
(1993) and also for the year 2000 but then using the land use grid of the year 2000.
It was observed that, although the method of estimation was same, the optimized
values of the parameters vary widely and randomly with the change in calibration
period and/or land use, all showing similar trend of model performances. The year
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7. Overall summary and Outlook
1996, an extreme case in the lower side (low precipitation and temperature), could
not be simulated properly except when the calibration is done for this year itself.
The WaSiM-ETH model may be incapable of simulating such low events. However,
it was noticed that the calibrated parameter set from the year 1996, which represent events of low magnitude (say unusual events of the simulation period), have
performed better throughout the simulation period than that from 1993 and 2000
which represent medium events of the simulation period. It implies the necessity of
the inclusion of or giving priority to unusual events during calibration for achieving
good model performance overall. Hence calibrating the unusual events of a period
is necessary condition but is it sufficient condition too; this remains an interesting
question for further research.
The monthly HSAs, calculated as the percentage of number of days that any pixel
generates surface runoff in that month during the sixteen years of simulation period
(1990-2005), were estimated from the daily simulated spatially distributed surface
runoff grids for all the three sets of the calibrated parameters. Attempt made to
relate these monthly probabilities of surface runoff generation with the easily measurable relevant proxy parameters (distributed values of precipitation, topographic
wetness index and runoff curve number) showed surprising and unacceptable results.
The surface runoff generation probabilities were found to be negatively correlated
with the topography wetness index and curve number in several cases. Also the
regression coefficients as well as the main influencing proxy parameter vary widely
and randomly among subcatchments and among the different set of the calibrated
parameters. So the general relationships applicable to identify HSAs through easily
obtainable parameters could not be devised.
It had also been observed that the pattern of spatially distributed surface runoff
varies not only among the different parameter sets with which they were simulated
but also varies abruptly and unrealistically among the subcatchments. Doubting to
the deficiencies in the adopted Gauss-Marquardt-Levenberg method, which is the
local search technique, the parameters estimation was redone using the year 1993
with land use grid of 1993 as before but with a more acceptable global optimization
technique – SCE-UA (Shuffled Complex Evolution) which required huge computation time. The calibrated values were found to vary widely with the change in the
optimization method too, however the model performances could not be improved
than what was obtained earlier from the considerably quicker method. The low
extreme events as in 1996 were simulated still poorly with the globally optimized parameters too thus confirming the deficiency of WaSiM-ETH model in simulating the
low events and necessity of using unusual events in calibration. The simulated surface runoff patterns were quite different for differently calibrated parameter sets thus
raising question of reliability to use particular pattern for calculating distributed soil
erosion. Further questionable was the unrealistic behaviour that the surface runoff
patterns were still totally different from one subcatchment to another.
In the further attempt to address the problem, a new and completely different approach of parameters estimation, the multidimensional data-depth based “Robust
Parameter Estimation (ROPE)” algorithm, had been applied. This new algorithm
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7.1. Overall summary
was developed in Department of Hydrology and Geohydrology, Stuttgart University
(Bárdossy & Singh 2008). The algorithm is based on the fact that robust parameter
sets are geometrically well-structured and lie in the interior of the parameters cloud in
multi-dimensional space. The estimation procedure is described in Chapter 5. With
this, it was aimed to estimate a set of robust parameter vectors instead of a single set
of optimized parameters like earlier and analyze them with their distributed results
to find the best set for the intended purpose, i.e. to achieve acceptable surface runoff
patterns, the HSAs. Besides the advantage of obtaining several number of robust
parameter sets, another beauty of this parameter estimation algorithm (ROPE), that
had been noticed during its use, is that every iteration/model run is independent of
previous run. This means unlike the other optimization methods, several computers can be used to compute the required number of model runs/iteration of a loop
independently and the results can be brought together to analyze after every loop.
This is huge advantage particularly for the CPU-intensive process-based models like
WaSiM-ETH. Thus, the ROPE algorithm has the computational efficiency comparable to the fast gradient-based method like PEST (Gauss-Marquardt-Levenberg
algorithm) without having danger of being trapped in local optima which PEST etc
does have.
Like earlier, the ROPE algorithm was also applied in the Rems catchment with 1993
as calibration year, with one preceding year (1992) as the spin-up period. Different
robust parameter vectors were estimated independently for each of the four subcatchments based on their respective observed discharge series and using observed
discharges to flow downstream from the upstream catchments. Again, it was observed
that despite the good model performance, the simulated surface runoff pattern are
still unrealistic. Besides among the different good parameter sets, the pattern varies
abruptly among the subcatchments. This was linked to the different subcatchments
having the different parameter sets which were calibrated independently with the
observed discharges at their corresponding gauges- a common practice of calibration. So with the aim to avoid the unreasonable inter-subcatchments variation of
the surface runoff patterns, the parameter set was not allowed to vary among the
subcatchments, which means same sets of robust parameter vectors were estimated
for whole Rems catchment. However the good parameter sets were defined not as
the best in the sum of the squared errors of whole catchment but were defined compromisingly best in sum of the squared errors of each subcatchment independently.
1955 number of acceptably good performing robust parameter sets were obtained
using the ROPE algorithm. In addition for the comparison, the optimized single
parameter set for whole catchment (not varying among subcatchments) was also obtained using once again the SCE-UA algorithm. Despite the similarly good model
performances, the obtained good/optimized parameters sets vary considerably (equifinality). However, it was observed that there were no more unacceptable random
variations of patterns among the subcatchments and pattern seem to be reasonable
then. Unacceptable variations of the distributed patterns among the subcatchments
could be thus avoided by assigning same parameter set for all the subcatchments.
The spatial correlation of values and rank of distributed surface runoff simulated by
the different good parameter sets were found to be quite high indicating that the
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7. Overall summary and Outlook
simulated patterns are quite similar. But when a simple quantitative analysis of
these distributed results from the good parameter sets was made, once again another
unacceptable result came in front. In spite of the good model performances and reasonable surface runoff patterns within the catchment, the mean surface runoff and its
total amount varies highly, as much as four times, among the different good parameter sets thus creating doubt to accept a particular distributed result quantitatively.
They would give unacceptably different results, at least quantitatively in this case,
when they are used further in estimating soil erosion by the surface runoff. Which
spatial prediction, although all from the equally good model performances, should
we believe for further use?
Through these series of unreasonable results in this research work, a general conclusion can be made. Distributed models are applied mainly to make use of their
distributed results; however they are and have to be generally calibrated with lumped
data observed at outlets or gauges. Result of such an application in the Ganspoel
catchment showed that the very good model performance and hydrographs matching
can be associated with completely unrealistic process representation within the catchment. Similar application in the Rems catchment with the use of different calibration
year, different land use and different optimization method showed that the estimated
different parameter sets may perform equally well when evaluated at catchment outlet but may produce entirely different distributed results within the catchment. In
addition the surface runoff patterns can be totally different from one subcatchment
to another. Even if uniform runoff patterns could be achieved somehow finally, the
quantitative estimates of the distributed results vary unacceptably widely. This all
shows that simply the better hydrograph prediction by a physically-based distributed
rainfall runoff model does not guarantee better hydrology representation by it within
the catchment. Thus it makes the reliability of distributed results, which is the main
aim of using distributed model, in doubt to be accepted if its parameterization is
verified only with observed data lumped at outlet. So one should be careful that
the model performance evaluation can be misleading as there could be very good
prediction of a distributed rainfall runoff model but for all wrong reasons.
The 1955 good parameter sets obtained with the ROPE algorithm were based on
minimum sum of squared error. Then further attempt was made in identifying the
good parameter sets by calculating their depth based on other performance criteria
mainly, the surface runoff volume error. Other considered criteria are 90% nonexceeding surface runoff value error, linear and log NS coefficients, root mean square
error (RMSE) of peaks, sum of squared error of biggest 10% flow values (top 10% of
flow duration curve) and base-flow volume error. For this the observed surface runoff
at the gauges was separated from the respective hydrographs using the digital filter
technique. Although they were found to be good in many of the mentioned criteria,
it was observed that there were hardly any parameter sets that were good in surface
runoff estimation too at the same time. So compromising with the small loss in other
performance criteria, the good parameter sets were searched in the 3007 parameter
sets which were generated at the second last step (lower performance than the last
step) of the ROPE algorithm. Several good parameters based on the surface runoff
estimation too could be found then. However, due to the large variability in the total
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7.1. Overall summary
amount of the simulated distributed results with the different good performing parameter sets, 20 different good and robust parameter sets (from the 3007 sets) based
on all performance criteria but focusing mainly on the surface runoff were selected
for the further analysis. The daily surface runoff grids (HSAs) for the sixteen years
were generated with the 21 parameter sets (including the SCE-UA optimized set)
and supplied to the simple modified USLE erosion model for spatially distributed
and temporally varying erosion risk estimation which is described in Chapter 6.
The spatially distributed surface runoff for each day of the sixteen years of simulation period (1990-2005) in each 100 m by 100 m grid cell of the Rems catchment
calculated by applying the WaSiM-ETH model with each of the selected 21 good
parameter sets were inputted to the purely runoff based, widely used MUSLE model
(Williams 1975, Williams & Berndt 1977) for the estimation of the spatially distributed daily erosivity (R-factor) in the Rems catchment. The required cell wise
peak runoff rate, Qp , was estimated for each day by using the area, slope and the
simulated runoff depth for that cell on that day following the method described in
CREAMS Model (Young et al. 1989). The calculated spatially heterogeneous and
temporally varying erosivity identified the Hydrologically Sensitive Areas (HSAs),
from the erosion point of view, in the Rems catchment.
As a small secondary part of research, an attempt was made to develop new relationships applicable to calculate the erosivity (R-factor) based on more readily available
daily rainfall data/parameters in the Rems catchment. As no rainfall intensity time
series were observed, the 5 minutes’ precipitation time series from 1958 to 2004 were
generated for three representative locations in the Rems catchment using a simulator called “NiedSim”. The stochastic precipitation time series generator “NiedSim”
is an operational system based on a non-parametric approach developed in the Institute of Hydraulic Engineering (IWS), Stuttgart University. The three representative
locations selected for the generation coincide with the location of existing rainfall
stations, situated at upstream, mid- and downstream region of the Rems catchment.
Following the basic definition, the R-factor was calculated for the erosive events of the
generated series, independently for the three stations. Then the seven different statistical parameters based on the daily series were considered as independent variables
for the multiple non-linear regressions which were carried out for each month and
each year (1958-2004) to estimate the R-factor. Conjugate Gradient Method (CGM)
was used for the determination of the regression coefficients. The regression models
were developed from the two of the stations and the third station was used for the
validation of the developed relationships. Although the attempt made here was quite
a preliminary one, covering the detailed investigation being outside the scope of this
thesis, the high correlation coefficients for the yearly and monthly models in both
calibration and validation pointed out the applicability of the NiedSim-generated
precipitation series in calculating rainfall erosivity factors and possibilities of obtaining those erosivities resonably through the use of more easily available daily rainfall
parameters in the region. However in the thesis work, the MUSLE erosivity model
based runoff erosivity factor was used to identify the Hydrologically Sensitive Areas
(HSAs).
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7. Overall summary and Outlook
On the other hand, the topographic or slope length and steepness factor (LS-factor),
crop cover factor (C-factor) and the soil erodibility factor (K-factor) were required
to estimate the spatially distributed and temporally varying Erosion Susceptible Areas (ESAs) in the Rems catchment. Several spatially distributed 1-D (considering
flow path length) and 2-D (considering upstream contributing area) approaches were
investigated to estimate the topographic LS-factor. It was observed that the 2-D
approach incorporates flow convergence in the estimation of the LS factor which is
a major factor causing the enhanced erosion risk in hillslope hollows. The upslope
contributing areas were calculated using the single flow, multiple flow and flow decomposition algorithm. The 2-D approach with flux decomposition routing algorithm
along with the Nearing’s slope factor was finally used to define the effect of topography in identification of the Erosion Susceptible Areas (ESAs) in the Rems catchment.
The crop cover or C-factor, as calculated in normal practices, is based on a temporally
static land use map which cannot provide the dynamics to the ESAs, although its
temporal variation is always a reality. However, in the presented research work such
temporal dynamics had been captured by utilizing the development and advancement in the field of remote sensing and satellite imagery. The Normalized Difference
Vegetation Index (NDVI), a widely used spectral indicator of vegetation growth, were
extracted (through LPDAAC data archive center) for the Rems catchment for the
period of year 2000 to 2008. Those NDVI time series were acquired from the Terra
platform of MODIS satellite and available as 16 days composite. The required projection transformation, format conversion, sub-setting and resampling for the long
time-series were automatized using the MODIS Reprojection Tool (MRT), Arc GIS
and FORTRAN. The obtained NDVI series at 16 days interval (2000 to 2008) were
temporally aggregated and averaged to determine the spatially distributed monthly
NDVI maps for the catchment. It was observed that the period of high rainfall erosivity (Jun-Aug) are normally counter-balanced with the high NDVI (higher vegetation
coverage) resulting the increasing resistance to soil erosion in that period. The prepared NDVI series were transformed to the spatially distributed monthly C-factor
for the Rems catchment by employing a scaling approach proposed by a study led
by European Soil Bureau (van der Knijff et al. 2000). Consequently, it was seen that
the higher erosivity was normally associated with higher crop resistance factor and
so the net effect on the soil erosion, as determined by the magnitude of their product, would be governed by either of the two. Both of these factors vary considerably
within a year and therefore they constitute an important aspect for estimation of
dynamics of soil erosion risk.
The spatial distribution of soil erodibility factor (K-factor), another important aspect to identify Erosion Susceptible Areas (ESAs) in a catchment, was calculated by
assigning corresponding erodibility value to each pixel based on the soil texture classification of that pixel. No field data on the support practices adopted by the farmers
on their agricultural land were available. So the conservation support practice factor
(P -factor) was considered as unity which corresponds to that no anti-erosion practices were adopted in the catchment.
The Erosion Susceptible Areas (ESAs) on every month in the Rems catchment was
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7.1. Overall summary
then obtained by intersecting the prepared distributed data sets of the topographic,
soil erodibility and monthly crop cover factors. Those monthly ESAs were intersected
with the Hydrologically Sensitive Areas (HSAs), described by the erosivities calculated with the selected 21 different good parameter sets. This resulted the 21 sets of
monthly varying spatially distributed sediment yield. Very high differences, as high
as more than four times, in the quantitative estimation of the total sediment yield
at the catchment outlet were observed among the good performing parameter sets.
The areal extent of erosion risk areas within the catchment was also found to vary
considerably (as high as three times) among them. The spatial distributions of the
annual sediment yield from the different good performing parameter sets were also
found to differ considerably in the magnitude. So it was uncertain and unreliable in
deciding or choosing any of the estimated results to define the soil erosion risk quantitatively because none of the results could be fully believed or all should be equally
believed. However, the spatial correlations of the value and rank of the distributed
sediment yield estimated by the different good performing parameter sets were found
to be quite high which claimed that, although the total quantitative estimates from
the catchment differ a lot, the spatial distribution within the catchment simulated
by the different good parameter sets are identical. Therefore, the results and hence
the approach could be considered reliable and reasonable to locate the distributed
soil erosion risk along with their temporal dynamics, i.e. identification of the Critical
Source Areas (CSAs).
So the spatial distribution of the sediment yield frequency, averaged over the results
from the 21 good parameter sets, was calculated on monthly and yearly basis (19902005) as the percentage of days that each pixel yields some amount of the sediment.
The high frequency region describe the location of Critical Source Areas (CSAs). The
temporal dynamics of the erosion risky or sediment source areas could be observed
such that the parts of areas risky at a time are not always risky throughout the year.
So, unlike the existing practices of having temporally static erosion risk maps which
would declare certain portion of the catchment to be permanently under high risk
and therefore to be prevented from being used for agriculture; the consideration of
temporal variation, like in this research work, will not force the farmers or the land
users to permanently abandon their land.
The temporal variability captured through HSAs and ESAs thus yields dynamics of
the erosion risk areas through CSAs. Such areas give guidance during planning process on where the soil conservation measures can be designed to prevent the problem
from occurring or to minimize the runoff. Such understanding helps in identifying
priority areas that require urgent management interventions in controlling soil erosion
or in determining the priority for implementing the needed BMPs (Best Management
Practices). This potentially lessens land use restrictions on landowners relative to
static land classification schemes. For example, the arable and agricultural fields
could be prioritized by their degree of hydrological and erosive sensitivity in ways
that unavoidable erosion and water pollution enhancing crops’ type and management
practices shall be adopted in areas/fields with the lowest extent or frequency of CSAs.
The identification of the Critical Source Areas (CSAs) or Critical Management Zones
(CMZs) for the prioritization of urgent anti-erosion measures within the catchment
165
7. Overall summary and Outlook
in this way would be more effective, fruitful, convincing and acceptable to farmers more so in the developing countries where agricultural land-dependence and erosion
problem is more severe. No erosion models or BMPs (Best Management Practices)
currently account for this type of dynamic behavior in hydrological sensitivity and
erosion risk in such a simple approach.
7.2 Outlook
Erosion modeling within GIS generally focuses on describing the spatial distributions, rather than calculating the values of soil loss. Predicting the location and
timing of high risk areas with the highest possible accuracy is extremely important
for erosion prevention as it allows identification of the proper location and type of
erosion prevention measures needed. The most important goal in the presented research work was ensuring reasonable erosion estimations by using GIS framework
with the simple USLE modeling technique augmented by a better hydrological representation for realistic decision making. Some of the important issues that shall be
considered for future development as extension of or in direction to the presented
study are discussed below in brief.
Either direct measurements or remotely sensed data would provide the most accurate
measures of runoff generation within a catchment, but such data are generally not
available for large enough areas or long enough periods to calculate probability of
runoff generation. Therefore, HSAs are best determined based on long term simulations using a physically based hydrological model. For this purpose, the WaSiM-ETH
model was chosen in this research work. However, the investigation and comparison
of capabilities of some other physically based distributed rainfall-runoff models too
in predicting the spatial heterogeneity and temporal dynamics of the HSAs or the
runoff source areas in a watershed have to be made to derive model-independent
conclusions. Further, the calibration and validation of the hydrological simulations
was restricted to discharges observed at outlet only. If observations become available, the calibration and validation should also include the other hydrological aspects
like ground water measurements and spatially distributed information, for example
satellite derived evapotranspiration estimations etc. The necessity of using unusual
events in calibration was shown in this study; however, its sufficiency shall be further
researched.
The inclusion of spatial distribution and temporal variation of resistance to erosion
by the vegetation coverage on the ground through the use of NDVI was one of the
important parts in this study. NDVI is positively correlated with the amount of
green biomass, so it can be used to give an indication for differences in green vegetation coverage. By using the MODIS-NDVI multi-temporal imagery, it was possible
to identify areas where the density of vegetation is very low or absent at a particular time, as the 16 days composite time series cover the phenological vegetation.
However, it is important to note that the C-factor values required for the erosion
modeling were a relative measure based on the NDVI values and had not been calibrated. Such C-factor values will have greater uncertainty for the lower range and
166
7.2. Outlook
higher range of NDVI values because during early growth stages thin vegetation covers are often over-estimated by the NDVI due to intense chlorophyll activity, and
during vegetation senescence NDVI usually decreases even when the cover remains
the same. However, for the erosion processes, vegetation condition is of minor importance as the senescent vegetation offers the same protection to the soil as vigorous
vegetation. Therefore, wherever and whenever possible the use of NDVI series in
C-factor estimation needs to be calibrated and validated instead of directly using
the established relationship between NDVI and C-factor developed somewhere else.
In addition, other relevant indices like Leaf Area Index (LAI), Enhanced Vegetation
Index (EVI) etc. should also be tried upon for the better representation of actual
ground conditions.
As a preliminary attempt, the regression models for the estimation of rainfall erosivity, the R-factor, were developed based on NiedSim generated 5 minutes’ rainfall
data for 3 stations geographically evenly distributed over the catchment. However,
the number of stations considered is not sufficient for developing the readily applicable regression models. The attempt shall be repeated using more number of stations
so that the location parameters of the stations can also be used as the independent
variables in the regression which would most probably improve the applicability of
the developed models.
And as a final recommendation, it has been foreseen that, given the current status
of available data in the field of soil erosion and sediment yield, the construction of
new, complex and more process-oriented models is not going to improve the prediction. The focus should be in collecting more data in types, quality and quantity.
However, even for the simple erosion models with current data status/limitation the
improvement can always be thought of through the improvement of hydrological representation in the modeling as observed in this research work.
167
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Vorstand (Stand 01.04.2009)
Prof. Dr. rer. nat. Dr.-Ing. A. Bárdossy
Prof. Dr.-Ing. R. Helmig
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Dr.-Ing. S. Hartmann
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PD Dr.-Ing. W. Marx
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Emeriti
Prof. Dr.-Ing. habil. Dr.-Ing. E.h. Jürgen Giesecke
Prof. Dr.h.c. Dr.-Ing. E.h. Helmut Kobus, PhD
Lehrstuhl für Wasserbau und
Wassermengenwirtschaft
Leiter: Prof. Dr.-Ing. Silke Wieprecht
Stellv.: PD Dr.-Ing. Walter Marx, AOR
Versuchsanstalt für Wasserbau
Leiter: Dr.-Ing. Sven Hartmann, AOR
Lehrstuhl für Hydromechanik
und Hydrosystemmodellierung
Leiter: Prof. Dr.-Ing. Rainer Helmig
Stellv.: Dr.-Ing. Holger Class, AOR
Lehrstuhl für Hydrologie und Geohydrologie
Leiter: Prof. Dr. rer. nat. Dr.-Ing. András Bárdossy
Stellv.: Dr. rer. nat. Jochen Seidel
VEGAS, Versuchseinrichtung zur
Grundwasser- und Altlastensanierung
Leitung: Jürgen Braun, PhD
Dr.-Ing. Hans-Peter Koschitzky, AD
Verzeichnis der Mitteilungshefte
1
Röhnisch, Arthur: Die Bemühungen um eine Wasserbauliche Versuchsanstalt an
der Technischen Hochschule Stuttgart, und
Fattah Abouleid, Abdel: Beitrag zur Berechnung einer in lockeren Sand gerammten, zweifach verankerten Spundwand, 1963
2
Marotz, Günter: Beitrag zur Frage der Standfestigkeit von dichten Asphaltbelägen
im Großwasserbau, 1964
3
Gurr, Siegfried: Beitrag zur Berechnung zusammengesetzter ebener Flächentragwerke unter besonderer Berücksichtigung ebener Stauwände, mit Hilfe von
Randwert- und Lastwertmatrizen, 1965
4
Plica, Peter: Ein Beitrag zur Anwendung von Schalenkonstruktionen im Stahlwasserbau, und Petrikat, Kurt: Möglichkeiten und Grenzen des wasserbaulichen Versuchswesens, 1966
2
Institut für Wasserbau * Universität Stuttgart * IWS
5
Plate, Erich: Beitrag zur Bestimmung der Windgeschwindigkeitsverteilung in der
durch eine Wand gestörten bodennahen Luftschicht,
und
Röhnisch, Arthur; Marotz, Günter: Neue Baustoffe und Bauausführungen für den
Schutz der Böschungen und der Sohle von Kanälen, Flüssen und Häfen; Gestehungskosten und jeweilige Vorteile, sowie Unny, T.E.: Schwingungsuntersuchungen am Kegelstrahlschieber, 1967
6
Seiler, Erich: Die Ermittlung des Anlagenwertes der bundeseigenen Binnenschiffahrtsstraßen und Talsperren und des Anteils der Binnenschiffahrt an diesem Wert, 1967
7
Sonderheft anläßlich des 65. Geburtstages von Prof. Arthur Röhnisch mit Beiträgen von Benk, Dieter; Breitling, J.; Gurr, Siegfried; Haberhauer, Robert; Honekamp, Hermann; Kuz, Klaus Dieter; Marotz, Günter; Mayer-Vorfelder, Hans-Jörg;
Miller, Rudolf; Plate, Erich J.; Radomski, Helge; Schwarz, Helmut; Vollmer, Ernst;
Wildenhahn, Eberhard; 1967
8
Jumikis, Alfred: Beitrag zur experimentellen Untersuchung des Wassernachschubs
in einem gefrierenden Boden und die Beurteilung der Ergebnisse, 1968
9
Marotz, Günter: Technische Grundlagen einer Wasserspeicherung im natürlichen
Untergrund, 1968
10
Radomski, Helge: Untersuchungen über den Einfluß der Querschnittsform wellenförmiger Spundwände auf die statischen und rammtechnischen Eigenschaften,
1968
11
Schwarz, Helmut: Die Grenztragfähigkeit des Baugrundes bei Einwirkung vertikal
gezogener Ankerplatten als zweidimensionales Bruchproblem, 1969
12
Erbel, Klaus: Ein Beitrag zur Untersuchung der Metamorphose von Mittelgebirgsschneedecken unter besonderer Berücksichtigung eines Verfahrens zur Bestimmung der thermischen Schneequalität, 1969
13
Westhaus, Karl-Heinz: Der Strukturwandel in der Binnenschiffahrt und sein Einfluß
auf den Ausbau der Binnenschiffskanäle, 1969
14
Mayer-Vorfelder, Hans-Jörg: Ein Beitrag zur Berechnung des Erdwiderstandes unter Ansatz der logarithmischen Spirale als Gleitflächenfunktion, 1970
15
Schulz, Manfred: Berechnung des räumlichen Erddruckes auf die Wandung kreiszylindrischer Körper, 1970
16
Mobasseri, Manoutschehr: Die Rippenstützmauer. Konstruktion und Grenzen ihrer
Standsicherheit, 1970
17
Benk, Dieter: Ein Beitrag zum Betrieb und zur Bemessung von Hochwasserrückhaltebecken, 1970
Verzeichnis der Mitteilungshefte
3
18
Gàl, Attila: Bestimmung der mitschwingenden Wassermasse bei überströmten
Fischbauchklappen mit kreiszylindrischem Staublech, 1971,
19
Kuz, Klaus Dieter: Ein Beitrag zur Frage des Einsetzens von Kavitationserscheinungen in einer Düsenströmung bei Berücksichtigung der im Wasser gelösten Gase, 1971,
20
Schaak, Hartmut: Verteilleitungen von Wasserkraftanlagen, 1971
21
Sonderheft zur Eröffnung der neuen Versuchsanstalt des Instituts für Wasserbau
der Universität Stuttgart mit Beiträgen von Brombach, Hansjörg; Dirksen, Wolfram;
Gàl, Attila; Gerlach, Reinhard; Giesecke, Jürgen; Holthoff, Franz-Josef; Kuz, Klaus
Dieter; Marotz, Günter; Minor, Hans-Erwin; Petrikat, Kurt; Röhnisch, Arthur; Rueff,
Helge; Schwarz, Helmut; Vollmer, Ernst; Wildenhahn, Eberhard; 1972
22
Wang, Chung-su: Ein Beitrag zur Berechnung der Schwingungen an Kegelstrahlschiebern, 1972
23
Mayer-Vorfelder, Hans-Jörg:
Variationsverfahren, 1972
24
Minor, Hans-Erwin: Beitrag zur Bestimmung der Schwingungsanfachungsfunktionen überströmter Stauklappen, 1972,
25
Brombach, Hansjörg: Untersuchung strömungsmechanischer Elemente (Fluidik)
und die Möglichkeit der Anwendung von Wirbelkammerelementen im Wasserbau,
1972,
26
Wildenhahn, Eberhard: Beitrag zur Berechnung von Horizontalfilterbrunnen, 1972
27
Steinlein, Helmut: Die Eliminierung der Schwebstoffe aus Flußwasser zum Zweck
der unterirdischen Wasserspeicherung, gezeigt am Beispiel der Iller, 1972
28
Holthoff, Franz Josef: Die Überwindung großer Hubhöhen in der Binnenschiffahrt
durch Schwimmerhebewerke, 1973
29
Röder, Karl: Einwirkungen aus Baugrundbewegungen auf trog- und kastenförmige
Konstruktionen des Wasser- und Tunnelbaues, 1973
30
Kretschmer, Heinz: Die Bemessung von Bogenstaumauern in Abhängigkeit von
der Talform, 1973
31
Honekamp, Hermann: Beitrag zur Berechnung der Montage von Unterwasserpipelines, 1973
32
Giesecke, Jürgen: Die Wirbelkammertriode als neuartiges Steuerorgan im Wasserbau, und Brombach, Hansjörg: Entwicklung, Bauformen, Wirkungsweise und
Steuereigenschaften von Wirbelkammerverstärkern, 1974
Erdwiderstandsbeiwerte
nach
dem
Ohde-
4
Institut für Wasserbau * Universität Stuttgart * IWS
33
Rueff, Helge: Untersuchung der schwingungserregenden Kräfte an zwei hintereinander angeordneten Tiefschützen unter besonderer Berücksichtigung von Kavitation, 1974
34
Röhnisch, Arthur: Einpreßversuche mit Zementmörtel für Spannbeton - Vergleich
der Ergebnisse von Modellversuchen mit Ausführungen in Hüllwellrohren, 1975
35
Sonderheft anläßlich des 65. Geburtstages von Prof. Dr.-Ing. Kurt Petrikat mit Beiträgen von: Brombach, Hansjörg; Erbel, Klaus; Flinspach, Dieter; Fischer jr., Richard; Gàl, Attila; Gerlach, Reinhard; Giesecke, Jürgen; Haberhauer, Robert; Hafner Edzard; Hausenblas, Bernhard; Horlacher, Hans-Burkhard; Hutarew, Andreas;
Knoll, Manfred; Krummet, Ralph; Marotz, Günter; Merkle, Theodor; Miller, Christoph; Minor, Hans-Erwin; Neumayer, Hans; Rao, Syamala; Rath, Paul; Rueff, Helge; Ruppert, Jürgen; Schwarz, Wolfgang; Topal-Gökceli, Mehmet; Vollmer, Ernst;
Wang, Chung-su; Weber, Hans-Georg; 1975
36
Berger, Jochum: Beitrag zur Berechnung des Spannungszustandes in rotationssymmetrisch belasteten Kugelschalen veränderlicher Wandstärke unter Gas- und
Flüssigkeitsdruck durch Integration schwach singulärer Differentialgleichungen,
1975
37
Dirksen, Wolfram: Berechnung instationärer Abflußvorgänge in gestauten Gerinnen mittels Differenzenverfahren und die Anwendung auf Hochwasserrückhaltebecken, 1976
38
Horlacher, Hans-Burkhard: Berechnung instationärer Temperatur- und Wärmespannungsfelder in langen mehrschichtigen Hohlzylindern, 1976
39
Hafner, Edzard: Untersuchung der hydrodynamischen Kräfte auf Baukörper im
Tiefwasserbereich des Meeres, 1977, ISBN 3-921694-39-6
40
Ruppert, Jürgen: Über den Axialwirbelkammerverstärker für den Einsatz im Wasserbau, 1977, ISBN 3-921694-40-X
41
Hutarew, Andreas: Beitrag zur Beeinflußbarkeit des Sauerstoffgehalts in Fließgewässern an Abstürzen und Wehren, 1977, ISBN 3-921694-41-8,
42
Miller, Christoph: Ein Beitrag zur Bestimmung der schwingungserregenden Kräfte
an unterströmten Wehren, 1977, ISBN 3-921694-42-6
43
Schwarz, Wolfgang: Druckstoßberechnung unter Berücksichtigung der Radial- und
Längsverschiebungen der Rohrwandung, 1978, ISBN 3-921694-43-4
44
Kinzelbach, Wolfgang: Numerische Untersuchungen über den optimalen Einsatz
variabler Kühlsysteme einer Kraftwerkskette am Beispiel Oberrhein, 1978,
ISBN 3-921694-44-2
45
Barczewski, Baldur: Neue Meßmethoden für Wasser-Luftgemische und deren Anwendung auf zweiphasige Auftriebsstrahlen, 1979, ISBN 3-921694-45-0
Verzeichnis der Mitteilungshefte
5
46
Neumayer, Hans: Untersuchung der Strömungsvorgänge in radialen Wirbelkammerverstärkern, 1979, ISBN 3-921694-46-9
47
Elalfy, Youssef-Elhassan: Untersuchung der Strömungsvorgänge in Wirbelkammerdioden und -drosseln, 1979, ISBN 3-921694-47-7
48
Brombach, Hansjörg: Automatisierung der Bewirtschaftung von Wasserspeichern,
1981, ISBN 3-921694-48-5
49
Geldner, Peter: Deterministische und stochastische Methoden zur Bestimmung der
Selbstdichtung von Gewässern, 1981, ISBN 3-921694-49-3,
50
Mehlhorn, Hans: Temperaturveränderungen im Grundwasser durch Brauchwassereinleitungen, 1982, ISBN 3-921694-50-7,
51
Hafner, Edzard: Rohrleitungen und Behälter im Meer, 1983, ISBN 3-921694-51-5
52
Rinnert, Bernd: Hydrodynamische Dispersion in porösen Medien: Einfluß von Dichteunterschieden auf die Vertikalvermischung in horizontaler Strömung, 1983, ISBN
3-921694-52-3,
53
Lindner, Wulf: Steuerung von Grundwasserentnahmen unter Einhaltung ökologischer Kriterien, 1983, ISBN 3-921694-53-1,
54
Herr, Michael; Herzer, Jörg; Kinzelbach, Wolfgang; Kobus, Helmut; Rinnert, Bernd:
Methoden zur rechnerischen Erfassung und hydraulischen Sanierung von Grundwasserkontaminationen, 1983, ISBN 3-921694-54-X
55
Schmitt, Paul: Wege zur Automatisierung der Niederschlagsermittlung, 1984, ISBN
3-921694-55-8,
56
Müller, Peter: Transport und selektive Sedimentation von Schwebstoffen bei gestautem Abfluß, 1985, ISBN 3-921694-56-6
57
El-Qawasmeh, Fuad: Möglichkeiten und Grenzen der Tropfbewässerung unter besonderer Berücksichtigung der Verstopfungsanfälligkeit der Tropfelemente, 1985,
ISBN 3-921694-57-4,
58
Kirchenbaur, Klaus: Mikroprozessorgesteuerte Erfassung instationärer Druckfelder
am Beispiel seegangsbelasteter Baukörper, 1985, ISBN 3-921694-58-2
59
Kobus, Helmut (Hrsg.): Modellierung des großräumigen Wärme- und Schadstofftransports im Grundwasser, Tätigkeitsbericht 1984/85 (DFG-Forschergruppe an
den Universitäten Hohenheim, Karlsruhe und Stuttgart), 1985,
ISBN 3-921694-59-0,
60
Spitz, Karlheinz: Dispersion in porösen Medien: Einfluß von Inhomogenitäten und
Dichteunterschieden, 1985, ISBN 3-921694-60-4,
61
Kobus, Helmut: An Introduction to Air-Water Flows in Hydraulics, 1985,
ISBN 3-921694-61-2
6
Institut für Wasserbau * Universität Stuttgart * IWS
62
Kaleris, Vassilios: Erfassung des Austausches von Oberflächen- und Grundwasser
in horizontalebenen Grundwassermodellen, 1986, ISBN 3-921694-62-0
63
Herr, Michael: Grundlagen der hydraulischen Sanierung verunreinigter Porengrundwasserleiter, 1987, ISBN 3-921694-63-9
64
Marx, Walter: Berechnung von Temperatur und Spannung in Massenbeton infolge
Hydratation, 1987, ISBN 3-921694-64-7
65
Koschitzky, Hans-Peter: Dimensionierungskonzept für Sohlbelüfter in Schußrinnen
zur Vermeidung von Kavitationsschäden, 1987, ISBN 3-921694-65-5
66
Kobus, Helmut (Hrsg.): Modellierung des großräumigen Wärme- und Schadstofftransports im Grundwasser, Tätigkeitsbericht 1986/87 (DFG-Forschergruppe an
den Universitäten Hohenheim, Karlsruhe und Stuttgart) 1987, ISBN 3-921694-66-3
67
Söll, Thomas: Berechnungsverfahren zur Abschätzung anthropogener Temperaturanomalien im Grundwasser, 1988, ISBN 3-921694-67-1
68
Dittrich, Andreas; Westrich, Bernd: Bodenseeufererosion, Bestandsaufnahme und
Bewertung, 1988, ISBN 3-921694-68-X,
69
Huwe, Bernd; van der Ploeg, Rienk R.: Modelle zur Simulation des Stickstoffhaushaltes von Standorten mit unterschiedlicher landwirtschaftlicher Nutzung, 1988,
ISBN 3-921694-69-8,
70
Stephan, Karl: Integration elliptischer Funktionen, 1988, ISBN 3-921694-70-1
71
Kobus, Helmut; Zilliox, Lothaire (Hrsg.): Nitratbelastung des Grundwassers, Auswirkungen der Landwirtschaft auf die Grundwasser- und Rohwasserbeschaffenheit
und Maßnahmen zum Schutz des Grundwassers. Vorträge des deutsch-französischen Kolloquiums am 6. Oktober 1988, Universitäten Stuttgart und Louis Pasteur Strasbourg (Vorträge in deutsch oder französisch, Kurzfassungen zweisprachig), 1988, ISBN 3-921694-71-X
72
Soyeaux, Renald: Unterströmung von Stauanlagen auf klüftigem Untergrund unter
Berücksichtigung laminarer und turbulenter Fließzustände,1991,
ISBN 3-921694-72-8
73
Kohane, Roberto: Berechnungsmethoden für Hochwasserabfluß in Fließgewässern mit überströmten Vorländern, 1991, ISBN 3-921694-73-6
74
Hassinger, Reinhard: Beitrag zur Hydraulik und Bemessung von Blocksteinrampen
in flexibler Bauweise, 1991, ISBN 3-921694-74-4,
75
Schäfer, Gerhard: Einfluß von Schichtenstrukturen und lokalen Einlagerungen auf
die Längsdispersion in Porengrundwasserleitern, 1991, ISBN 3-921694-75-2
76
Giesecke, Jürgen: Vorträge, Wasserwirtschaft in stark besiedelten Regionen; Umweltforschung mit Schwerpunkt Wasserwirtschaft, 1991, ISBN 3-921694-76-0
Verzeichnis der Mitteilungshefte
7
77
Huwe, Bernd: Deterministische und stochastische Ansätze zur Modellierung des
Stickstoffhaushalts landwirtschaftlich genutzter Flächen auf unterschiedlichem
Skalenniveau, 1992, ISBN 3-921694-77-9,
78
Rommel, Michael: Verwendung von Kluftdaten zur realitätsnahen Generierung von
Kluftnetzen mit anschließender laminar-turbulenter Strömungsberechnung, 1993,
ISBN 3-92 1694-78-7
79
Marschall, Paul: Die Ermittlung lokaler Stofffrachten im Grundwasser mit Hilfe von
Einbohrloch-Meßverfahren, 1993, ISBN 3-921694-79-5,
80
Ptak, Thomas: Stofftransport in heterogenen Porenaquiferen: Felduntersuchungen
und stochastische Modellierung, 1993, ISBN 3-921694-80-9,
81
Haakh, Frieder: Transientes Strömungsverhalten in Wirbelkammern, 1993,
ISBN 3-921694-81-7
82
Kobus, Helmut; Cirpka, Olaf; Barczewski, Baldur; Koschitzky, Hans-Peter: Versucheinrichtung zur Grundwasser und Altlastensanierung VEGAS, Konzeption und
Programmrahmen, 1993, ISBN 3-921694-82-5
83
Zang, Weidong: Optimaler Echtzeit-Betrieb eines Speichers mit aktueller Abflußregenerierung, 1994, ISBN 3-921694-83-3,
84
Franke, Hans-Jörg: Stochastische Modellierung eines flächenhaften Stoffeintrages
und Transports in Grundwasser am Beispiel der Pflanzenschutzmittelproblematik,
1995, ISBN 3-921694-84-1
85
Lang, Ulrich: Simulation regionaler Strömungs- und Transportvorgänge in Karstaquiferen mit Hilfe des Doppelkontinuum-Ansatzes: Methodenentwicklung und Parameteridentifikation, 1995, ISBN 3-921694-85-X,
86
Helmig, Rainer: Einführung in die Numerischen Methoden der Hydromechanik,
1996, ISBN 3-921694-86-8,
87
Cirpka, Olaf: CONTRACT: A Numerical Tool for Contaminant Transport and
Chemical Transformations - Theory and Program Documentation -, 1996,
ISBN 3-921694-87-6
88
Haberlandt, Uwe: Stochastische Synthese und Regionalisierung des Niederschlages für Schmutzfrachtberechnungen, 1996, ISBN 3-921694-88-4
89
Croisé, Jean: Extraktion von flüchtigen Chemikalien aus natürlichen Lockergesteinen mittels erzwungener Luftströmung, 1996, ISBN 3-921694-89-2,
90
Jorde, Klaus: Ökologisch begründete, dynamische Mindestwasserregelungen bei
Ausleitungskraftwerken, 1997, ISBN 3-921694-90-6,
91
Helmig, Rainer: Gekoppelte Strömungs- und Transportprozesse im Untergrund Ein Beitrag zur Hydrosystemmodellierung-, 1998, ISBN 3-921694-91-4,
8
Institut für Wasserbau * Universität Stuttgart * IWS
92
Emmert, Martin: Numerische Modellierung nichtisothermer Gas-Wasser Systeme
in porösen Medien, 1997, ISBN 3-921694-92-2
93
Kern, Ulrich: Transport von Schweb- und Schadstoffen in staugeregelten Fließgewässern am Beispiel des Neckars, 1997, ISBN 3-921694-93-0,
94
Förster, Georg: Druckstoßdämpfung durch große Luftblasen in Hochpunkten von
Rohrleitungen 1997, ISBN 3-921694-94-9
95
Cirpka, Olaf: Numerische Methoden zur Simulation des reaktiven Mehrkomponententransports im Grundwasser, 1997, ISBN 3-921694-95-7,
96
Färber, Arne: Wärmetransport in der ungesättigten Bodenzone: Entwicklung einer
thermischen In-situ-Sanierungstechnologie, 1997, ISBN 3-921694-96-5
97
Betz, Christoph: Wasserdampfdestillation von Schadstoffen im porösen Medium:
Entwicklung einer thermischen In-situ-Sanierungstechnologie, 1998,
ISBN 3-921694-97-3
98
Xu, Yichun: Numerical Modeling of Suspended Sediment Transport in Rivers,
1998, ISBN 3-921694-98-1,
99
Wüst, Wolfgang: Geochemische Untersuchungen zur Sanierung CKWkontaminierter Aquifere mit Fe(0)-Reaktionswänden, 2000, ISBN 3-933761-02-2
100 Sheta, Hussam: Simulation von Mehrphasenvorgängen in porösen Medien unter
Einbeziehung von Hysterese-Effekten, 2000, ISBN 3-933761-03-4
101 Ayros, Edwin: Regionalisierung extremer Abflüsse auf der Grundlage statistischer
Verfahren, 2000, ISBN 3-933761-04-2,
102 Huber, Ralf: Compositional Multiphase Flow and Transport in Heterogeneous Porous Media, 2000, ISBN 3-933761-05-0
103 Braun, Christopherus: Ein Upscaling-Verfahren für Mehrphasenströmungen in porösen Medien, 2000, ISBN 3-933761-06-9
104 Hofmann, Bernd: Entwicklung eines rechnergestützten Managementsystems zur
Beurteilung von Grundwasserschadensfällen, 2000, ISBN 3-933761-07-7
105 Class, Holger: Theorie und numerische Modellierung nichtisothermer Mehrphasenprozesse in NAPL-kontaminierten porösen Medien, 2001,
ISBN 3-933761-08-5
106 Schmidt, Reinhard: Wasserdampf- und Heißluftinjektion zur thermischen Sanierung kontaminierter Standorte, 2001, ISBN 3-933761-09-3
107 Josef, Reinhold:, Schadstoffextraktion mit hydraulischen Sanierungsverfahren unter Anwendung von grenzflächenaktiven Stoffen, 2001, ISBN 3-933761-10-7
Verzeichnis der Mitteilungshefte
9
108 Schneider, Matthias: Habitat- und Abflussmodellierung für Fließgewässer mit unscharfen Berechnungsansätzen, 2001, ISBN 3-933761-11-5
109 Rathgeb, Andreas: Hydrodynamische Bemessungsgrundlagen für Lockerdeckwerke an überströmbaren Erddämmen, 2001, ISBN 3-933761-12-3
110 Lang, Stefan: Parallele numerische Simulation instätionärer Probleme mit adaptiven Methoden auf unstrukturierten Gittern, 2001, ISBN 3-933761-13-1
111 Appt, Jochen; Stumpp Simone: Die Bodensee-Messkampagne 2001, IWS/CWR
Lake Constance Measurement Program 2001, 2002, ISBN 3-933761-14-X
112 Heimerl, Stephan: Systematische Beurteilung von Wasserkraftprojekten, 2002,
ISBN 3-933761-15-8
113 Iqbal, Amin: On the Management and Salinity Control of Drip Irrigation, 2002, ISBN
3-933761-16-6
114 Silberhorn-Hemminger, Annette: Modellierung von Kluftaquifersystemen: Geostatistische Analyse und deterministisch-stochastische Kluftgenerierung, 2002, ISBN
3-933761-17-4
115 Winkler, Angela: Prozesse des Wärme- und Stofftransports bei der In-situSanierung mit festen Wärmequellen, 2003, ISBN 3-933761-18-2
116 Marx, Walter: Wasserkraft, Bewässerung, Umwelt - Planungs- und Bewertungsschwerpunkte der Wasserbewirtschaftung, 2003, ISBN 3-933761-19-0
117 Hinkelmann, Reinhard: Efficient Numerical Methods and Information-Processing
Techniques in Environment Water, 2003, ISBN 3-933761-20-4
118 Samaniego-Eguiguren, Luis Eduardo: Hydrological Consequences of Land Use /
Land Cover and Climatic Changes in Mesoscale Catchments, 2003,
ISBN 3-933761-21-2
119 Neunhäuserer, Lina: Diskretisierungsansätze zur Modellierung von Strömungsund Transportprozessen in geklüftet-porösen Medien, 2003, ISBN 3-933761-22-0
120 Paul, Maren: Simulation of Two-Phase Flow in Heterogeneous Poros Media with
Adaptive Methods, 2003, ISBN 3-933761-23-9
121 Ehret, Uwe: Rainfall and Flood Nowcasting in Small Catchments using Weather
Radar, 2003, ISBN 3-933761-24-7
122 Haag, Ingo: Der Sauerstoffhaushalt staugeregelter Flüsse am Beispiel des Neckars - Analysen, Experimente, Simulationen -, 2003, ISBN 3-933761-25-5
123 Appt, Jochen: Analysis of Basin-Scale Internal Waves in Upper Lake Constance,
2003, ISBN 3-933761-26-3
10
Institut für Wasserbau * Universität Stuttgart * IWS
124 Hrsg.: Schrenk, Volker; Batereau, Katrin; Barczewski, Baldur; Weber, Karolin und
Koschitzky, Hans-Peter: Symposium Ressource Fläche und VEGAS - Statuskolloquium 2003, 30. September und 1. Oktober 2003, 2003, ISBN 3-933761-27-1
125 Omar Khalil Ouda: Optimisation of Agricultural Water Use: A Decision Support
System for the Gaza Strip, 2003, ISBN 3-933761-28-0
126 Batereau, Katrin: Sensorbasierte Bodenluftmessung zur Vor-Ort-Erkundung von
Schadensherden im Untergrund, 2004, ISBN 3-933761-29-8
127 Witt, Oliver: Erosionsstabilität von Gewässersedimenten mit Auswirkung auf den
Stofftransport bei Hochwasser am Beispiel ausgewählter Stauhaltungen des Oberrheins, 2004, ISBN 3-933761-30-1
128 Jakobs, Hartmut: Simulation nicht-isothermer Gas-Wasser-Prozesse in komplexen
Kluft-Matrix-Systemen, 2004, ISBN 3-933761-31-X
129 Li, Chen-Chien: Deterministisch-stochastisches Berechnungskonzept zur Beurteilung der Auswirkungen erosiver Hochwasserereignisse in Flussstauhaltungen,
2004, ISBN 3-933761-32-8
130 Reichenberger, Volker; Helmig, Rainer; Jakobs, Hartmut; Bastian, Peter; Niessner,
Jennifer: Complex Gas-Water Processes in Discrete Fracture-Matrix Systems: Upscaling, Mass-Conservative Discretization and Efficient Multilevel Solution, 2004,
ISBN 3-933761-33-6
131 Hrsg.: Barczewski, Baldur; Koschitzky, Hans-Peter; Weber, Karolin; Wege, Ralf:
VEGAS - Statuskolloquium 2004, Tagungsband zur Veranstaltung am 05. Oktober
2004 an der Universität Stuttgart, Campus Stuttgart-Vaihingen, 2004, ISBN 3933761-34-4
132 Asie, Kemal Jabir: Finite Volume Models for Multiphase Multicomponent Flow
through Porous Media. 2005, ISBN 3-933761-35-2
133 Jacoub, George: Development of a 2-D Numerical Module for Particulate Contaminant Transport in Flood Retention Reservoirs and Impounded Rivers, 2004,
ISBN 3-933761-36-0
134 Nowak, Wolfgang: Geostatistical Methods for the Identification of Flow and Transport Parameters in the Subsurface, 2005, ISBN 3-933761-37-9
135 Süß, Mia: Analysis of the influence of structures and boundaries on flow and
transport processes in fractured porous media, 2005, ISBN 3-933761-38-7
136 Jose, Surabhin Chackiath: Experimental Investigations on Longitudinal Dispersive
Mixing in Heterogeneous Aquifers, 2005, ISBN: 3-933761-39-5
137 Filiz, Fulya: Linking Large-Scale Meteorological Conditions to Floods in Mesoscale
Catchments, 2005, ISBN 3-933761-40-9
Verzeichnis der Mitteilungshefte
11
138 Qin, Minghao: Wirklichkeitsnahe und recheneffiziente Ermittlung von Temperatur
und Spannungen bei großen RCC-Staumauern, 2005, ISBN 3-933761-41-7
139 Kobayashi, Kenichiro: Optimization Methods for Multiphase Systems in the Subsurface - Application to Methane Migration in Coal Mining Areas, 2005,
ISBN 3-933761-42-5
140 Rahman, Md. Arifur: Experimental Investigations on Transverse Dispersive Mixing
in Heterogeneous Porous Media, 2005, ISBN 3-933761-43-3
141 Schrenk, Volker: Ökobilanzen zur Bewertung von Altlastensanierungsmaßnahmen,
2005, ISBN 3-933761-44-1
142 Hundecha, Hirpa Yeshewatesfa: Regionalization of Parameters of a Conceptual
Rainfall-Runoff Model, 2005, ISBN: 3-933761-45-X
143 Wege, Ralf: Untersuchungs- und Überwachungsmethoden für die Beurteilung natürlicher Selbstreinigungsprozesse im Grundwasser, 2005, ISBN 3-933761-46-8
144 Breiting, Thomas: Techniken und Methoden der Hydroinformatik - Modellierung
von komplexen Hydrosystemen im Untergrund, 2006, 3-933761-47-6
145 Hrsg.: Braun, Jürgen; Koschitzky, Hans-Peter; Müller, Martin: Ressource Untergrund: 10 Jahre VEGAS: Forschung und Technologieentwicklung zum Schutz von
Grundwasser und Boden, Tagungsband zur Veranstaltung am 28. und 29. September 2005 an der Universität Stuttgart, Campus Stuttgart-Vaihingen, 2005, ISBN
3-933761-48-4
146 Rojanschi, Vlad: Abflusskonzentration in mesoskaligen Einzugsgebieten unter
Berücksichtigung des Sickerraumes, 2006, ISBN 3-933761-49-2
147 Winkler, Nina Simone: Optimierung der Steuerung von Hochwasserrückhaltebecken-systemen, 2006, ISBN 3-933761-50-6
148 Wolf, Jens: Räumlich differenzierte Modellierung der Grundwasserströmung alluvialer Aquifere für mesoskalige Einzugsgebiete, 2006, ISBN: 3-933761-51-4
149 Kohler, Beate: Externe Effekte der Laufwasserkraftnutzung, 2006,
ISBN 3-933761-52-2
150 Hrsg.: Braun, Jürgen; Koschitzky, Hans-Peter; Stuhrmann, Matthias: VEGASStatuskolloquium 2006, Tagungsband zur Veranstaltung am 28. September 2006
an der Universität Stuttgart, Campus Stuttgart-Vaihingen, 2006,
ISBN 3-933761-53-0
151 Niessner, Jennifer: Multi-Scale Modeling of Multi-Phase - Multi-Component Processes in Heterogeneous Porous Media, 2006, ISBN 3-933761-54-9
152 Fischer, Markus: Beanspruchung eingeerdeter Rohrleitungen infolge Austrocknung
bindiger Böden, 2006, ISBN 3-933761-55-7
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Institut für Wasserbau * Universität Stuttgart * IWS
153 Schneck, Alexander: Optimierung der Grundwasserbewirtschaftung unter Berücksichtigung der Belange der Wasserversorgung, der Landwirtschaft und des Naturschutzes, 2006, ISBN 3-933761-56-5
154 Das, Tapash: The Impact of Spatial Variability of Precipitation on the Predictive
Uncertainty of Hydrological Models, 2006, ISBN 3-933761-57-3
155 Bielinski, Andreas: Numerical Simulation of CO2 sequestration in geological formations, 2007, ISBN 3-933761-58-1
156 Mödinger, Jens: Entwicklung eines Bewertungs- und Entscheidungsunterstützungssystems für eine nachhaltige regionale Grundwasserbewirtschaftung, 2006,
ISBN 3-933761-60-3
157 Manthey, Sabine: Two-phase flow processes with dynamic effects in porous
media - parameter estimation and simulation, 2007, ISBN 3-933761-61-1
158 Pozos Estrada, Oscar: Investigation on the Effects of Entrained Air in Pipelines,
2007, ISBN 3-933761-62-X
159 Ochs, Steffen Oliver: Steam injection into saturated porous media – process
analysis including experimental and numerical investigations, 2007,
ISBN 3-933761-63-8
160 Marx, Andreas: Einsatz gekoppelter Modelle und Wetterradar zur Abschätzung
von Niederschlagsintensitäten und zur Abflussvorhersage, 2007,
ISBN 3-933761-64-6
161 Hartmann, Gabriele Maria: Investigation of Evapotranspiration Concepts in Hydrological Modelling for Climate Change Impact Assessment, 2007,
ISBN 3-933761-65-4
162 Kebede Gurmessa, Tesfaye: Numerical Investigation on Flow and Transport Characteristics to Improve Long-Term Simulation of Reservoir Sedimentation, 2007,
ISBN 3-933761-66-2
163 Trifković, Aleksandar: Multi-objective and Risk-based Modelling Methodology for
Planning, Design and Operation of Water Supply Systems, 2007,
ISBN 3-933761-67-0
164 Götzinger, Jens: Distributed Conceptual Hydrological Modelling - Simulation of
Climate, Land Use Change Impact and Uncertainty Analysis, 2007,
ISBN 3-933761-68-9
165 Hrsg.: Braun, Jürgen; Koschitzky, Hans-Peter; Stuhrmann, Matthias: VEGAS –
Kolloquium 2007, Tagungsband zur Veranstaltung am 26. September 2007 an der
Universität Stuttgart, Campus Stuttgart-Vaihingen, 2007, ISBN 3-933761-69-7
166 Freeman, Beau: Modernization Criteria Assessment for Water Resources Planning; Klamath Irrigation Project, U.S., 2008, ISBN 3-933761-70-0
Verzeichnis der Mitteilungshefte
13
167 Dreher, Thomas: Selektive Sedimentation von Feinstschwebstoffen in Wechselwirkung mit wandnahen turbulenten Strömungsbedingungen, 2008,
ISBN 3-933761-71-9
168 Yang, Wei: Discrete-Continuous Downscaling Model for Generating Daily Precipitation Time Series, 2008, ISBN 3-933761-72-7
169 Kopecki, Ianina: Calculational Approach to FST-Hemispheres for Multiparametrical
Benthos Habitat Modelling, 2008, ISBN 3-933761-73-5
170 Brommundt, Jürgen: Stochastische Generierung räumlich zusammenhängender
Niederschlagszeitreihen, 2008, ISBN 3-933761-74-3
171 Papafotiou, Alexandros: Numerical Investigations of the Role of Hysteresis in Heterogeneous Two-Phase Flow Systems, 2008, ISBN 3-933761-75-1
172 He, Yi: Application of a Non-Parametric Classification Scheme to Catchment Hydrology, 2008, ISBN 978-3-933761-76-7
173 Wagner, Sven: Water Balance in a Poorly Gauged Basin in West Africa Using Atmospheric Modelling and Remote Sensing Information, 2008,
ISBN 978-3-933761-77-4
174 Hrsg.: Braun, Jürgen; Koschitzky, Hans-Peter; Stuhrmann, Matthias; Schrenk, Volker: VEGAS-Kolloquium 2008 Ressource Fläche III, Tagungsband zur Veranstaltung am 01. Oktober 2008 an der Universität Stuttgart, Campus StuttgartVaihingen, 2008, ISBN 978-3-933761-78-1
175 Patil, Sachin: Regionalization of an Event Based Nash Cascade Model for Flood
Predictions in Ungauged Basins, 2008, ISBN 978-3-933761-79-8
176 Assteerawatt, Anongnart: Flow and Transport Modelling of Fractured Aquifers
based on a Geostatistical Approach, 2008, ISBN 978-3-933761-80-4
177 Karnahl, Joachim Alexander: 2D numerische Modellierung von multifraktionalem
Schwebstoff- und Schadstofftransport in Flüssen, 2008, ISBN 978-3-933761-81-1
178 Hiester, Uwe: Technologieentwicklung zur In-situ-Sanierung der ungesättigten Bodenzone mit festen Wärmequellen, 2009, ISBN 978-3-933761-82-8
179 Laux, Patrick: Statistical Modeling of Precipitation for Agricultural Planning in the
Volta Basin of West Africa, 2009, ISBN 978-3-933761-83-5
180 Ehsan, Saqib: Evaluation of Life Safety Risks Related to Severe Flooding, 2009,
ISBN 978-3-933761-84-2
181 Prohaska, Sandra: Development and Application of a 1D Multi-Strip Fine Sediment Transport Model for Regulated Rivers, 2009, ISBN 978-3-933761-85-9
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Institut für Wasserbau * Universität Stuttgart * IWS
182 Kopp, Andreas: Evaluation of CO2 Injection Processes in Geological Formations
for Site Screening, 2009, ISBN 978-3-933761-86-6
183 Ebigbo, Anozie: Modelling of biofilm growth and its influence on CO2 and water
(two-phase) flow in porous media, 2009, ISBN 978-3-933761-87-3
184 Freiboth, Sandra: A phenomenological model for the numerical simulation of
multiphase multicomponent processes considering structural alterations of porous media, 2009, ISBN 978-3-933761-88-0
185 Zöllner, Frank: Implementierung und Anwendung netzfreier Methoden im Konstruktiven Wasserbau und in der Hydromechanik, 2009,
ISBN 978-3-933761-89-7
186 Vasin, Milos: Influence of the soil structure and property contrast on flow and
transport in the unsaturated zone, 2010, ISBN 978-3-933761-90-3
187 Li, Jing: Application of Copulas as a New Geostatistical Tool, 2010, ISBN 978-3933761-91-0
188 AghaKouchak, Amir: Simulation of Remotely Sensed Rainfall Fields Using Copulas, 2010, ISBN 978-3-933761-92-7
189 Thapa, Pawan Kumar: Physically-based spatially distributed rainfall runoff modelling for soil erosion estimation, 2010, ISBN 978-3-933761-93-4
Die Mitteilungshefte ab der Nr. 134 (Jg. 2005) stehen als pdf-Datei über die Homepage
des Instituts: www.iws.uni-stuttgart.de zur Verfügung.

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