ALPINE BIOGEOCHEMICAL MODELING: CASE STUDIES, IMPROVENOENTS, AND PARAMETER ESTIMATION by Thomas Meixner

ALPINE BIOGEOCHEMICAL MODELING: CASE STUDIES, IMPROVENOENTS,  AND PARAMETER ESTIMATION by Thomas Meixner
ALPINE BIOGEOCHEMICAL MODELING:
CASE STUDIES, IMPROVENOENTS, AND PARAMETER ESTIMATION
by
Thomas Meixner
A Dissertation Submitted to the Faculty of
HYDROLOGY AND WATER RESOURCES
In Partial Fulfillment of the Requirements
For the Degree of
DOCTORATE OF PHILOSOPHY
WITH A MAJOR IN HYDROLOGY
In the Graduate College
THE UNIVERSITY OF ARIZONA
1999
2
THE UNIVERSITY OF ARIZONA 8
GRADUATE COLLEGE
As members of the Final Examination Committee, we certify that we have
read the dissertation prepared by
Thomas Meixner
entitled Alpine Biogeochemical Modeling:
Case Studies, Model Improvements, and Parameter
Estimation
and recommend that it be accepted as fulfilling the dissertation
requirement for the Degree of Doctor of Philosophy
r
Date
.476%
Date
9-1/1
Date
(7 2_ 3 1/
-
Date
Dr. Eric Betterton
D t
Final approval and acceptance of this dissertation is contingent upon
the candidate's submission of the final copy of the dissertation to the
Graduate College.
I hereby certify that I have read this dissertation prepared under my
direction and recommend that it be accepted as fulfilling the dissertation
requirement.
Dissertation Director
Date
3
This dissertation has been submitted in partial fulfillment of requirements for an
advanced degree at the University of Arizona and is deposited in the University Library
to be made available to borrowers under rules of the library.
Brief quotations from this dissertation are allowable without special pennission,
provided that accurate acknowledgement is made. Requests for permission for extended
quotation from or reproduction of this manuscript in whole or in part may be granted by
the head of the major department or the Dean of the Graduate College when in his or her
judgment the proposed use of the material is in the interests of scholarship. In all other
instances, however peiiiiission must be obtained from the author.
SIGNED:
4
ACKNOWLEDGEMENTS
This work would not have been possible without the aid and support of a large
number of fellow researchers including: James Sickman, John Melack, Al Leydecker,
Walter Rosenthal, Ben Balk, Francisco Rojas, Mark Williams, Jill Baron, Don Campbell,
Don Cline, David Clow, Kelly Elder, Paul Brooks, Soroosh Sorooshian, Hoshin Gupta,
and Luis Bastidas. I also wish to thank the calibration research group at the University of
Arizona for the camaraderie and creativity they inspired. Most importantly I wish to
thank my adviser Roger Bales whose encouragement of independence of thought enabled
me to pursue cutting edge research for my dissertation. Ray Brice is to be thanked for his
assistance in manuscript preparation and general computer guru status. This work would
also not have been possible without the financial support of Canon USA through the
Canon National Park Science Scholarship program. The National Park Service, National
Park Foundation and the American Association for the Advancement of Science are all to
be thanked for their participation in the Canon National Park Science Scholars program.
Gary Machlis and Michael Soukup are also to be thanked for their creativity and support
for the Canon Scholars program through its early years. The National Park Service is to
be thanked for its years of support for research on alpine watersheds in the western
United States; without data from that research this dissertation would not have been
possible. My dissertation work was also supported by the National Science Foundation
through a Graduate Research Fellowship and an EGB grant (# EAR-9523886 ) and by
NASA through its EOS-IDS program (NAGW-2602 ). I also wish to thank my sisters
and my parents for their many visits to Tucson. I owe a large debt of gratitude also to my
wife Kathleen without whose love and support the completion of this dissertation would
have been difficult. I also owe a large debt of gratitude to Dr. Michael Stewart, Dr.
Richard Rosenberg, and the capable staff of Tucson Medical Center without whose
medical skill and care I would not have been around to complete this dissertation.
5
To my parents, who, at an early age, instilled in me a love of knowledge and the
persistence to pursue it.
6
TABLE OF CONTENTS
9
LIST OF FIGURES LIST OF TABLES 11
12
ABSTRACT I. INTRODUCTION 13
14
1.1 Alpine Hydrochemic al Model Description 1.2 Dissertation Format 15
1.3 Transporting AI-1M to Other Watersheds 16
17
1.4 Nitrogen Cycling in Alpine Catchments 1.5 Multi-Criteria Parameter Estimation 18
2 PRESENT STUDY 20
2.1 Summary of Paper #1: Importance of Biogeochemical Processes in Modeling
20
Stream Chemistry in Two Watersheds in the Sierra Nevada, California of
Paper
#2:
Stream
Chemistry
Modeling
of
Two
Watersheds
in
the
2.2 Summary
23
Front Range, Colorado 2.3 Summary of Paper #3 A Nitrogen Dynamics Model for Alpine Basins 26
2.4 Summary of Paper #4: Sensitivity Analysis Using Mass Flux and Concentration
28
2.5 Summary of Paper #5: Multi-Criteria Parameter Estimation for Hydrochemical
31
Models 34
3 CONCLUSIONS APPENDIX A - IMPORTANCE OF BIOGEOCHENMICAL PROCESSES IN
MODELING STREAM CHEMISTRY IN TWO WATERSHEDS IN THE SIERRA
42
NEVADA, CALIFORNIA 45
A.1 Introduction 46
A.2 Methods 46
A.2.1 Site 46
A.2.2 Sample Collection 47
A.2.3 Model 47
A.2.4 Model Calibration and Evaluation 48
A.3 Results 48
A.3.1 Water Balance 49
A.3.2 Precipitation Chemistry 49
A.3.3 Solute Concentrations and Ionic Pulse 50
A.3.4 Nitrogen Mass Balance 51
A.3.5 Watershed 1 Calibration and Evaluation 51
A.3.6 Watershed 2 Calibration and Evaluation 52
A.3.7 Sensitvity 7
TABLE OF CONTENTS - CONTINUED
A.4 Discussion 52
A.4.1 Water Balance 52
A.4.2 Base Cation and ANC Production 53
A.4.3 Nitrogen Cycling 54
A.4.4 Sensitivity to Changes in Loading 55
A.4.5 AHM Model Structure and Parameters 55
A.5 Conclusions 56
APPENDIX B - STREAM CHEMISTRY MODELING OF TWO WATERSHEDS IN
THE FRONT RANGE, COLORADO 58
B.1 Introduction 62
B.2 Methods 64
B.2.1 Site 64
B.2.2 Model Structure
65
B.2.3 Model Inputs 66
B.2.4 Parameter Estimation and Initial Conditions 68
B.2.5 Calibration 69
B.3 Results 70
B.3.1 Green Lakes Valley 70
B.3.2 Andrews Creek 72
B.4 Discussion 73
B.4.1 Model Performance 73
B.4.2 Base Stauration and pH 76
B.4.3 Nitrogen Dynamics 77
B.4.4 Flow Routing
78
B.4.5 Sensitivity to Deposition 79
B.5 Conclusions 81
APPENDIX C -A NITROGEN DYNAMICS MODEL FOR ALPINE BASINS .... 106
C.1 Introduction 109
111
C.2 Model Description D.2.1 Soil Carbon Model 112
D.2.2 Soil Nitrogen Model 115
D.2.3 Plant Growth Model 115
C.3 Case Study 117
C.4 Results 119
C.5 Discussion 121
C.6 Conclusions 124
APPENDIX D - SENSITIVITY ANALYSIS USING MASS FLUX AND
CONCENTRATION 138
8
TABLE OF CONTENTS - CONTINUED
D.1 Introduction D.2 Methods D.2.1 Site D.2.2 Model
D.2.3 Monte-Carlo Simulation D.2.4 MOGSA
D.3 Results D.4 Discussion D.4.1 Reasons for Different Information Content
D.4.2 Information About Natural Processes D.5 Conclusions APPENDIX E - MULTI-CRITERIA PARAMETER ESTIMATION FOR
HYDROCHEMICAL MODELS El Introduction E.2 Methods E.2.1 Multi-Criteria Parameter Estimation Methodology E.2.2 MOCOM-UA E.2.3 Site Description E.2.4 Model E.2.5 Applying MOCOM-UA to ARM
E.3 Results E.4 Discussion E.5 Conclusions APPENDIX F SOURCE CODE FOR A NITROGEN MODEL FOR ALPINE
WATERSHEDS (ANIMAL) REFERENCES 142
143
143
143
145
146
148
149
150
152
153
170
173
176
178
178
178
179
180
182
185
188
208
239
9
LIST OF FIGURES
Figure 1.1, Schematic of AHM Model of Emerald Lake 15
Figure A.1, Map of both watersheds. 46
Figure A.2, Modeled watershed compartments: 47
Figure A.3, Seasonal precipitation chemistry and hydrologic mass balance for 1992 and
1993 48
Figure A.4, Watershed 1 results 49
Figure A.5, Watershed 2 results 50
Figure A.6, Ratio of stream concentrations to bulk snow concentrations for each
watershed with fraction of flow as independent variable for 1992 50
Figure A.7, Comparison of modeled and measured soil chemistry for Watershed 1 52
Figure A.8, Comparison of modeled and measured soil chemistry for Watershed 2 53
Figure A.9, results for doubling wet deposition using 1992 data and calibration for both
watersheds 53
Figure B.1, Land cover map for Green Lakes Valley watershed 97
Figure B.2, Land cover map for Andrews Creek watershed 98
Figure B.3, Modeled watershed compartments 99
Figure B.4, Annual average volume weighted mean precipitation chemistry for GLV4
and Andrews for 1994 and 1996 100
Figure B.5, Modeled GLV4 inflow and measured stream chemical concentrations 101
Figure B.6, Observed and modeled stream chemical concentrations for the Andrews
Creek 102
Figure B.7, Nitrogen reactions and effects for models of both watersheds. 103
Figure B.8, Sensitivity of Green Lake 4 model to doubled wet deposition 104
Figure B.9, Sensitivity of Andrews Creek watershed model to doubled wet deposition
chemistry 105
Figure C.1, Carbon box diagram 133
Figure C.2, N soil organic matter flows 134
Figure C.3, Grass growth model diagram. 135
Figure C.4, Modeled and measured 30 day mean air temperature for Emerald Lake
136
Figure C.5, Modeled and observed NO3 concentrations for the Emerald Lake watershed.
-
137
Figure D.1, Elevation map of ELW
164
Figure D.2, Soils map of ELW 165
Figure D.3, AHM representation of the Emerald Lake watershed broken down into rock,
166
talus, soil, stream and lake subunits. Figure D.4, Measured and modeled concentration results for Wolford parameters [from
Wolford et al., 1996], for 1986 and 1987 water years. 167
10
LIST OF FIGURES - CONTINUED
Figure D.5, Measured and modeled mass flux results for Wolford parameters [from
Wolford et al., 1996], for 1986 and 1987 water years. 168
Figure D.6, Number of simulations versus number of sensitive parameters for ANC and
Na for 50% quantile, cc of 0.05 and 50 bootstraps. 169
Figure E.1, Simple demonstration of Pareto set in a two parameter three criteria situation
196
Figure E.2, Schematic of AHM model of Emerald Lake. 197
in
RMSE
Figure E.3, Improvement
and simulations with search population size with
discharge, Ca2+ , SO4 2- , and Cl - as criteria. 198
Figure E.4, Parameter space and criteria space results for MOCOM-UA runs for Emerald
Lake using discharge, H + , Ca2+ , SO4 2- , Si and NO3 - as criteria. 199
Figure E.5, Parameter and criteria space results for 6 criteria using a mix of mass flux and
concentration as the criteria (noted in red box) 200
Figure E.6, 6 Parameter and Criteria space results for MOCOM-UA runs using 4 criteria
as noted with red boxes on bottom x axis. 201
Figure E.7, Parameter and criteria space results for MOCOM-UA search with 4 criteria
using a mix of mass and concentration criteria as noted on bottom x axis by boxes in red.
202
Figure E.8, Parameter and Criteria space results from pushing 250 sets of random
parameter values within the feasible parameter set through the AHM 203
Figure E.9, Time series results for discharge, calcium, chloride and sulfate using Pareto
solutions with six previously identified concentration criteria (Figure 4) 204
Figure E.10, Time series results for discharge, ANC, silica and nitrate with the same
Pareto solutions used as in Figure 9. 205
Figure E.11, Time series results for driving AHM with 250 Pareto results as depicted in
Figure 7. 206
Figure E.12, Time series results for driving AHM with 250 Pareto solutions as shown in
Figure 7. Discharge, ANC, silica and nitrate shown. 207
11
LIST OF TABLES
Table A.1, Watershed Characteristics 47
Table A.2, Dissolved Inorganic Nitrogen Budgets 50
51
Table A.3, Target Runoff Concentrations Table A.4, Final Parameter Values 51
Table B.1, Soil Physical Properties 87
Table B.2, Mineral Weathering Rates 88
Table B.3, Soil Chemical Properties 89
Table B.4, Fitted Parameter Values 90
Table B.5, Nash-Sutcliffe values for Green Lakes Valley 4 92
Table B.6, Nash-Sutcliffe values for Andrews Creek watershed 93
Table B.7, Concentration Changes with Doubling of N Deposition 94
Table C.1, Ecosystem Components as Modeled for Emerald Lake 131
Table C.2, Ecosystem Processes as Modeled for Emerald Lake
132
Table D.1, Parameters Varied and Range Relative to Values by Wolford et al. [1996] 159
Table D.2, Parameter Sensitivity for Concentrations at 2000 Simulations 161
Table D.3, Parameter Sensitivity for Mass at 2000 Simulations
162
Table E.1, Parameters Varied and Range Relative to Values by Wolford et al. [1996] 194
12
ABSTRACT
The geochemical, biogeochemical, and hydrologic controls on the stream chemical
composition of alpine watersheds were investigated using the Alpine Hydrochemical
Model (AHM). This model was successfully applied to the Emerald Lake watershed and
two nearby watersheds as well as two watersheds in the Rocky Mountains, Andrews
Creek and the Green Lakes Valley. The results reveal that snowmelt in alpine watersheds
must come into contact with either soil, sub-talus, or reactive bedrock surfaces to explain
the geochemistry observed in alpine lakes and streams. These materials do not differ
geochemically but they do differ in their influence on the amount of mineral nitrogen
observed in alpine lakes and streams. Improvements to the carbon-nitrogen dynamics
portion of the ARM indicate that the Emerald Lake watershed is nearing nitrogen
saturation. A robust multi-criteria sensitivity analysis technique was used to determine
what processes were important for simulating the observed stream chemical composition.
This sensitivity analysis revealed that concentration and mass flux representations of
stream chemical composition contain different information about the watershed. The
sensitivity analysis results were used to guide a multi-criteria parameter estimation
algorithm. The results showed that stream chemical data is useful in discerning the
importance of different processes and the role they play in determining stream chemical
composition.
13
1. INTRODUCTION
The thin soils, limited vegetation, and snow-dominated hydrology of alpine
catchments limit their ability to buffer against changes in climate and atmospheric
deposition [Melack and Stoddard, 1991]. In the Sierra Nevada of California or the Front
Range of Colorado, predictions about the response of alpine watersheds have
implications for air quality, emissions standards and the health of aquatic resources.
Changes in emissions standards or the degradation of lakes and streams will have
important implications for the industries affected by these policy decisions [Takemoto et
al., 1995].
A method for improving our understanding of how alpine watersheds will respond
to perturbations is to simulate that response using an integrated watershed model.
Simulating alpine watershed response to perturbations in climatic and biogeochemical
inputs has three parts: i) the model used must have the proper structure, ii) a precise and
accurate estimation of the parameters used in the model must be made, iii) changes in
inputs to the model must be realistic.
Many stream chemical models exist for predicting stream chemical composition.
These models have been developed over the last several decades with particular interest
in the problems of catchment acidification ( e.g. [Cosby et al., 1985; Wolford et al.,
1996]) and nutrient dynamics ( e.g. PNET [Aber and Federer, 1992] and CENTURY
[Parton et al., 1987]).
14
The Alpine Hydrochemical Model (AHM) was developed specifically for the
study of alpine watersheds[Wo/ford et al., 1996]. Current simulations using the AHM
have problems in each of the areas outlined above: i) the structure of the nitrogen model
is too simple to extend simulations beyond current conditions, ii) existing parameter
estimation techniques for the ARM do not take advantage of all the information available
in the data, and iii) simulations of perturbed conditions have not been of realistic length
and perturbations of precipitation have not been realistic. This dissertation developed
and executed methods that will improve our ability to simulate alpine stream chemistry
under perturbed conditions by improving our understanding of the natural processes that
determine watershed response to changes in hydrologic and biogeochemical conditions.
1.1 Alpine Hydrochemical Model Description
The ARM [Wolford et al., 1996] is a daily time-step lumped/distributed model
designed specifically for the hydrology and biogeochemistry of alpine watersheds. The
model consists of multiple subunits representing different land classifications (rock, soil,
talus, stream, lake.) Each subunit contains different compartments representing the
snowpack, surface runoff, interception by trees and litter, soil horizons, surface runoff,
streamflow, ice, epilimnion and hypolimnion (Figure 1.1). The model produces daily
time step output of cations, anions, acid neutralizing capacity (ANC), pH, silica, and
volumetric discharge.
15
Figure 1.1 Schematic of AHM Model of Emerald Lake Watershed. A) Precipitation inputs and
output of evapotranspiration from subunits. B) Snowmelt runoff from the rock subunit is
distributed equally to the soil and talus subunits. C) Surface runoff and subsurface drainage
from the soil and talus subunit is routed to the stream. D) The stream flows into the lake. E)
Lake outflow is the discharge from the basin.
1.2 Dissertation Format
This dissertation contains several publications as part of its format. Five papers
are included in the appendix with a description of each paper included in Chapter 2.
Each of these papers contributes to at least one of the four questions identified below:
16
1) How transportable is the ARM outside of the Emerald Lake watershed?
2) How sensitive is the Emerald Lake watershed to nitrogen saturation?
3) What is the temporal and quantitative importance of mineral weathering and cation
exchange as the source of alkalinity for the Emerald Lake Watershed?
4) What information do the various calibration criteria contain and how should these
criteria be chosen in conducting parameter estimation using a stream chemical
model?
1.3 Transporting AHM to Other Watersheds
Prior to this research the ARM had only been applied to the Emerald Lake
watershed. Applying the model to other watersheds should enable us to investigate how
robust the model is at representing the processes controlling alpine stream chemistry. For
this research the AHM was applied to two small watersheds (less than 0.5 ha)
approximately 3 km from the Emerald Lake watershed [Meixner et al., 1998] (Appendix
A). The AHM was also applied to the Green Lakes and Andrews Creek watersheds in
the Rocky Mountains, Colorado [Meixner et al., 1999a] (Appendix B). These
applications of the ARM were used to investigate the ability of ARM to describe the
biogeochemical processes and to investigate which processes control stream chemical
composition in these catchments.
17
1.4 Nitrogen Cycling in Alpine Catchments
Many processes control nitrogen cycling in alpine watersheds. Nitrogen is an
essential nutrient for biomass; hence biological processes transform nitrogen into
different states, storing it and making it available for biota. These processes include
mineralization, immobilization, nitrification, denitrification, and uptake [Parton et al.,
1987; Aber, 1992; Parton et al., 1993]. These transformations also affect the acid-base
status of natural waters [Schindler et al., 1985; Henriksen and Brakke, 1988]. Currently
AHM can eliminate or create ammonium and nitrate in natural waters without regard to
nutrient demand or excess present in the basin [Wolford et al., 1996]. This structure does
not permit the modeling of chronic processes involving the nitrogen cycle like nitrogen
saturation [Aber et al., 1989; Aber et al., 1998], the process where nitrogen accumulates
in an ecosystem converting it from a nitrogen sink to a nitrogen source. This change can
weaken an ecosystem and increase the acidity of its waters [Henriksen and Brakke,
1988]. The current structure is in contrast to the process oriented structure of the
CENTURY model [Parton et al., 1987] or the BIOME-BGC model [Running and
Gower, 1991], which allows modeling of chronic processes. A robust carbon-nitrogen
cycling model was built that used AHM hydrologic output to investigate the effect on
carbon-nitrogen dynamics of various scenarios of nitrogen deposition and representations
of alpine hydroclimatology (Appendix C).
18
1.5 Multi-Criteria Parameter Estimation
Available parameter estimation techniques for watershed models are subjective.
They use a weighting scheme or the modelers judgment to equate the goodness of fit for
different species with each other. An objective parameter estimation technique for the
ARM is necessary. Past parameter estimation attempts using the AHM at Emerald Lake
have had two problems. One is the technique used to estimate the parameters, while the
other is the time scale over which parameters were estimated. Some applications of ARM
have used manual techniques to estimate model parameters [Wolford et al., 1996]. Ohte
and Bales [1995] also applied the ARM to the Emerald Lake watershed (ELW) using an
automatic technique based on Chang and Delleur [1992]. Both of these techniques
ignore the multi-criteria nature of parameter estimation of hydrochemical models. Fitting
AHM output to measured stream chemistry is fundamentally a multi-criteria problem,
with each species representing an objective function. Weighting removes each species as
a target and instead lumps all objectives into one, thus ignoring the differences between
chemical species.
Current estimation techniques ignore the importance of long-term processes such
as nitrogen transformations and base cation depletion on parameter values. Nitrogen
cycling in a watershed is subject to a process known as nitrogen saturation, which is
controlled by biological processes in a watershed and may take years to decades to exert
a significant influence on stream chemistry [Stoddard, 1994]. Cation depletion is the
19
process where the removal of cations from the cation exchange complex occurs more
quickly then they are replaced by mineral weathering. This process is gradual and takes
years to manifest its effect on stream chemistry [Likens et al., 1996]. Since, both of these
processes require long time series of data to properly estimate model parameters a data
record longer than one year should be used.
Two papers have grown out of the use of multi-criteria parameter estimation
methods in conjunction with the AHM. The first of these, "Mass Flux and Concentration
Sensitivity Analysis", [Meixner et al., 1999b] (Appendix D) dealt with applying
sensitivity analysis techniques developed by [Spear and Homberger, 1980] as extended
by [Bastidas, 1998] to the AHM model of Emerald Lake [WoIford et al., 1996].
Hydrological Processes has accepted this paper. The sensitivity analysis results revealed
the importance of several natural processes in controlling stream chemical composition in
alpine watersheds.
The second of these papers, "Multi-Criteria Parameter Estimation for
Hydrochemical Models", involved applying the MOCOM-UA algorithm [Yapo, 1996] to
the AHM model of the Emerald Lake watershed. The particular questions being asked
pertained to the proper selection of criteria for calibration of hydrochemical models. The
results indicate that the minimum number of criteria should be selected and that the
results of the sensitivity analysis may provide some useful information about which
criteria to select. This remains an area of ongoing research.
20
2 PRESENT STUDY
The methods, results, and conclusions of my research are presented in five
appendices attached to this dissertation. The following is a summary of the most
important findings of these papers.
2.1 Summary of Paper #1: Importance of Biogeochemical Processes in Modeling
Stream Chemistry in Two Watersheds in the Sierra Nevada, California
This paper was part of a larger project to describe the biogeochemical and
hydrologic processes that control stream chemistry in alpine basins. In particular the
importance of areas of soil and bare rock on the geochemistry of alpine watersheds was
investigated. The study centered around a two year field campaign in 1992 and 1993 that
involved weekly measurements of snow depth, density and chemical composition,
monitoring of soil water chemistry, meteorology, and stream chemical composition and
discharge. Two watersheds were monitored that differed significantly in the fraction of
each watershed that was covered by soil. Watershed 1 was 26% soil covered, while
watershed 2 was 10% soil covered. These watersheds were located approximately 3 km
from the Emerald Lake watershed in Sequoia National Park, California (36 ° 36' 30" N
118 ° 39' 55" W, elevation 2960 m). The initial measurements for 1992 were used to
21
systematically calibrate the ARM to each watershed. The calibrated models were then
evaluated with the 1993 field data. The calibrated models were also compared to reveal
the differences in process between the two watersheds. The major findings of this study
follow.
(1) The AHM is transportable.
This paper was the first application of the AHM outside the Emerald Lake watershed.
The calibration and evaluation showed the ARM to be able to represent the
biogeochemical processes controlling stream chemical composition in these two
watersheds. This result confirms that the conceptual structure chosen for the AHM is
robust enough to be applied to other watersheds.
(2) Developed manual calibration methodology for AHM.
A four step general methodology for calibrating the ARM in particular and stream
chemistry models in general to different watersheds was outlined as:
1)
Snowmelt optimization
2
Chemical calibration
a) Set soil pore water chemistry based on low flow conditions at end of melt season.
b) Adjust soil base saturation to match soil pH to late season observed stream pH.
c) Adjust exchange coefficients for each cation to match soil concentrations
d) Adjust snowpack elution parameters to match observed ionic pulse for CL
22
e) Adjust sulfate adsorption parameters to match expected soil concentrations and
observed stream concentrations
f) Calibrate nitrogen parameters to match observed nitrate and ammonium
concentrations
3)
Adjustment of hydrologic parameters
4)
Changes in model structure
(3) Flow routing in alpine catchments
Despite the very small soil coverage on watershed 2 it was still necessary to route
snowmelt through a soil subunit in order to have the model simulate the observed stream
chemistry of the rock dominated watershed. This along with similar results at Emerald
Lake [Wolford et al., 1996] points in the direction that snowmelt must come in contact
with soil or soil like material in alpine watersheds.
(4) Exposed bedrock surfaces are reactive.
Due to the lack of soil on watershed 2 the results also indicate that areas of exposed
bedrock in alpine watersheds are capable of contributing to the buffering capacity of
alpine watersheds to changes in acid deposition. This result supports the conclusions of
other researchers [Rueslatten and Jorgensen, 1978; Abrahamsen et al., 1979; Dahl et al.,
1979; Allan et al., 1993; Clow and Mast, 1995].
23
(5) Areas of exposed rock were a larger sink for nitrogen than areas of soil.
Areas mapped as exposed rock appear to be nitrate (as well as nitrogen) sinks in alpine
watersheds. There was more nitrate export from watershed 1 than watershed 2 indicating
that during snowmelt areas of soil and vegetation are possibly sources of nitrate export.
Areas of exposed bedrock, possibly due to litter fall from the previous growing season
gathering in hydrologically important cracks and crevices providing a carbon source for
microbes, act as a nitrate sink as evidence by the smaller nitrate export on watershed 2 as
opposed to watershed 1.
2.2 Summary of Paper #2: Stream Chemistry Modeling of Two Watersheds in the
Front Range, Colorado
We extended the use of the AHM to the Andrews Creek and Green Lakes Valley
watersheds in the Front Range of the Rocky Mountains, Colorado. The two watersheds
differed dramatically in the spatial distribution of soil and talus area. In Andrews Creek
talus fields dominated the valley bottom, while in the Green Lakes Valley soil dominated
the valley bottom. Both watersheds have comprehensive data sets describing their
geology, soils, vegetation, meteorology, water quality and hydrology. Good snow
covered area time series existed for both 1994 and 1996 for both watersheds. The 1994
data for each watershed were used for model calibration and the 1996 data were used to
24
evaluate that calibration procedure. The calibration followed the procedure as outlined
in [Meixner et al., 1998]. A summary of the major findings of this paper follows.
(1)
The AHM is applicable outside of the Sierra Nevada.
The calibration of the each of these watersheds resulted in very good modeling of the
stream chemical composition of each of these watersheds. These two watersheds with
significantly different climate and geology from the Sierra Nevada represented a difficult
test for the AHM to pass. This result indicates that the structure chosen for the AHM is
robust and easily applicable in locations well beyond the Sierra Nevada.
(2)
Further validation of our methodology of using spatial data and then
limited calibration to estimate model parameters.
The calibration and evaluation procedure we used resulted in good simulations of stream
chemistry in each of these watersheds with only a minimum number of parameters
adjusted. Now that 4 watersheds have been modeled with this procedure it should be
used in applying the ARM to other watersheds.
(3)
Soil base saturation measurements in the Green Lakes Valley are
higher than indicated by observed stream chemistry.
In calibrating the AHM model of the Green Lakes Valley the partial pressure of carbon
dioxide in the stream was raised from the atmospheric value of 10 -3.4 to 103 1 atm this
25
change indicates that the modeled soil base saturation was too high. The measurements
we relied on for the Green lakes Valley were taken during 1985. The lower percent base
saturation indicated by these results means either the original measurements were not
accurate or that the Green Lakes Valley has undergone cation depletion due to acid
deposition over the last 15 years [Caine and Thurman, 1990; Williams et al., 1996].
(4)
Snowmelt in alpine basins contacts soil or talus sufficiently long to
undergo geochemical transformation.
Despite the dominance of exposed bedrock and little true soil in alpine basins, stream
chemical composition in these catchments indicates that snowmelt must be contacting
soil or soil like material in the sub-talus and reacting with it. For species that are not
biotically important (i.e. Ca 2+ , Na, etc.) it does not make a difference if the snowmelt
contacts soil or talus.
(5)
Nitrogen dynamics are significantly different between areas of soil
and areas of talus.
Andrews Creek where talus was dominant had significantly more nitrate export,
especially during spring snowmelt, than the Green Lakes Valley. Independent
parameterization of flow routing in alpine watersheds is necessary because of the
differences in nitrate export for areas of soil and talus.
26
2.3 Summary of Paper #3 A Nitrogen Dynamics Model for Alpine Basins
Increased atmospheric deposition of nitrogen to alpine and remote wilderness
watersheds may have deleterious effects on terrestrial and aquatic ecosystem health
[Fenn et al., 1998]. The complexities of terrestrial carbon nitrogen dynamics prevent the
use of simple cause and effect relationships for the increase in atmospheric deposition of
nitrogen and changes in terrestrial carbon and nitrogen pools as well as the increased
export of mineral nitrogen from a catchment. To aid in the investigation of carbon
nitrogen dynamics in alpine catchments the CENTURY algorithm, developed by [Parton
et al., 1987; Parton et al., 1988; Parton et al., 1993] for simulating carbon-nitrogen
dynamics in alpine watersheds, was adapted for use in alpine watersheds. This
improvement, eventually designed to be incorporated into the AHM model, will replace
the currently inadequate nitrogen dynamics structure as can be seen by the results of the
previous applications of the AHM [Wolford et al., 1996; Meixner et al., 1998; Meixner et
al., 1999a]. Several improvements and adaptations were made to the CENTURY model
since it does not currently incorporate the full effects of soil warming that occurs under
deep snowpacks as observed by [Brooks et al., 1996] as well as other processes that are
important to simulating carbon-nitrogen dynamics in alpine watersheds. The CENTURY
algorithm was adapted to be linked to the AHM model in an offline mode using AHM
output as input to the adjusted algorithm.
The adapted algorithm was applied to the Emerald Lake watershed as a test of the
robustness of the model. Several different methods of estimating soil temperature were
27
used as well as three levels of atmospheric N deposition (low observed, high observed
and double the current high deposition observation). The major findings of this paper
follow.
(1)
The adapted CENTURY algorithm adequately simulated the carbon and
nitrogen dynamics of the Emerald Lake watershed.
The adaptation of the CENTURY model was successful in giving adequate
simulations of the carbon and nitrogen pools and fluxes in the terrestrial landscape. The
simulations did underestimate the amount of soil organic carbon as well as annual
biomass production when compared to the data of [Rundel et al., 1988.
] There were
several other difficulties with the simulations including over or underprediction of N
mineralization rates and the total flux out of mineral nitrogen out of the soil.
(2)
Snow cover properties and their effect on soil temperatures were important
in properly simulating soil-carbon nitrogen dynamics in alpine watersheds.
Simulations that were done incorporating snow cover information were better
than those that did not in simulating the carbon-nitrogen dynamics of the Emerald Lake
watershed.
( 3 )
The model captured some of the variability in mineral N export for the
Emerald Lake watershed.
28
During the late 1980's and early 1990's a gradual decline in the stream concentration of
NO, was observed for the Emerald Lake watershed. The model managed to capture
-
much of this decline but simulated concentrations rose before the real concentrations.
The simulated mineral N flux was two to three times that of the stream chemical
observations and the peak mineral N flux predated the observed peak by 30 days. This
may be due to hydrologic differences between the model and the real watershed.
(4) Changes in N deposition appear likely to increase NO3" export in the Emerald
Lake watershed.
Simulated nitrogen export increased dramatically with increases in deposition. This
indicates that Sierra Nevada watersheds may be very sensitive to increases in atmospheric
deposition. This result should be confirmed in a field experiment.
2.4 Summary of Paper #4: Sensitivity Analysis Using Mass Flux and Concentration
A robust multi-criteria sensitivity analysis was applied to the AHM model of the
Emerald Lake watershed for the 1986 and 1987 water years for 24 model parameters and
21 different criteria. The 24 model parameters govern the major chemical and hydrologic
processes described within the AHM. The 21 criteria were discharge and the
concentration and mass flux criteria for 10 chemical species. It was hoped that three
questions would be answered by applying sensitivity analysis techniques to the AHM
29
model of the Emerald Lake watershed. First, is parameter sensitivity different for mass
flux and chemical concentration measures of model error? Second, do the results indicate
that mass flux and concentration objective functions contain different information about
catchment and model behavior? Third, what information can the sensitivity analysis
provide about the biogeochemical and hydrologic processes that control stream chemical
composition? The major findings of this paper follow.
(1)
There were systematic differences in parameter sensitivity for chemical
concentration and chemical mass flux criteria.
Mass flux criteria were not affected by evapotranspiration (ET) and mineral weathering
parameters, while concentration criteria were. Cation exchange parameters were
important for the model's ability to simulate observed mass flux, while these parameters
were less important for simulating observed stream concentrations.
(2)
Mass flux criteria contain more information about processes that are
important during periods of peak spring snowmelt, the most sensitive period for
alpine watersheds to acid deposition.
The parameter sensitivity results indicate that processes with a quick response time (i.e.
cation exchange) were more important for improving model simulations of mass flux
observations. However those parameters that represent gradual or long-term processes
30
(i.e. evapotranspiration and mineral weathering parameters) had more of an effect on
the model's ability to simulate observed stream chemical concentrations.
(3)
In contrast to earlier results, cation exchange is an important process in
controlling the stream chemical composition of the Emerald Lake watershed.
Previous sensitivity analysis with the AHM model of Emerald Lake [Ohte et al., 1993]
indicated that cation exchange was not an important process in improving AHM
simulations of stream chemical conditions. Our results indicate that cation exchange is
important especially for improving simulations of mass flux.
(4)
The volume of talus and the rate of flow through soil are the two most
important hydrologic processes in controlling stream chemical composition of the
Emerald Lake watershed.
The sensitivity results indicated that of 42 possible sensitive-parameter-criteria
combinations for the reactive volume of talus 76% were sensitive, while for flow rate
through talus (21 possible combinations) 43% were sensitive. For soil the results were
opposite with 80% of the flow rate parameter-criteria combinations sensitive and 57% of
soil volume parameter criteria combinations sensitive.
31
2.5 Summary of Paper #5: Multi-Criteria Parameter Estimation for
Hydrochemical Models
The use of multiple response data to calibrate hydrochemical models has been
shown to be an effective methodology for calibrating hydrochemical models and for
investigating the structure of conceptual models of watershed chemistry [Mroczkowski et
al., 1997; Grosbois et al., 1988; Hooper et al., 1988]. The work to date has not
investigated how criteria should be selected and how to weigh the information content of
different criteria. In this work we applied the MOCOM-UA algorithm [Yapo, 1996] to
the AHM model of the Emerald Lake watershed [Wolford et al., 1996]. The purpose of
the research was to learn four things. Is it best to use more or fewer criteria when
calibrating hydrochemical models? What is the best methodology for selecting the
criteria to be used in multi-criteria parameter estimation? What can we learn about the
natural processes controlling stream chemical composition in the Emerald Lake
watershed from the automatic calibration of the AHM model? What can we learn about
the structure of the AHM model of Emerald Lake from this exercise? A summary of the
major findings of this paper follows.
( 1 )
The minimum number of criteria necessary should be used to conduct a
multi-criteria calibration of a hydrochemical model.
32
The calibration results from using six criteria were markedly inferior to those when
using only 4 criteria for calibrating the AHM model. This result may be due to
particulars of the AHM model and the Emerald Lake watershed. They are also due to the
simple mathematics of multi-criteria theory that adding criteria can only increase the size
of the Pareto set results.
(2)
Sensitivity analysis should be used to select the criteria that are to be used in
multi-criteria parameter estimation.
The sensitivity analysis results of Meixner et al. [1999b] were used to select three of the
four sets of criteria. The remaining set was chosen using a correlation analysis of the
observed chemical composition from the Emerald Lake outflow. The selection of criteria
using the sensitivity results proved successful in improving the parameter estimation
results for criteria used in the calibration as well as those not used in the calibration.
(3)
The current mineral weathering rate in the AHM model of the Emerald Lake
watershed is too low.
The parameter estimation results for two of the 4 criteria cases investigated indicate that
the current mineral-weathering rate is too low within the AHM. The results also indicate
that the elution parameter is set too high.
33
(4)
The model has difficulty simultaneously modeling both hydrologic
discharge and stream chemical composition due to structural problems with the
AHM model of Emerald Lake.
The two four-criteria calibration runs resulted in contrasting values for the hydraulic
conductivity of the soil subunit. Calibration with concentration criteria indicated that a
lower value of hydraulic conductivity was necessary to simulate stream chemical
composition, while the case using mass flux indicated that a higher value was needed.
This indicates that in order to simulate spring stream concentrations (as represented in the
mass flux measure of model error) a higher value was needed while to simulate summer
and winter stream concentrations a lower value was needed. The contrast indicates that
the behavior of the model depends on the criteria that we seek to minimize. This conflict
indicates an inadequacy in the current model structure. Possible solutions to the conflict
include: making exposed rock reactive, including preferential flow through soil, or
increasing the number of horizons in the soil.
34
3 CONCLUSIONS
The thread that weaves this dissertation together is the goal of describing the
geochemical, biogeochemical, and hydrologic processes that interact to create the
aqueous chemistry that is observed in alpine lakes and streams. Toward this end we have
used the AHM as a tool to investigate several hypotheses on what controls the stream
chemical composition of alpine lakes, streams, and soils. The five papers included in the
appendices can be categorized into one of three groups: extending AHM, improving
AHM, and testing AHM. The first two papers extended the application of the AHM
beyond the Emerald Lake watershed. "The Importance of Biogeochemical Processes in
Modeling Stream Chemistry in Two Watersheds in the Sierra Nevada, California" and
"Stream Chemistry Modeling of Two Watersheds in the Front Range Colorado" showed
the usefulness of the AHM as a modeling tool that can be used to investigate the
processes that control stream chemical composition in alpine watersheds.
These two papers together with the original papers on AHM [Wolford and Bales,
1996; Wolford et al., 1996] provide us with three insights into some of the overarching
hydrologic and biogeochemical controls on stream chemical composition in alpine
watersheds. First, snowmelt is interacting with a geochemical substrate (i.e. soil, talus, or
reactive bare rock surfaces) for a long enough period of time for snowmelt to take on the
geochemical characteristics of the substrate. The original hypothesis guiding acid
35
deposition research in alpine watersheds was that these watersheds would be among the
most sensitive to increases in acid deposition due to their thin soils and difficult-toweather bedrock [Melack and Stoddard, 19911. The results thus far in simulating stream
chemistry in alpine catchments do not indicate that this hypothesis was correct. If this
hypothesis were true we should see some snowmelt reaching the stream that did not show
the effects of interacting with a geochemical substrate. Instead the opposite is observed
at Emerald, the Pear Lake watersheds and the two Rocky Mountain watersheds simulated
as part of this dissertation, it was necessary to alter model structure or model parameter
values to ensure that all snowmelt came into contact with either soil or talus [Wolford et
al., 1996; Meixner et al., 1998; Meixner et al., 1999a]. Now that this result has been
observed at four catchments that are quite diverse in size (0.2 ha up to 220 ha), exposed
bedrock (30% to 90%) and geography (Sierra Nevada and Rocky Mountains) it is
possible to state that snowmelt in alpine watersheds invariably contacts a geochemical
substrate that the snowmelt interacts with, even in watersheds with extensive areas of
exposed bedrock.
Second, while snowmelt definitely comes in contact with geochemical material
which material it comes in contact with is important. At the two small Sierra watersheds,
areas mapped as exposed bedrock were a larger nitrogen sink than areas mapped as soil
covered. At the two Rocky Mountain watersheds areas of talus exported more NO3 than
-
areas mapped as soil. Combined, these results indicate that the spatial composition of
alpine watersheds is important in determining the relative ability of these watersheds to
36
behave as NO3" sinks or sources. It is therefore important to simulate areas of soil, rock
and talus separately not so much because of the variable geochemistry of each of these
areas but because of their variable biogeochemistry.
Third, the results from the two papers indicate that the general structure adopted
for the AHM model of Emerald Lake is suitable for simulating alpine stream chemical
composition. This conclusion builds from the multiple applications of the AHM
[Wolford and Bales, 1996; Wolford et al., 1996; Meixner et al., 1998; Meixner et al.,
19994 The same general structure was used each time the AHM was applied to a new
watershed. All five applications of the AHM have been successful at describing the
fundamental processes describing stream chemical composition.
The third paper, "A Nitrogen Dynamics Model for Alpine Basins", stands by
itself as an attempt to improve the AHM representation of carbon-nitrogen dynamics.
The original version of AHM included an inadequate model of nitrogen cycling. The
results from incorporating the CENTURY algorithm into the AHM in offline mode
indicate that the improvements once fully incorporated into AHM should be successful.
This incorporation of a robust carbon-nitrogen cycling model will enable the simulation
of the multiple effects of increases in atmospheric deposition of nitrogen as well as the
effects of climatic events like soil thawing and drought. The results with the carbonnitrogen model also reinforce the robustness of the soil organic matter and plant growth
dynamics of the CENTURY model.
37
The carbon-nitrogen dynamics modeling also gives us information about the
processes controlling nitrogen dynamics in the Emerald Lake watershed. First, multiyear drought appears to be of central importance in controlling carbon-nitrogen cycling.
The drought of the late 1980's and 1990's had a profound impact on the mineral N export
of the modeled watershed. Second, the length of snow cover had an effect on the total N
export with longer snow cover leading to more N export. Finally, under the current N
deposition rates, the Emerald Lake watershed is approaching N saturation. These results
need to be confirmed with further field research
The last two papers, "Sensitivity Analysis Using Mass Flux and Concentration"
and "Multi-Criteria Parameter Estimation for Hydrochemical Models", involved the
rigorous testing of the AHM model of the Emerald Lake watershed with multi-criteria
parameter sensitivity and parameter estimation algorithms developed at the University of
Arizona [Yapo, 1996; Bastidas, 1998; Bastidas et al., 1999; Gupta et al., 1999]. Both of
these papers provided valuable insight into how multi-criteria methods can be used to
discern the importance of different hydrologic and biogeochemical processes. These
papers also shed some light on some possible mechanisms that can be used to solve the
continuing problem of model calibration and evaluation. This problem has prevented the
use of watershed chemical models as scientific and predictive tools for future conditions
due to the low reliability of the calibrated parameters [Grosbois et al., 1988; Hooper et
al., 1988; Christophersen et al., 1993; Kirchner et al., 1996; Bassett, 1997].
38
Progress on the problem of calibrating hydrochemical models was made in two
ways. First, automatic techniques were developed to discern the importance of
hydrologic and geochemical processes and their importance in controlling stream
chemical composition. This progress was mostly made in the paper implementing
sensitivity analysis to the AHM model of the Emerald Lake watershed [Meixner et al.,
I 99913]. The results showed that the stream chemical time series give us information
about processes internal to the watershed. These results indicate that, with the calibration
and sensitivity algorithms used in this dissertation, stream chemical models can be used
on more than a comparative basis. In fact they indicate that stream chemical models,
when supported by the proper amount of data, can be used to more fully understand the
processes controlling stream chemical composition. This was demonstrated in the
sensitivity analysis with the result that cation exchange was a more important process
during spring snowmelt than mineral weathering. Moreover, the results show that stream
chemical models can be used to guide the development of field data collection efforts.
The parameter estimation work supports the results of the sensitivity analysis
paper in showing that stream chemical data can be used to determine the relative
importance of different hydrologic and geochemical processes. Progress in using multicriteria methods to calibrate hydrochemical models was made in this work but some
problems still present themselves. The use of the sensitivity results in determining which
and how many criteria for multi-criteria parameter estimation was successful but more
39
work is needed. Also the multi-criteria parameter estimation results showed promise at
discerning problems with model structure.
As important as the direct conclusions that can be drawn from this dissertation are
the further research questions that we can draw from their results. The three groups of
papers, extending, improving, and evaluating, each lead us to different sets of questions.
Extending the AHM to the two small Sierra Nevada watersheds and the two Rocky
Mountain watersheds leads to questions related to the incorporation of spatial information
into the ARM. Current practice with AHM overlays maps of snow-covered area on top
of established land cover maps that break the watershed down into soil, talus, and rock
subunits. Water is then routed between these based on landscape relationships between
the subunits. Two counter-intuitive results beg whether this is the best methodology to
follow. The results for watershed 2, of the paired Sierra Nevada watersheds, indicate that
exposed bedrock may be reactive; a process not currently incorporated into AHM. The
result for Green Lakes valley that talus was not important for determining stream
chemical composition disagrees with field results. Combined, these results lead to three
questions. First, how important are the geochemical and biogeoochemical processes that
occur on exposed bedrock? Second, can more robust flow routing determination using
TOPMODEL [Beven and Kirby, 1979] or other distributed hydrologic models be useful
in improving the simulated stream chemistry of the AHM. Third, can isotopic and
geochemical tracers be used to inform the flow routing used in AHM? Obviously the
40
results for these last two methodologies should be compared for consistency and for
evaluating the results of each.
The positive evaluation of the carbon-nitrogen dynamics modeling for the
Emerald Lake watershed opens up a suite of questions and a good deal of technical
follow up work. First, the modeling results need to be confirmed by field hydrologic and
fertilization experiments. Second, the algorithm needs to be incorporated directly into
AHM as opposed to being run in an offline mode as was done in this dissertation. Third
the algorithm needs to be extended to incorporate vegetation dynamics representative of
trees and of talus. Talus represents a special case since it contains little vegetation but
does receive organic material from uphill source areas and dryfall.
Some of the most interesting questions from this research develop out of the
application of multi-criteria methods to hydrochemical models. First, can a more
quantitative approach to determining which criteria to select produce better results than
those thus far? Second, can the multi-criteria methods be used to discern between
superior and inferior model structures? One test case would be to simplify the AHM
representation of Emerald Lake down to just a rock and a soil subunit. The soil subunit
would simply lump the soil and talus properties together. The multi-criteria methodology
would then be applied to see if the simulation results improved or deteriorated. A smaller
parameter space, objective space results closer to zero, and time series results bracketing
the observations tightly would all be indicative of a model improvement. Also, many
other combinations of criteria remain to be tested. The most likely mode for calibrating
41
watershed chemistry models will be to calibrate watershed hydrology with a limited set
of criteria. Next these calibration results using one group of criteria will be used to
determine the feasible parameter space for the calibration of the remaining criteria. The
final result would be a parameter set that could be evaluated with the nearly 20 years of
data now collected at the Emerald Lake watershed [Melack et al., 1998]. The final results
could also be used to simulate stream chemical composition under perturbed conditions.
The multiple parameter sets would result in giving a high and low bound of watershed
response to perturbations. Such a result should be useful to policy makers in setting
critical loads thresholds for alpine watersheds.
42
APPENDIX A - IMPORTANCE OF BIOGEOCHENMICAL PROCESSES IN
MODELING STREAM CHEMISTRY IN TWO WATERSHEDS IN THE SIERRA
NEVADA, CALIFORNIA
43
WATER
RESOURCES
RESEARCH
VOLUME 34
NOVEMBER 1998
NUMBER 11
PUBLISHED BY AMERICAN GEOPHYSICAL UNION
44
American Geophysical Union
Florida Avonue. NW
Washirgion. DC 2009
Tel - 41-202-462-690^
l-- ax *1-202-328-0556
2000
August 4, 1999
Mr. Tom Mcixner
Department of Hydrology and Water Resources
Room 203B, Building 411
PO I3ox 210011
University of Arizona
Tucson, AZ 85721-0011
Dear Mr. Meixncr:
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Please feel free to contact me again if you need further assistance. Thank you.
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Tne Amencan Guooilyscai Limon enc,npasse: Ina Eat ant: space
Geodesy. So.trno n dy. Ai nnosphorrzSclences, Geomaritildrn and Paleornagnevsm
Oce2n Sc n on,ot I iydron ogy Vo:cano nogy. Geocnern.clry and Potrolny
Tect000ynyst= . Planalology. Space Pnyscs and Awonarny
45
WATER RESOURCES RESEARCH. VOL. 34. NO. It. PAGES 3121-3133, NOVEMBER 1998
Importance of biogeochemical processes in modeling stream
chemistry in two watersheds in the Sierra Nevada, California
Thomas Meixner
Department of Hydrology and Water Resources, University of Arizona. Tucson
Aaron Brown'
Marine Sciences Institute, University of California. Santa Barbara
Roger C. Bales
Department of Hydrology and Water Resources, University of Arizona, Tucson
Abstract. Two small (0.22 and 0.48 ha) alpine watersheds in the Sierra Nevada of
California were studied during the 1992 and 1993 snowmelt seasons to evaluate the
importance of soil properties and processes on chemical concentrations in the discharges
from each watershed. Watershed 1 was surveyed as having 26% soil cover, whereas
watershed 2 was 10% soil covered. Watershed 2 had greater PV- and nitrogen
consumption than watershed 1 but similar cation and sulfate concentrations despite having
one fourth the surveyed soil volume per unit area as watershed 1. Daily stream
concentrations simulated with the Alpine Hydrochemical Model (AHM) matched the data
well, after a systematic model calibration with a subset of the data. We found that the
structure of the AHM and the hydrologic parameters developed for the nearby 1.2 km 2
Emerald Lake watershed could be applied to these watersheds with only small
adjustments; chemical parameters required considerably more adjustment, reflecting a
greater degree of chemical versus physical heterogeneity at this scale. Calibration for
watershed 2 gave a higher percent base saturation (19 versus 4%) and lower stream P op ,
(10 -3. ' versus 10 - 2 6 atm) than for watershed 1 and three times the soil reactivity
(expected) of a field survey. Areas mapped as exposed bedrock in the catchments
apparently contributed cations and alkalinity to stream water to a greater extent than did
neighboring areas of soil. Areas of exposed bedrock were a larger nitrogen sink than the
adjoining areas of soil. The pH and acid-neutralizing capacity of surface runoff in both
catchments were less sensitive to changes in atmospheric deposition than at the nearby
Emerald Lake watershed. This decreased sensitivity was due to (1) a less pronounced
ionic pulse, (2) less retention of sulfate in the soil, and (3) greater nitrate retention.
'
1. Introduction
Biogeochemical processes, including mineral weathering,
cation exchange, and nitrogen (N) cycling, are major determinants of the chemical composition of alpine lakes and streams
[Williams and Melack, 1991 ]. Determining the magnitudes and
locations of these processes is critical to understanding the
controls on stream chemistry and how stream chemistry may be
affected by changes in atmospheric deposition. Areas of exposed granite represent a large fraction of land cover in alpine
watersheds of the Sierra Nevada; for example, 54% of the area
of the Emerald Lake watershed (ELW) in Sequoia National
Park is covered by exposed granite [Tonnessen, 1991]. Biogeochemical modeling of alpine watersheds has treated areas of
exposed granite as unreactive and as having no influence on
stream chemistry [e.g., Wolford et al., 1996]. Some studies,
however, have found processes generally considered to occur
'Now at Chemistry Department, Ventura Community College, Ventura, California.
Copyright 1998 by the American Geophysical Union.
Paper number 98WR02172.
0043-1397/98/98WR-02172509.00
in soil occurring on areas of exposed granite, such as ion
exchange, mineral weathering, and N reactions [Rueslatten and
Jorgensen, 1978; Dahl et al., 1979; Abrahamsen et al., 1979;
Allan et al., 1993; Clow and Mast, 1995].
The sources and sinks of N in alpine regions are of particular
concern because of the thin soils and limited vegetation
present in alpine ecosystems. Considerable work has been
done in the Rocky Mountains investigating the N cycle and the
adverse effects of N saturation [Williams et al., 1996a]. This
work has suggested that the NO pulse observed in early
spring snowmelt is due to a release of NO from soil [Williams
et al., 1995; Kendall et al., 1995]. Other work has indicated that
soil microbes in areas covered by snowpack for long periods
are able to retain much of the NO and NH released during
the ionic pulse from seasonal snowpacks [Brooks et al., 1996].
The results of Clow and Mast [1995] indicate that bedrock may
play a role as an N sink in alpine watersheds.
In this study, two small watersheds in the Tokopah Valley of
Sequoia National Park were selected as paired watersheds that
differed in soil coverage. It was our hypothesis that this difference would result in higher concentrations of soil-derived
chemical species in the runoff from the watershed that had
more surveyed soil area and that areas of exposed rock were
3121
46
312.2
MEIXNER ET AL BIOGEOCHEMICAL PROCESSES. SIERRA NEVADA
%-°3625" N
Watershed 2
Met Meteorological
station
Soil lysimeters
sz Soil area
N
2
Watershed 1
Flume
50
0
so
,z46°
100m
Figure 1. Map of both watersheds. Elevations are in meters, with 2 m contour intervals. Gray area was
mapped as soil in a field survey. Watershed boundaries were determined with a level. They are more accurate
than the contour lines, which are the result of a more limited field survey. Note that Watershed 1 drains to
the north, while Watershed 2 drains to the southwest. There were two suction lysimeters at location 1, one at
a 100 mm depth and one at a depth of 300 mm. The other lysimeter locations all had one suction lysimeter
at 100 mm.
relatively unreactive with snowmelt runoff. Further, we expected
N export to be greater on the rock watershed since there was little
soil or vegetation to immobilize atmospheric inputs of dissolved
inorganic nitrogen. These watersheds were also used to evaluate
the varying importance of cation exchange, mineral weathering, sulfate adsorption, and N transformations on the chemical
composition of snowmelt runoff of Sierra Nevada watersheds.
Previous analyses done at the ELW show that soil has a
dominant effect on stream chemistry, with essentially all of the
snowmelt contacting soil during runoff; however, estimated
soil depth differed significantly from those estimated in a field
survey [Wolford et al., 1996]. Three issues addressed in this
paper are (1) the relative importance of biogeochemical processes on areas mapped as soil versus rock in catchments dominated by granitic rocks, (2) how well soil processes buffer daily
to weekly changes in stream chemistry when acid deposition to
the catchments changes, and (3) how well model structure and
parameters developed for the F.T.W describe the stream discharge and chemistry of other nearby alpine catchments.
2. Methods
2.1. Site
The watersheds studied were adjacent catchments in the
Tokopah Valley of California's Sierra Nevada (36°3630"N,
118°39'55'W, elevation 2960 m). These watersheds were located at a distance of 3 km from the previously studied ELW
[Tonnessen, 1991]. Streamflow on both watersheds is ephemeral, flowing only during snowmelt runoff. The glaciated bedrock of the watersheds is granodiorite with mafic inclusions up
to 200 mm in diameter. Fracturing and incipient exfoliation of
some granitic surfaces lies on a SW-NE axis and is more pronounced in watershed 2 (WS2). Watershed boundaries were
determined using a rod and a builder's level. Areas were
mapped as being soil if they had continuous fine material on
the surface, aside from fine material in rock fractures and small
crevices. Watershed 1 (WS1) (0.22 ha) is 26% soil covered, has
a 13% slope and a northern aspect, and includes 15 locieepole
pine (Pinus contona) trees with heights between 3 and 7 m.
WS2 (0.48 ha) is 10% soil covered (Figure 1), has a 17% slope
and a southwestern aspect, and has only 2 lodgepole pine trees,
both with a height <2 m. Aside from the lodgepole pines, the
vegetation on both watersheds is limited to perennial grasses,
wildflowers, and lichens. WS1 has more soil volume per unit
area and a more highly developed soil, as indicated by a higher
fraction of organic C and organic N, than WS2 (Table 1).
2.2. Sample Collection
Both watersheds had outlet flumes (H-type) located on bedrock equipped with pressure transducers (Stevens' Model SDT
47
ME1XNER ET AL.: B1OGEOCHEMICAL PROCESSES. SIERRA NEVADA H) and thermistors that permitted the recording of discharge
from each watershed continuously. Each outlet was also
equipped with an autosampler (ISCO Model 3500) that was
used to collect stream water at intervals varying from 2 hours
to 5 min between samples. Each of these samples was analyzed
for major ions. The multiple measurements of stream chemistry taken each day were flow averaged to allow comparison
between the data and model predictions. Soil water samples
were collected daily (if possible) with suction lysimeters at two
points in WS2 and at a three points in and near WS1 (Figure 1).
Chemical analyses of NO;, SOC, and C1 were done using
ion chromatography (Dionex, AS4A column). Each of these
samples was also analyzed for Ca 2 ", Mg 2. , K', and Na using
flame atomic absorption spectrophotometry. Thep H was measured using glass electrodes maintained for low ionic strength
waters. Acid-neutralizing capacity (ANC) was determined by
Gran titration. The field and laboratory techniques used are
described by Melack et al. [1998] and Brown et al. [1990]. A
snow survey was conducted at the time of peak accumulation
and weekly thereafter to measure snow water equivalence
(SWE) and snow-covered area (SCA). Spatial distribution of
snow depth and SCA was measured in a grid. Snow density was
measured in duplicate profiles in two snow pits per watershed.
Chemical deposition to the watersheds was measured using a
combination of snowpack chemistry samples and measurements of storm event quantity and quality after the snow survey. Storm events were sampled using a tipping bucket gauge
(Sierra Misco) for quantity and two rain buckets (DI-rinsed
polyethylene) to collect samples for measurement of precipitation quality. All monitoring was conducted during the 1992
and 1993 melt seasons.
23. Model
The University of Arizona Alpine Hydrochemical Model
(AHM) [Wolford et al., 1996] was used to integrate the data
and evaluate catchment biogeochemical processes. The AHM,
a lumped conceptual model, was developed at the ELW, also
in the Tokopah Valley, for evaluating watershed hydrology and
hydrochemistry and investigating the sensitivity of alpine
catchments to changes in atmospheric deposition and climate
forcing. In this application, the first of the AHM beyond the
ELW catchment, each watershed was represented by three
subunits: soil, rock, and stream. Each terrestrial subunit contains different compartments representing the snowpack,
snowpack free water, snowmelt, surface runoff, interception by
trees and litter, and zero, one, or multiple soil horizons. Stream
subunits consist of different compartments representing the
snowpack, snowpack free water, snowmelt, stream ice and
streamflow (Figure 2). Model subunits may be selected for use
according to the complexity of the watershed. Hydrologic processes are modeled separately from geochemical processes.
Table I. Watershed Characteristics
Characteristic
Watershed 1
Watershed 2
Area, km'
Average Slope, %
Percent soil cover
Soil volume, n-1 3
Soil pH
Soil organic C, %
Soil organic N, %
Soil C:N
0.0022
13
20
57
4.4
2.0
0.12
16
0.0048
17
10
24
4.2
1.2
0.09
13
2,3
3123
2,3
a.
b.
stream subunits
Figure 2. Modeled watershed compartments: (Figure la)
Soil subunits have compartments including (1) rainfall litter
interception, (2) snowfall canopy interception, (3) rainfall canopy interception, (4) snowpack, (5) snowpack free (liquid)
water, (6) snowpack drainage, (7) surface runoff leaving the
subunit, (8) soil drainage leaving the subunit, (9) contributed
soil drainage, (10) contributed surface runoff, (11) litter storage beneath the snowpack, and (12) one soil horizon. Rock
subunits (not shown) do not include compartments 2, 3, 8, and
12. Stream subunits (Figure lb) have compartments including
the (a) snowpack, (b) snowpack free water, (c) snowpack
drainage, and (d) streamflow; stream ice is not tracked other
than present or absent.
Routing between the subunits is handled separately from the
structure of the individual subunits.
AHM operates on a daily time step. At each time step, AHM
adjusts snow-covered area, computes interception, adjusts
snowpack for precipitation and melt, calculates influxes of materials to each soil and rock subunit, drains surface runoff,
computes evapotranspiration and sublimation, calculates kinetic reactions, calculates chemical equilibria in soil compartments, drains water from the soil horizon, calculates chemical
equilibria in streams, and produces output. Output can include
detailed descriptions of all chemical calculations, tracking of
both chemical and hydrologic storages and changes in storage
within the watershed, soil chemical concentrations, and stream
concentrations. Chemical speciation is handled using equations adapted from MINEQL [Westall et al., 1976]. The
strength of the model is its flexibility and precise mass balance
for both chemical species and hydrologic calculations [Wolford
et al., 1996].
In the current structure, runoff from the rock subunit was
routed to the soil subunit before draining to the stream for
WS1, on the basis of the physical location of soil and rock
(Figure 1). For WS2 we evaluated overland flow from rock
contributing directly to streamflow; however, this structure was
discarded because of poor simulations. Thus routing for WS2
also had overland flow intersecting soil area during its travel
through the watershed.
2.4. Model Calibration and Evaluation
As a starting point for parameter estimation, parameters
describing chemical processes and soil physical processes were
set equal to Wolford et al. [1996] values for the F.LW. Model
48
3124
MEIXNER ET AL BIOGEOCHEMICAL PROCESSES. SIERRA NEVADA
Figure 3. Seasonal precipitation chemistry and hydrologic
mass balance for both watersheds for 1992 and 1993. Note that
scales are different for each graph: (a) winter snow, (b) spring
precipitation, and (c) water balance.
parameters for extensive properties, such as watershed area,
soil area, and depth, were determined for each catchment
model from field measurements. The soil subunit on both
watersheds was represented by one horizon because of the
shallow nature of the soils on these watersheds.
Parameter estimation for each watershed was done using the
data for 1992. The model calibration involved four steps: (1)
snowmelt optimization, (2) chemical calibration, (3) adjustment of hydrologic parameters, and (4) changes in model
structure. Detailed snow surveys, precipitation records, watershed discharge, and an estimate of water losses to the atmosphere were used for snowmelt optimization. Evapotranspiration and sublimation rates were set at estimates for
evaporation from the F,LW of 2.0 mm c1 -1 and 0.5 mm
respectively [Melack et al., 1998]. Since snowmelt optimization
requires water balance on a modeled watershed, snowpack and
precipitation inputs must be equal to runoff and evaporation.
We therefore adjusted SWE to match the sum of runoff and
evaporation. Within the model the remaining water is lost to
an undefined hydrologic sink, for example, groundwater [Wolford et al., 1996].
Chemical calibration of the model for each watershed followed a stepwise process of adjusting model parameters to
match model output to the observed values (see Table 4 for
functionality of model parameters). First, cations, anions,
ANC, and pH during low flows late in the melt season were
assumed to originate from the soil. Concentrations of these
species were used as targets for modeling the soil chemistry.
Second, soil pH was fixed to this late season value, by adjusting
the percent base saturation of the soil. Third, cation concentrations were matched by adjusting the apparent exchange
coefficients for each cation until modeled soil concentrations
were close to the target values. Fourth, parameters describing
the intensity of the ionic pulse were adjusted to improve the fit
to stream CI - concentration. Fifth, SO.2, - adsorption parameters were changed to increase or decrease SO i. - concentrations
in the soil and stream waters of each catchment. Finally, the N
parameters governing the dynamics of N consumption in the
soil were altered to improve the fit to stream NO and NH :concentrations.
After chemical calibration, improving model predictions required further adjustments to the hydrologic parameters. On
both watersheds the hydraulic conductivity and surface runoffsoil water mixing ratio were adjusted to allow more mixing
between surface runoff and soil water. The surface runoff-soil
water mixing ratio controls the fraction of soil water in the top
horizon that mixes with surface runoff before the surface runoff leaves the soil subunit. Next, the equilibrium partial pressure of CO, (Po,) in the stream was optimized. Further
changes to model structure were required on WS2 to obtain a
good fi t, as described below.
Our evaluation of model performance follows a method
outlined by Kirchner et al. [1996] of establishing performance
criteria and a benchmark for comparison. The performance
criteria are outlined below. The benchmark was the initial
model on each watershed using Emerald Lake parameters.
Finally, we report how well the model matched data not used
for model calibration.
Calibration was done manually; however, we used a measure
of model error for the purposes of comparing the initial and
calibrated models. The measure used was the sum of absolute
differences, the numerical value of which has the same units as
the measurements:
F,=
E—
cz'ddl (1)
where F is the objective function, C is the concentration, and
k is the chemical species. The sum of absolute differences does
not increase the weight of larger differences relative to smaller
ones, as a least squares sum does. Since the objective function
Fk has different values for different chemical objectives, we
normalized each Fk by its initial value to facilitate comparison
between objectives and assess the success or failure of the
calibration:
Fk
Pk— r
(2)
F
The closer Pk is to zero, the better the fitting procedure improved the match between modeled and measured values; the
closer Pk is to one, the less improvement provided by the
model calibration.
3. Results
3.1. Water Balance
We used the snowmelt optimization feature of the AHM,
which accounts for evaporative processes, to determine the
water balance or lack thereof. Precipitation was consistently
greater than runoff (Figure 3c). For WS1, precipitation of 600
mm and 1740 mm was observed for 1992 and 1993, respectively, and runoff of 480 mm and 1110 mm was observed for
1992 and 1993, respectively. For WS2, precipitation of 460 mm
and 1280 mm was observed for 1992 and 1993, respectively,
and runoff of 240 mm and 1020 mm was observed in 1992 and
1993, respectively. Total modeled evaporation for both watersheds was 42 mm in 1992 and 96 mm in 1993. Since the
difference between precipitation and runoff is greater than
evaporation, some of the snowpack as surveyed must have
been lost to an unidentified hydrologic sink. For WS1, 70 mm
49
MEIXNER ET AL.: BIOGEOCHEMICAL PROCESSES. SIERRA NEVADA
3125
June Jul
May
A ril . Ma
of the surveyed 590 mm of SWE was unaccounted for in 1992,
120
r,
and 550 min of the 1700 mm surveyed amount was unac0
for in 1993. On VY'S2 the wrveyed SWE in 1992 was
counted
_Lc, 90
1992
1
993
450 mm, and 190 mm of that was assumed lost to an unknown
..
_
60
sink. In 1993, 1240 mm of SWE was measured in the survey,
... r:
unknown
sink.
Following
.
.
an
and 200 mm was assumed lost to
30
snowmeit optimization, modeled and measured values of dis,.. ,..
•
charge were nearly identical for both years (Figures 4 and 5).
, I .
- '
T f ------
7 30
3.2. Precipitation Chemistry
g 20
Solute concentrations in snow and rain (Figure 3) were very
dilute, similar to those observed at nearby Emerald Lake [Wol10
:-%:-.4
•__Lo 0
ford et al., 1996 1 , typical of precipitation in the Sierra Nevada.
are
opposed
to
snow
The higher concentrations in rain as
ilijilit
i
I
I
apparent by comparing the spring 1992 rain event with the
. in
of
4.6
mm
rainfall
The
3b).
(Figure
snow
event
spring 1993
6.5
.....
1992 had concentrations for NH, NW, and a of 23.1, 18.8,
oo
a 6.0
m
and 2.5 I.LeqL -1 , respectively. The snowfall of 41.2 mm SWE in
0
1993 had concentrations of 5.2, 4.5, and 3.3 p.eqL -1 , respec5.5
- , r ?-::" . ••;',;i-, t5-1-5VrtôV
tively. Average snowpack concentrations for NH:, NOV, and
1i1
Cl - were 4.5, 2.1, and 1.5 preqL -1 , respectively, in 1992 and 1.2,
1
1111
_
1.5, and 1.8 p.eqL -1 , respectively, in 1993. The generally higher
- 25
concentrations in 1992 as opposed to 1993 coincide with the
_
smaller amount of precipitation and runoff in 1992 (Figure 3c).
a) 15
--• , -14:-,..-1..;•.'.
33. Solute Concentrations and Ionic Pulse
eq
_
co
c5
outflow
from
both
watersheds
were
concentrations
in
Solute
o
illi
III
1 I I
dilute, with levels in WS2 generally being slightly more dilute
o Observations
than those in WS1 (Figures 4 and 5). For example, average
ELW parameters
ANC values were 8.1 and 7.5 J.LeqL for WS1 and WS2,
Optimized parameters
•
respectively, with corresponding average Ca 2 ' concentrations
_
it•-*
of 8.4 and 7.7 1./eqL -1 . The two watersheds also differed sig..,
_
I n ,
nificantly in their export of H. While both watersheds reL..t...,.
,..;
ceived the same concentration of H + in wet deposition, the
discharge from WS2 had a high pH and thus exported signif_
icantly less Fr than did WS1.
Ion concentrations at the beginning of snowmelt were gen_
erally higher than concentrations in later snowmelt, reflecting
. ,
a small ionic pulse associated with some solutes being washed
•.....,...! %,„ • '
Out of the snowpack with the first meltwater [Bales et al., 1989],
f
I
can
be
seen
clearly
by
pulse
ionic
dilution.
This
and subsequent
dividing the concentrations for 1992 in Figures 4 and 5 by C„,
the average concentration of each solute in the snowpack prior
to melt (Figure 3a). This calculation did not use the spring rain
event in 1992. For comparison between catchments these values are plotted versus fraction of melt (cumulative discharge
divided by total seasonal discharge). On both of these waterO
sheds at the beginning of snowmelt, the C/C for a , a con100 120 140 130 150 170 190
servative species, is a little greater than 2 (Figure 6). For WS1,
Day of Year
Day of Year
CL has a C/C„ above 1 for the entire season. The rainfall
event on May 6th is not responsible for the C/C,, value above Figure 4. Watershed 1 results. Observations are flow1 since the amount of rain, 4.6 mm, is small in comparison to weighted averages. Emerald Lake watershed (ELW) paramethe volume of snow remaining on the watershed on May 8th, ters represent the calibration starting point and are shown with
191 mm (from a late season snow survey). The most likely a dashed line. Optimized parameter values are described in
source of this mass balance problem is field or laboratory text and Table 4. The 1992 box indicates timing of a rain event.
The 1993 box indicates timing of a snow event.
contamination.
but
Cl
,
pulse
like
an
ionic
(NOD
also
exhibited
Nitrate
NO is not conservative and the NO observed in streamflow
may come from within the watershed through nitrification of WS1 were consistently higher than for WS2, indicating that
WS2 had.
NH:, either from snowpack or soil organic matter sources. WS1 had a larger ex-port of dissolved inorganic N than
Sulfate and cations had little or no ionic pulse; however,
Nitrate had a C/C„ value of around 2.0 as the melt season
began and rapidly dropped below 1.0, representing a net con- Figure 6 does show dramatic differences between precipitation
had a
sumption of NO (Figure 6) for WS2. Nitrate CiC,„ values for and stream concentrations for these species. Sulfate
.......•
-
-
-
3126
50
MEIXNER ET AL: BIOGEOCHEMICAL PROCESSES. SIERRA NEVADA
120
90
ru l May
April
1
1993
_ 1992
May
.7- ---..' :n-:
60
o
June
.i.,
"
g•
30
%
...4r:
:
I
I
30
rcir
) 20
10
o
z
0
-
Watershed 1
Watershed 2
,
6.5
-
I-
-•
_
0.
•
.
5.5
_
?.
-.
.
'
%. • n.• '
'
..:
.
14
7-)
10
-
ai
- 4
_
_
__ (6
_
•-•
.......•
.....
o Obs rvatiorls
ELW Parameters
Optimized parameters
-_ _
_
•••••
_
0 0 0.2 0.4 0.6 0.8 1 0
Fraction of Melt
Figure 6. Ratio of stream concentrations to bulk snow concentrations for each watershed with fraction of flow as independent variable for 1992. The arrows indicate the timing of
the May 6th rain event; arrows are different because the independent variable is a fraction of flow, not time.
,--.....
''.
-
.•':,:',..
f
. - '
120 140 110 130 150 170 190
Day of Year Day of Year
Figure 5. Watershed 2 results. Observations are flowweighted averages. FI.W parameters represent the calibration
starting point and are shown with a dashed line. Optimized
parameter values are described in text and Table 4. The 1992
box indicates timing of a rain event. The 1993 box indicates
timing of a snow event.
3.4. Nitrogen Mass Balance
Over the entire snowmelt season there was significantly
more dissolved inorganic N being deposited on both watersheds than was exported from these watersheds in streamflow
(Table 2). There were significant differences in N loading to
the watersheds due to differences in SWE on each of the
watersheds. Dissolved inorganic N output was almost entirely
in the form of NO since NH:', concentrations were below
detection limit for much of both melt seasons. For both 1992
and 1993, WS1 had a much greater net dissolved inorganic N
yield than WS2 had.
Table 2. Dissolved Inorganic Nitrogen Budgets
Input, mol ha'
Output,
C/C„ of about 2.0 for both watersheds throughout the melt
season, indicating significant S0 74-- export or concentration on
the watershed. Ca 2 ' had large C/C„ values for the entire 1992
melt season, 4.0-6.0, reflecting net export of cations from the
watersheds.
Watershed 1, 1992
Watershed 1, 1993
Watershed 2, 1992
Watershed 2, 1993
Yield,
NO NH: Sum mol ha -I%
13.3
21.7
10.8
16.4
7.3
20.7
6.1
15.7
20.6
42.4
16.9
32.1
3.4
7.0
0.6
3.32
16
16
4
10
57_
3127
MEIXNER ET AL.: BIOGEOCHEMICAL PROCESSES. SIERRA NEVADA
3.5. Watershed 1 Calibration and Evaluation
The simulation using ELW parameters gave ANC. p H, and
base cation values higher than observed (Figure 4). Averaging
of late season stream chemical concentrations (day of the year
(DOY) 135 and 136) resulted in the target runoff concentrations in Table 3. Values for parameters adjusted during calibration are in Table 4. For 1992 the calibration improved fits
for all species (Figure 4). In particular, ANC, p H, Ca", Mg",
and K. all saw large improvements in model performance,
with P k values of 0.21-0.33, that is, 67-79% decreases in the
sum of absolute differences from initial to calibrated simulations. Fits were slightly poorer for the evaluation year than the
calibration year, with Pk values of 0.29-0.52.
The match between modeled and observed Ca' concentrations was relatively good for both years, the main difference
being the greater day-to-day variability in the data versus the
model. CI showed a modest ionic pulse in both years, and
thus the elution parameter (D) was only 2 for both watersheds
(Table 4). Early season pulses for S0.i - were reversed by
subsequent higher concentration values around DOY 112 in
1992 and 132 in 1993, most likely representing a flush of S0i rich water from the watershed; as a result, we made adjustments to K-S0,2, - (Table 4). The apparent ionic pulses for
NO; are reflected in the model output, but to capture late
season low concentrations, the N reactions in the model were set
to consume all NO and NHZ that carne in contact with the soil.
Modeled ANC and pH both reflected the observed average
but failed to capture the day-to-day variability. In both years,
there were two periods with a poor match between measured
and modeled values (Figure 4). In 1992 the model missed both
the magnitude and trend of the data around DOY 120, when
pH and ANC exhibited opposite trends. This is apparently a
problem with the ANC values being too high. Over the whole
season the ion balance showed a 17% excess of cations over
anions, but days 119-120 had an ion balance near zero (data
not shown). The second period in 1992 was around DOY 130,
whenpH dropped and ANC varied each day. At the end of the
1993 melt season, modeled ANC and pH were higher than
observed. Further, the opposite trends in pH and ANC around
days 150 and 170 were not captured by the model.
While measurements of soil chemical concentrations were
not used for calibration, calibration significantly improved the
match between modeled and measured concentrations of several species in the soil (Figure 7). Two exceptions to this
general agreement were that measured ANC concentrations
from lysimeter la at a depth of 0.3 m were not captured by the
model, and the modeled NO concentrations of zero versus
nonzero measured concentrations.
-
3.6. Watershed 2 Calibration and Evaluation
Averaging of late season stream chemical concentrations
(DOY 130-132) gave the target soil chemical concentrations
Table 3.
Target Runoff Concentrations
Species
Watershed 1
Watershed 2
Ca 2 *, i.reqL
Me + ,
Na, geqL
K*, ikeqL
SOj , irreqL - '
5.4
8.5
2.0
7.5
3.5
5.0
5.7
8.0
2.0
4.0
2.0
4.0
pH
Table 4. Final Parameter Values
Parameter
ELW Watershed 1 Watershed 2
400
0.522
0.0
120
46
3534
-2.3
-2.9
4.0
Snowpack elution parameter .1Y
55
CEC, meq kg'
17.9
Base saturation, %
-5.23
Log K-Ca'
-5.73
Log K-Mg'
-0.85
Log K-1C- a
-3.01
Log K-Na'
17.45
Log K-50.i - `
27.63
Log K-Si'
0.989
aNH3toONf
0.70
aNO3toONf
8 x 10 -6
NO-basef
Hydraulic cond., cm day'
Water holding capacity
Surface runoff mixing"
Total area, ha
Soil area, %
Soil depth, cm
Log P c02 soil, atm
Log P co , stream, atm
400
0.522
0.5
0.22
20.76
10b
-2.3
-2.6
2.0
55
4.2
-4.90
-5.63
-0.72
-2.91
16.85
27.63
0.9999
0.9999
10-7
400
0.522
0.2
0.48
20'
7.55
-2.3
-3.1
2.0
18.3
17.9
-4.37
-4.88
-0.051
-3.01
16.45
27.63
0.9999
0.9999
10-7
ELW, Emerald Lake watershed.
'Surface runoff mixing determines the fraction of surface runoff that
can mix with the soil water of the top soil horizon.
b Values for WS1 are from field surveys. For WS2, soil area was
doubled and soil depth increased by 50% from original survey values.
Also, the rock portion of WS2 was allowed to consume N.
'Represents ratio of initial solute concentration in snowmelt to
snowpack average. All other elution parameters were unchanged from
ELW.
d Log K for exchange of cation with H+ on cation exchange site.
'Log K for adsorption of SOi - and H 2 SiO 3 . Total site concentrations from ELW optimization used here.
"These three parameters govern the two N reactions present in the
Alpine Hydrochernical Model (ARM): NH: <-+ organic N + H + and
NH: + 20 2 +-> NOT + 2H + . The aNH3toON determines what percent of the NH: is converted into organic N. NOT-base determines a
minimum concentration of N0'3- over which a fraction of the NOT as
governed by aNO3toON is converted into organic N.
shown in Table 3. Calibration following the scheme used on
WS1 resulted in only modest improvements in model predictions. The best opportunity for improving model output was to
adjust the soil volume on the watershed. A simple grid search
gave the best option as doubling soil area and increasing soil
depth from 5 to 7.5 cm.
After these adjustments, modeled NO; still did not match
the low observed concentrations. In order to consume all of the
NO within the model, we gave the rock portion of the watershed the ability to immobilize N equivalent to a 9 cm soil
depth but not the ability to exchange cations, weather minerals,
or any of the other soil processes in the AHM. During the rain
event of DOY 125-126 in 1992, however, modeled concentrations of NO; were lower than observed concentrations. This
was probably due to overland flow that was not reflected in the
calibrated model.
The calibration improved the match between modeled and
measured values for all species, as shown in Figure 5 for ANC,
pH, Ca", NO;, SW, - , and cr. The final parameter values
for all parameters that were adjusted during calibration are in
Table 4. P, values for ANC, pH, Ca', K + , and NO; of
0.18-0.78 indicate 22-82% improvements in simulation results. The fits for most species improved from the initial run to
the final calibrated run for 1993, the evaluation year (Figure 5).
For 1993, Pk values were 0.37-0.92, indicating 8-63% improvements in the evaluation year results from initial to cali-
I
52
3128
MEIXNER ET AL.: BIOGEOCHEMICAL PROCESSES, SIERRA NEVADA
40
1992 _ - ------
30
7_,
_
-
g 20
i —
\_
"444410
e
-
i
, I I { i j ,
_
1993... ..
.
9•0 .
. Vie_
.2P ... *8 4.
• `7111" 8P°.
j
I
f
, j ° ,
...
.
o
_, o
7
_..
,
5
---f---C
. •-_ -
4
30
25
--I 20
cr
a) 15
, - 10
6 5
20
11 11' 111 1 ,51 I
\
0
I
_
-
I
-
°
. g e
,0
4
.
"opt- ag ..... 0ge
4.1
°) 1 '
0
i
• Lysimeter la
...—
_
o Lyslmeter lb
-
0 Lyslmeter 2
—
ELW Parameters
_
— — Optimized parameters
-
°
a
0
- 0
-
3.7. Sensitivity
o
Sensitivity to inputs was greater on WS1 than WS2 (Figure
9), despite WS1 having 40% greater modeled soil volume per
unit watershed area. For both watersheds, NO, a , and
SCg - were the most sensitive to the doubling of wet deposition. a was especially sensitive since it is unreactive in the
-
-
-
-
15
cr
0
..,ô — •
5
—
0
In both years, modeled ANC and pH captured the average
concentrations. Yet some of the data's variability and its trends
were missed, for example, DOY 115-120 in 1992, when ANC
and pH went up even though discharge went up. The model
calculated an opposite trend because of dilution. Other chemical species failed to show the same trend for this period,
however. The poor ion balance for this period, 30% excess of
anions over cations (data not shown), suggests that measured
ANC may be too high. Late season periods were problematic
in both years. The model underpredicted ANC and pH at the
end of the 1992 melt season and overpredicted ANC at the end
of the 1993 melt season.
As with WS1, calibration improved the match between measured and modeled soil concentrations (Figure 8), with NO
and SO .i - concentrations notable exceptions. Modeled NOjconcentrations are at zero for the entire season, while measured concentrations exhibit a pronounced early season spike
in both years with some values greater than zero well into the
melt season. Concentrations of S0,2, - are steady in the soil,
while the modeled soil shows a decrease in S0i - during the
WS2 melt season in both years.
_
al %
4
10
o
o
0
—
9
........ a0 - '-- .............
.
f----,.
-----Ii2Z_
%
i e' 410 9ig
P f -
0
6
•°0. 6'
°
...t oe
e
a.
e
t 1 • ° -
'9
.
.'
-
-
g>
-
-
...> • .., % .9
.
__
e
0.
_1#444:5
,,„,,8
'
6,--1-11•Fir•74-7-7-71
,
0
100 120 140 130 150 170 190
Day of Year
Day of Year
Figure 7. Comparison of modeled and measured soil chemistry for Watershed 1. Symbols are average observed concentrations for the soil lysimeter indicated. Lysimeter la is at a
depth of 300 mm, while lysimeter lb is at a depth of 100 mm
at the same location. Simulated values for ELW parameters
and optimized parameters are shown. No attempt was made to
fit modeled soil concentrations to observed values.
brated models. ANC and Ca 2 + actually had more improvement from calibration in the evaluation year than in the
calibration year.
The overall match of model output to measured concentrations in the watershed was good for Ca 2 *, with the exception of
the period around DOY 123 in 1992 and DOY 110-130 in
1993. Calibration also improved the fit for a and SOL. The
model matched general trends in the data for both years but
not the day-to-day variability.
-
watershed. Cations, ANC, and pH were not very sensitive
because of buffering by cation exchange in the soil of both
watersheds. ANC depression due to the doubling of deposition
was 1 Aeql- -1 for both watersheds. Depression of pH was
around 0.03 units for both watersheds.
4. Discussion
There was less net 11+ and NO consumption on WS1 as
compared to WS2, suggesting that N chemistry is different
between the two. Both watersheds had approximately the same
relative export for base cations and SO,; - , indicating that both
watersheds have similar processes controlling these species.
Four aspects of data analysis and model calibration show
that more chemical changes are occurring on WS2 than expected by the surveyed amount of soil: (1) equivalent C/C„
values for WS1 and WS2 for cations and SOY, (2) higher
percent base saturation, (3) the need to add reactive capacity
equivalent to additional soil to adequately model stream concentrations, and (4) the greater N consumption.
4.1. Water Balance
The lack of water balance on these two watersheds is not due
to an underestimate of evaporation. Our estimated evaporation is an overestimate of reasonable evaporation rates during
the snowmelt season in alpine watersheds of the Sierra Nevada. Melack et al. [1998] found that only 50 mm of snow
evaporated during the 1993 snowmelt season at FILW. They
also calculated a range of evaporation for the Sierra Nevada of
29 mm up to 166 mm per year. An evaporation estimate on the
upper end of this range might explain the lack of water balance
on WS1 in 1992 but cannot explain the lack of balance for WS1
in 1993 or for WS2 in either year.
The fact that cumulative discharge was less than the water
volume estimated from the snow survey, even having ac-
53
MEIXNER ET AL: BIOGEOCHEMICAL PROCESSES, SIERRA NEVADA
counted for evaporation, could be because of interbasin transfers through the snowpack or subsurface leakage through the
cracked, exfoliated granodiorite. Snowpack structure can
change effective watershed boundaries, resulting in diversion
of snowmelt to basins outside the one monitored. As WS1 has
a total relief of 11 m and in 1993 a snowpack depth of over 5 m,
90
7
co
3129
A
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Ma
Watershed
Watershed 1
-
2
_
_
60
30
one can easily envisage channeling that would reroute water
away from our stream gauge. The granodiorite underlying both
of these watersheds is extensively cracked. During snowmelt
the ground surface of these watersheds is constantly saturated
and provides ample opportunity for water to infiltrate deep
Ma
A ril
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Doubled Inputs Calibrated Model:
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1 )0110 120 130 140 110 120 130 14 0
Day of Year
Day of Year
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9.
Results for doubling wet deposition using 1992
Figure
data and calibration for both watersheds. The solid line is
model output for doubled wet deposition. The dashed line is
model output from final calibrated model.
, . c) ° ,° I
0
100 120 140 110 130 150 170 190
Day of Year
Day of Year
into the rock outcrop to be exported from the watershed
through the subsurface.
8.
The field survey indicated that WS1 had 4 times the soil
volume per unit area as compared to WS2 (2.1 versus 0.5 cm).
However, the model fit suggested that the differences were
only about 40% (2.1 versus 1.5 cm). Since it is unlikely that the
field estimate of soil volume was off by this much, it appears
Comparison of modeled and measured soil chemFigure
istry for Watershed 2. Symbols are observed concentrations for
the soil lysimeter indicated. Simulated values for ET .W parameters and optimized parameters are shown. No attempt was
made to fit modeled soil concentrations to observed values.
4.2. Base Cation and ANC Production
54
3130
MEIXNER ET AL.: B1OGEOCHEMICAL PROCESSES. SIERRA NEVADA
that areas of exposed rock have the ability to buffer H. release cations, and take up nutrients. It is also unlikely that our
estimate of total watershed area had this large of an error. The
main areas of uncertainty in field verification of drainage divides were on exposed rock, so an overestimate of rock area
relative to soil area could help explain the apparent underestimate of soil on WS2.
It is possible that some areas of rock in alpine regions react
with precipitation in a manner equivalent to soil. Reports by
others offer evidence of pH buffering and ANC production on
exposed rock surfaces. Clow and Mast [1995] observed that the
chemical composition of rainfall runoff from a 30 m 2 granite
slab was much higher in cations and ANC than was the rainfall.
Comparison of Andrews Creek and Icy Brook in the Loch Vale
watershed of Rocky Mountain National Park suggests that soil
processes were the dominant control on stream concentrations
despite the relatively low abundance of soils and their early
stage of development [Campbell et al., 1995]. Rueslatten and
Jorgensen [1978] found that organic acids and weathering on
exposed surfaces contributed cations and acidity to snowmelt
runoff. Rock surfaces have also been found to have ion exchange capabilities [Dahl et al., 1979; Abrahamsen et al., 1979].
From studies on the Precambrian-Canadian shield, Allan et al.
[1993] concluded that areas of bare rock exported cations to
islands of soil present within the same Watershed, where the
cations were then immobilized. They also observed that soil
catchments had lower pH and ANC than did bare rock catchments, consistent with the higher pH and similar ANC and
cation concentrations on WS2 as compared to WS1.
Three other possible sources of the cation export and ANC
production on areas mapped as exposed rock are (1) soil
trapped in crevices and in rubble fields, (2) lichens that cover
the rock of these watersheds, and (3) dry deposition. A recent
study in the Buckskin Range, Nevada [Blank et al.. 1996],
reported that talus acted as a deposition zone for eolian dust,
resulting in significant soil genesis. These eolian soils had a
significant clay fraction, providing some ion exchange capacity;
there was also evidence of past weathering. Areas of loose
rocks and boulders within areas mapped as rock could serve as
traps for eolian dust on WS2.
Epilithic lichens have long been known to weather exposed
rock and have been shown to exchange cations with solution by
using an abiotic complex [Nash, 1996a, b; Jones, 1988].
Through a combination of weathering substrate and holding
weathered cations on an exchange complex, lichens in our
watersheds might be a source of the buffering capacity and
alkalinity production seen in this work. Lichens, however, do
not provide all of the cations or alkalinity production. For
lichens to provide all of the cation exchange capacity represented by the additional soil area on WS2. they would have to
be present in quantities around 4000 g m -2 [Nash, 1989]. No
measurements were made on this watershed as to the quantity
of lichens present. However, this value is far out of range from
literature values on epilithic lichens, considering that arctic
ecosystems with large quantities of lichens have total biomass
around 1300 g M -2 [Nash, 1996a].
Since the only period of significant hydrologic runoff on
these watersheds is spring snowmelt, the additional cation .
SOU, and alkalinity export we observed could be a result of
accumulated summer/fall dry deposition. Using 82 Sr/ 55 Sr ratios
to identify sources of dissolved Ca in runoff. Clow et al. [1997]
found that runoff from their microcatchment had nearly identical 82 Sr/ 56 Sr to precipitation, indicating that the dissolved Ca
in runoff came from wet and dry deposition to the rock surface.
Similar dry deposition processes may be at work in these two
watersheds.
43. Nitrogen Cycling
Both watersheds consumed a significant fraction of the deposited N (Table 2). In addition, the C/C,, values of NO; for
WS2 were always less than for WS1 (Figure 6), meaning that
less of the incoming N left this watershed. Table 2 indicates
that the yield of dissolved inorganic N from WS1 was nearly
twice that of WS2, because of greater consumption of the
incoming dissolved inorganic N on WS2. Previous experience
in alpine basins indicates that an ionic pulse should occur for
N0 3.- held in the snowpack [Bales et al., 1993]. Only a mild
pulse was observed in either of these watersheds, and stream
NO concentrations were consistently below those in the
snowpack.
These results are in contrast to findings at nearby watersheds. At ELW it was observed that the basin was a source of
N0'; in some years, while in others it was a sink [Williams and
Melack, 1991]. However, the ELW was shown to be an N sink,
receiving more NO; and NH:: in precipitation than dissolved
organic and inorganic N in lake outflow [Williams et al., 1995].
On the other hand, two other watersheds in the Tokopah
Valley were net sources of N during the snowmelt season
[Stoddard, 1995].
Isotopic evidence suggests that soil NO rather than snowpack NO is responsible for the pulse of N seen in snowmelt
runoff in the Loch Vale watershed in Colorado [Kendall et al.,
1995]. Recent work in the Colorado Front Range has indicated
that soil mineralization under snow cover, rather than the ionic
pulse from the snowpack, is the source of the springtime pulse
of NO; observed in spring melt waters [Williams et al.,
1996a, b]. Two findings suggest that the same may be true in
our small catchments. First, measured NO; concentrations
were higher on WS1, with very few of the zero values that were
present on WS2. Second, model structure had to be altered
greatly on WS2 in order to remove all NO; in the stream,
while no such alterations were needed on WS1. While saturated frozen soils may be the source of spring nitrate pulses in
alpine streams, we are still left with the question of where the
N in the snowpack is going. This sink must be large and somehow be stronger on exposed rock surfaces than on areas of soil.
Four possible sinks for N in these catchments are soil organic matter, vegetation, litter, and lichens. All of these sinks
have different temporal timescales and different storage capacities. Recent studies at Niwot Ridge, Colorado, have shown
that soil microbes can be quite active under deep winter snowpacks and can mineralize significant amounts of soil organic
matter and produce much greater quantities of dissolved inorganic N than are input to a watershed from the snowpack
[Brooks et al., 1996]. The microbial population can also assimilate the N that is mineralized or received from the snowpack,
depending on the carbon status of the soil and whether the
microbes must compete with vegetation for the mineralized N
[Hart et al., 1993; Fenn et al., 1998]. Soils can also immobilize
N abiotically, either by reaction of ammonium with cation
exchange sites or by abiotic immobilization of ammonium in humus [Johnson, 1992]. Denitrification can also cause gaseous export of N from soil [Tisdale et al., 1993]. These losses have been
shown to be large under seasonal snowpacks [Brooks et al., 1997].
Vegetation is an important long-term sink for N [Williams et
al., 1995] but less important over the short time (days to weeks)
55
MEIXNER ET AL. BIOGEOCHEMICAL PROCESSES. SIERRA NEVADA
of snowmelt runoff in alpine basins. However, vegetation is the
most likely long-term sink for N that is immobilized by the soil
microbial pool during spring snowmelt.
Litter is found on the soil surface and in cracks between
rocks where annual grasses and flowers grow. Soil microbes
need both N and water to decompose vegetative litter with its
relatively high C:N ratios (20-200) compared to the C:N ratios
(6-12) of soil microbes [Swift et al., 1979; Parton et al., 1987;
Tisdale et al., 1993]. Litter in cracks and crevices would be in
the flow path of snowmelt runoff, since melt is likely to travel
along cracks and crevices present on bare rock. Soil microbes
would thus have a high C:N organic matter source in the litter
that would serve as a substrate, and the dissolved inorganic N
contained in snowmelt would provide a necessary nutrient to
break down the litter. The dissolved inorganic N immobilized
by the soil microbes in the litter must eventually be exported
from the watershed or be incorporated into a long-term pool
for N, such as vegetation or soil organic matter.
Lichens covering the exposed granite present in alpine watersheds could be consuming precipitation inputs of N. Lichen
growth may be N limited [Crittenden et al., 1994]. Further,
lichens can absorb N species from solution and store for later
use [Rai, 1988]. Finally, Lang et al. [1976] have shown through
a series of experiments that lichens have the ability to remove
N from solution and contribute cations to the same solution.
Thus lichens might provide some of the extra buffering capacity and N uptake that our calibration indicates exist on WS2.
It is unlikely that soil is the primary .net sink for dissolved
inorganic N in these catchments. Both of these catchments
have less soil than the ELW (2.1 cm and 0.5 cm basinwide
equivalent soil depth as opposed to 13.6 cm at ELW) [Tonnessen, 1991; Wolford et al., 1996]. If soil organic matter and
vegetation were the sink for N, dissolved inorganic export on
WS2 would be greater than export on WS1 because of the
greater soil volume, larger biomass, and higher C:N ratio on
WS1 (Table 1). We observed the opposite, with higher NO;
concentrations on WS1 representing greater export of dissolved inorganic N on WS1 than WS2. Also, if soil were the
ultimate sink for N, we would expect NO concentrations, and
thus dissolved inorganic N export, to be lower at ELW than
these watersheds. What we see is the opposite: highest NO;
concentrations at ELW (5 geqL -1 ), intermediate levels on
WS1 (1.5 p.eqL -1 ), and lowest concentrations on WS2 (0.2
p.eqL 1 ). (In all of these watersheds, NH: flux is small compared to NO flux.)
Instead of a sink, the soils of these watersheds are a likely
source of inorganic N. The C:N ratios of the soils on each
catchment (16 for WS1 and 13 for WS2) are indicative of soils
in which soil microbes are mineralizing organic matter to produce inorganic N in excess of their demand for inorganic N
[Tisdale et al., 1993 ] . Greater export of inorganic N on WS1
may be due to its relatively larger amount of soil.
-
4.4. Sensitivity to Changes in Loading
The sensitivity calculations (Figure 9) further illustrate the
difference between these watersheds (Table 4); WS2 was actually less sensitive to increased chemical loadings than was
WS I. This is in contrast to our hypothesis, which was based on
the surveyed percent of soil cover. Also striking is the relatively
small sensitivity of both catchments to a doubling of chemical
fluxes in wet deposition, especially as compared to ELW [Wolford and Bales, 1996]. ANC and pH depression for these watersheds was an order of magnitude smaller than at ELW. At
3131
ELW, doubling inputs in wet and dry deposition resulted in a
maximum depression of 0.3 units and 9.1 p.eqL -1 for pH and
ANC, respectively.
Within the model, four parameters that control the effect of
the spring ionic pulse on stream chemistry combined to attenuatepH and ANC depressions on these catchments, relative to
F.I.W. First, the chemical elution parameter that determines
the strength of the ionic pulse was calibrated to a value of 2 on
both catchments as opposed to 4 at ELW, resulting in a weaker
ionic pulse. Second, the increase of the surface runoff mixing
parameter on both watersheds indicates greater contact of
runoff with soil on these watersheds than at ELW. The greater
contact of runoff with soil may reflect less downslope flow
through the snowpack and more flow along the ground surface,
possibly owing to the lower slope of these catchments as compared to ELW, a mean slope of 13% for WS1, 17% for WS2,
and 31% for ELW. The lower slope permits water to travel
more slowly on these catchments than at ELW and permits
longer interaction with soil and rock surfaces. Third, the SO;.-adsorption parameter of both watersheds is lower, so the SO.i concentrations are high. Measured and modeled SO 1 - concentrations (5 geqL -1 ) are already more than double concentrations in deposition to the watersheds (1.5 AeqL'). Thus
doubling S0 2,-- deposition to the watersheds will have a lesser
impact since stream S0,2, - concentrations are already relatively
high. Finally, the N parameters on both of these watersheds
were set so that almost all N was consumed. This attenuated
the effect of an increase in N deposition on stream chemistry.
More NO consumption combined with a higher percent
base saturation on WS2 explains the reduced sensitivity, as
compared to WS1, to changes in wet deposition. More NO is
consumed on WS2 than on WS1, and thus the sensitivity ofpH
and ANC are reduced. The higher percent base saturation of
WS2 means more cations are released from the soil when wet
deposition is increased, thus buffering the response of pH and
ANC to the increases in wet deposition.
4.5. AHM Model Structure and Parameters
The ARM was originally developed using the F.LW data.
and this is the first application of the ARM beyond that watershed. Both watersheds were modeled with the same general
model structure as on ELW. A subunit of rock and a subunit of
soil were capable of capturing the mean and general variability
of stream chemistry on these two watersheds. The one major
deviation from the ELW structure for both watersheds was
that the surface runoff mixing ratio was >0; it was set to 0.5 for
WS1 and 0.2 for WS2. The model, as applied to these two
watersheds, had eight hydrologic parameters; changing one to
improve fit represents only a small modification.
However, the final chemical parameter values for WS1 were
significantly changed from ELW values. The main differences
in the chemical parameterization are related to the pH of
stream water and the low NO; and NFIZ concentrations in the
stream. Also, the parameterizations had to achieve similar
SCg - and cation concentrations for both watersheds despite
the lower volume of soil surveyed on WS2.
The pH of stream water was significantly different between
these two watersheds. The streampH of WS1 was steady at 5.5,
and the stream pH of WS2 was a steady value around 5.8. In
calibrating the model, there are only two ways to affect stream
pH: a djust soil base saturation, and adjust the P of the
stream. For WS1 we adjusted both of these. On WSI the
percent base saturation was changed from 17.9 to 4.2%. An
56
NIF_DCNER ET AL.: BIOGEOCHEMICAL PROCESSES. SIERRA NEVADA
3132
increase in stream P co, to a value greater than atmospheric
was also necessary to lower the modeled stream pH. The P„,
of the stream on WS2 had to be decreased to match observed
pH, but it was still above atmospheric P oe,.
Stream P oe , was increased to lower pH On WS1; however,
organic acids (unmeasured) may also be contributing to the
lower pH. Coniferous vegetation, like that of WS1, can contribute organic acids to streamflow [Likens and Bormann,
1995]. Recent work by Boyer et al. [1995] has shown that dissolved organic carbon in alpine basins can be an important
flux. The CO 2 addition was a parameter adjustment to provide
a watershed-based source of acids, given our lack of knowledge
of organic acids in the catchments. It would take 1.5 kieqL -1 of
organic acids to explain the pH depression caused by the additional CO 2 that we have calibrated WS1 to have.
Differences in calibration needed to match the observed
stream NO and NH: were more striking. For both watersheds the N consumption parameters in the soil compartment
were set to their maximum values (Table 4). This change was
necessary to have the model capture the extremely low NO2concentrations that were observed in the stream and to remove
all NH:* from snowmelt since no NH: was observed in the
streams. In order to remove all of the NO from runoff on
WS2, it was necessary to give soil biogeochemical properties to
material mapped as rock. While these changes illuminated the
differences between the two watersheds, this alteration is conceptually unappealing for two reasons. First, suction lysimeters
did measure NO in the soil pore waters, which our model did
not capture. Second, significant changes to model structure
had to be made to account for the low NO concentrations on
WS2. The changes to soil depth and soil area highlight the
need to improve the N dynamics model of the AHM. Use of N
dynamics similar to those included in the CENTURY model
[Parton et al., 1987], which has a fuller representation of N
cycling, could help test hypotheses about the location and
causes of NO and NHZ immobilization during snowmelt
runoff at a watershed scale.
In order to have the two watersheds behave similarly with
respect to S0,1 - , cation export, and alkalinity production, it
was necessary to increase the soil reactive capacity of WS2 to
properly capture the concentrations and timing of ion release
during the melt season of WS2. This change in soil reactive
capacity was represented by the doubling of soil area and
increase in soil depth for the watershed. This step was necessary
to correctly match both the stream (Figure 5) and soil chemistry
(Figure 8). This adjustment in model structure should be
viewed as an attempt to quantitatively represent the extent and
intensity of biogeochemical processing on the watershed.
The large changes in chemical parameters on these two
watersheds and the small changes in hydrologic parameters
highlight the value of good soil chemical data for estimating
AHM parameters independent of calibration to stream measurements. We lacked that information for these watersheds,
so soil chemistry was calibrated from stream discharge chemistry.
At ELW, calibration was done using measured base saturation,
cation exchange capacity, and detailed data on soil chemical
reactions, as well as stream chemistry data [ho/ford et al., 1996].
-
5. Conclusions
The extent of biogeochemical processes in alpine watersheds
cannot be determined by simply mapping the relative amount
of soil area and inferring soil properties of the whole water-
shed from apparently similar soil on a nearby watershed. Areas
of exposed rock may have properties generally attributed to
soil, in that they are a source of cations and ANC. Despite the
larger volume of more developed soil on WS1, it has a lower
percent base saturation in the soil and a lower pH and higher
stream NO; than WS2. Thus WS1 produced more acidic waters than the exposed rock catchment of WS2. Further, WS2,
despite its dominance by areas of exposed granodiorite, had a
higher percent base saturation and greater nitrate consumption and thus was less sensitive to changes in deposition than
WS1.
Our results lead us to conclude that soils and vegetation are
not responsible for the greater N retention on WS2 as compared to WS1 during snowmelt. Litter on areas of rock and
lichens growing on rocks appear to be responsible for the
immobilization of snowpack-dissolved inorganic N. Whatever
the hypothesis is for N retention in these alpine watersheds,
the sink must be larger on areas of exposed rock than it is in
well-soiled and well-vegetated areas.
These watersheds are better buffered against changes in
stream chemistry from possible increases in acid deposition
than is ELW for three reasons. First, the ionic pulse was less
pronounced. This was apparently associated with the greater
mixing of surface runoff and soil water prior to entering the
stream. Greater runoff contact with soil may reflect less downslope flow through the snowpack and more flow along the
ground surface, possibly due to these catchments being less
steep than ELW. Second, these watersheds apparently had
higher stream sulfate concentrations and thus lower sulfate
adsorption. Finally, nitrate consumption and ANC production
are greater on these watersheds.
The AHM is generally transportable to watersheds similar to
ELW, with chemical parameters requiring considerably more
adjustment than physical (hydrologic) parameters. Estimation
of soil chemistry parameters by calibrating with stream discharge chemistry data was less satisfactory than for ELW,
where more data were available. Soil chemical data gave us a
secondary way to evaluate our model calibration. Measurement of soil exchange reactions and sulfate adsorption would
further constrain our model calibration. However, the heterogeneous nature of alpine environments and the degree of
lumping needed to conduct chemical modeling of these watersheds implies that calibration will still be needed, even with
extensive soil data.
The modeling of organic acids and N cycling at the watershed scale are areas for future investigation. An improved
understanding of sources and sinks is required before the representation of organic acids in the AHM can be improved.
Incorporating a model that more explicitly represents N cycling
in alpine watersheds might improve model performance for
both nitrate and ANC. Also, processes not currently in AHM
could be important in accurately modeling stream chemistry.
For example, lichens, areas of soil included within exposed
rock, and the influence of snow-covered area on soil microbes
need to be incorporated into biogeochemical models of alpine
basins.
Acknowledgments. Support for field work and analyses was provided by the California Air Resources Board A032-116; J. Melack was
a co-investigator. Thanks to A. Esperanza and D. Graber and the other
research staff of the National Park Service and United States Geological Survey at Ash Mountain for their support and permission to
conduct this research. The first author was supported by a NSF Grad-
57
MEIXNER ET AL: BIOGEOCHEMICAL PROCESSES, SIERRA NEVADA
uate Research Fellowship and a Canon National Park Science Scholarship. A NASA-EOS grant provided partial support for this work. N.
Ohte and R. Wolford both helped construct the model. The authors
would also like to thank R. Harrington, J. Rohrbough, J. Melack,
M. R. Williams, M. W. Williams, S. P. Anderson, K. Cotter, and an
anonymous reviewer for their helpful suggestions. R. Brice helped in
manuscript preparation.
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Hart, S. C., M. K. Firestone, E. A. Paul, and J. L. Smith, Flow and fate
of soil nitrogen in an annual grassland and a young mixed-conifer
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Johnson, D. W., Nitrogen retention in forest soils, J. Environ. Quai., 21,
1-12, 1992.
Jones, D., Lichens and pedogenesis, in CRC Handbook of Lichenology,
edited by M. Galun, vol. 3, pp. 109-124, CRC Press, Boca Raton,
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and C. C. Y. Chang, Tracing sources of nitrate in snowmelt runoff
using the oxygen and nitrogen isotopic compositions of nitrate, in
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K. A. Tonnessen, M. W. Williams, and M. Tranter, JANS Pub!., 228,
339-347, 1995.
Kirchner, J. W. , R. P. Hooper, C. Kendall, C. Neal, and G. Leavesley,
Testing and validating environmental models, Sci. Total Environ.,
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precipitation chemistry, Oecologia, 25, 779-241, 1976.
Likens, G. E., and F. H. Bormann, Biogeochemistry of a Forested Ecosystem , 2nd ed., Springer-Verlag, New York, 1995.
Melack, J. M., J. O. Sick.man, A. Leydecker, and D. Marrett, Comparative analyses of high-altitude lakes and catchments in the Sierra
Nevada: Susceptibility to acidification, Tech. Rep. CARS -A032 - 188,
Calif. Air Resour. Board, Sacramento, 1998.
Nash, T. H., Metal tolerance in lichens, in Heavy Metal Tolerance in
Plants: Evolutionary Aspects, edited by A. J. Shaw, pp. 119-131, CRC
Press, Boca Raton, Fla., 1989.
Nash, T. H., Nutrients, elemental accumulation and mineral cycling, in
Lichen Biology, edited by T. H. Nash, pp. 136-153, Cambridge Univ.
Press, New York, 1996a.
Nash, T. H., Photosynthesis, respiration, productivity and growth, in
Lichen Biology, edited by T. H. Nash, pp. 88-120, Cambridge Univ.
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precipitation at temperatures close to zero degrees celsius, Nord
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Stoddard, J. L., Episodic acidification during snowmelt of high elevation lakes in the Sierra Nevada Mountains of California, Water Air
Soil Pollution, 85, 353-358, 1995.
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* Tisdale, S. L., W. L. Nelson, J. D. Beaton, and J. L. Havlin, Soil Fertility
and Fertilizers, MacMillan, Indianapolis, Indiana, 1993.
Tonnessen, K. A., The Emerald Lake watershed study: Introduction
and site description, Water Resour. Res., 27, 1537-1539, 1991.
Westall, J. C., J. L Zachary, and F. M. M. Morel, MINEQL: A
computer program for the calculation of chemical equilibrium composition of aqueous systems, Tech. Note 18, EPA grant R-803738,
Dep. of Civ. Eng., Mass. Inst. of Technol., Cambridge, 1976.
Williams, M. W., and J. M. Melack, Solute chemistry of snowmelt and
runoff in an alpine basin, Sierra Nevada, Water Resour. Res., 27,
1575-1588, 1991.
Williams, M. W., R. C. Bales, A. D. Brown, and J. M. Melack, Fluxes
and transformations of nitrogen in a high-elevation catchment,
Sierra Nevada, Biogeochemisny, 28, 1-31, 1995.
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Sanford, Nitrogen saturation in the Rocky Mountains, Environ. Sci.
Technol., 30, 640-646, 1996a.
Williams, M. W., P. D. Brooks, A. Mosier, and K. A. Tonneson,
Mineral nitrogen transformations in and under seasonal snow in a
high-elevation catchment in the Rocky Mountains, United States,
Water Resour. Res., 32, 3161 3171, 1996b.
Wolford, R. A., and R. C. Bales, Hydrochemical modeling of Emerald
-
Lake watershed, Sierra Nevada, California: Sensitivity of stream
chemistry to changes in fluxes and model parameters, Limnot
Oceanogr., 41(5), 947 954, 1996.
Wolford, R. A., R. C. Bales, and S. Sorooshian, Development of a
hydrochemical model for seasonally snow-covered alpine water-
sheds: Application to Emerald Lake Watershed, Sierra Nevada,
California, Water Retour. Res., 32, 1061-1074, 1996.
R. C. Bales and T. Mebcner, Department of Hydrology and Water
Resources, University of Arizona, Harshbarger. Building 11, Tucson,
AZ 85721. (e-mail: [email protected]; [email protected])
A. Brown, Ventura Community College, Ventura, CA 93003.
(e-mail: [email protected])
(Received April 7, 1998; revised June 12, 1998;
accepted June 23, 1998.)
58
APPENDIX B - STREAM CHEMISTRY MODELING OF TWO WATERSHEDS IN
THE FRONT RANGE, COLORADO
59
American
Geophysical Union
2000 Fionda Avonue.
Wasnalgion. CC 20C,09
.1-202-462-6900
r'ax • 1-202-32B-0566
August 4, 1999
Mr. Torn Mcix.ner
Department of Hydrology and Water Resources
Room 203B , Building #11
P0 Box 210011
University of Arizona
Tucson, AZ 85721-0011
.
Dear Mr. Meixner:
We are pleased to grant permission for the use of the material requested for inclusion in your
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Trie A , e,an Guodlsys.cei Linon enmendasses Vee Earth sgrus: spa:, s.e , ses
Geodesy. Smsmology, AlmosphondSdlede<S, Georna;neliste and l'aleomag , evem
Ocean S,,ors..,os I tyd , ceo;), voic...snolo2y. Geochernst. -y a ne POI , C4 NY
To‘lorloylir.mn .S;JCe Physics and As•onarry
60
Stream chemistry modeling of two watersheds in the
Front Range, Colorado
Thomas Meixner, Roger C. Bales, Mark W. Williams', Don H. Campbell' and
Jill S. Baron'
Department of Hydrology and Water Resources, University of Arizona, Tucson
May 5, 1999
Received ; accepted Short title: FRONT RANGE WATERSHEDS
'Institute for Arctic & Alpine Res., University of Colorado, Boulder
2
USGS-WRD, Denver, Colorado
3
USGS-BRD, Fort Collins, Colorado
61
Abstract. We investigated the hydrologic, geochemical, and biogeochemical
controls on stream chemical composition on the Green Lakes Valley and Andrews
Creek watersheds using the Alpine Hydrochemical Model (ARM). Both sites
had comparable data sets from 1994 and 1996, including high-resolution spatial
data and high frequency time series of hydrology, geochemistry and meteorology.
The model of each watershed consisted of three terrestrial subunits (soil, talus,
and rock), with the routing between the subunits determined by spatial land
cover data. Using 1994 data for model calibration and 1996 data for evaluation,
AHM captured the dominant processes and successfully simulated daily stream
chemical composition on both watersheds. These results confirm our procedure
of using spatial, and site specific field and laboratory data to generate an initial
catchment model and then calibrating the model to calculate effective parameters
for unmeasured processes. A net source of nitrogen was identified in the Andrews
Creek watershed during the spring snowmelt period, whereas nitrogen was
immobilized in the Green Lakes Valley. This difference was most likely due to the
larger and more dominant area of talus in the Andrews Creek watershed. Our
results also indicate that routing of snowmelt through either soil or talus material
is sufficient for retention of H+ and release of base cations, but that N retention
is more important on areas mapped as soil. Due to the larger ionic pulse and
larger fraction of surface runoff the Green Lakes Valley was more sensitive to a
doubling of wet deposition chemistry than the Andrews Creek watershed
62
Introduction
The thin soils, limited vegetation, and snow dominated hydrology of alpine
regions limit their ability to buffer against changes in climate and atmospheric
deposition [Melack and Stoddard, 1991]. In the Front Range of Colorado, the
predicted response of alpine watersheds to changes in climatic and chemical
inputs has implications for the health of aquatic resources, and the setting of
emissions standards [Williams et al., 1996]. Due to their close proximity to
urban sources of air pollution, alpine catchments in the Colorado Front Range
are subjected to increased atmospheric deposition [Williams et al., 1996] and
are already undergoing N saturation, a process where previously N limited
systems begin to leak inorganic nitrogen [Aber, 1992; Williams et al. 1996].
More recently it has been hypothesized that areas of talus and the material
buried beneath talus are responsible for the high NO 3 concentrations observed in
-
early spring snowmelt and the high summertime concentrations observed in the
streams of the Front Range [Williams et al., 1997; Baron and Campbell, 1997].
Furthermore runoff flowpath exerts a large control on the stream chemistry, and
on the response to chemical perturbations of a watershed [Grosbois et al., 1988;
Campbell et al., 1995; Brown, 1998].
The Alpine Hydrochemical Model (AHM) was specifically designed to
investigate the problem of episodic acidification in alpine watersheds. AHM
differs from several other watershed acidification models such as MAGIC that
were designed with longer time steps to address questions of chronic acidification
[Cosby et al., 1985]. The problem of episodic acidification is especially important
in alpine watersheds due to the ionic pulse of chemicals in the snowpack and the
fact that even changes in watershed acidity of only three days can have an impact
63
on the aquatic biota of alpine watersheds [Barmuta et al., 1990]. The AHM uses a
conceptual representation of watershed hydrologic and biogeochemical processes
that differs from empirical approaches that have been developed for investigating
regional sensitivity to episodic acidification [Eshleman et al., 1995; Leydecker et
al., 1999]. This conceptual structure permits the investigation of the processes
and watershed properties that determine watershed sensitivity to acidification.
Areas of modeling uncertainty can be used to guide field research and improve
our understanding of alpine hydrologic and biogeochemical processes.
The Alpine Hydrochemical Model (AHM) was developed in part to improve
our understanding of how alpine watersheds will respond to perturbations
[Wolford et al., 1996]. AHM was initially used to simulate the hydrochemistry
of the 1.2 km' Emerald Lake watershed in the Sierra Nevada of California
[Wolford et al., 1996] and has since been applied to two watersheds near
Emerald Lake [Meixner et al., 1998]. Extension of the AHM to other alpine
catchments will improve both our confidence in the model and our understanding
of biogeochemical processes.
We applied the AHM to the Andrews Creek and Green Lakes Valley
watersheds of the Rocky Mountain Front Range to address four questions. First,
can the AHM describe the stream chemistry of these two watersheds using a
similar description of chemical processes as was used earlier to simulate the
Emerald Lake watershed in the Sierra Nevada? Second, what differences in
nitrogen dynamics exist between these two catchments, and how can the AHM
be used as a tool to investigate these differences? Third, since the physical
relationship between soil, exposed bedrock, and talus differs between these two
watersheds, what role does flow routing have in determining the hydrochemical
64
response of alpine watersheds? Finally, how do the models of these two
watersheds differ in their sensitivity to changes in atmospheric deposition?
Met hods
Site Green Lakes Valley and Andrews Creek are alpine watersheds in the Front
Range of the Rocky Mountains. Green Lakes Valley [Caine 1995] is part of the
Niwot Ridge Long Term Ecological Research site (LTER) and Andrews Creek
[Baron and Mast 1992] is part of the United States Geological Survey (USGS)
Water, Energy, and Biogeochemical Budgets (WEBB) program. In the Green
Lakes Valley, water quality for eight different locations along the first order
stream in the valley has been monitored since 1981. GLV4, the upper 2.2 km 2
of the 7 km 2 Green Lakes Valley, represents the alpine portion of the larger
catchment. GLV4 ranges in elevation from 3550 m at the outflow from Green
Lake 4 to over 4000 m at the continental divide with relatively equal areas of
rock (30%), talus (36%) and soil (30%) (Figure 1). The remaining 4% of the
watershed is covered by Green Lake 4 and 5. The soil in the Green Lakes Valley
is located along the valley floor and is adjacent to the stream. The areas of talus
are generally located up hill from the valley and drain into the soil. The areas
of exposed rock in the watershed are located most prominently along the tops of
ridges [Brown, 1998].
Andrews Creek, a catchment nested within the Loch Vale watershed, ranges
in elevation from 3200 to 4000 m and has an area of 160 ha. The watershed is
dominated by rock (57%), and talus (31%) (Figure 2). In contrast to the Green
Lakes Valley, soils (11%) are confined to a few areas of tundra and wetland soils
on the ridge line of the watershed and at the base of the watersheds respectively
65
[Walthall, 19851. Areas of talus dominate the valley bottom and are adjacent to
Andrews Creek.
The two watersheds share a common lithology of silver plume granite and
biotite gneiss [Cole, 1977; Pearson, 1980]. The hydrology of both watersheds
is dominated by a large wintertime snowpack that melts during the spring and
summer and frequent summer precipitation [Caine, 1995; Baron and Mast, 1992].
Both watersheds have no deep groundwater storage, and with the small volume
of soil present in the watersheds, there is little soil zone storage.
Both watersheds are drained by a single first order stream. Stream-water
discharge is monitored continuously at a gauging station at the base of each
watershed. Stream water samples are collected for chemical analysis at the same
locations. Both watersheds are topped by glaciers; GLV4, the 8-ha Arikaree
glacier, and Andrews, the 10-ha Andrews glacier.
Model structure The AHM [Wolford et al., 1996] is a lumped conceptual
model that was designed for simulating the hydrology and biogeochemistry of
alpine watersheds. Modeling a watershed with the AHM requires that a particular
structure be chosen to describe the hydrologic and biogeochemical cycles of a
watershed. The GLV4 and Andrews Creek watersheds were broken down into
three terrestrial subunits (soil, rock, and talus), with a single stream subunit.
The area and spatial relationships of soil, rock and talus were determined from
digitized soils maps [Brown, 1998; Walthall , 1985] For GLV4, flow from the rock
subunit was routed onto talus, and from there to the soil subunit before entering
the stream. For Andrews runoff from the rock and soil subunits, was routed to
talus and from there to the stream.
Each terrestrial subunit contains different compartments representing
66
the snowpack, snowpack free water, snowmelt, surface runoff, interception
by trees and litter, and zero, one or multiple soil horizons. Stream subunits
consist of different compartments representing the snowpack, snowpack free
water, snowmelt, stream ice, and streamflow (Figure 3). In addition to the
compartments described for the stream, lake subunits can be stratified with the
two lake layers varying in thickness. Hydrologic processes are modeled separately
from geochemical processes.
At each daily time step AHM adjusts snow covered area, computes
interception, adjusts snowpack for precipitation and melt, calculates influxes
of materials to each soil and rock subunit, drains surface runoff, computes
evapotranspiration and sublimation, calculates kinetic reactions, calculates
chemical equilibrium in soil compartments, drains water from the soil horizon,
calculates chemical equilibria in streams and produces output. Chemical
speciation is handled using equations adapted from MINEQL [Westall et al.,
1976]. One strength of the model is its precise mass and charge balance for both
chemical species and hydrologic calculations [Wolford et al., 1996].
Model Inputs Many model inputs for GLV4 were taken directly
from data downloaded from the Niwot Ridge LTER web site
(http://culter.colorado.edu:1030/). For Andrews, data were collected and
distributed as part of ongoing USGS efforts to study biogeochemical budgets
in the Loch Vale watershed [Baron and Campbell, 1997]. Inputs to the model
include: potential evapotranspiration (PET), potential sublimation (PS), snow
covered area (SCA), and precipitation quantity and quality.
Mean evapotranspiration from field measurements was used for both
catchments. During winter PET was set to 0.66 mm day -1 and 1.3 mm day-1
67
during the summer. PS was set to 75% of these values based on experience from
modeling evaporation at Emerald Lake [Wolford, 1992]. The model calculates
actual evaporation from soil and talus surfaces based on a parameter that defines
the fraction of PET that actually evaporates. (For this application evaporation
from soil was equal to PET and evaporation from talus was 0.9 of PET.)
Ingersoll [1995] developed a 1994 SCA time series for Andrews. Additional
SCA maps were developed from orthorectified airphotos of the Green Lakes
Valley in 1994 and 1996 and Andrews in 1996. For early dates (April 22, 1994 and
May 9, 1996), shaded areas were masked out during classification and classified
separately. These maps were evaluated using visual inspection, and classification
repeated until a good visual match resulted. SCA maps were overlayed with soils
maps to determine SCA for each subunit [Brown, 1998; Walthall, 1985]. Glaciers
were assumed to overlie talus.
For GLV4, precipitation quantity was recorded continuously at the Niwot
Ridge LTER D-1 meteorological station at the edge of the watershed (elevation
3743 m). The gauge is shielded by a snow fence and an alter shield to improve
estimates of precipitation during windy periods. Precipitation events were
classified as rain if mean daily temperature was above 0°C. Precipitation
chemistry is sampled weekly 2.2 km to the east of D-1 at the Niwot Ridge
Saddle Tundra Laboratory as part of the National Atmospheric Deposition
Program/National Trends Network [NADP/NTN, 1998; Peden, 1986] (Figure 4).
For Andrews, precipitation quantity was recorded continuously with two
Belfort rain gauges at a meteorological station in the nearby main valley of Loch
Vale watershed (elevation 3160 m). One gauge has a nipher wind shield and
the other has an alter wind shield. Previous studies have shown no significant
68
difference between the two and they are used interchangeably to produce the
most continuous record [Baron and Campbell, 1997; Bigelow et al., 1990].
Precipitation chemistry is sampled weekly at the same location as part of the
NADP/NTN [NADP, 1998] (Figure 4).
Two methods were used to estimate dry deposition to these watersheds.
Winter dry deposition for all species was calculated by subtracting winter wet
deposition from peak accumulation snowpits. Modeled summer N dry deposition
used the estimate of Baron and Campbell [1997] which was 1.3 kg ha -l yr'.
All other species were left at the values used for the Emerald Lake watershed
[Wolford 1992].
Parameter Estimation and Initial Conditions Using the model structure
defined by Wolford et al. [1996], field and laboratory measurements were used to
set most parameters and initial conditions, with remaining parameters estimated
by model calibration using 1994 stream chemistry data. Soil extent, depth and
bulk density were based on soil surveys [Brown, 1998; Litaor, 1985; Baron and
Mast, 1992] (Table 1). Mineral weathering rates based on a mass balance of the
entire Loch Vale watershed were used for both watersheds Mast et al. [1990]
(Table 2). Exchange coefficients and hydraulic conductivity parameters for the
soil and talus were set to the values for the Emerald Lake watershed. Depth
weighted averages of exchangeable ion amounts in soil were estimated using data
from Litaor [1985] and Walthall [1985]. Exchangeable cations for talus and soil
in GLV4 were assumed to be identical since no data were available for talus. For
Andrews, data for Entisols were used for the talus and values for Inceptisols used
for the soil subunit in Table 3. Parameters controlling sulfate adsorption were
based on data from Loch Vale [Baron et al., 1992], with a sulfate adsorption
69
capacity of 0.71 mmol kg -1 soil. Silica adsorption properties were based on values
from the Emerald Lake watershed [ Wolford et al., 1996]. Glaciers were assumed
to have a depth of 0.1 m of snow water equivalence (SWE) at the beginning and
end of the water year to allow for carry over of SWE from year to year and to
permit the identification of ablation or accumulation of the glacier.
Calibration Model calibration involved three steps: i) snowmelt optimization,
ii) chemical calibration, and iii) optimization of hydrologic parameters [Meixner
et al., 1998]. Snowmelt optimization estimated daily melt rates by subunit using
SCA and discharge to constrain the search for optimal snowmelt rates. As annual
discharge exceeded measured precipitation less estimated evaporation, snow was
added to both watersheds in both years to achieve mass balance.
Calibration proceeded as a stepwise adjustment of chemical parameters until
model output matched observations (Table 4). First, the ionic pulse parameter
(D) was adjusted to fit stream Cr. Second, cation exchange coefficients were
adjusted for each cation until modeled soil concentrations matched target values.
Third, SO ,i - adsorption parameters were changed to increase or decrease modeled
SO 42- concentrations in the soil and stream. Fourth, parameters governing N
consumption in the soil were altered to improve the fit to stream NO 3- and NH 4-Iconcentrations. N parameters were set at the beginning of each calendar month
and remained constant for the entire month. Finally, mineral weathering rates
and silica adsorption parameters and initial conditions were adjusted to capture
the observed Si concentrations. If necessary, hydrologic parameters were changed
to improve simulations. Model evaluation was done using inputs and stream
chemistry for 1996.
Calibration decisions and evaluation judgments were made by visually
70
comparing modeled stream time series with the available observations. For the
purposes of comparison the Nash-Sutcliffe statistic (coefficient of efficiency)
was calculated for the initial (uncalibrated) and calibrated models for both
watersheds for 1994 and 1996 for all species and hydrologic discharge. The
Nash-Sutcliffe value is calculated as:
1 0—
E = 1.0
.
E rt
P) 2
-
(
1
)
where, P is the predicted value, 0 is the observed, 0 is the mean observed value
and i is the observation number. A value of E less than zero indicates that the
mean of the observations is a better predictor of the observed data than the
model. Higher values (closer to 1) indicate better agreement between the model
and observations [Nash and Sutcliffe, 1970; Wilcox et al., 1990; Legates and
McCabe, 1999].
Results
Green Lakes Valley Optimization of water inputs and snowmelt achieved a
near perfect match between measured and modeled discharge except for a few
large rainfall events during the summer (Figure 5). Measured snowfall at D-1
in the 1994 water year was 1.05 m, while the model input was 1.11 m. In 1996,
measured snowfall at D-1 was 1.00 m, versus a model input of 1.35 m.
Little calibration was needed to improve the match between measured
and modeled stream concentrations, with soil chemical parameters being
most important. A total of 13 chemical parameters were adjusted from their
original Emerald Lake watershed (ELW) values during the calibration (Table
4). Adjusting hydrologic parameters, altering model structure, and adjusting
parameters controlling talus processes did not significantly improve modeled
71
stream chemical concentrations. After calibration, the match of model output
to measured stream concentrations was improved for much of both calibration
and evaluation years (Figure 5 and Table 5). Model results show day to day
variability not present in the data, due in part to sampling interval and in part
to comparing modeled stream to observed lake outflow.
The best matches of modeled and measured stream concentrations were for
ANC, pH and Nat. Only after water year day (WYD) 320 (August 20th) was
ANC overpredicted, with a small underprediction at the initiation of snowmelt
(around WYD 215, May 1st). Na + predictions were very good, especially when
compared to the initial model run, with some overprediction after WYD 320
(August 20th).
Predictions for Ca 2 + were not as good as for Na+. Early to mid-winter
(WYD 1-150, October 1st to March 1st) concentrations are overpredicted by the
model, while melt season (WYD 200-250, April 20th to June 10th) concentrations
are underpredicted. In general the matches between modeled and observed
SO, Me+, and K+ (not shown) were very good for the 1994 simulation and
simulation difficulties were similar as those for Ca 2 +.
The monthly calibration of nitrogen parameters resulted in a very good
fit between measured and modeled NO concentrations. Modeled values were
somewhat higher than observed during the initial stages of snowmelt (around
WYD 215, May 1st) for both 1994 and 1996. This is most likely due to the
high value used for snowpack elution (Table 4). The high value for the elution
parameter was necessary in order to capture the high Cl - concentrations in
1994 and avoid overpredicting the late summer concentrations. However, the
high value for the elution parameter also resulted in faster than observed Cl-
72
release from the snowpack in 1996. We were unable to match the observed C1
concentrations in the first half of the water year using this model structure.
Andrews Creek The meteorological station estimate of snowfall was 0.78 m
and 0.98 m for 1994 and 1996 respectively, versus model inputs, to meet mass
balance requirements, of 1.03 m and 1.28 m. After optimization there was a near
perfect match between measured and modeled watershed discharge, except for
following a few large summer rains (Figure 6).
The main improvement to the match between measured and modeled stream
concentrations came from adjusting only 12 parameters (Table 4), 11 of which
controlled processes in the talus subunit and the other parameter controlling
stream Pc 02 . Though many of the parameters controlling processes in the soil
subunit were adjusted, none significantly improved model performance (Figure
6 and Table 6). Both the mean and variability of the data are simulated well
by the calibrated model in both years with the partial exception of NO 3 , Si and
-
ANC. Despite monthly calibrated values of parameters for immobilizing NH T
and NO 3 , the spring snowmelt portion of the simulation (between WYD 220 and
-
275, May 10th to July 1st) underpredicts NO 3 concentrations.
-
The model captured the mean ANC for the season, but not the seasonal
trend of ANC. Early season predictions (before WYD 250, June 10th) are too
low while mid season predictions (WYD 250-280, June 10th to July 10th) are
too high for both 1994 and 1996.
Despite the general agreement between model simulation and observations
for Ca+, there is still disagreement between model and measured values. The
results for Ca+ typify those of cations and S0. Early season values are slightly
below measured values and late season predicted values (after WYD 325, August
73
20th) are below measured values (Figure 6).
Discussion
Model Performance The models of GLV4 and Andrews Creek were effective
in capturing the mean and seasonal variability of the observed stream chemistry
for both a calibration and an evaluation year. The models were effective by fitting
a few parameters and using field data to set model initial conditions, model
inputs, and several model parameters. Even though the model construction
and calibration can be considered a success, it was a variable one, with some
measurements better matched than others by the model.
Discharge was modeled successfully, due in large part to the snowmelt
optimization scheme. Optimization for GLV4 resulted in 11% and 35%
increases in modeled SWE over the amount measured at D-1 for 1994 and 1996,
respectively. At Andrews the increases were 25% and 24% for 1994 and 1996
respectively. The need to add additional snow may arise from i) estimates of
evaporation (and sublimation) that are too high, ii) underestimates of snowfall iii)
snow blown into the watersheds from over the Continental Divide or iv) ablation
of the Arikaree or Andrews glaciers. The estimates of evaporation we used are,
if anything, too low; the results of Hartman et al. [1999] indicated much higher
rates of evaporation. More likely is differences in total precipitation between the
two watersheds modeled and the precipitation gauges due to orographic effects.
It is also likely that snow is blown into both watersheds from over the continental
divide [Baron and Denning, 1992]. There is no available data concerning the
ablation of either the Andrews or Arikaree glaciers during the 1994 and 1996
water years.
74
There was some overprediction of discharge for several summer storms on
both watersheds (Figures 5 and 6), especially the large storms around WYD
300 (July 30th) in both 1994 and 1996 on GLV4. For the Andrews Creek
watershed in 1994 discharge for the storm after WYD 320 (August 16th) was
also vastly overpredicted by the model. That particular storm was also greatly
overpredicted by Hartman et al. [1999] when they simulated discharge for the
whole Loch Vale watershed using the RHESSys modeling package [Band et al.,
1993]. The overprediction of summer rainfall peak discharges may be due to
insufficient soil zone storage in both models, or using incorrect precipitation
measurements as input to the models. The AHM model also overpredicted
flows at the beginning of snowmelt, indicating that soil moisture status was not
accurately calculated during the mid-winter period. Both problems in modeling
discharge indicate a need to increase infiltration rates and subsurface water
storage in both watersheds.
The AHM was variably successful at predicting stream concentrations during
both 1994 and 1996, suggesting that the major processes controlling stream
chemical concentrations for both watersheds are captured by their respective
models. Information about the model and about the calibration procedure can
be garnered from investigating the Nash-Sutcliffe values for GLV4 and Andrews
for the calibrated and uncalibrated watershed models as well as by comparing
the results for the calibration and evaluation years. The Nash-Sutcliffe values
for Ca 2 +, ANC, K+, and Mg 2 + were closer to 1.0 for the evaluation year of
1996 than they were for the calibration year of 1994 for both watersheds. This
result indicates that the calibration was not overly tuned to the observational
data from 1994 (Tables 5 and 6). Therefore, we can be more confident in our
75
calibration procedure in general and the particular parameter values arrived at
in this analysis.
Model predictions for Si, N11 4-1", and Cl - in particular were inferior to the
observational mean as stream composition predictors (Tables 5 and 6). Silica
has an observable hysteresis in stream chemistry of Andrews Creek [Campbell
et al., 1995 ] . This hysteresis may be because of soil solution and talus solution
flushing processes not currently incorporated into the AHM models of these
two watersheds [D. W. Cow, personal communication]. The observed NH -44concentrations in both watersheds would be difficult for any model to simulate
due the almost random nature of the observed values. Still the AHM currently
nitrifies or immobilizes all NH in the snowpack on contact with the soil or soil
litter. These results indicate that an alternative scheme should be developed.
The Cl - simulations were significantly worse when compared to the mean of
the observations for 1996 than they were for 1994. The deterioration of the
simulations in the evaluation year of 1996 most likely represents a change in the
real ionic pulse between these two watersheds. While Cl - deposition was higher
in both watersheds in 1996 (Figure 3), the overprediction of spring snowmelt
stream Cl - concentration during 1996 indicates that there may be differences
in snowpack maturation between the two years [Harrington and Bales, 1998].
Unfortunately, there was no detailed snowpit data available to evaluate this
hypothesis.
Other problems with the models are only evident by looking at the time
series results. For example, late season cation concentrations for GLV4 are
overpredicted. Possible causes of this overprediction include: i) high soil percent
base saturation in the model, ii) too much soil and talus in the model, or iii)
76
not enough snowmelt routed through the soil, preventing depletion of the cation
exchange complex during snowmelt. Of these three possible causes the first is
the most likely, since the base saturation values for GLV4 are high for alpine
watersheds. The second goes against the hydrologic results for the summer
rainfall events, which were overpredicted, indicating that the model needs more
not less soil. The third item is plausible since model calculations of soil drainage
and surface runoff indicate only 70% of snowmelt comes in contact with soil.
While, the Nash-Sutcliffe results indicated a conflict between the magnitude
of the ionic pulse between the two years, the time series results indicate an
underprediction of winter stream Cl - at GLV4. This result indicates either a
weathering source of Cl - not included in the model, summer dry deposition of
Cl - at a greater rate than those used, or a pool of evaporated water in the GLV4
that provides the wintertime source of CI .
-
Base Saturation and pH The overprediction of late season stream cation
concentrations and the need to increase the stream P co , (Table 4) from that of
the ambient atmosphere indicate that the base saturation of soils in the model
of GLV4 is too high. The GLV4 has a soil base saturation that is 50% greater
than the average base saturation in Andrews Creek. Also, the cation exchange
capacity of the soils of GLV4 is nearly twice that of Andrews Creek (Table 3).
One result of this high CEC and base saturation is that the pH of soil water,
after degassing to atmospheric P co „ will be much higher at GLV4 compared to
Andrews Creek. Note the 0.3 pH difference between the calibrated (Pco, 10 -3.1
atm) versus uncalibrated (10 -3A atm) models of GLV4 (Figure 5).
There are several possible causes for the difference between the ambient
atmosphere Pco, and the calibrated Pco, of the stream. First, the real Pco, of
77
the samples may be below atmospheric P co , due to the grab sample methodology
of sample collection. Grab sampling prevents the degassing of CO 2 since a
sample is capped immediately while stream samples taken with an autosampler
(like those at Andrews Creek) are allowed to equilibrate with the atmosphere
over the days to weeks that the sample sits in the auto-sampler [Melack et al.,
1998]. Second, during winter and early spring lake ice may prevent the degassing
of CO 2 that accumulated due to respiration in the stream and lake. Third, these
results may indicate that the base saturation of GLV4 is now much lower than
measured in the mid 1980's, due to either errors in measurement or a real decline
in base saturation.
Cation concentrations and alkalinity have declined in the streams of Green
Lakes Valley [Caine, 1995], a phenomenon that, if occurring more widely in the
Front Range, will have policy implications in setting critical loads for atmospheric
deposition to the region. The hypothesis that base saturation has declined can
be tested by modeling GLV4 farther back in time using stream chemistry data
that is available back to 1981, but proxy data would be needed to extend the
time series of hydrologic information farther back.
Nitrogen Dynamics The model succeeds in matching the NO 3 concentrations
-
in part because it has been calibrated to match them on a month by month
basis. Few conclusions can be drawn from the ability of the model to capture the
seasonal variability of NO 3 ; however, it is useful to see what model output looks
-
like when all NO 3 is leached and all NI-It is nitrified and when the N reactions
-
are turned completely off (Figure 7). These different sensitivity tests were used
to identify and quantify the relative importance of nitrification, mineralization
and immobilization on the stream chemical composition of mineral nitrogen.
78
The N sensitivity results show that during the early part of the snowmelt
season (WYD 230 until 270) nitrification and immobilization are necessary for
the model of GLV4 to explain the measured NO 3 and NH 4E concentrations.
-
- -
This result is in contrast to Andrews Creek where AHM modeling indicates
a significant source of NO 3 from the watershed during snowmelt. For NH,
--
the sensitivity results indicate that nearly all N11,IF is assimilated or nitrified
-
on both watersheds. During the summer, observed stream NO 3* concentrations
-
indicate a significant NO3 sink on both watersheds. The summertime peak of N
-
consumption indicates vegetative, or soil microbial control of NO 3 in the GLV4
--
and Andrews Creek watersheds. There is undoubtedly stream NO 3 in both
-
watersheds from mineralization and nitrification. Our results indicate that GLV4
has a large N-sink that consumes more of atmospheric N deposition than does
Andrews. The larger N-sink is most likely due to the dominance of soil in the
valley bottom of GLV4. Soil is expected to be more biologically active than talus
and thus able to retain more N.
Flow Routing The results for these two watersheds, combined with those from
previous work at Emerald Lake [ Wolford et al., 1996] and two other Sierra Nevada
watersheds [Meixner et al., 1998], indicate that most snowmelt contacts either
soil or talus long enough to exchange hydrogen ions for cations and to undergo
other geochemical transformations. Furthermore, the sensitivity of parameters
for a particular terrestrial subunit depends on the flow routing parameters within
the AHM. For GLV4, all runoff was routed through the soil before reaching the
stream. At Andrews Creek, all runoff was routed through talus before reaching
the stream. At Emerald, half of the stream discharge came from talus while the
other half was from soil. For GLV4, the soil exchange parameters and hydrologic
79
parameters of the talus subunit had no effect on model output, while the soil
hydrologic and chemical parameters of the soil subunit were fundamental in
determining stream chemical composition. The opposite was true at Andrews.
Emerald Lake was intermediate with some talus and some soil parameters
important in determining model predictions. These model results indicate that
the observed stream chemistry has a similar dependence on the structure of the
landscape and the land cover most hydrologically connected to the stream.
Andrews and GLV4 also differ in the fraction of stream discharge that is
surface overland flow. Our model results show that there is virtually no surface
runoff on the soil and talus in Andrews, while for GLV4 about 30% of total
hydrologic flow for the soil and talus subunits occurs as surface overland flow.
These differences as well as the differences in flow routing between subunits for
the two watersheds highlight the first order importance of spatial and vertical
flow routing to the hydrochemical response of alpine watersheds.
Our results indicate the need for more intensive field measurements of flow
routing, including tracer tests, isotopic and geochemical mixing models, soil
wetness observations, and soil chemical observations, for determining the actual
hydrologic routing in these watersheds. Additionally more robust watershed
hydrologic models, such as TOPMODEL [Beven and Kirby, 1979], should be
evaluated as tools to support field observations and to aid in parameterizing flow
routing for the AHM.
Sensitivity to Deposition Doubling N deposition resulted in small
depressions in ANC and pH at GLV4 (Figure 8 and Table 7). The average ANC
depression and II+ increase of 3.4 and 0.1 peqL -1 , respectively, are similar to
the values (3.8 and 0.1 peqL -1 respectively) observed for the Emerald Lake
80
watershed under conditions of doubled wet N and S0 42 - deposition [Meixner et
al., 1998]. The Andrews Creek watershed model exhibited less sensitivity to
increases in atmospheric deposition than GLV4, with ANC depression and H+
increase of 2.0 and 0.02 pec1L -1 respectively (Figure 9 and Table 7) [Wolford et
al., 1996]. The slightly lower sensitivity of Emerald despite its lower CEC and
base saturation is probably due to the the very dilute nature of precipitation in
the Sierra Nevada. The lower sensitivity of Andrews to increases in deposition is
probably due the the significant increase in Ca2 + export observed under increased
deposition (Table 7) due to the greater contact of deposition with talus than in
GLV4.
The maximum concentration change due to doubling wet deposition (Table
7) gives a snapshot of the two watershed's sensitivity to episodic acidification.
The results indicate that GLV4 is more susceptible to episodic acidification
than is the Andrews Creek watershed. The maximum ANC depression and H+
increase for GLV4 were 32.2 and 2.9 yeqL -1 respectively, while for Andrews
they were 7.4 and 0.97 peciL -1 respectively. The greater sensitivity of GLV4 to
episodic acidification is due to the larger ionic pulse (D value of 10.0) as opposed
to Andrews Creek (3.4). The two Rocky Mountain watersheds are more sensitive
probably due to the much larger deposition currently occuring.
The result that GLV4 is more sensitive than the Andrews Creek watershed
agrees with the results of Wolock et al. [1989]. They found that watersheds
with less contact time and more surface runoff were more sensitive to acid
deposition. In our case the model of GLV4 had more surface runoff and thus less
soil contact than the Andrews Creek watershed. A model test was done in which
soil hydraulic conductivity was increased to eliminate surface runoff. Under this
81
scenario (results not shown), GLV4 was less sensitive to increased N deposition
than the Andrews Creek watershed. This sensitivity result gives further force to
the need for a more robust investigation of flow routing in alpine watersheds.
Conclusions
Five lessons were learned from this application of the AHM to the upper
portion of the Green Lakes Valley and the Andrews Creek watersheds. First,
calibration involving specification of flow routing and measured parameters
followed by fitting of soil and talus parameters that were not explicitly measured
was effective in capturing the observed stream chemical composition of the
catchments. This procedure should be followed in using AHM to simulate
other watersheds. Second, the Andrews Creek watershed releases significantly
more mineral N than GLV4. This is especially true during spring snowmelt
when the Andrews Creek watershed was a net source of mineral N. The greater
release of mineral N is most likely related to the dominance of areas of talus
in the Andrews Creek watershed. Third, snowmelt contacts either soil or talus
sufficiently long to undergo geochemical transformation. Still, independently
parameterized routing is necessary since nitrate retention, apparently biologically
related, is more important on areas mapped as soil as opposed to areas mapped
as talus. Fourth, GLV4 is more sensitive to changes in atmospheric deposition
than the Emerald Lake or Andrews Creek watersheds were on an average and
episodic basis. However, this result is dependent upon a confident estimate of
flow routing in both of the watersheds. Finally, our results indicate that the
soil base saturation estimated from measurements at GLV4 in the mid-1980's is
higher than supported by the model of stream composition developed here. This
82
result suggests that the base saturation of GLV4 soils was either not measured
properly in the 1980's or that soil base saturation has decreased over the past 15
years.
Acknowledgments. The
1996 aerial photographs for both watersheds were
orthorectified by B. Balk. The 1994 aerial photographs for Green Lakes Valley were
orthorectified by F. Rojas. Maps of snow covered area for Andrews Creek provided by
G. Ingersoll and M. Hartman,
orthorectified by D. Cline. Digitized soils map of Loch
Vale was provided by M. Hartman. Funding for the original data collection and field
work that this work depends on was funded by the National Park Service, the
USGS
and the National Science Foundation (LTER-DEB 9211776 and EGB EAR-9523886).
Funding for the primary author was provided by a Canon National Park Science
Scholarship. Additional support provided by the National Aeronautics and Space
Administration (NAGW-2602). R. Brice and K. Meixner assisted in manuscript
preparation.
83
References
Aber, J. D., Nitrogen cycling and nitrogen saturation in temperate forest
ecosystems, Tree, 7, 220- 224, 1992.
Baron, J. S., and D. H. Campbell, Nitrogen fluxes in a high elevation Colorado
Rocky Mountain basin, Hydrological Processes, 11, 783-799, 1997.
Baron, J., and A. S. Denning, Hydrologic budget estimates, in Biogeochemistry
of a Subalpine Ecosystem: Loch Vale Watershed, edited by J. Baron,
Ecological Studies Series 90, Springer-Verlag, 1992.
Baron, J., and M. A. Mast, Regional characterization and setting for the Loch
Vale watershed study, in Biogeochemistry of a Subalpine Ecosystem:
Loch Vale Watershed, edited by J. Baron, Ecological Studies Series 90,
Springer-Verlag, 1992.
Baron, J., P. M. Walthall, M. A. Mast, and M. A. Arthur, Soils, in Biogeochemistry
of a Subalpine Ecosystem: Loch Vale Watershed, edited by J. Baron,
Ecological Studies Series 90, Springer-Verlag, 1992.
Beven, K., and M. J. Kirby, A physically based, variable contributing area model
of basin hydrology, Hydrological Sciences Bulletin, 24, 43-69, 1979.
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and alter-shielded Universal Belfort precipitation gages at two Colorado
deposition monitoring sites, Environmental Science and Technology, 24,
758-760, 1990.
Brown, S. M., Hydrologic Sources, Flowpaths, and Residence Times Along a
Longitudinal Gradient in the Green Lakes Valley, Colorado Front Range,
84
USA, Master's thesis, Department of Geography, University of Colorado,
Boulder, CO, 67 p., 1998.
Caine, N., Temporal trends in the quality of streamwater in an alpine
environment: Green Lakes Valley, Colorado Front Range, U.S.A,
Geografiska Anna ler, 77A, 207-220, 1995.
Campbell, D. H., D. W. Clow, G. P. Ingersoll, A. Mast, N. Spahr, and J. T. Turk,
Processes controlling the chemistry of two snowmelt dominated streams in
the Rocky Mountains, Water Resources Research, 31, 2811 2821, 1995.
Grosbois, E. D., R. P. Hooper, and N. Chistophersen, A Multisignal Automatic
Calibration Methodology for Hydrochemical Models: A Case Study of the
Birkenes Model, Water Resources Research, 24, 1299-1307, 1988.
Harrington, R., and R. C. Bales, Modeling ionic solute transport in melting
snow, Water Resources Research, 34(7), 1727-1736, 1998.
Hartman, M. D., J. S. Baron, R. Lammers, D. Cline, L. Band, G. Liston, and
C. Tague, Simulations of snow distribution and hydrology in a mountain
basin , Water Resources Research, 35, in press, 1999.
Ingersoll, G. P., Estimating Snowmelt Contribution to the Seasonal Water
Balance in a Small Alpine Watershed, Master's thesis, Department of
Geography, University of Colorado, Boulder, CO, 137 p., 1995.
Litaor, M. Z., Soil genesis and soil water chemistry in the Green Lakes Valley,
Colorado Front Range, 1982-1983, Long-Term Ecological Research Data
Report DR-85/2, University of Colorado, Boulder, Colo., 1985.
85
Mast, M. A., J. I. Dreyer, and J. Baron, Chemical weathering in the loch vale
watershed, rocky mountain national park, colorado., Water Resources
Research, 26, 2971 2978, 1990.
Meixner, T., A. D. Brown, and R. C. Bales, Importance of biogeochemical
processes in modeling stream chemistry in two watersheds in the Sierra
Nevada, California., Water Resources Research, 34, 3121- 3133, 1998.
Melack, J. M., and J. L. Stoddard, Acidic deposition and aquatic ecosystems:
Sierra Nevada, California, in Regional Case Studies: Acidic Atmospheric
Deposition and Ecological Consequences, edited by D. F. Charles, 503- 530,
Springer-Verlag, New York, NY, 1991.
NADP/NTN Data Base, National Atmospheric Deposition Program (NRSP3)/National Trends Network., NADP/NTN Coordination Office, Illinois
State Water Survey, 2204 Griffith Drive, Champaign, IL 61820, 1998.
Peden, M. E., Methods of collection and analysis of wet deposition, technical
report 73, Illinois State Water Survey, 1992.
Westall, J. C., J. L. Zachary, and F. M. M. Morel, MINEQL A computer program
for the calculation of chemical equilibrium composition of aqueous systems,
Dept. of Civil Engineering, M.I.T., tech. Note No. 18, EPA Grant No.
R-803738, 1976.
Williams, M. W., J. S. Baron, N. Caine, R. Sommerfeld, and J. R. Sanford,
Nitrogen saturation in the Rocky Mountains, Environmental Science and
Technology, 30, 640-646, 1996.
Williams, M. W., T. Davinroy, and P. D. Brooks, Organic and inorganic nitrogen
pools in talus fields and subtalus water, Green Lakes Valley, Colorado
86
Front Range, Hydrological Processes, 11, 1747-1760, 1997.
Wolford, R. A., Integrated hydrochemical modeling of an alpine watershed:
Sierra Nevada, California, technical report 92-040, The University of
Arizona, Dept. of Hydrology and Water Resources, 1992.
Wolford, R. A., and R. C. Bales, Hydrochemical modeling of Emerald lake
watershed, Sierra Nevada, California: Sensitivity of stream chemistry to
changes in fluxes and model parameters, Limno logy and Oceanography,
1 (5), 947-954, 1996.
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model for seasonally snow-covered alpine watersheds: application to
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Research, 32W, 1061 1074, 1996.
This manuscript was prepared with the AGU LATEX macros v3.0.
87
Table 1. Soil Physical Properties
Property
GLV4
Andrews
Talus
Soil
Talus
Soil
Area, ha
81.3
68.0
51.21
17.82
Pb, g cm -3
1.1
1.3
1.1
1.3
Depth, m
0.25
0.30
0.26
0.30
K sat , cm day'
400
400
400
400
88
Table 2. Mineral Weathering Rates
a
Value
H+
Ca 2 +
Mg 2 +
Na +
K+
Si0 2
S0 24 -
Anion
mol yr -1
7380
21310
6070
11800
3440
27050
1970
19350
mol day -1
20.211
58.4
16.6
32.34
9.43
74.1
5.39
53
k 2 /10 - " a
0.586
1.69
0.481
0.91
0.274
2.15
0.156
1.53
k2 is model stoichiometric parameter and it defines the mol day' of a given
species that weather when multiplied by soil volume, soil bulk density, and
specific surface area.
89
Table 3. Soil chemical properties
Property
Andrews Talus
Andrews Soil
GLV4
CEC, meg kg -1
67
76
138
PBS b , %
52
70
85
Ca 2 + c , meg kg -1
mg 2+c , meg kg-i.
27.5
38
102
4.1
13
11.6
K+c, meg kg'
1.7
1.6
2.6
Na, meg kg -1
1.4
1.0
0.8
a
Cation Exchange Capacity, expressed in meg of charge per kg of soil.
b
Percent base saturation, the percent of the total CEC that is occupied by base
cations as opposed to hydrogen ion or aluminum ions.
c Quantity of exchangeable ion, by species, in the soil.
90
Table 4. Fitted parameter values
ELW
Andrewsa
GreenLake4a
1.25
10.25
1.25
log Pco 2 stream (atm)
-2.9
-3.4
-3.1
Snowpack elution parameter DC
4.0
3.4
8.0
Talus Log K-Ca 2 + d
-6.15
-5.63
-6.15
Talus Log K-Mg 2 + d
-6.00
-5.83
-6.00
Talus Log K-K+ d
-1.00
-1.30
-1.00
Talus Log K-Na+ d
-2.95
-2.15
-2.95
Soil Log K-Ca 2 + d
-5.23
-5.23
-4.83
Soil Log K-Mg 2 + d
-5.73
-5.73
-5.03
Soil Log K-K -E d
-0.85
-0.85
-1.20
Soil Log K-Na+ d
-3.01
-3.01
-2.11
Log K-S0 42 - e
17.45
17.95
17.70
Log K-Sie
27.63
27.93
27.88
95
90
70
aNH3toONg
0.989
0.000
0.200
aNO3toONg
0.70
0.5
0.5
NC4-baseg
8 x 10 -6
5 x 10 -5
3 x 10 -5
0.16
0.16
0.18
Parameter
Deep K
at ,
cm day'
Exchangeable Si f
ah
a
For Andrews Creek soil parameters had no effect on model output. For Green
Lakes Valley talus parameters had no effect on model output. This result is
discussed more extensively in the text.
b
Deep hydraulic conductivity refers to lower horizon hydraulic conductivity.
91
• Represents ratio of initial solute concentration in snowmelt to snowpack
average. All other elution parameters were unchanged from ELW.
d
Log K for exchange of cation with H+ on cation exchange site.
e Log K's for adsorption of SO 42- and H 2 SiO 3 .
e The model contains a Si exchange complex. The numbers in this row refer to
initial condition of complex by % saturation of exchange sites. Total site
concentrations from ELW optimization were used here.
g These three parameters govern the two N reactions present in AHM:
NILT OrganicN H+
NH,t + 20 2 N%- + 2H+
aNH3toON determines what percent of the NI-1 4-F is converted into organic N
with the remainder being nitrified. NO 3- -base determines a minimum
concentration of NO 3- over which a fraction of the NO 3- as governed by
aNO3toON is converted into organic N.
h
The weathering coefficients a is part of the weathering equation:
Mol =Axkx[Hl a where Mol is moles added to the subunit, A is total area of
the surfaces involved in reactions, [H+] is hydrogen ion concentration, and k and
a are constants. The total surface area is determined as the product of the soil
depth, area, bulk density, and specific surface area.
92
Table 5. Nash-Sutcliffe Values for Green Lakes Valley 4
1994
1996
Species
Uncal.
Cal.
Uncal.
Cal.
ANC
-7.7
-0.32
-3.32
0.49
Ca 2 +
-1.3
0.22
0.12
0.59
-0.20
-0.01
-0.02
-0.31
K+
-1.2
-0.38
-0.74
0.16
Mg 2 +
-27.5
0.25
-13
0.63
Na +
-150
0.12
-130
0.28
N11 4 "
-0.45
-0.44
-0.88
-0.88
NO
0.23
0.74
0.36
0.35
H+
-1.7
0.065
-1.9
-1.3
Discharge
0.97
0.98
0.99
0.99
Si
-2.7
0.015
-0.37
-0.086
SO ?i -
-43.1
-0.71
-12
0.53
93
Table 6. Nash-Sutcliffe Values for Andrews Creek Watershed
1994
1996
Species
Uncal.
Cal.
Uncal.
Cal.
ANC
-0.36
-0.11
-2.0
0.12
Ca 2 +
-0.40
0.79
0.48
0.90
Cl -
0.18
0.22
-5.9
-3.6
K+
-4.1
0.29
-2.0
0.34
Mg 2 +
-2.0
0.31
-0.44
0.86
Na+
-50
0.66
-55
0.045
NETt
-0.15
-0.15
-1.3
-1.32
NO
-0.56
0.06
-.14
0.52
H+
-310
-0.056
-7.5
0.14
Discharge
0.98
0.95
-.92
0.92
Si
-12
-2.5
-3.25
0.04
S0 42 -
-17
0.58
-18.6
0.10
94
Table 7. Concentration changes with doubling of N deposition
Average Change
GLV4
Maximum Change
Andrews
GLV4
Andrews
Species
1994
1996
1994
1996
1994
1996
1994
1996
ANC, yeciL -1
-2.3
-4.6
-1.7
-2.4
-32.2 -28.2
-3.5
-7.4
H+, peqL -1
0.07
0.18
0.014
0.025
0.87
2.9
0.033
0.097
Ca2 +, peqL -1
0.7
0.3
4.7
4.7
8.0
4.1
11.4
12.0
peqL -1
2.6
5.5
8.7
9.7
34.5
35.2
21.3
23.6
-0.60
-0.80
-2.9
-1.9
-3.5
-3.8
peqL -1
-0.45 -0.20
95
Figure 1. Land cover map for Green Lakes Valley watershed.
Figure 2. Land cover map for Andrews Creek watershed.
Figure 3. Modeled watershed compartments: a) soil subunits have compartments
including 1) rainfall litter interception, 2) snowfall canopy interception, 3) rainfall
canopy interception, 4) snowpack, 5) snowpack free (liquid) water, 6) snowpack
drainage, 7) surface runoff leaving the subunit, 8) soil drainage leaving the subunit,
9) contributed soil drainage, 10) contributed surface runoff, 11) litter storage
beneath the snowpack and 12) one or more soil horizons. Rock subunits (not
shown) do not include compartments 2, 3, 8, and 12. Stream subunits b) have
compartments including the a) snowpack, b) snowpack free water, c) snowpack
drainage, and d) streamfiow; stream ice is not tracked other than present or absent.
Figure 4. Annual average volume weighted mean precipitation chemistry for
GLV4 (a, 13) and Andrews (c, d) for 1994 and 1996. Data was collected at NADP
sites located near each watershed.
Figure 5. Modeled GL4 inflow and measured stream chemical concentrations
for the outflow of Green Lake 4. Dotted line is final calibrated model, pluses are
data, and dashed line is uncalibrated model using field and Andrews results for
model parameter values. Water year day 1 is October 1st.
Figure 6. Observed and modeled stream chemical concentrations for the Andrews
Creek. Dotted line is final calibrated model, pluses are data, and dashed line is
uncalibrated model using field and Emerald Lake results for model parameter
values.
Figure 7. Nitrogen reactions and effects for models of both watersheds.
96
Figure 8. Sensitivity of Green Lake 4 model to doubled nitrogen deposition
chemistry. Dotted line is current conditions and solid line is model output for
doubled deposition.
Figure 9. Sensitivity of Andrews watershed model to doubled nitrogen deposition
chemistry. Dotted line is current conditions and solid line is for doubled
deposition.
97
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106
APPENDIX C - A NITROGEN DYNAMICS MODEL FOR ALPINE BASINS
107
A Nitrogen Dynamics Model for Alpine Basins
Thomas Meixner
Dept. of Hydrology and Water Resources, University of Arizona, Tucson, AZ
108
Abstract
Several ecosystems in the western US are already undergoing nitrogen saturation, a
condition where previously N limited ecosystems become N sources. Due to the
complexities of terrestrial carbon-nitrogen dynamics, modeling is required to understand
the effects of increases in nitrogen deposition. Existing carbon nitrogen models do not
permit easy coupling to hydrologic models. Also existing models do not contain the full
effects of snow cover on carbon and nitrogen processes. For these reasons a nitrogen
model for alpine ecosystems was developed to fully implement the effects of snow cover
into a carbon nitrogen model. The model was also constructed to permit ease of interface
with hydrologic and energy transfer models. The model was applied to the Emerald Lake
watershed. The model adequately simulated major terrestrial carbon and nitrogen pools
and fluxes. The model over predicted observed stream nitrate concentrations. The model
duplicated the gradual decline in stream nitrate at the Emerald Lake watershed observed
over the last 15 years but the model shows an increase in stream nitrate before the real
watershed. The model also predicts an earlier spring peak in nitrate concentration than
the real watershed. This may be due to the fact that the model is simulating soil nitrate
concentration not stream concentration, or it may be due to hydrologic lag or mixing not
currently represented in the model.
109
Introduction
Over the last several decades there has been increasing concern about the damage
that human perturbations to the nitrogen cycle may be causing [Galloway et al., 1995]. A
particular focus for the forested and wildland catchments of the world has been the
increase in atmospheric deposition of reactive nitrogen to remote watersheds throughout
the world. The increases in atmospheric deposition appear to have caused an increase in
nitrate export from forested, chaparral, subalpine and alpine catchments. Many have
hypothesized that long term increases in atmospheric deposition of nitrogen have resulted
in a decreased ability of terrestrial ecosystems to retain additional inputs of nitrogen
[Fenn et al., 1998] [Henriksen and Brakke, 1988; Aber et al., 1989; Stoddard, 1994]. In
the urbanizing western U.S. the Front Range of the Rocky Mountains and the chaparral
and coniferous zones around Los Angeles are currently undergoing nitrogen saturation
[Baron et al., 1994; Williams et al., 1996; Fenn et al., 1998]. The alpine zone of the
Sierra Nevada Range could undergo nitrogen saturation with increased atmospheric
deposition that could result from the ongoing urbanization of the Central Valley,
California [Jim Sickman, personal communication].
While increases in atmospheric deposition to terrestrial ecosystems have been
implicated in the rise in nitrate concentrations in aquatic ecosystems, the link is difficult
to prove due to the complexities of the terrestrial carbon-nitrogen cycle [Parton et al.,
1993; Baron et al., 1994]. Large pools of nitrogen already on the landscape prevent
simple cause effect assumptions about the correlation between increased atmospheric
110
deposition and increases in nitrate export from terrestrial ecosystems. In fact a diverse
array of causes may result in the effect of increasing nitrogen export from an ecosystem,
including: changes in climate, history of disturbance, fife history, soil freezing,
wintertime snowpack, and drought [Sickman and Melack, 1998]; [Brooks et al., 1996];
[Fenn et al., 1998; Aber et al., 1998].
Due to the impact that increased nitrogen deposition can have on aquatic
ecosystems and the complexity of the problem a unified approach incorporating
modeling, monitoring, site cross comparison and experimentation is needed. Sporadic
efforts in the United States and a coordinated effort in Europe have followed this model
of science. This paper deals with the modeling component of this scientific venture.
Several models of watershed or plot scale nitrogen dynamics already exist
including PNET [Aber and Federer, 1992], CENTURY [Parton et al., 1987] BIOME-
BGC [Running and Gower, 1991], and MAGIC-WAND [Jenkins et al., 1997]. All of
these models have tightly coupled hydrologic and biogeochemical components. If you
wish to substitute a different representation of watershed or plot hydrology none of these
models provide a simple avenue on which to proceed. None of them address the
particular concerns for modeling catchment biogeochemistry in alpine catchments such as
the effects of snow cover duration, the insulating effect of the snowpack or soil freezing
events. These difficulties necessitate the development of A NItrogen Model for the
ALpine (ANIMAL). Such a model should meet five basic goals:
111
1)
Incorporate state of the art knowledge of carbon nitrogen cycle modeling.
2)
Incorporate the known soil microbial activity underneath the snowpack.
3)
Incorporation of hydrologic information as a time series enabling input to be
generated from any hydrologic model.
4)
Incorporate soil temperature data as a time series so any suitable energy budget
model or soil temperature assumption can be used
5)
A simple object oriented design to allow changes to model structure and code
simply and efficiently.
Model Description
Several models of catchment and plot scale nitrogen dynamics exist (CENTURY
and PNET for example) [Parton et al., 1987; Aber and Federer, 1992], all depend on a
simplified representation of the nitrogen cycle for determining the process controlling
carbon and nitrogen cycling in a watershed. The CENTURY model is one of the more
widely used carbon-nitrogen dynamics models currently being used in the scientific
community and it has been applied to alpine ecosystems previously with some success
[Baron et al., 1994]. The CENTURY model includes a simplified hydrologic budget
model that is used to drive portions of the soil biogeochemical cycling and plant growth
portions of the model. CENTURY at this time does not include the incorporation of the
effect of snow cover on soil temperatures and the resultant effects on soil microbiology
112
and root dynamics [Brooks et al., 1996]. The Alpine Hydrochemical Model (AHM) has
a better representation of alpine hydrology than the current models and a more flexible
algorithm incorporation was sought to permit the use of AHM (or any other hydrologic
model) output to be used to drive a point scale biogeochemical model. For these two
reasons the CENTURY carbon-nitrogen dynamics algorithms as described in [Parton et
al., 1987; Parton et al., 1993] were incorporated into a computational model that takes
AHM output as well as soil temperature and nitrogen deposition as inputs into the model.
The carbon nitrogen model itself consists of three parts: a soil carbon dynamics
model, a nitrogen dynamics model linked to the carbon model and a plant growth model
linked to the other two components. The fundamentals for all three components were
gathered from the literature on the CENTURY model [Parton et al., 1987; Parton et al.,
1988; Parton et al., 1993]. The following three sections contain a brief overview of the
CENTURY model structure and the changes that were necessary to adapt it to apply as
desired in an offline coupled mode with AHM. The complete code for the model is
included in Appendix D.
Soil carbon model
The soil carbon model consists of 8 separate compartments with the flows in and
out of each compartment controlled by properties of each pool as well empirically
determined rate constants for soil organic matter decay [Parton et al., 1987]. The 8 pools
113
are: surface litter structural, soil structural material, surface litter metabolic, root litter
structural and root litter metabolic, surface microbes, soil microbes, slow soil carbon and
passive soil carbon. A flow chart description of the soil carbon model taken as [Parton et
al., 1993] is included in Figure 1. The decomposition rate for each of the pools is as
follows:
dC,
= K i Lc ACII =1,2
dt
(1)
dC,
= K 1 ATm
C1 I = 3
dt
(2)
dC,
—K J AC,
dt
(3)
Tm = (1— 0.75 T)
Lc
.
I = 4,5,6,7,8
(4)
e (-1 L'' )(5)
where CI = the carbon in pool; I= 1,2,3,4,5,6,7,8 which are surface and soil structural
material, active SUM, surface microbes, surface and soil metabolic material, slow and
passive SUM fractions respectively; 1(1 is the maximum decomposition rate (day') for
each of the above pools (K1= 0.010685, 0.01315, 0.02, 0.16438, 0.40548, 0.050685,
0.000548, 0.0000123); A is the combined effect of soil moisture and soil temperature on
decomposition, T m is the effect of soil texture on active SUM turnover, T is silt plus clay
content (fraction); and L e is the impact of lignin content of structural material (L s ) on
114
structural decomposition. The maximum decomposition rates used in this model are
simply those used by Parton et al., [1993] divided by 365. The C flows to each pool and
the corresponding fraction lost to respiration are included in Figure 1.
A number of adjustments to the CENTURY model structure were necessary to
permit easy coupling with the AHM. First, the non-linear equation describing the effect
of soil temperature on soil organic matter decomposition from Baron et al. [1994] had to
be extended down to -5 C ° , which is the temperature at which Brooks et al. [1993]
observed no soil respiration in the alpine tundra of Niwot Ridge, Colorado. Second, the
effect of soil moisture on soil organic matter decomposition had to be redefined using soil
moisture status. The equation used in ANIMAL was:
M e = (0, — O w )/(0 —O w )
(6)
where M e is the effect of soil moisture on organic matter decomposition, O t is the soil
water content at timestep t, O w is the water content at which plants wilt, 0, is the saturated
soil water content. Me is equivalent to the fraction of pores filled with water in the soil.
Third the leaching parameters in the CENTURY model use monthly water leached below
30 cm in the soil profile. In this application we use daily drainage from the soil profile
(as modeled by AHM) as an input to the model. These two facts result in a need to
multiply the daily drainage by 30 to produce the correct leaching fraction from the active
soil organic matter pool.
115
Soil nitrogen model
The soil nitrogen model mirrors that of the soil carbon model (Figure 2). Organic
nitrogen flows follow those of carbon at the C:N ratio of the pool receiving the flow of C
and N. The C:N ratios of the eight pools are 150, 150, 3-15, 10-20, 12-20, and 7-10
respectively for surface and soil structural material, active SOM, surface microbes, slow
and passive SOM fractions. The C:N ratio of surface microbes varies with the n content
of plants. The C:N ratio of the three soil organic matter pools varies according to the
mineral N concentration of the soil. The C:N ratio of the surface and subsurface
metabolic pools depends on the C:N ratio of the incoming litter and its lignin [Parton et
al., 1987; Parton et al., 1988; Parton et al., 1993].
Only one change was required of the nitrogen submodel as a result of decreasing
the time step of modeling from monthly to daily. The fraction of mineral N lost to the
atmosphere in the form of N2 was divided by 30.
Plant growth model
Only a grassland plant growth submodel is currently incorporated into the
ANIMAL algorithm. This was done because grasslands are fairly simple to model and
the incorporation of a grassland model permitted a quick method of validation for the
model. A diagram of the grassland model is included in Figure 3. After Parton [1993]
the maximum production each day was calculated as:
116
Pp =P
p PS
P
maxTM
(7)
where P p is potential plant production rate (g m -2 day -1 ), P rnax is maximum potential
aboveground plant production rate (8.3 g rT1-2 day -1 ), T p is the effect of soil temperature on
plant production rate, M p is the effect of soil moisture on plant production rate, and
S p is the effect of self shading on plant production rate. Root and shoot death and root to
shoot ratios were treated as Parton et al. [1993] but for the exceptions noted below.
As with the carbon and nitrogen submodels changes were necessary to permit the
coupling of the carbon nitrogen model with AHM. First, the maximum potential plant
production was divided by 30 to achieve a daily value. Second, root and shoot death
calculations were divided by 30 to achieve a daily value. Third, the effect of soil
temperature on plant growth was assumed to be for C3 plants due to the alpine nature of
the model application. Fourth, the effect of soil moisture on plant growth was simplified
to a single function as:
M p = Oa *1.24 — 0.060
(8)
where M p is the effect of soil moisture on plant production rate, O a is the fraction of soil
pores filled with water, and the two constants were calculated from Figure 6a in Parton et
al. [1993].
117
Case Study
ANIMAL was applied to the Emerald Lake watershed in Sequoia National Park,
California as a test of the algorithm and its applicability to alpine watersheds. This
application builds on the AHM modeling already conducted at Emerald. The Emerald
Lake watershed is a 120 ha headwater catchment located in the Sierra Nevada (36 35' N,
118 40' W), with elevation ranging from 2800 m at the lake to 3417 m at the summit of
Alta Peak. The watershed is 48% covered by exposed granite and granodiorite, 23% by
soil and 23% by talus and includes a 2 ha lake [Tonnessen, 1991; Wolford et al., 1996].
Emerald was selected for four reasons: a long time series of stream chemistry
measurements [Melack et al., 1998], over a decade of data on atmospheric deposition
[Melack et al., 1997], good measurements of biomass and soil properties for the
watershed [Rundel et al., 1988; Brown et al., 1990], and familiarity of modeling the
watershed with previous applications of the AHM [Wolford et al., 1996; Meixner et al.,
1999].
Estimation of four time series inputs were necessary to permit ANIMAL
modeling of the Emerald Lake watershed: soil temperature, atmospheric N deposition,
water draining the soil, and soil water content. Soil temperature was estimated in two
ways. The first method for estimating soil temperature was to use a 30 day average of air
temperature in the Emerald Lake watershed. Daily mean air temperature was
reconstructed using the 52 year record of minimum and maximum recorded air
118
temperature at the Grant Grove Ranger Station in Sequoia National Park [A. Esperanza,
personal communication]. The ? for the regression equation used to develop the
reconstructed time series of Emerald Lake mean air temperature was 0.86. A graph of
the reconstructed time series with the available Emerald Lake data from the 1980's and
1990's shows that the reconstructed values, while not perfect, are effective at capturing
that major variability of air temperature at Emerald Lake (Figure 4). The reconstructed
air temperatures were only used when no observations were available for the Emerald
Lake watershed. The second methodology was to take the reconstructed air temperature
time series and to assume that when the soil was snow covered (using data from the 47
year Emerald Lake runs) that the effective air temperature was -0.1 C 0 . The purpose of
this second methodology was to investigate the effect that snow cover would have on the
biogeochemistry of alpine catchments.
Three levels of atmospheric deposition were used as inputs to the model. Two of
the deposition amounts were the lowest (1 kg ha t yr i ) and highest (3.6 kg ha:' yr1 )
observed N deposition to the Emerald Lake watershed [Melack et al., 1997]. An
additional simulation was done with twice the N deposition as the highest observed N
deposition (7.2 kg ha ' yr -1 ). This N deposition was assumed to occur at a constant rate
-
throughout the year.
A 47 year AHM model simulation has been completed for the Emerald Lake
basin using reconstructed discharge data developed from stream gauging data and
California cooperative snow survey data [C. Gutmann, personal communication]. Output
119
from this simulation pertaining to soil drainage and soil water state was used as input to
ANIMAL.
The 47 year input time series of predicted soil temperature was used to simulate
the plant growth and soil organic matter dynamics with ANIMAL. A total of six
different simulations were conducted three with 30 day mean air temperature as the
predicted soil temperature (one each for the three deposition levels) and three with the
soil temperatures fixed under the snow covered area (SCA) and using the 30 day mean air
temperature when snow free. For each simulation a total of 1880 years were simulated.
Only the last 47 years of each simulation were analyzed. The long runs are necessary to
permit equilibration of ecosystem dynamics, including plant and soil processes [Baron et
al., 1994].
Results
The long runs permitted the equilibration as expected with only minor differences
in model output noted for the final period of 47 years simulated as opposed to the
preceding 47 years. Four major results can be seen looking at the modeling results for
individual ecosystem components (Table 3.1.). First, increased atmospheric deposition
resulted in more biomass and more soil organic matter. Second, using soil temperatures
as predicted from using snow cover as a -0.1 C ° resulted in less live biomass and smaller
soil organic matter pools for carbon and nitrogen. Third, the predicted below ground
120
biomass for the low deposition scenario comes closest to the observed below ground
biomass [Rundel et al., 1988]. Fourth, neither the results using average 30 day air
temperature or the SCA soil temperature time series come close to the observed soil
organic carbon of Rundel et al. [1988 ]. The results for both soil temperature time series
are well below the observed 17,500 g m2 ", the results using 30 day mean air temperature
are closer but still a factor of 2 less than the observed values.
The results for the modeling of ecosystem processes (Table 3.2) are similar to
those for the ecosystem component results. Five things can be learned from looking at
the results for ecosystem processes. First, using the SCA soil temperature time series
resulted in smaller annual production and smaller N fluxes per year. Second, increasing
N deposition resulted in greater biomass production and larger fluxes of N per year.
Third, both soil temperature time series inputs underpredict observed above ground
biomass production. Fourth, the SCA soil temperature time series does a better job of
simulating net N mineralization, coming closest to the observed value. Fifth, the SCA
temperature series slightly underpredicts plant N uptake while the 30 day mean prediction
of soil temperature overpredicts plant N uptake.
Comparing model predicted N fluxes and the observed N fluxes for the Emerald
Lake watershed reveals a number of interesting facts about the model and about the
carbon and nitrogen dynamics of the watershed (Figure 5). First, the drought years
during the late 1980's and early 1990's resulted in large spikes of mineral nitrogen in the
soils of the watershed in late summer early fall. These spikes were probably caused by
121
large-scale root death due to the severe drought conditions present in the watershed.
These large fall spikes of mineral N were not observed in the discharge time series from
Emerald Lake. Second, a spring peak for mineral N was observed in the model
simulations. It is of larger magnitude than the spring pulse of NO 3 observed at Emerald
-
Lake. This pulse also predates the observed pulse of NO 3 for the Emerald Lake
-
watershed by several months. Third, the SCA temperature scenario does a better job than
30 day mean air temperature at simulating the observed pulse of NO3 . Finally, doubling
-
deposition increases modeled NO3 concentrations for either soil temperature scenario.
-
Discussion
The carbon nitrogen cycle modeling using ANIMAL and ARM output for
Emerald Lake provides us with information about the natural processes governing
nitrogen dynamics in alpine watersheds as well as the model chosen to simulate these
dynamics. Four things were learned with this exercise: the conversion of the CENTURY
algorithm to a daily format receiving four time series inputs was successful, snow
covered area improves simulations of N dynamics, current rates of deposition appear
capable of inducing nitrogen saturation at Emerald Lake, and the model was capable of
capturing the trends of mineral N export at Emerald Lake with some displacement.
The CENTURY model was originally built to simulate the carbon-nitrogen
dynamics of the Great Plains, U.S.A [Parton et al., 1987]. Transferring this model to the
122
alpine meadows of the Sierra Nevada is a stretch for the CENTURY representation of
terrestrial carbon-nitrogen dynamics. The results from this modeling exercise indicate
that the CENTURY algorithm is able to adequately simulate carbon-nitrogen dynamics in
alpine ecosystems. This result was earlier confirmed by Baron et al. [1994]. However,
their application of the CENTURY model was in the Rocky Mountains, which are
significantly different from the Sierra Nevada both in climate and vegetation.
These simulations do indicate some problems with CENTURY's representation of
carbon-nitrogen dynamics in alpine watersheds. The CENTURY algorithm was unable
to adequately model total soil carbon as it was in Baron et al. [1994]. The results
overpredicted live subsurface biomass. The algorithm was also unable to properly
predict the amount of above ground biomass production on an annual basis. The model
was fairly successful in simulating N mineralization and plant N uptake. As a whole
these results indicate that the current algorithm is a good starting point for further
research into carbon-nitrogen dynamics in alpine watersheds.
The use of SCA to adjust the soil temperature predictions was successful in
improving model simulations. The SCA time series resulted in better simulations of NO;
flux, plant N uptake, N mineralization and below ground live biomass. The 30 day mean
air temperature results were significantly different from the results using SCA. Almost
all biomass or soil organic matter pools are nearly double or even triple those simulated
with the SCA time series. The fluxes of NO; and mineral N are also much larger for the
30 day mean air temperature time series. These results indicate that snow cover
123
information should be incorporated into any simulation of biogeochemistry in alpine
catchments.
Even with the low current deposition rates of mineral N to the Emerald Lake
watershed the model indicates that relatively large fluxes of NO; should currently be
observed in the Emerald Lake watershed. These large fluxes are not currently observed
at Emerald Lake. Still current stream chemistry observations do indicate significant NO;
losses from the watershed. The simulations also indicate that with any significant
increase in deposition over current levels the watershed should experience significant
mineral N export. This simulation result should be confirmed with field fertilization
experiments. This simulation result also indicates that care should be taken in setting
critical loads for alpine areas in California. While, the Sierra Nevada currently receive
some of the lowest atmospheric deposition in the world these results indicate that
relatively small increases in loading from currently levels could cause major terrestrial
and aquatic ecosystem changes.
The simulations did duplicate observed trends in NO; flux for Emerald Lake.
The gradual decline in NO; export observed in the late 1980's early 1990's was
duplicated by the model but the simulations increased export earlier than observed in the
real watershed. The simulations also had large spikes in NO export in the late summer
and early fall of drought years. The model contains a so-called drought effect that does
not appear to occur in the real watershed. A secondary drought effect, the decline in
124
stream NO; concentrations during the late 1980's and early 1990's drought, does occur
in both the model and the real watershed.
The lack of a fall spike in simulated NO; and the model's simulated NO; peak
which predates and is much larger than the observed spring peak may indicate a
hydrologic disconnect between the soils and surface waters of the Emerald Lake
watershed. The NO; concentrations in Emerald Lake soils may indeed spike in the late
summer of drought years but this spike may either not reach the streams or the signal may
be mixed out by more dilute waters from talus areas or from rock fractures. As for the
spring peak being delayed in the real watershed as compared to the modeled catchment,
this may be due to areas of talus releasing more NO; than areas of soil and talus areas
melting later in the season. This asynchrony may also be due to a flushing episode that
the AHM hydrologic input to the algorithm does not currently capture. This hypothesis
put forth by Creed et al., [1996] states that as soils saturate they release NO; that has
been hydrologically disconnected from the stream during a seasonal or longer period
drought. These results indicate that a mechanism for the delay of these NO; pulses needs
to be incorporated into AHM.
Conclusions
The incorporation of AHM output as input into a copied CENTURY algorithm was
successful. It was a variable success, which should be improved upon through validation
125
of the modeling results using field experiments. The incorporation of SCA as an input
to biogeochemical models for alpine watersheds appears to be necessary to achieve good
simulations of watershed carbon-nitrogen dynamics. These results also indicate that
increases in N deposition could easily increase NO 3 export from the watershed. This
result should be verified with extensive field experimentation since it could have a
dramatic impact on the setting of air quality standards in California. Finally,
improvements in the hydrology of ARM appear to be necessary to adequately time the
pulse of NO from the Emerald Lake watershed during spring. A number of tasks remain
to be done to fully apply this model to alpine watersheds. First, soil freezing and its
effect on stream NO 3 export should be incorporated [Likens and Bormann, 1995; Brooks
et al., 1996]. Second, a more robust energy budget model should be used to drive the soil
temperature inputs of the algorithm.
Acknowledgements
A Canon National Park Science Scholarship made this work possible to the lead author.
Additional support provided by NASA and NSF. Ray Brice and Kathleen Meixner aided
in manuscript preparation. Chris Gutmann and Jim Sickman are thanked for their
contributions of data, model output, and insight in to the processes occurring at Emerald
Lake.
126
References
Aber, J. D. and C. A. Federer, A generalized, lumped-parameter model of phtsynthesis,
evapotranspiration and net primary production in temperate and boreal forest
ecosystems, Oecologia, 92:463-474, 1992.
Aber, J. D., W. McDowell, K. J. Nadelhoffer, A. Magill, G. Berntson, M. Kamakea, S.
McNulty, W. Currie, L. Rustad, and I. Fernandez, Nitrogen saturation in
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Aber, J. D., K. J. Nadelhoffer, P. Steudler, and J. M. Melillo, Nitrogen Saturation in
northen Forest ecosystems, BioScience, 39:378-386, 1989.
Baron, J. S., D. S. Ojima, E. A. Holland, and W. J. Parton, Analysis of nitrogen saturation
potential in Rocky Mountain tundra and forest: implications for aquatic systems,
Biogeochemistry, 27:61-82, 1994.
Brooks, P. B., M. W. Williams, and S. K. Schmidt, Preliminary information on
winter/spring nitrogen cycling in the Colorado alpine, EOS, Trans. AGU,
74(43S):257, 1993.
127
Brooks, P. B., M. W. Williams, and S. K. Schmidt, Microbial activity under alpine
snowpacks, Niwot Ridge, Colorado, Biogeochemistry, 32:93-113, 1996.
Brown, A.D., Lund, L.J. & Lueking, M.A. Integrated soil process studies at Emerald
Lake watershed. California Air Resources Board, Sacramento. (1990). Final
Report, Contract A5-204-32.
Creed, I. F., L. E. Band, N. W. Foster, I. K. Morrison, J. A. Nicolson, R. S. Semkin, and
D. S. Jeffries, Regulation of nitrate-N release from temperate forests: a test of the
N flushing hypothesis, Water. Resource. Res., 32:3337-3354, 1996.
Fenn, M. E., M. A. Poth, J. D. Aber, J. S. Baron, B. T. Bowman, D. W. Johnson, A. D.
Lemly, S. G. McNulty, D. F. Ryan, and R. Stottlemyer, Nitrogen excess in North
American ecosystems: A review of geographic extent, predisposing factors,
ecosystem responses, and management strategies, Ecological Applications, In
press, 1998.
Galloway, J. N., W. H. Schlesinger, H. Levy, A. Michaels, and J. L. Schnoor, Nitrogenfixation - anthropgenic enhancement - environmental response, Global
Biogeochemical Cycles, 9(2):235-252, 1995.
128
Henriksen, A. and D. F. Brakke, Increasing contributions of nitrogen to the acidity of
surface waters in Norway, Water Air and Soil Pollution, 42:183-201, 1988.
Jenkins, A., R. C. Ferrier, and B. J. Cosby, A dynamic model for assessing the impact of
coupled sulfur and nitrogen deposition scenarios on surface water acidification, J.
Hydrol., 197:111-127 , 1997.
Likens, G. E. and F. H. Bormann, Biogeochemistry of a forested ecosystem second
editionSpringer-Verlag, New York, 1995.
Meixner, T., H. V. Gupta, L. A. Bastidas, and R. C. Bales, Sensitivity Analysis Using
Mass Flux and Concentration, Hydrol. Procecces, in press: 1999.
Melack, J.M., Sickman, J.O., Leydecker, A. & Marrett, D. Comparative Analyses of
High-Altitude Lakes and Catchments in the Sierra Nevada: Susceptibility to
Acidification. Sacramento: California Air Resources Board. (1998). A032-188,
Melack, J.M., Sickman, J.O., Setaro, F. & Dawson, D. Monitoring of Wet Deposition in
Alpine Areas in the Sierra Nevada. Sacramento: California Air Resources Board.
(1997). A932-081,
129
Parton, W. J., D. S. Schimel, C. V. Cole, and D. S. Ojima, Analysis of factors
controlling soil organic matter levels in the Great Plains grasslands, Soil Sci. Soc.
Am. J., 51:1173-1179, 1987.
Parton, W. J., J. M. O. Scurlock, D. S. Ojima, T. G. Gilmanov, R. J. Scholes, D. S.
Schimel, T. Kirchner, J.-C. Menaut, T. Seastedt, E. Garcia-Moya, ApinanKamnalrut, and J. I. Kinyamario, Observtaions and modeling of biomass and soil
organic matter dynamics for the grassland biome worldwide, Global
Biogeochemical Cycles, 7:785-805, 1993.
Parton, W. J., J. W. B. Stewart, and C. V. Cole, Dynamics of C, N, P, and S in grassland
soils: A model, Biogeochemistry, 5:109-131, 1988.
Rundel, P.W., St.John, T.V. & Berry, W.L. Vegetation process studies. Sacramento:
California Air Resources Board. (1988). Progress Rep., Contr. A4-121-32,
Running, S. W. and S. T. Gower, Forest-BGC, a general model of forest ecosystem
processes for regional applications. II. Dynamic carbon allocation and nitrogen
budgets, Tree Physiology, 9:147-160, 1991.
130
Sickman, J. O. and J. M. Melack, Nitrogen and sulfate export from high elevation
catchments of the Sierra Nevada, California, Water Air and Soil Pollution,
1 05:217-226, 1998.
Stoddard, J. L., Long-term changes in watershed retention of nitrogen - its causes and
aquatic consequences, in Environmental Chemistry of Lakes and Reservoirs,
edited bypp. 223-284, 1994.
Tonnessen, K. A., The Emerald Lake watershed study: introduction and site description,
Water. Resource. Res., 27:1537-1539, 1991.
Williams, M. W., J. S. Baron, N. Caine, R. Sommerfeld, and R. Sanford, Nitrogen
saturation in the Rocky Mountains, Environmental Science and Technology,
30:640-646, 1996.
Wolford, R. A., R. C. Bales, and S. Sorooshian, Development of a hydrochemical model
for seasonally snow-covered alpine watersheds: Application to Emerald Lake
Watershed, Sierra Nevada, California, Water. Resource. Res., 32(4):1061-1074,
1996.
131
Table 3.1 Ecosystem Components as Modeled for Emerald Lake. Values are mean for last 15
years of an 1880 year simulation, and for observations by Rundel et al. [1988]. Observed values
multiplied by 0.45 to convert biomass to g carbon.
Mean air temperature
SCA and mean air temp.
Obs.
Low
High
Double
Low
High
Double
Data
Live shoots (g m-2)
34
45
53
9
21
31
n/a
Live roots (g m -2)
1570
2100
2500
440
1018
1584
392
25
34
41
7
17
26
n/a
Total soil C (g rn-2 )
8300
10400
11900
3700
6000
8243
17500
Total soil N (g rn-2)
500
610
690
280
390
510
1195
Active soil C (g m-2)
300
410
480
86
200
310
n/a
Active soil N (g m -2 )
20
27
32
6
13
21
n/a
Dep.
Live N (g rn -2)
132
Table 3.2 Ecosystem Processes as Modeled for Emerald Lake. Values are mean for last 15 years
of an 1880 year simulation, and for observations by Rundel et al. [1988], Brown et al. 1986.
Observed values multiplied by 0.45 to convert biomass to g carbon.
Mean air temperature
Dep.
Above ground C
SCA and mean air temp.
Obs.
Low
High
Double
Low
High
Double
Data
59
88
110
10
32
60
143.1
65
100
120
11
36
61
n/a
2
3.2
3.9
0.002
0.7
1.9
0.924
1.9
2.9
3.6
0.3
1
1.8
1.89
production (g rri 2 yr- ')
Below ground C
production (g m 2 yr 1 )
Net Mineralization
(g m-2 yr-i )
Plant uptake
cg m-2 yfl)
133
SURFACE LITTER
0.55
C C,,=
= 003-•
• 009*T
c
UN = Lignin:nitrogen ratio
A = Soil temp. and soil moisture effect
T = Silt plus clay fraction
Ts = Sand fraction
Tc = Clay fraction
L s= Fraction of sturctural C as lignin
L c= exp(-3.0*L 5 )
I-120 = Water leached out each day times 30
F = Metabolic fraction of litter
K 1 = Max. deacy rate (day -1 )
Figure 1 Carbon box diagram
ROOT LITTER
134
N dep
.05*NO3
N 20, NO
MINERAL
--6,..02*G N
NO3
F
N
--------
I or M
I or M
I or M
I or M
SURFACE LITTER
STRUCTURAL
I ,,,,
LIGNIN 1 ''.
!CELLULOSE
ROOT LITTER
oM
: STRUCTURAL
I ,,,
. LIGNIN'I
1 CELLULOSE
'
METABOLIC
METABOLIC
,
N
N
••••
SURFACE
MICROBE
N
ACTIVE SOM
N
I'
SLOW SOM
N
LEACHED
N
PASSIVE SOM
N
N dep= Atmospheric deposition of nitrogen
GN= Gross N mineralization
I = Immobilization of mineral N
M = Mineralization of organic matter
F = Fraction of mineral N leached, function of texture and water flow
Figure 2 N soil organic matter flows. N flows follows those of carbon with nitrogen
moving from one box to the next having the C:N ratio of the receiving compartment.
135
LIVE SHOOTS
•
STANDING DEAD
SURFACE
LITTER
PLANT GROWTH
LIVE ROOTS
•
ROOT LITTER
Figure 3 Grass growth model diagram. Plant growth rate depends on soil temperature,
soil moisture and a self-shading factor. Root and shoot death depends on soil moisture
function and for live shoots on plant senescence at the end of the growing season.
136
30
— — - Reconstructed temperatures
— — Observed temperatures
20
I 1
I1
f 11,
) ,
,,,r
i
El ,
1,
, ,
ri!
\I
, )
r
i
I
r '
,
,
1
l i, ,)
el
t
r,
')
1,.
lilli
Io
r
i li)
I'l
—10
—20
1986
1988
1990
1992
1994
1996
Year
Figure 4 Modeled and measured 30 day mean air temperature for Emerald Lake
137
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_ 1 ball '_ 6 0N
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138
APPENDIX D - SENSITIVITY ANALYSIS USING MASS FLUX AND
CONCENTRATION
•
139
Forwarded by JoAnne Peirce/Chichester/Wiley on 07/05/99 14:51
I
Tom Meixner <[email protected]> on 04 105199 20:16:45
4111gt,7541
,
To:JoAnne Peirce/Chichester/VViley
cc:
Subject: Re: Hydrological Processes
Jo.
/ mailed off my copy of the form yesterday.
I have a question for you. I am currently in the process of wrapping up
my dissertation. I would like to include the paper "Sensitivity analysis
using mass flux and concentration" as an appendix to the dissertation.
I am the first author of the paper. The dissertation will be reatined by
the University of Arizona and microfilmed by University Microfilms
Incorporated (UMI). UmI may sell, on demand, single copies of the
dissertation including the paper in question for scholarly purposes.
Thanks,
Tom
On Fri, 30 Apr 1999 jpeirceewiley.co.uk wrote:
> From: JoAnne PeirceeW1LEY on 04/30/99 11:22 AM
•> To:
ranziebsing.ing.unibs.it, gerry_jones(PINRS-EAU.UQuebec.CA,
•
pratapecc.nih.ernet.in, ntutejaadlwo.nsw.aov.au, Pfisteraslf.ch,
•
ipquiseredline.ru, gaoehwr.arizona.edu, bruendleslf.ch,
•
tomOhwr.arizona.edu, wintherenpolar.no
> cc:
> Subject: Hydrological Processes
Perrnis&ongnmitadfortheuserequested.
Proper credit must be given to our publication.
(
3-
Copyright& Licensing Department
JohnWiley&SonslimIted
il ma:terlat apposro hi our work with credit to another
souro3, autnortsation trom is source must be obtnined.
following
Credit must Include the work,
the
components: Title of
Editor(s) name(s).
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Fleproduced with
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j tC;,9
140
Sensitivity Analysis Using Mass Flux and Concentration
Thomas Meixner, Hoshin V. Gupta, Luis A. Bastidas, and Roger C. Bales
Department of Hydrology and Water Resources, University of Arizona, Tucson
Received accepted Short title: CONCENTRATION VS. MASS
141
Abstract.
Sensitivity analysis for hydrochemical models requires
consideration of the multivariate nature of watershed response. A robust
multiobjective generalized sensitivity analysis (MOGSA) procedure, recently
developed at the University of Arizona, was used to fully investigate the single
objective parameter sensitivity of the Alpine Hydrochemical Model (AHM). A
total of 20,000 simulations for a two-year period were conducted for the Emerald
Lake watershed in Sequoia National Park, California. For each simulation 21
objective functions were evaluated: they were discharge and both concentration
and mass flux for 10 chemical species. The MOGSA procedure revealed that only
2000 simulations were necessary to establish the parameters sensitive to mass
flux or concentration. We found significant differences in parameter sensitivity
for concentration versus mass flux objective functions. For example, a snowpack
elution parameter and a number of hydrologic parameters were sensitive for
Cl concentration, while only the snowpack elution parameter was sensitive
-
for Cl mass flux. By using mass flux instead of concentration fewer mineral
-
weathering parameters and more soil exchange parameters were sensitive. Mass
flux calculations emphasize the spring snowmelt and peak discharge events of
the early summer. Our results indicate that using mass instead of concentration
permits better identification of the model parameters that most affect stream
conditions during peak springtime flows and that some combination of mass flux
and concentration objectives should be used in evaluating model performance.
142
Introduction
Alpine watersheds are susceptible to changes in biogeochemical conditions
due to their thin soils, limited vegetation, and snow dominated hydrology
[Melack et al., 1998; Stoddard, 1995; Melack and Stoddard, 1991]. In the Sierra
Nevada of California, predictions about the response of alpine watersheds
have implications for the health of aquatic resources and thus for air quality
management [Takemoto et al., 1995]. The Alpine Hydrochemical Model (AHM)
is an integrated watershed model that was designed to improve our understanding
of how alpine watersheds will respond to perturbations in climate and deposition
[Wolford et al., 1996]. Proper simulation of a perturbed watershed must include a
precise and accurate estimation of model parameters, based on an understanding
of the parameter sensitivity within AHM.
Sensitivity analysis and model calibration of stream chemistry models
depends on the formulation of one or more objective functions that will be used
as criteria for goodness of fit, i.e., the error between observations and model
output [Gupta et al., 1998; Mroczkowski et al., 1997; Ohte and Bales, 1995;
Chang and Delleur, 1992]. Different conceptual and mathematical formulations
of objective functions for catchment hydrochemical models exist; e.g. the sum
of squared errors, sum of absolute values of errors, likelihood methods etc.
[Hornberger et al., 1985; Sorooshian and Dracup, 1984 applied to concentrations
of various chemical species. While the mass flux of solutes is often used to gain
insight into catchment biogeochemical processes [Anderson et al., 1997; Pilgrim
et a/., 1979], it does not appear to have been used as an objective function for
parameter sensitivity analysis.
In this study, a generalized parameter sensitivity analysis [Spear and
143
Hornberger, 1980; Bastidas, 1998] of the AHM model was conducted for the
Emerald Lake watershed (ELW) located in Sequoia National Park, California.
Observed and simulated values of concentration and mass flux for each of 10
chemical species, as well as discharge at the lake outflow, for the period of the
1986 and 1987 water years (a water year begins on October 1st), were used as
the basis for the analysis of model parameter sensitivity.
The study was focused around the following three questions: First, is
parameter sensitivity different for chemical mass flux and chemical concentration
objective functions? Second, do the differences in parameter sensitivity indicate
that objective functions based on mass flux and concentration emphasize different
aspects of the underlying hydrologic and chemical processes controlling stream
chemistry? Finally, can a sensitivity analysis of this nature provide information
about how best to allocate resources for the study of alpine catchment processes?
Methods
Site This application of AHM builds on the original application of the model
to the ELW during an intensive field campaign conducted from 1985 until 1987
[Tonnessen, 1991; Wolford et al., 1996]. ELW is a 120 ha headwater catchment
located in the Sierra Nevada (36° 35' N, 118° 40' W), with elevation ranging
from 2800 m at the lake to 3417 m at the summit of Alta Peak (Figure 1). The
watershed is 48% covered by exposed granite and granodiorite, 23% by soil and
23% by talus and includes a 2 ha lake (Figure 2).
Model The AHM [ Wolford et al., 1996] is a lumped conceptual model that was
designed for simulating the hydrology and biogeochemistry of alpine watersheds.
144
It was originally applied to the ELW with the intent of investigating the
sensitivity of Sierra Nevada watersheds to changes in climate and deposition.
Modeling a watershed with the AHM requires specification of the particular
watershed structure in which the hydrologic and biogeochemical processes occur.
The ELW was partitioned into three terrestrial subunits (rock, talus and soil)
and a stream (Figure 3). Within this structure, a set of parameters define the
routing of flow from the rock subunit to the talus and soil subunits, and from
there sequentially into the stream, the lake and out of the watershed.
Each terrestrial subunit is made up of different compartments (representing
the snowpack, snowpack free water, snowmelt, surface runoff, interception by
trees and litter) and may contain multiple soil horizons. Stream subunits are
made up of different compartments representing the snowpack, snowpack free
water, snowmelt, stream ice and streamflow. Lake subunits contain similar
compartments to the stream subunits as well as a layered lake model which
includes a hypolimnion and epilimnion. Model subunits may be selected for use
according to the complexity of the watershed. Hydrologic processes are modeled
separately from geochemical processes. Routing between the subunits is handled
separately from the structure of the individual subunits.
AHM simulates the watershed response on a daily time step. At each
time step the model adjusts snow covered area, computes interception, adjusts
snowpack for precipitation and melt, calculates influxes of materials to each
soil and rock subunit, drains surface runoff, computes evapotranspiration and
sublimation, calculates kinetic reactions, calculates chemical equilibrium in soil
compartments, drains water from the soil horizon, calculates chemical equilibria
in streams and produces output. The outputs can include detailed descriptions
14.5
of all chemical calculations, tracking of both chemical and hydrologic storages
and changes in storage within the watershed, soil chemical concentrations and
stream concentrations. Chemical speciation is handled using equations adapted
from MINEQL[ Westall et al., 1976] . The "strength" of the model is its precise
calculations of mass and charge balance for chemical species and hydrologic
fluxes [ Wolford et al., 1996].
Monte-Carlo Simulation Instead of simulating the 1986 and 1987 water
years separately as was done in previous studies [ Wolford et al., 1996; Ohte and
Bales, 1995], the 2 water years were run as a continuous simulation (Figures 4 and
5). This continuous run was made possible with data from the Lodgepole Ranger
Station in Sequoia National Park (A. Esperanza, personal communication),
which permitted the estimation of winter storm occurrences at ELW.
A total of 20,000 Monte-Carlo simulations of ELW response were conducted
for the selected two year period. Each simulation was conducted by uniformly
selecting values for the 24 model parameters from the ranges specified in Table 1:
10 of them are hydrologic parameters (five for each subunit), and 14 are chemical
parameters (4 cation exchange coefficients on each of the soil and talus subunits
and 6 chemical parameters that are constrained by model structure to be the
same for all subunits). For each simulation, 21 different objective functions
were calculated, each being the sum of squared error (SSE) between a model
simulated output and its associated value measured at the Emerald outflow. For
each of the 10 chemical species, 2 objective functions were calculated: i) the SSE
between the measured and modeled concentration and ii) the SSE between the
measured mass and the modeled mass flux. This second objective function was
146
calculated as:
ssE k = E [(c io4b
r
d=1
Q obs ) _
(o rnod,/X ‘ze
nm d 1
° »
Ni
k ,d
6
2
(1 )
where k is each chemical species, d is day, n is total number of observations,
C is concentration of chemical species, and Q is daily discharge. Differences
between the concentration and mass flux objective functions can be understood
on a qualitative level by looking at the distance between modeled and measured
values of concentration and mass flux for Ca 2 +, ANC and Cl - over both of
the years simulated (Figures 4 and 5). These figures show that the mass flux
objective functions are heavily dependent on the chemical observations in 1986
and particularly on those observations made at the highest flows.
MOGSA The 20,000 Monte-Carlo simulations were used as the basis for
a multiobjective generalized sensitivity analysis (MOGSA) [Bastidas, 1998].
MOGSA is an extension of the methodology developed by Spear and Hornberger
[1980] that has come to be called generalized sensitivity analysis (GSA). In the
GSA method, a series of Monte-Carlo simulations is conducted by randomly
sampling over a feasible parameter space defined by establishing upper and lower
limits for the possible values of each parameter. The samples are then classified
as being behavioral (B) (i.e., having desired qualities) or non-behavioral (B)
- typically the desired quality is a low value for the objective function. The
discrimination into behavioral and non-behavioral sets is entirely subjective and
depends on the selection of a threshold "acceptable" value for the objective
function. For each parameter (0 k ) the empirical cumulative distribution function
is computed for both behavioral,
FA I B) and non-behavioral, FA I B)
outcomes. The Komolgorov-Smirnov (K-S) statistic is used [Stephens, 1970]
147
to discern whether the sampling distributions belong to the same underlying
population distribution or not. If not, the parameter in question is deemed to be
sensitive.
MOGSA extends the GSA methodology to multiple objectives by
introducing the notion of Pareto ranking [Goldberg, 1989] into the selection of
the discriminatory threshold between behavioral and non-behavioral categories,
thereby using additional information to overcome weaknesses of the original
method [Beck, 1987]. To avoid dependence of the results on the sampling
procedure, bootstrapping [Efron, 1979] has been incorporated into the algorithm,
and for robustness, the median of the K-S statistic is used as the indicator for
sensitivity at a particular significance level. When working with single objectives,
the MOGSA code uses a quantile of the objective function as the threshold for
discerning between behavioral and non-behavioral solutions.
The results presented in this paper use the 50% quantile to partition the
samples into behavioral and non-behavioral categories. The selection of the 50%
quantile is based on tests of MOGSA which have indicated that this quantile
tends to coincide with the most stable multiobjective solution for sensitive
parameters (results unpublished). Fifty bootstraps were conducted for each of the
sample sizes of 500, 750, 1000, 2000, 3000, 5000, 10,000, and 15,000 (selected from
the 20,000 simulations with replacement) to determine the sensitivity of model
parameters to the number of simulations used for sensitivity analysis. For each
sample size, the K-S statistic was calculated and the probability of the acceptable
and unacceptable distributions being the same was recorded. A significance
level (a) of 0.05 was used to discriminate sensitive from insensitive parameters,
i.e., a < 0.05 means that the behavioral and non behavioral distributions of a
148
parameter are not drawn from the same population and therefore the parameter
being tested is sensitive.
Results
The MOGSA procedure revealed that only 2000 simulations were necessary
to establish parameter sensitivity for mass flux or concentration objective
functions. This result is illustrated for ANC and Na + in Figure 6. Similar results
occurred for all of the objectives, with the sensitive parameters for some of the
objective functions requiring as few as 500 simulations to be identified (data not
shown).
There were more sensitive hydrologic parameters than sensitive chemical
parameters for concentration objective functions (Table 2). There were fewer
sensitive hydrologic parameters for Si and SO 42- than for other concentration
objectives. The Pc o2 in the subsurface, two weathering parameters, and a, and
the elution parameter, D, were sensitive for the largest number of concentration
objectives. Exchange coefficients for the cations, Si and SO ?1 - were important for
the species they are associated with and few other species.
The sensitivity analysis for the mass flux objectives tells a different story
(Table 3). While more sensitive ion exchange parameters were found for mass
flux objective functions, there were fewer sensitive hydrologic parameters. For
example, only the elution parameter D was sensitive for Cl - mass flux, while
there were several sensitive hydrologic parameters for Cl - concentration. In
total, there were 40 sensitive chemical parameters for the 10 mass flux objective
functions, while there were 41 sensitive chemical parameters for the concentration
objective functions. However, the sensitive chemical parameters for concentration
149
and mass flux were different. Fewer weathering parameters (15 weathering
parameters for concentration, 7 for mass flux) but more exchange parameters
(13 exchange parameters for concentration, 22 for mass flux) were found to be
sensitive for mass flux objective functions.
For hydrologic parameters, using mass flux as opposed to concentration
greatly decreased the number of sensitive parameters. There were 63 sensitive
hydrologic parameters for chemical concentration as opposed to only 44 for mass
flux. There were fewer sensitive hydrologic parameters for each of the chemical
species except for Si, which saw no change, and SO 42- which had 6 sensitive
hydrologic parameters for mass flux as opposed to 2 for concentration. The
evapotranspiration parameters (ET) for both of the subunits were important
parameters for concentration objective functions, with a total of 10 sensitive ET
parameters either on the soil or on the talus subunit; however, when mass flux
was used, only ET on the soil subunit was sensitive with respect to
Discussion
The results show systematic differences in parameter sensitivity for objective
functions calculated from a chemical species concentration as opposed to mass
flux of the same species, for this application of AHM to ELW. There is a high
degree of confidence in these results due to the large number of simulations that
were executed and the bootstrapping technique which shows the results to be
repeatable and robust. Using concentration as an objective function revealed
parameter sensitivities that are important all year and especially during periods
of low flow. Examples are fraction of potential evapotranspiration (ET)and the
mineral weathering parameters
(K
and a). Using mass flux as the objective
150
function revealed parameters that can have a large effect for a short period
of time, and especially during higher flows. Examples are ion exchange and
snowpack elution parameters.
Differences for hydrologic parameters other than ET are more mixed.
Hydrologic parameters that determine soil pore-water volume (O sa t and soil depth
) and residence time in that volume (Ksa t and N) are important year round.
These parameters determine the mixing volume of the subsurface and the rate of
exchange between surface and subsurface water, respectively. These hydrologic
parameters affect stream chemical composition throughout the year. We might
therefore expect mixed results for parameter sensitivity using mass flux as
opposed to concentration as the objective function. In general, fewer hydrologic
parameters were sensitive when mass flux was used as the objective function
possibly because the chemical parameters that mainly influence individual species
were relatively more important when using mass flux as the objective.
Reasons for different information content Stream chemical concentrations
for Emerald Lake are relatively constant and the data are representative of
many stages of discharge (Figure 4); therefore, concentration objective functions
equally weight errors in model output among observations. Thus, model
output for the entire year is important in determining parameter sensitivity for
concentration objective functions. Mass flux objective functions weight periods
of high discharge more heavily in calculating total model error (Figure 5). Trends
of stream concentration during periods of high discharge have long been used
to investigate storm-water dilution, weathering and flow paths in headwater
catchments [Anderson et al., 1997; Webb and Walling, 1996]. Particularly in
alpine catchments of the Sierra Nevada, dilution [Stoddard, 1987] and acidification
151
[Williams and Melack, 1991] have been identified as important processes in
controlling ANC during spring snowmelt, the period of highest discharge for the
ELW.
Our results indicate that mass flux and concentration objective functions
contain different information about watershed processes. In particular, mass flux
emphasizes parameters that have a faster response within the model and possibly
within the watershed. Exchange coefficients and snowpack elution parameters
influence modeled stream chemistry over shorter periods of time, with the
elution parameter in particular influencing modeled stream chemistry during
peak discharge. These processes are important in determining stream chemical
composition during spring snowmelt, the period of greatest sensitivity to acid
deposition for alpine catchments [Williams et al., 1993]. Using concentration
as an objective function highlighted sensitivities to evapotranspiration and
mineral weathering parameters, which affect model output throughout the year
and influence the mean model output. Thus for investigating model error and
structure with the goal of improving catchment models, it is important to include
measurements of model error that incorporate both mass flux and concentration
objective functions.
Mass flux objective functions place a heavier weight on chemical observations
during high flows than on observations during low flows (Figure 5). This reliance
permits the extraction of information about short time scale watershed processes.
However, it also makes parameter estimation and sensitivity analysis dependent
on the accuracy of a reduced number of chemical observations during periods
of high flow. Our confidence in the stream chemical composition observations
is high due to the extensive quality control and quality assurance protocols of
152
the laboratory that conducted the analysis of stream samples [Melack et al.,
1998]. However, the measurement errors for mass flux observation are also
heteroscedastic (increasing error with increasing measurement value) due to the
multiplication of observed concentration with discharge. While heteroscedasticity
has been well studied in the context of rainfall runoff models [e.g.,Sorooshian
and Dracup, 1980] little similar work has been done for hydrochemical models.
Investigations of this issue, using model output as "true data", would need to be
done to further investigate the effects of using mass flux as a measure of model
error prior to using mass flux objective functions in a parameter estimation
context [Kirchner et al., 1996].
Information about natural processes Our sensitivity analysis differed from
the more limited analysis of Ohte and Bales [1995] in that similar parameters
for different subunits and the exchange coefficients for each applicable chemical
species were varied independent of each other. These changes allowed the
identification of differing sensitivities for each exchange coefficient by objective
function and subunit. Ohte and Bales found that Ca 2 + and Me+ objective
functions were unaffected by exchange coefficient parameters, while our results
showed exchange coefficients to be important.
Also, our results indicate that the volume of talus and residence time of
water in the soil subunit were among the most important hydrologic parameters
in determining model output. Each subunit has two parameters that represent
soil water holding capacity (O sa t and soil depth) and two parameters that
represent rate of flow through that water holding volume (Ksat and N for
unsaturated flow). Summing the results from Tables 2 and 3 shows that for
soil, 22 flow rate parameters and 24 soil volume parameters were sensitive for
153
chemical (concentration or mass flux) objective functions. For talus, 18 flow rate
parameters and 32 talus volume parameters were sensitive for chemical objective
functions. These results indicate that the AHM model of ELW is more sensitive
to talus volume than it is to flow rate through the talus. These results also
indicate that flow rate through soil is more important than is flow rate through
talus. Campbell et al. [1995] and Williams et al. [1997] have recently concluded
that areas of talus are more important than previously thought in determining
alpine stream chemistry. They also state that there is a lack of knowledge as
to the total reaction volume of talus volume in a watershed. Isotopic methods
have shown some promise in estimating talus volume [Mast et al., 1995]. Our
results indicate that more time should be spent in the field trying to estimate the
reactive volume of talus fields. Until talus volume is more accurately measured
in the field it will need to be estimated using calibration techniques.
Conclusions
Testing model sensitivity with different measures can reveal more information
about both the model and the natural system. Mass flux objective functions
revealed greater parameter sensitivity for cation exchange and snowpack elution
parameters, while mineral weathering and evapotranspiration parameters were
more important for concentration objective functions. The mass flux objective
function emphasized processes that are most important during periods of peak
discharge while concentration emphasized more long term processes. Since
peak discharge is the period when alpine ecosystems are most in danger of
being impacted by acid deposition, mass flux objective functions provide
information about watershed processes that are important in addressing acid
154
deposition questions in alpine watersheds. However, using mass flux objective
functions introduces the problems of heteroscedasticity into the parameter
estimation problem for hydrochemical models. These issues would need to be
further investigated before using mass flux in a parameter estimation context.
Our results also indicate that future field efforts for alpine basins should be
concentrated on talus and soil hydrologic properties. These efforts should
emphasize discerning the volume of talus in a watershed and the conductivity of
the soils.
Acknowledgments.
Fellowship
The first author was supported by a NSF Graduate Research
and a Canon National Park Science Scholarship. A NASA-EOS grant
(IDP-88-086) provided partial support for this work. N. Ohte helped in initial coding
for Monte Carlo simulations. Thank you to J. Sickman for providing insight and data
about the Emerald Lake watershed. We wish to thank K. Meixner and B. Matson
for comments on an earlier version of this manuscript. We also wish to thank two
anonymous reviewers whose comments improved this manuscript.
155
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This manuscript was prepared with the AGU LATEX macros v3.0.
159
Table 1. Parameters varied and range relative to values by Wolford et al. [1996]
Parameter'
Range
ET b
0-1
Soil — depthc
0.5-1.5
Nc
0.8-1.8
K at
0.2-4
0.5-1.5
El u ti on (Dc)
0.5-1.5
K-Ca 2 +e
0.5-1.5
K_m g 2+e
0.5-1.5
K- Na+e
0.5-1.5
K-K+
0.5-1.5
K-SOr
0.5-1.5
K-Si r
0.5-1.5
Soil P, 02
0.5-1.5
0.5-1.5
ah
a
0.5-1.5
The hydrologic parameters and cation exchange coefficients were varied
independently for each subunit within the same mathematical range.
b
ET represents the fraction of potential evapotranspiration that is permitted to
occur; the varied range is the possible range.
The parameters Soil-depth, N, K sat , and O sa t represent total depth of soil on a
subunit, a drying coefficient for unsaturated flow, saturated hydraulic
conductivity and saturated soil water holding capacity.
160
d
The equation used to represent snowpack elution in AHM is:
-= A x B e(—BXX) (1 — A) x D x e(-DxX). In the models current form A
and B are small so D is the dominant parameter and was thus the parameter
used in the sensitivity analysis.
e
Log K for exchange of cation with H+ on cation exchange site.
f
Log K for adsorption of SO 42- and H 2 SiO 3 . Total site concentrations from ELW
optimization used here. These parameters cannot be varied independently for
the soil and talus subunit.
g The partial pressure of carbon dioxide P c° , was varied simultaneously for both
subunits.
h
The weathering coefficients K and a were varied independently of each other
but uniformly for all species due to issues of charge balance. They contribute to
weathering via the equation: Mol =Axnx [H 41' where Mol is moles added to
the subunit, A is total area of the surfaces involved in reactions, [11+] is
hydrogen ion concentration, and K and a are constants. The total surface area is
determined as the product of the soil depth, area, bulk density, and specific
surface area.
161
Table 2. Parameter Sensitivity for Concentrations at 2000 Simulations
Objective Function
Parameter
ANC
ET (soil)
x
Soil-D (soil)
x
N (soil)
Ksat
X
61 sa t (SOH)
X
Ca2
C1
K+
Mg 2 +
x
x
x
x
x
x
x
x
x
x
X
X
X
x
x
x
x
x
N (talus)
x
x
x
K sat (talus)
x
x
X
X
X
x
x
x
x
x
x
x
x
x
x
x
x
x
x
x
x
x
x
x
x
x
x
x
x
Elution (D)
x
K-Ca 2 + (soil)
x
x
x
x
x
x
x
x
K-Mg 2 + (soil)
x
S0 42 -
x
x
X
x
e sa t (talus)
Si
x
x
x
Q
x
x
Soil-D (talus)
H+
x
x
ET (talus)
NO
.x
x
X
Na+
X
x
x
x
x
K-K+ (soil)
x
K- Na + (soil)
x
K-S0 42 - (both)
x
K-Ca 2 + (talus)
x
x
K-Mg 2 + (talus)
x
K-K+ (talus)
x
K- Na + (talus)
x
x
K-Si (both)
K-H 2 CO 3 (both)
x
x
x
(all species)
x
x
x
a (all species)
x
x
x
x
x
x
x
x
x
x
x
x
x
x
x
162
Table 3. Parameter Sensitivity for Mass at 2000 Simulations
Objective Function
Parameter
ANC Ca 2 + Cl - K+ Mg 2 + Na + NO H+ Si S0 24 -
x
ET (soil)
Soil-D (soil)
x
x
N (soil)
x
x
x
X
X
Ksat
O sa
(soil)
X
X
X
(soil)
X
X
x
X
X
x
x
X
X
X
X
x
x
ET (talus)
Soil-D (talus)
x
x
x
N (talus)
x
'< sa, (talus)
x
x
x
x
O sa , (talus)
x
x
x
Elution (D)
K-Ca 2 + (soil)
x
x
x
K-Mg 2 + (soil)
x
x
x
x
x
x
x
x
x
x
x
x
K- Na + (soil)
x
K-S0?1 - (both)
x
x
K-Ca 2 + (talus)
x
x
x
x
x
K-Mg 2 + (talus)
K-K+ (talus)
x
x
x
x
K- Na + (talus)
x
K-Si (both)
x
x
x
x
x
x
x
x
(all species)
a (all species)
x
x
K-K+ (soil)
K-H 2 CO 3 (both)
x
x
x
x
x
x
x
x
x
x
x
163
Figure 1. Elevation map of ELW.
Figure 2. Soils map of ELW.
Figure 3. AHM representation of the Emerald Lake watershed broken down into
rock, talus, soil, stream and lake subunits. All subunits include compartments that
represent the snowpack including the preferential elution of ions during snowmelt.
Soil and talus subunits include snowpack compartments and two horizons that
incorporate major soil physical and chemical processes. Stream compartments
include snowpack compartments, stream ice and discharge. Lake compartments
include snowpack compartments, ice cover, a hypolimnion, an epilimnion (both
for the lake) and lake or stream discharge. Inputs and outputs to each subunit
are shown by arrows. A) Inputs of precipitation quantity and quality, and dry
deposition to subunits. Output of evapotranspiration from subunits. B) Snowmelt
runoff from the rock subunit is distributed equally to the soil and talus subunits.
C) Surface runoff and subsurface drainage from the soil and talus subunit is routed
to the stream. D) The stream flows into the lake. E) Lake outflow is the discharge
from the basin.
Figure 4. Measured and modeled concentration results for Wolford parameters
[from Wolford et al., 1996], for 1986 and 1987 water years.
Figure 5. Measured and modeled mass flux results for Wolford parameters [from
Wolford et al., 1996], for 1986 and 1987 water years.
Figure 6. Number of simulations versus number of sensitive parameters for ANC
and Na+ for 50% quantile, a of 0.05 and 50 bootstraps.
164
lnflowing Streams
Contour Interval
25 Meters
NORTH
165
166
-{
167
7
>+ 40
cts
30
E 20
V
c.
° io
60
cr
40
5
20
(
< 45
-I+++
-
-H
I
I
+
+
I
H-
II
I
+_
+
++
+
LIII
+
-1-1-
tF±t
+-1+-1-1+
_L___
-±±_— 200
100
200
300 0
100
300
Water year day
Water year day
I
.
168
-'-
-F
-7 -,-
1986
_
-
Modeled
± Measured
-
-
100
200
Water year day
300
100
200
Water year day
1
1987 -
300
169
2
a) 24
465 20
oc = 0.05
sT 16
co
°
12
F.,
8
CI)
-
Na +
Na* mass
ANC
ANC mass
4
0
1000 3000 5000
10000
N points in sample
15000
170
APPENDIX E - MULTI-CRITERIA PARAMETER ESTIMATION FOR
HYDROCHEMICAL MODELS
171
Multi-Criteria Parameter Estimation for Hydrochemical Models
Thomas Meixner, Luis A. Bastidas, Hoshin V. Gupta and Roger C. Bales
Dept. of Hydrology and Water Resources, University of Arizona, Tucson, AZ 85721
172
Abstract
The calibration of hydrochemical models using stream chemical composition and
discharge data is commonly done by manual methods. A body of literature is being
developed on the automatic calibration of hydrochemical catchment models using
multiple response data. These past multiple response model calibration studies have
neglected to investigate which criteria should be used in a multi-criteria framework for
the purposes of parameter estimation and model evaluation. We applied the MOCOMUA algorithm to the Alpine Hydrochemical Model of the Emerald Lake watershed. The
model was calibrated in different ways by varying both the criteria used as well as the
total number of criteria used in the MOCOM-UA algorithm. The results indicate that
fewer criteria yield improved performance for parameter estimation problems with
hydrochemical models. The results also indicate that a mix of mass flux and
concentration criteria should be used in calibrating hydrochemical models. The model
calibration also revealed that the current weathering rate in the AHM model is too low.
The results also raise doubts about the completeness of the current description of
catchment hydrology.
173
Introduction
During the last two decades, many stream chemistry models have been developed
to address issues ranging from acidification, chemical denudation rates, non-point source
pollution, climate change, and land use change [Cosby et al., 1985; Christophersen et al.,
1993; Wolford et al., 1996]. Models of catchment hydrology and hydrochemistry suffer
from two fundamental problems that have uncoupled these models from rigorous
hypothesis testing: i) calibration data do not contain enough information to uniquely
determine model parameters, and ii) state variables within catchment biogeochemical
models are difficult to relate to field observations (e.g. model represents average field
conditions while field measurements are point scale measurements). Two solutions to
these problems have been proposed: i) an improvement in field observations of the
processes that govern stream chemistry, and ii) investigation of hydrochemical models
with synthetic data sets, as has often been done with hydrologic models [Christophersen
et al., 1993]. The first of these solutions has been pursued by a number of different
researchers [Anderson et al., 1997; McDonnell et al., 1998]. While the second has been
pursued, the results are more limited [Kirchner et al., 1996; Mroczkowski et al., 1997].
Recent developments in multi-criteria analysis of hydrologic problems provide a tool that
can be used to solve calibration, estimation, sensitivity and model evaluation problems in
catchment hydrochemical modeling [Gupta et al., 1998].
174
The core issue in multi-criteria analysis of catchment hydrochemical models is
the need to investigate all of the non-commensurate measures of model error
simultaneously. This investigation must occur with recognition of the tradeoffs inherent
in trying to predict several model fluxes simultaneously. As an example, for
hydrochemical modeling of a forested watershed to be successful it is necessary for the
model to match both stream discharge and observed alkalinity. The "best" set of model
parameters for discharge may be a poor set for ANC or vice versa. It is important to
understand that compromises must be made to account for the errors in the structure of
catchment hydrochemical models. The real watershed produces the measured output that
the model is trying to predict but the model must compromise in coming to a "best
solution" that is less accurate than the observed stream chemistry. Therefore, multicriteria parameter estimation is a tool to investigate conceptual errors in catchment
hydrochemical models.
Several applications have been made using multi-criteria model calibration
methods with hydrochemical and hydrologic watershed models. In one recent example
Mroczkowski et al. [1997] investigated using discharge, groundwater state and stream
salinity for a watershed model calibration. They investigated the structure of the model
and chose between two possible model structures. In this study they successfully showed
that using multiple criteria can be used to improve model structure. Another example of
using multiple criteria in model calibration and evaluation is the Birkenes series of papers
[Grosbois et al., 1988; Hooper et al., 19881, which used discharge and 18 0 isotope ratios
175
to calibrate the hydrologic parameters within the Birkenes model. Their work was
successful at improving the Birkenes model but not without incorporating unrealistic
flow paths into the model [Stone and Seip, 1989; Lundquist et al., 1990].
Past studies that used multiple criteria for parameter estimation and model
evaluation have neglected to investigate which criteria should be used. The purpose of
this study was to determine:
i)
what subset of criteria available for AHM calibration at the Emerald Lake
watershed (ELW) are necessary for parameter estimation and model
evaluation,
ii)
what methodology is best suited to selecting the criteria,
iii)
what do the calibration results imply about the hydrologic and
hydrochemical processes that control stream chemical composition in the
ELW, and
iv)
what do the results imply about the model structure?
176
Methods
Multi-Criteria Parameter Estimation Methodology
A thorough discussion of the application of multi-criteria theory to calibration of
conceptual physically based models can be found in [Gupta et al., 1998]. The following
is a brief summary of that methodology. Consider a model with parameters
0 = {O h ...., on) that is to be calibrated with observations (0,) over m simulated model
output variables. For each simulated response X, it is possible to define a criterionfl Co)
that represents the distance between the simulated value X and the observations 0, The
criterion f; may be defined with any number of measures of model error or residual. The
root mean squared error (RMSE) is commonly used since its units are the same as those
of the observations and its values are easy to comprehend. RMSE can be represented as
RMSE(q)=(O — X,(0)) 2(1)
n
with 0 the set of model parameters, n the total number of observations 0, and X the
simulated value at time step t. The multi-criteria model calibration problem can formally
be stated as:
Minimize F(0) = { fi (0),..., f„(0)} subject to 0 c 0
(2)
where the goal is to find values for 0 within the feasible set 0 that minimize all of the
criteria (f( e), 1.1,...,m) simultaneously.
177
In practice it is not possible to minimize all criteria simultaneously. Instead a
set of solutions is commonly found, with the property that within the set of solutions it is
necessary to deteriorate performance at simulating one criteria in order to improve the
performance of a second criteria. Figure I illustrates a multi-criteria problem with two
parameters (0, and 02 ) and three criteria (f,, f, and f, ). Figure la shows the feasible
parameter space e and Figure lb is a projection of the multi-dimensional criteria space
onto a 2-dimensional plot. The points a, p, and yindicate the three solutions which
minimize each of the individual criteria. The shaded region indicates the Pareto set
solution to the minimization problem. The points 8 and E represent arbitrary points in the
feasible space in and outside the Pareto set. Every point 5 is superior to every point E, i.e.
(S) <4(8), for all j = 1,...3. However no point within the Pareto set is superior to any
other point. A particular point may be superior for one or more criterion, but it will be
inferior to other points for at least one criterion. The Pareto set is sometimes called the
trade-off set, non-inferior set, non-dominated set or the efficient set. The Pareto set
represents the best solution available through model calibration without incorporating the
subjective judgment stating that one or more of the criteria are more important than the
others. The size of the Pareto set is related to errors in model structure and the calibration
data set. Only when a perfect model and perfect data are available will the Pareto set be a
unique solution.
178
MOCOM-UA
A number of different methodologies are available for solving the multi-criteria
problem. Recently, [Yapo, 1996] presented an efficient population-based optimization
strategy that provides an approximate representation of the Pareto set with a single
optimization run. This algorithm, Multi-Objective Complex Evolution (MOCOM-UA),
is based on the successful SCE-UA optimization method [Duan et al., 1992; Duan et al.,
1993]. The MOCOM-UA method begins by sampling the feasible space (9 at a number
of preset locations and then evolves that population using multi-criteria methods to drive
the sample towards the Pareto set; for details see [Yapo, 1996]. The final solution
consists of a set of points that approximate the Pareto set.
Site Description
This application of AHM builds on the original application of the model to the
ELW during an intensive field campaign conducted from 1985 until 1987 [Tonnessen,
1991; Wolford et al., 1996]. ELW is a 120 ha headwater catchment located in the Sierra
Nevada (36 ° 35' N, 118 ° 40' W), with elevation ranging from 2800 m at the lake to 3417
m at the summit of Alta Peak. The watershed is 48% covered by exposed granite and
granodiorite, 23% by soil and 23% by talus and includes a 2 ha lake.
179
Model
The ARM [Wolford et al., 1996] is a lumped conceptual model that was designed
for simulating the hydrology and biogeochemistry of alpine watersheds. It was originally
applied to the ELW with the intent of investigating the sensitivity of Sierra Nevada
watersheds to changes in climate and deposition. Modeling a watershed with the ARM
requires specification of the particular watershed structure in which the hydrologic and
biogeochemical processes occur. The ELW was partitioned into three terrestrial subunits
(rock, talus and soil) and a stream (Figure 2). Within this structure, a set of parameters
define the routing of flow from the rock subunit to the talus and soil subunits, and from
there sequentially into the stream, the lake and out of the watershed.
Each terrestrial subunit is made up of different compartments (representing the
snowpack, snowpack free water, snowmelt, surface runoff, interception by trees and
litter) and may contain multiple soil horizons. Stream subunits are made up of different
compartments representing the snowpack, snowpack free water, snowmelt, stream ice
and streamflow. Lake subunits contain similar compartments to the stream subunits as
well as a layered lake model that includes a hypolimnion and epilimnion. Model subunits
may be selected for use according to the complexity of the watershed. At each time step,
hydrologic processes are modeled separately from geochemical processes. Routing
between the subunits is handled separately from the structure of the individual subunits.
180
AHM simulates the watershed response on a daily time step. At each time step
the model adjusts hydrologic and chemical inputs, outputs, and state variables for 13
separate compartments representing, snow, vegetation, infiltration, and soil processes.
Model output can include detailed descriptions of all chemical calculations, tracking of
both chemical and hydrologic storages and changes in storage within the watershed, soil
chemical concentrations and stream concentrations. Chemical speciation is handled
using equations adapted from MINEQL [Westall et al., 1976]. The "strength" of the
model is its precise calculations of mass and charge balance for chemical species and
hydrologic fluxes [Wolford et al., 1996].
Applying MOCOM-UA to AHM
The MOCOM-UA algorithm was applied to the AHM model of ELW for the
1986 and 1987 water years. The parameters used and their feasible space were
determined from available field data or generally accepted understandings of the
variability of hydrologic parameters in the field (Table 1) [Meixner et al., 1999]. The
AHM model of ELW simulates a total of 11 fluxes that can be readily compared with
available stream observations. The wealth of criteria available for model calibration
provides both opportunities and difficulties in applying multi-criteria methods to this
model. Since criteria containing similar information should not be used simultaneously
in a multi-criteria optimization problem [Gupta et al., 1998], we developed four sets of
181
criteria that were independent of each other. The first set chosen was on the basis of a
correlation analysis of the observations of stream chemical composition at the Emerald
outflow. The correlation analysis showed that the time series for discharge, H + , Ca 2+ ,
SO4 2 , NO3 - , and Si were not correlated with each other (p < 0.6). The concentration
criteria for these five chemical species were used.
The remaining three sets of criteria used were selected on the basis of information
gained from the sensitivity analysis [Meixner et al., 1999]. Two changes to the 6 selected
criteria were made for the second of the four criteria sets used. Since the current
representation of nitrogen chemistry in the AHM was known to be inadequate and the
sensitivity results had shown that the Cl - mass flux criteria was very good for estimating
the ionic pulse, the NO3 - criteria was replaced by the Cl - mass flux criteria. The Ca2+
concentration criteria was replaced by the Ca2+ mass flux criteria due to the greater
parameter sensitivity shown for the mass flux criteria.
For the third and fourth of the criteria sets the number of criteria used was
reduced from 6 to 4. The large number of criteria (6) could cause a very large Pareto set
to be found and by reducing the number of criteria it might be possible to reduce the size
of the Pareto set. For both cases discharge, Ca2+ , SO4 2- , and
cr were used as the set of
criteria. For the first case all chemical criteria were represented as concentration and for
the second case Ca 2+ and CI mass flux criteria were used instead of the concentration
-
criteria.
182
For each of these sets of criteria three estimations of the Pareto set were
conducted. One using a set of 20,000 Monte-Carlo simulations and two using the
MOCOM-UA algorithm, one with a population of 100 points and one with a population
of 250 points. The results were compared to the original results of Wolford [1992] as
well as the available stream chemical observations for 1986 and 1987.
Results
Increasing the search population size enabled an improved calibration of the
model with smaller RMSE values as shown in Figure 3. The random search gave inferior
results to the MOCOM-UA algorithm and the search with 100 points gave results inferior
to those with 250 points. Comparing the RMSE values for the MOCOM-UA parameter
estimation results with the RMSE values from manual calibration [Wolford, 1992] shows
that for the chemical criteria the RMSE results are superior while for discharge the
original Wolford results are generally superior.
The calibration results for each of the four sets of criteria used in the MOCOMUA algorithm can be viewed in four different ways: parameter space, criteria space, time
series for criteria included in the calibration, and time series for criteria not included in
the calibration. The results for each of these methods will be presented separately for the
250-point search case.
183
The parameter space results for each of the sets of criteria show a tightening of
the parameter space in the four as opposed to the six criteria space. In fact the results for
the parameter space for both of the 6 criteria cases cover almost the entire feasible
parameter space (Figure 4 and 5). The parameter space is much more confined for the
two searches conducted with 4 criteria (Figure 6 and 7). The parameter space results for
the two cases using 4 criteria with the MOCOM-UA algorithm differ for soil hydraulic
conductivity (Ksat). Using two mass flux criteria results in a higher estimated Ksat
value. Also using mass flux criteria resulted in a higher and more precise estimate for the
ET parameter on the talus subunit. The incorporation of mass flux data also resulted in
more precise estimations for cation exchange parameters (K-Ca(soil), K-K(soil), K-
Ca(talus), and K-Mg(talus) despite including more exchange parameters than in the 4
criteria case using all concentration criteria (more parameters were added as the results
from the sensitivity analysis indicated [Meixner et al., 1999]. More precise estimates
were also made for the K-SO4 and PCO2 parameters when mass flux criteria were
incorporated into the search algorithm. Finally for both cases using just 4 criteria a
higher value of the mineral weathering parameter a than used by [Wolford and Bales,
1996]was indicated.
The results also show significant differences in the criteria space for each of the
four sets of criteria used in the MOCOM-UA search. The criteria space is shown in each
of the figures as the calculated RMSE divided by the mean observed value for the criteria
184
in question (Figure 4, 5, 6 and 7). This was done to facilitate ease of interpretation of
the results and to make comparisons of the results for different calibrated and noncalibrated criteria easier. RMSE represents the variance of the simulated values, dividing
by the mean gives us an order of magnitude representation as to how accurate the
simulations were for each of the 250 Pareto set results from the MOCOM-UA algorithm.
For each of the 4 figures the criteria results for Wolford et al. [1996] (shown in black) can
be used as benchmarks to compare the results of each of the criteria sets used. Both cases
where 6 criteria were used in the MOCOM-UA algorithm show dramatically inferior
Pareto set criteria space results as compared to the results using only 4 criteria. In fact
the results almost represent what is produced by randomly varying the parameter values
across the feasible space (Figure 8).
The results for 4 in the criteria space (Figure 6 and 7) were much better than those
using 6 criteria (Figure 4 and 5). In some cases the MOCOM-UA results represent
dramatic improvements over the calibration results found by Wolford et al. [1996]. This
result is particularly true when a mix of mass flux and concentration criteria are used
(Figure 7).
One benefit of the multiple parameter sets that are a result of multi-criteria
parameter estimation algorithms, such as MOCOM-UA, is that each set can then be used
to drive the model and show the user what the time series space results for the estimated
parameters look like. Good parameter estimates should bound the observations as well as
provide precise simulation of those observations. This is equally true for observations
185
that were included in the search as well as those that were not. The time series results
for the 6 criteria (just concentration) and the 4 criteria cases (using concentration and
mass flux) show that the 6 criteria search results do bound the observation but only by
having very wide bounds around the observations (Figure 9 and 10). This is equally true
whether the criteria were included in the calibration or were not included in the
calibration. The 4 criteria results do a relatively good job of bounding those observations
included as criteria during the search (Figure 11) but does an inferior job in terms of
bounding the observations for criteria not incorporated in the search algorithm (Figure
12). The mean simulated concentration for the Pareto set simulations also show some
improvement over the concentration simulations garnered by Wolford and Bales [1996]
(Figure 11). This is not true for the species not used in calibration (Figure 12).
Discussion
These results indicate that fewer rather than more criteria are preferable for multicriteria calibration of hydrochemical models. There are three possible reasons for the
improved performance of the calibration with fewer rather than more criteria. First, by
adding criteria it is impossible to decrease the size of the Pareto set. Referring back to
Figure 2 you can see that the Pareto set in a two criteria case is a line. When a third
criteria is added the Pareto set can remain the same (if the optimum point for the third
criteria is on that line) or become larger as is the case in Figure 2. Second the 6 criteria
186
we selected may contain similar information about the hydrologic and hydrochemical
processes in the ELW. If they do contain similar information then adding criteria simply
adds more noise and presents particular difficulties for multi-criteria methods since the
criteria must contain non-commensurate information [Gupta et al., 1998]. The results for
the 6 criteria cases would appear to indicate that using a correlation analysis of stream
chemical observations is not the optimal method for determining the criteria that should
be used for parameter estimation of hydrochemical models. Finally, the observations of
stream chemical composition in the ELW may contain distinct and non-commensurate
information about the hydrologic and hydrochemical processes of the watershed but an
inadequacy of model structure does not permit this information to be expressed in the
calibration process.
The use of the sensitivity analysis results in developing both of the 4 criteria cases
indicates that the results of generalized sensitivity can be used to determine what set of
criteria should be used in multi-criteria parameter estimation problems. The results were
superior for both of the more limited sets over the 6 criteria problems. Also the 4 criteria
case which incorporated Ca 2 + and Ci mass flux show marked improvement over the case
where only the concentration criteria were used. This result is evidenced in the superior
performance of the mix of mass flux and concentration criteria in both the parameter and
criteria space (Figure 6 and 7). The choices of criteria in this work were qualitative and
subjective based on an expert's view of the sensitivity analysis results for selecting the
criteria that were to be used for the multi-criteria calibration. A more objective and
187
rigorous approach to utilizing the sensitivity results for criteria selection should be
pursued.
The calibration results for the four criteria calibration also give us information
about the natural processes that control stream chemical composition in the ELW. In his
original manual calibration of the AHM model of the ELW, Wolford [1992] cut the
weathering rate in half due to model overpredictions of observed ANC. The calibration
results here for either of the 4 criteria cases indicate that the weathering rate chosen was
too low as the calibrated values for the mineral weathering parameter a for all 250 points
for either 4 criteria case are greater than the Wolford parameter value. The 4 criteria
results also indicate that a smaller ionic pulse would best simulate the observed stream
chemistry since both of the limited criteria calibrations resulted in lower estimated values
of the elution parameter. Since the two 4 criteria cases gave conflicting results for the
various hydrologic parameters the calibration results give us little information about the
hydrologic process controlling stream chemical composition.
The lack of coherence in the hydrologic parameter results may be giving us
information about the current structure of the model. The significant differences in
parameter space for the two 4 criteria results indicate that simulating mass flux requires
more rapid flow through soil while simulating concentration requires slower flow through
soil. The conflict indicates that the hydrologic representation of the ELW by the AHM
may not be complete and should be investigated to see what changes in model structure
could improve the multi-criteria calibration results. Possible changes to the model that
188
could be investigated are: lumping soil and talus together as a single process, or
incorporating a third soil and/or talus horizon that has even slower release of water than
the second horizon currently present in both soil and talus subunits within the AHM
model of the ELW.
Conclusions
Multi-criteria parameter estimation is a promising avenue for investigating the
accuracy and structure of hydrochemical watershed models. A number of steps must be
completed before the full power of multi-criteria techniques can be realized. The
preliminary results from this work indicate a need to limit the number of criteria used in
multi-criteria analysis of hydrochemical models. The sources of difficulty with using
more criteria lie in the methodology as well as the structure of hydrochemical models.
The results from generalized sensitivity analysis showed promise in being used to
determine the proper number and which criteria should be used in multi-criteria
parameter estimation problems. A more rigorous framework should be developed so that
criteria selection is objective and complete. The multi-criteria parameter estimation
results for the AHM model of the ELW indicated a need to increase the rate of mineral
weathering and decrease the magnitude of the ionic pulse. The results also indicated a
need to investigate the hydrologic structure of the model for inaccuracies and
inadequacies.
189
Acknowledgements
This work was made possible by a Canon National Park Science Scholarship to the
primary author. This work was conducted, in part, for completion of a Ph.D. by the lead
author at the University of Arizona. Partial support for this work was provided by
NASA-EOS, NSF and NOAA research grants. Special thanks to Jim Sickman, Al
Leydecker and John Melack for their help in interpreting field data and to the Surface
Water Calibration Research Group at the University of Arizona for the many good
conversations and quality insight into model calibration and parameter estimation.
190
References
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191
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model for the Birkenes Catchment, J. Hydra, 11 6:391-401, 1990.
192
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New method developed for studying flow on hillslopes, EOS, Trans. AGU,
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Mass Flux and Concentration, Hydrol. Processes, in press: 1999.
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Stone, A. and H. M. Seip, Mathematical models and their role in understanding water
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18:192-199, 1989.
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Water. Resourc. Res., 27:1537-1539, 1991.
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193
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194
Table 1. Parameters varied and range relative to values by Wolford et al. [1996]
Parameter'
Range
ET b
0-1
Soil — depth'
0.5-1.5
NC
0.8-1.8
I<L,t
0.2-4
Osat
0.5-1.5
Elution(D d )
0.5-1.5
K-Ca 2 +e
0.5-1.5
K-Mg 2 +e
0.5-1.5
K-Na+e
0.5-1.5
0.5-1.5
K-S0 42 -f
0.5-1.5
K-Si r
0.5-1.5
Soil P
02
0.5-1.5
0.5-1.5
ah
a
0.5-1.5
The hydrologic parameters and cation exchange coefficients were varied
independently for each subunit within the same mathematical range.
b
ET represents the fraction of potential evapotranspiration that is permitted to
occur; the varied range is the possible range.
The parameters Soil-depth, N, K sat , and O sa t represent total depth of soil on a
subunit, a drying coefficient for unsaturated flow, saturated hydraulic
conductivity and saturated soil water holding capacity.
195
d
The equation used to represent snowpack elution in AHM is:
—BxX)
—DxX).
1 — A) x D x e (I
=AxBxe ((
n the models current form A
v ave
and B are small so D is the dominant parameter and was thus the parameter
used in the sensitivity analysis.
e Log K for exchange of cation with H+ on cation exchange site.
f
Log K for adsorption of SO 42- and H 2 SiO 3 . Total site concentrations from ELW
optimization used here. These parameters cannot be varied independently for
the soil and talus subunit.
g The partial pressure of carbon dioxide P co , was varied simultaneously for both
subunits.
h
The weathering coefficients bc and a were varied independently of each other
but uniformly for all species due to issues of charge balance. They contribute to
weathering via the equation: Mol = A x
[H+r where Mol is moles added to
the subunit, A is total area of the surfaces involved in reactions, [H+] is
hydrogen ion concentration, and and a are constants. The total surface area is
determined as the product of the soil depth, area, bulk density, and specific
surface area.
196
a) Parameter Space
b)Criterion Space
f2
fi
L
Parameter 01
t3
fi
f2
Figure 1 Simple demonstration of Pareto set in a two parameter three criteria
situation.
197
Figure 2 Schematic of AHM Model of the Emerald Lake
Watershed. A Represents precipitation and evapotranspiration.
B represents flow routed from rock subunit onto soil and talus
subunits. C is surface and subsurface flow to stream from soil
and talus. D is inflow to lake. E is lake outflow.
198
0
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207
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208
APPENDIX F SOURCE CODE FOR A NITROGEN MODEL FOR ALPINE
WATERSHEDS (ANIMAL)
209
Program nmodel
This program is a recreation
from the published literature of the CENTURY
model without the soil temperature model or
the hydrology of the CENTURY model. The only
portion of CENTURY incorporated into
this model is its N dynamics. Some additional
improvements will be made to the model once
translated into fortran.
1)
incorporation of SOil T under snow
2)
breaking up landscape subunits to
represent variable SCA of basin.
3)
driving model input with AHM output
include common sets of parameters.
INCLUDE 'nparams.inc'
INCLUDE 'ndeclare.inc'
INCLUDE 'ncommon.inc'
210
---- Read in user defined variables form a file --C
subroutine reads in constants, initial condition
location information and input time series
WRITE (*,*) ' Read in parameters from User defined Files'
CALL READNDAT
Calculate variables that will stay
constant for the entire run.
WRITE (*,*) ' Caluclate constants dependent on inputs'
CALL CONSTCALC
the following subroutine represents the bulk of the model
it also further calls several other subroutines.
CALL NCYCLE
STOP
END
211
SUBROUTINE READNDAT
•
This subroutine reads in user defined N parameters from the file
uservar
include commmon sets of parameters.
INCLUDE 'nparams.inc'
INCLUDE 'ndeclare.inc'
INCLUDE 'ncommon.inc'
INTEGER i
CHARACTER*11 varname
The file name 'constants is for
•
all parameters that should be inputed as
user defined constants currently this is
•
commented out as I have hardwired in these constants
for now.
TM 9/1/98
OPEN(unit=40, file='constants',status='OLD')
READ(40,*) kl,varname
READ(40,*) k2,varname
READ(40,*) k3,varname
READ(40,*) k4,varname
212
READ(40,*) k5,varname
READ(40,*) k6,varname
READ(40,*) k7,varname
READ(40,*) k8,varname
CLOSE(unit = 40)
readin information from file name initial
OPEN(unit=41, file='initial',status='OLD')
READ(41,*) mineraln(1),varname
READ(41,*) c(1,1),varname
READ(41,*) c(2,1),varname
READ(41,*) c(3,1),varname
READ(41,*) c(4,1),varname
READ(41,*) c(5,1),varname
READ(41,*) c(6,1),varname
READ(41,*) c(7,1),varname
READ(41,*) c(8,1),varname
READ(41,*) c2n(1,1),varname
READ(41,*) c2n(2,1),varname
READ(41,*) c2n(3,1),varname
READ(41,*) c2n(4,1),varname
READ(41,*) c2n(5,1),varname
READ(41,*) c2n(6,1),varname
READ(41,*) c2n(7,1),varname
213
READ(41,*) c2n(8,1),varname
READ(41,*) liveroot(1),varname
READ(41,*) liveshoot(1),varname
READ(41,*) rootn(1),varname
READ(41,*) shootn(1),varname
READ(41,*) stddead(1),varname
READ(41,*) stddeadn(1),varname
CLOSE(unit = 41)
if ( mineraln(1)
.LE. 2.0) c2n(3,1) = -6.0*mineraln(1) + 15
if ( mineraln(1)
.LE. 2.0) c2n(7,1) = -4.0*mineraln(1) + 20
if ( mineraln(1)
.LE. 2.0) c2n(8,1) = -1.5*mineraln(1) + 10
n(1,1) = c(1,1)/c2n(1,1)
n(2,1) = c(2,1)/c2n(2,1)
n(3,1) = c(3,1)/c2n(3,1)
n(4,1) = c(4,1)/c2n(4,1)
n(5,1) = c(5,1)/c2n(5,1)
n(6,1) = c(6,1)/c2n(6,1)
n(7,1) = c(7,1)/c2n(7,1)
n(8,1) = c(8,1)/c2n(8,1)
OPEN(unit=42, file='location',status='OLD')
WRITE(*,*) 'reading in location defined parameters'
READ(42,*) tsi,varname
READ(42,*) thetawilt,varname
214
READ(42,*) thetasat,varname
READ(42,*) depth,varname
READ(42,*) ts,varname
READ(42,*) tc,varname
READ(42,*) appt,varname
READ(42,*) pmax,varname
READ(42,*) totdays,varname
CLOSE (UNIT=42)
read inputs
WRITE(*,*) 'Reading in time series inputs'
OPEN(unit=43, file='inputs',status='OLD')
DO 150 i = 1,totdays
READ(43,*) temp(i),dep(i),aguaout(i),theta(i)
150
CONTINUE
CLOSE(unit=43)
C
RETURN
END
215
SUBROUTINE CONSTCALC
This subroutine calculates parameters that depend
on user defined inputs. The Parameters are
then used for the remainder of the
model run.
include
commmon
sets of parameters. INCLUDE 'nparams.inc'
INCLUDE 'ndeclare.inc'
INCLUDE 'ncommon.inc'
tm is the factor that helps control the decomposition of
active SOM
text = tsi + tc
tm = 1 - 0.75*text
ft controls the fraction of active SOM that ends
up as CO2
ft = 0.85-0.68*text
cap controls fraction of active som that becomes passive som
tc is the fraction of the soil that is clay
216
cap = 0.003+0.032*tc
csp controls the fraction of slow sent to passive
csp = 0.003 - 0.009*tc
csa controls amount of slow allocated to active
csa = 1 - csp - 0.55
cmax and cmin determine maximum and minimum C:N ratios
for biomass
cmax = 44 + 0.2*appt
cmin = 39 + 0.2*appt
root to shoot ratio is determined by using
annual precipitation to determine the ratio
this equation is based on Parton et al. 1987
pamax = -40 + 7.7 *appt
rmax = 100 + 7.0*appt
root2shoot = rmax/pamax
217
1 is lignin fraction of biomass
C
C
calulated using annual mean precipitation
C
lr is for roots
C
la is for soils
C
lr = 0.26 - 0.0015 * appt
la = 0.02 + 0.0012 * appt
C
N fixation is also dependant on annual precipitation
C
C
C
nfix = -0.18 + 0.014 * appt
nfix = 0.0
RETURN
END
218
SUBROUTINE NCYCLE
C
This subroutine conatins the entire
C
C
SOM dynamics and production models.
C
The equations for this subroutine are
C
culled from PArton et al. 1987 and 1993
C
INCLUDE 'nparams.inc'
INCLUDE 'ndeclare.inc'
INCLUDE 'ncommon.inc'
First I need to declare some local varaibles
C
INTEGER i,j,k,jj
REAL cal,fn,cas,c2nin(box),thetaabs,mp,production,tp,
&
fg,navail,possc2n,nuptake,prod(days),newroot,newshoot,tpl,
&
newrootn,newshootn,rd,sd,anfrac,rnfrac,12na,12nr,fma,fmr,
&
fsa,fsr,lca,lcr,td,md,a,dec(box),minc(box),inc(box),
&
nlossc(box),nin(box),mnrlzdextra(box),minctot(days),origprod,
&
minlosston2o(days),minlosston2,minlosttoleach,norig,
&
mnrlzdxtra(days),litterfall(days),rootlitter(days),
&
litterfalln(days),rootlittern(days),rootlitterc2n(days),
&
litterfallc2n(days),td1,abiomass(days),rbiomass(days),track,
&
ninputs,noutputs,nstored,nstoredlast,deltas,nbal,deltas2,
& nprod,prelive,predead,livedead,stddeadc2n(days),shootndie(days),
219
& shootdead,liga,noliga,ligr,noligr,availh2o,
& live2dead,sp
DO 500 jj = 1,40
IF ( JJ .GT. 1 ) THEN
c(1,1) = c(1,totdays)
c(2,1) = c(2,totdays)
c(3,1) = c(3,totdays)
c(4,1) = c(4,totdays)
c(5,1) = c(5,totdays)
c(6,1) = c(6,totdays)
c(7,1) = c(7,totdays)
c(8,1) = c(8,totdays)
n(1,1) = n(1,totdays)
n(2,1) = n(2,totdays)
n(3,1) = n(3,totdays)
n(4,1) = n(4,totdays)
n(5,1) = n(5,totdays)
n(6,1) = n(6,totdays)
n(7,1) = n(7,totdays)
n(8,1) = n(8,totdays)
mineraln(1) = mineraln(totdays)
liveroot(1) = liveroot(totdays)
liveshoot(1) = liveshoot(totdays)
rootn(1) = rootn(totdays)
220
shootn(1) = shootn(totdays)
rootc2n(1) = rootc2n(totdays)
shootc2n(1) = shootc2n(totdays)
stddead(1) = stddead(totdays)
stddeadn(1) = stddeadn(totdays)
stddeadc2n(1) = stddeadc2n(totdays)
c2n(1,1) = c2n(1,totdays)
c2n(2,1) = c2n(2,totdays)
c2n(3,1) = c2n(3,totdays)
c2n(4,1) = c2n(4,totdays)
c2n(5,1) = c2n(5,totdays)
c2n(6,1) = c2n(6,totdays)
c2n(7,1) = c2n(7,totdays)
c2n(8,1) = c2n(8,totdays)
ENDIF
Next I need to OPEN and afterwards close several files
OPEN(unit=44, file='carbon',status='UNKNOWN')
OPEN(unit=45, file='nitro',status='UNKNOWN')
OPEN(unit=46, file='biomass',status='UNKNOWN')
OPEN(unit=47, file='c2nratios',status='UNKNOWN')
OPEN(unit=48, file='production',status='UNKNOWN')
221
C
C
DO loop covers the rest ot this subroutine
DO 200 i = 2,totdays
C
C
First calculate the items that are constant for this iteration
cal is the fraction of active som leached
cal = (aguaout(i)*30.0/18.0)*(0.01+0.04*ts)
C
C
fn is fraction of mineral n lost to subsurface
during a time step
fn = (aguaout(i)/18)*(0.2+0.7*ts)
C
cas is the fraction of active som that goes
C
to the slow som compartment
cas = 1 - cal - cap -ft
track = i /1.0
if ( (track/10000) .EQ. (int(track/10000))) WRITE (*,*) track
C
Calculate new C/N ratios for all compartments
222
c2nin(1) = 150.0
c2nin(2)
= 150.0
c2nin(5)
=
c(5,i-1)/n(5,i-1)
c2nin(6) =
c(6,i-1)/n(6,i-1)
c2nin(3) =
3
if ( mineraln(i-1) .LT. 2.0) c2nin(3) = -6.0*mineraln(i-1)+15
c2nin(7) = 12
if ( mineraln(i-1) .LT. 2.0) c2nin(7) = -4.0*mineraln(i-1)+20
c2nin(8) = 7
if ( mineraln(i-1) .LT. 2.0) c2nin(8) = -1.5*mineraln(i-1)+10
c2nin(4) = 10
if ( (anfrac*100) .LT. 2.0) c2nin(4) = -5*(anfrac*100) + 20
---- add in deposition from atmosphere C
mineraln(i) = mineraln(i-1) + dep(i)
write(*,*)i,mineraln(i-1)+dep(i)-mineraln(i)
C
C
Temperature requirements for plant production
tp = tp1(temp(i))
C
Water availability limits on plant production
223
C
changed from CENTURY to use state variable as
C
opposed to CENTURY which uses rain+stored over PET
thetaabs = (theta(i)-thetawilt)/(thetasat-thetawilt)
mp = (thetaabs) * 1.24 - 0.060
if (thetaabs .GT. 0.85) mp = 1.00
if (mp .LT. 0) mp = 0
write(*,*)i,mp,md
C
C
Effects
of shading
live2dead = liveshoot(i-l)/(stddead(i-1))
IF (live2dead .GT. 2.0) THEN
sp = 1.0
ELSEIF
(live2dead .LT. 1.0) THEN
sp = 0.4*live2dead + 0.3
ELSE
sp = 0.3*live2dead + 0.5
ENDIF
C
calculate possible production
production = pmax * tp * mp * sp
224
C
write(*,*)i,mp
introduce nutrient limitation
C
fg = 1.0 -(0.8 * (exp(-0.015*liveroot(i-1)*2.2)))
fg = fg
navail = fg * mineraln(i)
C
nprod = navail
nprod = navail + nfix
C
incorporate nutrient limitation on production.
origprod = production
norig = nprod
ninputs = navail
possc2n = production/nprod
nuptake = 0
IF (possc2n .GE. cmax) THEN
production = cmax*nprod
possc2n = cmax
ENDIF
IF (possc2n .LE. cmin) THEN
nuptake = production/cmin
nprod = nuptake
possc2n = cmin
225
ENDIF
IF ( nprod .LT. norig ) THEN
IF( nprod .LT. nfix) THEN
navail = 0.0
ENDIF
IF( nprod .GT. nfix) THEN
navail = nprod-nfix
ENDIF
IF (nprod .EQ. 0.0) navail = 0.0
ENDIF
prod(i) = production
mineraln(i) = mineraln(i) - navail
C
write(*,*) i,prod(i),origprod
C
root to shoot ratio for produced biomass
C
is dependent on precipitation as described in Parton et al. 1987
newroot = root2shoot*(production/(root2shoot + 1))
newshoot = production/(root2shoot+1)
liveroot(i) = liveroot(i-1) + newroot
liveshoot(i) = liveshoot(i-1) + newshoot
newrootn = root2shoot*(nprod/(root2shoot + 1))
newshootn = nprod/(root2shoot+1)
rootn(i) = newrootn + rootn(i-1)
shootn(i) = newshootn + shootn(i-1)
226
rootc2n(i) = liveroot(i)/rootn(i)
shootc2n(i) = liveshoot(i)/shootn(i)
write(*,*)i,newshoot,production,root2shoot+1,
C
C
&
production/(root2shoot+1)
C
On above I currently incorporate tracking for each
C
compartment independent of each other
C
in reality I only need to tack either c2n ratio or n stored
C
Now to incorporate the death model
availh2o = (theta(i)-thetawilt)*depth
rd = 0.12*(exp(-5.0*availh2o))/30
sd = 0.20*(exp(-5.0*availh2o))/30
C
rd = 0.04/30.0
C
sd = 0.06/30.0
C
C
write(*,*)i,rd,sd,availh2o,depth,theta(i),thetawilt
litterfall
and standing dead biomass prelive = shootn(i)
predead = stddeadn(i-1)
IF ( temp(i) .LT. 0 .AND. temp(i-1) .GT. 0) THEN
rd = 0.12*(exp(-5.0*availh2o))/30
sd = 0.95
C
rd = 0.04/30.0
C
sd = 0.96
rootlitter(i) = liveroot(i)*rd
227
liveroot(i) = liveroot(i) - rootlitter(i)
rootlittern(i) = rootn(i)*rd
rootn(i) = rootn(i) - rootlittern(i)
rootlitterc2n(i) = rootlitter(i)/rootlittern(i)
shootdead = liveshoot(i)*sd
liveshoot(i) = 1iveshoot(i) - shootdead
stddead(i) = shootdead + stddead(i-1)
shootndie(i) = shootn(i)*sd
shootn(i) = shootn(i) - shootndie(i)
shootndie(i) = shootndie(i)*0.96
stddeadn(i) = stddeadn(i-1) + shootndie(i)
litterfall
litterfall(i) = stddead(i-1)*(0.2/30.0)
litterfalln(i) = stddeadn(i-1)*(0.2/30.0)
litterfallc2n(i) = litterfall(i)/litterfalln(i)
stddead(i) = stddead(i) - litterfall(i)
stddeadn(i) = stddeadn(i) - litterfalln(i)
write(*,*) i,rootlitter(i),rd,sd,liveroot(i),availh2o
ELSE
rootlitter(i) = liveroot(i)*rd
liveroot(i) = liveroot(i) - rootlitter(i)
rootlittern(i) = rootn(i)*rd
rootn(i) = rootn(i) - rootlittern(i)
rootlitterc2n(i) = rootlitter(i)/rootlittern(i)
shootdead = liveshoot(i)*sd
228
liveshoot(i) = liveshoot(i) - shootdead
stddead(i) = shootdead + stddead(i-1)
shootndie(i) = shootn(i)*sd
stddeadn(i) = stddeadn(i-1) + shootndie(i)
shootn(i) = shootn(i) - shootndie(i)
litterfall
litterfall(i) = stddead(i-1)*(0.2/30.0)
litterfalln(i) = stddeadn(i-1)*(0.2/30.0)
litterfallc2n(i) = litterfall(i)/litterfalln(i)
stddead(i) = stddead(i) - litterfall(i)
stddeadn(i) = stddeadn(i) - litterfalln(i)
write(*,*) i,rootlitter(i),rd,sd,liveroot(i),availh2o
ENDIF
stddeadc2n(i) = stddead(i)/stddeadn(i)
write(*,*) i,rootlitter(i),rd,sd,liveroot(i),availh2o,
& newroot
nitro is Nitrogen fraction of biomass
calculating fraction of n in biomass
requires calculating biomass and then
n fraction of that biomass
for now I will multiply carbon
by 2.222 to get biomass of a compartment
229
abiomass(i) = 2.222 * litterfall(i)
rbiomass(i) = 2.222 * rootlitter(i)
C
anfrac is for above ground n fraction
C
rnitorfrac is for below groudn n fraction
anfrac = litterfalln(i)/abiomass(i)
rnfrac = rootlittern(i)/rbiomass(i)
C
C
12n is the ratio of lignin to N
find lignin to n ratio for incoming litter of each compartment
12na = la/anfrac
12nr = lr/rnfrac
C
fm determines partioning between structural and metabolic
C
litter pools
fma = 0.85 - 0.018*12na
fmr = 0.85 - 0.018*12nr
C
flip side of above
fsa = 1 -fma
fsr = 1 -fmr
230
lc is a further correction factor for structural litter that
depends on the lignin content of the particular
pool of interest
liga = la/fsa
ligr = 1r/fsr
noliga = 1 - liga
noligr = 1 - ligr
lca = exp(-3.0*(liga))
lcr = exp(-3.0*(ligr))
write(*,*)i,fsa,liga,fsr,ligr,lca,lcr
Decay amounts for each of the eight compartments
td = td1(temp(i))
md = (theta(i)-thetawilt)/(thetasat-thetawilt)
write(*,*)i,td,md,td*md
a = td * md
dec(1) = c(1,i-1)*kl*a*lca
dec(2) = c(2,i-1)*k2*a*lcr
dec(3) = c(3,i-1)*k3*a*tm
dec(4) = c(4,i-1)*k4*a
dec(5) = c(5,i-1)*k5*a
dec(6) = c(6,i-1)*k6*a
231
dec(7) = c(7,i-1)*k7*a
dec(8) = c(8,i-1)*k8*a
N lost to mineralized pool
C
from compartment due to decay of organic matter
C
C
mineralization
minc(1) = (dec(1)/c2n(1,i-1))*0.3*liga +
&
(dec(1)/c2n(1,i-1))*0.6*noliga
minc(2) = (dec(2)/c2n(2,i-1))*0.3*ligr +
&
(dec(2)/c2n(2,i-1))*0.55*noligr
minc(3) = (dec(3)/c2n(3,i-1))
* ft
minc(4) = (dec(4)/c2n(4,i-1))
* 0.6
minc(5) = (dec(5)/c2n(5,i-1))
* 0.6
minc(6) = (dec(6)/c2n(6,i-1))
* 0.55
minc(7) = (dec(7)/c2n(7,i-1))
* 0.55
minc(8) = (dec(8)/c2n(8,i-1))
* 0.55
C
Increases in each carbon compartment due to litterfall
C
and fluxes of C due to movement of C from one
C
box to the next.
inc(1) = fsa * litterfal1(i)
inc(2) = fsr * rootlitter(i)
232
inc(3) = dec(2)*noligr*0.45 + dec(6)*0.45 +
&
csa*dec(7) + dec(8)*0.45
inc(4) = (dec(1)*no1iga)*0.4 + dec(5)*0.4
inc(5) = fma * litterfall(i)
inc(6) = fmr * rootlitter(i)
inc(7) = dec(2)*ligr*0.7+dec(1)*liga*0.7+
dec(4)*0.4+ cas*dec(3)
&
inc(8) = csp*dec(7) + cap*dec(3)
C
write(*,*)i,cas,cal,cap,ft,cas+cal+cap+ft
C
write(*,990) i,dec(3),inc(3),dec(2)*noligr*0.45,dec(6)*0.45,
C
& csa*dec(7),dec(8)*0.45,c(3,i-1)
C990
FORMAT(I5,6F10.6,F10.2 )
C
C
(dec(2)*noligr)*0.45,dec(6)*0.45,
&
C
C
csa*dec(7),dec(8)*0.45
dec(1)*liga*0.7,
&
dec(4)*0.4,cas*dec(3)
C
C
n lost from each compartment and put into other compartments
C
nlossc(1) = (dec(1)*noliga)*0.4/c2n(1,i-1) +
&
dec(1)*liga*0.7/c2n(1,i-1)
nlossc(2) = ((dec(2)*noligr)*0.45)/c2n(2,i-1) +
233
&
dec(2)*(ligr)*0.7/c2n(2,i-1)
nlossc(3) = cas*dec(3)/c2n(3,i-1) + cap*dec(3)/c2n(3,i-1)
+ cal*dec(3)/c2n(3,i-1)
&
nlossc(4) = dec(4)*0.4/c2n(4,i-1)
nlossc(5) = dec(5)*0.4/c2n(5,i-1)
nlossc(6) = dec(6)*0.45/c2n(6,i-1)
nlossc(7) = csa*dec(7)/c2n(7,i-1) + csp*dec(7)/c2n(7,i-1)
nlossc(8) = dec(8)*0.45/c2n(8,i-1)
C
n contributed to a compartment from other compartments
C
through transfer of c to the compartment Nitrogen content
C
of N that is transfered is dependent on C:N ratio of compartment
C
receiving carbon
C
N
income
into
each
box nin(1) = fsa*litterfall(i)/150
nin(2) = fsr*root1itter(i)/150
nin(3) = (dec(2)*noligr*0.45)/c2nin(3) +
& dec(6)*0.45/c2nin(3)+csa*dec(7)/c2nin(3)+dec(8)*0.45/c2nin(3)
nin(4) = (dec(1)*noliga)*0.4/c2nin(4) +
&
dec(5)*0.4/c2nin(4)
nin(5) = litterfalln(i) - nin(1)
nin(6) = rootlittern(i) - nin(2)
nin(7) = dec(2)*ligr*0.7/c2nin(7) +
&
dec(1)*liga*0.7/c2nin(7) + dec(4)*0.4/c2nin(7) +
234
&
cas*dec(3)/c2nin(7)
nin(8) = csp*dec(7)/c2nin(8) + cap*dec(3)/c2nin(8)
•
since nitrogen content of transfer depends on C:N ratio
•
of receiving compartment there is a need to account for the
•
nitrogen that leaves with the carbon from compartment A but
•
does not arrive at compartment B.
•
compartment from which the carbon left
EXTRA
This section is done by the
N mineralization
mnrlzdextra(1) = nlossc(1)-(dec(1)*noliga)*0.4/c2nin(4)&
dec(1)*liga*0.7/c2nin(7)
mnrlzdextra(2) = nlossc(2)-(dec(2)*noligr*0.45)/c2nin(3)-
&
- dec(2)*ligr*0.7/c2nin(7)
mnrlzdextra(3) = nlossc(3) - cas*dec(3)/c2nin(7) -
&
cap*dec(3)/c2nin(8) - cal*dec(3)/c2n(3,i-1)
mnrlzdextra(4) = nlossc(4) - dec(4)*0.4/c2nin(7)
mnrlzdextra(5) = nlossc(5) - dec(5)*0.4/c2nin(4)
mnrlzdextra(6) = nlossc(6) - dec(6)*0.45/c2nin(3)
mnrlzdextra(7) = nlossc(7) - csa*dec(7)/c2nin(3)
&
-
csp*dec(7)/c2nin(8)
mnrlzdextra(8) = nlossc(8) - dec(8)*0.45/c2nin(3)
mnrlzdxtra(i) = mnrlzdextra(1) + mnrlzdextra(2) + mnrlzdextra(3)
&
+ mnrlzdextra(4) + mnrlzdextra(5) + mnrlzdextra(6) +
&
mnrlzdextra(7) + mnrlzdextra(8)
235
5 % of mineral n is lost to N2 during each time step
also a percentage is leached out of the water column defined above
by fn which needs to be turned into a function call
minlosston2 = mineraln(i)*(0.05/30)
mineraln(i) = mineraln(i) - minlosston2
minlosttoleach = mineraln(i)*fn*0.1
minlosttoleach = mineraln(i)*fn
IF ( minlosttoleach .GT. mineraln(i) ) write(*,*)i,mineraln(i),
minlosttoleach,fn
mineraln(i) = mineraln(i) - minlosttoleach
New n content before additional immobilization
of each compartment
0.98 represents fraction that reaches mineral n pool
minlosston2o represents the loss of n to the atmosphere during
mineralization
minctot(i) = 0.0
k= 0
DO 518 k=1,box
518
minctot(i)=minc(k)+minctot(i)
mineraln(i) = mineraln(i) + 0.98*mnrlzdxtra(i) +
& minctot(i)*0.98
236
minlosston2o(i) = mnrlzdxtra(i)*(0.02) + minctot(i)*(0.02)
- New carbon and nitrogen content of each compartment
DO 300 j = 1,box
c(j,i) = c(j,i-1) - dec(j) + inc(j)
n(j,i) = n(j,i-1) - minc(j) -nlossc(j) + nin(j)
c2n(j,i) = c(j,i)/n(j,i)
300
CONTINUE
j = 0
Error checking write line
ninputs = 0.0
ninputs = production
noutputs = 0.0
noutputs = litterfall(i) + rootlitter(i)
nstoredlast = nstored
nstored = 0.0
nstored = stddead(i) + liveroot(i) + liveshoot(i)
deltas = 0.0
deltas2 = 0.0
DO 402 j = 1,box
noutputs = dec(j) - inc(j) + noutputs
nstored = c(j,i) + nstored
nstoredlast = c(j,i-1)
237
write(*,990) i,j,ninputs,noutputs,deltas,deltas2,nbal
C 990
FORMAT(I5, 5F10.6 )
CONTINUE
C 402
deltas = nstored-nstoredlast
deltas2 = ninputs-noutputs
nbal = deltas2-deltas
write(*,990) i,ninputs,noutputs,deltas,deltas2,nbal
C990
FORMAT(I5, 5F10.2 )
IF ( ninputs .LT. noutputs) write(*,*)
minlosston2o(i),minlosston2,minlosttoleach,
(cal*(dec(3)/c2n(3,i-1))),mineraln(i)
402
CONTINUE
WRITE(44,980)
&
c(7,i),c(8,i)
FORMAT(I5, 8F8.1 )
980
WRITE(45,981)
&
981
i,c(1,i),c(2,i),c(3,i),c(4,i),c(5,i),c(6,i),
i,n(1,i),n(2,i),n(3,i),n(4,1),n(5,i),n(6,i),
n(7,i),n(8,i),mineraln(i),mnrlzdxtra(i)+minctot(i)
FOR11AT(I5, 10F8.2 )
WRITE(46,982) i,liveroot(i),liveshoot(i),rootn(i),shootn(i),
rootc2n(i),shootc2n(i),stddead(i),stddeadn(i),stddeadc2n(i)
982
FORMAT(I5, 9F8.1)
WRITE(47,983) i,c2n(1,i),c2n(2,i),c2n(3,i),c2n(4,i),c2n(5,i),
238
c2n(6,i),c2n(7,i),c2n(8,i)
983
FORMAT(I5, 8F8.2 )
WRITE(48,984) i,prod(i),newroot,newshoot,nprod
984
FORMAT(I5, 4F10.5 )
200
CONTINUE
CLOSE(unit=44)
CLOSE(unit=45)
CLOSE(unit=46)
CLOSE(unit=47)
CLOSE(unit=48)
500
CONTINUE
RETURN
END
239
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