INFORMATION TO USERS
INFORMATION TO USERS
This numuscript has been reproduced from the microfilm master. UMI films the text directly firom the original or copy submitted. Thus, some thesis and dissertation copies are in typewriter &ce, while others may be from any type of computer printer.
The quality of this reproduction is dependent upon the quality of the
copy submitted. Broken or indistinct print, colored or poor quality
illustrations and photographs, print bleedthrough, substandard margins, and improper alignment can adversely affect reproduction.
In the unlikely event that the author did not send UMI a complete manuscript and there are missing pages, these will be noted. Also, if unauthorized copyright material had to be removed, a note will indicate the deletion.
Oversize materials (e.g., maps, drawings, charts) are reproduced by sectioning the original, b^inning at the upper lefthand comer and continuing from left to right in equal sections with small overlaps. Each original is also photographed in one exposure and is included in reduced form at the back of the book.
Photographs included in the original manuscript have been reproduced xerographically in this copy. Higher quality 6" x 9" black and white photographic prints are available for any photogn^hs or illustrations appealing in this copy for an additional charge. Contact UMI directly to order.
UMI
A BeU & Howdl Infimiiation Conqiany
300 North Tada Road,. Aon Aibor MI 481061346 USA
313/7614700 800/5210600
NOTE TO USERS
The original manuscript received by UMI contains pages with indistinct and/or slanted print. Pages were microfilmed as received.
This reproduction is the best copy available
UMI
USE OF GEOMORPHIC INDICATORS IN
PARAMETERIZING AN EVENTBASED
SEDIMENTYIELD MODEL by
Howard Evan Canfield
Copyright © Howard Evan Canfield 1998
A Dissertation Submitted to the Faculty of the
DEPARTMENT OF AGRICULTURAL
AND BIOSYSTEMS ENGINEERING
In Partial Fulfillment of the Requirements
For the Degree of
DOCTOR OF PHILOSOPY
In the Graduate College
THE UNIVERSITY OF ARIZONA
UMX Nmnber: 9906527
Copyright 1998 by
Canfleld, Howard Bvan
All rights reserved.
UMI Microform 9906527
Copyright 1998, by UMI Company. All rights reserved.
This microform edition is protected against unauthorized copying under Title 17, United States Code.
UMI
300 North Zeeb Road
Ann Arbor, MI 48103
THE UNIVERSITY OF ARIZONA ®
GRADUATE COLLEGE
As members of the Final Examination Committee, we certify that we have read the dissertation prepared by Howard Evan Canfield entitled ll.se of Geomorphic [ndicators in Parameterizing an
Eventbased SedimentYield Model
2
and recommend that it be accepted as fulfilling the dissertation requirement for the Degree of Doctor of Philosophy
Dr./ William 0* ttasmussen
Date
Date
Date
Date
//
L
\
Final, apfiroval 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 reqtiiremf
sJM
Dissertation Director^ Or. William 0. Rasmussen
Dati
Dr. Vicerite Lopes
3
STATEMENT BY AUTHOR
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 permission, provided that accurate acknowledgement of source is made. Requirements for permission for extended quotation from or reproduction of this manuscript in whole or part may be granted by the copyright holder.
4
Acknowledgements
This dissertation is the product of many efforts.
First, I want to thank my wife Magdalena for encouraging me and helping me with the research. My dissertation advisor,
Dr. Vicente Lopes, provided helpful advice on research methods and how to prepare the dissertation. This dissertation is undoubtedly better because of his contribution. Dr. William Rasmussen, my academic advisor, encouraged me and provided useful advice in how to get through graduate school. I forced all three of these people to share my frustration at one time or another and I am thankful for their tolerance.
Dr. David Goodrich and Dr. Hoshin Gupta provided many helpful comments in doing the research and preparing the dissertation. Carl Unkrich spent many hours helping me debug computer code and retrieve data. Kamran Sayed showed me the TOPAZ program, and allowed me to use a module he had developed for partitioning and writing the KINER0S2 input files. Tim Keefer and Dr. Roger Smith provided me with some previously unpublished data.
I am grateful to Dr. Lloyd Gay for introducing me to the BROOK90 hydrologic model, and allowing me to teach in his class. Dr. C.A. Federer and Tim Keefer read and commented on the BROOK90 portion of the dissertation. Dr.
Bruno Marino turned me back on to earth science, for which
I am grateful.
Brenda Tadaro helped edit the dissertation. I especially appreciate her efforts in preparation of the final draft, when my energy waned. My parents. Dr. Robert
Canfield, and the soontobe Dr. Rita Canfield, gave me encouragement and insights on the graduate school process.
They never lost confidence in me, though my own confidence flagged.
Research and sustenance costs came from a United
States Department of Agriculture National Needs Fellowship, the University of Arizona Graduate School, Rain Bird
Manufacturing and the Watershed Resources Program of the
School of Renewable Natural Resources. GEOVARIANCES of
Fontainebleau, France and GEOMATH of Houston, Tx. allowed me to use the ISATIS Geostatistics Software in this research.
For my brother, Stephen, my wife, Magdalena, and my daughter, Ariana
6
TABLE OP CONTENTS
LIST OF ILLUSTRATIONS
LIST OF TABLES
ABSTRACT
1. INTRODUCTION AND APPROACH
1.1 Problem Statement
1.2 Scope of This Research
1.3 Approach
1.4 The Lucky Hills and Walnut Gulch
2. TERRAIN ANALYSIS AND LANDSCAPE EVOLUTION CONCEPTS 40
2.1 Chapter Objectives
2.2 Introduction
2.3 Slope and Area as Indicators of Process Scale
2.4 Relationships Between Material and Landscape Form
49
50
3. TERRAIN ANALYSIS
3.1 Chapter Objectives
3.2 Introduction
3.3 Field Survey Methods
3.4 Quality of the Survey Data
3.5 Data Processing
3.6 SlopeArea Relationships
3.7 Partitioning the Watershed
3.8 Summary
57
57
57
59
62
67
69
81
4. SOILS DATA
4.1 Chapter Objectives
4.2 Introduction
4.3 Field Methods
4.4 Lab Analysis
4.5 Results
4.6 Estimating Critical Shear Stress
Based on Soil Texture
4.7 Identification of Soil Mapping Units
4.8 Enrichment of Coarser Particles in the Upper Layer
4.9 Summary
9
15
16
18
18
29
31
35
83
83
83
85
87
89
91
98
99
103
7
TABLE OF CONTENTS  Continued
5. INTEGRATION OF LANDSCAPE AND SOILS DATA
5.1 Chapter Objectives
105
105
5.2 Introduction and Background 105
5.3 Soils Particle Size Relationships in Channels.109
5.4 Landscape Form and Particle Size on Hillsopes.119
5.5 Conclusions on Soils and Landscape Form 132
6. MODEL SETUP AND PARAMETER IDENTIFICATION
6.1 Chapter Objectives
6.2 Introduction
6.4 Parameter Identification Method
137
137
137
143
145
7. RESULTS OF EROSION MODELING
7.1 Chapter Objectives
7.2 Introduction
7.3 Hydrology Parameters
7.4 Modeling the Sedigraphs
8. FINDINGS, CONCLUSIONS AND SUGGESTIONS
FOR FUTURE RESEARCH
8.1 Chapter Objectives
8.2 Introduction
8.3 Findings of the Survey and
Soils Data Analysis
8.4 Findings of the Modeling Effort
8.5 Discussion of the Findings
8.6 Future Research
153
153
153
154
164
179
179
179
183
182
185
190
APPENDIX A: DETERMINING SOIL MOISTURE CONTENT
USING THE BROOK90 MODEL
Appendix B: USE OF GEOSTATISTICS TO ESTIMATE SOIL
ERODIBILITY
APPENDIX C: DISCUSSION OF THE RELATIONSHIP OF SOIL
TEXTURE TO CHANNEL LOCATION ON THE
LUCKY HILLS 104 WATERSHED
APPENDIX D: METHOD TO CALCULATE KS FROM SOILS
PARTICLE SIZE DATA
193
229
255
271
TABLE OF CONTENTS  Continued
APPENDIX E: SOILS PARTICLE SIZE DATA
APPENDIX F: STATISTICAL OUTPUT
REFERENCES
8
274
281
286
9
LIST OF ILLUSTRATIONS
Figure 21 Relationship Between Slope and Area
Figure 22 Slope and Area for Stream in Bedrock and Alluvium
Figure 31 Location of Survey Points Collected on Lucky Hills 104
Figure 32 CrossSection Comparing Field Survey with 1" = 40'Contour Map
Figure 33 Channel Slope vs. Drainage Area
51
53
63
65
71
Figure 34 SlopeArea Diagram for the Lucky
Hills 104 Watershed Calculated Using GRASS
Figure 35 Partitioned Watershed with 312 Elements
Figure 36 Locations of Channel Heads by Field
Survey and Channels Defined by TOPAZ
75
78
79
Figure 37 SlopeArea Diagram for the Lucky
Hills 104 Watershed Calculated Using TOPAZ 80
Figure 41 Particle Size Distributions for Two Soils...100
Figure 42 Relative Enrichment of Coarse Particles in
Surface Armoring 102
Figure 51 Location of Soil Samples Collected in Channels 110
Figure 52 Decrease in Coarse Particles and Increase in Finer Particle Size Classes in Channels 115
Figure 53 Downstream Fining of the D65 in
116
Figure 54 Location of Soil Samples on
Hillslopes of the Watershed 121
10
LIST OF ILLUSTRATIONS  Continued
Figure 56a Plot of D65 vs. Slope on Hillslopes
Figure 56b Plot of D6^vs. Accumulated Drainage
Area on Hillslopes
Figure 57 Plot of Multiple Regression Estimate of %> 16mm vs. Sample Value
131
131
133
Figure 58 General Trends for Soil Texture for
Hillslopes and Channels
Figure 61 An Eighteen Element Partitioning of
Lucky Hills 104 Watershed
136
139
Figure 62 Graph Showing Success of SCEUA in Finding the Total Sum of Squares Objective Function
Minima in KINER0S2 for Kg, CV
KS
and n 150
Figure 63 Graph Showing Minimization of the
Objective Function Value for Multipliers on
Transport Capacity (Mtc) and Rain Splash (Mspl)...151
Figure 7la Simulation of the August 23, 1982 Event
Using a Lower Value of the Multiplier on
CV
KS
Figure 7lb Simulation of the August 23, 1982 Event
Using a Lower Value of the Multiplier on
CV
KS
Figure 72a September 11, 1982 Fitted Hydrograph for the 312 Element Watershed Configuration
Figure 72b September 11, 1982 Fitted Hydrograph for the 18 Element Watershed Configuration
Figure 73a September 20, 1983 Fitted Hydrograph for the 312 Element Watershed Configuration
Figure 73b September 20, 1983 Fitted Hydrograph for the 18 Element Watershed Configuration
157
157
161
161
162
162
11
LIST OF ILLUSTRATIONS 
Continued
Figure 74a July 30, 1985 Fitted Hydrograph for the 312 Element Watershed Configuration
Figure 74b July 30, 1985 Fitted Hydrograph for the 18 Element Watershed Configuration
163
Figure 77a Fitted Sedigraph for the July 30, 1985
Event, 312 Element Configuration
163
Figure 75a Fitted Sedigraph for the September 11, 1982
Event, 312 Element Configuration 167
Figure 75b Fitted Sedigraph for the September 11, 1982
Event, 18 Element Configuration 167
Figure 76a Fitted Sedigraph for the September 20, 1983
Event, 312 Element Configuration 168
Figure 76b Fitted Sedigraph for the September 20, 1983
Event, 18 Element Configuration 168
169
Event, 18 Element Configuration
Figure 78a Hydrograph for the September 10, 1983
Event, 312 Element Configuration
Figure 78b Hydrograph for the September 10, 1983
Event, 18 Element Configuration
Figure 79a Sedigraph for the September 10, 1983
Event, 312 Element Configuration
Figure 79b Sedigraph for the September 10, 1983
Event, 18 Element Configuration
Figure 7lOa Hydrograph for the August 25, 1984
Event, 312 Element Configuration
Figure 7lOb Hydrograph for the August 25, 1984
Event, 18 Element Configuration
169
171
171
172
172
173
173
12
LIST OF ILLUSTRATIONS 
Continued
Figure 7lla Sedigraph for the August
2 5 ,
1984
Event, 312 Element Configuration
Figure 71lb Sedigraph for the August 25, 1984
Event, 18 Element Configuration
Figure 712a Hydrograph for the August 5, 1988
Event, 312 Element Configuration
Figure 712b Hydrograph for the August 5, 1988
Event, 18 Element Configuration
Figure 713a Sedigraph for the August 5, 1988
Event, 312 Element Configuration
174
174
175
175
176
Figure 713b Sedigraph for the August 5, 1988
Event, 18 Element Configuration
Figure A1 TDR Moisture Probe Measurements
176
203
Figure A2 Observed Volumetric Soil Moisture
Under Bare Cover
Figure A3 Observed Volumetric Soil Moisture
Under Shrub
Figure A4a Average Volumetric Soil Moisture 1990
Uncalibrated Parameters (015cm)
204
204
206
Figure A4b Average Volumetric Soil Moisture 1991
Uncalibrated Parameters (015cm)
Figure A5a Average Volumetric Soil Moisture 1990
Uncalibrated Parameters (30cm+50cm)
206
207
Figure A5b Average Volumetric Soil Moisture 1991
Uncalibrated Parameters (30cm+50cm) 207
212 Figure A6 Effect of Rain Days on Simulation
Figure A7 Monthly Precipitation at Lucky Hills (RG83).213
LIST OF ILLUSTRATIONS 
Continued
Figure A8 Volumetric Soil Moisture 1990 (015cm)
Calibration Based on 1990 and 1991 Data
Figure A9 Volumetric Soil Moisture 1991 (015cm)
Calibration Based on 1990 and 1991 Data
221
222
Figure A10 Volumetric Soil Moisture 1990 {30cni+50cin)
Calibration Based on 1990 and 1991 Data 223
Figure A11 Volumetric Soil Moisture 1991 {30cm+50cm)
Calibration Based on 1990 and 1991 Data 224
Figure B1 Kriged Map of the Greater than 16mm Portion.235
Figure B2 Kriged Map of the Less than 2ram Portion 236
Figure B3 Experimental Variogram for Background
Variables Related to Slope
Figure B4 Anisotropy in Background Variables
241
242
Figure B5 Fitted Variogram for the Greater than
16mm Portion
Figure B6 Fitted Variogram for the Less than
2mm Portion
Figure B7 Cokriged Map of the Greater than
16mm Portion
Figure B8 Cokriged Map of the Less than
16mm Portion
Figure B9 Cokriged Map of the Less than
8mm Portion
Figure B10 Cokriged Map of the Less than
2mm Portion
Figure B11 Cokriged Map of the Less than
0.125 mm Portion
244
245
247
248
249
250
251
14
LIST OF ILLUSTRATIONS  Continued
Figure C1 Ternary Diagram of Texture of Underlying
Uneroded Soils
Figure C2 Cumulative Particle Size Distribution
Uneroded Soils
Figure C3 Location of Channels on Lucky Hills 104
259
260
263
Figure C4 Number of Channels Initiated at Elevation...264
Figure C5 Slope vs. Area (channels) 265
Figure C6 Cross Section AA' 268
15
LIST OF TABLES
Table 11 Summary of Results for Five EventBased
Models in a Blind Study
Table 41 Estimates of Critical Shear Stress for
Hillslope Samples
Table 42 Estimates of Critical Shear Stress for Channels
Table 43 Estimates of Critical Shear Stress for Transition Samples
21
94
95
96
Table 51 Descriptive Statistics of
Channel Bed Material
Table 52 Correlation Between Particle Size Slope and Area in Channels
112
113
Table 53 Correlation of Surface Armoring to Underlying
Uneroded Soil 122
Table 54 Correlation Between Soils and Landscape
Variables on Hillslopes
Table 61 Summary of Event Characteristics
Table 71 Summary of Hydrograph Fitting Parameters
Table A1 Statistical Difference In Soil Moisture
Between 1990 and 1991
127
142
155
214
217 Table A2 Results of Sensitivity Analysis
Table A3 Parameter Values and Parameters Estimated
Using Parameter Estimation Techniques
Table B1 Summary Statistics of Soil Particle Size
Table B2 Sxammary of Sample, Cokriged and Multiple
Regression Particle Size Estimates
Table C1 S\ammary of Differences in
Particle Size Class
225
234
253
257
16
ABSTRACT
This research developed a method for parameterizing a physicallybased distributed rainfallrunoff model to more effectively model erosion on small semiarid watersheds.
Topographic survey was done to characterize the form of a small watershed near Tombstone, Az. Soil samples were collected to characterize the spatial variability of soils.
It was found that a relationship between slope and area can be used to determine the critical source area necessary to initiate a channel. These estimates agreed with the location of channel heads identified in the field.
This provided a basis for partitioning the watershed into subcatchment elements based on processscale rather than topographic map scale.
The Engelund and Hansen (1967) transport capacity relationship in the KINER0S2 model can be parameterized using soil particle size data. Soils on the surface of the hillslopes are the least variable, while soils in the channels are the most variable. The coarsest soils on the watershed occur at the transition from hillslope to channel. Particle size in channels were estimated using drainage area and channel slope as predictors, because
17 downstream fining occurs in channels. Particle size distributions on hillslopes were estimated using geostatistics and regression relationships.
To see whether these methods improved model estimates, simulations from a simplified 18 element representation of the watershed using lumped parameter estimates were compared to simulations from a 312 element partitioning of the watershed using distributed parameter values.
Data from six events could be precisely modeled (model efficiencies > 0.9) which minimized the effect of hydrologic error on erosion modeling. A multiplier was placed in front of the raindrop impact sediment entrainment term, and in front of the transport capacity term, the two primary erosion mechanisms.
The model predicted sediment yield for some events well (model efficiencies 0.85 and 0.97). Results from the complex configuration of the watershed were better than the simple configuration. Multiplier values on the splash term were 5 (complex) and 12 (simple). The multiplier on the transport capacity term was between 1.2 and 1.70. These multiplier values are unrealistic suggesting that the multipliers are acting as fitting coefficients, and may not have any physical significance
18
CHAPTER 1
INTRODUCTION AND APPROACH
1.1 Problem Statement
Soil erosion is an underappreciated and poorlyunderstood environmental problem. The World Watch Institute continues to rate soil loss as a major environmental problem
(Brown et al., 1997). However, methods for estimating the amount of soil loss are imprecise. While significant progress has been made in describing and predicting the movement of water using hydrodynamics, describing the movement of sediment on small watersheds is a task that continues to be most accurately described using empirical methods.
While reliance on empirical methods may not appear to be a problem, it indicates that the processes themselves are not well understood. This study is an attempt to further the understanding of the erosion process through better characterization of the scale at which different erosion mechanisms occur, and to develop methods for estimating spatial variability of soil erodibility. However, since the larger goal of this research is to further the understanding of the erosion process, it will address related issues as it becomes necessary to do so.
19
In recent years, physicallybased models using hydrodynamic principals have successfully been used to model rainfall and runoff (e.g. Goodrich, 1990). Among the most successful physicallybased rainfallrunoff models are those relying on the kinematic wave approximation to the full dynamic wave equation. Some of the models using the kinematic wave approximation include WESP (Lopes, 1987),
CASC2D (Julien et al., 1995), SHE (Abbott et al., 1986;
Wicks and Bathurst, 1996; Storm et al., 1987), KINEROS
(Woolhiser et al., 1990; Smith et. al, 1995) and TOPOG
(O'Loughlin, 1986).
The hydrodynamic approach to modeling erosion offers a number of benefits over more empirical methods. One of the major benefits is that these expressions can be used to describe response to a single event, because they describe the physics of water movement. Among the potential benefits of physicallybased distributed sediment models (i.e. erosion models based on hydrodynamic principals) is the potential to describe where and when erosion and deposition are occurring (Nearing et al., 1994). In contrast, the most widelyused empirical method for estimating soil loss is not intended to be used on an event basis [Universal Soil Loss
Equation  USLE (Wischmeier and Smith, 1978)]. The USLE can be used to estimate annual soil loss, but not to describe
20 erosion on an event basis. It neither describes detachment by flowing water, nor does it consider the subtractive effect of infiltration on overland flow.
In practical terms, physicallybased distributed water and sediment models have the potential to describe the movement of sedimentborne contaminants, and the effect of changes in watershed management practices (Jensen and
Matoglou, 1992), as well as model the impact of environmental change on erosion and sediment yield (Hawkins et al., 1991; Tucker and Slingerland, 1997).
Despite the fact that humans have grappled with the problem of erosion for centuries and the fact that there are many potential benefits, developing a hydrodynamic approach to describing movement of sediment is a task that continues to frustrate and confound hydrologists. For example, results from a recent comparative study of eventbased models illustrates the problems of estimating sediment yield on an event basis (Goodrich and Smith, 1997 pers. comm.).
Modelers were given rainfall, runoff and sediment yield data, as well as data on watershed characteristics and asked to model the rainfall, rxinoff and sediment yield on the watershed. The results are siammarized in Table 11. Note that results are widely divergent for the different models.
While the models had significant problems estimating flow
21
Tabl* 11
Suomary of Reatata for Five Bv«nt:Baaect Models In a Blind Study
USSM
Validate
86.6
95.6
343.6
153.8
Calibrate
226.7
174.9
Average
AOta
Validate
86.6
153.8
Calibrate
226.7
174.9
Average
FLOW
PEAK
F*_OW
PEAK
LOW
PEAK
FLOW
TOTAL
FLOW
TOTAL
FLOW
TOTAL
SEDI.*1ENT
TOTAL
SEDIMENT SEDIMENT
TOTAL TOTAL
Measured Modeled » Error Measured Modeled % Error Measured Modeled % Error
KZ)nitOS2
Validace
96.6
95.6
343.6
153.8
Callbcace
::7.3
116.2
116.1
198.4
35.5%
21.5%
66.2%
29.0%
553
241.5
357.8
805.9
7c:
570.5
351
26.8%
136.2%
1.9%
46.1%
622
2914
29346
9038
3314
1588
690
465.0%
45.5%
97.6%
45.4%
226.7
174.9
Average
211
230 31.5%
38.1%
436.6
499
723
752
48.6%
50.7%
62.0%
1900
870
2995
2579
57.6%
196.4%
181.5%
MBDALOS
Validace
36.6
95.6
343.6
153.8
Calibrate
226.7
174.9
Average
20.9
20.7
79.7
25.3
62.3
79.5
75.9%
78.3%
76.3%
83.6%
72.5%
54.5%
88.3%
469.9
241.5
362.2
2448.6
481.6
456.7
199
311.5
174.4
616.5
57.7%
29.0%
51.8%
71.9%
11.1%
35.0%
51.3%
622
2914
29346
9038
1900
870
165.8
373.6
772.S
232.4
773.1
728.5
73.3%
87.0%
97.4%
97.4%
59.3%
16.3%
MJMPS
Validace
86.6
95.6
343.6
153.8
Calibrate
226.7
174.9
Average
40.6
15
4
403.6
22.7
53.1%
98.8%
162.4%
90.0%
91.9%
116.1%
469.9
384.1
241.4
2448.6
481.6
456.7
633.4
633.4
211.1
2533.5
527.8
527.8
34.8%
64.9%
12.6%
3.5%
9.6%
13.6%
28.2%
622
2914
29346
9038
1900
870
1120
1210
560
3890
310
2320
80.1%
58.5%
98.1%
57.0%
83.7%
166.7%
108.8%
278.5 221.6%
1230.7
1187.3*
1001.4
201.3
269.2
297.6
98
175
271
153
191.4%
30.9%
18.7%
70.2%
344.0%
13.2%
13.3%
19.5%
12.5%
11.8%
651.3
288.3
415.2
638
486.6
499
651.3
638
486.6
499
351.3
1212
1181.8
690.7
327.7
338.4
729
655
489
502
46.1%
320.4%
184.0%
8.3%
32.7%
32.2%
124.7%
11.9%
2.7%
0.5%
0.6%
3.1%
622
2914
2934S
9038
1900
870
622
9038
1900
870
2150
26753
25014
256
1616
1544
7880
12205
1757
1161
245.7%
818.1%
14.8%
97.2%
14.9%
77.5%
253.6%
1166.9%
35.0%
7.5%
33.4%
248.6%
Average all Models 119.68%
53.87% 175.73%
22 volume (mean error 54%), errors on total sediment were over
Furthermore, the models did not effectively describe either the calibration or validation events for sediment, and some events (e.g. 3rd validation event) were drastically underpredicted by all models. Some models systematically underestimated sediment yield (e.g. Medalus). Other models tended to overestimate sediment yield (e.g. ACRU).
In addition, the sediment yield equations themselves show that erosion remains less understood than other hydrologic processes. Relationships describing erosion continue to be revised to reflect different conditions and data sets with new relationships currently being proposed
(Wilcock, 1998).
For example, in contrast to the Chezy formula which is used much like originally proposed by Chezy in 1753, Du
Boys' (1879) equation describing sediment transport as a nonlinear function of shearing force has been modified and changed to reflect different flow conditions and different data sets. One review recognized 25 different equations to describe sediment transport as a fiinction of hydrodynamics
(Julien and Simons, 1985). These authors point out that all of these equations share similar elements, and can be written in a generic form where all expressions are a
23 function of flow, slope, and soil erodibility coefficients.
However, exponents and coefficients vary in such a way that the equations yield dramatically different estimates of sediment yield.
The sediment transport relations have also been criticised for being based on laboratory flume studies so that they do not perform well in natural watersheds (Haff,
1996). A review of 12 bed load equations (Gomez and Church,
1989) concluded that, "on the basis of tests performed by us... none of the selected formula, and, we guess no formula, is capable of predicting bed load transport in gravel bed rivers." Because of these difficulties in selecting a model to describe the movement of sediment, often a hydrologic model will allow the user several choices for describing the movement of sediment.
Despite these difficulties, several hydrologic models have begun to rely upon the Engelund and Hansen (1967) sediment transport relationship to describe the transport of sediment. For example, KINER0S2 (Smith, et al., 1995) uses the Engelund and Hansen relationship exclusively, while the previous release of KINEROS (Woolhiser et al., 1990) included choices for six different descriptions of the sediment transport. Likewise TOPOG (O'Loughlin, 1986) uses
24 only the Engelund and Hansen (1967) relationship. In addition, the SHE (Abbott et al., 1986) model, which is arguably the most sophisticated distributed hydrologic model available, allows the user only two choices for sediment yield relationship: Engelund and Hansen (1967) and Ackers and White (1973). Furthermore, Wicks and Bathurst (1996) showed that SHESED (a derivative of the SHE model) could be successfully used to model sediment yield on a small agricultural watershed in Iowa using the Engelund and Hansen
(1967) relationship.
Many researchers have attempted to determine the values of erosion parameters on small plots, and then apply these to the watershed. However, Lopes (1987) and at least one other study (Wicks et al., 1992) have noted that erosion parameter values obtained from small plots did not adequately simulate sediment yield on the watershed studied.
Lopes (1987) found that parameter values for an erosion model used to model erosion on small plots varied by a factor up to seven. Furthermore, he observed that values for channel erosion parameters needed to be increased by a factor of up to 16 for simulated results to match measured sediment yield on a small watershed. On the other hand, they foiind good agreement between simulated and observed runoff based on infiltration parameters obtained from small plots.
25
Successful application of sediment yield models at the watershed scale are few. Furthermore, even results from these isolated cases may be inconclusive. For example,
Wicks and Bathurst (1996) found good agreement between simulated and measured runoff and sediment yield for a small agricultural watershed in Iowa However, they were only able to model the three largest events. They were unable to effectively model the four smaller events. While error in simulated peak sediment discharge was less than 6% for all three events, the error in sediment volume was higher. For the largest and smallest of the the three large events, sediment volume was overestimated by 37% and 70% respectively. For the middle of the three events there was essentially no error.
Wicks and Bathurst (1996) used this particular data set because of the relative density of sediment yield sampling.
Sediment samples were collected at one minute intervals which makes this data set valuable. However, soil infiltration parameters and antecedent soil moisture were not available for these events. Therefore, they were unconstrained by measurement in adjusting these parameter values. Furthermore, since each of the three modeled events occured at a different time of the cropping season, erosion parameters were adjusted separately for each of the events.
26
As such, it is not clear whether the fitted parameter values reflect the state of the watershed at that time of year or are simply best fit coefficients.
These criticisms of Wicks and Bathurst (1996) are intended to illustrate some of the difficulties in modeling erosion at the watershed scale. In fact, the results are satisfactory when compared with the study summarized in
Table 11.
Despite the difficulties, some encouraging results have been noted by researchers working at the rainfall simulator plot scale. Several studies have reported successful application of a physicallybased model to model erosion on small plots using a rainfall simulator (e.g. Lopes and
Lane,1990; Laguna and Girardez 1993; Wicks et al., 1992).
Unfortunately, one of the drawbacks of using rainfall simulator plot data to parameterize an eventbased model is that simulator plot data are not typically spatiallydistributed. Therefore, while the data may be useful for understanding erosion mechanics, it does not provide a basis for estimating the spatial variability of erodibility on a small watershed. This may be one of the reasons that researchers using lumped erosion parameter values derived from simulator plot studies have had difficulty scaling up to small watersheds.
27
Theoretically, a physicallybased distributed rainfallrunoff model linked to a model describing the entrainment of soil ought to adequately describe erosion on a watershed during a rainfall event. Because the hydrodynamic approach has worked successfully to model erosion on small plots, it may be possible to scaleup to small watersheds. In addition, since the hydrodynamic approach has worked well for modeling rainfallrunoff on the Lucky Hills watershed where this research will take place (Goodrich, 1990), a good description of the hydraulics that drives erosion may greatly improve the likelihood of successfully modeling erosion on the small watershed scale.
Typically, the hydrodynamic approach to modeling erosion and sediment yield recognizes two distinct erosion processes; entrainment by raindrop impact; and entrainment by flowing water. While the processes are widely recognized, the understanding of where those processes begin to dominate on a rangeland watershed are not clear.
Channels form as the result of entrainment of soil by flowing water. However, recognizing where a channel begins and, therefore, where entrainment by flowing water dominates is less clear. Such recognition is typically done with topographic maps (e.g. Lopes, 1987; Goodrich, 1990).
Therefore, the partitioning of the watershed becomes
28 somewhat a consequence of the available map scale, and the subjectiveness of the person partitioning a particular watershed.
To summarize the above discussion, researchers attempting to use a hydrodynamic approach to modeling erosion on small watersheds have been plagued by the following:
1.) Little objective basis for recognizing the scale at which entrainment by flow or entrainment by raindrop impact are the dominant mechanisms on small watersheds.
2.) An inability to describe the spatial variability of soil erosion parameters.
3.) Questions about the ability of the existing sediment yield relationships to describe the entrainment and transport of sediment.
In addition to the abovedescribed difficulties are the following general difficulties recognized with the hydrodynamic approach to modeling described by Beven (1989):
4. )An inability to adequately define properties of an element from point data (Freeze, 1980; Phillip,
1980).
5. )An inability to adequately identify parameters because of parameter interaction (especially in
29 overparameterized models) (e.g. Lopes, 1987; Blau et al., 1988; Freedman, 1996)
6. ) An inability to accurately calibrate the model because of errors in observation of both inputs and outputs (Hornberger et al., 1985).
1.2 Scope of This Research
Since this research is an attempt to improve the overall understanding of how erosion occurs on a small watershed, it will address each of the above six items.
However, it will focus primarily on the first two items.
Essentially, this is a study of how to develop spatial estimates of soil erodibility at the watershed scale in the absence of spatiallydistributed rainfall simulator data, and how to partition the watershed so that the model representation effectively preserves the spatial relationship of dominance of entrainment by raindrop impact versus entrainment by flowing water. In a more general sense it is an attempt to gather enough information about a small watershed to make it feasible to scale up erosion studies to the watershed scale. In fact, it is hoped that by gathering enough spatiallydistributed data it will be possible to further understand the mechanisms operating at the watershed scale.
30
The primary source of additional information about the erosion process is the landscape itself. The geomorphology
(landscape form) of a natural drainage basin should reflect the interaction between runoff and erosion. Landscape evolution models begin with the principle that the landform shapes the hydrologic response of a watershed, and that the hydrologic response, in turn, shapes the form of a watershed through the erosion process. Strongly implicit in terrain analysis is the identification of thresholds at which different processes become important.
The location of channels is one example of a geomorphic feature controlled by a threshold. Horton (1945) proposed that channels begin to form where a critical shear stress is exceeded in overland flow. Using this theory he predicted a threshold distance from the divide, Xc, where channels would begin to form. A number of subsequent landscape development models (Schaefer, 1979; Montgomery and Dietrich, 1988, 1989;
Willgoose et al., 1991a,b) relied upon this threshold concept to describe the evolution of channels.
A related, but slightly different, theory is that of
Gilbert (1877, 1909, 1914), who said that channels form as a response to the dominance of processes that incise the landscape (such as flowing water), over processes that can be described in terms of Fickian diffusion of sediment
31 downslope (such as raindrop impact).
1.3 Approach
The general approach in this research is to gather data on form and materials and relate these to the erosion process. Specifically, landscape form was characterized using topographic surveys, and the materials on the landscape were characterized using soil particle size analysis. A geographic information system (GIS) was used to calculate landscape variables. Statististics and geostatistics were used to relate landscape variables to soils particle size data. A total of 2993 survey points were collected on the 4.4 ha Lucky Hills 104 watershed. In addition, 132 soil samples were collected and analyzed for
13 particle size classes up through 64ram.
The observed landscape relationships were used as a basis to partition the watershed to preserve the relationship between areas dominated by entrainment by flow and those dominated by entrainment by raindrop impact.
Observed relationships between soils particle size and landform were used to develop spatial estimates of soil erodibility. Finally, simulated results from the KINER0S2
(Smith et al., 1995) rainfallriinoff and sediment yield model were compared with results from observed events.
32
KINER0S2 is a distributed rainfallrunoff and soil erosion model that describes Hortonian overland flow, and is therefore wellsuited to describing the hydrodynamics of soil erosion on semiarid watersheds. KINER0S2 describes a watershed as a series of cascading plane and channel elements. Each element is characterized with infiltration, hydrologic and soil erosion parameters, which thus allows the user to input the spatial variability of parameters on the watershed.
One of the benefits of using KINER0S2 is that it employs an expression that describes movement of multiple particle size classes based on the work of Engelund and
Hansen (1967) of the form:
^ /T"/ ~ Cnafit/ ' Cs(n
/J ^ ^
where: e/f„) = entrainment by flow for particle size class(n)
31 = erosion rate coefficient for particle size class (n) w = width of flow c mc(n)= transport capacity of particle size class(n) c 3(n)= concentration of suspended sediment entering node
In this expression,
= COH * Pct(n)* vslf„,aPAV)
where:
1.2
33
COH = cohesion of soil
Pct(n) = Percentage of particle class size n vsl(n) = settling velocity of particle size n
(L/T)
PAV = erosion pavement fraction (i.e. full coarse particle cover = 1)
For noncohesive soils with no pavement, Pi reduces to the settling velocity [vsl (n)]. Since most of the surface of the Lucky Hills is covered with noncohesive sediment, this characterization greatly simplifies parameterization.
Therefore, for noncohesive soil, the only external input to the expression is soil particle size which is used in estimating the soil erodibility term. Pi, and in the transport capacity term, Cmxin). Therefore, parameterizing the spatial distribution of flowinduced soil erodibility becomes a task of estimating the spatial distribution of soil particle size class.
Entrainment by raindrop impact (ei) is described by the following relationship: where:
K L = parameter describing the susceptibility of the soil particles to be detached and entrained by raindrop impact (T/L) i = rainfall rate (L/T) c = parameter describing the attenuation effect of
34 flow depth (L"M h = flow depth (L)
Ki. is based on soil and watershed characteristics. In this case it was approximated from the final infiltration rate according to the methods of BenHur and Agassi (1997).
In this case, c is based on the size and terminal velocity of the raindrop. In KINER0S2, c is 200 which was calculted for a mean rain drop diameter of 3 mm (200 is approximately
2/(rain drop diameter in feet)). This results in approximately a 50% drop in erosion rates for a water depth of one third drop diameter (i.e. 1mm depth for a raindrop
3mm in diameter).
It is important to recognize that entrainment by raindrop impact (ei) is unrelated to soil particle size class in this expression. In fact, the model assumes that all particle size classes are entrained by raindrop impact.
Subsequent transport of the particles then is dependent upon the transport capacity of the particle size class Cmxtm •
Therefore, while the expression for raindrop impact suggests that even very coarse particles are entrained by raindrop impact, in fact these coarse particles may be too large to transport, and as such will not be moved off the modeling element.
35
1.4 The LucJcy Hills and Walnut Gulch
The study area is located on the Walnut Gulch
Experimental Watershed near Tombstone, Arizona, and operated by the USDAARS in Tucson. The study used data from the
Lucky Hills 104 watershed [LH104 (4.4 ha.)]. Lucky Hills 104 watershed contains two nested watersheds [LH102 (1.46 ha) and LH106 (0.36 ha)1. Sediment, flow and precipitation data are available for nine events on LH104. Flow and rainfall data are available as well for the two nested watersheds
(LH102 and LH106).
Soils on the watershed are mapped as a single soil type
(Bernadino Sandy Loam, Breckenfield pers. comm. 1996). The surface of the watershed is covered with coarse gravelly layer that has little cohesion. This kind of layer is sometimes called a debris layer or an erosional lag, but will be called surficial armoring in this study. Vegetation is a sparse acacia and creosote cover.
Hydrology and scale issues related to runoff from this watershed have been studied extensively (Goodrich et. al,
1995; Faures et al., 1995; Goodrich 1990; Woolhiser and
Goodrich, 1988). Since hydraulic shear drives erosion, the hydrologic model component drives the erosion model component. For this reason, it is important to accurately model the hydrology of a watershed for erosion modeling
36 purposes
Goodrich (1990) found that KINEROS could predict runoff peak and volume accurately. Using the NashSutcliff (1970) model efficiency statistic, [(Ep) 1 = perfect fit] he found calibrated and validated Ep for storm volume and peak flow rates of: 0.98 and 0.79 for LH106; 0.93 and 0.93 for LH104 and 0.99 and 0.96 for LH102. Because of the results in modeling runoff on the Lucky Hills 104 were so successful, estimates of hydraulic parameters for the model come from
Recent studies have shown that rainfall depth and intensity has tremendous spatial variation even on a 4.4 ha watershed such as LH104 (Michaud and Sorooshian, 1994;
Goodrich et al. 1995). Using 30m x 30m sampling grid on the watershed the authors show that fully half of all errors in runoff modeling can be attributed to errors in rainfall sampling. Furthermore, errors in rainfall sampling cause more error in erosion modeling than hydrologic modeling
(Lopes, 1996). For this reason, two recording rain gages were used in this research.
Goodrich (1990) among others (e.g. Binley et al., 1989) pointed out that a single value of hydraulic conductivity cannot accurately represent the infiltration process on a model element because of the great spatial variability in
37 infiltration rates. For this reason, Goodrich optimized for variability by optimizing the
CV
KS
/ where
CV
KS
is the coefficient of variation of the hydraulic conductivity.
(Note: Since hydraulic conductivity is lognormally distributed, the
CV
KS
is calculated using the geometric mean and the log standard deviation.) However, he found that this spatial variability effect was more pronounced for smaller events. The distribution of saturated hydraulic conductivity, Ks, and net capillary drive, G, for LH 104 has described in Appendix D.
Goodrich (1990) maintained the distributed nature of the model parameters throughout optimization using multipliers. Initial estimates of the distribution of parameters are based on the distibuted soil sampling, subsequent Ks estimates based on the particle size distribution, and field description to estimate Manning's roughness coefficient (n). The relative spatial distribution of parameters is preserved by multiplying all distributed parameters by a multiplying factor (multiplier). This multiplier is then increased or decreased to improve model simulations. The multiplier was then optimized, thus maintaining the spatially distributed nature of the model parameters. The technique of optimizing multipliers was
38 also used to estimate erosion parameters for this study.
In addition to hydrologic modeling, Walnut Gulch has been the location of numerous erosion studies (e.g. Lopes,
1987; Simaton and Renard 1985; Hernandez 1992). In a study relating topography to erosion, Abrahams and Parsons (1991) studied the relationship between slope and susceptability to erosion using a rainfall simulator at Walnut Gulch. They found that sediment yield increased with slope up to a slope of about 12%, at which point sediment yield declined so that at 33% slopes sediment yield had decreased to similar sediment yield rates as the initial shallow gradients. The authors attributed these findings to the fact that the size of particles in the surface armoring and and surface roughness increased downslope thus increasing infiltration, and decreasing runoff and sediment yield.
In siammary, researchers have had difficulty in modeling erosion on an event basis for a number of reasons. This research will attempt to address problems associated with model complexity and spatial variability. The KINER0S2
(Smith et al., 1995) model will be used to simulate erosion on a small semiarid watershed near Tombstone, Az. This watershed is wellsuited for study because the hydrology parameter values for the model are available. Furthermore, rainfall and sediment data are available as well. Since the
39 hydrologic component of the model drives the erosion component of the model and the hydrology is well understood based on previous studies, this research can focus on the erosion modeling.
40
CHAPTER 2
TERRAIN ANALYSIS AND
LANDSCAPE EVOLUTION CONCEPTS
2.1 Chapter Objectives
The main objectives of this chapter are:
1) to describe the parallels between landscape evolution theory and erosion processes,
2) to describe how erosion process scale is related to landscape form, and
3) to describe how materials are related to landscape form.
2.2 Introduction
Attempts to model erosion on an event basis, and efforts at describing longterm landscape evolution have proceeded on a somewhat parallel path. Both eventbased erosion models, and longterm landscape evolution models recognize that two very different types of erosion processes occur on a watershed; those processes which occur in areas where flow converges to form channels and rills, and those processes that occur on the upper reaches of a hillslope where there are no rills or channels.
41
It is important to keep in mind that landscape evolution theory considers the longterm interaction of erosive processes on the landscape. Furthermore, it is not clear how to relate the magnitude of a given rainfall event to the landscape form that develops. However, the way in which water is routed on a landscape during a rainfall event, and the erosion that occurs, is a response to the existing landscape form. Therefore understanding the relationship between erosion processes and landscape form is important for understanding erosion during a rainfallrunoff event.
Researchers have long recognized the scale dependence of erosion processes. Horton (1945) proposed that channels begin to form where a critical shear stress is exceeded in overland flow. Using this theory he predicted a threshold distance from the divide, Xc, where channels would begin to form. A number of subsequent landscape evolution models
(Schaefer, 1979; Montgomery and Dietrich, 1988, 1989;
Willgoose et al., 1991a,b) relied upon this threshold concept to describe the evolution of channels.
Earler workers recognized that these thresholds were the result of interaction of erosion processes. Gilbert
(1887, 1909, 1914) argued that ridge and valley topography developed because of the varying spatial dominance of
42 diffusive vs. incisive processes. Incisive processes such as rilling or gullying cut into the landscape resulting in channel formation. Processes such as rainsplash, animal burrowing, or soil creep result in diffusion of particles downslope. Such processes can be described in terms of
Fickian diffusion with higher rates occuring at higher gradients (i.e. higher slopes).
The capabilities and characteristics of diffusive erosion processes produce a different landscape profile than incisive processes. Rain drops and soil particles are of finite size. As such, the shear stress imparted by a raindrop on a particle is limited (about 90 kPa, Julien,
1995). If a particle moves because of the shear stress imparted by a rain drop, its direction of movement and distance of movement are limited. Because the diffusive process move soil particles in a lessdirected way than concentrated flow, they cause a distinctive convex form.
Efforts to model the longterm effects of diffusive processes such as raindrop impact suggest they produce a convex hillslope profile (e.g. Fernandes and Dietrich, 1997;
Kirkby, 1971). In contrast, runoff converging at a channel head tends to cut or incise the soils as water flows over a slope, incising the landscape, which results in a concave profile.
43
Assiiming steady state landscape evolution. Smith and
Bretherton (1972) demonstrated using a simulation model where perturbations (i.e. rills or gullies draining into a channel) would tend to grow and form valleys where incisive processes dominate over diffusive processes. In contrast, where diffusive processes dominate, sediment will move downslope filling rills and the upper reaches of channels.
As such, incisive processes can be thought of as processes that dissect topography and cause relief. In contrast, diffusive processes infill depressions, degrade relief and round hillslopes (Montgomery and Dietrich, 1994).
Studies have shown that incisive processes become more dominant if rainfall intensity increases or vegetation is removed (Montgomery and Dietrich, 1992; Tucker and
Slingerland, 1997), However, more vegetation and less intense rainfall result in filling of gullies and decreased importance of the incisive processes.
Channel locations are also related to the erosion process. In areas sxibject to Hortonian overland flow, initiation of a channel occurs at the point where the shear imparted by overland flow exceeds the critical shear necessary to remove the majority of the particle sizes present at a point. In other words, for a channel to begin, runoff from a hillslope must be great enough to initiate
44 incision by exceeding the critical shear threshold of the sediment. The total area of hillslope (critical support area) necessary to produce this flow can be related to shear stress. Montgomery and Dietrich (1994) derived the following relationship for critical contributing area for laminar flow as follows:
2Tc'g pkvr'S'
And for turbulent flow is;
2.1
g
2 . 2
where: ac = critical support area per unit contour length (L) p = the uniform rainfall excess rate (L/T) k = dimensionless coefficient whose value depends on the geometry of the bed r = sediment laden specific gravity
V = kinematic viscosity (L^/T) n = Manning roughness coefficient
Tc = critical shear stress (L'/T) g = gravitational acceleration (L/T^)
S = slope
The empirical relationship describing the support area necessary for initiation of a channel can, therefore, be related to critical shear stress. Manning's roughness
45 coefficient and other variables used in more physicallybased models of the erosion process.
Because incisive processes produce different landscape characteristics than diffusive processes, the distribution of channels and unrilled uplands reflects the interaction of erosive processes. At the transition to the channel head, incisive processes overwhelm diffusion processes to maintain a channel. However, on the upper slopes, diffusional processes prevent incision by filling depressions. Based on this description Smith and Bretherton (1972) formulated the following description of the erosion at any point on the landscape:
= 2.3
where: qs = sediment transport (i.e. sediment yield) f(s) = sediment transport by diffusional processes as a function of slope (s) f(q,s)= sediment transport by incisional processes as a function of slope (s) and flow (q)
In mathematical terms the erosion process can be described as sediment dynamics at any point along a surface
46
rC4>f^rCQ;= e(x.O+q/x.t)
where:
C = sediment concentration (M/L^)
A = crosssectional area of flow (L^)
Q = flow discharge (L^/T) e = sediment flux to the flow (M/LT) qa. rate of lateral sediment inflow (M/LT)
X = distance in the flow direction (L) t = time (T)
Sediment flux e(x,t) is assumed to be composed of entrainment by raindrop impact and fluvial process so that:
e ( x , t ) = e , ^ e f
2.5
where:
Qi = soil particle entrainment by raindrop impact e£ = entrainment by flow
It is important to note that (2.3) is approximately the same statement as (2.5), with (2.5) being the integrated form of (2.3). In other words, the entrainment by flow component in (2.5) is analogous to the incision component in
(2.3). Furthermore, the diffusion component in (2.3) is analogous to the raindrop impact component in (2.5).
However, since the landscape evolution description includes processes that occur between storms, the diffusion component
47 in (2.3) includes rain drop impact as well as animal burrowing, soil creep and other longterm processes which are all considered slopedependent. However, in the sediment yield relationship (2.5) diffusive entrainment processes depend only on raindrop impact (ei), which is not described as slopedependent.
At the core of the parallels between landscape evolution models and erosion is the importance of slope and flow. Using drainage area as a proxy for flow (i.e. area of the watershed draining through a given point), it can be seen that drainage area and slope control the spatial distribution of shear stress imparted by flowing water on the watershed.
Using a simplified description of erosion by flow, and an empirical description for flow, the importance of slope and area in the erosion process can be easily demonstrated.
Julien and Simons (1985) developed a generic expression for entrainment by flow as follows: q,=Biq^S' where: qa = sediment discharge (M/T)
Bi = a sediment transport coefficient q = discharge per unit width (L^)
2.6
48
S = slope e = exponents y = exponents
This expression is for overland flow using a unit stream powertype expression for erosion such as the
Engelund and Hansen (1967) relationship used in KINER0S2.
Into this expression can be substituted a simplified expression for flow such as the rational equation:
qr,
= ciA
where: qp = peak flow per unit width (for wide rectangular flow) (L^/T) c = fraction of rainfall that runs off i = rainfall intensity (L/T)
A = drainage area (L*)
Substitution of equation of 2.7 into equation 2.6 leads to the following expression for sediment discharge at peak flow:
2 . 8
Note that rainfall intensity is the only input variable in this expression for sediment discharge. Assuming a watershed with a sediment transport coefficient (Bi)
4 9
constant on the watershed, the sediment discharge becomes a function of slope (S) and area (A). For this reason, higher erosion rates will occur where slopes are steeper, and where area draining through a grid node is greater. Therefore, local slope and area draining through a grid node become important variables in understanding the spatial distribution of the erosion process on a watershed.
2.3 Slope and Area as Indicators of Proceaa Scale
Many researchers (e.g. Hack, 1957; Flint, 1974;
Tarboton et al., 1989) have noted a relationship between slope and area on natural landscapes of the following form:
A'S = constant
2 . 9
where:
A = contributing drainage area (L^)
S = mean slope of the stream segment above the point of interest
a = a scaling coefficient
In fact, this relationship is nothing more than another way of describing how upland portions of hillslopes tend to be convexupward, while at the base of hillslopes a transition occurs to a concave form. Willgoose et al.,
(1991c) have shown that the slope of the slopearea curve is
50 positive in areas dominated by diffusion processes, such as raindrop impact, and negative in areas dominated by fluvial process (Figure 21). Willgoose et al. (1991c) and Willgoose
(1994) have also shown that the sedimentyield relationships themselves can be derived from the slopearea diagram if a watershed is assvuned to be in equilibrium with longterm erosion processes. Therefore, the relationship between slope and area can be a very powerful one for understanding process and the scale at which processes occur.
For the purposes of understanding scale, the critical support area necessary to initiate a channel is explicitly given by the interception of the positive and negative sloping lines on a plot of slope vs. area. While this is a theoretical interpretation of the observed relationship between slope and area, it provides a basis for understanding the scale at which processes occur.
Understanding this relationship allows a modeler to partition a watershed based on process rather than topographic map scale.
2.5 Relationships Between Material and. Landscape Form
In general, shallower channel slopes occur in areas with more erodible material. Montgomery et al. (1996) studied the relationship between slope and area for channels
51
Figure 21
Relationship Between Slope and Area
100
o
Q.
O
€0
10
1
Diffusion
Scaling Line
Combined
Scaling Line
Channel Scaling
Line
0.1
0.1 10 1000
Drainage Area
100000
On hillslopes/ where diffusive erosion processes dominate, the steepness of the slope increases moving from the top of the slope to the bottom of the slope as the area drained on a hillslope increases from the top to the bottom of the slope. This results in a positive relationship between the log of slope and the log of drainage area on hillslopes. In contrast, the slope steepnes decreases in channels as the drainage area increases. This plots as a negative relationship between the log of drainage area and the log of slope in channels.
52 in bedrock and alluvium. They showed that slopes are greater in channels in bedrock than in alluvium (Figure 2
2). They noted that slopes tend to be greater when transport capacity is greater than sediment supply, and that slopes are shallower in areas where supply exceeds capacity.
This relationship is intuitively obvious in that slopes on mountains (which have a rock core and are sediment poor) are steeper than hillslopes in soils where sediment is less limiting.
Montgomery et al.'s (1996) study is recent dociimentation of the relationship between slopes and sediment supply first described by Gilbert (1877). Such a relationship is the basis of the transport capacity approach to describing sediment transport. Momentiim must be transferred from flowing water to the particle to keep the particle in suspension. Since particles are more dense than water, the transfer of momentum is greater for a sediment particle than for water. As such, the transfer of momentum from water to a soil particle means that the average velocity of the water decreases with increasing sediment load, all else being equal. In such cases, sediment transport is limited by transport capacity. If sediment supply in the flow is greater than trainsport capacity.
Figure 22
Slope and Area for Streams in
Bedrock and Alluvium
^q4
L_
10'
~i —
A
Bedrock
AP
'OA A o a A A
Alluvial
•••'  '—
10^
Slope (m m')
•
10'
• AA
A

10®
After Montgomery et al., 1996
54 sediment is deposited in the stream bed. When sediment is limiting, no momentum need be passed to transport sediment, and average velocity does need not to decrease.
Therefore, if slopes in certain parts of a watershed systematically plot above the slopearea line, this suggests that sediment is more limiting in this portion of the watershed. Likewise, if slopes in certain parts of the watershed systematically plot below this slopearea line, sediment can be assumed to be more available.
Higher erosion rates have also been associated with higher drainage density (e.g. Branson et al., 1981). This relationship is consistent with the earlier discussion about critical support area. Note that in equations 2.1 and 2.2 which describe the conditions for initiating a channel, critical source area is proportional to critical shear stress. As such, smaller source areas are required to initiate a channel in a sediment which is easier to erode
(as indicated by a lower critical shear stress). This will result in more channel per unit area (i.e. greater drainage density).
Landscape form can also be used to estimate where erosion will be occurring on hillslopes. Ahnert (1987) used landscape form as a basis for describing where erosion will occur on a landscape based on watershed form. Ahnert notes
55 among other things that the highest erosion rates occur at the point where slope changes the most {e.g. the second derivative of the elevation vs. distance). He found that on slopes further down a valley where erosion had occurred for a longer period of time, the relative change in slope is gradual. However, on less mature slopes a point existed where the relative change in slope was greater. Therefore, using Ahnert's model, and a DEM, it should be possible to identify points on the slope more likely to be eroded.
In summary, terrain analysis provides a theoretical basis for relating geomorphic indicators to erosion processes. The most important of these indicators are slope and area. Because flow is related to drainage area, the slopearea diagram becomes an empirical way for describing two of the most important factors in the flowbased erosion equations. Furthermore, since the observed relationship is positive in areas dominated by flowbased erosion, and negative in areas dominated by diffusive erosion such as rain drop impact, the interception of these two relationships defines the scale at which each of these processes is important. Finally, topography indicates information about the erodibility of materials with shallow slopes and higher drainage density suggesting more erodible materials.
56
As mentioned previously, watersheds are typically partitioned using topographic maps. However, the relationship between the scale of the topographic map and the scale of the hydrologic process is not clear. Terrain analysis provides a basis for linking process to landform and therefore a basis for partitioning based on process scale rather than topographic map scale.
57
CHAPTER 3
TERRAIN ANALYSIS
3.1 Chapter Objectives
The main objectives of this chapter are:
1) to describe the method used to prepare a detailed digital elevation model (DEM) of the watershed studied,
2) to assess the quality of the data set, and
3) to describe how the survey data and relationships between slope and area were used to partition the watershed into planes and channel elements.
3.2 Introduction
With the wide availability of digital elevation models
(DEMs) and tools for analysis of spatial data such as geographic information systems (GIS) it has become easier to describe and to extract information about a watershed in a somewhat quantitative and objective manner.
Since one aspect of this dissertation is to use terrain analysis to help in partitioning a watershed for use with a physicallybased erosion model, a detailed DEM was prepared
Among the items to be recognized from analysis of the DEM are the following:
1) the threshold at which a channel begins.
58
2) the threshold at which diffusive processes, such as rain drop impact, dominate over incisive processes such as erosion by flow, and
3) the relative scaling factor (a) in the relationship between slope and area for both channels and hillslopes.
There is a valid argioment for an objective measure of what constitutes a channel. It has been noted that channels are somewhat a function of map scale, with smaller channels not being apparent on maps with larger contour intervals.
The primary means to address this problem is to recognize the difference between processscale and map scale. As described in Chapter 2, the relationship between slope and area provides a basis for understanding processscale.
For the purposes of this study, the transition from convex hillslope profiles to concave profiles with an identifiable incision constitutes the initiation of a channel. On the Lucky Hills, microincisions, such as rills, are not widely apparent, so identifying a macroincision that can be described as a channel is a somewhat objective process. In some cases, this point is easily identified as the location of a head cut where a gully begins. In most cases on the Lucky Hills this transition is gradual, and the choice of the exact point at which a channel begins is
59 somewhat subjective. However, the point of channel initiation can be identified within +/ 10 meters. The area upstream of this point then becomes the critical support area described in Chapter 2 (Montgomery and Dietrich, 1994;
Pilotti, 1996).
Therefore, for this study, the field effort was aimed at producing a DEM detailed enough so as not to be limited by map scale. Such a DEM can be used to identify convexity and concavity on the landscape, and, by inference, the location of the dominance of diffusive vs. incisive processes. The DEM was an accurate source of data for producing a slopearea diagram (such as the one in Figure 2
1) which was also used to identify the scale at which diffusive or incisive processes dominate.
3.3 Field Survey Methods
A 5m X 5m grid was selected as a basic scale for the survey. This was assumed to be detailed enough because it was about as small as practically feasible on a 4.4 ha watershed. In addition to surveying on a grid, additional survey points were collected in the channels and at the head of the channels. The watershed was surveyed using a SOKIA
Set IIIC total station. Control elevation and Northing and
Easting in UTM coordinates were brought in from a site known
60 as Mineral Monument on the northwest edge of Tombstone.
According to SOKIA, the error on distance is 1 x 10 of the distance measured using this particular total station.
Because the total station was typically less than 200 meters from the survey point, measurements on the watershed were assiamed to be accurate to the nearest cm (10"® x 200m = 2mm) though values were recorded to the nearest mm. The survey was closed by surveying from a control point near Tombstone
{Mineral Monument) to the Lucky Hills and back  a distance of approximately 2,500m each way.
Survey points were collected on a 5m x 5m grid spacing covering the watershed and going up over the watershed divide. To lay out the grid, stakes were placed throughout the watershed on a 20m x 20m grid spacing. Stakes were located using the total station. For accuracy, points were taken in an iterative fashion until the stake was within 5cm of the grid point in both the Northing and Easting coordinates. To further limit error, only three different sites were used as setup points (i.e. turning points) from which to shoot the elevations.
After staking the 20 x 20 m stakes, additional stakes were placed at 5m intervals on at least two lines in the center of the watershed. These points were placed by stretching a surveyor's tape between two 20m stakes and
61 placing the 5m stakes at the 5m, 10m and 15m marks on the tape. The primary purpose of placing the 20m x 20m grid stakes and the 5m stakes was to provide a point of initial reference for taking a survey point. Siting along the 5m x
5m stakes at the center of the watershed allowed the person holding the survey rod to locate themselves at the approximate location of the grid point. In total, 400 survey stakes were used in laying out the grid.
To better define lines of each 5m point, different color flagging was used to distinguish the stakes along the lines of site (e.g. yellow for 5m, red for 10m, white for
15m). In the dense brush that occurs on the southern edge of the watershed, flagging was used extensively to keep a line of site visible. Survey points were collected on each
5m X 5m grid point using this method. The rod was moved until the survey point was within 25cm of the actual grid point in both the Northing and the Easting measurement.
Mean errors were 6cm from the measured point to the grid point (s.d. 5.2 cm) in both the Easting and Northing with a mean total error of 9 cm (s.d. 6 cm). Because the three setup points were used several times, their coordinates were known well. When these setup points were resurveyed, they were typically within a cm on all three measurements
(Northing, Easting, elevation). Therefore, errors in
62 measurement were probably 1cm or less. However, in more dense vegetation, and when a tall survey rod was used, this error was probably greater than 1cm. However, because stones on the surface of the watershed might add one or more cm to the elevation, errors in elevation were assumed to be minimal (i.e. to be precise to the limits of accuracy).
In addition to the grid sampling, survey points were collected in the washes, so that the drainage network could be defined. An additional 1005 survey points were collected in the channels. Special care was given to locate where first order channels (FOCs) began. Survey points were also collected proceeding down the channel so that the geometry of channel segments could be defined. The location of all survey points is shown in Figure 31.
3.4 Quality of the Survey Data
The elevation of points from two other OEMs and a high resolution topographic map prepared using photogrammetry were compared with the DEM prepared from this data set. The first DEM was prepared for the United States Department of
Agriculture Agricultural Research Service in 1988 from an aerial survey producing a 15m x 15m DEM.
Figure 31
Location of Survey Points Collected on
Lucky Hills 104
63
Survey Point + too
meters
•
• • •
• •
« « • •
• • • ^ • • • • • •
> • • • • • • •
•
 •
> « • • • •
• •
••
•
» •
•
XJ^*
• • • • • < •
• • •
«4V
^ ^
^
•
• vw «
>••••«••••u•
•
•«*««••
•
• • • •
<•# •
»•
• •
^
•
• *
^ •
V# • •
:i;
•V
•W.r:
• •
^ « •• •
• •«,• • •
•
» • • • • • • •
*T ^
^ • •
• • • •
««««««
^ • ^ ^ •
^ « « « « * * « «
4»« •4%^'^4>% • •
»•»yy^y••
• 4^^# ^»#J» V^
»• <>ji^•
• • •
• •
••••••••^^ • •
••••<
• 4
4^
V$«« «•#«
•
• 4
. ^
• « • # •#
• • • • • • •
4 • « • • # • • • • •
•
^ ^
• «
• 4
1#^
J
4
••««•«• ••4
4 •
• •
•
•S
• •
*
• 4
•VTTTVm
• >•
Survey points were collected using a total station. In total, 2993 survey points were collected (1988 on grid nodes and the remainder in channels).
64
The second DEM was the USGS 30m x 30m DEM. Elevation of field survey data averaged 1.34 m higher than the 15m x
15m DEM with a standard deviation of 0.44m. The standard deviation value suggests good agreement in relative topographic change in the two data sets, though absolute elevation difference did show a difference.
In contrast, elevation data from 30m x 30m USGS DEM was substantially different than this survey. USGS data are only given to a precision of 1 meter, instead of nearest centimeter as reported by this survey. Mean elevations from this survey were 4.3 m lower than the USGS data set.
Furthermore, the standard deviation on the difference between the two surveys was 1.7 m. This suggests that even relative differences in elevation cannot be accurately estimated from the USGS DEM.
In addition to these two DEMs, a detailed 1" = 40' contour map of the Lucky Hills also exists. It was prepared in 1975 based on an aerial survey flown at a height of 1200 feet (Cooper Aerial Survey, 1997 pers. comm.). Because one of the original panel points could be located in field, the contour map could be tied in with the field survey. A profile generated from this survey was compared with one based on the field survey (Figure 32). Some distortion
65
Figure 32
CrossSection Comparing Field Survey with 1" = 40' Contour Map
1370
1 3 6 8
1366
!2 1364
1362 i! 1360
1356
1356
100 1 5 0
Distance (meters)
•1"=40' Aceal Survey
•Field Survey I
r s c
Comparison between field survey and contour map going down the main interfluve of the watershed is similar suggesting that the 1"= 40' contour map is similar in quality to the topographic survey done for this study.
66 exists from the aerial survey process, which results in a shorter profile distance. However, since the two profiles vary only slightly, it suggests that this I"=40' contour map is a good description of the landscape. Preparing a DEM from this contour map would be a more thorough test. Still, the substantial similarities in the profile indicate that such a 1" = 40' contour is an accurate description of the landscape. The precision and accuracy of the survey methods suggest that this survey can be used to accurately describe the landscape form on the watershed. The fact that elevations fall between those from the USGS DEM (4.3 m higher on average) and those from the 15m x 15m DEM (1.3 m lower on average) also and that relative difference are closer to the more accurate of the these other DEMs (the
15m X 15m DEM) also suggests that the survey is precise and accurate.
Therefore, the USGS DEM is not a good descriptor of landscape form, and the 15m x 15m DEM from aerial survey would be good for some characterization of landscape form.
The 1"=40' contour map could probably be used to prepare a
DEM very similar in quality to the one prepared with field survey.
67
3.5 Data Processing
The survey data were processed using the Geographic
Resources Analysis Support System version 4.1 (GRASS)
Geographic Information System (GIS) operating on a PC running the Linux operating system. DEIMs were prepared at both the 5m x 5m scale, and at the 2.5m x 2.5m scale.
Analysis were done with the OEMs to identify differences in watershed characteristics.
It is important to recognize that raw grid data may not be an accurate description of the landscape form. With grid locations overlaid on a natural landscape, grid nodes located near channels may not reflect the actual landscape form. In some cases, pseudopits and pseudodams will occur.
In cases where the DEM is more coarse than the resolution of channels, it may be necessary to process the
DEM to force a channel network to form. For this reason, the elevations of some grid nodes may need to be raised or dropped so that these pseudopits and pseudodams are removed and more natural drainage paths restored. This depitting process can be done automatically (Pilotti,
1996).
Even with a 2.5m x 2.5m DEM, channel networks are distorted. Clearly a first order channel is not 2.5m wide.
68
In this case, algorithms in GRASS were used to fit a DEM using all 2993 survey points (i.e. both grid nodes and channel survey points). The data were imported into GRASS as centimeters and processed as meters because GRASS does not process floating point data (i.e. 1366.54 meters was imported as 136654 cm to avoid truncation). For this reason, more precise estimates of slope and other landscape measures could be calculated processing the data as meters.
While more sophisticated algorithms exist in GRASS, it was found that a simple inverse distance weighting method with a minimxam of points produced the least error between input DEM and processed DEM. The algorithm had to interpolate on slopes in the 2.5m x 2.5m DEM since, unlike channels, slopes were only surveyed on a 5m x 5m grid spacing. However, since topographic changes were less abrupt on the slopes, interpolated 2.5m x 2.5m values on the slopes were assxamed to be good.
In GRASS multiple analysis were done including identification of watershed boundaries and extraction of channel networks. For each grid node GRASS calculated measures of convexity, concavity, slope, accumulated drainage areas (i.e. the area draining through each grid node) and other indices were calculated. TOPAZ (Garbrecht and Campbell, 1997), a nongraphical DEM processing tool.
69 was also used to identify subwatersheds, distances to channels and other landscape variables.
3.6 SlopeArea Relationships
As described in Chapter
2 ,
slope and area have been shown to be useful variables for describing relationships on watersheds. Many studies have reported a relationship between slope of a channel link and the area draining through a link (equation 2.9). For this reason, relationships between slope and area were studied on the
Lucky Hills 104 watershed.
Slopes of channel segments were calculated using the channel survey data and accumulated drainage area determined in GRASS. The drainage area of the segment was measured at the outlet of the channel. However, the drainage area needed to initiate a channel [i.e. a first order channel
(FOC)] was also determined. The upland drainage area at the surveyed location for where a channel begins was calculated using TOPAZ and the 2.5m x 2.5m DEM.
The average area needed to initiate an FOC, as determined by field identification of the channel heads, was
The minimum critical support area at which a channel initiated was 81 m^ The maximxom critical support area was
70
331 Based on field identification there are 30 FOCs, 10 second order channels (according to the classification of
Strahler ,1964), and 8 greater than second order channels.
Using the channel slopes and drainage area at the end of a link, a slopearea diagram was constructed for the channels by fitting a power function regression to the data set. This relationship is shown on a loglog plot of slope vs. accumulated drainage Figure 33.
As mentioned previously, Willgoose et al., (1991c) have shown that theoretically it is possible to determine the exponents on the flow and slope terms common to most erosion equation from this slopearea relationship.
However, in this case, the correlation coefficient (r was
0.52, and even slight changes in estimates of slope or area caused the value of a to vary between 0.4 and 0.25.
As Figure 33 shows, a in this case has a value of
0.31. Typically, this a value is between 0.4 and 0.7
(Hack, 1957, Tarboton et al., 1989). Therefore, a in this case is less than in the typical case. This may be due to the extensive degree of degradation of the watershed. It may also reflect the fact that all measurements were collected in a relatively small area, and that additional
71
Figure 33
Channel Slope vs. Drainage Area
c
«
o a o
a o
(0
100
100
1000 10000
Drainage Area (square meters)
100000
Slopes were calculated for each Strahler (1964) link based on field survey. The drainage area was calculated from the accumulated drainage map calculated in GRASS for the downstream end of the link.
slope and area measurements further down the watershed (i.e. where drainage area is greater) would result in more data points and better correlation between slope and area.
Because of the variability of the calculation of a, and the fact that a is less than that of previous studies suggest that a cannot be used in this case to estimate the exponents on the slope and flow terms in the description of erosion by flow. Therefore, the exponents will be those of the Engelund and Hansen (1967) relationship which is used in
KINER0S2.
Both erosion by flow, and erosion by diffusive processes act on a hillslope. As mentioned at the beginning of the chapter, diffusive processes tend to produce convex hillslope profiles. Concave profiles on hillslopes are thus the result of both diffusive and overland flow erosion processes. To illustrate this difference, slopearea diagrams were prepared from both the convex and concave portions of the hillslope.
Using GRASS, grid nodes from both convex and concave portions of the hillslope were identified. The slope and area draining through these elements were calculated using
GRASS. In this case, because movement of sediment was assxamed to be occurring along a stream tube, width was normalized to unit width (i.e. movement on a 2.5m x 2.5m
73 grid element was assxamed to occur in a Im meter wide section
2.5m long). For each element size (i.e. 2.5 m^ , 5.0 m*, 7.5 m^ 10 m^ etc.) mean, mean of the natural log transformation, and median were calculated. Coefficients calculated for these equations were similar for the median and log transformed values. However, the highest correlation coefficients were calculated for loglog fits of the mean of the natural log. For this reason, the mean of the natural log for each element size was calculated and used to produce the slopearea diagrams.
Fitted values are similar for slopearea relationships derived for both convex and concave nodes. However, correlation coefficient for the convex slope is stronger (r^
= 0.87) than the correlation coefficient for concave slopes
(r ^ = 0.65).
According to theory, both incisive erosion processes
(which tend to result in a negative relationship between slope and area) and diffusive processes (which tend to result in a positive relationship between slope and area) are operating on concave slopes on hillslopes. As such, one would expect a more clearly defined relationship for convex portions of hillslopes where the diffusive processes should be dominant.
74
Better correlation coefficients for convex hillslopes suggest that such diffusive processes are more clearly dominant on convex hillslopes. The fact that the relationship between slope and area is less clear for concave slopes suggests that processes that form concave slopes on hillslopes are less directed.
These relationships further suggest that the slopearea relationship on convex hillslopes may be a good indicator of diffusive processes on hillslopes. For this reason, only the slopearea relationship on convex slopes will be used to estimate the threshold between diffusive and incisive processes (though either relationship would result in a similar estimate of threshold values).
Setting the two slopearea relationships equal and solving for area, produces a transition from dominance by diffusive processes to dominance by incisive processes at about 178 m^ at a slope of about 15.5 percent. The relationship between the two slopearea regression relationships is shown on Figure 34 where the slope of the diffusive slopearea curve intercepts the slopearea curve for channels.
The agreement between the critical support area derived from the slopearea diagram (178 m^) is similar to the average critical support area determined by field survey
Figure 34
SlopeArea Diagram for the Lucky Hills 104 Watershed
Calculated Using GRASS i74X""^
87
= 0.52
•
• • •
W
• f
•
• •
•
1 10 100 1000
Drainage Area (sq. meters)
AHillslopes •Channels
10000 100000
The triangles represent the average slope of grid elements draining a given area. For example, the smallest drainage area is one grid element. Since slope is lognormally distributed, the mean of the natural log of slope was used to calculate the slopearea relationship.
NOTE TO USERS
Page(s) not included in the original manuscript and are unavailable from the author or university. The manuscript was microfilmed as received.
76
This reproduction is the best copy available.
UMI
77 source areas from 81 to 331 m^) was used as input data.
The spatial distribution of the critical support area was determined using inverse distance weighting using the critical support areas calculated based on the field identification of the location of channel heads. Five different critical support areas were used. The partitioned watershed contained 312 different elements. Figure 35 shows the partitioning of the watershed. Figure 36 shows the locations where channels began as identified by field data as well as the channels indicated by TOPAZ were used.
Note that the partitioning in TOPAZ produces channel locations that are very much in agreement with the field survey.
To determine whether the slopearea relationship was a robust measure, it was recalculated using the TOPAZ program to calculate drainage area and slope. Instead of using
Strahler (1964) link slopes, the slope and drainage area of the channel element calculated in TOPAZ was used. This produced a critical source area of 171.5 m^ at 15.5% slope which is almost identical to the values calculated in GRASS.
The slopearea relationship calculated using TOPAZ is given in Figure 37.
Figure 35
Partitioned Watershed With 312 Elements
78
Partitioned Watershed: Partitioning was done using TOPAZ which divided the watershed into 312 elements. The black areas are channels, and the outlined areas are hillslope elements. The partitioning was done based on field identification of channel heads. The partitioning is consistent with the slopearea relationship shown in Figure
34.
Figure 36
Locations of Channel Heads by Field Survey and Channels
Defined by TOPAZ
79
1Q0 meters
The locations of channel heads were located in the field using the total station. The channel elements were calculated in TOPAZ using 5 different source areas.
Figure 37
SlopeArea Diagram for the Lucky Hills 104 Watershed
Calculated Using TOPAZ
1 0 0
80
= 0.90
102.43X^^
= 0.51
I
I
(0
10000 100000
AHIUslopes •Channels
The triangles represent the average slope of grid elements draining a given area. For example, the smallest drainage area is one grid element. Since slope is lognormally distributed, the mean of the natural log of slope was used to calculate the slopearea relationship.
81
3.8 Suinmary
In summary, highlydetailed 2.5m x 2.5m and 5m x 5m
DEMs of Lucky Hills 104 were prepared to serve as a basis for performing terrain analysis. Comparison with a 15m x
15m DEM based on photogrammetry and the 30m x 30m USGS DEM suggests that these other DEMs would not produce the same degree of accuracy. However, comparison with a 1"=40' detailed 1' interval contour map of the watershed suggests that detailed aerial surveys could be used to prepare a DEM of similar quality.
Survey data indicated that channels were initiated with a support area of approximately 200 m". Slopearea relationships were calculated for channels and hillslopes using both GRASS and TOPAZ. Setting these relationships equal suggests that the transition from diffusiondominated convex hillslope form to incision occurs at approximately slopearea determination is robust, and that with a high resolution topographic map, it might be possible to identify the processscale transition from hillslope to channel using the slopearea diagram.
Partitioning of the watershed using TOPAZ produced 312 hillslope and channel elements. The TOPAZ partitioning was
consistent with fieldidentified locations of channel initiation.
82
83
CHAPTER 4
SOILS DATA
4.1 Chapter Objectives
The main objectives of this chapter are:
1) to describe the importance of the soil sampling,
2) to describe the method used to sample and analyze the soils, and
3) to describe how the particle size distribution can be used to estimate critical shear stress and what these values suggest about the erodibility of soils on slopes and in channels.
4.2 Introduction
Because the modeling efforts will attempt to describe how different particle size classes are transported and deposited on the watershed, it is important to understand the existing distribution of soil particles on the watershed. These particle size data can then be used in a variety of ways including identifying and mapping soils that may have different hydraulic and erosive characteristics.
Previous studies suggest that these soils are alluvial in origin. While alluvial material is generally deposited in horizontal layers, such alluvial deposits may vary
84 horizontally, and have pockets and lenses of more fine grained material (Walker and Cant, 1979). For this reason, the soil unit mapped as the Bernadino Sandy Loam contains anywhere from 20 to 55 percent material > 2mm.
(Breckenfield, 1996 pers. comm.).
Since the distribution of particles on the surface is a reflection of the erosion process on the watershed, the distribution of soils on the watershed may contain information about the way particles move. Because overland flow on the watershed most resembles Hortonian overland flow, flow will tend to concentrate on its way to the channels. Also, in the upland areas of the watershed where little overland flow occurs, the soil particle distribution will reflect the actions of diffusive processes such as rainsplash.
In watersheds such as the Lucky Hills, a coarse surface layer forms on the hillslopes because of removal of fine materials. This is the surface armoring mentioned previously. Therefore, hillslope materials are essentially two layers, a very thin coarse surface layer that constitutes the surface armoring, and the underlying uneroded soil. Previous studies in the Sacaton Mountains of southern Arizona (Kirkby and Kirkby, 1974) have shown that particles in the surface armoring which are larger than 20mm
85 are relatively immobile except on steep hillslopes.
However, particles between Bmiti and 25inm may be mobile under certain circumstances.
For this reason, the purpose of the sampling was to characterize both soil mapping units and the characteristics of the surface armoring. A secondary purpose was to see the relative enrichment of coarser particles and depletion of finer particles in the surface, so as to gain an intuitive sense of the degree of enrichment caused by the formation of the surface armoring. In addition, samples were collected from the channels, so that channel elements could be characterized.
4.3 Field Methods
Both the surface armoring and the underlying uneroded soils were sampled. To obtain samples representative of the soils on different slopes, samples were taken on a catena sampling at 3 to 5 points at intermediate distances from the top of the slope to the channel at the base of the slope.
Additional samples were collected later to improve the spatial distribution of sampling points so that geostatistics could be used. On the slopes, soils representative of the surface armoring were collected to characterize the particle size distribution of soil over
86 which water flows. Samples were collected immediately beneath the surface armoring to characterize the nature of the underlying uneroded soils. In the channels, representative samples were collected from a number of locations in all orders of stream present on the watershed
(first through fourth order).
All samples came from the A horizon of the soil profile. Samples were collected with a garden hand shovel.
Noncohesive coarser soil typical of the surface armor was collected at 50 locations on the watershed. Generally the surface armoring could be distinguished from the underlying uneroded soil in being slightly lighter in color due to the dominance of sand in the soil portion of the surface armoring. Typically, about half of a square meter was scraped to a depth of 0.5cm to collect this material.
The soil directly beneath this surface armoring was assumed to be indicative of the underlying uneroded soil in the A Horizon of the soil profile. In total, 48 samples were collected from the underlying uneroded soil. These samples were used to characterize soil mapping units on the watershed because these samples were assumed to be representative of the native material from which the surface armoring was derived. Samples typical of the underlying
87 uneroded portion of the soil profile were collected to a depth of approximately 5cm.
Channels were sampled in 30 locations on the watershed.
In general, only the surface sample was collected in the channels, though an underlying soil sample was collected from two of the samples collected from first order channels.
Samples were placed in a gallonsize freezer bag and labeled with the watershed number and a letter designating the sample location (e.g. LH 1061). For the first 78 samples collected in 1996, the location of each sample was determined by orienting the location with the 400 stakes used for surveying the grid. This method was assumed to be accurate to within about 5m of the actual location since surveying stakes for orientation were densely located. For the remaining 54 samples collected in 1998, the locations were surveyed in using the total station. A photo was taken of each sample location, so that visual comparison could be made between sample locations,
4.4 Lab Analysis
Soil samples were analyzed for particle size and color.
A total of 132 samples were analyzed. Particle size analysis was done using sieve sizes in the phi scale classification (Lane et al., 1947) from the 6 phi (64mm) to
88 were analyzed using hydrometer analysis to identify the clay
(<0.002mm) and silt (0.063ram  0.002mm) portions of the soils finer than the finest sieve.
Sieve analysis of the soil fraction (i.e. the less than
2mm portion) was done according to the methods of the Soil
Water and Environmental Science Laboratory at the University of Arizona. These methods were an adaptation of the methods described by Gee and Bauder (1986). Briefly, this meant using a 40 gm sample which was subsequently wetsieved to remove the less than 0.063mm portion. The 2mm to 0.063mm portion (1 phi to +4 phi, with 5 particle size breaks) were drysieved. Duplicate samples were taken every 10 samples for comparison purposes. Also, one soil lab standard sample was analyzed for each 10 samples.
The entire > 2mm portion of the sample was sieved and weighed. Sieve sizes 2 phi (4mm) to 6 phi (64mm) were used including 1.5 phi and 3,5 phi sieves. All told, this resulted in 13 different particle size classes based on sieves for all samples.
The color of the soil was analyzed using a colorimeter according to the methods of Post et al. (1993). Only the less than 2mm portion was used for the identification of color. Both dry and wet colors were recorded. The colors
89 were then adjusted to reflect soil scientist color using regression relationships from Post (pers. comm. 1997) similar to those described by Post et al. (1993).
Initially, it was hoped that color might be helpful in identifying soils mapping units of different texture. While some soils on the western edge of the watershed are more red, no clear relationships between color and textural differences were noted in this case.
4.5 Results
Because the volume of the data was so great the results are presented in Appendix E. The results show, in many of the samples over half of the sample was composed of particle sizes greater than 2nim. In such cases traditional sand, silt, clay soils classification would ignore over half of the particles in the distribution. This is especially true for the surface armoring.
As would be expected, the particles of the surface samples were substantially coarser than the underlying soil samples. Comparing texture of the upper soils with the underlying soils, shows that there has been an enrichment of coarser particles in the upper soils and a depletion of finer particles in relation to the lower soils from which they were derived.
90
The duplicate soil samples used in the < 2mm portion showed that errors did occur in analysis, especially in the coarser sand fraction. In some cases errors were as great as 100% {2% vs 4%). However, typically lumping two particle size classes together minimized these errors because, if a duplicate showed a higher percentage for one particle size class, it would have a lower percentage in the subsequent particle size class. Furthermore, use of the cumulative distribution tended to minimize the importance of these types of differences.
While there were no duplicates in the > 2mm fraction, examination of photographs of each of the sample sites shows areas with many large stones next to areas with few large stones. This suggests that spatial differences exist in relatively small areas, so that very large samples would need to be collected to properly characterize this coarse component. Also, a single large stone could skew the whole sample. For example, a single stone in the >64ram portion sample of a sample weighed 623g in a 4.1kg sample. Since only a few samples had a > 64mm component, and these were single, large stones, the > 64mm component was removed, because it was not considered to be representative.
91
4.6 Estimating Critical Shear Stress Baaed on Soil Texture
While traditional approaches to estimating critical shear stress are limited to estimates based on a single particle size class, recent studies suggest that it may be possible to estimate the critical shear stress necessary to initiate erosion of a multiple particle size soil sample.
Such an analysis allows topographic indicators (such as slope or area draining through a grid node) to be related to a single value describing the erodibility (as indicated by critical shear stress) of a soil sample at a point.
Wiberg and Smith (1987) used existing soils data and previous studies to estimate the critical shear stress of particles in multiple particle soil sample. They note that
Shield's (1936) results are generally true for samples composed of grains of a uniform particle size. However, studies of particle movement in a variety of multiple particle size conditions show that larger particles often move at a rate similar to smaller particles. For example, a study in Sagehen Creek, Ca. showed approximately equal mobility for particles between 12cm and 0.6cm (Andrews and
Erman, 1986). For this reason, Wiberg and Smith (1987) conclude that the soil particle distribution of the surface over which the water is flowing is a more important variable than any single particle size class.
92
While the equal mobility of different particle size classes noted at Sagehen Creek seem to be counterintuitive,
Wiberg and Smith show that these results are consistent with other studies showing that a coarse particle on a finer bed is more exposed to the shear stress generated by the flowing water. Also, on an incline, the center of gravity of a large spherical particle is higher, so that gravity will better aid it to begin moving downslope. Conversely, a small particle sitting in a bed of large particles may be sheltered from the flow somewhat, and the particle's angle of repose may not aid it in downstream movement.
Based on these observations, Wiberg and Smith developed a series of curves based on the Shields model, but plotting dimensionless shear stress vs. bed roughness length (Ks*) which is a description of the critical Reynolds number for the bed as a whole. Using this system, the critical descriptor becomes Ks*. While Wiberg and Smith do not themselves suggest a method for calculating Ks*, they note that Fisher et al. (1983) used D65 (the diameter at which
65% of the sample is smaller) to calculate Ks*. Wiberg and
Smith (1987) also provide curves for estimating the critical shear stress for estimating the mobility of particles both larger and smaller than Ks* (5xKs* to 0.2xKs*). For this reason, critical shear stress for most particles can be
93 estimated. However, based on Wiberg and Smith's estimate, most have approximately equal mobility.
For this reason, critical shear stress of the soil sample were calculated based on Ks*. The D65 and critical shear stress for the Ks* for the samples collected on slopes are presented in Table 41. Estimates from the channels are presented in Table 42. Estimates from transitional locations, hillslope nodes draining more that
100 m", or channels draining less than 250 m^ are given in
Table 43. Critical shear stress for surface samples was approximately an order of magnitude greater than for uneroded soils.
The calculated estimate of critical shear stress is less variable in the surface armoring than in both the uneroded underlying soils and samples from the channels.
This higher variability is indicated by a coefficient of variation (CV) of 0.33 for the surface samples, but a factor of two greater for the uneroded soils (CV = 0.77). Samples from the channel showed the greatest variability (CV =
0 . 8 6 ) .
The relatively small variability in the calculated shear stress values for the surface armoring suggests that the slopes of the watershed have become somewhat equally protected by the surface armoring. In contrast, variation
SasiDle
Tabl* 41
Estimates of Critical Shear Stress
For Hillslope Samples
Surface Armoring
D 65 mm Tc (Pal
Underlying Uneroded Soils
D 65 mm Tc (Pa)
94
Mean
Stdev
CV
is.aj
5.49
0.35
14.
5.07
0.35
i . a o
0.69
1.73
0.77
Table 42
Estimates of Critical Shear
Stress for Channels
Tc (Pa)
Sample
102
102
102
102
102
104
104
104
104
106
Chan
Chan chan
Chan
Chan chan chan chan chan chan chan chan chan chan chan chan chan chan
20
21
22
Mean
Stdev
CV
10
12
13
14
15
17
18
H
N
F
1
2
3
4
5
A
B
C
M
R
A
F
6
8 o
1.31
13.86
17.84
0.82
2.42
3.53
4,41
0.76
6.98
29.48
5.79
8.55
9.67
7.99
14.25
16.84
21.65
5.38
7.36
17.56
5.03
4.84
1.65
5.94
34.82
11.06
7.60
7.20
9.81
8.43
0.86
1.23
13.01
16,75
0.55
2.21
3.31
4.14
0.71
6.55
27.68
5.44
8.03
9.08
7.44
13.14
15.54
19.63
4.70
6.91
16.49
4.23
3.92
1.12
5.67
31.00
10.11
7.13
6.76
9.02
7.74
0.86
96
Table 43
Estimates of Critical Shear Stress For Transition Samples
(Drainage Areas on Slope > 100 sq. meters or channel drainage < 250 sq. meters)
106
102
104
104
104
106
106
D
H
Suppl B
Suppl
L
Suppl
Q
Chan
16
Chan 19
N
D
B
0
P
Mean
Stdev.
CV
Surface Sample
D 65 nrni Tc (Pa)
19.48
17.84
13.92
19.04
34.22
23.52
4.31
20.12
17.97
23.14
17.02
18.53
19.09
6.87
0.36
18.29
16.61
13.07
17.87
31.85
22.08
16.58
20.97
15.98
16.94
17.75
6.36
0.36
Underlying Sample
D 65 mm Tc (Pa)
2.61
3.06
2.15
7.88
1.75
1.80
3.63
1.69
2.45
2.87
2.02
3.76
7.40
1.64
1.22
3.06
1.15
97 estimates of critical shear stress for the uneroded soils show greater variability in critical shear stress. This suggests that in the absence of a surficial armoring, the rates of erosion would be more variable on the watershed.
The surface armoring then tends to protect the underlying uneroded soils on the slopes.
The coarsest soils on the watershed occur at the transition from hillslope to channel as indicated by the higher shear stress value. Average critical shear stress for the samples from the slope/wash transition was 17.75 Pa, which is higher than the average for the surface armoring
(14.39 Pa) or the channels (9.02 Pa). The higher critical shear stress on the transition from slope to wash shows that this transition has the highest degree of armoring. This may serve to further protect the slope against further upslope incision.
The wash samples had the highest coefficient of variation in estimates of critical shear stress as indicated on Table 42. This suggests that characteristics of flow in channels is variable, and that both soils relatively resistant to shear and soils unresistant to shear exist in the channels on the watershed.
98
4.7 Identification of Soil Mapping Units
The soils data were used to identify soils mapping units that could be used to estimate the distributed nature of the underlying uneroded soils. These data could potentially be used to estimate infiltration and other hydrologic parameters used in KINSR0S2 using methods similar to those described in Appendix D. The data show that the soils in the middle elevations on the watershed between
1362 m and 1366 m tended to be finer grained than soils either above or below. While these differences were statistically significant, the underlying soils data were not explicitly used in this study. For this reason they will not be discussed further here.
4.8 Enrichment of Coarser Particles in the Upper Layer
Since the soils from the surficial armoring are substantially coarser than those in the underlying uneroded soils, this difference indicates an enrichment of the coarser particles in this surficial armoring. This is caused by both the depletion of the fines by erosion, and enrichment in particle size classes too big to be transported down slope.
99
Assigning a critical shear stress to a soil based on the D65 as was done in section 4.6 is a useful exercise for parameterizing an eventbased sedimentyield model.
However, examining the relative enrichment of different soils allows a more intuitive understanding of the erosion processes on different types of soils. To illustrate these differences, the relative enrichment of coarse particles will be described for two soils. The cumulative distributions for both soils are shown in Figure 41. Soil
102E has an estimated critical shear stress of the surface armoring of 15.87 Pa and an estimated critical shear stress of the underlying uneroded soil of 3.63 Pa. For soil 102N the estimated critical shear stress of the surface armoring is 11.09 Pa, and the estimated critical shear stress of the underlying uneroded soil is 0.43 Pa. Therefore, while the estimated critical shear stress of the surface armoring of the two soils is similar, there is an order of magnitude difference in the underlying soils. This suggests that more fines had to be removed from 102N to get a surface armoring sufficient to protect the underlying soils from erosion.
Such an analysis allows us to see not only the total enrichment of coarser particles in the upper soil, but also which particle size classes are being enriched. In this case, less relative enrichment in the coarser elements has
100
Figure 41
Particle Size Distributions for Two Soils
100
90
80
70
I 60 e
El
c 50
8
£ 40
30
20
10
0.01 t 1 i
1
1
1 i i ! i
1 j j i
1 i
! i ' M i
/
1
/
/
J
\
\
l y
1 i
1
/•
• j i ^
1 j i
! > 1
' ' j
d
A
A
•'
/ /
/
l \ \
1 ' r I i i j
/
!
!
I i i 1 i .
•
1
7
! i i M i 1
J r * i
y
/ y
1
\
1 i
!
i
1 1
k
1 i
1
: 1
1 i !
M i i l
' 1 1
! I ! i i i
1 1
! i i l i ! ! 1 i
11 iii
0.1 100
10
Particle Size (mm)
• 102 E arnionng 102 N arnioring —A—102 E uneroded —B— 102 N uneroded I
The uneroded soil from sample 102 N is much finergrained than the other samples as indicated by the much higher percent finer. This difference is most apparent at about 1mm.
101 occurred in soil 102E relative to soil 102N. The percent of the particle size class in the lower level was subtracted from the upper layer. For coarser particle size classes, this number was generally positive, because the percent of coarse material was greater in the surface layer. In contrast, the number was negative in the finer particle size classes where the percent of fine material was greater in the uneroded soils.
Because both the percentage of surface soils and uneroded soils sum to 100 percent, the cumulative difference begins at zero, goes positive in the coarser materials, and returns to zero in the fine particle size classes. By talcing the integral of the difference it is possible to see the cumulative difference between the surface soil and the uneroded soil. (For the purpose of the integral, the xaxis value was phi units, so that half phi sizes were multiplied by a half, and full phi size was multiplied by one). The graph of the differences for these two soils is shown in Figure 42.
Soils with greater cumulative differences indicate more enrichment of coarse materials than fine materials. For example, the cumulative difference (i.e. integrated over all particle size classes) is 259 for soil 102 N while it is 192
102
Figure 42
Relative Enrichment of Coarse Particles in Surface
Armoring
£ 25
I 20
4>
a.
15
10
5
45
40
35
30
0.01 j
)
1
1
! i
1
1
!
1
I
J i
K
1
• j / n
K
1
J
i f
' i
0.10 iT
/
/
M
i
1
A
r'
1 — I 1 1 i —
M i l !
j j
I
!
i
' '
1
~
; i i !
i
1.
1 ^
^ . 1 i
1 i
'
1 t
I
I — "
( {
i !
1 t i
M i
!
1
\ I
!
i i i l
1 1 i j
1 i i
'
! 1
!
1
) t i i
1 i i i 1 1
1 . !
1 1 ! ' • ! i
1 p i j
1 i ' ! i . i l i i !
! '
1.00
Particle Size Class (mm)
i
«102E A102n'
10.00 100.00
Relative enrichment calculated by subtracting the percent of a particle size class in the underlying uneroded soil from the percent of that size class in the surface armoring. In this case, the D65 of the surface armoring of the two soils is similar though the
D65 of the underlying soil for 102N is finer than that of 102E. Therefore more of the finer soil has been winnowed from 102N to produce a similarly coarse surface soil.
103 for soil 102E which is a coarser soil. The particle size class where the maximvun cumulative difference occurs is also the last particle size class enriched in coarser materials. For this reason, this particle size class is also an indicator of the degree of enrichment of coarse materials in the surface soil. In other words, to get enough coarse particles to protect the surface can be done by eroding less soil from a coarse soil than from a fine soil. Also, in the coarser soil, coarser particle size classes will provide protection. Therefore, in a finer soil such as 102N, 2.83mm particles (fine gravel) may provide relative protection from erosion to finer particles. While in a coarse soil such as 102E, particles such as 8mm gravel are available after removing a smaller portion of the fines.
4.9 Summary
In siammary, it is apparent that there are differences in the soils on the watershed. Surface soils are very coarse reflecting enrichment in coarser particle sizes derived from the underlying soils. Estimates of critical shear stress based on the assiimption of equal mobility show that there is less variability in the surface armoring than either the underlying uneroded soil and samples collected from the channels. In the absence of the armoring, the
104 spatial variability of erosion on the hillslopes would probably be greater because the coefficient of variation
(CV) of the critical shear stress is a factor of two greater than the CV of the underlying soils. Furthermore, the relative enrichment of the surficial armoring is greater on finer grained soils.
The greatest variability in the estimates of critical shear stress was in the channels. This suggests that the highest variability in soil erodibility occurs in channels.
The least erodible soils as suggested by the critical shear stress values are those at the transition from hillslope to channel. This suggests that the upper reaches of channels are protecting themselves from further incision.
105
CHAPTER 5
INTEGRATION OF LANDSCAPE AND SOILS DATA
5.1 Chapter Objectives
The main objective of this chapter is to develop quantitative spatial estimates of soil particle size distributions based on the relationship between soils and landscape. In particular the objectives are as follows:
1) to estimate soil particle size class of soils in the channels as a function of channel slope and area drained by a channel link, and
2) to estimate the particle size distribution of the surficial armoring which characterizes the soil available for erosion on hillslopes using slope, area and other landscape characteristics derived from the
DEM.
5.2 Introduction and Background
Chapter 4 described the general nature of soils studied on the watershed, and Chapter 3 described topographic relationships. This chapter describes how landscape form and soil type are related. It begins with a description of how slope and drainage area are related to soil particle size class in channels. Then it proceeds to describe
106 statistical relationships between landscape form and individual soils particle size classes in the surficial armoring that serves as the basis for estimating the distribution of soils particle size classes on hillslopes.
The distribution of particle size classes on the surface of the watershed serve as a basis for parameterizing the flowbased component of the Engelund and Hansen (1967) relationship used in KINER0S2.
KINER0S2 allows up to 5 particle size classes for parameterization of the Engelund and Hansen relationship.
In this case, the ranges of soil particle size class were as follows:
1) 22.7mm  representative of the 16mm  32mm portion,
2) 11.2mm  representative of the 8mm  16mm portion,
3) 4mm  representative of the 2mm  8mm portion,
4) 05mm  representative of the 0.125mm  2mm portion, and
5) 0.03mm  representative of the less than 0.125mm portion.
These particle size classes were selected, because each class represented about 15%25% of the average of all samples of the surficial armoring. However, they also represented the channel sediment well, because channel sediment included a wide range of textures. In addition to
107 these five classes, the 16min  64mm portion of the soil was used to get an initial estimate of the PAV parameter, i.e. the very coarse material that is essentially immobile and acts as paving. Previous studies in southern Arizona
(Kirkby and Kirkby, 1974) have shown that particles larger than 20mm are relatively immobile except on steep hillslopes. However, particles between 8mm and 25mm may be mobile under some circumstances. For this reason, sometimes the coarser particles are pavement (i.e. PAV in equation
1.2) and sometimes they are available for erosion. In this case, the greater than 16inm portion (16mm  64mm) of the
Lucky Hills samples was taken to be the erosion pavement.
However, the 16mm  32mm portion was allowed to be transported. As such, there is an overlap in the 16mm 
32mm portion to allow this portion to act both as PAV, and be available for transport if transport capacity of the flow is great enough.
Since all the physicallybased erosion equations use both slope and flow as variables (Julien and Simons, 1985), and a relationship between slope and drainage area (as a proxy for flow) has been observed, the relationship between local slope, drainage area, and particle size distribution was particularly important. However, other variables that could be derived from a DEM including aspect and curvature
108 were also considered. Furthermore, since there are numerous algorithms that describe these topographic relationships, several different algorithms were used to calculate each of these relationships. Bivariate correlation was used to characterize the relationships between soil textural classes, and landscape variables. Stepwise multiple regression was the primary predictive methodology.
While soil types clearly influence landscape form, they are by no means the only factor. Climate, land use and cover type clearly play a role in where erosion occurs. In addition, a drop in the channel slope caused by faulting or other natural processes eventually will cause tributary channels to downcut, thus forcing hillslopes to erode to a more stable profile (e.g. Ruhe, 1969). For this reason, even natural landscapes, such as the rangelands surrounding the Lucky Hills, may not truly be in equilibrium with the longterm erosion processes. Therefore landscape form is not simply a fiinction of soil type, but the result of complex interaction between climate, land use, channel hydrology, and long term tectonic history.
At the larger scale (e.g. Walnut Gulch), one cannot assume that local differences in soil type are responsible for differences in landscape form since cover type, land use and channel hydrology will be more varied at larger scales.
109
Furthermore, even longterm average local precipitation rates have been found to vary spatially on Walnut Gulch
(Osborn and Hickok, 1968) suggesting that climate cannot be assumed to be constant at larger scales.
5.3 Soils Particle Size Relationships in Channels
Soils particle size data are available for 33 soil samples at 31 locations in channels on the watershed studied. Figure 51 shows the locations of soil samples collected from channels on the watershed. Note that these locations were selected to be representative of all orders of channels on the watershed. The slope of the channel and the area draining through a channel at a grid node were calculated using TOPAZ. Then, statistical relationships were explored between particle size class, slope and drainage area. Printouts of regression relationships and correlation between variables are given in Appendix F.
The percent finer than a given particle size class was used rather than individual particle size class. Using the percent finer resulted in better correlation values probably because error was associated only one measurement.
Therefore, the actual variables were as follows:
1) Percent less than 16mm (for the 16mm  32mm portion),
2) Percent less than 8mm,
Figure 51
Location of Soil Samples
Collected in Channels
100 meters
110
Diamonds show the location of soil samples collected in channels. Locations were selected to be representative of different stream orders and drainage areas on the watershed.
Ill
3) Percent less than 2iiim, and
4) Percent less than 0.125inin
From these, the five particle size classes 22.7mm, 11.2mm,
4inm, 0.5mm and 0.03mm could be derived. In addition to the above variables, the greater than 16mm portion (i.e. 16mm 
64mm) portion was used as an estimate for PAV in equation
1.2. Table 51 gives the descriptive statistics for the five particle size breaks. Note that on average, the different particle size classes are well represented in this sample, with differences in tne mean between 12% (less than 16mm to less than 8mm) and 37% (less than 2mm and less than
0.125mm). In fact these values suggest that the average channel sample is largely sand and fine gravel with 62.6% of the sample composed of particles between 8mm and 0.125mm.
Such values are intuitively reasonable.
However, examining the relationship of particle size to channel slope and drainage area show that these variables are good predictors of particle size class in channels.
Table 52 summarizes the correlation of soils to slope and area Both hydraulic slope (flowweighted mean slope) and terrain slope are calculated by TOPAZ, so they were both used in the analysis. Furthermore, the cube root of drainage area and square root of hydraulic slope were found to be better correlated with particle size than the
Tcible 51
Descriptive Statistics of Channel
Bed Material
N
Minimum
Maiximum
Mean
Std.
Deviation
Skewness
Greater Less than
16 mm than
16mm
31
0.00%
57.66%
22.77%
15.88%
31
58.52%
100.00%
84.49%
10.71%
0.56 0.70
Less than
8mm
31
40.15%
72.50%
13.70%
0.34
Less than
2 mm
Less than
0.125 mm
31
27.27%
87.00%
46.97%
15.13%
31
3.70%
28.66%
9.93%
6.32%
1.05 2.06
112
113
Table 52
Correlation Between Particle
Size Slope and Area in Channels
Greater than 16inin
Less than Less than
16 nan amm
Cube Root of Area
Hydraulic
Slope
0.60
0.66
0.64 Sq. Rt.
Hyd.
Slope
Terrain
Slope
0.52
0.61
0.60
0.60
0.45
0.58
0.55
0.57
0.46
Less than
2 mm
0,29
0.39
0.46
0.50
Less than
0.125 mm
0.35
0.09
0.16
Notes
lvalues in Bold Significant at 0.01 Level of Significance
2 Values in Italics are not statistically significant
114 the untransformed variable. Note that the particle size classes are correlated at greater than 0.5 for most variables and most particle size classes. In general, the coarser particles are better correlated.
The general trend suggested by these statistics is dovmstream fining. In fact, this is commonly observed in channel bed material in semiarid environments (e.g. Frostick and Reid, 1979). To illustrate these trends the percent greater than 16mm and percent less than 8mm are plotted vs. drainage area (Figure 52). The increase in percent less than Bitrni suggests that channels become finer with more sand and fine gravel. The plot also shows that percent greater than 16inm drops off to very low values at drainage areas of greater than 1 ha which suggests that most of the very large particles either are not transported away from the channel heads, or they are broken into smaller particles. This trend is also shown in representative particle size classes.
In Chapter 4, the D65 size was used as a representative particle size for calculating critical shear stress. Figure
53 shows downstream fining of the D65 in the channel sediment. Note that the nonlinear trend already present in this relationship is accentuated for this representative particle size.
115
Figure 52
Decrease in Coarse Particles and
Increase in Finer Particle Size Classes in Channels
100%
90%
80% 
70% •
60%
50% •
40%
30%
20%
10% •
0%
100 o o
1000
10000
j
A
Greater than 16inm o Less than 8 irni
100000
The percent greater than 16inm (i.e. the very coarse material) gets smaller in the channels as the percent less than 8znm gets larger. This indicates a general downstream fining of sediment in channels.
116
Figure 53
Downstrecim Fining of the D65 in
Channel Sediment
35 •
E
E
20 • in
IO
a
15 •
10 • y = 113.2x'*""
R' = 0.3732
100 1000
10000
Drainage Area (sq. meters) lOOOOOl
The D65 used to calculate the critical shear stress for sediment also decreases downstream in channels. The nonlinear relationship is accentuated as indicated by the use of a power function for calculation of the regression relationship. The estimated critical shear stress, as given in Tables 41, 42, and 43 shows the same accentuated nonlinear trend.
117
While the general trend indicates a higher percentage of greater than 16mm portion at smaller drainage areas, there are a few low values in the greater than 16mm portion at low drainage areas. This was attributed to the fact that some of the first order channels tended to be stairstepped rather than having a gradual slope. In the stairstepped channels, finer sediment collects behind coarser stones, so that the sediment in the flatter portions tends to be finer.
Because slope and drainage areas are good predictors of particle size class, a series of regression relationships were developed for estimating particle size class for channel elements for which there were no samples. Since slope and area are strongly correlated with each other in channels (with slopes decreasing with increasing drainage areas), multiple regression did not improve the predictive power of the relationships. However, to verify this observation stepwise regression was used. As expected, the cube root of drainage area and square root of hydraulic slope were the best predictors for the greater than 16mm, less than 16mm and less than 8mm portions. Also, terrain slope was the best predictor for the less than 2mm and less than 0.125mm portions. The regression relationships then are as follows for the different particle size classes:
118
% > 16inm = 19.593  2.647 x (Cube Root of Area) + 1.705
X (Hydraulic Slope) [R = 0.717]
5.1
% < 16inm = 88.341 + 2.110 x (Cube Root of Area)  4.44
X (Square Root of Hydraulic Slope)
[R = 0.699]
5.2
% < Smm = 77.03 + 2.568 x (Cube Root of Area) 5.343 x
(Square Root of Hydraulic Slope)
[R = 0.661]
5.3
% < 2inm = 68.017  0.023 x (Terrain Slope)
[R = 0.496]
5.4
% < 0.125 mm = 5.395  1.293 x (Cube Root of Area) +
1.224
X
(Flow Vector) [R = 0.476]
5.5
Because there is variability caused by local factors such as the stair stepping described above, these relationships are probably as good as can be expected.
Fortunately, in this case, there are 31 soil samples from 97 channel elements, so soil particle size data are available for about onethird of the channel elements. Furthermore, much of the variability occurs in the first order channels, so that the regression relationships should be more useful
119 for channel elements closer to the outlet. These elements close to the outlet are particularly important, because the sediment load will need to be in equilibrium with the modeled transport capacity at the last channel element. The transport capacity leaving the element is a function of the sediment load from the upstream end as well as the transport capacity of the sediment in the node. Therefore, knowing the character of the channels near the point of measurement is particularly important.
The observed downstream fining of sediment is common in fluvial systems (Ritter, 1978). However, it is impossible to say how much of the downstream fining is caused by preferential transport of finer material, and how much is caused by breaking large particles into smaller particles.
Should the process of breaking larger particles into smaller particles be an important one, it presents a fundamental modeling problem, because the model is unable to account for generation of smaller particles from larger ones.
5.4 Landscape Form and Particle Size on Hillalopes
It is necessary to develop empirical relationships between soils particle size classes that can be used to estimate the spatial distribution of particle size classes on the watershed. However, analysis of how soils and
120 landscape are related also offers some insights to understanding erosion processes on hillslopes. Figure 54 shows the location of soil samples on hillslopes.
In general, the statistical relationships for soils and hillslopes were not as clear as those for channels. In fact, the strongest correlation was between soil particle size class of the surface soils and soils particle size class of the underlying soils below. These relationships are sLuranarized in Table 53.
The high correlation of soil particle size classes with other particle size classes in the surficial armoring is essentially an artifact of the percentages siamming to 100%
(i.e. more coarse means that there will be less fines). It is interesting to note that while the surface armoring must be a product of erosion, it is still strongly correlated with the underlying uneroded soil from which it is derived.
Note that the correlation is particularly good for the coarser particle sizes with correlation between the greater than 16mm portion and the less than 16mm portion correlated at about 0.6. In other words, the data show that coarser underlying soils tend to be eroded to form a coarser surface armoring.
Figure 54
Location of Soil Samples on the
Hillslopes of the Watershed
121
Soil samples on hillslope are shown by (+), Locations were selected originally to sample on a catena to get downslope trends. Later, additional samples were collected to improve geostatistical estimates. Since both short and long spacings are needed for geostatistics, the spatial distribution of samples proved to be good for geostatistical analysis.
122
Table 53
Correlation of Surface Armoring to
Underlying Uneroded Soil
Underlying
Soil
> 16inm
< 16inm
< 8inm
< 2iiiin
Grea'ter than 16inm
Less than
16 mm
Less than
Slum
Less than Less theui
2mni 0.125nim
0 . 6 4
 0 . 6 5
 0 . 5 5
 0 . 5 4
 0 . 2 5
0 . 6 3
0 . 5 6
0 . 4 9
0 . 1 8
0 . 5 0
0 . 5 0
0 . 3 9
0 . 1 7
 0 . 3 7
0 . 4 3
0 . 4 3
0 . 4 4
0 . 2 6
 0 . 2 4
0 . 3 7
0 . 4 0
0 . 4 5
0 . 5 7
< 0
Surface
Armoring
> 16mm
< 16mm
< 8mm
< 2mm
< 0.125mm
1 . 0 0
 0 . 9 2
 0 . 7 7
1 o
 0 . 5 4
1 o
O O
0 . 8 9
0 . 8 2
0 . 6 1
 0 . 7 7
0 . 8 9
O O
0 . 9 3
0 . 7 4
 0 . 7 3
0 . 8 2
0 . 9 3
1 . 0 0
0 . 8 5
 0 . 5 4
0 . 6 1
0 . 7 4
0 . 8 5
1 . 0 0
Notes lvalues in Bold axe Sigxiiflcant a't 0.01 Level o£ Significance
2
Values in Italics are not statistically significant
123
Furthermore, it is interesting to note that there are no statistically significant relationships between the less than 0.125inm particle size class and any of the particle size classes above 0.125mm in the surficial armoring. In fact, the correlation of the 0.125mm fraction between surface armoring and the underlying soil may reflect sample collection errors, because the surface armoring sample was scraped from the surface of the underlying soil. Because the siobtle differences in the underlying soil cannot be accurately mapped, the daLa on the underlying soil is not directly usable for estimating particle size class of the surface armoring. However, it does indicate that the coarser particles tend to move less than the finer ones. In fact, this is what is to be expected. Furthermore, it appears that the texture of the underlying soils may influence the location of channel heads on the watershed.
Since this is not directly related to parameterizing
KINER0S2, it is discussed in Appendix C.
Because the DEM provides a means of estimating topographic variables at the DEM grid scale, relationships between topography and the surface armoring are more directly usable than the relationships between the underlying soil and the surficial amoring. Furthermore, since the underlying soil can be related to topographic
124 differences (e.g. locations where channels initiate), using topographic relationships as predictors of texture for the surficial armoring, implicitly includes the nature of the underlying soil.
Numerous topographic relationships were derived from the 5m x 5m DEM using algorithms in GRASS and the TOPAZ
(Garbrecht and Campbell, 1997) program. While, the 2.5m x
2.5m DEM had a higher resolution, the 5m x 5m showed more generalized relationships. Furthermore, because geostatistics was to be used the 5m x 5m DEM would be less computationally intensive for the geostatistics.
The landscape variables were of essentially four types: slope, area draining through a grid node, aspect, and hillslope curvature. The variables were as follows:
1. Slope Variables
Terrain Slope (TOPAZ)
Hydraulic Slope (TOPAZ)
Slope of Flow Vector (TOPAZ)
Surface Slope (from r.slope.aspect in GRASS)
Slope Steepness (USLE variable calculated in
GRASS)
2. Variables describing drainage area
Accxamulation Map (from r.watershed in GRASS)
Distance to Channel (TOPAZ)
125
Upland Area Map (TOPAZ)
Slope Length (USLE variable calculated in GRASS)
Slope of flow Vector (TOPAZ)
3. Aspect Variables
Aspect (from r.slope.aspect in GRASS)
Terrain Aspect (TOPAZ)
Aspect of Flow Vector (TOPAZ)
4. Landscape Curvature Variables
Mean Curvature (from s.surf.tps in GRASS)
Tangential Curvature (from s.surf.tps in GRASS)
Profile Curvature (from s.surf.tps in GRASS)
Algorithms for slope, aspect and curvature produced values that were highly correlatea with each other suggesting that any of the algorithms could be used to produce a reasonable estimate. In some cases, the values were identical. For example, aspect calculated in GRASS was identical to the value in TOPAZ. However, the algorithms for estimating drainage area produced very different estimates on the uplands. TOPAZ and GRASS would locate channels in approximately the same place. However, the upland area calculation in TOPAZ is based on a tortuous path from the upland to the channel. In contrast, the accumulation map in GRASS assumes a path from the top of the hillslope overland to the channel. For this reason, the
126 correlation between the accumulation map value in GRASS and the upland area value from TOPAZ was only 0.117. The GRASS accumulation map value was better correlated with the distance to channel value calculated in TOPAZ (0.324).
Because soils variables were better correlated with the accumulation map, the accumulation map was used more than the other means of calculating drainage area. However, the great disparity between the different methods suggests that estimating the area draining through a grid node on a hillslope is not a trivial task.
The correlation data are given in Appendix F. However, for illustrative purposes, Table 54 shows correlation data between the soil particle size classes on the hillslopes, and representative landscape variables. What can be seen on this table is that for the coarser particle size classes slope and accumulated drainage area are correlated.
However, unlike the channel sediment, the correlation is not good enough to use in a predictive sense.
What is perhaps most interesting on this table is the relatively high correlation between aspect of the flow vector and all particle size classes. Aspect of the flow vector is the direction to which water flows from a grid node to one of eight adjacent grid cells Furthermore, the aspect of the flow vector is well correlated with both the
1 2 1
Table 54
Correlation Between Soils and Landscape
Variables on Hillslopes
Surface Armoring
Greater than 16inin
Less than 16nuii
Less than 8 mm
Less than 2mm
Less than 0.125 mm
Underlying Soil
Greater than 16mm
Less than 16mm
Less than 8 mm
Less than 2mm
Less than 0.125 mm
Accumulated Aspect of
Drainage Flow
Vector
Mean
Curvature
0 . 3 2
 0 . 2 9
 0 . 2 0
 0 . 1 7
 0 . 1 6
C . 3 3
 0 . 3 6
 0 . 2 7
 0 . 1 2
 0 . 1 0
0 . 3 9
 0 . 3 3
 0 . 2 9
 0 . 3 4
 0 . 4 2
0 . 2 4
 0 . 3 1
 0 . 3 3
 0 . 2 7
 0 . 3 5
0 . 1 5
 0 . 1 8
 0 . 0 7
 0 . 0 8
 0 . 1 2
0 . 1 2
 0 . 2 1
 0 . 1 2
 0 . 1 3
 0 . 0 9
Slope
0 . 3 8
 0 . 3 8
 0 . 2 3
 0 . 2 7
 0 . 1 5
0 . 3 3
 0 . 2 8
 0 . 2 5
 0 . 3 5
 0 . 0 2
Notes:
1. Values in
Bold
are Significant at 0.01 Level of
Significance.
2. Values in
Italics
are not statistically significant
128 most coarse, least erodible and finest, most erodible soil classes. The percent less than 0.125mm is plotted vs. aspect of the flow vector in Figure 55. Note that hillslopes oriented between about 200 and zero degrees have less of the percent 0.125mm particle size class, while hillslopes oriented between about 60 degrees and 150 degrees have more. While at first glance these trends may suggest that aspect is a good predictor of the location of finergrained soils on the watershed, it is also worth noting that westnorthwest facing hillslopes oriented between 200 and zero degrees also tend to be on the eastern edge of the watershed, while east southeast facing hillslopes oriented between 60 and 150 degrees are located on the western edge of the watershed. It is not clear whether the higher availability of finer material on these east southeast facing hillslopes is related to orientation (e.g. more sun, less vegetation), or to spatial variability (more fine grained soils on the western side of the watershed). In either case, the fact that aspect seems to be better correlated than slope or area, raises questions about whether variables more clearly linked to hydrodynamics (e.g. slope and area) are the best to use to estimate spatial variability of soil texture. To make this variable more
Figure 55
Plot of % < 0.125imn vs Aspect of the Flow Vector
129
E 20 g 10
50 100 150 200
Aspect of Row Vector (Degrees)
250 300
Plot of percent < 0.125nmi in the surface armoring plotted against the aspect of the flow vector (the direction downhill from the current grid cell). Note the general sine wave trend of the plot suggesting that the distribution of fine grained soils is a function of flow direction.
130 useful the sine of the aspect of the flow vector was used in these calculations.
Figure 56a,b plots the D65 vs. slope and vs. accumulated drainage area, respectively. Note that in general the surface armoring get coarser with steeper slopes and greater drainage area. The trend for accumulated drainage area is less clear, so a trendline was not included. Stepwise multiple regression was used to derive estimates for each particle size class using the landscape variables. In order to obtain reasonable estimates, only one of each kind of variable was used (e.g. one measure of slope). It was found that the multiple regression estimates might not be reasonable (i.e. greater than 100 percent or negative percent) when used to estimate soil texture for all grid nodes on the watershed. Using more than one measure of slope, for example, in a multiple regression model might yield unrealistic results on very shallow or steep slopes.
The relationships are as follows:
% > 16mm = 11.1  7.405 x (Sin Aspect of Flow Vector) +
6.418
X
(Hydraulic Slope) t 1.30 x (Accumulated
Drainage) [R = 0.604]
5.6
Figure 56a
Plot of D65 vs. Slope on Hillslopes
131
5 10 15
2 0
Figure 56b
Plot of D65
vs.
Accxamulated Drainage Area on Hillslopes
100 150 200
300
132
% < 16inm = 76.855  0.808 x (Terrain Slope) + 4.896 x
(Sin of the Aspect of the Flow Vector) + 0,153 x
(Distance to the Channel) [R = 0.591]
5.7
% < 8inia = 47.583 + 7.214 x (Sin of Aspect of Flow
Vector) + 0.242 x (Distance to the Channel)
[R = 0.557]
5.8
% < 2inm = 36.213 + 7.215 x (Sin of Aspect of Flow
Vector)  0.524 x (Terrain Slope) + 0.179 x (Distance to the Channel)
[R = 0.591]
5.9
% < 0.125inm = 13.202 + 4.001 x (Sin of Aspect of Flow
Vector)  0.771 x (USLE LS term)
[R = 0.635]
5.10
These relationships were used to calculate the particle size distribution at each grid node. As a point of comparison, the multiple regression estimate for % greater than 16mm is plotted vs. the observed values in Figure 57.
5.5 Conclusions On Soils amd Landscape Form
Soil particle size and landscape form are related on the Lucky Hills 104 watershed. Individual particle size
E 60
Figure 57
Plot of Multiple Regression Estimate of
% > 16mm vs Sample Value
133
10 20 30 40 50
Regression Estimate (%>16mm)
60
Regression plot of observed values vs. multiple regression estimate for the percent greater than 16mm in surface armoring. The multiple regression estimates are good, but do not display the same degree of variability observed in the sample. The multiple regression estimates for all particle size classes have a variance about half of the observed sample value.
134 classes on hillslopes can be related to the underlying soil type, local slope, aspect, curvature and area draining through a grid element. Sediment in channels becomes finer going downstream with a decrease in the most coarse particles and a corresponding increase in sand and fine gravel. Since many of the channel elements have been sampled, soil particle size in channel elements is fairly well documented. Furthermore, statistical relationships relating particle size class to drainage area and slope were fairly good. Therefore, even though sediment in channel is the most variable, it can also be estimated using landscape variables.
The statistical relationships relating hillslope variables to sediment particle size class described in this chapter are not in and of themselves strong enough to be used in a predictive manor to estimate particle size distributions on a grid node on the watershed. However, these relationships give a qualitative understanding for the erosion processes on the watershed. On hillslopes steeper slopes and more area draining through a grid node are correlated with a higher percentage of the coarser particles, and a lower percentage of the finer particle size classes. This suggests that to begin erosion on slopes, higher slopes are necessary on coarser underlying material.
135
Channels showed a general down stream fining with the coarsest particle size class present in significant quantities only in the upper reaches of the channels where slopes were higher and areas draining through the grid node were lower.
Overall, the distribution of particle size classes on the watershed is consistent with a hydrologic explanation for sorting. Figure 58 shows the general trends relating particle size class to landscape form. These trends are based on Tables 41, 42 and 43, as well as on Figures 53 and 56a,b. In general, for both channels and slopes, shallower slopes were correlated with finer particle size classes, while coarser particle sizes occurred on steeper slopes. However, the trends relating area draining through a grid node, and particle size distribution on hillslopes was the opposite of those in channels. More area draining through a grid node on the slopes was correlated with coarser particle size classes, while more area draining through a grid node in a channel was associated with finer particle size classes.
136
Figure 58
General Trends for Soil Texture for
Hillslopes and Channels
100
Increasingly Coarse
Grained as a Function of Slope
Increasingly Fine
Grained as a Function of Drainage Area
10
Hillslopes
Channels
1
1
10 100 1000
Drainage Area (square meters)
10000
100000
On Hillslopes, texture becomes more coarsegrained with steeper slopes and increasing drainage area. In channels, soils become increasingly finegrained with increasing drainage area. These trends are supported by Tables 41, 42 and 43 as well as Figures 52, 53 and 56a,b.
137
CHAPTER 6
MODEL SETUP AND PARAMETER IDENTIFICATION
6.1 Chapter Objectives
The main objectives of this chapter are the following:
1) to describe the means to compare this effort with a more simplified approach,
2) to describe what data were put into the parameter file for KINER0S2, and
3) to describe how the SCEUA search algorithm was used to identify parameter values.
6.2 Introduction
In previous chapters, means for partitioning a watershed and developing parameter estimates using geomorphic indicators were described. Implicit in this approach is an assumption that partitioning a watershed and developing high resolution, physically realistic parameter values will improve estimates of soil erosion over previous attempts. As such it is necessary to establish a basis for comparison. Goodrich, (1990) determined that runoff could be adequately modeled on the Lucky Hills 104 watershed with a critical support area of 0.53 ha. Using this critical support area, and the TOPAZ partitioning program results in
138 a watershed of 18 elements (vs 312 with a more detailed approach). Lopes (1987) partitioned the Lucky Hills 103 watershed (a paired watershed to Lucky Hills 104) into 13 elements in his efforts to model erosion. Since both of these researchers chose to use a similar level of complexity, the 18 element watershed was used as a basis for comparison. While Goodrich (1990) used distributed estimates of hydrologic parameters. Lopes (1987) used data from rainfall simulator plots for his estimates of erodibility. Therefore, Goodrich (1990) distributed estimates for hydrologic parameters, and nondistributed values for soil erodibility parameters based on particle size data were used. The mean soil texture on hillslopes was used to estimate flow based soil erodibility values for hillslopes, and the mean value for channels was used in channels. Figure 61 shows the simpler discretization of the watershed.
Nine events with riinoff and sediment yield are available for the Lucky Hills 104 watershed. These events occurred between 1982 and 1988. Rainfall is available from two rain gauges on the watershed for each of these events.
One of the events is very large, September 1, 1984. It occurred after several wet days, so that the soil was
Figure 61
An Eighteen Element Partitioning of the
Lucky Hills 104 Watershed
100 meters
139
Eighteen element partitioning done with TOPAZ was based on a critical source area of 0.53 ha which was proposed by Goodrich (1990) as the coarsest simplification at which the hydrology could be accurately modeled.
140 abnormally wet, and the event produced more than twice as much runoff and, almost 15 times as much sediment as the next largest event. In more traditional approaches this is probably the event of most interest, because it may activate erosion process thresholds. However, in this case using the
September 1, 1984 event for parameter identification might overwhelm the other events. For this reason, if it was used for parameter identification, values would be adjusted to best fit the September 1 event. These parameter estimates might not compare favorably with those in the verification data set, which does not include a similar event.
Furthermore, one of the rain gauges aoes not have timedistributed data for the event. It has only the accumulated depth at 83 minutes. Therefore, while a clear peak was identified in the observed data, the modeled event had a lower, longer duration peak. For these reasons, the
September 1, 1984 event was not used.
Of the remaining eight events there were two each from
1982, 1983 and 1984. In each of these cases, the events occurred within two weeks of one another. In addition, there was one event from 1985, and one from 1988. The event on August 5, 1988 has 5mm of runoff while rain gauge data
141 show only 3inm of rainfall. However, there was a rainfall event on August 6, 1988, which was most likely the event that produced the observed hydrograph.
The remaining seven events had rainfall between 12mm and 33mm. Runoff varied between 2mm and 8mm. Runoff and sediment yield data were available for these events with throughout the peak flow period for the event. The runoff for the August 23, 1982, and the August 18, 1984 events could not be modeled accurately. These were added to the verification data set. The events, with values of sediment yield, precipitation, and runoff are given in Table 61.
Parameters which had multipliers in KINER0S2 were used for parameter identification. In other words, these were spatiallydistributed parameters. In parameter identification, the parameters were adjusted up or down by multiplying the spatially distributed initial parameter values by a multiplier. In this case parameter identification was done in a twostep process. Parameters for hydrology were identified first, and once these were selected, parameters for sediment were identified.
Table 61
Summary of Event Characteristics
Date Rain
(mm)
Runoff
(mm)
Parameter Identification Events
llSep 1982
20Sep 1983
30Jul 1985
3 2 . 0 0
1 8 . S 4
2 5 . 6 5
8 . 1 1
2 . 2 8
2 . 6 9
Verification Events
18Aug 1984
23Aug 1952
10Sep
1983
25Aug 1984
5Aug 1988
2 3 . 3 7
3 0 . 7 3
3 0 . 2 3
1 2 . 4 5
2 6 . 1 6
6 . 2 9
4 . 5 9
4 . 1 8
2 . 0 9
5 . 7 5
Sediment
Yield
(Kg/ha)
2 3 6
2 0
1 0 8
2 2 5
170
5 7
5 7
190
142
143
6.3 Initial Parameter Estimates
Initial parameter estimates for hydrology came from
Goodrich (1990). These were the initial values multiplied by a multiplier which was fit by optimization. Antecedent soil moisture was estimated using the BROOK90 hydrologic model (Federer, 1995) with parameter values selected using soil moisture data from TDR moisture measurements collected on the Lucky Hills 104 in 1990 and 1991. BROOK90 uses the
Shuttleworth and Wallace model for evapotranspiration and the Clapp and Hornberger (1978) equations for describing soil moisture movement. The soil moisture modeling is described in Appendix A.
For the more complex case (i.e. 312 elements), initial parameter values for sediment were selected using the methods described in Chapter 5. The particle size distribution in channels was estimated using the regression relationships for each particle size class as described in
Chapter 5. However, if a soil sample was available for a given channel segment, it was used rather than the regression estimate. For the simple case (i.e. 18 elements), only the mean values for sediment samples in channels were used.
Particle sizes of soils on hillslopes were initially estimated using cokriging. However, errors were found in
144 the data. A description of the cokriging process and the previous estimates are included in Appendix B. In this case, the multiple regression estimates as well as inverse distance weighted estimates were used to estimate soil particle size distributions on hillslopes. The multiple regression estimate was weighted at 2/3 and the inverse distance weight was 1/3. The greater than 16mm portion served as the initial estimate for the PAV fraction. The remaining fractions were estimated by subtracting the subsequent particle size class from the ciimulative distribution curve. For example, the 8mm  16mm fraction was estimated by subtracting the percent less than 8mm from the percent less than 16mm. For the simple case, only the mean particle size value was used.
The entrainment by splash parameter was estimated from the Ka value using the methods described by BenHur and
Agassi (1997) who provide several different equations based on the kinetic energy of raindrops. In this case, the following equation was used:
=531,705146,792 »1 ii
(A:,) 6.1
where:
Ki = WEPP interill erodibility factor
Ks = saturated hydraulic conductivity (mm/hr)
145
Since Kt in the WEPP model provides detatchment values in mass per time, and Kt in KINER0S2 (equation 1.3) is used in a volume per time estimate, the WEPP Ki value had to be divided by 1000 Kg/m^ * 2.65 (i.e. specific gravity of soil particles) to produce equivalent units. However, it must be noted that since the detatchment equations for KINER0S2 and
WEPP are different, these are not equivalent values even with a units adjustment. They simply provide a reasonable starting estimate.
In KINER0S2 it is necessary to estimate the temperature of the water because this affects viscosity and therefore transport capacity. In this case, it was estimated at 33''C.
It was also assumed that the surface temperature would be very warm prior to an event, and that the rain would be cool.
6.4 Parameter Identification Method
Parameter identification was done using the shuffled complex evolution UA (SCEUA) search algorithm (Duan et al.,
1992) and the total sum of squares objective function
(TSSR). Essentially, this is a search algorithm which is an extension of the simplex method (Nelder and Mead, 1965).
However, it uses multiple simplexes, and after several search steps, the points in the simplex are shuffled with
146 points from other simplexes. New simplexes are formed using points from the previous simplexes.
Both least squares and NashSuttcliffe (1970) objective functions were tried. For both runoff and sediment, the observed value for each measured time was compared with the simulated value for that time In this way, the full hydrograph or sedigraph was fit, rather than simply optimizing for peak or volume.
Since the clocks on the rain gauges and flumes were analog and not highly precise, the actual starting time of the rainfall and runoff might not be known precisely. For this reason, a time shifting was introduced. The model was run with the initial estimates from Goodrich (1990). At that point, the time to peak was estimated based on the modeled hydrograph. The observed time to peak was then set at this initial estimate. However, the objective function was calculated by shifting the hydrograph both forward and back in time from 3 to 7 minutes before and after the estimated peak time. Therefore, if Manning's n changed, for example, and the peak shifted in time slightly, the optimization function would still find the best fit.
For hydrology, multipliers for Manning's n, K, and the coefficient of variability of Ka (CV^) were used as fitting parameters. For Walnut Gulch, Goodrich (1990) found that G
147
(the net capillary drive) could be estimated as a function of Ka. Therefore, the multiplier for G was calculated using this regression relationship for each new value of K,. For sediment a multiplier was used on the splash parameter as well as on the transport capacity term. Multipliers on the
PAV term (i.e. the paved portion of the surface as described in equation 1.2) and cohesion term were also tested, but were ultimately not used because, unique parameter values could not be found. Even though unique parameter values for
PAV could not be found, the other parameters had unique values and the correct simulated parameter values were found. This suggests that the model is relatively insensitive to cohesion and PAV, at least in the simple test case used here. Therefore, the multipliers on sediment were as follows:
efln) =
6.2 where: ef(„) = entrainment by flow for particle size class(n)
Mtc = Multiplier for Transport Capacity pi = erosion rate coefficient for particle size class (n) w = width of flow
Cmx(n)= transport capacity of particle size class(n)
148
Csini = concentration of suspended sediment entering node ei = Msp^Kfe"" 6.3 where:
Msp = Multiplier on the Splash parameter
K i = parameter describing the susceptibility of the soil particles to be detached and entrained by raindrop impact i = rainfall rate c = parameter describing the attenuation effect of flow depth h = flow depth
Many researchers (e.g. Lopes, 1987; Freedman, 1996) have had difficulty finding unique parameter values for other models similar to KINER0S2. Furthermore, Goodrich
(1990) had to resort to exhaustive gridding to find unique parameter values for K,, CV and n on the Lucky Hills 104 watershed. Exhaustive gridding is perhaps more accurate, but much more computationally intensive. For this reason, use of a search routine such as SCEUA would be beneficial if it proved to work well.
To test whether coupling SCEUA to KINER0S2 could be used, a simplified plane to channel configuration was used.
The observed rainfall from four events; August 23, 1982;
September 20, 1983; August 18, 1984 and July 30, 1985 were used as inputs to the simple plane and channel model. The model simulated runoff and sediment for the case where
149 multipliers were 1.0 and these were used as pseudoobserved data (i.e. simulated data). Both the total sum of squared residuals (TSSR) and the sum of the NashSuttcliffe (1970) values for the four events were used as objective functions.
The simple least squares objective function required fewer shuffling loops to find the optimal parameter set than the NashSuttcliffe (1970) objective function. The results for hydrology parameters showing the number of shuffling loops and the least squares objective function value are shown in Figure 62. Note that the simple least squares converges rapidly.
This parameter identification method also worked well for the sediment parameters. Since the splash erosion term has been showed to vary over orders of magnitude, the splash term was allowed to vary up to three orders of magnitude greater than or less than the initial value. The multiplier on transport capacity was allowed to vary by a factor of 10 up or down.
Once this method had been verified to work on the small two element system, it was tested on the 18 element and 312 element watersheds. Once again, the initial parameter values used to generate the synthetic data were found.
Figure 63 shows the results of the search for sediment parameters on the 18 element watershed. Therefore, the
Figure 62
Graph Showing the Success of SCEUA in Finding the Total Sum of Squares Objective Function Minima in
KINER0S2 for K,, CV
k
, and n
150
100000
10000
I I •
1000
100
5
I e o
1 « i §
>
2*
O
10
1
0.1
0.01
0.001 •
0.0001
0.00001
0.000001 
0.0000001 a • Q •
10
• •
• 15
•
•
23
! Function
Function
Number of Shuffling Loops
The SCEUA with the Total Sum of Squared Residual (TSSR) function resulted in rapid convergence of the search at the Multiplier values used to produce the hydrologic simulation. This indicates that the method should be able to find multiplier values for hydrologic parameters in the observed data set if the model reasonably describes the rainfallrunoff process.
151
Figure 63
Graph Showing the Result of the SCEUA in Minimizing the
Objective Function Error for
Multipliers on Transport Capacity (Mtc) and
Rain Splash (Mspl) r
10000000
1000000
1
100000
10000 g u
§
0
1
1000
100
.
0.1 •
0.01 •
0.001
0.0001
•
a
Q a o s
10
• •
• •
•
•
15
n • a I a
20
Numder of ShufRing Loops
i •
I
Function
J
j • j
1
! Function
;
i
The SCEUA with the Total Sum of Squared Residual (TSSR) objective function resulted in rapid convergence of the search at the Multiplier values used to produce the sedimentyield simulation. This indicates that the method should be able to find multiplier values for sedimentyield parameters in the observed data set if the model reasonably describes the rainfallrunoff process.
152
KINER0S2 model is a process based model, and the SCEUA can be used to find optimal parameter values in KINER0S2. If
KINER0S2 reasonably describes the processes which result in the observed measurements of runoff and sediment, and if
KINER0S2 has been reasonably parameterized, the KINER0S2
SCEUA should be able to find good parameter sets for the observed events. Furthermore, comparison of a complex characterization of the watershed based on field observation should be the most accurate description and should improve estimates over a more simplified approach represented by the
18 element watershed.
153
CHAPTER 7
RESULTS OF SOIL EROSION MODELING
7.1 Chapter Objectives
The main objectives of this chapter are the following:
1) to describe the details of the modeling and the results of the modeling in terms of being able to predict runoff and erosion on the Lucky Hills 104 watershed given rainfall, and
2) to compare the results from the 312 element partitioning of the watershed with the 18 element partitioning.
7.2 Introduction
To compare the effect of a complex distributed partitioning with a more simple lumped approach, parameter values were selected for both the 312 element and the 18 element partitioning of the watershed. Optimal parameter multiplier values for
K,,
n and
CVks
were selected for each event individually using the SCEUA and the TSSR. Values for the multiplier for the splash parameter and the multiplier on transport capacity were selected using the SCEUA with the
TSSR objective function for three events from the parameter estimation data set. In order to ensure that parameter
154 values had converged to a minima, the optimization was done twice using a different random nuinber seed each time. The better of the two results, in terms of having a smaller squared residual was used as the parameter set.
7.3 Hydrology Parameters
In order to minimize the effect of errors in hydrologic modeling on sedimentyield modeling, an optimal parameter set was selected for each event. Multiplier values and the associated NashSutcliffe model efficiency statistic are listed in Table 71. The NashSuttcliffe (1970) statistic is calculated as follows:
£=l['='
1 = 1
1 7.1
where:
= observation at time i
0i =
simulated value at time i
0 = mean of all observed values
This is also referred to as the model efficiency (ME).
Note that for most of the events the values converged to reasonable values in the parameter space. However, best
Table 71
Summary of Hydrograph Fitting Parameters
Multipliers
Parameter Estimation Events
312 Element
K, n CV
k,
Nash
Sutcliffe
20Sep 1983
2.44 0.94 0.75
30Jul 1985
3.87
1.07 1.07
11Sep 1982
1.38 0.32 0.68
0.99
0.98
18 Element
20Sep 1983
1.97 0.67 0.55
30Jul 1985
3.23 1.44 1.52
11Sep 1982
1.20 1.54 0.88
0.97
0,99
1.00
Multipliers
Parameter Verification Events
312 Element
K, n
CV
k^
2 1982
6.00 0.97 2.973
10Sep 1983
4.85 1.15 0.55
18Aug 1984
3.13 0.49 1.317
25Aug 1984
1.92 1.06 1.271
5Aug
1988
5.93 1.74
1.24
Nash
Sutcliffe
0.77
0.97
0.78
0.90
0.98
18 Element
2 1982
4.35 0.79 2.999
10Sep
1983
4.72 0.93 1.044
18Aug 1984
2.61 0.35
0.989
25Aug 1984
1.32
0.84 0.906
5Aug 1988
3.43 2.52
0.467
0.78
0.92
0.77
0.91
0.73
Noces a b
Multipliers for August 23, 1982 Event are
Unrealistic
Fit of Hydrograph is Poor for August 18,
1984
156 parameter fit values for the August 23, 1982 event always were on, or very near, the upper bound for the multiplier on
CV
ks
. This is a particularly important event in calculating the TSSR, because there are 18 observed values for this event, while the other events had ten or less values.
The August 23, 1982 event is a doublepeaked hydrograph. Figure 7la shows the fitted and observed hydrographs for the TSSR for this event for the 312 element configuration with the bound on the multiplier on
CVks
set to 1.5. Figure 7lb shows the fitted and observed values for the multiplier bound on
CV
ks
set to 3.0. Clearly the higher
CVks
values improve the fit of the hydrograph by increasing the first peak and reducing the second. Note also, that while the Ka value increased by a factor of 2, the volume of the discharge from the two simulations is approximately the same. Therefore, this suggests that there are conditions under which increasing parameter values to unreasonable values results in improved fits to the observed data.
Since the rain gauges have analog clocks, it is possible that the observed time of the rainfall is offset from the true time of the rainfall, resulting in errors in modeling the peaks. In either case, the August 23, 1982
157
Figure 7la
Simulation of the August 23, 1982 Event Using a
Lower Value of the Multiplier on CV
K
^
12 •
10 •
ME = 0.23
U.
4 •
!
!
0
20
40 60
Time (minutes)
80
100 120
I
i
Figure 7lb
Simulation of the August 23, 1982 Event Using a
Higher Value of the Multiplier on
CVks
12
1 0 • •
E
i
Ik
4 •
0
20
40 60
Tim* (minutes) ao
100
158 event could not be modeled using reasonable parameter estimates, so it was not used in parameter estimation. However, because the data set is limited, it was kept for verification.
The hydrologic parameters for the remaining events were similar to each other. However, to get the most reasonable erosion parameter estimates, it is best to use the best hydrologic parameter values for each event. In this way, the errors caused by using a single set of hydrologic parameters to fit all events will not further amplify the associated error in modeling sediment yield.
In addition, the watershed is not static. Changes in canopy cover as the result of dry or wet years may change roughness, or even the
CVks
. Furthermore, the Lucky Hills underwent imprinting treatments and was used for testing herbicides. For this reason, the hydrologic response of the watershed may change through time.
For the remaining events Ka needs to be increased by a factor of 23 to improve error between the observed and simulated hydrographs. These values are very much in line with Goodrich's (1990) preoptimization multipliers.
159
Goodrich (1990) multiplied original estimates of Ks by 0.3 to 0.55, so that increasing Ka by a factor of 23 is in line with original estimates based on soil texture.
An increase in K, could be attributed to the fact that the BROOK90 model was used to determine soil moisture values. BROOK90 soil moisture estimates tended to be wetter than the values used by Goodrich (1990) which were generated in CREAMS (Kniesel, 1980) (Sayed, Pers. Comm. 1998). With slightly more moist soil, would have to increase to duplicate the same response. Furthermore, KINER0S2 uses the
Corradini et al. (1994) infiltration routine rather than the
Smith and Parlange (1978) routine used by Goodrich (1990), so that the infiltration routines are different and may respond differently requiring different parameter values.
In addition, to the above changes, fitted n and
CVk
values were slightly different than original estimates.
Goodrich (1990), increased the n value by a factor of 2.2 for Lucky Hills 104 and Lucky Hills 102. The events have optimal roughness values between, or similar to, Goodrich's optimal values and his original estimates. The multipliers on
CV
k3 are similar to Goodrich's (1990) original estimates of between 0.8 and 1.0. However, soil moisture has been
160 shown to be spatially and temporally variable on the Lucky
Hills 104 watershed (Whitaker, 1993). Such variability can then cause spatial and temporal changes in rates of infiltration. For the model, this is reflected in a change of the
CV
k3 value on an event by event basis.
Figures 72a,b, 73a,b and 74a,b show the fitted hydrographs for the 312 and 18 element watersheds for the
September 11, 1982, July 30, 1985 and September 20, 1983 events respectively. There was essentially no difference between the goodness of fic between the 18 element and 312 element watersheds, though the TSSR for the 312 element cases were generally lower. Furthermore, the hydrographs from the 18 element watersheds were a little more rounded with lesspronounced peaks. The simulation for all three events for both of the watershed configurations can be considered to be very good because the NashSutcliffe (1970) statistics between 0.98 and 1. Since hydrology has been shown to have a pronounced effect on sediment yield with the
KINER0S2 model (Smith et al. in press), use of simulations with minimal hydrologic error provides an opportunity to minimize the compounding effects of hydrology on modeling sediment yield.
161
Figure 72a
September 11, 1982 Fitted Hydrograph for the 312
Element Watershed Configuration
ME = 0.99
90 110
Time (minutes)
Figure 72b
September 11, 1982 Fitted Hydrograph for the 18
Element Watershed Configuration
45
40
35
30
1 ^
 2 0
^ 15
10
5
0so
A
j \
ME
70
f \
/ \
i S=—.—
130 150
90 110
Time (minutes)
162
Figure 73a
September 20, 1983 Fitted Hydrograph for the 312
Element Watershed Configuration
I
I
I
I
20 •
I
15 •
1 o 10
Time (minutes)
Figure 73b
September 20, 1983 Fitted Hydrograph for the 18
Element Watershed Configuration
25
I i
20
I
i
' S 15 •
o 10 •
0 20
40
Time (minutes)
60
I
I
I t i
u.
18 •
16 
14 •
12 •
10 •
4 
0
163
Figure 74a
July 30, 1985 Fitted Hydrograph for the 312
Element Watershed Configuration
!
20 1
18
16
14
1
E, 10 t 8 iZ
6
4
2
0
0
—
A
7
ME = 0.98
10
J
/ \
V \
/
/ \
i \
20 30
I .
— —
40 so 60 70 ;
Time (minutas) i
{
Figure 74b
July 30, 1985 Fitted Hydrograph for the 18 Element
Watershed Configuration
20 40
Tiim (minutes)
60
164
7.4 Modeling the Sediqraphs
The TSSR from the Septeinber 11, 1982, July 30, 1985 and
September 20, 1983 events was the objective function used to estimate the multipliers for splash and transport capacity.
Two runs were made with different random number seeds to ensure that multiplier values converged to the same region of the parameter space. While values converged to the same part of the parameter space, there did appear to be some parameter interaction as indicated by the fact that some of the slightly worse objective functions were produced by multipliers with much higher values of the multiplier on transport capacity, and lower multiplier factor on the rain splash. Furthermore, examination of the MsplMtc response surface showed that one event, September 11, 1982, showed a clear minima, while the response surface for the September
20, 1983 and July 30, 1985 events appeared to show parameter interaction. Furthermore, the search routine converged in the portion of the parameter space of the minima for the
September 11, 1982 event. Therefore, parameter interaction appears to be a problem though a clear minima was identified.
Multipliers for the two watershed configurations
165 are as follows:
312 Element
18 Element
M Transport Capacity
1.70
1.24
M Splash
5.04
12.51
Ideally, if the model had been perfectly parameterized, and the model describes the processes well, all multipliers should be 1.0. Therefore, these multipliers suggest that the parameterization was not ideal. In this case, the multiplier on transport capacity has values in line with the expected value of 1.0. While the apparent parameter interaction suggests these values may not be representative, values of 1.70 or 1.24 on transport capacity seem reasonable considering the potential sources of error. These sources of error include using current field survey data and soils data to estimate conditions for events that occurred 10 to
16 years ago, and describing channels as having uniform crosssections when, in fact, the cross section changes through different reaches.
Multipliers on splash on the order of 5 to 12 clearly suggest a problem. However, Smith et al. (in press) multiplied splash by 10 to 20,000 to get reasonable estimates of sediment yield using the KINER0S2 model. While there is clearly a problem, it is not clear whether it is
166 merely a computational problem, or if it points to a lack of understanding of the rain splash process.
Regardless of the logic that such multiplier values are unreasonable, these multipliers produced good fits between simulated and observed sedigraphs. Figure 75a,b shows the fitted sedigraph for the September 11, 1982 event for the
312 and 18 element configurations respectively. Figure 7
6a,b shows the sedigraphs for the September 20, 1983 event.
Figure 77a,b shows the sedigraph for the July 30, 1985 event.
In general, the model simulates the sedigraphs well.
The negative model efficiency statistic for the September
20, 1983 event is largely because of a single point on the trailing end of the sedigraph. There is very little variation in the observed values resulting in very small differences between the mean observed value and the observations. Therefore one bad point can accentuate this problem. However, it should be noted that the more complex watershed was as good or better than the simulation using the 18 element watershed. Furthermore, the results from the
312 element simulations were better for the largest and smallest of the three events.
At any rate, the test of the success of the parameter estimation process is how well the verification events fit
Figure 75a
Fitted Sedigraph for the September
11, 1982 Event 312 Element Configuration
167
^ 4
o
> 3
I
50 70 130
Figure 75b
Fitted Sedigraph for the September
11, 1982 Event 18 Element Configuration
3.5
90 110
Time (minutes)
150 '
i
It
«
>
I
I
0.5 
50 70 90
110
Time (minutes)
130 150
I
I
I
i
I
i
Figure 76a
Fitted Sedigraph for the September
20, 1983 Event 312 Element Configuration
ME = 0.85
0.2 •
0
20 eo
80
Figure 76b
Fitted Sedigraph for the September
20, 1983 Event 18 Element Configuration
168
O
>
c
I
1
2 •
0
20
40
60
80
Figure 77a
Fitted Sedigraph for the July r i
3 0 ,
1985 Event 312 Element Configuration
1.8
1.6 •
1.4 •
ME = 0.61
I i
t
I
5 0.6 •
0.4 •
0.2 •
0 10 20
X
Time (minutes)
40 50 eo
Figure 77b
Fitted Sedigraph for the July
30, 1985 Event 18 Element Configuration
2.5
ME = 0.63
^ 1.5 •
0.5 
0 10
20 30
Time (minutes)
40 50
60
169
170 using the identified parameter values. In this case, the
August 23, 1982 event and August 18, 1984 events were considered to be of marginal value, because the hydrographs could not be simulated as well as the other three events.
Figures 78a,b and 79a,b show the hydrograph and sedigraph fits for the September 10, 1983 event. Figures 710a,b and
71la,b show the hydrograph and sedigraph fits for the
August 25, 1983 event. Finally, Figures 712a,b and 713a,b show the hydrograph and sedigraph fits for the August 5,
1988 event. Note that some events fit well, and some do not. In fact, the NashSuttcliffe model efficiency values range from a high of 0.97 for the September 10, 1983 simulation for the 312 element watershed to 0.62 for the
August 25, 1984 simulation for the 312 element watershed.
While being able to simulate a hydrograph successfully must improve the likelihood of modeling the sedigraph, it is not a certainty. In two of the simulations, events with hydrographs having model efficiency statistics near to 1.0 produced sedigraphs with negative model efficiency statistics. Furthermore, while the model did a good job of simulating the two events from 1983, it did poorly on events from 1984. Therefore, perhaps there is a need to look for state variables that would help characterize temporal changes on the watershed. Such state variables might
171
Figure 78a
Hydrograph for the September 10, 1983 Event, 312
Element Configuration
I
1 8  •
16 •
1 4  •
I 12 •
E 10 •
6
4 •
)
1
ME = 0.97
Time (mmutas)
Figure 78b
Hydrograph for the September 10, 1983 Event, 18
Element Configuration
18
16
14 •
12 •
E
i
u.
4 •
0
10
20 30 40
Time (minutes)
50 60 70
172
1
Figure 79a
Sedigraph for the September 10, 1983 Event, 312
Element Configuration
ME = 0.97
I
I
I
> 0.8 ••
I i
I i
<n
0.4  •
0.2
0
10
20
30
Time (minutes)
40 50 60
Figure 79b
Sedigraph for the September 10, 1983 Event, 18
Element Configuration
2.5 s
s
>
s
I
I
o.s 
0
10
20
30
40
Time (minutes)
50 60 70
Figure 710a
Hydrograph for the August 25, 1984 Event, 312
Element Configuration
173
10 
ME = 0.90
t
1
u.
I
I
1
I
0
10
20 30
Time (minutes)
40 50 60
Figure 7lOb
Hydrograph for the August 25, 1984 Event, 18
Element Configuration
1 2 • •
1 0  •
o
4 •
ME = 0.91
0
10
20
30
Time ^inute^
40 50 60
I
I i
Figure 711a
Sedigraph for the August
2 5 ,
1984 Event, 312
Element Configuration
2.5
1
I
r 1.5
0.5
50
174
Figure 7lib
Sedigraph for the August 25, 1984 Event, 18
Element Configuration
2.5
HI
2 •
S
£
>
i
0.5 •
0
10
20 30
Time ^inutea)
40 50
60
Figure 712a
Element Configuration
30
25 •
20 • i
(
I
1
u. 10 .
ME = 0.98
0
10
20 30
Time (minutes)
40 50
i
Figure 712b
Hydrograph for the August 5, 1988 Event, 18
Element Configuration
ME = 0.85
I
I
25 •
20 •
1
10 
5 
175
Figure 713a
Sedigraph for the August 5, 1988 Event, 312
Element Configuration
7
6
5
ME = 0.51
176
1
0
0
10
20
Time (minutes)
30
40
I
Figure 713b
Sedigraph for the August 5, 1988 Event, 18 Element
Configuration
6 •
ME = 0.09
I
2 4
0
10
30
40
177
include changes in sediment storage in a channel, or length of time since the previous event to account for airborne silt contributions. Furthermore, it might be possible to account for the fact that soil tends to be looser in the spring because of the effect of freezethaw through the winter or the fact that in wet years a larger canopy cover or higher leaf area index might increase interception and limit the effect of rain splash.
Even with the limited number of events used for this study, it is clear that there is some benefit to using a more complex geometric representation of the watershed. The two very best sedigraph simulations (ME = 0.85 for the
September 20, 1983 event, and ME = 0.97 for the September
10, 1983 event) were simulated using the more complex representation. Furthermore, for the two events with poorer hydrograph simulations, August 23, 1982 and August 18, 1984, the sedigraphs from the more complex representation were slightly better than the 18 element watershed configuration.
In addition, the very worst simulation (ME = 48.8 for the
September 20, 1983 event) was produced using the 18 element configuration. On the other hand, the simulation from the
312 element for that same event was very good (ME = 0.85).
In addition to the goodness of fit statistics, it was apparent that in some cases, the shape of the sedigraphs
178
from the 18 element configuration was not as reasonable as the one for the 312 element configuration (e.g. September
11, 1982 event). The better fits and more reasonable sedigraph shapes suggest that there is a benefit to using a more complex representation of the watershed, and distributed erodibility values estimated from sediment samples.
179
CHAPTER 8
FINDINGS, CONCLUSIONS AND
SUGCSSTIONS OF FUTURE RESEARCH
8.1 Chapter Objectives
The main objectives of this chapter are:
1) to describe the findings of this research as they apply to geomorphology,
2) to describe the findings of this study as they apply to modeling sediment, and
3) to suggest possible directions of future research based on the findings of this study.
8.2 Introduction
This study considered two levels of model complexity: a
312 element watershed which was partitioned according to theory; and an 18 element watershed which was partitioned based on pragmatism (i.e. it was the least complex scale for which there would be negligible error in modeling the runoff). Because of the relative success of the less complex watershed in terms of modeling sediment as well as runoff, it is necessary to separate the theory that resulted in selection of the 312 element partitioning from the pragmatism that resulted in selection of the 18 element
180
watershed.
8.3 Findings of the Survey and Soils Data Analysis
The findings of the study of landscape form showed the following:
1.) High resolution topographic maps such as the 1" =
40' contour map of the Lucky Hills 104 watershed are nearly of equal quality in describing topographic features as the DEM derived from survey of 2993 points on the watershed. In contrast, neither the
30m X 30m USGS DEM, nor the 15m x 15m DEM prepared from aereal survey provide this level of resolution.
2.) A slopearea diagram (a plot of mean log of slope vs. log of drainage area) can be used to estimate the critical source area necessary to initiate a channel on the watershed. This is based on the fact that the value of critical source area derived from the slopearea diagram is nearly identical to the area determined by locating the channel head in the field, and it was verified using two different computational methods.
3.) Critical shear stress estimates derived from detailed soils data collected on the Lucky Hills 104
Watershed show that the greatest variability in
181
critical shear stress of the sediment occurs in the channels. In contrast, the surficial armoring on the hillslopes is more uniform. However, the soils with the highest critical shear stress occur at the transition from hillslope to channel.
4.) The texture of channel sediment shows the oftenobserved trend of downstream fining. Correlation of texcural classes with drainage area and slope are good and can be used to estimate the spatial distribution of particle size class in channels.
5.) Different algorithms for determining slope, aspect and curvature produced similar estimates. In contrast, algorithms for estimating area draining through a grid node were not well correlated, suggesting that is is difficult to properly assess this measure.
6.) Soil particle sizes on hillslopes are also correlated with slope and drainage area. However, the sine of the aspect of the flow vector (i.e. which of 8 directions does the water flow from one grid node to another) was fovind to show the best correlation with particle size class for both the most coarse and least coarse sediment.
182
7.) CoJcriging and other multivariate geostatistics (as described in Appendix B) can be used to improve the spatial estimates of soils particle size class, and thus the potential spatial variability of soil erodibility.
8.) The texture of the underlying soils appeared to play an important role in location of channels. As is described in Appendix C , more channels are initiated in the 1362 m  1366 m elevation which also coincides with the location of finergrained soils on the watershed.
8.4 Findings of the Modeling Effort
Efforts to model soil erosion and hydology of selected events showed the following:
1.) The SCEUA. search routine (Duan et al., 1992) can be used to find values of multipliers that minimized errors between observed and simulated hydrologic data. In particular, the SCEUA can be used to find multipliers for Ks, Manning's n and the coefficient of variation of K, (
CV
k
^) .
2.) Multipliers placed in front of the entrainment by splash term, and the transport capacity term were identifiable using the SCEUA. The SCEUA can
183
repeatedly find the parameter values which produced the simulated erosion data. Furthermore, when an alternative random number seed was used, the SCEUA would repetedly find the same parameter space in the observed data. However, the MsplMtc response surface for the observed data appeared to show parameter interaction. Therefore, while the SCEUA can be used with simulated data to find parameter values for sediment, the parameter interaction problems in the observed data suggests that it may not be possible to find representative multiplier values for observed data.
3.) The ability of the SCEUA to obtain hydrologic parameters which produced individual hydrographs for individual events with minimal error, allowed separation of problems of sedimentyield modeling from hydrologic modeling. Realistic hydrologic parameter values were identified for each individual event producing hydrographs with NashSuttcliffe
(1970) model efficiency statistics exceeding 0.90 in six of the eight events, and 0.97 in five of the events.
4.) There was negligable error in hydrograph modeling introduced by simplifying the 312 element watershed
184
to an 18 element watershed. Model efficiency statistics were almost identical, though hydrographs from the 18 element configuration tended to have less pronounced peaks and tended to be less able to simulate more rapid change than hydrographs from the
312 element configuration.
5.) Soil erosion multipliers were identified for both the 312 element and 18 element configuration. Three events were used for parameter identification and five events were used for verification. Visual inspection of the fitted sedigraphs suggested that the fits were good. In some cases, the poor model efficiency is attributed to the fact that for many of the events, many of the observed values tended to be small, thus there was little variability about the mean. For this reason, errors in fitting steep sedigraphs, or higher sedimentyield values, produced poor model efficiencies.
6.) Multipliers for transport capacity and splash
were
identified for both the 18 element and 312 element watersheds. These proved to have predictive capability in the verification data set.
7.) Multiplier values were unrealistic suggesting that they are operating more as fitting coefficents than
parameters with physical significance. This is particularly true for the splash multiplier which was up to 12 times the intial estimate.
185
8.5 Discussion of the Findings
This study has been an effort to understand how soils and landform are related in the erosion process. It has been an effort to gain an intuitive understanding of the process on one small watershed as a basis for understanding the erosion process in general. Confirmation that the slopearea diagram can be used as a process scale indicator of where erosion by flowing water becomes the dominant mechanism is an important contribution toward the understanding of the interaction between erosion and landform characteristics. It suggests that with a highresolution DEM or topographic map, it is possible to estimate critical source area without identifying channel heads in the field.
The soils data collection effort lays the ground work for understanding the erosion process at the watershed scale. Having accurate locations of the samples is important, because these allow a basis for improved spatial estimates of soilrelated properties. Such properties include hydraulic conductivity and porosity as well as
186
particle size class estimates used to estimate erosion.
Use of the soils data to estimate critical shear stress showed that the least erodible soils occur at the transition from hillslope to channel. This is an important observation because others have noted (e.g. Prosser et al., 1998) that landforms favor delivery of sediment to first order streams.
For this reason, they suggest that erosion protection efforts should be aimed at first order streams. However, the fact that the coarsest soils occur at this transition from hillslope to channel suggests that the landform has the highest degree of protection at this transition. Therefore, first order streams may not be the best location for erosion protection efforts.
Recognition that both the coarsest and finest soils on the watershed occur in the channel is important because many previous efforts to study erosion on small watersheds have focused on hillslopes and used rainfall simulator studies.
The fact that soil particle size can be predicted in channels based on drainage area and slope allows an opportunity to minimize errors associated with estimating available sediment for transport capacity.
Finding relationships between soil particle size class and landscape variables allows for the spatial variability of soils to be better estimated. In fact, the multiple
187
regression, and the cokriging efforts, used to parameterize the spatial distribution of soils particle size class, may improve the understanding of the general trends on hillslopes (e.g. soils are coarser on steeper slopes draining more upland).
Understanding both the topographic and soils relationships allowed estimation of the spatial variability of erosion parameters, and to partitioning of the watershed into elements based on process scale features rather than map scale. Because of the success of SCEUA in fitting hydrolgic parameters and good initial estimates from
Goodrich (1990), hydrographs from eight events could be modeled with a minimum of error, thus allowing the effort to focus on the erosion parameters.
The fact that unique multiplier values could be identified for both the 18 element and 312 element partitioning, suggests that it is realistic to expect to be able to model erosion on an event basis on a small watershed. However, the apparent parameter interaction problems suggest that these are unique because one event only had a clear minima. Furthermore, the fact that the multipliers are much different than they should be, suggests that the processes remain poorly understood.
The fact that this study, like the study by Smith et
188
al. (in press), found that the splash multiplier needed to be raised to unreasonable values, [10 to 20,000 (Smith et al, in press) or 5 to 12 (this study)], may suggest that the
KINER0S2 model is not describing the processes correctly.
This may be because the processes themselves are not understood at scales larger than rainfall simulator plot scale.
The fact that the multiplier on transport capacity of sediment is not 1.0 may point to possible errors in describing sediment transport. However, these errors could have numerous roots. Even the detailed survey done for this study is not adequate to describe the geometry of channels on the watershed. The width of a channel can vary greatly in a short reach, thus changing the wetted perimeter, velocity and sediment transport capacity. Furthermore, since the sedimentyield data does not contain particle size information, it is not clear which particle sizes are being transported.
Since the 18 element lumpedparameter partitioning performed nearly as well as the 312 element configuration with distributed parameter values, it appears that it is not necessary to partition to preserve the configuration observed in the field. However, since the splash multiplier values were so much different for the two cases, this
189
suggests that the multipliers are a function of level of discretization, and possibly hydrology.
The negative aspect of the difference between the multipliers for the two different scales is that multipliers may have to be changed greatly for every partitioning. The positive side is that it may be possible to develop equivalent multiplier values as a function of partitioning scale and hydrology. Therefore, if reasonable multiplier values were identified at a base scale (e.g. 312 element scale) it might be possible to scale down to a coarser scale using concepts similar to the equivalent roughness concepts used in hydrology. Therefore it may be possible to estimate equivalent splash coefficients as the watershed is simplified. In its current state, it is not clear whether the benefits of a physicallybased model like KINER0S2 can be realized. It is not clear if the simulations describe where and when sediment is being eroded, for example. The
18 element case probably describes a different scenario than the 312 element case in terms of where and when erosion is occurring.
Despite the fact that splash multipliers make no physical sense in this case, being able to fit a sedigraph, and estimate coefficients that can be used in a predictive manner allows for the possibility of refining the
190
understanding of sediment transport. Further understanding of the process then may allow us to refine the model so that it better describes the physical processes.
8.6 Future Research
The findings of this study open many possibilities for future research. Among them are the following:
1. ) The range of soil erodibility needs to be studied.
The range of variability may be a more useful way to describing erosion on hillslopes. For example, much of the Lucky Hills is covered with a patchy surficial armoring. As such, the location where erosion on hillslopes occurs may be a function of where the soil surface is not protected by armoring
(e.g near animal burrows), as well as finer or coarser armoring. Furthermore some areas of the armoring are less coarse. Therefore, in a larger event the shear stress threshold may be exceeded allowing for much more sediment to be eroded from that location. Use of geostatistical conditional simulation techniques such as simulated annealing may be useful in describing both the general trends on hillslopes as well as identifying a range of possible soil erodibility values.
191
2. ) The sediment, landscape relationships need to be further refined. Concepts such as sorting ratios may add to the understanding of how sediment moves on landscapes.
3. ) Geostatistics should be used to characterize the underlying uneroded soils. Such a study might improve the understanding of how landform is related to soil type. Furthermore the data could be used to improve estimates of the spatial variability of K, and other hydrologic variables.
4. ) The splash parameter in KINER0S2 needs to be further studied. If KINER0S2 performs well on rainfall simulator data, a reason for the need to increase initial estimates by a factor of 5 or more needs to be found.
5. ) A detailed sensitivity analysis needs to be performed on the sedimentyield portion of the
KINER0S2 model. This needs to include a sensitivity analysis of the effect of hydrologic parameters as well as transport capacity and rainsplash related parameters.
6. ) More events need to be studied so that more solid conclusions can be developed regarding the description of sediment movement and erosion on a
192
watershed. Multiple particle size samples may improve the understanding of transport capacity.
7. ) Simulations need to be run for many events (i.e. including events for which there is only rainfall) for several seasons to see if the model reasonably describes sediment movement on the watershed. For example, KINER0S2 can provide a sediment budget for any element in watershed partitioning. By observing temporal changes in sediment storage on several elements over a monsoon season, it might be possible to determine if the model reasonably describes sediment storage. Furthermore, if a channel element is a sink, it might be possible to determine if the stored sediment has a reasonable particle size distribution. In that way, it may be possible to further assess whether the model reasonably describes the erosion process.
193
APPENDIX A
ESTIMATION OF SOIL MOISTURE CONTENT
A.l Objectives
The main objective of this appendix is to describe how the BROOK90 model (Federer, 1995) was used to estimate initial soil moisture.
A.2 Introduction and Background
Initial soil moisture content affects soil moisture tension and therefore must be estimated prior to each event.
A number of infiltration equations, (e.g. Smith Parlange,
1978; Green and Ampt, 1911; Corradinl, 1994) use an expression for saturation deficit (B) similar to the following:
A1 where
G = effective net capillary drive (L)
() = porosity
Sreax = maximum relative saturation
Si = initial relative saturation
194
In this description of infiltration Si is a state variable that describes the initial soil moisture content prior to an event which, in turn, affects the initial rate of infiltration. Therefore, St needs to be estimated prior to each event. Since it rains very little in the desert, and rates of evapotranspiration (ET) are high, soils tend to be dry. However, during the suimner monsoon rain may fall several times during a week. Field data from the Lucky
Hills show that depending on the volume of rain, S^ may vary by a factor of two or more during this period. As such, in some cases, it is important to estimate initial soil moisture content.
A.3 Methods
In this case, the BROOK90 model (Federer, 1995) was used to estimate soil moisture. BROOK90 is a hydrologic model originally developed to describe the hydrology of the
H\ibbardBrook experimental watershed in New Hampshire.
Because the hydrology of New Hampshire is dramatically different from that of the desert southwest, the emphasis of the model is dramatically different from models of
Hortonian hydrology such as KINER0S2. Rather than emphasize infiltration and runoff, the model has a strong physicallybased description of ET for sparse canopieS/ (Shuttleworth
195
and Wallace, 1985), and redistribution of infiltrated water
(Clapp and Hornberger, 1978). It describes processes such as snowmelt, subsurface return flow and variable source area flow which occur in the deciduous forests of the northeast.
However, because BROOK90 is a continuous simulation model based on the concept of the water balance, and since
ET and redistribution of soil moisture are part of the hydrologic cycle, the model can be used to describe these processes in the desert southwest. To make BROOK90 a somewhat universal, continuous, physicallybased model,
Federer has included numerous parameters (50+), most of which do not need to be modified from the default values.
BROOK90 approaches the problem of overparameterization by providing guidelines on which parameters should not be modified, which parameters are less important, and which pathways can be turned off. According to Federer "all parameters are provided externally, are physically meaningful, and have default values." While climate input data are not always easily found, the model can estimate values for all climatic inputs except temperature and precipitation.
In this case, net precipitation, rather than total precipitation was used, so that BROOK90 operated only as a soilmoisture accounting model, rather than a rainfall
196
runoff model. Therefore, runoff measured at flume 104 was the upper edge of watershed LH 104. In this case, daily maximum and minimum temperature data for Tombstone were obtained from the National Weather service. Daily total horizontal solar radiation measured at Fort Huachuca was obtained from Arizona Climate Summaries (monthly publication of Laboratory of Climatology, Office of State
Climatologist). Vapor pressure was calculated using average daily dew point temperature recorded at Tucson. Daily wind speed was approximated using the monthly average recorded at
Tucson, since daily measurements were not available at
Tombstone. The temperature, precipitation and solar radiation measurements should be representative. The vapor pressure and wind speed data will be less representative.
The expression of the Shuttleworth and Wallace (1985) used in BROOK90 has the following form: where:
Lv = Latent heat of vaporization for water (L^/T) p„ = density of water (M/L^)
E = Total Evaporation Rate (L/T)
Ec = Evaporation from Canopy (L/T)
Eg = Evaporation from Soil (L/T)
Through algebraic manipulation and elimination, this simplifies to:
L.P.E =
Cc
+ C,
197
where:
M =
M (c p£),Ar^4)/(r,+r^)
A/ =
A^
^ + r + y r „ l i r „ ^ r „ )
A8
A9
198
A10
Rc
=(A +
^TTu
where:
A = slope of the saturation vapor pressure temperature curve (M/T^LC) y = Psychometric Constant (M/T^LC)
A = Available energy at the canopy height (Net Solar
Ground flux) (M/LT^)
As = Available energy at the soil surface (Net Solar
Ground flux) (M/LT^) raa = resistance between source height and reference height (T/L) (reference height is height at which temperature, humidity and wind speed are measured) rac = resistance to movement out of leaves to air (T/L) rac = resistance to vapor movement from the leaf surfaces to the effective source height for water vapor in the canopy (T/L) raa = resistance to movement from the soils to the source height (T/L) raa = resistance to movement inside the soils to the soil surface (T/L)
199
Initial parameter values for the ShuttleworthWallace
(1985) relationship were estimated using values compiled by
Federer et. al. (1996) based on the worlc of Brutsaert
(1982), Dickinson et, al. (1988) and Korner (1994) for xeric shrub. Some minor modifications were made to reflect field observations. Maximum canopy height was changed from 8 m to
3 m to better reflect conditions on the watershed. Initial root density values and canopy cover densities were also based on field estimates.
Soil moisture movement in BROOK90 is based on the Clapp and Hornberger (1978) relationships describing unsaturated hydraulic conductivity. However, input parameters have been changed to describe conditions at field capacity rather than saturation. Federer (1995) reasons that relationships between soil moisture tension and water movement can be consistently defined at field capacity rather than at saturated hydraulic conductivity which varies logarithmically. In BROOK90, field capacity is defined as a rate of soil moisture movement of 2 mm/day for all soil moisture types. Then, the Clapp and Hornberger (1978) input parameters are recalculated at field capacity as follows:
A11
200
w
A12
w
A13 where:
W = wetness
0 = volumetric water content
03= volumetric water content at saturation
(approximately equal to porosity)
\\i = matric potential (M/T^L) y/f = matric potential at field capacity (M/T^L)
K = hydraulic conductivity (L/T)
Kf = hydraulic conductivity at field capacity (L/T) b = exponent on wetnesstension relationship
(empiricallydetermined)
Wf = wetness at field capacity {(i.e. 0f/03) where 0f is volumetric water content at field capacity}
Federer (1995) provides estimates for these parameters at field capacity for the USDA soil textural classes.
These values were based on the work of Li et. al. (1976) who
201
tested the soil moisturetension relationships for 1845 different soil samples. Thus for any soil type, initial values for each of these parameters can be estimated.
Volumetric soil moisture content was measured using time domain reflectometry (TDR) probes installed horizontally in pits located just north of LH 104. All told, six pits were dug, three under desert shrub (shrub), and three in unshaded locations (bare). According to
Keefer, probes were installed at depths of 5cm, 10cm, 15cm,
20 cm, 30 cm and 50 cm. Probes had three parallel probes spaced 2.5 cm apart. Thus the probes measured the volumetric moisture content averaging the 2.5 cm above and below the actual measurement point. Thus, the probe at 5cm actually measured the volumetric moisture content between
2.5cm and 7.5cm. A schematic diagram showing the sampling relationships is shown in Figure A1.
To calibrate the model, soil moisture data collected on the watershed in 1990 and 1991 was used. During 1990, soil moisture was sampled intensively throughout the monsoon as part of an effort known as Monsoon 90. The following year
(1991) additional data were collected during the monsoon.
For much of the monsoon soil moisture was sampled daily.
Toward the end of the monsoon, sampling slowed to every 3 to
202
7 days (Keefer, T., pers. comm. 1997). Since 1991 samples have been collected on a biweekly basis on average.
The active depth of infiltration was estimated based on the observed volumetric moisture data collected in 1990 for the shriib and bare conditions. Figure A2 shows a plot of soil moisture vs. day of the year for days 200 to 230 of 1990 for the bare condition based on average values for the three sample pits. Soil moisture change is greatest in the upper
5 cm, but the plot also shows that soil moisture content changes to a depth of 30 cm on days when it rains as shown by a "spike" up in volumetric moisture content. Figure A3 shows soil moisture for the same period from the three pits under the shriabs. For the shruJo condition, soil moisture seems to influence the upper 15 cm. In contrast, soil moisture changes in the 20cm 30cm and 50cm depths under the shrubs are more gradual and change very little on the day of an event. Based on this observation, the top 15 cm were assumed to be the zone of active infiltration during an event. Therefore, the S^ used in equation A.2 was based on the average value to a depth of 15 cm.
Initially, BROOK90 was configured to model the "shrub" condition separately from the "bare" condition. However, describing the "bare" condition as a situation in which no transpiration occurs, resulted in erroneously high soil
203
Figure A1
TDR Moisture Probe Measurements
"Shrub" 3 replicates
"Bare" 3 replicates
204
Figure A2
Observed Volumetric Soil Moisture Under Bare Cover
210 215
Oay of Year (1980)
220
Figure A3
Observed Volumetric Soil Moisture Under Shrub
b5
•^b10
—A—b15
   • b 2 0
230
.ob50
! 5  
200 205 210 215
OayofYur(ISM)
220 22S 230
•s5
•S10
•S15
•O.S20
205
moisture content. Assiaming bare conditions without plant transpiration caused simulated soil moisture to increase throughout the monsoon, especially deeper in the profile.
The measured soil moisture content, however, decreased toward the end of the monsoon as rainfall slowed.
This observation led to the realization that these pits reflect "bare" conditions only at the surface. In fact, since the soils are not sealed on the sides like a lysimeter, transpiration removes moisture from the soil on all sides of the pit. Plant roots may be actively removing moisture beneath the bare surface as well. Therefore, a single configuration was used. Based on an aerial photo of the site, plant cover was estimated at 40% at the location of the soil pits. Therefore, a weighted measurement of 40%
"shrub" and 60% "bare" was used as a calibration data set for BROOK90.
Simulations were run using BROOK90's default (Federer,
1995) parameter estimates, with minor modifications to account for field observations. Figures A4 a,b show the observed and simulated volumetric soil moisture for the top
15cm for days 200 to 300 in 1990 and 1991 respectively.
Figure A5 a,b shows the observed and simulated volumetric soil moisture for the average of the 30cm and
Figure A4a
Average Volumetric Soil Moisture 1990
Uncalibrated Parameters (015cm)
ME = 4.9
0.35
0.3
0 . 2 5 , ^
0.1
0.05 •
200
210
220
230 240 250
260
Day of Year (1990)
270 i
• Avg (015cm) Observed —O— Avg (01 Son) Simulated
280
290 300
Figure A4b
Average Volumetric Moisture Content 1991
Uncalibrated Parameters (0 IS cm)
1
i
0.300
0.250 •
0.200 •
ME = 3.3
: I 0.150 • •
0.100 
I
I i
0.050 • • \
0.000
200
210
220
230
240
250
260
Day of Year (1991)
270
I
• Avg (015cm) Obsened » Avg (015cm) Simulated
280
290 300
206
Figure A5a
Average Volumetric Soil Moisture 1990
Uncalibrated Parameters (30cm»50cm)
ME = 0.31
S 0.15
200 210 220 230 240 250 260 270 280
Day of Year (1990)
! • Avg (30cm^S0 cm) Observed  Avg (30cnf)»50 cm) Simulated
290 300
Figure A5b
Average Volumetric Moisture Content 1991
Uncalibrated Parameters (30cm SOcm)
0.160
0.140 •
0.120 •
0.100 •
0.080 
0.060 
0.040 •
0.020 •
0.000
200
ME = 19.20
220 240 260
Day of Year (1991)
• Avg (30cm»50 cm) Obsened
280 300
 Avg (30cm»S0 cm) Simulated I
320
207
208
50cm measurements for that same period. The NashSuttcliffe
(1970) model efficiency statistic is given. This statistic is calculated as follows:
]
1=1 where:
d i =
observation at time i di= simulated value at time i
0= mean of all observed values
A14
Using this statistic, a simulation which has a positive statistic is better than using the average observed value.
A perfect simulation has a statistic of 1.0, and a simulation with a negative statistic is worse than using the average observed value. Note that in this case, the efficiency statistic is negative for both simulations in the upper 15 cm. (4.90 for 1990 and 3.30 for 1991). It is very negative for the 30cm + 50cm measurement for 1991 (
19.20) and it is marginally positive for lower depth in
1990. The negative efficiency for these simulations indicate that using the average observed values for soil moisture would be better than running the model. The poor
209
simulations resulting from using the default parameters suggested that it would be necessary to calibrate the model by varying the parameter values.
Observation of the results from the initial runs with the default parameter set showed that on some days, the model will badly overestimate soil moisture in the upper 15 cm. Figure A6 shows a regression relationship between simulated and observed volumetric soil moisture for 1990.
While most of the modeled points fall close to the regression line, on some days the model will predict much higher moisture content. On further review, it was noted that these overestimates occurred on days when it rained more than 10mm. Since the TDR measurements were taken in the morning, and the rain storms typically occur in the late afternoon, the daily measurement would indicate a dry condition. However, BROOK90 is simulating on a daily time step and would include the rainfall as input into the daily simulation and would simulate a wetter conditions. For this reason, BROOK90 tended to overestimate soil moisture in the upper layers. When four rain days with 10mm or more of rain were removed (days 200, 213, 215 and 224) and the estimation process repeated, the model efficiency statistic improved for the average of the upper 15 cm. Removing these
210
days also marginally improved the statistic for the lower portion of the soil as well. Therefore data from days with greater than 10mm rain were removed as calibration points.
Initially, an attempt was made to use 1990 as a calibration year and 1991 as a validation year. However, these years were found to be very different. Figure A7 shows a histogram of the monthly rainfall collected from rain gage (RG 83) on the Lucky Hills from January, 1990 to
December, 1991. This histogram shows that the rainfall is greater in the simmer of 1990 than in the summer of 1991.
Furthermore, the wettest month in this two year period is
July 1990 at the beginning of the monsoon in 1990. Indeed the soil moisture observations for 1990 and 1991 show that the soil is more moist in 1990. Table A1 shows a statistical comparison of the soil moisture data between days 200 and 300 of the two years. Note that 1990 is a more wet year, and the primary difference is deeper in the profile where volumetric soil moisture is significantly higher in 1990 (16% vs. 9.1% for 1991 at the 0.025 level of significance).
Because the two years were so different, the decision was made to calibrate across both years assiaming that the two years represented a wetter year and a drier. Therefore
211
the parameter values identified would be useful in simulating wetter and drier years.
A.4 Sensitivity Analysis
Since BROOK90 contains so many parameters, calibrating all parameters would be a monumental task. For this reason, a sensitivity analysis was performed to select parameters affecting ET and soil moisture. An initial set of ET parameters based on the estimates in the BROOK90 model manual (Federer, 1995) and in Federer et al. 1996 were used.
Initial soils parameters were based on an initial attempt at calibration adjusting only soils parameters.
Therefore, all but the soils parameters were estimated based on initial estimates. Soil parameters that were varied included; exponent on soilmoisture conductivity relationship (b), volumetric soil moisture at field capacity parameters were set at one standard deviation above or below soils on the watershed are borderline sandy loam/ loamy sand, with surfaces soils tending to be more loamy sand, the highest upper or lower bound for sandy loam and loamy
212
Figure A6
Effect of Rain Days on Simulation
I
0
0
0.25
Simulated and Observed Volumetric Soil Moisture 1990 (015cm)
.
3 5
.
3
i 1 0.2
I s
;
i
I i
0.1
0.05
0 ,
0 0.02 0.04 0.06 0.08 0.1
Observed
0.12 0.14 0.16 0.18 0.2 i
:
I
1
I
I
'
Note: open symbols are rain days
Figure A7
Monthly Precipitation at Lucky Hills
160
140
» 120
—
m
1 100
I
60
I
40
20
1
1
1
1 la
I I I i i a i
1 1
1 l l l l l l l l a a l l l ^ a l
S S S S S S s s CO A 0> Ok
S 5 ^ ^ « S a
^ ^
3 i
CO
g
Z
Month
213
214
Table A1
Statistical Difference In Soil Moisture Between
1990 and1991
mean i std. dev. n
Volumetric Soil Moisture (0 15cm)
1990 1991 ao8S 0,128
0.027
4S
0.039
34 df=
alpna
(aoS) alpna (0.02S) alpna (0.0i)
No Significant Difterence
1.05
77
167
2X
239
Volumetric Soil Moisture (30cm +50cm)
1990
1991
0165
0027
45
0.091
0005
34 alpha (005) alpha (0.025) alpna (0.01)
Single tailed test
77
1 87
2.00
239
215
sand were allowed for the upper 15 cm. Values of porosity
(), were allowed to vary over the range of values of porosity determined by Whitaker (1993) for LH 104 with a mean of 0.4, case of hydraulic conductivity at field capacity (Ks;) where a range of values were not known, a lower estimate of
Imm/day was used and an upper estimate of 4 mm/day was used.
ET parameters were changed from these initial estimates using the upper and lower observed value for the parameter from all canopy types. In other words, the parameter values included the upper and lower value from the literature for any canopy type. While the upper and lower bounds for the parameters may not reflect a standard deviation from the mean value for that ET parameter, it was felt that these upper and lower boxinds were more reflective of the range of possible values than a sensitivity analysis which changed each parameter value by a given percentage. Such perturbations by given percentage are not very useful in comparing the sensitivity of parameters that vary within a few percentage {e.g. porosity) with those that vary exponential (e.g. matric potential). Only one parameter was
216
changed at a time. Results of the sensitivity analysis are summarized on Table A2.
Results are given by percent change in daily simulated value caused by perturbing parameter values from the base set. Both the average daily change, and maximum change on any one day are given. The table shows that model is most sensitive to: canopy density, volumetric moisture content at field capacity, maximum plant conductivity, maximum leaf area index, exponent on soil tension, soil evaporation resistance at field capacity, exponent of soil evaporation to water potential, matric potential at field capacity maximum leaf conductance and hydraulic conductivity at field capacity. It is relatively insensitive to albedo, relative distribution of rainfall in the top three layers, allowing or disallowing deep drainage, and porosity.
Parameters selected for parameter estimation included: canopy density, volumetric moisture content at field capacity, maximiam plant conductivity, maximiam leaf area index, exponent on soil tension, soil evaporation resistance at field capacity, exponent of soil evaporation to water potential, maximum leaf conductance and hydraulic conductivity at field capacity.
Table A2
Results of Sensitivity Analysis
Theta at Rdd Capacity
Maine Potential at Rdd Capacity
1 laisTiili aire I ti% I zs* M ftao I
it*
I 40« I
HBH
1 m 1 <9% 1
rw
>r_^3^^
B§
lltSiiiiiiiiiWMiiiM
im
14%^
17% ^LTO
HSBISiiiiiltliBMlMl
IHydratiic Conductivity at Retd Capacity hmnviol
2
II
Dislribut'on of Infiltration in Top 3 Layers
l^i MMWIMfW
0.72 0.5
on,
1*
11*
II
1 I 3» I 11%
I
•2%
fBoBltBSO.
BSSSgBSSSSB;
1 1%
y*,
Deep Drainage
Porosity
0
1
1* 6% 0.2 OK 1*
0.41<ta OJSO OK
1*
0.460 0« 1% a. Avangaaradaiillavan
Shaded Rows are for ET parameters. Unshaded rows are for
Soils Parameters
217
218
A.4 Parameter Estimation
Since data exists for six layers, and ten parameters were modified, niimerous possibilities of different parameter combination are possible. For this reason, a parameter estimation program called PEST (Watermark Software) was used to estimate optimal parameter values. This program uses a
Gausstype downhill search routine modified by Marquardt
(1963) based on the work of Levenberg (1944). The objective function is based on a leastsquares criteria and convergence criteria are based largely on user choices.
M i n i m i z e
E = E , + E ^
m n
Ea = 1 1 ( 0 / y  0
^
y=l/=l
j = 1.2.3...m i = 1.2.3...n
A.1S
A.16
Q i j
= observation at time i for layer j
E
P
f I a P J. 
» = I ; = 1
k = 1.2.3...0 j = 1.2.3...m A.17
= parameter value for layer j parameter k mean parameter value for parameter k
219
The purpose of the first part of the objective function
(eq. A.16) is to minimize the error in the observation. The second part of the objective function (eq. A.17) is to keep the parameters as reasonable as possible. To keep parameter values in the range of expected values, the mean value for a parameter was weighted in the objective function, so that objective function values would increase if the parameter value became too different from the expected values. To further improve the simulation in the top 15 cm, the average volumetric water content of the top 15 cm was more heavily weighted than the volumetric water at 20cm, 30 cm and 50 cm.
The parameter estimation was far more problematic than initially anticipated. Among the difficulties encountered were; an inability of the PEST program to always find the same set of parameter values, unrealistic parameter combinations, large errors in simulated vs. measured soil moisture for some layers, large errors toward the end of the simulation period where measurement were less frequent, and unrealistic changes in parameters from gauged to unguaged soil layers.
To then improve simulation the parameters for the two deepest soil layers were set at reasonable values for sandy loam soil which is prevalent on the watershed. Unguaged layers were linked to gauged layers by assigning an error to
220
differences in parameter values for the unguaged layers to the parameter values for the adjacent layers. After obtaining similar values for the soils parameters for the unguaged layers, the parameter values for all soil layers were fixed.
After testing the importance of different weights to the expected values of the parameters, a combination that produced reasonable parameter values, and a reasonable simulation was selected. To test the robustness of these values, the optimization routine was repeated starting with different initial parameter estimates. Each time, a different, but similar, set of parameter values resulted.
Measures of model efficiency were almost identical for the different sets of parameter values.
A.5 Discussion of Results
The parameter values selected through parameter estimation, and the range of possible parameter values for these parameters in a sandy loam soil are summarized on
Table A3 for the parameters of interest. Figure A8 shows a plot of the simulation and observed values for the top 15 cm of the profile (layers 13 of the simulation) for days
200 to 300 of 1990. Figure A9 a shows those same plots for the simulation averaging the values for 1991. Figures A.10
Figure A8
V o l u m e t r i c S o i l M o i s t u r e 1 8 9 0 ( 0 • I S c m ) C a l i b r a t i o n b a s e d o n 1 9 9 0 a n d 1 9 9 1 d a t a
0 26
0 IS
^ Avg (O'IScm )
OI)»«rv«d
—
A
VQ
(0<19cm )
SimuUUd
0.05
200 2tO 220 230
240 250 260
Day of Y»ii (16I0) aimutaUd and Obtatvatf Sol) Meuiura (0 • 16cm)
270 260 200 300
I 11
Model
Efficiency = 0.76
$
••• ••• 9 1 *12 *14 til Via
• I
• •4
0 300
0 . 1 0 0
0 100
0 140
0 . 1 2 0
0 100
O.OiO
0 010
0 040
0 030
0.000
210
Figure A9
Bs Volumatric S o i l M o l s t u r a
Calibration batod on
Itti
( 0 • 1 6 c m )
IttO
and
Itti
240 250 200
0«y of V«af Oiti)
210
I •••
OftMrv«4
O Avg (0>t5e«)
Av9 (015cfli)
Sim ulaltd
Model
Efficiency = 0.77
Figure A10
V o l i i m A t r l c S o l i M o l i t u r * 1 9 9 0 ( 3 0 c m • 9 0 c m )
C a l i b r a t i o n b a t a d o n 1 9 9 0 • 1 9 9 1 d a t a
0.25 o.ta o.os
2 0 0
2 1 0
2 2 0
2S0 240
260
D«y of y«tr M«I01
270
9lrmJlittd
and Obstrvtd Soil Molstura pOcm ^ SOcn^ y a 0 94x
210
300
O Avp (30cm •
Ofe»trv«d
•^—Avg (30cm«90 cm)
SImultUd
Model
Efficiency = 0.53
DkMriad
NJ
M
Figure A11
V o l u m c l r i c S o i l M o i s t u r e 1 9 S 1 ( 3 0 c m * 6 0 c m )
C a l i b r a t i o n b a s e d o n 1 9 9 0 a n d 1 9 0 1
0 120
0 100
0 oso
0 060
0 0 4 0
0.020
0 . 0 0 0
2 0 0 2 1 0 2 2 0 2 3 0 2 4 0 2 6 0 2 6 0
2 7 0
SlwwIaUtf and Otoaarvad SoW Molatura
 9 0 c m
*
tO
c m ) y • 1 e7R  0 0 6
R ' • 0 3 6
0 A v g ( 3 0 c t n « d 0 c m )
Obttrvad
 A v g ( 3 0 c m « 5 0 c m )
SimulaUd
Model
Efficiency = 5.68
I Ml till • • til » till 0 OIQ • 0 0 910
225
Table A3
Parameter Values and Parameters Estimated
Using Parameter Estimation Techniques
Top of Botitom Depth Relative Matrie Volxmetric Porosity Exponent
Layer o£ of TDR Root Potential Hater
Layer
Probe Density at Field Content at on
Wetness
Capacity Field
Capacity
Tension
(Vf)
( O f ) <b)
cm cm
0
7 . 5
7 . 5
1 2 . 5
1 2 . 5
1 7 . 5
1 7 . 5 2 2 . 5
2 2 . 5
2 7 . 5
2 7 . 5 3 2 . 5
3 2 . 5 4 7 . 5
4 7 . 5 5 2 . 5
5 2 . 5 7 2 . 5
7 2 . 5
I C Q
cm
5
1 0
1 5
2 0
3 0
5 0
Kpa
0 . 1 0
 4 . 8 b
0 . 1 7 5 b
0 . 4 4 0 a 3 . 4 4 b
0 . 1 0
 7 . 9 b 0 . 1 7 5 b 0 . 4 3 0 a 3 . 5 1 b
0 . 1 2  9 . 6 b 0 . 1 7 9 b 0 . 4 2 0 a 3 . 4 4 b
1 . 0 0
 2 0 . 2 b
0 . 1 7 5 b 0 . 4 2 0 ,
5 . 2 1 b
0 . 8 0
 1 7 . 7 b 0 . 2 3 b 0 . 4 0 0 a 4 . 7 2 b
0 . 6 0
 1 4 . 0 b
0 . 1 7 5 b
0 . 4 0 0 a 5 . 2 6 b
0 . 6 0
 8 . 1 b
0 . 2 3 0 b 0 . 4 0 0 ,
5 . 2 9 b
0 . 3 5
 7 . 0 b 0 . 2 2 8 b 0 . 4 0 0 a 5 . 5 1 b
0 . 1 7  1 2 . 0 0 . 1 9 0
0 . 4 0 0 a
6 . 0 0
0 . 0 9  1 2 . 0 0 . 1 9 0 0 . 4 0 0 a
6 . 0 0
a  Estimated based on observed relationships, field observations and trends noted during fitting of parameters, not parameterized during final parameter estimation runs b  Estimated using parameter estimation
Other Parameters
Canopy Cover 0.52 Exponent on Soil 0.78
Hydraulic Conductivity at Field Capacity
2.42
Soil Evaporation Resistance 773
Meucimum Leaf 2.04
Area Index
Msixiimun Plant 9.99
Conductance at Field Capacity
M^imum Leaf Conductance 0.005
Notes:
1.) TDR probes have three prongs 2.5 cm apart, and measure a cylindrical area 2.5 cm from center, so a probe at 10 cm depth actually measures volumetric moisture content from 7.5 cm to 12.5 cm
2.) Porosity {(j)) on soils at the Lucky Hills 104 watershed have a mean value of 0.40 with a standard deviation of 0.05 giving a range of 0.35 to 0.45 as possible values. (Whitaker, 1993)
3.) The exponent on the Wetness Tension relationship
(b) has been found to have a mean of 4.9 for sandy
226
loam soils with a standard deviation of 1.75 giving a possible range of values as 3.15 to 5.65 (Clapp and Hornberger, 1978)
4.) Soil moisture tension at field capacity has a mean value of 12Kpa for sandy loam soils (Federer,
1995). However soil moisture tension has been found to vary greatly between soil types. A coefficient of variation of 1 was noted for sandy loam soils for soil moisture tension at saturation
{Clapp and Hornberger, 1978), so tension was allowed to go to a lower (i.e. negative) bound of 
24 Kpa.
227
and A.11 show those same plots for the 30cm and 50 cm depths in 1990 and 1991 respectively. For comparison purposes, the simulated values are also plotted against the observed value, and the Nash and Suttcliffe (1970) model efficiency statistic is also given. Model efficiencies exceeding 0.75 were found for the upper 15cm in both the wetter year (1990) and the drier year (1991). Furthermore, since the regression of simulated vs. observed volumetric soil water is approximately 1;1, there appears to be no systematic bias in the estimate of soil moisture in the upper 15 cm.
The model did not do as good a job in estimating soil moisture in the lower portion of the soil profile as measured by the 30 cm + 50 cm volumetric soil moisture.
The simulation for the wetter year (1990) was reasonably good as indicated by a model efficiency statistic of 0.53.
The regression line on simulated vs. observed is also good
(simulated = 0.94 x observed). However, the simulation was very poor at the 30cm + 50cm depth as indicated by a 5.68 model efficiency. Part of the reason for this poor statistical value is that the observed values of soil moisture do not change markedly. Therefore, the average observed value is very close to the observed value for any single observation.
228
A.6 Conclusions
The soil moisture simulation and calibration showed that BROOK90 could be used to estimate soil moisture. The simulation of soil moisture in the upper 15cm which will be used to estimate soil moisture (Si) in KINER0S2 had a model efficiency of 0.76 for a wetter year and 0.77 for a drier year which can be considered to be a good simulation.
Little systematic error was noted as indicated by the regression of simulated vs. observed values to have an approximate 1:1 relationship. On average the model neither underestimated nor overestimated soil moisture content.
While the model did overestimace soil moisture on days that it rained more than lOmm, it produced good results in all other cases, including the days following a rain.
Fitted parameter values are within what can be considered reasonable for a sandy loam soil. No values fell outside one standard deviation of estimated parameter values. Because a unique set of parameters were not found, the parameter values presented here should not be considered to be optimal. It is not clear whether they represent a more accurate measure of the true parameter values on the watershed.
229
APPENDIX B
USE OF CTOSTATISTICS
TO ESTIMATE SOIL ERODIBILITY
B.l Objective
The main objective of this appendix is to describe how the spatial variability of erodibility was estimated using cokriging.
[Note: Errors were found in the soil input data that was used to do the cokriging. In addition, there were problems accessing the software. Therefore, this appendix should be viewed as a discussion of the potential benefit of using multivariate geostatistics to estimate soil erodibility.}
B.2 Introduction to Cokriging
Geostatistics, unlike more traditional statistical approaches, begins with the assumption that samples are correlated. In particular, samples are spatially correlated. For example, a simple geostatistical approach is inverse distance squared weighting. In inverse distance squared weighting, the value of a variable (e.g. percent sand) at a location where it has not been measured is estimated based on a weighted average of the values of nearby samples. Weights are based on the inverse square of
230
the distance from the location to be estimated. The closer a sample is to a location, the higher the weight. The problem with inverse distance weighting is that beyond some distance, samples may be essentially uncorrelated.
In kriging, like inverse distance squared weighting, the value of a variable of interest at a given location is estimated based on its proximity to other locations.
However, unlike inverse distance squared weighting, the way in which samples vary spatially is described by a statistical model (usually a variogram). Typically, a variogram will give a distance at which samples are uncorrelated (range) and a model of how well correlated samples are within a range. Variograms models are selected based on the spatial correlation of existing samples. These model types are selected from a set of models that are known to have positive values for all values of spatial separation so that they can be used to produce positive definite matrices.
Cokriging is typically used when samples are not dense enough to provide a good estimate of the variable of interest. However, if the variable of interest is correlated with a variable which is more densely sampled
(background variable), the correlation between the variable of interest and the background variable can also be used to
231
estimate the variable of interest. In real terms, cokriging allows the use of both spatial correlation and regression.
The formation of the cokriging equations are discussed by
Myers (1982, 1983, 1984) among others (e.g. Goovaerts,
1998).
Cokriging has been used in hydrology to estimate mean annual precipitation (MartinezCob, 1996; Helvesi et. al.
1992) where the correlation between elevation and precipitation was used along with available rain gauge data.
It has also been used to some degree describing characteristics of soils (e.g. Chien et.al. 1997),
In this case, characteristics of the surface armoring were estimated using cokriging. There has been limited application of cokriging using DEMderived variables as background variables in cokriging (Odeh et. al.l996).
B.3 Cokriging Soil Particle Size Class
While the soil sampling on the Lucky Hills is relatively dense sampling for a watershed of this size, in fact what is actually known of the watershed is minimal.
For example, if each sample is representative of a 1 m^ characterized (i.e. about 1/1000).
232
Variables derived from the DEM are available at each grid node, and thus act as denselysampled background variables. Variables derived from a DEM have been correlated with soil particle size class as described in
Chapter 5. The objective of the geostistical study was to estimate the spatial distribution of five soil particle size classes (i.e. Pct{n) ), and the fraction of the coarse particle size cover (PAV) described in equation 1.3. The following analysis concerns only the surface armoring, because this is assumed to be the portion available for erosion.
Previous studies in southern Arizona (Kirkby and
Kirkby, 1974) have shown that particles larger than 20 mm are relatively immobile except on steep hillslopes.
However, particles between 8 mm and 25 mm may be mobile under some circumstances. For this reason, sometimes the coarser particles are pavement (i.e. PAV in equation 1.2) and sometimes they are available for erosion. In this case, the greater than 16mm portion (1664mm) of the Lucky Hills samples was taken to be the erosion pavement (i.e. the PAV portion; Variable GTR16UP).
The cxammulative distribution of the particles less than
32mm was then used as a basis for estimating the soil erodibility (i.e. Pct(n)in equation 1.2). One advantage of
233
using the cumulative distribution is that random errors are related to only one side of the distribution. Four cutoffs were selected resulting in five particle size classes.
These were as follows:
1. ) Percent less than 16mm (i.e. cumulative distn.  %
1632mm, variable LESS16UP)
2. ) Percent less than 8mm {LESS8UP)
3. ) Percent less than 2mm (LESS2UP)
4. ) Percent less than 0.125mm (LESS125UP)
Detailed data are available from 132 soil samples at 81 locations on the Lucky Hills 104 watershed. Soils representative of the surface of the hillslopes constitute
51 of these samples.
Summary statistics on the soil particle size classes are given in Table B1. As can be seen all particle size classes are slightly skewed to the lower values. However, since the distribution does not differ significantly from the normal curve (except for possibly the Less than 2mm portion) the data were not transformed.
Initial attempts to use kriging to estimate the spatial distribution of these particle size classes suggested that kriging alone would not provide adequate estimates of spatial variability, and that cokriging would be a better alternative. For example. Figures 31 and B2 illustrate the
TABLE B1
Summary Statistics for Soil
VARIABLE
#
Min. Max. Mean S.D. Var. Skew
> 16 mm 51 1 . 6 2 7 1 . 8 6 3 6 . 7 6
1 3 . 2 1
1 7 4 . 5 4 0 . 0 2
< 0.125mm
51 6 . 1 2 2 3 . 6 6 1 1 . 6 6 3 . 6 0 1 2 . 9 8 0 . 9 6
< 16 mm
51 5 3 . 9 4 9 8 . 3 8 7 1 . 6 7
8 . 4 4
7 1 . 2 9 0 . 6 0
< 2 nim
51 2 1 . 2 3 6 5 . 5 9 3 2 . 9 1 7 . 6 3 5 8 . 2 2 1 . 9 9
< 8 mm
51
3 3 . 7 3
8 4 . 6 9 5 1 . 4 4 9 . 4 7 8 9 . 6 2 1 . 1 3
234
Figure B1 Kriged Map of Greater than 16mm Portion
Kriged Map Std.Dev. of Estimate
20dd
Figure B2 Kriged Map of the Less than 2nun Portion
Kriged Map
Std.Dev. of Estimate
6&0 7*00 T60 d&o
2260
!200 f<50
?100
'OM
2200
2150
2100
2060
•000
9&0
2000
"^5) ^ 'c/
\ R
\ . y l A
1
660 roo 760 &00 060
i
li
1060
•260
650 T^OO r60 ftOO 550
2250
•200
•160
2200
S y ) % W 
2150
2100
'100
'060
W/*
1 }
4
'
0 /
{ '
•000
960
•
//•'
550
Ai
roo
i . 1^:'
r50 500 550
V
1050
2000
2050
NJ
U) a>
237
kriged estimate and standard deviation for the greater than
16mm and the less than 2mm portion of the surface armoring, respectively. Note that the contouring is inconsistent with correlations with slope and other landscape variables described in Chapter 5. Furthermore, the standard deviation is too great to instill confidence in the kriged values.
For this reason cokriging was used to relate these soil particle size classes to the landscape characteristics described in Chapter 5. In this case, the 5m x 5m grid data rather than the 2.5m x 2.5m DEM because cokriging is computationally intensive. In this case, the following variables were derived directly from the DEM using the GRASS
GIS and the TOPAZ DEM processing program:
1. TSLOPE  terrain slope at a grid node grid node (transformed by square root to make it more normally distributed)
3. Acciam  Area draining through a grid node
4. LS  The length slope term used in the empirical universal soil loss equation (USLE).
5. STEEP  The slope steepness term in the USLE
6. ELEVCM  Grid elevation in centimeters
238
In addition, other variables were derived from these data as follows:
1. FACl  Principal component 1 of the above data
2. FAC2  Principal component 2 of the above data
3. FAC3  Principal component 3 of the above data
4.MRGT16UP  A multiple regression estimate of the greater than 16mm portion (i.e. PAV).
5. MRLS16UP  A multiple regression estimate of the less than 16mm portion
6. MRLS8UP  A multiple regression estimate of the less than 8mm portion
7. MRLS2 UP  A multiple regression estimate of the less than 2mm portion
8. MRLS125UP  A multiple regression estimate of the less than 0.125mm portion
The multiple regression relationship had a correlation coefficient of between 0.6 and 0.7 for all soils variables.
Individual landscape variables were correlated at about 0.5 or less. Stepwise regression was used in the multiple regression estimates. To get somewhat realistic estimates, only one measure of slope, one measure of acciamulated drainage area and one measure of lauidscape curvature.
While the idea of generating a multiple regression model has an appeal, the range of variability was
239
significantly less than the observed variability for all particle size classes. For example, the sample variance for multiple regression estimate was less than half the observed for all particle size classes(e.g. 11 vs. 58 for the less than 8mm portion). Furthermore, the range of observed values of for the multiple regression estimate was less than the observed. For example the range of observed values for the less than 2mm portion was 21% to 65%. The multiple regression estimate was 22% to 43%. Therefore the multiple regression estimate was unable to reproduce the range of variability observed in the sample even though the multiple regression estimates were for 1547 locations while the observed samples were only at 51 locations. One would expect that the multiple regression estimate would have a greater range because the range of the background variables is greater than observed for the 51 locations for which there are soil samples. This suggests that the use of multiple regression might not provide realistic estimates.
B.4 Variogram Fitting
Because data were available for each grid node for the landscape variables, I chose to do collocated cokriging.
Because of the detail of the landscape variables, the variogram structure for the background variable could be
240
easily determined. The coarsest particle size (GRTR16QP), was fit with spherical, exponential and nugget structures.
The remaining variograms were fit using a nugget, a gaussian and an exponential structure.
Examples of the experimental variograms for the background variables are given in Figure B3 and B4
Variograms for slope Figure 33 (i.e. SQRHSLOPE and TSLOPE) tended to have an exponential structure and a range between
50m and 60m. The USLE variables LS and STEEP tended to be more spherical with a range between 30 and 40m. No drift was present in any of the background variables except elevation.
However, anisotropy was apparent as shown in Figure B4 with range being greater in the Y direction (North) than the X direction (East).
While the structure of the background collocated variables were clearly apparent, sample variograms for the target soil variables were less clear. Because of the limited number of soil samples and the wide dispersion of the samples, it was impossible to identify anisotropy in the soil sample variograms. In general, soil samples had a gaussian structure with a nugget. The lag distance was adjusted to between 6 and 8 meters.
Figure B3 Experimental Variogram for Background Variables
Related To Slope e.0S«'0S
O. 10
6.05*05
S.06«05
4.05»*05
4.05«0S
3.DB905
3,O0«O0
2.00«0s
1,05«08
0.00000
I i I L
I
i 1
i  .1
O. 10. 20. 90. 40. 60. 00. 70. 60. 00.
6qRH*lop«
1.05«05
0.0009
O. 10. 20. 60. 40. 60. 60. 70. 60. 60.
T
1
D : .
0.00(^0020
0.0002 0.0002
0.0001
0.00(^1
0.0000
0.0001
0.0000
0.0010
•0,0001
0.0002
0.0009 i
J
1
_i i.
O. 1 0 .
20 90. 40. 60. 60. 70 60. 60. tftlopo / 6qRH»lopo
0,0003 o.oooo
10. 20. 30. 40. 60. 60. 70. 60. 60.
"T —I 1 1 1 r 1 i 1"
0.0020
0.0016
0.0010
0 0005 i .
i
_ . l _ X
10. 20 30. 40. 60 60. 70 60. 60
0.0000
Ulopo
N)
»{:k
7.05«05 e.o0*oo
0.oo«*oe
4>O0**Oo
9.O0«O0
2.0D«00
1,00«*0o o.ooooo o.oso
0.025
0.000
•0.026
Figure B4 Anisotropy in Background Variables
8qRH»lope
7.0S«00 a.06«06
O.O0«*QO
4.oe«*oo
3.0S«00
2.0S*'00
1.00« 00
O.OOOOO
0.050
1 0 0 .
o.o2e
0.000
•0.02S 30.
10.
20.
90.
 I
20.
 i .
30.
M r O t 1 6 u p
40.
—I
100.
ftO.
0 2 .
ao.
70.
60.
50.
40.
30.
20.
1 0 .
o.
MrQtlGup y SqRHslopA
N)
ro
243
All variograms and cross variograms were calculated using the automatic sill fitting function in the ISATIS geostatistics package. The automatic sill fitting function weights the values in the experimental variogram, so that fitting is somewhat more objective than some other geostatistics packages. Since the variograms of the target variable were less clearly defined, the primary objective in variogram fitting was to fit the background variable.
However, some attempt was made to fit the cross variogram as well.
Experimental and model variograms and cross variogram models for the target variables are shown in Figures B5 and
B6 for the Greater than 16mm and Less than 2mm portions respectively. The dashed line above the modeled crossvariogram (i.e. graph in lower left corner) represents a line of perfect correlation. Note that results suggest good spatial correlation between the multiple regression estimate and the variable of interest.
In general, the more coarse particle size classes tended to have a stronger exponential variogram component, while the finer particle size classes tended to have a stronger gaussian component. While no gaussian components were noted in the background variables, variograms from the uneroded
Figure B5  Fitted Variogram for Greater than 16 nun Portion
(Spherical range = 38.7m, Exponential range= 41.7m; Nuggett)
100
90
60.
TO.
60.
60.
40.
SO.
2 0 .
10
0
10. 20. »0. 40. 00. 60. 70. AO. 90.
—I 1 1 1 1 1 1 i r
100
90
60.
ro.
60
60
40
iO.
20.
10
I I _i J I. I 1
10. 20 50 40 60 60.
ro
60
MrO16u>
_..IJ
90
0
O 10 70 30 4 0 60 60 70 00 00
—I • T "~T r~ —, ,
500 500
100
200
0 200
200
• / /
100
100
200
. 1 J
1 0 2 0
1  1  1. . 1.
50 40
60 60 ai16oi>
I 1
70 60
00
100
(O
Figure B6 Fitted Variogram for Less than 2mm Portion
(Exponential range= 42.7m; Gauss range= 43.7m; Nugget)
MrLe«a2up
La*a2up / MrLaa«2up
Les»2up
NJ
CJi
246
soils tended to have a gaussian structure. This suggests that the uneroded soils have a greater importance to describing the finer particle size classes, while local slope is a more important component in the coarser particle size classes.
B.5 Cokriqed Estimates
Because the background variable was available at each grid node, collocated cokriging was used. In this case collocated cokriging is a simplification of cokriging that takes advantage of the fact that an estimate is available at each grid node. This particular type of collocated cokriging will give the same result as the cokriged estimate, and does not rely on che intrinsic hypothesis
{Wackernagel, 1995 describes collocated cokriging with the intrinsic hypothesis). A 70ra x 70m moving neighborhood was used with 4 angular segments.
The cokriged maps for all target variables with the kriging standard deviations are given in Figures B7 through
B11. Comparison of these maps with the kriged maps in
Figures B1 and B2 show that the cokriged estimates reflect more of the correlation with topography described in Chapter
5. The kriged map shows no clear pattern, while the cokriged map shows increased coarser material on steeper
Figure B7 Cokriged Map of GRTR16UP
Cokriged Standard Deviation
660 roo r6o
600
660 660
700 760
600 660
!»6}
' a
m m
• *fiOM
m
m»
1»»6» i2«00
f^w
1 ^'i v'/I^
660
'fm.
«BHte «• \
I ^
»
y> •
^ I'
700 760
600
660
17060
20)0
) O i O «
660
700 760
600
660
1960
M
Cokriged
Figure B8 Cokriged Map of LES316UP
Standard Deviation
0»l ItlOlnilSfia)
(ISO UKfcapa)
Figure B9 Cokriged Map
Cokriged
LESS8UP
Standard Deviation
TOO. 7S0
2250
2200
2tS0
2t00
2060
12000
1960
J : I
Figure B10 Cokriged Map of LESS2UP
Cokriged Standard Deviation iioa
Cokriged
Figure B11 Cokriged Map of LESS125UP
Standard Deviation
«vA
U A
252
slopes closer to channels which is consistent with other observations of particle size distributions on landscapes in southern Arizona (Abrahams and Parsons, 1991).
Despite the improved estimates from the cokriging, the estimates are not highly precise. Examination of the standard deviation maps for cokriging (Figures B7 through
B11) show that the standard deviation of the estimate increases rapidly going away from the sample locations. In many cases on the cokriged map, the sample locations can also be identified by the rapid change in contour. Only the estimate for LESS2UP (Figure BIO) shows a gradual enough change to suggest a good degree of confidence in the estimate. In fact, this is not surprising since the cross variogram for LESS2UP was a very good fit between the background variable and the sample variable.
Table B2 summarizes the values for cokriging, multiple regression and the observed samples. Note that while the cokriged estimates have a higher variance than the multiple regression estimates, the variance is still less than the observed sample. Furthermore, the range of the cokriged estimates is the same as the sample. This suggests that cokriging provides a more realistic estimate of the variability of particle size class than multiple regression, but that it is not entirely realistic. Estimates might be
% > 16inm
Table B2
Comparison of Sample, Cokriged and
Multiple Regression Estimates
Min. Max. Mean S. D. Var.
51 1.62 71.86 36.76 13.21 174.54
1547 1.62 72.45 35.61 10.66 113.69
1547 20.72 77.05 36.80 8.09 65.47
51 53.94 98.38
71.67 8.44 71.29
1547 53.94 98.38
72.20 5.95 35.42
1547 48.61 79.27 71,61 4.67 21.78
51
33.73
84.69 51.44 9.47
89.
1547 31.47 84.69
51.44
7.64 58.36
1547 33.50 58.15 51.71 3.64 13.28
51 21.23 65.59 32.91 7.63 58.22
1547
20.12
66.47
32.54
6.80 46.27
1547 22.07 42.88 33.23 3.33 11.09
51 6.12 23.66 11.66 3.60 12.98
1546 5.51 23.66 11.30 2.83 8.02
1546 5.08 25.71 11.46 1.57 2.47
253
improved with the use of geostatistical conditional simulation techniques such as simulated annealing or sequential gaussian simulation which are akin to spatial
MonteCarlo simulation and, as such, produce a spatial representation more like the observed variation.
254
B.6 Conclusions
Cokriging with a collocated background variable greatly improved the reliability of the spatial estimates of the particle size classes. Spatial distribution of particle size class respected the trends described in Chapter 5, and as such gave a more realistic representation than the kriged estimates. Furthermore cokriging substantially reduced kriging standard deviation.
This makes the DEM a very useful tool for improving estimates of undersampled target variables such as the soils particle size classes cokriged in this exercise.
Unfortunately the cokriged estimates do not reflect the variability of the sample. The minimiim and maximum of the cokriged estimate was the same as the values for the observed sample, even though there were fifty times more samples in the cokriged estimate. This suggest that the cokriged estimates may not reflect the full range of values present on the watershed.
255
APPENDIX C
DISCUSSION OF RELATIONSHIP OF TEXTURE OF
UNDERLYING SOILS TO CHANNEL LOCATIONS
C,1 Underlying Uneroded Soils
[Note: This appendix does not use all the available soils data. Therefore, it is useful for understanding the general relationships, but is not complete.]
The soils data were used to identify soils mapping units that could be used to estimate the distributed nature of the underlying uneroded soils and the values of erosion and hydrologic parameters used in KINER0S2. For this characterization, only the underlying uneroded soils on the hillslopes were used (e.g. LH 106 A 2), because they were thought to be representative of the soil units rather than the product of erosion.
A ternary diagram was used as a simple graphical tool for initially characterizing the soil units. Because the soils are so coarse, the USDA sand  silt  clay ternary diagram would not show differences in the soil types. For this reason the three classes used were as follows:
1.) percentage greater than 4nim (the percentage of the
2.) percentage in 1  4mm fraction
256
3.) percentage in the < 1 mm fraction
Plotting the particle size on the ternary diagram showed that there are a variety of particle size distributions in the underlying soils. I noted that many of the finer particle size samples came from approximately the same elevation (1362 1366 m). The ternary diagram (Figure C1) shows the distribution of particle sizes on the watershed, and the distribution for 1355m1362m, 1362m1366m, and
1366m1373m.
While the diagram does not clearly show that particle size distribution is finer in the 13621366 elevation range, in general the coarser samples occur above and below the
1362 to 1366 elevations. Furthermore the finest samples tend to occur in the 1362 1366 meter range. Because the soils on the watershed are alluvial in origin (i.e. deposited by flowing water) coarser and finer lenses of soils are interspersed. For this reason, even though soils in the 1362  1366 meter elevation tend to be finergrained than those either above or below, some coarse samples occur in this middle unit, and some finer samples occur in the units above or below.
However, to determine if the soils are, in fact, finer in the 1362  1366 meter range, t  tests were run.
These tests showed significant differences in the soils
Figure C1
Ternary Diagram of Texture of Underlying Uneroded Soils
0.8
0
< 1mm (fines)
0.6
0.4
0.2
a \
4mm  64mm (coarse)
o
1mm to 4mm (medium)
o
C 13551362
J 13621366
G 13661373
257
258
based on elevation with the finer grained unit in the 1362 
1366 m. elevations being significantly finer grained than the other two units which were composed of coarser material.
The ttest showed that by several measures of finer texture the soils from the 13621366 m elevations (middle unit) were significantly finer than soils from the 13551362 m elevations (lower unit) and the 13661373 m elevations
(upper unit). These measures are summarized on Table C1.
Specifically, this middle unit has significantly less gravel
(4mm  16mm) and coarse sand/fine gravel (1mm  4mm), and significantly more fine sand (0.025mm  0.063mm) and fines
(<0.063) than the upper or lower units.
Figure C2 shows the ciomulative particle size distribution for three soil samples typical of the three soil units. Note that sample 102N from the middle unit differs most from the other two units in the ciomulative distribution which tends to be convex up on this plot centered on approximately the 1 mm particle size class.
In general the ttests suggest that there are few differences in the surface soils of three units, though some significant differences do exist. For example, there are significantly more fines (< 0.063mm) in the middle unit than
259
Tedjle C1
Summary of Differences in Particle Size Class
Lower Unit
1355m
1362m
Middle
1362m
Unit
1366m
Upper
1366m
Unit
1373m
Particle
Size Class mean std. dev. mean std. dev.
16  64mm 16.97 5.91 a, 7.87 6.32 a mean
8 1 std. dev.
5.38 c
4  16mm 18.69 2.9 a
14.2
3.6 a,b 19 16 6.35
1  4mm 18.21 2.13 15.05 5.08 b 20 27 3.63
0.125ram 
Imm
22.86
5.34 a
30.93 7.15 a
27 59
< 0.125 mm 23.25 2.21 a 31.94 10.47 a, 24 89
6.43
6.12 a Differences between lower and middle unit significant at
0.05 b Differences between upper and middle unit significant at
0.05 c Differences between lower and upper unit significant at
0.05
Figure C2
100.00
if
« 30.00
20.00
0.01
0.1 1
Parflde Size (mm)
10
100
260
261
the lower unit (though differences with the upper unit and middle unit are not significant). Furthermore, there is significantly more gravel in the surface soil of the middle unit than the upper unit (though differences with the lower
16mm) is greater in the upper and lower unit than the middle unit, though the difference is not significant.
The fact that the soils in this middle unit are significantly different from those in the other two units is consistent with the soils noted in the road cuts near
Tombstone. Texturally similar soils are in horizontal layers. Finer grained, more erodible layers tend to be more horizontal, and more resistent layers tend to be more verticle.
C.2 Channel Initiation and Soil Type
Analysis of the data show that the three underlying soils units described in chapter 4 are a factor in controlling where channels begin on the watershed. More channels are initiated in the middle, finer grained, soils unit (1362
1366m). Furthermore, channels initiated in the middle finergrained unit tend to have a shallower slope than channels in either of the coarser units above or below this middle unit. More channels are initiated in the finer
262
grained middle unit (13621366) just below the transition from the upper coarse unit to this middle finergrained unit. This effect can be seen in Figure C3 which shows the location of channels on the watershed and the three soils units. Note the many channels that are initiated just below the transition between the upper coarse grained unit, and the middle, finer grained unit. The histogram in Figure
C4 confirms this relationship showing that more channels are initiated in the 1365  1366m elevations (the elevation of the transition from the middle to upper units) than any other elevations on the watershed.
The characteristics of the channels initiated in this middle soils unit also suggests that soils in this middle unit are more erodible. According to the analysis of
Montgomery et. al. 1996, lower slopes tend to occur where sediment is less limiting, while steeper slopes occur when sediment is more limiting. Plotting channel slope vs. channel drainage area on a loglog plot shows that channels initiated in the 1362 1366m elevations plot below the slopearea regression line, while those initiated at elevations the coarser units above or below plot above the regression line (Figure C5). The average slope for first order channels in the middle finergrained unit is 10.5 percent, while it is 15.0 percent in the rest of the
Figure C3
Location of Channels on Lucky Hills 104
1366m
1366m
1362m
1362m
263
Figure C4
Number of Channels Initiated at Elevation
•a
(O
«
C e
(O
O a»
j a
E
3
^

Elevation (m)
^ ^
^
I Lower Unit • Middle Rnergrained Unit • Upper Unit
264
265
Figure C5
100
Slope vs Area (channels)
_
—
—
Fr

_ r
— — —
"U"
A A fc
1
1

1—
h\
! u
—
— —
1
1 n
[
~AJ
! c c
"O j
.1^°
1 i
1 ! ! ! i
~
: 0
—
—
—
— — 
"E: i h
E
4±t
1 !
! i I " !
>
1 ! i
•
'
1
1 j
1
1
_J
 i!
!
1=::
1 —
5 i
1 o i
' i
1
1 i ! i—'
—
• krr
1 1
1 1
1
! I j i hi
1000 10000
Drainage Area (aq. meter^
100000
266 watershed. The differences in slope for channels initiated in the 13621366 m elevation from the rest of the first order channels on the watershed is significant at the 0.05 level (singletailed ttest t = 2.56 d.f. =13). Since channels initiated in this middle finergrained unit tend to be shallower, this suggests that sediment is less limiting in this 13621366m zone, indicating higher longterm erosion rates. One interesting observation from the plot of channel slope vs. channel area (Figure C5) is that contributing areas needed to initiate first order channels do not seem to change with soil type. In contrast to the relationships between channel slope and underlying soils types, there are no significant differences is the area necessary to initiate a first order channel in the finergrained, middle unit, and the other two units. This observation suggests that channel initiation is more slopedependent than areadependent. In other words, channels initiated in finergrained material require the same support area, but can form at shallower slopes.
For the LucJcy Hills, there are interesting implications for the observation that channel initiation is approximately constant with area, but that slope changes with soil type.
Since saturated hydraulic conductivity has been found to vary less than one order of magnitude on the watershed
267
(Goodrich, 1990; Whitaker, 1993), runoff volume is essentially a function of area, while runoff peak is a function of average slope all else being equal. Therefore, first order channels will deliver approximately the same volume of water from the contributing area for channels developed in any soil type. However, peak will be lower, but of longer duration in the finer grained soils. This suggests a potential for a longer duration of an event in channels developed in finer grained soils. The same volume of water discharged over a longer period of time over a more erodible material results in a greater volume of soil removed from a finergrained unit.
C.3 Soil Type and Hillslope Form
The general theme of shallower slopes in the finer grained, middle unit carries over to the slopes. Figure C6 shows the elevation of a profile up the main interfluve on the the watershed (location shown in Figure C3). Note that the slope is shallower in the 1362  1366m elevation.
Using the GRASS averaging function (r.average) the average slope for grid elements on the hillslopes in the 1362m hillslope grid elements in the upper unit (13661372) was
Figure C6
Cross Section AA'
1370 J
1368 
1366 
?
1364 c
1362 
10
1360 lU
1358 
1356 
1354 
50 100
Distance (m)
150
200
268
269 found to be 8.8%, and that of the lower unit (1355 1362m) is 13.0%.
A way of characterizing the relationship between hillslopes and channels is drainage density (length of channel per unit area) or its inverse (drainage area/ length of channel) (e.g. Kirkby, 1994). Higher drainage density has been associated with greater erosion rates
(Branson et. al. 1981). In this case, only the drainage density of first order channels was used to characterize the system. This choice was made, because drainage network self similarity suggests that the highest absolute drainage density will occur in the unit closest to the outlet.
Another way of looking at the drainage density relationship is to count the average number of grid nodes draining through a grid node. A higher number indicates that the average distance from the drainage divide to a channel is greater. In this case, the average number of grid elements draining through an element in the middle unit is 2.41, while it is 2.80 and 2.75 in the upper and lower units, respectively (using the 5m x 5m DEM). This observation further strengthens the notion that soils in the 1362 to
1366m elevation are more subject to erosion than either the soils above or below this middle, finer grained, unit.
270
In conclusion, subtle but significant differences in landscape form can be related to differences in the soil units on the watershed. The fact that the density of channel initiation is greatest along 1365m and 1366m elevations suggests a zone of more erodible material at this elevation. The picture of the process that arises is one of eroding upslope in a zone of more easily erodible soils with more resistant soils above and below this layer. This observation is further supported by the fact that most of the channels having a head cut occur along this transition. and 1366m along with the active head cuts in this elevation suggest that channels are eroding back along a zone of more erodible material undercutting the more coarse overlying unit. Slopes are significantly shallower in this middle finergrained unit on the hillslopes and in the channels from (1362m to 1366m). This suggests that, in general, there is more soil available for erosion in this middle finergrained unit than above or below this unit.
APPENDIX D
A METHOD TO CALCULATE K, FROM
SOILS PARTICLE SIZE DATA
271
272
Initial estimates of Ks were determined using the following relationship:
Ks = 80.709(%clay/""'
The initial estimate was further corrected to account for the high percentage of rock in the soil using the relationship described by Bouwer and Rice (1984) as follows;
e, ln(lVr) 0.2
where: eb = void ratio of field soil es = void ratio of fine earth fraction (< 2mm i.e. silt and clay) n = total porosity
Vr = percent rock by volume
This relationship was then further refined to reflect the ground cover and canopy cover as follows:
D.3
where
GC = percent ground cover
= (l%bare)
273
CC = percent canopy cover
Estimates of GC and CC were determined from rainfall simulator plots. In practice this translated to a cover factor such that Ksc = Ksr * 2.10 for channels, and Ksc =
Ksr *2.95 for overland flow areas.
APPENDIX E
SOILS PARTICLE SIZE DATA
274
Surl.ii.u Aimoiiiuj tuU
EASTlNn NORTHIH'"'
I 2
b4 16
 I 2
1116 B11 4B J.H4 22.6 12
IMII
U
.B
lmm 0.250.5 0.0630. <0.063
102 n
102 P
5B9762.5 3512152.5
13.6% 2 5 . 4 *
589722.5 3512127.5 1 0 . 7 * 1 7 . 7 *
7 . 8 *
3 . 7 *
4 . 9 * a . 2 *
4 . 7 *
1 3 . 9 *
4 . 1 *
8 . 7 *
2 . 6 *
102 E
2 . 4 * 7.6%
102 F
102 G
102 H
102 I
102 J
102 L
569737.5 3512177.5
569627.5 3512172.5
589617.5 3512162.5 1 6 . 8 * 3 1 . 7 * 1 0 . 1 *
102 I liiip 589817.6 35121C2.5 1 8 . 0 * 3 1 . 7 * 1 0 . 1 *
569812.5 3512157.5 27 . 5* 2 7 . 3 *
589777.5 3512107.5
5 . 2 * 1 4 . 3 *
509837.5 3512187.5 1 0 . 3* ^ 5 . 1 *
9 . 9 *
6 . 7 *
4 . 6 * 2 3 . 2 * 1 3 . 2 *
7 . 3 *
7 . 8 * 1 3 . 4 *
4 . 8 *
5 . 7 * 3 . 6 * 5 . 7 *
7 . 4 * 7 . 0 *
5 . 6 * 3 . 6 *
1 0 . 7 *
1.2*
3 . 5 *
2 . 5 * 5 . 3 * 6 . 4 *
5 . 3 * 4 . 6 * 2 . 3 *
6 . 9 *
6 . 0 * 7 . 8 *
3.B* 2.B* 6 . 3 * 7 . 6 *
6 . 7 * 5 . 9 *
3 . 4 *
8 . 2 *
4 . 2 * 6 . 1 * 2 . 7 * 1 . 8 *
3 . 8 * 3 . 3 *
4 . 0 * 4 . 6 *
2 . 4 * 6 . 5 *
4 . 2 *
6 . 1*
2 . 7 *
1 . 8 * 3 . 5 * 3 . 3 *
4 . 2 * 5 . 0 *
2 . 4 * 6 . 3 *
4 . 4 *
7 . 1 *
3 . 1* 2 . 3 * 3 . 7 *
4 . 2 *
3 . 7 *
3 . 0 *
1 . 4 * 4 . 6 *
1 . 0 * 1 2 . 9 * 1 1 . 3 *
1 1 . 9 * 1 4 . B * 4 . 1* 2 . 5 *
3 . 6 * 6 . 6 * 7 . 4 *
7 . 9 * 5 . 0 * 1 0 . 7 *
102 N
102
0
5B9752.5 3512162.5
569742.5 3512122.5
589732.5 3512122.5
8 . 0 t 2 9 . 5 * 1 1 . 7 *
0 . 0 * 2 3 . 2 * 1 3 . 4 *
5 . 3 * 2 9 . 8 *
1 5 . 0 *
6 . 9 *
7 . 0 *
5 . 9 *
B.3*
9 . 2 *
7 . 6 *
3 . 8 *
3 . 6 *
2 . 9*
2 . 4 *
2 . 4 *
2 . 0 *
5 . 1 *
3 . 9 *
2 . 9 *
5 . 2 *
4 . 5 *
2 . 7 *
4 . 4 *
6 . 7 *
2 . 9 *
4 . 6 *
9 . 3 *
4 . 3 *
4 . 7 * 1 2 . 0 *
3 . 6 *
1 5 . 1 *
5 . 2 *
4 . 8 *
6 . 8 *
7 . 0 *
6
. 0 *
6 . 4 *
4 . 7 *
5 . 1 *
3 . 9 *
2 . 3 *
7 . 7 *
2 . 1 * 1 0 . 1 *
102 Q
104 B
589707.5 3512127.5
569747.5 3511997.5
4.9» 15.21 6 .3t
1 . 7 *
2 6 . 0 *
1 3 . 2 *
3.61
6 . 3 *
7 . 0 *
9 . 0 *
5.2*
4 . 2 *
3 . 9 *
3 . 3 *
6.7*
10.
at
5 . 3 * 5 . S *
9.1*
S . 2 * e.e*
5 . 2 *
5 . 2 *
1 3 . 4 *
3 . 0 *
B . l *
104 B dup 589747.5 3511997.5 1 . 7 * 2 8 . 0 *
1 3 . 2 * 8 . 3 * 9 . 0 *
4 . 2 *
3 . 3 *
6 . 0 * 4 . 8 * S . 2 I
5 . 5 * 2 . 7 * a . i *
104 C 589737 . 5 3511987.5 1 4 . 9 * 2 7 . 3 * 1 0 . 5 * 6 . 5 * 6 . 5 * 4 . 0 *
3 . 2 * 4 . 6 * 3 . 7 * 3 . 2 *
3 . 9 * 2 . 4 * 9 . 3 *
104 D 569732.5 3511977.5 3 . 5 * 1 6 . 3 * 1 4 . 0 *
1 1 . 2 *
(1.2*
3 . 4 * 2 . 6 *
'..2* 6 . 9 * 6 . 2 * fi.S*
4 . 0 * 9 . 9 *
104 E
589722.5 3511957.5 l l . U * 2 5 . 5 * 1 1 . 7 * 6 . 5 *
8 . 1 * 3 . 5 * 2 . 9 *
4 . 6 * 5 . 7 * 4 . 5 *
4 . 1 * 2 . 3 * 6.8*
104 I
589762.5 3512047.5 o . a *
1 8 . 0 * 1 3 . 3 *
8.9*
1 3 . 5 * 5 . 8 * 1 . 8 *
5 . 0 * 6 . 0 * 6.1*
7 . 1 * 4 . 8 * 7 . 8 *
104 I. 509792.5 3511997.5 3 . 4 * 2 4 . 4 * 1 7 . 4 * 1 1 . 8 *
U ' . 9 » 5 . 1* 1 . 4 *
4 . 9 * 3 . 9 * 3 . 4 * 2 . 9 *
1 . 4 * 5 . 2 *
104 M
106 G
569802.5 3511977.5 2 / . J * 2 2 . 4 *
589682.5 3512092.5
6 . 9 * 6 . 5 * 9 . 2 *
8 . 1 * 1 4 . 7 * l u . o *
1 0 . 4 * 1 3 . : . *
5 . . ' *
104 0
104 P
104 Q
1U4 R
589817.5 3512022.5
1 2 . 1 *
3 0 . 6 *
589827.5 3512027.5 3 8 . 8 * 2 6 . 2 *
569632.5 3512027.5 1 6 . 1 *
2 2 . 4 *
1 1 . 8 *
569647.5 35120?2.5 1 9 . 0 *
3 0 . 5 *
104 R ilui
589047.5 3512022.5 1 9 . 0 *
3 0 . 5 *
104 S
106 D
589662.5 3512022.5
3 . 0 *
3 3 . 6 * 1 4 . 8 * 1 0 . 2 *
569662.5 3512067.5 2 1 . 9 * 2 9 . 6 *
5 . 9 *
4 . 7 *
9 . 5 *
U. 5*
U.5*
5.B* 1 0 . 0 *
2 . 9 *
7 . 6 *
5.C*
5 . 6 *
4 . 6 *
4 . 8 *
7..1*
2 . 7 *
4 . 1 *
1 . 8 * 2 . 5 * 3 . 0 *
2 . 9 * 2 . 3 * 1 . 0 *
? . l \
4 . 1 * 5 . 2 *
5 . 5 * 5 . 1 * 1 . 8 *
7 . 1 * 3 . ; *
2 . 8 * 3 . 5 *
4 . 9 * 4 . 2 * 3 . 3 *
; . 1* 1. / *
. M l * 4 . 7 *
4 . 4 * 4 . 0 * i . l *
1 . I t
. M l *
. ' . 0 *
2 . 4 * 5 . 0 * 5 . 6 * 5 . 0 *
1 . 6 *
1 . 3 *
2 . 3 *
5 . 9 *
5 , 2 *
1.1*
3 . 0 *
2 . 7 *
4 . 6 *
3 . 3 *
4 . 5 *
2 . 0 *
4 . 1 *
2 . 0 *
3 . 9 *
2 . 8 *
1 . 7 * 6.5*
4 . 3 *
6 . 2 *
4 . 1 *
4 . 1 *
5 . 5 »
2 . 6 *
1 0 . 5 *
106 E 589667.5 3512087.5 lU.O* 2 9 . 3 * 1 0 . 4 * 6 . 1 *
6.7*
. 1.*
J . l * 3 . 0 * 3 . 7 *
4 . 5 * 4 . 9 *
2 . 3 * 6 . 3 *
S . I *
3.U*
4 . 1 *
3 . 5 *
5 . 7 *
2 . 7 *
4 . 3 *
2 . 3 *
5 . 0 *
2 . 3 *
5 . 3 *
1 . 9 *
3 . 2 *
6 . 9 *
9 . 9 *
106 H 589677.5 351210;'.5
3 9 . 3 * 1 7 . 0 * 7 . 8 * 4 . 9 * fc. 1*
2 . / * 1 . 8 *
3 . 2 * 4 . 0 * 3 . 6 *
2 . 9 * 1 . 7 * 5 . 2 *
106 K 569667.5 3512087.5
2 . 4 *
2 4 . ' ) *
9 . 0 * 9 . 1 *
12 . t * S.ll* 1
.6*
4 . 7 *
4 . 6 * 4 . 2 *
4 . 3 * 3 . 2 * 1 1 . 4 *
106 L 589677.5 3512077.5
13.1.* J 5 . 9 *
9.3*
5 . 5 *
5.4*
. !.* 1 . 9 *
2
.0*
3 . 3 * 3 . 2 *
4 . 2 * 3 . 3 *
9 . 2 *
106 0 569647.5 3512067.5
1 4 . 2 * 1 7 . 2 *
5.9*
6 . 9 *
14.0* 6.B*
4 . 0 * 5 . 3 * 3 . 6 *
4
.0*
4 . 5 * 2 . 5 *
1 1 . 3 *
106
0 dup
569647.5 3512067.5 1 4 . 2 * 1 7 . 2 *
5.9*
6 . 9 *
14.0*
6 . 8 *
4.0*
4 . 5 * 3 . 4 *
4 . 2 * 5 . 0 * 2 . 8 *
1 1 . 4 *
106
P
589647.5 3512047.5
0.0*
1 . 6 *
5.U*
8.7*
1 2 .
u* i.4*
3 . 1 * 8 . 1 *
1 0 . 2 * 1 2 . 1 *
1 1 . 5 * 6 . 3 * 1 7 . 4 *
106
Q
569667.5 3512067.5
3.7*
2 1 . 1 *
9.5* 7 . 1 *
14.;'*
6 . 4 *
4 . 6 *
B.9*
6 . 0 *
4.6*
3 . 5 *
1 . 6 *
6.6*
M
U1
Uiiderlyiiii) llneiudeil Siiil 5dmplu:i Fall 1946
102 D
102
C
102 F
102 G
102 H
102
I
102 J
102
1.
102 N
102 0
102 P
102 Q tlaatinq Northiiu) i2b4
589762.5 3512152.5 o . o t
1632
15.8%
1116
5.5%
B11
589752.5 3512162.5
589737.5 3512177.5
589837.5 3512187.5
589827.5 3512172.5
589817.5 3512162.5
589812.5 3512157.5
509777.5 3512107.5
589742.5 3512122.5
589732.5 3512122.5
589722.5 3512127.5
589707.5 3512127.5
102
Q dup
589707,5 3512127.5
104
B
104 C
104
D
589747.5 3511997.5
589737.5 3511987.5
11.9%
589732.5 3511977.5
104
E
589722.5 3511957.5
104
E dup
589722.5 3 5 I I 9 5 7 . 5
104
I
104
J
104
L
104 M
104 0
104 P
104 Q
104 R
104 S
106
E
569762.5 3512047.5
589792.5 3511997.5
589802.5 3511977.5
589817.5 3512022.5
589827.5 3512027.5
589832.5 3512027.5
589847.5 3512022.5
589862.5 3512022.5
589682.5 3512067.5
589687.5 3512087.5
106
E dup
589687.5 3512087.5
106
H l o e
K
106
L
106
0
106
P
589677.5 3512102.5
0.0% 15.8% 10.2%
5.3% 10.1%
0.0% 0.9%
4.8%
< .8%
589667.5
3.512087.5 0.0%
4
.7%
6.9%
9.0% 13.6%
8.2%
4.5%
7.1% 17.6%
0.0%
19.5%
589677.5 3512077.5 0.0%
18.1%
589647.5 3512067.5 13.9%
4.3%
589647.5 3512047.5
106
P dup
589647.5 3512047.5
106 Q 589667.5 3512067.5
2.1% 11.9% o . o t o . u t
0.0%
0.0%
0 . 0 1
0.0%
2.5%
0.0%
0.0%
0.0%
2.7%
0.0%
4.0%
0.0%
0.0%
2.0%
2.0%
0.0%
0.0%
0.0%
0.0%
1.1%
5.2%
6.1%
3.5%
1.8%
1
.8%
3.8%
3.8%
7.2%
6.5%
1.7%
5.4%
5.4%
2.4%
6.5%
4.1%
9.8%
9.8%
8.1%
4.9%
2.9%
2.9%
6.2%
£.0%
1.6%
4.0%
5.0%
6.4%
3.4%
2.5%
2.0%
3.9%
3.3%
3.3%
5.7%
4.4%
5.0%
4.8%
4.8%
4.5%
8.0%
3.7%
3.7%
4.7%
6.2%
7.8%
2.0%
4.2%
4.4%
4.4%
4.4%
3.C*
6.1%
4.2%
1.3%
1.3%
5.6%
46 2.64 22.6 l2iiin. (l.Slnm 0.2!i0.!> 0.12S0. <0.063
4.1%
4.7%
3.2%
2.3%
3.4%
3.5%
1.8%
7.0%
9.7%
6.7%
6.6% 18.1%
6.5%
7.2% 12.6%
4.1% 12.2%
5.4%
3 . 9%
4.5%
6.2%
4.1% y.6%
5.0%
7.0%
6.0%
3.9%
3.2%
2.1%
3.6% 5.3%
9.4% 9.9% 9.7%
4.9% 20.2%
5.4%
4.2%
7.1%
7.7%
8.1%
10.3%
8.6%
13.7%
9.3%
14.6%
5.4% 15.4%
8.0%
24.7%
5.4% 9.0% 10.2%
7.9% 6.6%
5.8% 1 1 . U
10.8% 10.8%
10.9%
4.4% 8.8%
5.0% 5.4% 6.9%
5.9%
7.1% 7.4% 6.9%
6.1%
2.8%
2.8%
2.0%
5.7%
5.3%
3.2%
9.7%
7.5%
11.3%
15.9%
3.4%
4.2%
5.4%
3.8%
3.2%
12.9%
20.2%
13.0%
17.2%
12.1% 15.4% 10.9%
25.5%
4.8% 8.8%
8.7%
7.8%
30.5%
58.5%
3.6%
9.7% 8.6%
7.8% 10.9% 10.5% 8.0% 7.2%
5.0% 23.0%
3.6%
3.6%
4.5%
6.7%
6.7%
7.3%
4.0%
4.0%
4.8%
3.7% 8.2% 12.7%
11.0% 10.6%
3.7%
10.1% 11.0% 10.6%
11.1%
3.9% 9.2% 7.8%
8.5% 10.0%
5.6%
7.9%
5.0%
6
.1% 8.8%
6
.0%
19.6%
7.2% 20.1%
6.5%
22.1%
2.6%
4.0%
6.9%
8
.8%
5.9%
6.4%
4.7% 11.2% 10.2% 9.8%
11.3%
5.5%
22.9%
6.3%
20.6%
4.4% 11.?% 8.3% 7.5% 8.4%
9.2% 7.8% 7.4%
5.1% 20.4%
4.4% U.2% d.3%
7.5% 9.9%
8
.2% 7.9% 7.8%
4.3%
20.2%
4.7%
7.0%
4.6%
7.4%
19.7%
11.9%
4.4% B.4% 5.6%
2.8%
6.3%
4.1%
5.9%
8.5%
7.8%
9.0% 11.7%
15.0%
4
.6% 4.1%
4
.7%
8.2% 9.5% 10.8%
9.7% 20.1%
3.1%
17.0%
5.7%
20.8%
4.6% 12.1% 7.5%
4.8% 6.9%
4.9% 4.2%
4.9% 3.8% 19.9%
4.8% 12.6% 7.9%
4.9% 8.8% 6.2% e.9%
7.0% 3.2%
20.0%
3.8%
5.C%
1 . J%
4.1%
2.7%
2.7%
2.5%
4.7%
2.7%
3.5%
3.5%
4.9%
9.7%
7.9%
4.8*
6.0%
6 . 3 t fa.3i
7.8%
4.5%
10.
4.7%
7.3%
5.8%
5.8%
8.7%
5.6%
5.7%
4.9%
3.3%
3.8%
3.8%
5.6%
4.9%
).2%
5.0%
2.9%
2.9%
6.4%
4.6%
4.1%
4.4%
3.5%
6.1%
5.5%
6.9%
7.5%
8.6%
9.6%
8.4%
10.1%
13.3%
7.0%
9.7%
9.8% 15.3%
14.4% 12.0%
15.2%
2.5% 13.6%
4.2%
11.8%
6.3%
17.5%
7.2%
22.5%
2.5%
4.7% 9.9% 12.0%
12.8% 7.3% 21.6%
2.5%
4.6%
7.8%
10.6%
8.8% 11.2% 12.9%
10.0% 11.2% 10.2%
6.1%
21.7%
4.8% 2 0
.2%
4.7% 6.2%
7.5% 8.1% 9.8%
7.4%
27.5%
2.5%
5.5%
5.3%
7.1% 11.5% 7.4%
23.8%
4.5%
2.4%
2.4%
6.0%
6.7% 10.2%
5.7%
6.5%
9.5%
13.9% 16.5% 9.0%
25.9%
6.1% 11.3%
14.2% 15.1%
10.4% 24.3%
9.8%
7.8%
8.6%
10.4%
7.6%
5.4% 22.8%
4.7%
20.6%
N)
O
a\
Clhdlinel Sample:! Tali I'J'Ji) tASTlNG NOkTHlNii
J^t)4tnnt lt)~3<^rTUT> Hl<)rTun Bllmm 46nju 2.b4nim 22.HtmT> l~2njn 0,b"lmm 0.250. 0.1250 0.0630 <0.063in
1 0 2 A 58977.3 3 5 1 2 1 1 0
1 0 2 B
58976B 3 5 1 2 1 3 3
1 0 2 C
5B976B 351214.i
0 . 0 1
7 . 9 *
7 . 3 *
5 . B t
2 3 . B *
9 . 2 *
1 0 2 M 5B9763 3 5 1 2 1 1 3
1 0 2 R
5B9798 3 5 I 2 0 6 B
104 A
5 8 9 7 5 3 3 5 1 2 0 0 3
0 . 0 *
2 . 0 *
6 . 7 *
3 . 3 *
104 F
5 8 9 8 1 3 3 5 1 1 9 5 8
104 M
5 8 9 8 1 3 3 5 1 1 9 6 8
0 . 0 *
4 . 4 *
0 . 0 *
4 . 3 *
7 . 6 *
0 . 0 *
1 0 4 N 5 8 9 8 0 8 3 5 1 2 0 2 3
0 . 0 * 5 . 5 *
1 0 6 r 589678 351208B
3 2 . 3 * 2 3 . 1 *
1 0 6 r 58967B 351208B 1 2 . 0 *
1 5 . 8 *
1 0 6 N 5 8 9 6 6 8 3 5 1 2 0 4 8 n . o * 5 . 3 *
1 0 6 N 5 8 9 6 6 8 3 5 1 2 0 4 8
7 . 5 * 3 8 . 4 *
3 . 2 1
7 . 9 1
. 0 *
U.O*
5 . 7 *
3 . 0 *
G. 1 *
1 . 2 *
3.8%
6 . 2 *
4.6%
4 . 3 *
9.8%
3 . 7 *
7 . 1 *
3 . 0 *
7 . 2 *
9 . 0 *
1 1 . 2 *
6 . 1 *
6 . ; *
4 . B t
4 . 3 *
5 . 6 *
6 . 9 *
1 1 . 5 *
7 . 5 *
1 1 . 2 *
4.7%
3.8%
11.4%
3.3%
2 . 1 *
1 . 6 *
6 . 1 *
3 . U *
4 . 1 *
4 . 0 *
3 . 6 *
4 . 5 *
1 0 . 6 * 1 0 . 5 * 9.5%
8.4%
B.B* 1 6 . 3 *
1 6 . 6 % 1 3 . 3 %
4 . 0 *
1 0 . 1 * 7 . 2 * 6 . 0 *
1 1 . 1 * 1 5 . 3 * 1 7 . 1 % 1 0 . 5 %
5 . 0 * I B . 6 *
1 1 . 3 * 1 0 . I *
7 . B *
1 3 . 0 * 12.1% 6.7%
6 . 7 *
1 1 . 9 *
0 . 7 *
2 . 5 *
7 . 0 *
3 . 4 * b . 3*
5 . 2 *
7 . 2 *
1 5 . 9 * 1 3 . 4 * 1 1 . 4 *
1 2 . 7 *
9 . 7 *
9 . 3 *
1 8 . 6 *
3 0 . 3 *
1 4 . 2 %
12.1%
29.3%
1 0 . 6 %
3.1%
1 2 . 2 %
4.9%
4 . 9 * 6 . 3 * 2 . B * 1 . 9 * 3 . 5 * 3.9% 3.7% 3.3%
5 . 6 * 1 0 . 6 *
6 . 5 *
6 . 7 *
5 . 5 *
4 . 2 *
? . B *
4 . 5 *
3 . 4 *
2 . 0 *
5 . 5 *
6 . 2 *
3 . 1 *
6 . 7 *
8 . 0 %
3.6%
5 . 9 *
5.1%
9.2% 1 0 . 1 %
3.9%
6 . 1 *
1 . 6 *
4 . 1 * 2 2 . 5 *
4 . 0 * 1 9 . 6 *
2.2%
1.4%
0.5%
1.5%
1.0%
1.9%
2 2 . 6 *
7 . 6 *
5 . 5 *
6 . 7 *
4 . 0 *
4.1%
2.8%
6.1%
3.2% 14.9%
6.0%
2.3%
22.9%
8.9%
Surfacb Ajmoiintj Sampleii May,
Easting Nottrung i2b4 1632 1116 6
Supplemenla> A bB9B22.S 3512217.5
5.2t 16.5%
Supplemental B 5B91B2.S 3512192.5 12.9t
Supplemental D 569632.5 3512132.5
33.0%
Supplemental c
589797.5 3512142.5 1£.6I 26.
9.9% 30.7%
12.9%
10.6%
7.1%
IB.9%
Supplemental E 5B9612.5 3512112.5
2.9t 34.5% 13.6%
Supplemental F 5B9B37.5 3512102.5 11.3%
23.2% 13.7%
Supplemental G 5B9B07.5 3512072.5
21.7% 20.1% B.7%
Supplemental H 569B]7.5 3512062.5
Supplemental 1
569642.5 3511977.5
4.9%
4.1%
25.9%
23.1%
13.0%
9.0%
Supplemental J 569772.5 3511957.5
3.4% 23.6% 14.2%
n
17.2%
5.6%
10.1%
4a
5.4%
7.1%
9.2%
5.9%
12.2%
13.9%
10.4%
:'.d4
7.5%
7.3% a.4%
9.2%
6.9%
12.6%
6.0% 14.1%
12.2% 16.5%
4.2%
3.9%
5.0%
2.3%
4.1%
3.6%
5.7%
3.6%
6.5%
2  2 . 6
6.3%
2.5%
2.6%
2.7%
1.6%
2.6%
2.5%
4.0%
2.1%
6.0%
3.3% l'2r>m
3.9%
4.2%
4.6%
2.9%
5.3%
5.5%
5.7%
3.5%
9.7%
4.7%
Supplemental K 5B9702.5 35119B7.5
Supplemental L 5B9722.5 3512012.5
5.5%
6.7%
17.9%
34.1%
15.2%
16.9%
Supplemental H 569667.5 3512022.5 25.4%
22.6% 10.7%
Supplemental N 569737.5 3512047.5 17.7*
25.7%
Supplemental 0 5B9712.5 3512057.5
11.5% 31.9%
11.0%
11.5%
Supplemental P 569767.5 3512077.5
4.61 30.71
Supplemental Q 569727.5 3512062.5
22.11 27.5%
14.2%
9.9%
11.6%
7.4%
5.0%
6.6%
7.9%
5.0%
6.3%
11.3%
7.0%
7.0%
7.6%
6.5%
B.7%
5.5%
4.6%
2.6%
3.1%
4.1%
2.7%
4.61
2.3%
4.0%
2.2%
2.1%
2.9%
1.9%
3.1%
1.6%
B.4%
4.6%
3.6%
3.6%
3.7%
5.4%
3.5%
4.9%
3.9%
3.3%
2.3%
4.5%
4.2%
4.B%
3.5%
6.2%
4.7%
5.6%
3.2%
2.6%
3.4%
3.2%
4.8%
2.7%
5.2%
4.6%
2.6%
2.9%
4.0%
4.7%
3.2%
4.6%
4.1%
3.2%
4.8%
2.6%
3.7%
3.9%
3.9%
4.9%
3.7%
6.1%
4.6%
3.6%
4.2%
4.5%
5.2%
2.6%
5.7%
2.9%
2.0%
4.1%
3.1%
4.6%
4.6%
5.3%
5.1%
5.3%
3.4%
1.6%
2.5%
1.9%
2.6%
2.4%
1.9%
2.6%
1.4%
1.0%
1.8%
2.3%
2.2%
2.5%
2.6%
2.7%
2.7%
4.2%
4.7%
6.9%
4.9%
5.5%
5.1%
6.6%
5.9%
5.0%
4.9%
5.1%
6.B%
7.1%
6.2%
7.3%
6.21
6.9%
Underlying Uneioded Soil Samples Hay, 199B
Supplemental A
Supplemental B
Eaating Northing 3264 s e 9 8 ; 2 . s 3512217.5
589782.5 3512192.5
O.Ol
2 . 7 1
1632 1116 flll
4 . I t
6 . 5 t
5 . 9 t
3 . 3 t
Supplemental C
Supplemental D
5B919T.5 3512142.5
O.Ot
589832.5
3512132.5
1.51
5 . 7 1
9 . I t
2 . 9 t
1 0 . 9 t
Supplemental E
Supplemental F
589812.5 3512112.5
3 . 5 t
589837.5
3512102.5
0 . 0 1
9 . 9 t
5 . 0 t
B.Ot
3.2t
5 . 6 t
<fl
7 . 9 t
2.Q* 22.6
3.81 3 . I t
3 . 0 t
2 . 2 t
8 . 6 t
8 . 7 t
B.3t 1 1 . 5 t
4 . a t
2 . 8 t
9 . 8 t
7
. 4 t s
6 . 2 t s
. e t
. o t
S . 6 t
S
. 2 t
4 . I t
S . S t
3 . 9 t
4 . I t
4 . 0 t
8 . 6 t e . 3 t 1 2 . 2 t 17.61
6 . 8 1 1 0 . 9 1
11. 9 t 11.Bt
7 . 8 1
6 . 0 1 6 . I t 9.61
4 . 2 t e . 4 t
7
. 4 t
6 . 0 t
5
. 9 t
9.3t
0.250.5 0.1250. 0.0630. <0.063
7 . 2 t
7 . 6 t
1 1 . 6 t
1 2 . l t
1 1 . 2 t
16.71
B.31
6 . 4 1
7 . 3 t
6 . I t
S.3I
14.St
1 6 . 3 t
31, 9 t l S . l t
17. 3 t
9 . 3 t 1 7 . 7 t
Supplemental G
Supplemental H
589807.5 3512072.5
589837.5 3512062.5
2.9t
2.11
7.
I t
6 . 8 t
4 . 3 t
4 . 4 t
4.51 13.
4 t
3 . I t 6 . S t
6.31
3 . 8 t
5.SI
3.01
8
. 4 1
6 . I t
8 . 3 1 6 . 7 1
7.11
7 . S t 1 1 . 4 t IB.Ot
4 . 7 1 ie
. 9 t
8 . 0 1
19.
3 t
4 . 8 t
I S . S t
Supplemental I
Supplemental J
589842.5 3511977.5
589772.5 3511957.5
0.0%
O.Ot
6
. 4 t
3.3t
4 . 2 t
4.31
3.2t
9 . 4 t
4 . 7 t
12.
6 t
7 . 3 t
7 . 7 t
S
. 4 t
11
. 4 1 1 0 . 9 t 1 0 . e t 1 0 . 7 t
4 . 7 t 9 . I t 9 . e t
9
. 4 t 9.Bt
S
. l t 1 9 . 7 t
Supplemental K
Supplemental
589702.5 3511987.5
O.Ot
L 589722.5
3512012.5
6 . 2 t
Supplemental
H 589687.5 3512022.5 5 . 8 t
2 . 3 t
8
. 4 t
3.2t
4 . S t
3 . 0 t 8 . 6 t
4 . 3 t 1 0 . l t
6 . 9 t
S . 6 t s
. o t
11.31 11.
S t
12.
7 t
1 2 . 9 1
4 . I t
S
. 3 t e . 4 t 6 . 7 t
8.71
4 . 3 t 9 . 7 t 7 . 0 t
7
. 4 t
9
. 4 t
S . 9 t
16.
6 t
6 . 0 t 2 3 . 7 t
5 . 5 t
1
. 8 t
2
. 4 t 8 . 3 t 6 . 0 t
4 . 4 t 28. Ot
Supplemental
N 589737.5 3512047.5 4 . 4 t 1 0 . 9 t 4 . I t
4 . e t
11.
S t 9 . St 5 . 7 t 7 . 0 t
5 . 2 t
6
. 4 t
8.81
S . 2 t
16.
Supplemental 0
Supplemental
589712.5 3512057.5 6 . 2 t
6
. 4 t 4 . 8 t
4 . I t
9 . 2 t
5.71
4 . 3 t 7 . 9 t 6 . 7 t
7 . 5 t 10.Ot 4.Bt 22. S t
r
S89767.5
3512077.5
O.Ot
12.
5 t
5
. e t 4 . 3 t 1 0 . 2 t
5
. 6 1
4 . 3 t
6 . 2 t 7 . I t l G . l t
12.
4 t S . l t 1 6 . 6 t
Supplemental
Q 589727.5
35120S2.5
2 . 8 t l l . l t 3 . 4 t 3 . 3 t 6 . 4 t
3.61
2 . 8 t 6 . 6 t
6.
I t 8 . 7 t 1 4 . S t
7.
I t
23.
6 t
chan chan chan chan chan chan chan chan chan chan chan chan chan chan chan chan chan char. chan chan
Channel Samples May 1996
Eaatinq Northing 3264 1632 1116 611
1 589727.5 3512057.5
S 589727.5 3512007.5
8 . 4 t 7.2%
2 569722.5 3512047.5
1 6 . 2 1
10.6%
3 589727.5 3512027.5
1 2 . 3 t 14.6%
4 589722.5 3512022.5
6.2% 12.9%
3.4%
29.0%
6 589737.5 3512007.5
16.1% 20.4% e 589752.5 3512032.5
22.5% 22.2%
9 589757.5 3511992.5
0.0% 4.1%
1 0 569772.5 3511987.5
3.2% 8.9%
12 589787.5 3512037.5 22.1% 14.9%
1 3 569812.5 3512207.5 3.5% 10.5%
14 589622.5 3512102.5
2.2% 11.3%
1 5 589602.5 3512167.5
2.4% 4.3%
1 6 569817.5 3512132.5
16.6% 20.2%
17 589797.5 3512182.5
8.3% 9.2%
IB 569602.5 3512097.5
39.9% 17.8%
1 9 589807.5 3512157.5
14.5% 26.0%
20 589807.5 3512112.5
8.6% 18.6%
2 1 589777,5
3512152.5
9.2%
10.9%
22
569762.5
3512122.5
11.4% 13.4%
4.9%
J.7%
5.7%
5.6%
6.6%
5.4%
4B
16.6%
14.1%
5.4%
12.8%
8.1% 20.9%
2.84 22.6 12
8.8%
7.9%
6.9%
9.2%
7.6%
5.6%
4.4%
6.2%
7.6% 12.8%
6.1% 11.9%
3.3%
9.5%
7.5%
26.5%
5.9%
5.5%
4 . 5 1
10.2%
9.6% 10.0% 26.6% 11.1%
4.5% 4.9% 8.4% 4.9%
5.6%
5.0%
2.2%
6.7%
6.4%
4.8%
6.7%
6.9%
7.9%
4.1%
5.6% 14.6%
7.0%
13.1%
3.1% 8.4%
6.7%
14.0%
5.0% 14.1%
2.9%
4.7%
7.2%
6.2% 10.7%
4.6%
6.5%
7.5%
11.7%
9.6%
9.0%
5.9%
5.5%
5.9%
6.3%
3.2%
4.9%
5.4%
5.1%
6.2%
6.7% 8.6% 12.1% 8.5%
4.8%
4.9%
5.3%
4.9%
3.4%
3.6%
3.4%
6.8%
4.1%
3.7%
6.0%
7.9%
6.2%
8.9%
9.1%
7.3%
6.0%
7.4%
7.0%
9.7%
6.4%
7.9%
6.1% 12.0%
11.7%
6.6%
6.5%
6.0%
6.0%
5.0%
7.4%
9.8%
4.2%
3.9%
4.9%
3.9%
2.3%
6.5%
6.3%
4.4% 9.5% 10.4% 11.3% 9.9%
5.5% 13.2%
19.0% 16.1% 10.6%
3.9%
5.7%
2.5%
3.9%
3.4%
8.6%
6.1%
7.5%
5.6%
13.4%
3.3%
7.6%
5.5%
6.9%
9.5%
7.5%
7.0%
11.0%
2.9%
8.6%
6.1%
7.2%
8.1%
6.3%
5.3%
8.1%
3.1%
5.5%
8.3%
4.8%
5.2%
3.8%
3.2%
4.7%
3.9%
3.7%
7.7%
4.4%
4.5%
9.1%
9.7%
O.S1 0.2S0. 0.1250 Q.0630 <0.063
12.0%
10.3%
9.3%
9.4%
6.4%
7.2%
i.e%
1.6%
1.9%
1.2%
1.5%
0.9%
2.1%
1.4%
0.6%
2.5%
1.6%
3.7%
2.2%
1.3%
1.3%
1.9%
1.4%
2.5%
2.5%
2.4%
5.0%
5.9%
6.2%
3.8%
3.7%
4.1%
6.0%
4.9%
3.0%
4.9%
3.7%
6.2%
5.7%
3.6%
4.4%
7.4%
5.0%
7.7%
6.4%
7.1%
APPENDIX F
STATISTICAL OUTPUT
281
Pearson 6T16UP
Correlat LS16UP
LS8UP
LS2UP
LS125UP
GT16DN
LS16DN
LS8DN
LS2DN
I.S125DN
ACCUM
ASPECT
CRTACCUM
DISTCH
ELEVCM
FLOVASPE
FLOVECSL
FLOVEC
HSLOPE
MCURV
SINASPCT
SQRTHSLP
TASPEC
TCURV
UPAREA
SLOPE
STEEP
LS
D65DN
Correlations
GT16UP
1.000
LS16UF
.919*
Lsaup
.773*
LS2UP LS125UP GT16DN
LS16DN
.735*
.539*
.642* .653*
LS8DN
.546*
.919* 1.000 .890* .816*
.773*
.735*
.539*
.816*
.606*
.929*
1.000
.745* .853*
.642* .581* .417*
.375*
.653*
.546*
.535*
.249
.320*
.890*
.562*
.488*
.182
.292*
1.000
.496*
.496*
.386*
.174
.201
.
.288*
.261
.929*
.432*
.433*
.437*
.256
.166
.301*
.
.853*
.581*
.745* .417*
.375*
.625*
.496*
.432*
.562*
.496*
.433*
1.000
.237
.237
1.000 .859*
.373* .859* 1.000
.400*
.784*
.922*
.400*
.453*
.574*
.375*
.784*
.667*
.334*
.330* .358*
.274
.180
.922*
.700*
.441*
.261
1.000
.833*
.562*
.289*
.226
.240
.233
.152
. .328*
. .358*
.193
.234
.177

.216
.163
.214
.250
.338*
.000
.272
.204
.316*
.236
.296* .236
.188 .108
.183 .139
.310" .325* .417*
.143 .434*
.349* .310*
.411* .148 .184
.424*
.333*
.291*
.137
.148
.337*
.212 .344*
.370* 
.181
.311*
.066
.352*
.084
.432*
.272 .377*
.306*
.156
 . 3 7 3 *
.224
.288* .261
.190 .072
.222
.166 .105
.376* .304* .230
.032
.060
.571*
.137 .179
.092
.072
.267
.117
.166
.544* .487* .519*
.120
.555*
.241
.375*
.126
.093
.149
.474
.123
.410* .335* .291*
.180 .261 .289*
.130
.145
.
.206
.298*
.215
.209
.279
.124
.346*
.133
.116
.251
.045
.138 .160
.079
.157
.730* .748* .847*
M
00
K)
Pearson
GTieuP
Correlat i,si6UP
LS8UP
LS2UP
LS125UP
GT16DN
LS16nN
LSBDN
IiS2DN
LS125DN
ACCUM
ASPECT
CRTACCUM
DISTCH
ELEVCM
FLOVASPE
FLOVECSL
FLOVEC
HSLOPE
MCURV
SINASPCT
SQRTHSLP
TASPEC
TCURV
UPAREA
SLOPE
STEEl'
LS
D65DN
Correlations
LS2DN LS125DN
.535* .249
.488*
.386*
.437*
.453*
.182
.174
.256
ACCUM
.320*
.292*
.201
.166
.574* .161
.667*
.700*
.833*
ASPECT
.306*
.288*
.261
.301*
.375*
.334*
.330*
.441*
.358* .261
.562* .289*
1.000
.701*
.118
.214
.083
.073
.188
.273
.441*
.155
.400*
.129
.333*
.400*
.701*
.118
1.000 .102
1.000
.325*
.034
1.000
.325*
.077
.034
.305*
.324*
.007
.167*
.019
.353'
.057
.291*
.004
.086
.057*
.088*

.001
.285«
.126*
.018
.111* .064*
.484* .068* .902*
.008
.325'
.
.022
.034 1.000*
.214
.141
.042
.345*
.029
.036
.089
.084
.023
.027
.114*
.
.237*
.656'
.060*
.032
 .026
 .022

.893* .591* .235
CRTACCUM
.233
.240
.193
.163
.150
.272
DISTCH ELEVCM FLOVASPE
.226 .106 .392*
.233
.234
.214
.000
.204
.152
.177
.250
.184
.316*
.328*
.292*
.338*
.417*
.236
.310* .296*
.236
.083
.077
.188
.108
.073
.305*
.139
.188
.007
.961* .324* .167*
.019 .015 .164*
.325*
.273
.353*
.057*
.932*
.041 1.000 .305* .147*
.305* 1.000
.429*
.147*
.041
.429* 1.000
.048
.121*
1.000
.104* .410*
.397*
.005
.092* .361*
.136* .464*
.462*
.133* .127* .094*
.005
.254*
.006
.052*
.064*
.019
.022
.159*

.015
.049
.136* .130* .089*
.102* .086*
.268* .468*
.705*
.173*
 .494*
.067*
.827* .215* .089*
.146
.063
.291*
.866*
.004
.932*
.050*
.000
.006
.013
.004
.315*
Pearson GT16UP
Cocrelat LS16UP io" LS8UP
LS2UP
LS125UP
GT16DN
LS16DN
LS8DN
IiS2DN
LS125DN
ACCUM
ASPECT
CRTACCUM
DISTCH
ELEVCM
FLOVASPE
FLOVECSL
FLOVEC
HSLOPE
MCURV
SINASPCT
SQRTHSLP
TASPEC
TCURV
UPAREA
SLOPE
STEEP
LS
D65DN
Correlations
FLOVECSL
.380*
.358*
.216
FLOVEC
.137
.212
HSLOPE
.376*
.370*
.344*
.223
MCURV SINASPCT SQRTHSLP TASPEC
.148
.337*
.377*
.306*
.181
.066
.311*
.352*
.373* .288*

.224 .261
TCURV
.156
.072
.432* .272 .301* .092
.284*
.349*
.342*
.184
.272
.143
.434*
.411*
.142
.148
.424*
.084
.120
.123
.333* .206
.555*
.241
.298*
.143
.410*
.335*
.375*
.180
.261
.126
.130
.215
.310*
.441*
.182
.155
.291* .124
.400* .129
.346* .291*
.289*
.133
.400* .214 .141
.057 .291* .004 .086 .484*
.008 .325* .089
.088*
.027
.104*
.001 .126*
.285* .018
.005 .136*
.111*
.064*
.133*
.068*
.902*
.064*
.022
.049
.142*
.022
.034
1.000*
.019
.482*
.015
.441* .164*
.114*
.060*
.136*
.130*
.089*
.410*
.397*
.005
.092* .464*
.361*
.254*
.462*
.006
.127*
.094*
.052*
1.000
.247*
.247*
1.000
.952*
.233*
.062*
.053*
.952*
.233*
1 .000
.075*
.062*
.053*
.075*
1.000
.062* .011
.075* .069*
.933* .229*
.027
.985*
.285*
.018
.090*
.064*
.056* .061* .070* .982*
 . 8 6 6 *
.062*
.011
.075*
.069*
1.000
.072*
.902*
.064*
.004
.933*
.229*
.985*
.090*
.072*
1.000
.022
.027
.285* .061*
.018
.064*
.902*
.022
1.000
.056*
.070*
.982*
.064*
.086*
.060*
.086* .060* 1.000
.063* .048
.883* .214*
.135*
.009
.146* .010
.509* .314*
.064* .019
.940*
.113*
.155*
.150*
.171*
.491*
.147*
.107
.028
.081*
.051'
.398*
.109* .032
.936* .026
.188*
.022
.204*
 .010
.483* .235
.022
.107*
.149*
.117
Pearson GT16UP
Correlat LS16UP
LS8UP
LS2UP
LS125UP
GT16DN
LS16DN
LSEON
LS2DN
LS125DN
ACCUM
ASPECT
CRTACCUM
DISTCH
ELEVCM
FLOVASPE
FLOVECSL
FliOVEC
HSLOPE
MCURV
SINASPCT
SQRTHSLP
TASPEC
TCURV
UPAREA
SLOPE
STEEP
LS
D65DN
Correlations
UPAREA
.222
.166
SLOPE
STEEP
.376*
.032
.384*
.038
.230 .109
LE
.060
.137
D65DN
.571*
D65UP
.842*
.544* .838*
.105
.072
.093
.145
.209
.116
.042
.084
.267
.149
.251
.345*
.023
.117
.126
.045
.057
.079
.029
.058
.179
.166
.145
.138
.160
.157
.036
.027
.487*
.519*
.474*
.450*
.730*
.748*
.847*
.893*
.656*
.631*
.675*
.632*
.535*
.528*
.591* .211
.117* .237*
.519* .656* .146
.032
.026 .022
.010
.104*
.268* .705* .827*
.102* .468*
.173* .215*
.235
.146
.063
.304*
.072
.182
.086* .494* .067*
.089*
.291* .175
.000
.063*
.048
.064*
.019
.028
.109*
.032
.022
1.000
.006
.006
.883*
.214*
.940*
.113*
.081*
.013
.009
.155*
.150*
.036
.004
.146*
.010
.171*
.147*
.315*
.509*
.314*
.491*
.404'
.422*
.085
.204
.051* .398*
.326*
.936*
.026
.107*
.006
1.000
.186*
.022
.153*
.052*
.301'
.204*
.010
.149*
.483*
.235
.117
.064* 
.420*
.434*
.304*
.213
.098
.394*
.052*
.064'
.301* 1.000
.314* .937*
.420* .048
1.000
.091
.091
1.000
.102
.589*
286
REFERENCES
Abbott, M.B., Bathurst, J.C., Cunge, J.A., O'Connell, P.E. and Rasmussen, J. 1986. An introduction to the European
Hydrological System  Systeme Hydrologique Europeen.
SHE.,2. structure of a physically based distributed modeling system. Journal of Hydrology., 87 (12), 6177
Abrahams, A.D. and Parsons, A.J. 1991. Relation between sediment yield and gradient in debriscovered hillslopes. Walnut Gulch, Arizona. Geological Society of America Bulletin, Vol. 103, 11091113
Ackers, P. and White, W.R. 1973. Sediment transport: new approach and analysis; Proceedings of the ASCE Journal of Hydraulics Division, Vol. 99(HY11), 20412060
Ahnert, F. 1987. Approaches to dynamic equilibrium in theoretical simulations of slope development. Earth
Surface Processes and Landforms, Vol. 12, 315
Andrews, E.D. and Erman, D.C. 1986. Persistence in the size distribution of surficial bed material during extreme snowmelt floods. Water Resources Research, Vol. 22.,
No. 2, 191197
BenHur, M. and Agassi, M. 1997. Predicting interrill erodibility factor from measured infiltration. Water
Resources Research, Vol. 33. No. 10., 24092415
Bennett, J.P. 1974. Concepts of mathematical modeling of sediment yield. Water Resources Research, Vol. 10, No.
3, 485492
Beven, K., 1989. Changing ideas in hydrology  the case of physicallybased models. Journal of Hydrology, Vol.
105., 157172
Binley, A., Beven K. and Elgy, J., 1989. A physicallybased model of heterogeneous hillslopes 2. Effective hydraulic conductivities. Water Resources Research,
Vol. 25, No. 6., 12271233.
Blau, J.B., Woolhiser, D.A. and Lane, L.J., 1988.
Identification of erosion model parameters.
Transactions of the American Society of Agricultural
Engineers, Vol. 31, 839845
287
Bouwer, H. and Rice, R.C. 1984. Hydraulic properties of stony vadose zone soils. Groundwater Vol. 22, No. 6,
696705
Branson, F. A., Gifford, G.F., Renard, K.G. and Hadley,
R.F. 1981. Rangeland Hydrology. KendallHunt. pp. 339
Brown, L,R. and World Watch Institute. 1997. State of the
World, 1997 ; a WorldWatch Institute report on progress toward a sustainable society. New York. Norton, pp. 229
Brutsaert, W. 1982. Evaportation into the Atmosphere:
Theory, History and Applications. Kluwer Academic
Press. Norwell, Ma., pp. 299
Chien, Y.J., Lee, D.Y., Guo, H. and Huong, K.H. 1997.
Geostatistical analysis of soil properties of midwe^t
Taiwan soils, Soil Science, Vol. 162, No. 4, 291298
Clapp, R.B. and Hornberger, G.M. 1978. Emperical equations for some soil hydraulic properties. Water Resources
Research, Vol. 14., No. 4., 601604
Corradini, C., Melone, F. and Smith, R.E. 1994. Modeling infiltration during complex rainfall sequences. Water
Resources Research, Vol. 30., No. 10, 27772784
Dickenson, R.E. and HendersonSellers, A. 1988. Modelling tropical deforestation: A study of GCM landsurface parameterizations, Q.J.R. Meterological Society, Vol.
114., 439462
Duan, Q., Sorooshian, S. and Gupta, V.K. 1992. Effective and efficient global optimization for conceptual rainfallrunoff models. Water Resources Research, Vol. 28, No.4,
10151031
DuBoys, M.P. 1879. Le Rhone et les Rivieres a Lit affouillable, Mem. Doc. Ann. Pont et Chaussees, Ser. 5
Vol. 18
Engelund, F. and Hansen, E. 1967. A Monograph on Sediment
Transport in Alluvial Streams, Teknisk Forlag,
Copenhagen, 62 pp.
Faures, J.M. 1990. Sensitivity of runoff to small scale spatial variability of observed rainfall in a distributed model. M.S. Thesis. University of Arizona.
288
Tucson
Faures, J.M., Goodrich, D.C., and Woolhiser, D.A. 1995.
Impact of smallscale spatial rainfall variability on runoff modeling. Journal of Hydrology Vol. 173,, No.
4.
Federer, C.A. 1995. BROOK90, A Simulation Model for
Evaporation, Soil Water, and Streamflow. Version 3.1
Computer Freeward and Documentation. USDA Forest
Service, P.O. Box 640, Durham, N.H. 03824
Federer, C.A., Vorosmarty, C. and Fekete, B. 1996.
Intercomparison of methods for calculating portential evaporation in regional and global water balances,
Water Resources Research, Vol. 32., No. 7., 23152321
Fernandes, N.F. and Dietrich, W.E. 1997. Hillslope evolution by diffusive processes: The timescale for equilibrium adjustments. Water Resources Research, Vol. 33, No. 6.,
13071318
Fisher, J.S., Sill, B.L., and Clark, D.F. 1983. Organic detritus particles: Initiation of motion criteria on sand and gravel beds. Water Resources Research, Vol.19,
No. 6, 16271631
Flint, J.J. 1974. Stream gradient as a function of order, magnitude and discharge. Water Resources Research, Vol.
10, No. 5., 969973
Freedman, V.L. 1996. Erosion Parameter Identification in
Overland Flow Areas: Application of a Global and Local
Search Algorithm. Unpublished M.S. Thesis. School of
Renewable Natural Resources, University of Arizona,
Tucson, Az.
Freedman, V.L., Lopes, V.L. and Hernandez, M. 1998.
Parameter identifiability for catchmentscale erosion modeling: a comparison of optiiaization algorithms.
Journal of Hydrology, Vol. 207, 8397
Freeze, R.A. 1980. A stochasticconceptual analysis of rainfallrunoff processes on a hillslope. Water
Resources Research, Vol. 16, No. 2, 391408
289
Frostick, L.E. and Reid, I. 1979. Drainagenet control of sedimentary parameters in sandbed ephemeral streams.
P. 173201 in: Geographical Approaches to Fluvial
Processes^ A. Pitty (Ed) Norwich: Geobooks
Garbrecht, J and Campbell. J. 1997. TOPAZ VI.2: An
Automated Digital Landscape Analysis Tool for
Topographic Evaluation, Drainage Identification,
Watershed Segmentation and Subcatchment
Parameterization. Rpt. GRL #974 USDAARS Grazinglands
Research Laboratory El Reno, Ok
Gee, G.W. and Bauder, J.W. 1986. Particle size analysis, p.
383403 In: Methods of Soil Analysis Part 1  Physical and Mineralogical Methods. Second Edition. Klute, A.
(Ed) Soil Science Society of America
Gilbert, G.K. 1877. Geology of the Henry Mountains. QSGS
160pp.
Gilbert, G.K. 1909. The convexity of hilltops. Journal of
Geology, Vol. 17, 344350
Gilbert, G.K. 1914. The transport of debris by running
Water, US Geological Survey Professional Paper No. 86
Goodrich, D.C. 1990. Geometric simplification of a distributed rainfallrunoff model over a range of basin scales. Ph.D. Dissertation. University of Arizona.
Goodrich, D.C., Faures, J.M., Woolhiser, D.A., Lane, L.J. and Sorooshian, S. 1995. Measurement and analysis of smallscale convective storm rainfall variability.
Journal of Hydrology, Vol. 173., No. 4., 283308
Goovaerts, P., 1998. Ordinary cokriging revisited.
Mathematical Geology, Vol. 30, No. 1, 2142
Gomez, B. and Church, M. 1989. An assessment of bed load sediment transport formulae for gravel bed rivers.
Water Resources Research, Vol. 25, 11611186
Green, W.H. and Ampt, G.A. 1911. Studies on soil physics I.
The flow of air and water through soils. Journal of
Agricultural Sciences, Vol. 4, No. 1, 124
290
Hack, J.T. 1957. Studies of longitudinal stream profiles in
Virginia and Maryland. U.S. Geogolical Survey
Professional Paper 292B, 4597
Haff, P.K. 1996. Limitations on predictive modeling in geomorphology. pp. 337358 in: The Scientific Nature of
Geomorphology; Proceedings of the 27*^^ Binghamton
Symposium in Geomorphology. Rhodes, B.L. and Thorn,
C.E. John Wiley
Hawkins, R.H., Lopes, V.L., Parker, R.A. and Weltz, M.A.
1991. Effects of global climate change on erosion stability in arid environments using WEPP. p. 8591
In: Proceedings of United StatesPeople's Republic of
China Bilateral Symposium on Droughts and Arid Region
Hydrology; US Geological Survey Open File Report 91
224,
Helvesi, J.A., Istok, J.D. and Flint, A.L. 1992.
Precipitation in mountainous terrain using multivariate geostatistics. Part I: structural analysis. Journal of
Applied Meteorology, Vol. 31, No.7, 666676
Hernandez, M. 1992. Analysis of the quasistate approximation on parameter identifiability for a dynamic soil erosion model. Unpublished Ph.D.
Dissertation. School of Renewable Natural Resources.
University of Arizona, Tucson, Az.
Hornberger, G.M., Beven. K.J., Cosby, B.J. and Sappington,
D.E. 1985. Shenendoah Watershed study: calibration of a topographybased, variable contributing area, hydrologic model to a small forested catchment. Water
Resources Research, Vol. 21, 18411850
Horton, R.E. 1945. Erosional development of streams and their drainage basin; Hydrophysical approach to quatitative morphology. Geological Society of America
Bulletin, Vol. 56, 275370
Jensen, K.H. and Mantoglou, A. 1992. Future of distributed
Modelling, Hydrological Processes, Vol. 6, 255264
Julien, P. Y., Saghafian, B., and Ogden, F.L. 1995. Rasterbased hydrologic modeling of spatiallyvaried surface runoff. Water Resources Bulletin, Vol. 31, No. 3, 523
536.
291
Julien, P.Y. 1995. Erosion and Sedimentation^ Cambridge
Press, 280 pp.
Julien P.Y and Simons, D.B. 1985. Sediment transport capacity of overland flow. Transactions of the American
Society of Agricultural Engineers, Vol. 28, p.755762
Kirkby, M.J. 1971. Hillslope processresponse models based on the continuity equation. Institute of British
Geographers Special Publication, No. 3, 1530
Kirkby, A.V.T. and Kirkby, M.J. 1974. Surface wash at the semiarid break in slope, Zeitschrift fur
Geomorphologie, Supplementband No. 21, 151176
Korner, C. 1994. Leaf diffusive conductances in the major vegetation types of the globe, pp. 463490 in:
Ecophysioloqy of Photosynthesis. Schulze, E.D. and
Caldwell, M.M. (Eds) SpringerVerlag, New York
Knisel, W.G. (editor). 1980. CREAMS: A Field Scale Model for
Chemicals, Runoff, Erosion and Agricultural Management
Systems. QSDA Science and Education Administration
Conservation Research Report No. 26, pp. 643
Laguna, A. and Girardez, J.V. 1993. A kinematic wave model of erosion. Journal of Hydrology, Vol. 145, 6583
Lane, E.W., Brown, C., Gibson, G.C., Howard, C.S., Kriombein,
W.C., Mathes, G.H., Rubey, W.W., Trowbridge, A.C. and
Staub, L.G. 1947. Report of the subcommittee on sediment terminology. Transactions of the American
Geophysical Union, Vol. 28, No. 6, 936938
Levenberg. K. 1944. A method for the solution of certain nonlinear problems in least squares, Q. of Appl. Math.
Vol. 2, 164168
Li, E.A., Schanholz, V.O. and Carson, E.W. 1996. Estimating
Saturated Hydraulic Conductivity and Capillary
Potential at the Wetting Front. Dept. of Agr. Eng.
Virginia Polytech Inst, and State University,
Blacksburg, Va.
Lopes, V.L. 1987. A Numerical Model of Watershed Erosion and
Sediment Yield. Ph.D. Dissertation. University of
Arizona, Tucson.
292
Lopes, V. L., 1996. On the effect of uncertainty in spatial distribution of rainfall on catchment modeling, Catena,
Vol. 28, 107119
Lopes, V.L. and Lane, L.J. 1990. Simulating runoff and sediment yield on semiarid watersheds. In: ASCE
National Symposium on Watershed Management. Durango,
Co., 174183
Marquartdt, D.W. 1963. An algorithm for leastsquares estimation of nonliear parameters. Journal of the
Society of Industrial and Applied Mathematics, Vol. 11,
No. 2, 431441
MartinezCob, A. 1996. Multivariate geostatistical analysis of evapotranspiration and precipitation in mountainous terrain, Journal of Hydrology, Vol. 174, 1935
Meyer, L.D. 1984. Evolution of the Universal Soil Loss
Equation, Journal of Soil and Water Conservation, Vol.
39, No. 2, 99104
Myers, D.E. 1982. Matrix formulation of cokriging.
Mathematical Geology, Vol. 14, No. 3, 249257
Myers, D.E. 1983. Estimation of linear combinations and co
Kriging, Mathematical Geology, Vol. 15, No. 5, 633637
Myers, D.E. 1984. Cokriging  new developments, p. 295305 in: Geostatistics for Natural Resources
Characterization. Part 1. D. Reidel publishing
Michaud, J.D. and Sorooshian, S. 1994. Effect of rainfallsampling errors on simulations of desert flash floods,
Water Resources Research, Vol. 30, No. 10, 27652775
Montgomery, D.R., Abbe, T.B., Buffington, J.M., Petersen,
N.P., Schmidt, K.M. and Stock, J.D. 1996. Distribution of bedrock and alluvial channels in forested mountain drainage basins. Nature, Vol. 381, 587589
Montgomery, D.R. and Dietrich, W.E. 1988. Where do channels begin?. Nature, Vol. 336, 232234
Montgomery, D.R. and Dietrich, W.E. 1989. Source areas, drainage density and channel initiation. Water
Resources Research, Vol. 23, 19071918
293
Montgomery, D.R. and Dietrich, W.E. 1992. Channel initiation and the problem of landscape scale. Science, Vol. 255,
826830
Montgomery, D.R and Dietrich, W. E. 1994. Landscape dissection and drainage areaslope thresholds, p. 221
246 In: Process Models and Theoretical Geomorphology,
M.J. Kirkby (Ed) John Wiley
Nash, J.E. and Sutcliffe, J.V. 1970. River flow forcasting through conceptual models, I. A discussion of principles. Journal of Hydrology, Vol. 10, 282290
Nelder, J.A. and Mead, R. 1965. A simplex method for function minimization. The Computer Journal, Vol. 7,
No. 4, 308313
Nearing, M.A., Lane, L.J. and Lopes, V.L. 1994. Modeling soil erosion, p. 127156 In: R. Lai (Ed.) Soil Erosion
Research Methods. 2nd. Ed. Soil and Water Conservation
Society. Ankeny, la.
Odeh, I.O.H., McBratney, A.B. and Chittelborough, D.J.
1994. Spatial prediction of soil properties from landform attributes derived from a digital elevation model, Geoderma, Vol. 63, 197214
O'Loughlin, E.M. 1986. Prediction of surface saturation zones in natural catchments by topographic analysis.
Water Resources Research. Vol. 22, No. 5, 794804
Osborn, H.B. and Hickok, R.B. 1968. Variability of rainfall affecting runoff from a semiarid rangeland watershed.
Water Resources Research, Vol. 4, 199203
Phillip, J.R. 1980. Field heterogeneity: some basic issues.
Water Resources Research, Vol. 16, 443448
Pilotti, M. 1996. Identification and analysis of natural, channel networks from digital elevation models. Earth
Surface Processes and Landforms, Vol. 21, No. 11, 1007
1020
Post, D.F, Bryant, R.B., Batchily, A.K., Huete, A.R.,
Levine, S.J., Mays, M.D. and Escadafal. 1993.
Correlations between field and laboratory measurements of soil color. In Soil Color, Soil Science Society of
America, Special Piiblication No. 31, 3549
294
Prosser, I.P., Bowling T.I., Rustomji, P. 1998. Catchment
Scale Sediment Delivery to Streams: Linking Process
Models, Network Structure and Hillslope Topography. AGU
Spring Meeting Abstracts with Program
RodriguezIturbe, I. and Mejia, J.M. 1974. The design of rainfall networks in time and space. Water Resources
Research, Vol. 10, No.4, 713728
Ritter, D.F. 1978. Process Geomorphology. Wm. C. Brown
Publishing. Dubuque, Iowa. 603pp
Ruhe, R.V. 1969. Quaternary Landscapes In Iowa; Iowa State
University Press, Ames. 255p.
Schaefer, M.G. 1979. The Zero Order Watershed. Unpublished
Ph.D. Dissertation. University of MissouriRolla,
Missouri, 69 p.
Simaton, J.R. and Renard, K.G. 1985. Time related changes in rangeland erosion. In: Proceedings of the Rainfall
Simulator Workshop, January 1415, 1985. Tucson,
Arizona
Smith, R.E., Goodrich, D.C. and Unkrich, C.L. in press.
Simulation of selected events on the Catsop Catchment by KIJIER0S2  A report for the GCTE Conference on
Catchment Scale Erosion Models
Smith, R.E., Goodrich, D. C., Woolhiser, D.A. and Unkrich,
C.L. 1995. KINEROS  A Kinematic Runoff and Erosion
Model, Ch. 20. p. 697632. In: Computer Models of
Watershed Hydrology, V.J. Singh (Ed), Water Resources
Publications,
Smith, R.E and Parlange, J.Y. 1978. A parameterefficient hydrologic infiltration model. Water Resources
Research, Vol. 14, No. 3, 533538
Smith, T.R. and F.P.Bretherton. 1972. Stability and conservation of mass in drainage basin evolution. Water
Resources Research, Vol. 8, No. 6, 15061529
Shields, A. 1936. Anwendun der Ahnlichkeitsmechanik und
TurbulenzforsChung auf die Gescheibebewegung, Mitteil.,
PVWES, Berlin, no. 26
295
Shuttleworth, W.J. and Wallace, J.S. 1985. Evaporation from sparse cropsan energy combination theory, Quarterly
Journal of the Royal Meteorological Society, Vol. Ill,
839855
Storm, B., Jorgensen, G.R. and Styczen, M. 1987. Simulation of water flow and erosion processes with a distributed physicallybased modeling system, p.595608 In: Forest
Hydrology and Watershed Management. Swanson, R.H. ,
Bernier, P.Y. and Woodward, P.D. (Eds)IAHS publication
No. 167
Srahler, A.N. 1964. Quantitative geomorphology of drainage basins and channel networks, pp. 439  476 In:
Handbook of Hydrology, V.T. Chow (Ed), McGrawHill, New
York.
Tarboton, D.G, Bras, R.L. and RodriguezIturbe, I. 1989.
Scaling and elevation in river networks. Water
Resources Research, Vol. 25, No. 9, 20372051
Tucker, G.E., and Slingerland, R. 1997. Drainage basin response to climate change. Water Resources Research.
Vol. 33, No. 8, 20312047
Wackernagel, H. 1995. Multivariate Geostatistics: An
Introduction with Applications. SpringerVerlag. Berlin
256pp.
Walker, R.G. and Cant, D.J. 1979. Sandy fluvial systems, p.
2332 In: Facies Models. Walker, R.G. (Ed.). Geoscience
Canada Reprint Series 1.
Whitaker, M.P.L., 1993. Smallscale spatial variability of soil moisture and hydraulic conductivity in a semiarid rangeland soil in Arizona. Unpublished Master of
Science Thesis. University of Arizona
Wiberg, P.L. and Smith, J.D. 1987. Calculation of the critical shear stress for motion of uniform and heterogeneous sediments. Water Resources Research, Vol.
23, No. 8, 14711480
Wicks, J.M, Bathurst, J.C. and Johnson, C.W. 1992.
Calibrating the SHE soilerosion model for different land covers. ASCE, Journal of the Irrigation and
Drainage Engineering, Vol. 118, No. 5, 708723
296
Wicks, J.M. and Bathurst, J.C. 1996. SHESED: A physicallybased, distributed erosion and sediment yield component for the SHE hydrological modelling system. Journal of
Hydrology, Vol. 175, 213238
Wilcock, P.R., 1998. Twofraction model of initial sediment motion in gravelbed rivers, Science, Vol. 280, 410412
Willgoose, G. 1994. A physical explanation for an observed areaslopeelevation relationship for catchments with decilining relief. Water Resources Research, Vol. 30,
No. 2, 151159
Willgoose, G., Bras, R.L., and RodriguezIturbe, I. 1991a. A coupled channel, network growth and hillslope evolution model 1: Theory, Water Resources Research, Vol. 27, No.
7, 16711684
Willgoose, G., Bras, R.L., and RodriguezIturbe, I. 1991b. A coupled channel, network growth and hillslope evolution model 2: Aplication, Water Resources Research, Vol. 27,
No. 7,16851696
Willgoose, G., Bras, R.L., and RodriguezIturbe, I. 1991c. A physical explanation for an observed link areaslope relationship. Water Resources Research, Vol. 27, No. 7,
16971702
Willgoose, G. and Riley, S. 1993. The assessment of the longterm erosional stability of engineered structures of a proposed mine rehabilitation, p. 66767J In:
Environmental Management, GeoWater and Engineering
Aspects. Choudury and Sivakumar, (eds)
Wischmeier, A.H. and Smith, D.D. 1978. Predicting rainfall erosion losses a guide to conservation planning. Agr. handbook No. 537, USDA. Washington D.C., 58 pp.
Woolhiser, D.A. and Goodrich, D.C. 1988. Effect of storm rainfall intensity patterns on surface runoff. Journal of Hydrology, Vol. 102, 335354
Woolhiser, D.A., Smith, R.E. and Goodrich, D.C. 1990. A kinematic runoff and erosion model: Docxamentation and user manual. Report #77. Agricultural Research Service,
United States Department of Agriculture
IMAGE EVALUATfON
TEST TARGET (QA3)
/
€ i
<is
< e
1 oomm
6
1653 East Main Street
Roctiester. NY 14609 USA
Ptione: 716/4820300
Fax: 716/2885989
* Your assessment is very important for improving the work of artificial intelligence, which forms the content of this project
Related manuals
advertisement