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Hysteretic, variably saturated, transient flowand transport models with numerical inversion

techniques to characterize a field soil in central Arizona

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Authors Thomasson, Mark John

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HYSTERETIC, VARIABLY SATURATED, TRANSIENT FLOW AND TRANSPORT MODELS WITH NUMERICAL INVERSION TECHNIQUES TO CHARACTERIZE A

FIELD SOIL IN CENTRAL ARIZONA

by

Mark J. Thomasson

Copyright © Mark J. Thomasson 2000

A Dissertation Submitted to the Faculty of the

DEPARTMENT OF HYDROLOGY AND WATER RESOURCES

In Partial Fulfillment of the Requirements For the Degree of

DOCTOR OF PHILOSOPHY WITH A MAJOR IN HYDROLOGY

In the Graduate College

THE UNIVERSITY OF ARIZONA

2000

UMI Number: 9992070

Copyright 2000 by

Thomasson, Mark John

All rights reserved.

UMI UMI Microform 9992070

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unauthorized copying under Title 17, United States Code.

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P.O. Box 1346 Ann Arbor. Ml 48106-1346

2

THE UNIVERSITY OF ARIZONA ® GRADUATE COLLEGE

As members of the Final Examination Committee, we certify that we have

read the dissertation prepared by J- Thomasson

entitled Hysteretic, Variably Saturated. Transient Finw anH

Transport Models with Numerical Inversion Techniques to

Characterize a Field Soil in Central Arizona

and recommend that it be accepted as fulfilling the dissertation

requirement for the Degree of Doctor of Philosophy

/ J Zdoo Date ' Dr. Pe J. wiere

dy L. Bassett Date

/0/4 Date

0 ?) "E?

Sr. Arthur W. Warrick

Date

Date

Dr. Tian-Chyi J. \ ) Date Final approval and acceptance of this dissertation is contingent upon the candidate's submission of the final copy of the dissertation to the Graduate College.

I hereby certify that I have read this dissertation prepared under my direction and recommend that it be accepted as fulfilling the dissertation requirement.

)issertation^irect

-7/ ,7 Qrr -̂ Di ssertaticfn Di

-2. Dr. Peter J. Wierenga Date

»-o

rector Dr. Randy L. Bassett li /J Date

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 acknowledgment of source is made. Requests for permission for extended quotation from or reproduction of this manuscript in whole or in part may be granted by the copyright holder.

SIGNED:

4

ACKNOWLEDGEMENTS

Many people were involved in the successful completion of this dissertation. I

would first like to thank my committee for their valuable time and input: Dr. Peter

Wierenga, Dr. Randy Bassett, Dr. Paul Ferre, Dr. Arthur Warrick, Dr. Shlomo Neuman,

and Dr. Jim Yeh.

I thank Dr. Peter Wierenga and the College of Agriculture for funding this

research. Dr. Wierenga has provided me with thoughtful guidance throughout this

project and his keen observations and questions have challenged me to grow as a

scientist. Dr. Wierenga also dedicated a tremendous amount of his time to the reading

and editing of this dissertation.

Dr. Randy Bassett has supplied me with a great deal of invaluable mentoring

throughout my graduate academic career. He has consistently contributed

encouragement and expert advice. Dr. Bassett's enthusiastic approach to teaching and

research has always inspired me to match his enthusiasm. In addition. Dr. Bassett

provided numerous opportunities to grow as an instructor, encouraging me to teach a

wide range of topics in his classes.

I thank Dr. Paul Ferre for the copious amount of time he has spent with me

discussing both my research ideas and the challenges I have faced during the course of

this project. His perceptiveness and impressive scientific knowledge have not only

offered me many ways to overcome obstacles, but also have stimulated a wealth of new

directions to explore.

Dr. Arthur Warrick, Dr. Shlomo Neuman, and Dr. Jim Yeh, have all given their

time to explore specific issues and have challenged me, through their courses, to

continue to develop my scientific knowledge.

Finally, there are a number of people that I have encountered throughout my

graduate academic career that have enhanced my experience at Arizona: Rob, Ty,

Leslie, Dave, Lori, Ingrid, Emory, Eric, and Evan. Most importantly, a big thank you

and much love to Alissa and Bo.

DEDICATION

To my friends and family with love. Thank you.

6

TABLE OF CONTENTS

LIST OF FIGURES 8

LIST OF TABLES 13

ABSTRACT 14

1. INTRODUCTION AND OBJECTIVES 16 l . L O v e r v i e w 1 6 1.2. Objectives 16

2. INFILTRATION EXPERIMENTS 19 2.1. Site Description 19 2.2. Infiltration and Transport Experiments 20

3. FLOW IN VAIUABLY SATLFRATED HETEROGENEOUS MEDL\ INCORPORATING HYSTERESIS 29 3.1. Introduction 29 3.2. Materials, Methods, and Theory 30

3.2.1. Water Budget 30 3.2.2. Modeling Water Flow 31

3.3. Results and Discussion 46 3.3.1. Textural Characterization 46 3.3.2. Water Budget 46 3.3.3. Simulation of Cases I and II 59 3.3.4. Comparison of Cases II and III: Incorporating Hysteresis 64 3.3.5. Simulation of Cases IV and V 71 3.3.6. Water Contents with Depth, Experiment 1 72 3.3.7. Simulation of Cases VI and VII, Experiment II 78

3.4. Conclusions 83

4. FIELD SCALE SOLUTE TRANSPORT THROUGH VARIABLY SATURATED MEDIA INCORPORATING HYSTERESIS 86 4.1. Introduction 86 4.2. Transport Models 89

4.2.1. Parameter Estimation and Analytical Solutions to Solute Transport 89 4.2.2. Numerical Modeling of Solute Transport 92

4.3. Measured Bromide Concentrations 95 4.4. Methods 101

4.4.1. Mass Balance 101 4.4.2. Approach 102

4.4.2.1. Parameter Estimation 103 4.4.2.2. Predictions Using an Analytical Model 105

7

TABLE OF CONTENTS - Continued

4.4.2.3. Numerical Solute Transport Simulations 107 4.5. Results and Discussion 113

4.5.1. Mass Balance 113 4.5.2. Modeling 117

4.5.2.1. Parameter Estimation, Cases I and II 117 4.5.2.2. Evaluation of the Local and Global Approaches Using Analytical

Models, Cases in - VI 119 4.5.2.3. Numerical Solute Transport Simulations, Cases VII - X 122

4.5.2.3.1 Effect of Hysteresis on Bromide Transport 122 4.5.2.3.2 Preferential Transport 130

4.6. Conclusions 145

5. CONCLUSIONS 149

APPENDIX: CHARACTERIZATION 157

REFERENCES 167

8

LIST OF FIGURES

Figure 2.1. Location of the Maricopa Agricultural Center (MAC) 21

Figure 2.2. Experimental plot showing locations where data were collected 22

Figure 2.3. Monitoring island schematic 23

Figure 2.4. Input concentrations of bromide during Experiment 1 28

Figure 3.1. Locations where soil cores were collected 36

Figure 3.2. Representative soil tension profile for the monitoring island locations 40

Figure 3.3. Hydraulic conductivity versus water content. Solid circles are the field-calculated values fi'om O.S to 3 m in 0.5 m intervals; the solid line is based on a laboratory-derived value of 45.8 cm d"' for Ks, the solid line with open circles is based on a Ks of450 cm d ' 41

Figure 3.4. Model initial conditions and observed initial conditions. The circles represent the mean observed water contents. The horizontal lines represent ± one standard deviation and the solid line represents the interpolated water contents used in the model (HYDRUS) 44

Figure 3.5. Mean percent sand, silt, and clay composition at three locations 47

Figure 3.6. Mean percent gravel (circles) and mean measured water content (solid line) versus depth 48

Figure 3.7. Spatial distribution of the water budget data for irrigation day 4, 1.0 m depth. Diamonds represent vertical neutron probe access tube locations. The numbers represent under- or over-estimation of water applied (in percent) relative to the water meter data. On average the neutron probe data over- predicted how much was actually applied by 28.4 percent 50

Figure 3.8. Spatial distribution of the water budget data for irrigation day 5, 1.0 m depth. Diamonds represent vertical neutron probe access tube locations. The numbers represent under- or over-estimation of water applied (in percent) relative to the water meter data. On average the neutron probe data under- predicted how much was actually applied by 17.6 percent 51

Figure 3.9. Spatial distribution of the water budget data for irrigation day 18, 9.0 m depth. Diamonds represent vertical neutron probe access tube locations. The numbers represent under- or over-estimation of water applied (in percent) relative to the water meter data. On average the neutron probe data over- predicted how much was actually applied by 0.2 percent 53

9

LIST OF FIGURES - Continued

Figure 3.10. Computed water depths applied versus the water depths applied according to the water meters for 34 access tube locations on irrigation days when data are available. The dashed line represents +/- 32 percent error from the true amount applied 55

Figure 3.11. Computed water depths applied versus the water depths applied according to the water meters for the perimeter access tube locations (8 locations). The dashed line represents +/- 32 percent error from the true amount applied 56

Figure 3.12. Computed water depths applied versus the water depths applied according to the water meters for the access tube locations located at least 5 m within the irrigated perimeter (26 locations). The dashed line represents +/- 32 percent error from the true amount applied 58

Figure 3.13. Comparison of the mean measured and predicted water contents and wetting front arrivals at the 7.5 m depth. The vertical lines denote ± one standard deviation in the mean water content 62


Figure 3.15. Comparison of the simulated water content time series to the mean measured water contents for the 1.5 m depth. Triangles depict tension 66



Figure 3.18. Retention curves for hysteretic model and models based on parameters derived from wetting experiments and drying experiments 69

Figure 3.19. Comparison of the mean measured and predicted water contents and wetting front arrivals at the 7.5 m depth. The vertical lines denote ± one standard deviation in the mean water content. A, Case III with Ks = 250.0 cm d"', B, Case II with Ks = 450.0 cm d"', C, Case V with Ks = 1250.0 cm d ', D, Case IV with Ks = 450.0 cm d"' 73

Figure 3.20. Water content measurements and model predictions for day 22. The circles represent measured water contents 74



10


Figure 3.23. Model initial conditions and observed initial conditions for Experiment II. The circles represent the mean observed water contents. The horizontal lines represent ± one standard deviation and the solid line represents the interpolated water contents used in the model (HYDRUS) 79




Figure 4.1. Model initial conditions and observed initial conditions. The circles represent the mean observed water contents. The horizontal lines represent ± one standard deviation and the solid line represents the interpolated water contents used in the model (HYDRUS). The dashed line represents the initial conditions for the bromide used in the model (HYDRUS) 94

Figure 4.2. Relative bromide concentrations from the NMI, east side 96

Figure 4.3. Relative bromide concentrations from the NMI, west side 97

Figure 4.4. Relative bromide concentrations from the SMI, east side 98

Figure 4.5. Relative bromide concentrations from the SMI, west side 99

Figure 4.6. Amounts of bromide recovered at the monitoring islands from day 5 to day 15, the solid line represents 100 percent recovery 114

Figure 4.7. Comparison of measured bromide data and the predicted bromide concentrations at the SMI, west location. The solid line represents model predictions from Case III based on transport properties estimated locally (Case I), the dashed line represents model predictions from Case IV based on transport properties estimated globally (Case II) 120

Figure 4.8. Comparison of measured bromide data and the predicted bromide concentrations at the monitoring island locations. The dashed line represents model predictions from Case V based on average transport properties estimated locally (Case I), the solid line represents model predictions from Case VI based on transport properties estimated globally (Case II) 123

II


Figure 4.9. Comparison of all measured bromide data from around the monitoring islands and the predicted bromide concentrations. The solid line represents model predictions with hysteresis in the hydraulic properties (Case VIII); the solid line with solid diamonds represents model predictions with no hysteresis in the hydraulic properties (Case VII) 124

Figure 4.10. Measured bromide concentrations and model predictions for day 16, irrigation day 16 127

Figure 4.11. Measured bromide concentrations and model predictions for day 24, the last day of irrigation 128

Figure 4.12. Measured bromide concentrations and model predictions for day 93, the last measured day of redistribution 129

Figure 4.13. Comparison of measured bromide data and the predicted bromide concentrations at the monitoring island locations, 50 cm depth. The solid line with triangles represent results from Case VI (analytical model, R = 0.87), the solid line represents results from Case VIII {R ~ 0.87), the dashed line represents results from Case IX (/? ~ 1.0), the solid line with solid circles represents results from Case VIII (/? ~ 0.8) 131

Figure 4.14. Comparison of measured bromide data and the predicted bromide concentrations at the monitoring island locations, 100 cm depth. The solid line with triangles represent results from Case VI (analytical model, R = 0.87), the solid line represents results from Case VIII {R ~ 0.87), the dashed line represents results from Case IX (/? ~ 1.0), the solid line with solid circles represents results from Case VIII (/?-0.8) 132

Figure 4.15. Comparison of measured bromide data and the predicted bromide concentrations at the monitoring island locations, 150 cm depth. The solid line with triangles represent results from Case VI (analytical model, R = 0.87), the solid line represents results from Case VIII {R ~ 0.87), the dashed line represents results from Case IX (/? ~ 1.0), the solid line with solid circles represents results from Case VIII (/?-0.8) 133

Figure 4.16. Comparison of measured bromide data and the predicted bromide concentrations at the monitoring island locations, 200 cm depth. The solid line with triangles represent results from Case VI (analytical model, R = 0.87), the solid line represents results from Case VIII {R ~ 0.87), the dashed line represents results from Case IX (/? ~ 1.0), the solid line with solid circles represents results from Case VIII (/?~0.8) 134

12


Figure 4.17. Comparison of measured bromide data and the predicted bromide concentrations at the monitoring island locations, 250 cm depth. The solid line with triangles represent results from Case VI (analytical model, R = 0.87), the solid line represents results from Case VIII {R ~ 0.87), the dashed line represents results from Case IX (/? ~ 1.0), the solid line with solid circles represents results from Case VIII (/? ~ 0.8) 135

Figure 4.18. Comparison of measured bromide data and the predicted bromide concentrations at the monitoring island locations, 300 cm depth. The solid line with triangles represent results from Case VI (analytical model, R = 0.87), the solid line represents results from Case VTII {R ~ 0.87), the dashed line represents results from Case IX (/? ~ 1.0), the solid line with solid circles represents results from Case Vin(/?~0.8) 137

Figure 4.19. Comparison of measured bromide data and the predicted bromide concentrations at the NMI, west location. The solid line represents model predictions from Case VTU {R ~ 0.87), the dashed line represents model predictions from Case IX (/? = 1.0, Young et al., 1999), and the solid line with solid circles represents model predictions from Case VIII {R ~ 0.80) 138

Figure 4.20. Comparison of measured bromide data and the predicted bromide concentrations at the NMI, east location. The solid line represents model predictions from Case VIII {R ~ 0.87), the dashed line represents model predictions from Case IX (/? = I.O, Young et al., 1999), and the solid line with solid circles represents model predictions from Case VTII (/? ~ 0.80) 139

Figure 4.21. Comparison of measured bromide data and the predicted bromide concentrations at the SMI, west location. The solid line represents model predictions from Case VIII (/? ~ 0.87), the dashed line represents model predictions from Case IX (^ = 1.0, Young et al., 1999), and the solid line with solid circles represents model predictions from Case VIII (/? ~ 0.80) 140

Figure 4.22. Comparison of measured bromide data and the predicted bromide concentrations at the SMI, east location. The solid line represents model predictions from Case VTII (/? ~ 0.87), the dashed line represents model predictions from Case IX (/? = 1.0, Young et al., 1999), and the solid line with solid circles represents model predictions from Case VIII {R - 0.80) 143

Figure 4.23. Comparison of all measured bromide data from around the monitoring islands and the predicted bromide concentrations. The solid line represents model predictions using a uniform input concentration (Co = 31.6 mg /1, Case VIII); the dashed line represents model predictions using variable input concentrations (Figure 2.4, Case X) 144

13

LIST OF TABLES

Table 2.1. Tabulated values of applied water for Experiment 1 26

Table 2.2. KBr applied during Experiment I* 27

Table 3.1. Mean Hydraulic Properties and the statistical parameters for the core samples obtained by the various laboratory methods 37

Table 3.2. Calculated unsaturated hydraulic conductivity values for the NMI and SMI locations 42

Table 3.3. Summary of mean hydraulic properties used in models 45

Table 3.4. Computed depths of water added on irrigation day 5 at 1.0 m 52

Table 3.5. Mean square error* for Cases I - VTI 60

Table 3.6. Saturated hydraulic conductivity values used for Cases I - VII 63

Table 4.1. Breakthrough times for the monitoring island locations 100

Table 4.2. Locations where bromide breakthrough occurred within the irrigation timeframe 104

Table 4.3. Input parameters used in the inverse models. Cases I and II 106

Table 4.4. Transport parameters for the analytical model, Cases III - VI 106

Table 4.5. Mean transport properties used in the numerical models, Cases VII - IX.. 109

Table 4.6. Summary of test cases for field scale solute transport 112

Table 4.7. Estimated transport properties from Cases I and II 118

Table 4.8. MSE values for Cases III - VI 121

Table 4.9. Mean transport properties from Cases I and II used in Cases V and VI 121

Table 4.10. Mean square error for Cases VI - IX using average measured bromide concentrations 125

14

ABSTRACT

Field-measured data collected from infiltration experiments conducted at the Maricopa

Agricultural Center, Arizona, and one-dimensional numerical models were used in an

iterative approach to develop conceptual models of unsaturated flow and transport.

Conceptual models were developed using field data, estimates of hydraulic and

transport properties, and assimiptions regarding the types of processes occurring in the

field plot. Using the field data and numerical models in an iterative approach revealed

that adjustments to the parameterization of the conceptual models were necessary to

allow for acceptable predictions of flow and transport. In addition, the numerical

models delineated where the conceptual models needed adjustment and indicated where

further analysis of the field data was necessary. Specifically, in regards to the

unsaturated water flow, it was found that: 1) without increasing the laboratory

determined value of Ks tenfold, it was impossible to make acceptable predictions for the

infiltration experiments; 2) the laboratory-derived hydraulic properties provided a

superior first approximation to texturally based hydraulic properties taken from an

internal database; 3) incorporation of hysteresis into the soil hydraulic functions

resulted in predictions of the water contents through time and soil water content profiles

that were marginally better than not incorporating hysteresis; and 4) based on the mean

square errors of the predictions and a post-audit based on the adjusted hydraulic

properties, the use of a homogeneous soil profile was supported. In regard to the

unsaturated solute transport, it was found that: I) inversion techniques to estimate the

15

unsaturated transport properties at each location (local approach) yielded the best results

with respect to the fit of the data compared to the techniques which fit data from all

depths simultaneously (global approach); 2) predictions using unsaturated transport

properties averaged fi-om the global approach yielded the best results compared to the

average local approach properties; 3) incorporating hysteresis had little effect on the

predicted bromide breakthrough curves and concentration profiles, yielding only

marginally better results than predictions fi-om models with no hysteresis; 4) it was

impossible to accurately predict the breakthrough of bromide at depths deeper than 200

cm without using a retardation factor less then one.

16

1. INTRODUCTION AND OBJECTIVES

1.1. Overview

Topical introductions are offered at the beginning of chapters specific to the

subject being examined. Chapter One outlines the objectives of this dissertation.

Chapter Two gives a description of the experimental plot where the infiltration studies

were conducted and outlines the specific details of the infiltration experiments. Chapter

Three examines the unsaturated water flow. Chapter Four investigates the unsaturated

solute transport. Chapter Five summarizes the conclusions of the unsaturated flow and

transport modeling.

1.2. Objectives

The objective of this dissertation was to use field measured data and numerical

models in an iterative approach to assess and quantify the conceptual model of flow and

transport. Specifically, the objective was to determine how changes to the

parameterization of the conceptual model affect the flow and transport predictions.

This objective was attained by separate treatments of the water flow and the transport of

a solute through a variably saturated heterogeneous field soil. These objectives are

discussed in detail in two chapters: Chapter 3 focuses on simulating the unsaturated

water flow; Chapter 4 investigates the transport of a solute.

17

The simulation of the unsaturated water flow was compared to data obtained from

infiltration experiments conducted at a field plot. The infiltration and redistribution of

water into a large (50 m by 50 m), controlled and monitored field plot was modeled and

the results compared with measured data. Effects of the inclusion of hysteresis in the

retention and hydraulic conductivity functions were determined, and the ability of

laboratory derived hydraulic parameters from core samples to accurately predict the

propagation of the wetting firont under a field setting was examined. Both the wetting

front arrival and the changes in water content using laboratory derived hydraulic

properties incorporating hysteresis were modeled. Sub-objectives of the study were:

1. assess the ability of hydraulic properties measured on soil cores in the laboratory to

represent field properties,

2. compare the results of models using laboratory derived hydraulic properties to

models using hydraulic properties taken from a database based on textural

considerations,

3. examine the effects of incorporating hysteresis into the soil hydraulic functions on

unsaturated flow predictions, and

4. evaluate the validity of using a homogeneous representation of the profile to capture

the average field behavior.

The transport of a solute through a variably saturated field soil was simulated

using analytical and numerical models. This was achieved through integrating the

18

estimation of the transport properties, the development of a conceptual model, and the

impact of the model on transport predictions. The techniques for estimating transport

properties were evaluated and the effects of spatial averaging of point measurements (0,

R, D, a) on the construction of an equivalent porous media were investigated. Location

specific and spatially integrated inversion methods were compared to assess their ability

to characterize the flux and transport properties. Additionally, the impact of averaging

these properties on the prediction of flow and transport and the effects of hysteresis on

solute transport were investigated. Sub-objectives of the study were:

1. use inversion techniques to estimate the solute transport properties,

2. evaluate two schemes for averaging the estimated transport properties and assess

which scheme provides the best results using analytical models,

3. examine the effects of incorporating hysteresis into the soil hydraulic functions on

the solute transport predictions, and

4. assess and examine the effect of the retardation coefficient on the solute transport

predictions.

19

2. INFILTRATION EXPERIMENTS

2.1. Site Description

The field study was conducted by Young et al. [1999] at the Maricopa

Agricultural Center (MAC) of the University of Arizona starting in the spring 1997 and

ending in the summer 1998. The MAC site is located 42 kilometers (km) southwest of

Phoenix [Young et al., 1999] (Figure 2.1). The study was designed and implemented to

evaluate unsaturated zone monitoring techniques and strategies applicable to low-level

radioactive waste (LLW) disposal facilities [Young et al., 1999]. The study consisted of

two successive infiltration experiments.

The MAC site is situated within a northwest trending alluvial basin, situated

within the Basin and Range region. The Basin and Range region is characterized by

northwest to southeast trending mountain ranges separated by broad alluvial valleys

[Resources, 1993]. The alluvium in the basin is anywhere fi-om 60 to 150 meters (m) in

thickness, and is comprised primarily of unconsolidated to slightly consolidated sands

and gravels. Some finer grained lenses are distributed throughout the unit. The

regional groundwater table is at approximately 200 m depth. The site lies in the

alluvium with localized perched zones of groundwater at approximately 11 - 12 m

depth. The region is in a semi-arid environment and receives approximately 20

centimeters (cm) of rainfall annually. Precipitation is characterized by intense, short

duration summer storms and longer duration low intensity winter rains. The region

20

experiences hot siunmers, and mild winters with an average annual temperature of 21°

Celsius.

2.2. Infiltration and Transport Experiments

Solute transport tracer experiments were conducted on a 50 m by 50 m plot

located within field plot F-115 at the MAC site (Figure 2.2). The 50 m by 50 m plot

was covered by a 60 m by 60 m, 0.081 cm thick Hypalon® pond liner to minimize

surface evaporation. The two monitoring islands shown as circles on Figure 2.2 were

constructed using 4 m long, 3.65 m diameter highway culverts placed vertically in 3.7

m diameter auger holes. Through ports in the culvert walls, the undisturbed soil around

the culvert could be accessed (Figure 2.3). Single-chamber solution samplers were

installed through the walls of the north and south monitoring islands (NMI and SMI)

from 0.5 m to a depth of 3.0 m in 0.5 m intervals [Young et al., 1999]. Dual-chamber

solution samplers were installed in the nested boreholes at depths of 3, 5, and 10 m at

the locations shown by solid triangles in Figure 2.2.

Water with potassium bromide (KBr) was applied to the experimental plot using

164 drip lines. The parallel drip lines were spaced 0.3 m apart with self-cleaning

emitters every 0.3 m along the line. A total of 27,000 emitters were so distributed over

the 50 m X 50 m area.

21

M7

Phoenix area

Maricopa site 1-8

1-10

Tucson 100

1-1!

MEXICO

Figure 2.1. Location of the Maricopa Agricultural Center (MAC).

22

Covered area Field Plot F-115

^ Irrigated area

h O Monitoring island

• Neutron probe access tube

Tensiometer

10 meters

Figure 2.2. Experimental plot showing locations where data were collected.

23

Annular backfill

Tensiometers, Single chamber solution sampler

Neutron probe access tube

Plan view Soil Surface

0 m

0.5 m

3.0 m

Side view

Figure 2.3. Monitoring island schematic.

24

Experiment I lasted 93 days, starting April 28, 1997 and ending on July 30,

1997. A KBr solution with a mean concentration of 31.6 milligrams per liter (mg /1)

was applied for 15 days immediately followed by a 9 day application of irrigation water

that contained less than 1.0 mg / 1 of bromide (April 28, 1997 to May 21, 1997) at an

average flux rate of 1.85 centimeters per day (cm d ') (Table 2.1) for an application of

44.4 cm of water and 2.19 x 10^ mg of KBr (Table 2.2). Redistribution of the solute in

the profile was measured for 70 days following cessation of irrigation. Although a

mean value of 31.6 mg / 1 of bromide was applied during Experiment I it should be

noted that the input concentration was quite variable during application with a standard

deviation of 6.1 mg /1 (Figure 2.4). The variability of the input bromide concentrations

cannot be explained by analytical error alone. Other sources of error are incomplete

mixing of the KBr in the mixing tank and a non-uniform distribution of the bromide by

the application system. Young et al. [1999] noted that it was difficult to control the

fluid volume in the mixing tanks thereby creating a variable input bromide

concentration during the irrigation period. Day 12 represents an extreme case of the

mixing problems where the fluid overflowed the top of the mixing tank resulting in a

very low input bromide concentration for that day.

Experiment II lasted 210 days starting on December 3, 1997 and ending July 1,

1998. Water was applied at an average flux rate of 1.97 cm d"' for 33 days (total of 64.8

cm applied) with redistribution measured for the following 177 days. Although no KBr

added to the irrigation water during the infiltration phase of Experiment II, samples

were collected from the solution samplers to quantify the displacement process.

During the 93 days of Experiment I, 898 samples were collected and analyzed for

bromide from the monitoring island locations, 426 of these samples were collected

during the irrigation period. For the duration of Experiment II, 258 samples were

collected and analyzed for bromide from the monitoring island locations. All of these

were collected during the irrigation phase of the experiment.

26

Table 2.1. Tabulated values of applied water for Experiment I

Time Experiment I Experiment II (days) Applied (cm) Sum applied (cm) Applied (cm) Sum applied (cm)

0 1.81 1.81 0.72 0.72 1 1.84 3.64 1.33 2.04 2 1.85 5.49 1.96 4.01 3 1.82 7.31 1.97 5.97 4 1.95 9.26 1.97 7.94 5 1.87 11.12 1.99 9.93 6 1.87 12.99 1.96 11.89 7 1.86 14.86 1.97 13.85 8 1.86 16.71 1.96 15.82 9 1.85 18.56 1.97 17.79 10 1.86 20.42 1.91 19.70 11 1.82 22.23 1.98 21.68 12 1.82 24.05 1.98 23.66 13 1.84 25.89 1.98 25.64 14 1.83 27.72 1.98 27.63 15 1.83 29.55 1.98 29.60 16 1.83 31.38 1.97 31.58 17 1.85 33.23 1.96 33.54 18 1.83 35.06 1.99 35.53 19 1.84 36.90 1.97 37.50 20 1.85 38.75 1.97 39.48 21 1.86 40.61 1.97 41.45 22 1.84 42.45 1.93 43.38 23 1.96 44.41 1.93 45.31

Table 2.1 (Continued). Applied water for Experiment I

Time Experiment I Experiment II (days) Applied (cm) Sum applied (cm) Applied (cm) Sum applied (cm)

24 1.92 47.23 25 1.92 49.15 26 1.97 51.13 27 1.97 53.10 28 1.97 55.07 29 1.96 57.03 30 1.96 58.98 31 1.95 60.93 32 1.95 62.87 33 1.95 64.82

Mean 1.85 1.96 SD 0.04 0.02

CV (%) 1.90 0.99

Table 2.2. KBr applied during Experiment I*

Time (days) Concentration (mg cm'^) 0 0.0345 1 0.0337 2 0.0312 3 0.0300 4 0.0365 5 0.0405 6 0.0276 7 0.0311 8 0.0350 9 0.0400 10 0.0344 11 0.0290 12 0.0158 13 0.0266 14 0.0278

Mean 0.0316 * from Young et al. [1999]

28

45

CO

40

S 35

30

31.6 mg/1

t

c o u c o U

25

20

15

0 6 8 Time (day)

10 12 14

Figure 2.4. Input concentrations of bromide during Experiment I.

29

3. FLOW IN VARIABLY SATURATED HETEROGENEOUS MEDIA INCORPORATING HYSTERESIS

3.1. Introduction

Water flow in unsaturated soils is often difficult to quantify because it is a

function of moisture content, matric potential and hydraulic conductivity. Water flow

problems are usually solved numerically although analytical solutions are available for

simplified systems. However, these simplified systems rarely exist in the real world.

Understanding and quantifying the mechanisms of a wetting front advance in an

unsaturated soil profile is an important step in studying the complex nature of

unsaturated flow. The advance of a wetting front is also important in understanding the

transport of contaminants under unsatiu^ted conditions.

A field study was conducted at the Maricopa Agricultural Center (MAC) (Figure

2.1) of the University of Arizona starting in the spring 1997 and ending in the summer

1998. The MAC s i te i s loca ted 42 ki lometers (km) southwest o f Phoenix [Young e t a i ,

1999]. The study was designed and implemented to evaluate unsaturated zone

monitoring techniques and strategies applicable to low-level radioactive waste (LLW)

disposal facilities [Young et al., 1999]. The study consisted of two successive

infiltration experiments.

The objective of the present study is to analyze the data obtained fi*om these two

experiments, to simulate the advance of the wetting firont and compare the results with

measured data, to determine if inclusion of hysteresis in the retention and hydraulic

30

conductivity functions affects the above outcome, and to evaluate the ability of

laboratory derived hydraulic parameters from core samples to accurately predict the

propagation of the wetting front.

3.2. Materials, Methods, and Theory

3.2.1. Water Budget

A water budget was calculated for the first experiment using the measured water

content data from the neutron probe access tubes. The water budget compares the

amount of water applied to the upper surface of the plot through the trickle system, to

the amount of water contained within the soil profile at specific times during the

experiment. The measured amount of water in the soil profile was determined from the

field measured water contents by integrating the soil water profile at specific times

during the experiment. The amount of water applied to the plot through the trickle

system was calculated from water meters located at the inlet water pipes of the irrigated

plot. A water budget was calculated according to the following equations;

Water budget = measured - fv .

known (3.1)

fV{z , t ) = Water measured = (3.2) 0

^0=^,-.One-^..O (3.3)

31

where Wmeasured IS thc depth (cm) of water applied, Az is the vertical depth interval along

the length of the neutron probe, and ^is the water content. The water budget was

calculated for various depths and times to determine the difference between water

applied and water measured in the soil profile. This also provided us with an

independent check of the neutron probe calibration and allowed us to quantify the

effects of two-dimensional flow at the perimeter of the irrigated plot. It should be noted

that the depth interval and times over which the mass balance was conducted were

carefully chosen to make certain that the termination point was in front of the wetting

front and that the water content profile was not truncated.

3.2.2. Modeling Water Flow

HYDRUS 1-D [Simuneket al., 1998] was utilized to simulate the flow of water

through the soil profile. HYDRUS 1-D solves a mixed form of Richards' equation.

The governing equation, without a source or sink term, is given by:

= (3-4) dt dz ^ dz y 3z

where ^is the volumetric water content, t is time, K is hydraulic conductivity, h is the

water pressure head, and z is elevation.

The initial and boundary conditions with respect to water content for this study

are given as:

Kz, t ) = h ,{z ) t=t„ (3.5)

32

-K

-K

dz

dz

= -1.85 cm/d r= l l J

= 0

r=113

0 < r < 23 days

/> 23 days

t > 0 days

(3.6)

(3.7)

(3.8)

where Equation (3.5) is the initial distribution of pressure head, hi is a prescribed

function of z, to is the time the simulation begins, and z represents the position in the

soil profile (i.e. z = 11.5 m at the soil surface, z = 0 m at the bottom of the profile); a

water table condition (perched water table) is imposed at the lower boundary. The 11.5

m profile was discretized using a grid spacing of 0.10 m, resulting in a total of 116

vertical nodes.

The soil-hydraulic functions of van Genuchten [1980] were used for the cases

not employing hysteresis and are given by:

/ ,<0 \m (3.9)

h > 0

0 = ( '+M")

0

K{h) = K^S°^ l - ( l -5 j "" ) ' " J (3.10)

(3.11)

where 6r and 6s are the residual and saturated water content, h is the pressure head, K is

the unsaturated hydraulic conductivity, and Se is the effective saturation. Equations

33

(3.9) and (3.10) are subject to the /w=l—(!/«) condition (« >1) [van Genuchten,

1980].

HYDRUS incorporates hysteresis into the retention function using an empirical

model developed by Scott et al. [1983] and modified by Kool and Parker [1987] to

account for air entrapment. The air entrapment effects incorporated into the model were

developed by Land [1968] and given by Aziz and Settari [1979]. Hysteresis is

incorporated into the hydraulic conductivity function using a model analogous to that of

Kool and Parker developed by Vogel et al. [1996] in which they apply an approach

similar to that used in the hysteretic retention function. Specifying hysteresis in the

retention and hydraulic conductivity functions requires that the user define both the

main wetting and drying curve. In addition, the initial conditions must be specified as

falling on either the main wetting or drying curve. Hysteresis is incorporated by scaling

scanning curves from the main wetting or drying curve. The wetting scanning curves

are scaled from the main wetting curve and drying scanning curves are scaled from the

main drying curve. The following discussion outlines the methodology of the hysteretic

model as outlined by Kool and Parker [1987]. The approach used to implement

hysteresis in HYDRUS is slightly different, but inspection reveals that both approaches

yield identical results.

Assumptions of the empirical model include the restrictions:

n ' '=n '^=n (3 .12)

where 0r is the residual water content, tar and n are empirical fitting parameters, the

superscripts w and d refer to wetting and drying, respectively. The main wetting and

34

drying curves are defined in the HYDRUS code by sending the parameter vectors

, 9^, d", /i) and to the following modified version of the van

Genuchten expression given by:

/? —f) 0,+ " ^ h<h^

f f (h ) = \ ( l + M") (3 .13)

_0. h>h.

Wetting scaiming curves are obtained by scaling the wetting curve to pass through a

reversal point. The scaled wetting curve is calculated by using the parameter vector

, in (3.13). The parameter ^ replaces 0^ in the parameter vector and

in effect forces the scanning wetting curve to pass through the reversal point. This

scaling parameter, ^, is defined as:

. 0. -O,S:(hA

where 0^ is the water content at the reversal point and is the effective

saturation on the main wetting curve at the reversal pressure head, and is given by

(3.11). By analogy, drying scanning curves are calculated using the parameter vector

{^0^, d],a'', ri^) where is calculated to adjust the main drying curve to pass through

the reversal point and is given by:

. 0^-0[ \ -SUhA\

35

Air entrapment effects are accounted for in the model by allowing the saturated water

content to be defined in terms of a wetting or drying saturated water content, and

ffl; this results in a hysteresis loop that is not closed at saturation. In general, studies

have found that < 0^ [Hopmans et al., 1987]. Air entrapment during the re wetting

phase can be approximated by the following empirical equation:

and 0^ . Equations (3.16) - (3.17) are used with (3.14) to predict the scanning

wetting curves. When the regime shifts from drying to wetting equations (3.16) - (3.17)

are used to calculate 9^ which is then used in place of 6^ in solving equations (3.13)

and (3.14). This substitution can also be used in equation (3.15) if another reversal

occurs.

HYDRUS uses an analogous procedure for applying hysteresis to the hydraulic

conductivity function given by (3.10). The same parameter vectors are used as in the

retention functions in addition to the requirement for and K'l to be specified.

Hydraulic properties were estimated using 11 core samples. The 11 core

samples were collected from an north south transect through the 50 m by 50 m plot at a

depth of approximately 1.5 m (Figure 3.1). Table 3.1 lists the mean, standard deviation.

(3.16)

where

(3.17)

36

Covered area Field PIotF-II5

iiii^aicu cuca •— —Depth • 1.49 m

• Depth = .49 m

• Depth = .45 m

• Depth = .38 m

• Depth = .50 m

• Depth = .61 m

NMI • Depth = .50 m

O o

• Depth = .49 m

SMI • Depth = .74 m

• Depth = .41 m

—•— Depth " :45-nt

-L J- X

O Monitoring island

• Location of soil core

h 10 meters

Figure 3.1. Locations where soil cores were collected.

37

Table 3.1. Mean Hydraulic Properties and the statistical parameters for the core samples obtained by the various laboratory methods

dr (cm^ cm "^) 4(cm^cm'^) ar(cm'') n Ks (cm d ') Y Saturated Hydraulic Conductivity Experiment

Mean 0.301 45.8 S.D. 0.034 23.3 Max 0.353 80.8 Min 0.262 16.6

CV (%) I I .4 50.9 Multi-step Outflow Experiment

Mean 0.00035 0.0425 1.312 S.D. 0.00041 0.0217 0.062 Max 0.00099 0.0788 1.145 Min 0.00003 0.0136 1.223

CV (%) 116.8 51.0 4.7 Wetting Experiment (upward infiltration)

Mean 0.0610 0.0984 1.33 -0.489 S.D. 0.0513 0.0821 0.20 1.253 Max 0.1420 0.2920 1.74 0.916 Min 0.0000 0.0408 1.11 -3.44

CV (%) 84.1 83.4 14.9 -256.2 Drying Experiment (evaporation)

Mean 0.0942 0.0534 1.746 -1.35 S.D. 0.0599 0.0665 0.376 1.58 Max 0.2030 0.2360 2.420 0.002 Min 0.0000 0.0097 1.220 -4.57

CV (%) 63.5 124.4 21.500 -116.8

38

maximum and minimum, and coefficient of variation for the hydraulic parameters for

the 11 core samples. The following outline of experimental work conducted on the core

samples and the estimation of the hydraulic parameters is summarized from

unpublished work conducted by John Fleming (1999). The intact soil cores collected

were 7.62 cm in length and 7.62 cm in diameter. The following experiments were used

to estimate the hydraulic properties: saturated hydraulic conductivity (Ks); multi-step

outflow (MSO); upward infiltration (UI); and evaporation (EV). After the completion

of the experiments, the bulk density and particle density (pipette method ) of the cores

were determined. The experiments were conducted in such a way that the ending

conditions for one experiment coincided with the required initial conditions for the

following experiment. The saturated water content was also experimentally determined.

The remaining parameters, a, n, and 0r, and y were optimized by using the inverse

procedure of the numerical code HYDRUS 1-D {Simunek et al., 1998] utilizing data

from aforementioned experiments. The optimizations in HYDRUS 1-D were also

conducted by Mr. Fleming. Efforts were made to characterize these hydraulic

properties using field-measured data with mixed results. Some of these approaches are

outlined in Appendix A.

The hydraulic conductivities calculated using Equation (3.10) and the data in

Table 3.1, were compared to field measured hydraulic conductivity values. This

comparison allows the predictive hydraulic conductivity relationship to be scaled to the

measured values. The concept is a variation of the scaled-predictive method introduced

by Mace et al. [1998]. In the scaled-predictive method the predictive K(0) relationship

39

is scaled using a single measurement of unsaturated hydraulic conductivity that replaces

the saturated hydraulic conductivity as the matching point. The approach utilized here

makes use of several unsaturated hydraulic conductivity measurements to scale the

predictive unsaturated hydraulic conductivity relationship. The methodology used to

calculate the field measured unsaturated hydraulic conductivities involved computing

an average pore-water velocity determined from the observed tensiometer data and

combining this with the observed mean water content at some depth to derive a flux

value. The tensiometer data measured at the monitoring islands (Figure 2.2) at depth

intervals of 0.5 m to a depth of 3 m was used to calculate the fleld measured unsaturated

hydraulic conductivities. Making a unit gradient assumption, supported by the observed

tensiometer data , the subsequent unsaturated hydraulic conductivity values can be

calculated and compared to those generated using Mualem's [1976] model based on the

laboratory derived hydraulic properties. Figure 3.2 shows a representative soil tension

profile from the monitoring island locations. After approximately 5 days of irrigation, a

steady-state unit gradient profile is attained. Figure 3.3 shows the hydraulic

conductivity as a function of water content based on the soil hydraulic properties model

of Mualem [1976] as well as calculated hydraulic conductivities from the field-

measured data from 0.5 to 3 m in 0.5 m increments. Table 3.2 shows the calculated

unsaturated hydraulic conductivity values as well as the values used to arrive at the

calculated values. As seen, when the saturated hydraulic conductivity is raised to 450

cm d ', the hydraulic conductivity curve passes through the field calculated values,

while the curve based on a laboratory derived hydraulic conductivity value of

40

Tension (cm H,0)

0 200 400 600 800

Initial conditions (early time)| Steady-state (later time) - m O O®

T^^nJ ! I ~ 5 days

100

E

a. u Q

200 r

300

Figure 3.2. Representative soil tension profile for the monitoring island locations.

41

>

o •o o u

3 CO L. -a

50

40

30 -a E u

S ^20 T3 O

« U3 C

10

0

0.32 0.28 0.24 0.2 0.16 0.12 0.08

Water content (cm^ cm"^)

Figure 3.3. Hydraulic conductivity versus water content. Solid circles are the field-calculated values from 0.5 to 3 m in 0.5 m intervals; the solid line is based on a laboratory-derived value of 45.8 cm d ' for Ks, the solid line with open circles is based on a Ks of 450 cm d"'.

42

Table 3.2. Calculated unsaturated hydraulic conductivity values for the NMI and SMI locations.

Depth (cm)

Location WF arrival'

(day) Velocity

(cm / day) Water

content^ K(0)^

(cm / day) 50 SMI West 4.0 12.50 0.26 3.25

East 4.0 12.50 0.26 3.25 NMI West 4.0 12.50 0.26 3.25

East 3.0 16.67 0.26 4.33 100 SMI West 7.5 13.33 0.25 3.33

East 6.5 15.38 0.25 3.85 NMI West 5.5 18.18 0.25 4.55

East 4.5 22.22 0.25 5.56 150 SMI West 9.5 15.79 0.24 3.71

East 9.0 16.67 0.24 3.92 NMI West 6.0 25.00 0.24 5.88

East 7.5 20.00 0.24 4.70 200 SMI West 11.0 18.18 0.23 4.18

East 11.5 17.39 0.23 4.00 NMI West 8.0 25.00 0.23 5.75

East 9.0 22.22 0.23 5.11 250 SMI West 13.0 19.23 0.21 4.04

East 13.0 19.23 0.21 4.04 NMI West lO.O 25.00 0.21 5.25

East 11.5 21.74 0.21 4.57 300 SMI West 14.0 21.43 0.21 4.46

East 14.0 21.43 0.21 4.46 NMI West 11.0 27.27 0.21 5.67

East 12.0 25.00 0.21 5.20 ' Determined from measure tensiometer data ^ Average water content at that depth behind the wetting front ^ Computed using a unit gradient assumption

43

45.8 cm d ' under-predicts the field calculated values by 72 to 98 percent (treating the

field calculated values as the known values). The same procedure was followed when

applicable for the other cases where different soil hydraulic properties were used (fi-om

the laboratory derived hydraulic properties).

The initial distribution of pressure head for the model was obtained from the

observed initial averaged water contents (Figure 3.4) given by the neutron probe data,

and the water retention model Equation (3.9).

Seven simulation tests, labeled Cases I through VII (Table 3.3), were conducted

using different soil hydraulic properties. The same initial and boundary conditions were

used for Experiment I (Cases I - V); different initial conditions were used for

Experiment II (Cases VI - VII). Hysteresis was incorporated into the models that use

laboratory derived hydraulic properties by using a combination of the properties

estimated from the wetting and drying experiments.

The interpolated initial conditions (water contents) as calculated by the model

and the observed water contents are shown in Figure 3.4.

44

0 0.1 Water Content (cm^ cm'^)

0.2 0.3 0.4 0.5

Figure 3.4. Model initial conditions and observed initial conditions. The circles represent the mean observed water contents. The horizontal lines represent ± one standard deviation and the solid line represents the interpolated water contents used in the model (HYDRUS).

45

Table 3.3. Summary of mean hydraulic properties used in models

Case dr (cm^ cm'^) 0s (cm^ cm'^) ar(cm"') n Ks (cm d"') y

I Experiment I, drying properties 0.06 0.301 0.053 1.75 45.8 -1.35

II Experiment I, wetting properties 0.06 0.301 0.098 1.33 45.8 -0.489

III Experiment I, drying and wetting properties 0.06 0.301 0^ = 0.098 1.33

ct = 0.053 45.8 -0.489

IV Experiment I, HYDRUS database properties with no hysteresis 0.065 0.410 0.075 1.89 106.1 0.5

V Experiment I, HYDRUS database properties with hysteresis 0.065 0.410 q>^ = 0.15 1.89 106.1

£/ = 0.075 0.5

VI Experiment II, wetting properties 0.06 0.301 = 0.098 1.33 45.8 -0.489

VII Experiment II, drying and wetting properties 0.06 0.301 a^ = 0.098 1.33

= 0.053 45.8 -0.489

46

3.3. Results and Discussion

3.3.1. Textural Characterization

The mean percent (from three locations) sand, silt, and clay with depth is shown

in Figure 3.5. Based on the data the soil is classified as a sandy loam. Figure 3.6 shows

the mean percent (from the same three locations) gravel, and the mean (from nine

locations) observed water content versus depth. Collectively, the information was used

to delineate six approximate boundaries at depths of 3 m, 6 m, 7.5 m, 9 m, 10 to 11 m,

and 12 m.

3.3.2. Water Budget

The computed depths of water added for each of the neutron probe access tube

locations were calculated for the 0 to 1.0 m depth interval on irrigation days 4 and 5,

and for the 0 to 9.0 m depth interval on irrigation day 19. The computed depths of

water application at each access tube were then compared to the depth of water applied

through the drip system. The magnitude of the error associated with the water budget

revealed a problem with the neutron probe calibration. A small change in the slope of

the neutron probe calibration equation, consistent with data from a small plot adjacent

to the large plot, improved results for the water budget. Plotting the computed depths of

the water added against the actual amount of water applied revealed a strong two-

dimensional flow component at the perimeter access tubes locations.

47

400

c u 800

o. u Q

1200

1600 20 10 60 70 80 90 0 10 20 0

Sand Silt Clay

Figure 3.5. Mean percent sand, silt, and clay composition at three locations.

48

0 0

20

Percent gravel

40 60 80 100

400

800 a. u Q

1200

1600

0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4

Water content (cm^ cm'^)

Figure 3.6. Mean percent gravel (circles) and mean measured water content (solid line) versus depth.

49

Figure 3.7 shows the spatial distribution for the water budget at the 1.0 m depth

on irrigation day 4, and is based on data from 26 neutron probe access tubes. On

average, the neutron probe data over-estimated how much water was actually applied,

as measured by the water flow meters, by 28.4 percent. While the mass balance

calculation yielded acceptable results with respect to the mean computed depths of

water added, the standard deviation was quite large, 33.7 percent. Note also that the

neutron probe access tubes are located at least 5 m within the irrigated area.

Figure 3.8 shows the spatial distribution for the water budget at the 1.0 m depth

on irrigation day 5, and is based on data from 26 neutron probe access tubes. On

average, the neutron probe data under-estimated how much water was actually applied,

as measured by the water flow meters, by 17.6 percent. While the mass balance

calculation yielded acceptable results with respect to the mean computed depths of

water added, the standard deviation was quite large, 32.9 percent. Table 3.4 more

clearly shows the spatial variability of the computed depths of water added for each of

the neutron probe access tube locations.

Figure 3.9 is a plot of the spatial distribution for the water budget to the 9.0 m

depth on irrigation day 18, based on data from 9 neutron probe access tubes. On

average, the neutron probe data over-estimated how much water was actually applied,

as compared to that measured by the flow meters, by 0.2 percent. The standard

deviation of the error was 34.0 percent.

50

Over-Estimates (%)

Under-Estimates (%)

Figure 3.7. Spatial distribution of the water budget data for irrigation day 4, 1.0 m depth. Diamonds represent vertical neutron probe access tube locations. The numbers represent under- or over-estimation of water applied (in percent) relative to the water meter data. On average the neutron probe data over- predicted how much was actually applied by 28.4 percent.

51

Over-Estimates (%)

Under-Estimates (%)

Figure 3.8. Spatial distribution of the water budget data for irrigation day 5, 1.0 m depth. Diamonds represent vertical neutron probe access tube locations. The numbers represent under- or over-estimation of water applied (in percent) relative to the water meter data. On average the neutron probe data under- predicted how much was actually applied by 17.6 percent.

Table 3.4. Computed depths of water added on irrigation day 5 at 1.0 m

Location x (m) y (m) Total W (cm) % Difference*

402 10 5 7.61 -17.83 403 23 5 9.22 -0.45 404 30 5 6.17 -33.31 405 40 5 3.67 -60.42 412 5 15 8.96 -3.23 413 15 15 10.57 14.17 414 22.5 15 10.98 18.62 415 35 15 4.06 -56.16 416 45 15 6.63 -28.35 422 10 25 1.30 -85.94 423 23 25 8.86 -4.26 424 30 25 10.16 9.74 425 40 25 4.84 -47.78

432 5 35 7.93 -14.36 433 15 35 8.34 -9.92 434 22.5 35 5.26 -43.21 435 35 35 6.54 -29.32 436 45 35 5.46 -41.06 442 10 45 8.79 -5.11 443 22.5 45 9.71 4.90 444 30 45 8.30 -10.31 445 40 45 5.95 -35.74 454 22.5 10 8.76 -5.40

455 22.5 20 8.48 -8.42 456 22.5 30 4.80 -48.14 457 22.5 40 17.11 84.75

Mean 7.63 -17.6

Std. Dev. 3.05 32.9 Compared to 7.31 cm, as measured by the water flow meters

53

Over-Estimates (%)

Under-Estimates (%)

Figure 3.9. Spatial distribution of the water budget data for irrigation day 18, 9.0 m depth. Diamonds represent vertical neutron probe access tube locations. The numbers represent under- or over-estimation of water applied (in percent) relative to the water meter data. On average the neutron probe data over- predicted how much was actually applied by 0.2 percent.

54

The data in Figure 3.7 and in Figure 3.9 show considerable spatial variation and

there are no clear trends in the two figures. This would indicate that the water is applied

in a uniform manner. The computed depths of water added for the neutron probe access

tube location 422 (x = 10 m, y = 25 m) under-estimates how much water was actually

applied, as measured by the water flow meters, on both irrigation days. However, this

is not interpreted as a bias in the water application system as this under-estimation

would be expected to show up on Figure 3.9. This under-estimation is more likely

attributable to a disturbed soil profile in the upper 0.5 m due to plot preparation. There

does appear to be a spatial trend in Figure 3.9. The east side shows an under-estimate

of the amount of water applied, while the west side displays an over-estimate of the

amount of water applied. Also, for a field experiment of this magnitude, a difference of

28.4 percent for irrigation day 4, the 0 to 1.0 m depth, 17.6 percent for irrigation day 5,

the 0 to I.O m depth data (26 access tubes both days) and 0.23 percent (9 access tubes)

for the 0 to 9 m depth data are quite acceptable.

Because of lateral flow from the wet plot to the drier surrounding soil, the access

tubes at the perimeter under-estimated the amount of water applied by 50 to 60 percent,

a much larger error than predicted using the interior access tubes. Plotting the

computed depths of the water added versus the actual amounts of water applied

revealed a strong two-dimensional flow component at the perimeter access tube

locations (Figure 3.10 and Figure 3.11). Figure 3.10 shows all the neutron probe access

tube locations (34 locations, including the locations at the perimeter) through the

irrigation phase of the experiment. The solid circles represent locations at least 5 m

55

CJ o o Urn c. o C/3

-T3 'S &0 o

1 1 ' i ! i 1 1

•

' H ^ V ^ Over-predicts « \m ^ ^

•

0

Under-predicts

0 10 20 30 40

Water applied (cm)

50 60

Figure 3.10. Computed water depths applied versus the water depths applied according to the water meters for 34 access tube locations on irrigation days when data are available. The dashed line represents +/- 32 percent error from the true amount applied.

56

Over-predicts

Under-predicts

Water applied (cm)

Figure 3.11. Computed water depths applied versus the water depths applied according to the water meters for the perimeter access tube locations (8 locations). The dashed line represents +/- 32 percent error from the true amount applied.

57

within the irrigated perimeter; the open squares represent the perimeter locations. As

can be seen, the access tubes located on the perimeter under-estimate the computed

depths of the water applied to a much larger degree than the access tubes locations 5 m

within the plot. Figure 3.11 shows only the access tubes located on the perimeter (8

locations) and more clearly shows the trend of under-estimation. Figure 3.12 shows

only the neutron probe access tube locations at least 5 m within the irrigated perimeter;

the majority of these locations fall within the error bars of one standard deviation. The

solid line on both figures represents the values where the amount applied as measured

by the water meters equals the computed depth of water applied (0 percent error), the

dashed lines represent +/- 32 percent of this value. The range of +/- 32 percent

represents the mean value of the standard deviation from all the irrigation days. The 32

percent was calculated by first, determining the average depth of water applied (based

on data available from 26 access tubes) for each irrigation day, then calculating the

associated standard deviation of the access tubes for each irrigation day. The

percentage the standard deviation represented of the mean depth of water applied was

calculated for each irrigation day, and finally, a mean of all the computed percentages

was calculated. This approach was used because of the large degree of variation in the

standard deviation. It should be noted that for both figures not all locations possess data

for each irrigation day.

58

Over-predicts

Under-predicts

0 10 20 30 40 50 60

Water applied (cm)

Figure 3.12. Computed water depths applied versus the water depths applied according to the water meters for the access tube locations located at least 5 m within the irrigated perimeter (26 locations). The dashed line represents +/- 32 percent error from the true amount applied.

59

3.3.3. Simulation of Cases I and II

The "goodness of fit" for the models (Cases I - VII, Table 3.3), were evaluated

using three criteria; the ability of the model to predict the arrival time of the wetting

front, and the ability of the model to accurately predict the water contents during the

irrigation and redistribution phases of the experiment. The ability of the model to

predict the arrival time of the wetting front was evaluated by comparing the simulated

arrival time to the observed arrival time using the tensiometer data. The tensiometers

are very responsive to the changes in water content. In addition, tensiometer

measurements were collected at six-hour time intervals, thus the tensiometer data

provided a more accurate measure of the wetting front arrival time as compared to the

neutron probe data and was one of the criteria used to evaluate the ability of the model

to predict the arrival time of the wetting front. The mean square errors (MSE) for the

observed versus predicted water contents for a particular depth was the method used to

evaluate the ability of the model to accurately predict the water contents during the

irrigation and redistribution phases of the experiment. The MSE for a particular depth

was computed according to:

2

MSE = -"^(0,-0) (3.18)

w h e r e ^ ^ , a r e t h e m e a s u r e d a n d p r e d i c t e d v o l u m e t r i c w a t e r c o n t e n t s r e s p e c t i v e l y , f o r

a particular depth, and / represents the time interval. Table 3.5 lists the MSE values

(multiplied by 1000 to better illustrate the differences) for the particular cases at

specified depths.

60

Table 3.5. Mean square error* for Cases I - VII

Depth (m) Ossc

1.5 3.0 5.0 7.5 I 3.82 1.62 2.62 1.58 II 0.68 0.22 0.40 0.14 III 0.51 0.19 0.21 0.10 IV 1.61 0.50 0.88 0.40 V 1.96 0.72 1.48 0.67 VI 0.55 0.36 0.47 0.18 VII 0.32 0.34 0.40 0.30

Note that the MSE was multiplied by 1000

61

Figure 3.13 presents the measured (circles with vertical bars) and the simulated

water contents versus time for the 7.5 m depth (Cases I and II). The simulated wetting

front arrived at approximately 24 days at the 7.5 m depth. The hydraulic properties

obtained from the drying cores clearly result in underestimation of the soil water

content at this depth (Figure 3.13, A). However, the arrival of the wetting front is

reasonably well predicted using the properties from the wetting experiments. An

increase in the saturated hydraulic conductivity to 75 cm day"' makes the prediction of

the water content during the redistribution phase worse (Figure 3.13, B).

Using the hydraulic properties from the wetting cores (Case II, Table 3.3) with a

measured saturated hydraulic conductivity of 45.8 cm day"' (Table 3.1), caused the

simulated wetting front to lag approximately 33 days behind the measured wetting front

(Figure 3.13, C). A 10-fold increase (450 cm day"') in the saturated hydraulic

conductivity in accordance with the data in Figure 3.3, greatly improved the wetting

front arrival time prediction, and also resulted in a good fit during the drainage phase

(Figure 3.13, D). These same results could not be obtained with the properties from the

drying experiments unless major adjustments were made to a, n, and y. Thus the best

results for the 7.5 m depth were obtained with wetting properties and a Ks of450 cm

day"'. Table 3.6 summarizes the adjustments made for Cases I and II as well as

subsequent cases (Cases III - VII).

62

c u c o U L. o "S

c c o u a>

- A, Drying, = 46 cm day

_ I -

-1 B, Drying, K^ = 15 cm day 1

0.16 -

0.12 r

r C, Wetting, AT- = 46 cm day"' D, Wetting, = 450 cm day"' -! 0.24

0.2 r

0.16

0.12

0 20 40 60 80 0 20 40 60 80 100

Time (Days) Time (Days)

Figure 3.13. Comparison of the mean measured and predicted water contents and wetting front arrivals at the 7.5 m depth. The vertical lines denote ± one standard deviation in the mean water content.

63

Table 3.6. Saturated hydraulic conductivity values used for Cases I - VII

Case Description Ks (cm d'^) Adjusted Ks (cm d"')

I Experiment I, drying properties 46.0 75.0

II Experiment I, wetting properties 46.0 450.0

III Experiment I, drying and wetting properties 46.0 250.0

IV Experiment I, HYDRUS database properties with 106.1

no hysteresis 450.0

V Experiment I, HYDRUS database properties with hysteresis 106.1 1250.0

VI Experiment II, drying and wetting properties 46.0 250.0

VII Experiment II, drying and wetting properties 46.0 250.0

64

3.3.4. Comparison of Cases II and III: Incorporating Hysteresis

Hysteresis was incorporated into the soil hydraulic model incrementally (first in

the water retention function, and then in the water retention and hydraulic conductivity

functions). Incorporating hysteresis into just the water retention function decreased the

accuracy of the predicted water contents (results not shown). Figure 3.14 compares the

simulated water content time series with hysteresis included (Case III, Table 3.3), and

the simulated water content time series with no hysteresis (using hydraulic parameters

from the wetting experiment. Case II) with the mean measured water content time

series. Adjustment of the saturated hydraulic conductivity from 46.0 cm day"' to 250.0

cm day ' for the model incorporating hysteresis (Case III) yielded much better

predictions with respect to the wetting fi-ont arrival time as well as a better fit during the

drainage phase, in comparison with using a Ks of 46.0 cm d"'.

The predictions based on the model with no hysteresis (Case II) match closely to

the predictions of the model incorporating hysteresis (Case III) although, as indicated

by the MSE (Table 3.5) the model incorporating hysteresis (Case III) yielded better

results at every depth (Figure 3.15 to Figure 3.17), including the shallower depths. This

may be attributed to ±e fact that the retention curve from the model with no hysteresis

(Case II) falls on the main wetting curve of the model incorporating hysteresis (Case

III). Figure 3.18 illustrates this idea; the main wetting and drying curves based on the

parameters used in the hysteretic model (Case III) are plotted along with the retention

curves based on the drying and wetting parameters with no hysteresis (Cases I and II,

respectively).

u « 0.14 ^ "S I

^ 0 1 2 - " " ' C a s e D , K s = 4 5 0 . 0 c m / d j Case in, Ks = 250.0 cm / d

0 . 1 ^ ^ ^ ^

-20 0 20 40 60 80 100

Time (day)


66

0.3

E O n E CJ 0.2 t.

C o o

CJ

"S

i } f

0.1 -

0

0

- 400

- 300 ^ wJm - E

Case n, Ks = 450.0 cm / d Case in, Ks = 250.0 cm / d

200

T 100

0

20 40 60 80 100

c _o c ti H

Time (day)

Figure 3.15. Comparison of the simulated water content time series to the mean measured water contents for the 1.5 m depth. Triangles depict tension.

67

0.3 -

0.2

c CJ o

U ba o

0.1 T

0

0

- 300

- 200

^ 100

- - Case n, Ks = 450.0 cm / d —Case in, Ks = 250.0 cm / d

0

20 40 60

Time (day)

80 100

O r4 X E u c o c u


68

0.3 - ^ 400

0

- 300

- 200

^ 100

- - Case n, 450.0 cm / d Case in, 250.0 cm / d

0

O <N

s u e ,o 'cn C u

20 40 60 Time (day)

80 100


69

0.4

i O . 3

I 0-2 O

O "S

Main drying curve. Case HI ™ Main wetting curve. Case III, main wetting and drying cu^eTCase Main wetting and drying curve. Case I

0.1 10 100 1000 10000 100000 1

Suction (cm of H2O)

Figure 3.18. Retention curves for hysteretic model and models based on parameters derived from wetting experiments and drying experiments.

70

The retention curve for the model using parameters taken from the wetting

experiment falls on the main wetting curve of the hysteretic model (as expected since

the parameters are the same) while the retention curve based on the parameters from the

drying experiments differs significantly from the others. This is because of the use of a

different shape factor, n, as well as a and y. With models developed using the drying

parameters (Case I), I was unable to achieve a satisfactory calibration without large

adjustments to the parameters. This would indicate that for these field conditions,

where the profile stays fairly wet during most of the experiment, the wetting parameters

yield better results. In addition, the similarity of the results between Cases II and III

would indicate that hysteresis does not play a large role in determining the wetting front

arrival and the shape of the water content curves. However, it should be noted that

incorporation of hysteresis did result in the use of a more realistic value for the

saturated hydraulic conductivity as compared to the case without hysteresis (Case II).

The suitability of using a homogeneous representation for this site was evaluated

by comparing the simulated results with data from shallower depths (1.5, 3.0, and 5.0

m). Figure 3.15 through Figure 3.17 compare the simulated water content time series

for the 1.5, 3.0 and 5.0 m depths to the observed water content and tension time series.

The open triangles are the mean measured tension time series from a representative

location within the experimental plot. Because of noise inherent in the water content

data, the observed tensiometer response was also used to delineate the arrival of the

wetting front and the beginning of the drainage phase for the shallower depths.

Tensiometers are very responsive to changes in water content and provide a more

71

distinct delineation of the wetting front arrival time as well as of the time that the

drainage phase begins. The plots (Figure 3.15 - Figure 3.17) clearly illustrate how the

measured tensiometer response agrees with the predicted water contents with respect to

the arrival of the wetting front and the start of the drainage phase. In addition, the plots,

as well as the MSE, support the use of a homogeneous representation for this field site.

3.3.5. Simulation of Cases IV and V

The uniqueness of the laboratory-derived parameters was also evaluated by

comparing the results from Cases II and III, against a model using hydraulic parameters

taken from an internal database in HYDRUS 1-D [Simuneket al., 1998]. The hydraulic

parameters chosen from the internal database are based on textural considerations, as

stated previously; a sandy loam is the dominant texture throughout the profile at the

site. Table 3.3 lists the hydraulic parameters used as a first approximation from the

internal HYDRUS database; Case IV corresponds to the model with no hysteresis. Case

V incorporates hysteresis into the retention and hydraulic conductivity functions.

Calibration of the models using hydraulic parameters taken from the internal database

followed the same methodology used in calibrating the models based on the laboratory

derived hydraulic properties: saturated hydraulic conductivity was used as a fitting

parameter to adjust the arrival time of the wetting front and minor adjustments were

made to alpha (a) and n to adjust the shape of the curve. Using this methodology it was

not possible to fine-tune either of the two models using hydraulic properties taken from

72

the internal database (Cases IV and V) as a first approximation to the same degree of

quality as the models using the laboratory derived properties (Cases II and III). This is

supported by the MSE values (Table 3.5). Figure 3.19 shows the final results for the

four cases for the 7.5 m depth. Using the laboratory derived hydraulic parameters

clearly resulted in a superior fit as compared to using the internal database parameters

from HYDRUS (Figure 3.19). This implies that under these circumstances the

laboratory derived parameters provide a better first approximation for predicting the

wetting front arrival and the shape of the curves than parameters taken from the internal

database solely based on textural considerations.

3.3.6. Water Contents with Depth, Experiment I

The mean measured vertical water content profiles for the plot are shown for

days 22 (Figure 3.20), 24 (Figure 3.21), and 93 (Figure 3.22). Also shown are the

predicted water contents for the two models based on the laboratory derived hydraulic

parameters, with and without hysteresis. The plots for days 22 and 24 represent the day

before and the day after the end of the irrigation phase, respectively. Day 93 is the last

day neutron probe measurements were taken during the drainage phase of the first

experiment.

73

3 c o U

Urn CJ

c o c o U

WH o rt

0.28

0.24

0.2

0.16

_ Wetting & drying properties J Wetting properties _ 1 y - - K^ = 250.0 cm d' _J -^-Ar^ j= 450.0 cm d'

~ T d i i l i f i i : ^ : o ;—, ** 1 " . ~ j p o ^ ^ ^ ^

- ' i ' i J " L ^

r 1

— i

i i 1 i i i ; 1 ! 1 1 , I , ; , 1 : : n

Database properties, hysteresis J Database properties, no hysteresisj , r K = 1 2 5 0 . 0 c m d - ' -Kj = 450.0 cm d '

0 20 40 60 80

Time (Days)

0 20 40 60 80 100

Time (Days)

Figure 3.19. Comparison of the mean measured and predicted water contents and wetting front arrivals at the 7.5 m depth. The vertical lines denote ± one standard deviation in the mean water content. A, Case III with Ks = 250.0 cm d ', B, Case II with Ks = 450.0 cm d ', C, Case V with Ks = 1250.0 cm d ', D, Case IV with Ks = 450.0 cm d-'.

74

Water Content (cm^ cm"^)

0 0.05 0.1 0.2 0.25 0.35 0.15 0.3 0

4

8

Case II, Ks = 450.0 cm / d i Case III, Ks = 250.0 cm / d |

12

Figure 3.20. Water content measurements and model predictions for day 22. The circles represent measured water contents.

75

o. o Q

0 0

8 —

12

0.05

Water Content (cm^ cm*^)

O.i 0.15 0.2 0.25 0.3 0.35

Case II, Ks = 450.0 cm / d"

Case III, Ks = 250.0 cm / d i


76

Water Content (cm^ cnr^)

0.15 0.2 0.25 0.35 0 0.05 0.1 0.3 0

4

8

Case n, Ks = 450.0 cm / d~j Case III, Ks = 250.0 cm / d I


77

The simulated profile based on the model incorporating full hysteresis (Case III)

provides the best overall results for this situation as compared to the model with no

hysteresis. These results are supported by similar findings by Pickens and Gillham

[1980] who found that including or neglecting hysteresis had the most pronounced

effect on the pressure head and water content profiles. With regard to the simplification

of using a homogenous profile model to describe a heterogeneous field profile, the

model appears to do an adequate job during the first 24 days of infiltration (flux

controlled irrigation) with the quality of the predictions decreasing as the water moves

deeper in the soil profile and drainage is dominant. During the drainage phase (and

without layering in the model) the simulated profile moves toward a more homogeneous

profile. The predictions from the hysteretic model (Case III) provide visually better

results to the observed profile during the infiltration phase than the model with no

hysteresis (Case II). The quality of these results may be due to the variability of the

initial conditions and the different retention characteristics between the two models, and

are therefore somewhat artificial. Given a different set of initial conditions the non-

hysteretic model may have produced superior results compared to the model

incorporating hysteresis. Clearly both models fail to accurately predict the shape of the

soil water profile as the late time drainage phase progresses. It should also be pointed

out that the model was adjusted with respect to the wetting front arrival and drainage

time series. Had the model been adjusted using soil water profiles instead of the

drainage time series better predictions for the soil water profile could have been

78

obtained. However, taking this approach would have necessitated the use of a multi-

layered model.

3.3.7. Simulation of Cases VI and VII, Experiment II

A post audit of the model was conducted to verify the quality of the predictions.

The post audit was carried out using data from the second infiltration experiment and

the hydraulic parameters from the two models (Cases II and III), one without hysteresis

(wetting parameters. Case VI) and the other employing hysteresis (Case VTI). Figure

3.23 shows the initial conditions for the second experiment; they are the final water

contents observed at the end of Experiment I. Figure 3.24 through Figure 3.26 show the

mean measured water content time series for the 1.5 m, 3.0 m and 7.5 m depths. As for

the Experiment I cases, the case with no hysteresis specified (using hydraulic

parameters based on the wetting experiment. Case VI) provided comparable results to

the case incorporating hysteresis in both the retention and hydraulic conductivity

functions (Case VII). The predicted water content time series for Experiment II at the

1.5 m depth (Figure 3.24) fit the observed data with a higher degree of accuracy than

the predictions from Experiment I (Figure 3.15) and provided comparable results to

Experiment I simulations at other depths (Table 3.5). The change in the tensiometer

readings during passage of the wetting front again clearly delineates the wetting front

arrival and the start of the drainage phase and coincides almost exactly with the

simulated results.

79

0.05 Water content (cm^ cm'^)

0.1 0.15 0.2 0.25 0.3

Figure 3.23. Model initial conditions and observed initial conditions for Experiment II. The circles represent the mean observed water contents. The horizontal lines represent ± one standard deviation and the solid line represents the interpolated water contents used in the model (HYDRUS).

80

-50

1 }

0 50

" Case VI, Ks = 450.0 cm / d

—Case Vn, Ks = 250.0 cm / d

160

140

+ 120 ^ O

100 = E

80 ^ §

60 g o

+ 40 ^

20

0

100 Time (day)

150 200 250


81

-50 0 50

120

100

80

- 60

x E o

40 I E-

Case VI, Ks = 450.0 cm / d -|- 20

Case Vn, Ks = 250.0 cm / d

100

Time (day)

150 200 250


82

0.2 <>

- - Case VI, Ks = 450.0 cm / d

Case Vn, Ks = 250.0 cm / d

0 50 100 150 Time (day)

200 250


83

3.4. Conclusions

The arrival of the wetting front was simulated and compared to observed data

from two successive field infiltration events. Several models were developed using

hydraulic properties derived from drying and wetting experiments. These models were

then compared and fine-tuned if necessary, against data taken from the first infiltration

experiment. A post-audit of the models from Experiment I was conducted using data

from a second experiment. Using the hydraulic properties from Experiment I,

simulations were performed and the results compared to the measured data from

Experiment II to assess the quality of the predictions as well as the assumption

regarding using a homogeneous representation of the soil profile.

From this study it was determined that the saturated hydraulic conductivity, Ks,

had to be adjusted to predict the time of the wetting front arrival and the changes in

water content observed in the field during and after infiltration. A modified version of

the scaled-predictive method introduced by Mace et al. [1998] offered a valuable tool

for determining how much to adjust Ks to adjust the predictive hydraulic conductivity

relationship. Without increasing Ks tenfold from the value of 46 cm d"', determined in

the laboratory, to 450 cm d"', determined in the field from tensiometer observations at a

range of depths from 0.5 to 3 m from around the monitoring islands, acceptable

predictions for Experiments 1 and II could not be made. Thus Ks became an effective

saturated hydraulic conductivity, Ks.eff, which incorporates uncertainties not included in

the laboratory determined Ks. Simulations solely based on hydraulic properties

estimated in the laboratory with core samples as first approximations yielded poor

84

results with regards to estimating the arrival of the wetting front at various depths as

well as predicting the drainage phase of the experiment. Adjustments made to the

parameter, lead to reasonably good results for estimating the arrival of the wetting front

and changes in water content. The results also support the use of a homogeneous

vertical soil profile for this particular field site. The simulations utilizing properties

taken from wetting experiments (Case II) and the case incorporating hysteresis into the

retention and hydraulic conductivity functions (Case III) yielded the best results as

compared to the results from utilizing hydraulic properties taken from drying

experiments. Comparison of the results from Cases II and III indicate that hysteresis

was not a dominant mechanism during these experiments; this may be because the soil

profile remained in the "wet" region of the retention curve during most of the

experiment. Incorporation of hysteresis into the soil hydraulic functions, however,

yielded superior predictions of the soil water content profile as compared to predictions

without hysteresis and is supported by similar findings of Pickens and Gillham [1980].

Another factor affecting these results is that while Case III follows a separate main

drying curve from Case 11 (Figure 3.18), the maximum difference between the drying

curves for Cases II and III is approximately 7 % at 100 cm of suction; this would

indicate that a large difference should not be seen between the two cases. However,

incorporation of hysteresis did result in the use of a more realistic value for the

saturated hydraulic conductivity as compared to the case without hysteresis (Case II).

Utilizing hydraulic properties (based on soil texture) taken from an internal,

general database in HYDRUS (Cases FV and V) the question of whether or not the

85

laboratory derived hydraulic properties (Cases II and III) offer an advantage over the

database properties was addressed. Using saturated hydraulic conductivity as a fitting

parameter it was not possible to adjust either of the two models using hydraulic

properties taken from the internal database (Case IV and V) as a first approximation to

the same degree of quality as the models using the laboratory derived properties (Case

II and III). This is supported by the MSE values (Table 3.5). Based on these results,

the laboratory-derived parameters provide a superior first approximation for predicting

the wetting front arrival and the shape of the curves.

A post-audit of the fine-tuned models, using fine-tuned laboratory derived

hydraulic parameters, conducted by simulating a second irrigation event in the same

plot, yielded good results, with the MSE (Table 3.5) of the same order as the results

obtained from Cases II and III. In addition, it would appear that the assumption

regarding the use of a homogeneous soil profile is supported.

In conclusion, for this field site, and under these conditions, the use of a relatively

simple one-dimensional model is suitable for predicting processes such as wetting front

advance at the scale of tens of meters. The results also show that, although laboratory

derived hydraulic properties may be limited in their applicability to field settings, for

this field setting they clearly offered a superior first approximation as compared to

hydraulic properties based on textural considerations taken from a database.

86

4. FIELD SCALE SOLUTE TRANSPORT THROUGH VARIABLY SATURATED MEDL\ INCORPORATING HYSTERESIS

4.1. Introduction

Prediction of flow and transport through variably saturated porous media requires

the estimation of hydraulic and transport properties. Solution of the unsaturated flow

component, approximated by Richards' equation, requires that the unsaturated hydraulic

properties be estimated. In most cases the van Genuchten model [van Genuchten, 1980]

requires a minimum of five parameters: reduced water content (fir), saturated water

content (6^), the empirical parameters affecting the shape of the hydraulic functions (a,

m and n) and the saturated hydraulic conductivity (/Tj). The equilibriimi CDE, used to

predict the transport of solutes, requires that at least three parameters be defined: the

retardation factor (/?), the average pore-water velocity (v), and the dispersion coefficient

(Z)), a parameter that combines the effects of mechanical mixing and molecular or

fickian diffusion. These properties are often difficult to define with any confidence,

even for homogeneous laboratory columns. Further complications arise when

estimating these properties in field settings because of heterogeneous conditions and

experimental uncertainties associated with field scale experiments. This study

addresses the issues affecting the estimation of flow and transport at the field scale. The

effects of spatial averaging of point measurements to infer these properties are also

evaluated here by their subsequent use in analytical and numerical models. The effects

of incorporation of hysteretic relationships into the unsaturated flow model are

87

investigated through simulation of solute transport and comparison with field

measurements.

There is no clear consensus among investigators regarding the dependence of

transport properties on the flow conditions. Many investigations have observed a linear

increase of the dispersion coefficient with increasing depth for higher flow rates in

saturated media in field scale transport studies [Ellsworth et al., 1996; Jacques et al.,

1998; Vanderborght et al., 2000]. In contrast, Porro et al. [1993] found no scale

dependence of the dispersion coefficient in unsaturated layered soil proflles up to 6 m

deep where the layer thickness is small relative to the scale of observation. Jacques et

al. [1998] found deviations from the expected linear increase in dispersivity with depth

for steady-state chloride transport through two heterogeneous field soils. Finally,

Padilla et al. [1999] show a dependence of dispersivity on both the properties of the

media as well as the water content.

As with scale dependence of flow and transport properties, there is no generally

accepted approach to spatial averaging of point measurements for large-scale analyses.

For example, Porro et al. [1993] found significant differences in the estimation of

transport properties using data from individual locations (local approach) as opposed to

using the data to simultaneously fit data fi-om all depths to estimate the transport

properties (global approach). In this study, the local and global approaches for both the

flow and transport properties are compared and forward models generated using these

averaged properties are compared with field measurements. The effects of averaging

88

these properties are evaluated by using them in a simple analytical solution to the CDE

and a numerical model, HYDRUS 1-D [Simunek et al., 1998],

Hysteresis presents a further complication when estimating flow parameters for

variably saturated media. Pickens and Gillham [1980] examined the effects of

incorporating hysteretic relationships into the unsaturated hydraulic functions on the

pressure head, water content and concentration profiles for a hypothetical one-

dimensional case where a slug of water containing a non-reactive tracer is introduced

into a column of sand and allowed to infiltrate and redistribute. They concluded that the

effect is greatest on the pressure head and water content profiles with a negligible effect

on the concentration profile. This treatment is repeated in this study to evaluate the

effects of hysteresis on solute flow through a variably saturated heterogeneous media.

A slug of water is introduced containing a non-reactive tracer followed by a slug of

solute free water and allowed to redistribute.

Generally, the objective is to simulate the transport of a solute through variably

saturated media integrating the steps necessary to achieve this goal. It is the intention to

convey a unified overall approach to modeling the transport of a solute fi'om estimation

of the various properties required to model this process, the development of a

conceptual model to describe the system being modeled, and how this conceptual model

impacts transport predictions.

Specifically, the objectives of this paper are to; evaluate location specific and

spatially integrated inversion methods on the ability to characterize the transport

parameters, to investigate the effects of spatial averaging of the estimated transport

89

properties and the impact on transport predictions when used in transport models, and

finally to investigate the effects of hysteresis and the retardation coefficient on solute

transport predictions.

4.2. Transport Models

4.2.1. Parameter Estimation and Analytical Solutions to Solute Transport

Parameter estimation was accomplished by using CXTFIT 2.1 [Toride et al.,

1995] in the inverse mode with observed concentration data from the SMI and NMI

locations. These estimated parameters were then averaged and used as first

approximations in analytical and numerical models. The analytical model is based on

an analytical solution to the one-dimensional CDE [van Genuchten and Alves, 1982].

HYDRUS I-D [Simunek et al., 1998] was used to numerically simulate flow and

transport using the estimated parameters. The results of the analytical and numerical

models were then compared to observed data and to each other to optimize the transport

parameters. The transport parameters were modified by an iterative comparison of the

results from the analytical and numerical models to the measured data.

The retardation factor and the dispersion coefficient were estimated using

CXTFIT 2.1 [Toride et al., 1995]. This code uses a nonlinear least-squares parameter

optimization method to estimate the solute transport parameters using any of three one-

dimensional transport models: the deterministic equilibrium CDE, the deterministic

90

nonequilibrium CDE, and the stream tube model for field-scale transport. CXTFIT 2.1

numerically evaluates analytical solutions to these transport models.

The observed data were analyzed in terms of the conventional equilibrium CDE

to estimate the solute transport parameters and to simulate the transport of bromide and

is given by:

where v is the average pore-water velocity ( y = q / 0 ) (cm d ') and R is the retardation

factor (dimensionless). R is given by:

r = 1 + (4.2)

where pb is the soil bulk density (mg cm'^), and Kd is the distribution coefficient (cm^

mg ') relating solute adsorption on the solid phase to the solute concentration in the

liquid phase and was assumed to obey a linear isotherm equilibrium. No decay or

production terms were included for the tracer. For this particular system, the inverse

boundary-value problem was solved by minimizing an objective function describing the

tit of a mathematical solution of equation (4.1) to the observed concentration data

[Toride et al., 1995] for the R and D parameters.

A third-type boundary condition was used at the soil surface and a zero

concentration boundary was applied at the groundwater table. The initial and boundary

conditions for the solute transport models are given by:

c(z,0) = c,(z) = 0 /=/„ (4.3)

91

\ d z j

+ qc = 31.6 mg /1 r=lIJ

-l9D

dc dz

dc^ = 0

r=llJ

= 0

0 < / < 15 days

/ >15 days

t > 0 days

(4.4)

(4.5)

(4.6) r=0

where D is the dispersion coefficient (cm^ d"') and q is the fluid flux density (cm d ').

The plot was irrigated at a rate of 1.85 cm per day for a total of 24 days; for the first 15

days the irrigation water contained 31.6 mg /1 of bromide (average concentration).

The following solution of the deterministic equilibrium CDE, with no

production or decay terms [van Genuchten and Alves, 1982] is used to estimate the

solute transport properties and to simulate the transport of bromide:

\ c i + { c „ - c , ) A i z , t ) 0 < t < t o

) ^ ( 2 ' , 0 - A ( z , t - t j t > L (4.7)

with

A { z , t ) = 0 . 5 e / f c Rz-vt

2 (£>/?/)"

^ 2, V t

^tvDR J exp

{ R z - v t f

ADRt

-0.5 V

2 . \ , V Z V t 1 + — +

D DR exp

D erfc

J

Rz + vt

2 { D R t ) OJ

(4.8)

where c, is the initial solute concentration in the soil profile, Co is the input

concentration, and to represents the length of the solute pulse after which the input

concentration is 0. This solution is subject to the condition where the volumetric water

content and flux are constant in time and space (steady-state condition).

92

4.2.2. Numerical Modeling of Solute Transport

HYDRUS 1-D [Simunek et ai, 1998] was utilized to simulate the transport of

bromide through a variably saturated soil profile. Separate governing equations were

solved for the solute transport and water flow when solving coupled problems in

HYDRUS. HYDRUS couples Richards' equation with the CDE to solve problems of

flow and transport through variably saturated media. For this study, two previously

developed flow models (Section 3.3.4, Cases II and III) were coupled to the transport

model to simulate the transport of the solute, bromide. The first flow model does not

incorporate hysteresis into the soil hydraulic functions while the second does.

The governing solute transport equation, solved in HYDRUS 1-D for this

system, is given by:

d0Rc _ d f

d t 5 z V & dz (4.9)

The retardation factor, R, and dispersion coefficient, D, are given by:

R = (4.10) 0 (l + 7c^)

D = av^D^T^ (4.11)

where, (412)

where/is the fraction of exchange sites assumed to be in equilibrium with the solution,

ks, P, and rj are empirical constants, a is the dispersivity (cm), Dy, is the binary diffusion

coefficient in free water for a particular solute (cm^ d"'), and Tw is a tortuosity factor

93

developed by Millington and Quirk [1961]. Wben^ = 1, adsorption occurs according to

the Langmuir model, when»/ = 0, adsorption occurs according to the Freundlich model,

and when P = I and 7 = 0, adsorption occurs according to a linear adsorption isotherm.

Setting ks = 0 specifies no adsorption (/? = 1). The values of water content, 0, and the

flux density, q, are required to solve this equation and are determined by solving a

mixed form of Richards' equation. Note that R cannot be fixed to a constant value

when solving coupled systems since ^is solved by Richards' equation and is a function

of the soil hydraulic functions.

The initial concentration throughout the 11.5 m profile was specified as 0 mg /

cm^. The initial water contents were calculated for each modeled depth by linear

interpolation of the observed water contents (Figure 4.1). The initial and boundary

conditions for solute transport are given by Equations (4.3) - (4.6).

The initial distribution of pressure head was calculated from the average water

content measured with the neutron probe at each depth (Figure 4.1) using the water

retention model (3.9).

94

0

1200

-0.5

0.1 Water Content (cm^ cm'^)

0.2 0.3 0.4

-0.25 0 Concentration (mg cm"^)

0.25

0.5

0.5

Figure 4.1. Model initial conditions and observed initial conditions. The circles represent the mean observed water contents. The horizontal lines represent ± one standard deviation and the solid line represents the interpolated water contents used in the model (HYDRUS). The dashed line represents the initial conditions for the bromide used in the model (HVDRUS).

95

4.3. Measured Bromide Concentrations

The bromide concentrations used were measured at the 50 - 300 cm depths (50 cm

intervals) at the NMI and SMI locations (Figure 4.2 - Figure 4.5). Only the SMI, west

side experienced breakthrough of bromide at all depths within the irrigation time period,

with the bromide breaking through at approximately 19 days at the 300 cm depth (Table

4.1). At the 300 cm depth, bromide breakthrough occurred at 29 days for the NMI, east

side, and 37 days for the SMI, east side locations. The NMI, west side location

exhibited a very dispersed breakthrough at 200 cm, with this behavior continuing at the

250 and 300 cm depths (relative concentration below 0.5). The SMI, east side location

also demonstrated some dispersive behavior at a depth of 200 cm and below with the

bromide breakthrough curves flattening somewhat as compared to the breakthrough

curves at the shallower depths. The NMI, east side and SMI, west side locations

experienced very strong bromide breakthrough even at the 300 cm depth with the

breakthrough curves exhibiting sharp bromide interfaces with both locations

experiencing greater than 80 percent of the bromide breaking through within 4-10

days. Table 4.1 lists the breakthrough times of the bromide at the monitoring island

locations. This breakthrough time is defined as when relative concentration of the

bromide reaches 0.5 or larger. Locations where relative concentrations exceeded one

can be explained in part by the fact that an average input concentration of 31.6 mg /1

was used to normalize the concentrations when in fact input concentrations exceeded 40

mg /1 on some irrigation days (Table 2.2).

96

_o

nj CJ c o CJ o >

o QC

s o

s o u c o o u >

o 2sj:

c o

c o u c o CJ >

a:

1-2 o 50 cm

0.8

JO

o

200 cm

oo °c5b o ̂ o o

O O o o

no

^ 0.4 o o

0

1.2

^ftrtCnpinnn o! O !Q ^ °!o

100 cm 250 cm

°c^

° o °

0.8 •— o'

0.4 ^—o °°o

ooo oo

Oo po,

0 oj O ,o o o ,o

o o

o o

LO

1.2 :— CP o

°150 cm

0.8 o 6*

o o

300 cm

o — o o o O

O r\ oo o° o

S 0.4 o

o

0

o o O !

(JB> I

0 20 40 60 80 0 20 40 60 80 100


Figure 4.2. Relative bromide concentrations from the NMI, east side.

97

c o 1.2 50 cm 200 cm

c O U c o u o >

cs:

c

"cS b. c o o c o o o >

o a:

"S u. C a> o c o o o >

o

0.8 -O o o o

S 0.4

o o

O o o o

o o

0 j § : ^oo°o o o; O o o ° o

OD o

1.2 -

0.8 H

100 cm

o O O O

o o •« 0.4 r o

o

O O O

0

1.2

0.8

n 0.4

150 cm

o Oo°oo° ^ o

o o -

o

o o o ,

0

250 cm

O O

poo°0 O O

300 cm

o o O

CQp OQO

Oo °

0 20 40 60 80 0 20 40 60 80 100


Figure 4.3. Relative bromide concentrations from the NMI, west side.

98

c o

o u c o CJ o

G O CJ C o CJ >

c

13 Urn

c o u c o u u >

1.2

0.8

50 cm

0.4 "-Q"

0

200 cm

° o O o ° " o

o o

;0

o o '^6^0r,'0^ O oi o O 6 ^ o

S 1.2 100 cm 250 cm

0.8 ~o O o 5_i

O Q O O

S 0.4 - cP o oO o o ^ o o

R- O

jS-0

1.2

0.8 i—

OO

CP p '

150 cm o o 0°Oo o ° n O o O O O o ^

o ° o

1 0.4 O

QC

6>

cP 2̂° ̂I

300 cm

o o

^Oo o o

CD O

0 20 40 60 80 0

Time (Days)

20 40 60 80 100

Time (Days)

Figure 4.4. Relative bromide concentrations from the SMI, east side.

99

1.6

c _o « W c

c o u o >

OC

c _o

b. c o u c o ZJ a >

OL

c

"S c o u c o u o > "5 o

_o o

1.2 50 cm 200 cm

0.8 o

0.4

o Q

°o o O o

O ̂ O (5—

0 9y»yO nUn o Q! O o ri O io O

1.2 ;— i On

0.8

100 cm — 6'

250 cm

o° o o^o O o ° O o

•« 0.4

— ° ' o

o o

0 <9,

o °0 0 ' i '

OOP o oi n o ri Q o o

idlTl

1.2 —

0.8

150 cm 300 cm o cP

O O

Oq O O O O O o ° o ~

o oO

0.4 — o o

0 (9 s ol LSJgl

0 20 40 60 80 0 20 40 60 80 100


Figure 4.5. Relative bromide concentrations from the SMI, west side.

100

Table 4.1. Breakthrough times for the monitoring island locations

Depth (cm) North monitoring island South monitoring island

Depth (cm) West East West East

50 6.5 4 3 5 100 12.5 11.5 9 11 150 19 19 15 21 200 37 21 15 25 250 27 18 39 300 29 19 37

101

Two locations, NMI (west) and SMI (east), exhibit what may be preferential

transport. The locations show what are perceived as the breakthrough of bromide at

two different times. This behavior can be observed at depths of 150, 200 and 250 cm at

the NMI (west) locations and the 150 and 200 cm at the SMI (east) locations. Possible

causes for this behavior are discussed below.

4.4. Methods

4.4.1. Mass Balance

A mass balance was calculated for bromide. Experiment I. The mass balance

compared the amount of bromide in the water applied to the upper surface of the plot

through the trickle system to the amount of bromide in the water contained within the

soil profile at the monitoring island locations at specific times during the experiment.

The bromide mass present in the soil profile was determined by integrating the soil

solution mass profile with depth for specific times during the experiment. The amount

of bromide applied to the plot through the trickle system was calculated as a fxmction of

time as the average KBr input concentration multiplied by the volume of water

measured fi-om water meters located at the inlet water pipes of the irrigated plot. A

mass balance was calculated according to the following equations;

Mass balance = (4.13)

= (4.14) 0

102

A(^c) = (^cX_-(5'c),̂ o

(4.15)

where M is ±e mass of bromide (mg cm'^), Az is the vertical depth interval represented

by a given solution sampler (cm), A^is the change in water content from the initial

condition, Ac is the change in concentration from the initial condition (mg cm'^), and i

represents a measurement interval.

4.4.2. Approach

The approach for achieving the objectives involves multiple steps. First, the

measured data used for estimating transport properties and evaluating predictions from

different transport models are presented and summarized. Secondly, two approaches

are investigated for estimating the transport properties using CXTFIT 2.1 {Toride et al.,

1995]. Thirdly, averaging schemes using the estimated transport properties from the

two approaches are evaluated by using analytical and numerical models in the forward

mode. Fourth, numerical models are used to quantify the effects of hysteresis on solute

transport. Finally, numerical models are used to quantify the effects of possible

mechanisms, such as anion exclusion or preferential flow, which require the adjustment

of the retardation coefficient on solute transport.

103

4.4.2.1. Parameter Estimation

Two approaches similar to that of Porro et al. [1993] were taken for estimating

the transport parameters, a local approach and a global approach. For both approaches

the inverse model estimates the retardation factor and dispersion coefficient and

requires that the average pore water velocity be defined. The classical form of the

equilibrium CDE used for estimating the transport properties (Equation (4.1)), requires

that the water content and average pore water velocity are constant in both time and

space (steady-state flow). Based on these restrictions, the average pore water velocity

was calculated differently for each method. The two approaches were evaluated using

analytical models in the forward mode. The estimated transport properties were then

averaged using two different schemes. The averaging schemes were also evaluated

using analytical models in the forward mode. Six test cases were conducted to

accomplish these tasks. Table 4.6 summarizes all the test cases for the readers benefit.

In the local approach (Case 1), the parameters were estimated for each individual

depth and monitoring island location for which the breakthrough of bromide occurred

within the irrigation time period (Table 4.2). A total of 16 out of a possible 24 locations

fulfilled this criterion. Because of the above named restrictions, an average pore water

velocity was computed for each location by averaging the water contents behind the

wetting front for each particular depth interval and location and using an applied upper

flux rate of 1.85 cm d"' {y = q I Oavg).

For the global approach (Case II), the observed data from all six depths were

fitted simultaneously to estimate the solute transport parameters at each sampling

104

Table 4.2. Locations where bromide breakthrough occurred within the irrigation timeframe

Depth (cm) North monitoring island South monitoring island

Depth (cm) West East West East

50 X X X X 100 X X X X 150 X X X X 200 X X 250 X 300 X

105

location (i.e. four locations, NMI and SMI, east and west sides). The average pore

water velocity was computed for the upper 300 cm of the soil profile using the average

water content measured behind the wetting front from all the depths above 300 cm and

the applied flux rate of 1.85 cm d '. Table 4.3 shows the input parameters used in the

inverse models for Cases I and II.

4.4.2.2. Predictions Using an Analytical Model

The estimated transport properties were evaluated using analytical models in the

forward mode. The estimated transport properties were not averaged for these cases.

Cases III and IV investigated the localized and global methods for estimating the

transport properties. Case III solved the equilibrium CDE using transport parameters

estimated for each depth, for the SMI west location (Case I). Case FV solved the

equilibrium CDE using transport parameters estimated for the SMI west location using

the data from all depths collectively (Case II). This location was chosen because it is

the only location where the breakthrough of bromide was measured down to the 300 cm

depth within the irrigation timeframe (Table 4.2). Table 4.4 lists the input parameters

used in Cases III — VI.

The estimated transport properties were averaged according to the method by

which they were estimated. Cases V and VI evaluated which averaging scheme

provided the best results when compared to the measured bromide concentrations.

106

Table 4.3. Input parameters used in the inverse models. Cases I and II

Depth (cm) Case I Depth (cm) a * vavc (cm / d) R D (cm" / d) 50 0.26 7.12 1.00 10.00 100 0.25 7.40 1.00 10.00 150 0.24 7.71 1.00 10.00 200 0.23 8.04 1.00 10.00 250 0.22 8.60 1.00 10.00 300 0.22 8.60 1.00 10.00

Location Case II NMI, west 0.235 7.87 1.00 10.00 NMI, east 0.235 7.87 1.00 10.00 SMI, west 0.235 7.87 1.00 10.00 SMI, east 0.235 7.87 1.00 10.00

* average water content behind wetting front, in the upper 300 cm for Case II ^ v = q / davg, <1= 1.85 cm / d

Table 4.4. Transport parameters for the analytical model. Cases III - VI

Depth (cm) R £>(cm^ d"') V (cm d"') a (cm) Case III, SMI west, properties from localized approach

50 0.50 4.74 7.12 0.67 100 0.66 3.03 7.40 0.41 150 0.76 2.06 7.71 0.27 200 0.61 3.90 8.04 0.48 250 0.61 3.65 8.60 0.42 300 0.56 3.54 8.60 0.41

Case IV, SMI, west, properties from global approach 0-300 0.57 24.47 7.87 3.11

Case V, properties averaged from local approach 0-300 0.78 8.89 7.64 1.18

Case VI, properties averaged from global approach 0-300 0.87 21.71 7.87 2.76

107

Case V solved the CDE using transport parameters formed by averaging all 16 locations

(properties estimated from Case I, Table 4.4). This approach was taken, rather than

averaging the averages of each individual depth, because of biased weighting that

would result for the depths where breakthrough occurred at only one or two locations.

Case VI used transport parameters produced by averaging the parameters estimated

globally from Case II. The four sets of transport properties using the global method

were averaged to yield one set to describe transport through the entire soil profile.

It should be noted that both schemes could introduce a certain bias into the

transport properties. Depending on what fraction of locations experience dispersed or

"plug" flow transport processes at a specific location could be misrepresented by the

mean transport properties. Four analytical models were tested (Cases III - VI) to

evaluate the two approaches for estimating the transport properties and the averaging

schemes of these estimated properties.

4.4.2.3. Numerical Solute Transport Simulations

Numerical models were used to investigate the effect of hysteresis and the

retardation coefficient on the transport of bromide. The results of the numerical model

were also used to evaluate how well the average transport properties, estimated using

analytical models, represented the average behavior of bromide when used in a

numerical model. In addition, the results from the numerical models and the " best fit"

analytical model (Case VI) were compared to evaluate the strengths and weaknesses of

108

each approach. Three cases were simulated to explore these issues. Cases VII and VIII

used the average estimated transport properties from Case VI, which provided the best

results with respect to the MSE. The effect of hysteresis on the breakthrough of

bromide, as well as on the bromide profiles, was tested in Cases VTI and VIII. Case VII

used the flow model without hysteresis incorporated into the soil hydraulic functions.

Case VUI utilized the results from a flow model that incorporated hysteresis into the

soil hydraulic fiinctions. The results of Case VIII, which incorporated hysteresis into

the unsaturated flow model, was compared to the breakthrough of bromide with no

hysteresis specified in the unsaturated flow model (Case VII).

Case IX used transport parameters estimated by Young et al. [1999] assuming

bromide is conservative and is not subject to adsorption {ks = 0) (Table 4.5). The results

from the flow model incorporating hysteresis were used in this case. The predictions

from this case are compared to predictions from cases that use a retardation coefficient

less than one (Cases VII and VIII). Because of the manner in which R is defined,

(4.10), ks had to be estimated using a single average water content representative of the

soil profile behind the wetting front. A linear adsorption isotherm was used for this

case with negative adsorption {R< 1). It is further assumed that 100 percent of the

exchange sites were in equilibrium with the fluid.

Solutes or dissolved species subject to attenuation travel at a rate that is retarded

relative to the average pore-water velocity. Solutes may also travel at a rate that is

faster than the average pore-water velocity due to mechanisms such as negative

adsorption (anion exclusion) or preferential flow. The retardation coefficient is

109

Table 4.5. Mean transport properties used in the numerical models, Cases VII - IX

Case R or (cm) ks (mg cm'^)' f P n Flow Model

VII 0.87 2.76 -1.95 X 10'^ 1 1 0 No hysteresis

VIII 0.87 2.76 -1.95 X 10'̂ 1 1 0 Hysteresis

IX I.OO 3.1 0.0 1 1 0 Hysteresis

X^ 1 ^ ,

0.87 2.76 -1.95 X 10'̂ 1 1 0 Hysteresis Calculated using a constant water content of0.225 behind the wetting front

^ Variable input concentration boundary condition (Figure 2.4)

110

typically used to account for the net effects of a solute or dissolved species that is

attenuated in some manner with R values typically greater than 1. In cases where

solutes or dissolved species travel faster than the average pore-water velocity R values

typically less than 1 are used. Many mechanisms that are difHcult to quantify have been

identified by investigators that affect the transport of solutes. These mechanisms include

variations in local unsaturated hydraulic conductivities, variable local pore-water

velocities, preferential or macropore flow, and anion exclusion. Variations in local

unsaturated hydraulic conductivities has been attributed to variability in local pore-

water velocities creating a scale dependency in the dispersion coefficient [Ellsworth et

al., 1996]. Variability in local pore-water velocity fields in turn are attributed to

concentration hotspots, irregular concentration distributions, and the observation of

local scale dispersion coefficients that are much smaller then global scale dispersion

coefficients [Hammel and Roth, 1998]. Preferential flow has also been found to have a

significant impact on the transport of solutes. Roth et a/. [1991] found that mechanisms

they attributed to preferential flow caused a single uniform solute pulse to split into

several pulses of varying velocities causing a depletion of the main pulse with respect to

mass. Due to the number of unsaturated variables affecting transport and the non-

linearity of these properties they were unable to delineate the details of preferential

flow. Anion exclusion has been found to have a significant impact on the transport of

anions with respect to solute arrival times and concentrations [James and Rubin, 1986;

Porro et al., 1993]. Anion exclusion is the process whereby the anion, carrying a

negative charge, is repelled by the electrostatic double layer of clay particles within the

I l l

soil. The repulsion of anions away from the interface of soil particles forces the anions

into the center of the pores. Anions traveling in the center of the pores, i.e. the point in

the velocity profile where the fluid velocity is greater than the average pore water

velocity, travel farther than predicted using the average pore water velocity (i.e. /? = 1).

An additional case (Case X) was made to evaluate how the boundary conditions

as defined affect the predicted bromide breakthrough curves. Instead of using an

average input bromide concentration of 31.6 mg /1 (Equation (4.4)) a variable input

concentration was used as shown in Figure 2.4. This was done to assess if the

variability of the input bromide concentrations could help describe the observed

behavior of dual bromide breakthrough curves discussed in Chapter 4.3. Table 4.6

summarizes all the test cases for field scale solute transport for the readers benefit.

The nine models were evaluated according to their ability to accurately predict

the breakthrough time of the solute front and the mean square errors (MSE) of the

predicted versus observed solute concentrations at each depth. The MSE for one depth

is given by:

where c,, c., are the measured and predicted solute concentrations for bromide

respectively, for a time interval, i.

2

(4.16)

112

Table 4.6. Sununary of test cases for field scale solute transport

Case Description I Transport properties estimated using local approach II Transport properties estimated using global approach III Evaluation of local approach using analytical model in forward mode IV Evaluation of global approach using analytical model in forward mode V Evaluation of average transport properties from local approach using

analytical model in forward mode VI Evaluation of average transport properties from global approach using

analytical model in forward mode VII Evaluation of excluding hysteresis on solute transport using numerical models

(anion exclusion included) VIII Evaluation of incorporating hysteresis on solute transport using numerical

models (anion exclusion included) IX Evaluation of ignoring anion exclusion on solute transport using numerical

models (hysteresis incorporated)

113

4.5. Results and Discussion

4.5.1. Mass Balance

A mass balance calculation was performed using equations (4.13) - (4.14).

Figure 4.6 shows the bromide mass measured in the soil profile at the two monitoring

islands for each day during the time of bromide application. At the SMI (west side), the

amount of bromide recovered was on average only 51 percent of the amount applied; 35

percent of the applied mass was recovered on the east side. At the NMI, 46 and 29

percent was recovered from the east and west sides. At the four locations the amounts

of bromide recovered follow a trend with, on average, 41 percent of the bromide

recovered, which falls on the 59 percent error line shown. Possible sources of this error

are anion exclusion, preferential transport, bias introduced by the measurement device

(i.e. solution samplers), integration of the soil water profile, and analytical error in

measuring the bromide concentrations.

Analysis by various investigators have found a large variation in mass recovery

of bromide using solution samplers. Ellsworth et al. [1996] found that solution

samplers consistently under-estimated the applied mass for three tracers, bromide,

nitrate, and chloride. The consistency between the breakthrough curves suggested that

the poor mass recovery was not attributable to spatial variability or an inadequate

number of measurements. Rather, the solution samplers measure the concentration only

at the cup location and therefore do not provide a complete spectrum of the solute flow

paths [Ellsworth et al., 1996]. Adams and Gelhar [1992] found similar results when

114

1 ^

5 0.8 CO

o E 0.6 0 a.

1 0.4 •o o « eb 0.2

• SMI, west • SMI, east • NMI, west o NMI, east

' 59 % error

Excess recovery

Incomplete recovery

I

0

0.2 0.4 0.6 Amount applied (mg cm ")

0.8

Figure 4.6. Amounts of bromide recovered at the monitoring islands from day 5 to day 15, the solid line represents 100 percent recovery.

115

analyzing data from a 20-month natural gradient tracer study in the saturated zone of a

highly heterogeneous aquifer. The solution samplers recovered 45 to 300 percent of the

bromide mass which was attributed to spatial variability in hydraulic conductivity and

the sampling methodology. The poor mass recovery reflects the effects of plume

truncation, sampler bias, and possibly some type of tracer adsorption mechanism.

Butters et al. [1989] refer to solution samplers as flux concentration detectors and also

measured some variation in the recovery of bromide mass using solution samplers. The

variation was attributed to variations in local flux rates, imprecision of solution

samplers as flux concentration detectors, transient solute application rates and error

introduced from sample extraction rates that are higher or lower than the drainage flux

which can cause an over- or under-estimation of the bromide mass [Butters et al.,

1989]. Roth et a/. [1991] used data from a chloride tracer test that was monitored using

solution samplers to quantify preferential flow. Using predictions from a fitted

convection-dispersion model it was found that due to preferential flow the main pulse

would contain less than half of the applied solute mass while the remaining mass is

contained in several smaller solute pulses of varying velocities that split from the main

solute pulse.

Two potential mechanisms attributed to anion exclusion could contribute to the

bromide mass balance error. Due to anion exclusion the bromide is located only in the

center of the pore channels. The pore water extracted using the solution samplers is

from the entire pore channel (excluding of course the adhesive water around the soil

grain) which includes the water from the sides of the pore channels that contain no

116

anions, an excluded volume. Extraction of the excluded volume water in addition to the

volume containing the bromide anion results in a diluted measured concentration of

bromide. In addition, due to the anion traveling faster than the average pore-water

velocity some of the bromide may have traveled further than the bottom solution

sampler of the monitoring island during the sampling time interval resulting in a

truncation of the solute concentration profile. This effect could be further enhanced by

local average pore-water velocities that are greater than the calculated values.

Preferential transport could have led to bromide bypassing the area around the

lysimeter resulting in incomplete recovery of bromide. The truncation of the solute

concentration profile could be caused by the solution samplers measuring the solute

concentration of either a depleted main solute pulse or, a smaller solute pulse that split

from the main pulse due to a mechanism such as macropore flow or anion exclusion.

As Roth et a/. [1991] point out due to the number of variables and the complexities of

the relationships for unsaturated flow and transport it is difficult to determine the details

of preferential transport.

Another source of error can be attributed to the integration of the soil water

profile. On average, the calculated water applied under-predicted the actual amount

applied by 17 percent over the time period examined (day 5 — day 15). The under-

prediction of the applied water would reduce the calculated bromide mass according to

Equation (4.14). Experimental error in measuring the bromide concentration in the

samples could also account for some of the calculated discrepancies. Finally, Destouni

[1992] makes the observation that the random character of the average pore-water

117

velocity in natural fields implies that the mass flux and mass accumulation cannot be

evaluated deterministically. This concept could be applied analogously to the sampling

methodology which is deterministic in that the measurements are point measurements.

4.5.2. Modeling

4.5.2.1. Parameter Estimation, Cases I and II

The results for the local method (Case I) yielded good results for all locations

with correlation coefficients ranging between 0.72 and 0.98 (Table 4.7). The global

method (Case II) yielded somewhat poorer results with correlation coefficients ranging

between 0.66 and 0.95. The results from both approaches clearly show that transport

occurs at a rate faster than the average pore-water velocity, R values less than 1 were

found for most locations. As expected, the approach using the local method yielded

slightly better results as reflected by the lower r^ values. The poorer results of the

global method are most likely due to a combination of factors: the observed

breakthrough of bromide occurring almost simultaneously at 2 depths at the same

location, or in some cases, a deeper depth experiencing an earlier breakthrough than the

depth above it (Table 4.1); the presence of outliers at each depth having more weight

when considered collectively, and incomplete or faulty recovery of bromide combined

with experimental error in measuring the bromide concentrations, causing the

breakthrough curves to appear either more or less dispersed than they are in reality.

Porro et al. [1993] found a larger variation in dispersion than in retardation factors in

Table 4.7. Estimated transport properties from Cases I and II

Case / Location R £)(cm^/d) a (cm) r^ MSB Case I, 50 cm

NMI, west 1.03 8.34 1.17 0.80 0.0179 NMI, east 0.51 7.14 1.00 0.94 0.0124 SMI, west 0.50 4.74 0.67 0.87 0.0286 SMI, east 0.79 10.96 1.54 0.72 0.0195

Case I, 100 cm NMI, west 0.94 18.13 2.45 0.96 0.0067 NMI, east 0.84 14.07 1.90 0.96 0.0056 SMI, west 0.66 3.03 0.41 0.81 0.0188 SMI, east 0.81 5.77 0.78 0.95 0.0077

Case I, 150 cm NMI, west 1.00 18.03 2.34 0.98 0.0021 NMI, east 0.96 7.09 0.92 0.98 0.0028 SMI, west 0.76 2.06 0.27 0.93 0.0126 SMI, east 1.11 19.02 2.47 0.94 0.0028

Case I, 200 cm NMI, east 0.84 12.83 1.60 0.98 0.0012 SMI, west 0.61 3.90 0.48 0.88 0.022

Case I, 250 cm SMI, west 0.61 3.65 0.42 0.95 0.0121

Case I, 300 cm SMI, west 0.56 3.54 0.41 0.98 0.004

Mean 0.78 8.89 1.18 0.91 0.0111 CV (%) 24.63 65.80 66.00

Case II NMI, west 1.05 16.61 2.11 0.95 0.0072 NMI, east 0.85 25.45 3.23 0.80 0.0361 SMI, west 0.57 24.47 3.11 0.66 0.0633 SMI, east 1.00 20.32 2.58 0.88 0.0202

Mean 0.87 21.71 2.76 0.82 0.0317 CV (%) 24.87 18.72 18.71

119

parameters estimated using the local and global approaches in uniform and layered

laboratory columns. Similar results regarding the increased variability of dispersion

were found in this study, however, only when estimating the transport properties using

the local approach. Also, larger values of dispersion were estimated using a global

method than the local method, this is supported by the Porro et al. [1993] study. No

scale dependency with depth is observed in the dispersivity values (Table 4.7). hi

addition, the dispersivity values of 1 (local) to 3 (global) are small for field scales but in

agreement with lab data.

4.5.2.2. Evaluation of the Local and Global Approaches Using Analytical Models, Cases III - VI

The Uvo sets of transport properties estimated using the SMI west side measured

data were incorporated into the analytical model (Cases III and IV) and compared to the

observed data and to each other (Figure 4.7). The model based on transport properties

estimated for each depth and location (Case III) clearly yielded superior results as

compared to Case IV. Case III has lower MSE values (average MSE is 0.0149) than

Case IV (average MSE is 0.0670, Table 4.8). Additional cases that were simulated (not

shown) yielded similar results. As expected the models using parameters from the local

approach performed better than models using parameters from the global approach at

specific locations.

The model using average transport properties estimated globally (Case VI)

yielded better results than the model using average properties derived locally, from the

120

c o

c u u c o o o > w w

c o

1.2 — o 50 cm

0.8 r

/ 0.4 — ,

0 , ; /

1 •J

" o o

0 ' /' I

1.2 r

b

T

\0\ , O 1

100 cm

200 cm

o— / /o ° o d/

/; / o

^r\ n ^ ? ,q/

250 cm

o o 5 o u > _ra u Q[£

c c

o u c o u o >

u Qi.

0.8

0.4

0

1.2

0.8

Is O O O \ // o o o o o o ° I

\ o —r ! o

I ^^ ' J !

150 cm

Y ° o ° a ° /

« 0.4 ^— / L

0

/ o? / \ o ° J \

-L

o o

0/

^6 /

ojp

300 cm

O o

'O O f t 2/

0 / 1

I / / / o //

0 5 10 15 20 0

Time (Days)

10 15 20 25

Time (Days)

Figure 4.7. Comparison of measured bromide data and the predicted bromide concentrations at the SMI, west location. The solid line represents model predictions from Case III based on transport properties estimated locally (Case I), the dashed line represents model predictions from Case IV based on transport properties estimated globally (Case II).

121

Table 4.8. MSE values for Cases III - VI

NMI SMI Case Depth (cm) West East West East

50 0.0450

III Local

Approach

100 0.0167 III Local

Approach

150 200 250 300

0.0107 0.0037 0.0102 0.0034

Mean 0.0149 50 0.0567

IV Global

Approach

100 0.0658 IV Global

Approach

150 200 250 300

0.1352 0.0183 0.0413 0.0844

Mean 0.0670 50 0.1026 0.0861 0.1392 0.0238

v 100 0.0565 0.0183 0.0442 0.0133

Averaged from Case I

150 0.1146 0.1160 0.0275 0.2265 Averaged from Case I 200 0.1225 0.0049 0.2519 0.1171 Averaged

from Case I 250 0.0011 0.0005 0.4676 0.0011 300 0.0010 0.0015 0.3431 0.0013

Mean 0.0664 0.0379 0.2122 0.0639 50 0.0587 O.I 160 0.1730 0.0182

VI Averaged

from Case 11

100 0.0231 0.0060 0.0633 0.0115 VI Averaged

from Case 11

150 0.0457 0.0423 0.0751 0.1210 VI

Averaged from Case 11 200 0.0480 0.0059 0.3050 0.0424

VI Averaged

from Case 11 250 0.0006 0.0005 0.4680 0.0006 300 0.0009 0.0015 0.3420 0.0013

Mean 0.0295 0.0287 0.2377 0.0325

Table 4.9. Mean transport properties from Cases I and II used in Cases V and VI

Parameter Case V Case VI R 0.78 0.87

D (cm^ d"') 8.89 21.71 V (cm d"') 7.64 7.87

a (cm) 1.18 2.76

122

16 breakthroughs (Case V), for every location except the SMI west location (Figure

4.8). Case V had a mean MSE value of0.0951. Case VI had a mean MSE value of

0.0821 with a difference between the two cases of 15 percent. Case VI provides

significantly better results than Case V at the NMI (east and west) and SMI (east)

locations (Table 4.8). These locations yielded better results using the averaged

transport properties from Case II because the above named locations all behaved in a

very similar manner as opposed to the SMI (west) location that experienced a much less

dispersed breakthrough than the other locations.

4.5.2.3. Numerical Solute Transport Simulations, Cases VII - X

4.5.2.3.1 Effect of Hysteresis on Bromide Transport

Both Cases VII and VIII use a retardation coefficient less than 1. Because of the

manner in which R is defined, (4.10), ks had to be estimated using a single average

water content representative of the soil profile behind the wetting front. A linear

adsorption isotherm was used for this case with negative adsorption (anion exclusion).

Incorporating hysteresis into the soil hydraulic frmctions had little effect on the

bromide breakthrough curves (Figure 4.9); Case VIII (hysteresis) yielded marginally

better results than Case VII (no hysteresis)(Table 4.10). Figure 4.9 shows the measured

123

c

c o CJ o >

OC

c o

c u u c o

>

0^

ca K-c o c o C-)

>

o Q:i

r r

2 1.2 r © ° o

o ' _ z'

50 cm

0.8 — ° '/

§° 2 ° oSa> 9§8' o

0.4

O , ^ .' / d

//o

0 ^

1.2 I—

n

0.8 i— !

0.4 ;—

/ I L' ! -yQ i

O o \

o

J ! ^ o a la 0 I !

0

2 1.2 ;—

0.8 ^

0.4 r

0 0

100 cm

8

/o ^89o!8^ '

° I ° 1 I

150 cm

' n n g

200 cm O

O NO 0° o°e :

! O nifi e I-J^a o

250 cm

O O i ° O

I O t-» n ala a a a o^b a A.o-8i° 8

300 cm

Oo i

o °1

5 10 15 20 0

Time (Days)

J i n o?a Q J) 8 8!o a e 0 8!^ '

5 10 15 20 25

Time (Days)

Figure 4.8. Comparison of measured bromide data and the predicted bromide concentrations at the monitoring island locations. The dashed line represents model predictions from Case V based on average transport properties estimated locally (Case 1), the solid line represents model predictions from Case VI based on transport properties estimated globally (Case II).

124

C o

c o c o CJ ZJ >

QJ OC

c .2

c a> o c o CJ > "5

0^

c .2 "S U* C o o c o u o >

o cd

50 cm 200 cm

o o " 6 b ° - 8

° °°! o O ol o ° ° ° °

100 cm 250 cm

_ o ° 150 cm CP o 300 cm

20 40 60 80

Time (Days)

20 40 60 80 100

Time (Days)

Figure 4.9. Comparison of all measured bromide data from around the monitoring islands and the predicted bromide concentrations. The solid line represents model predictions with hysteresis in the hydraulic properties (Case VIII); the solid line with solid diamonds represents model predictions with no hysteresis in the hydraulic properties (Case VII).

125

Table 4.10. Mean square error for Cases VI - IX using average measured bromide concentrations

Depth (cm) Cases

Depth (cm) VI VII VIII, R ~ 0.87 Vni, R ~ 0.80 I X , R = 1

50 0.0195 0.0165 0.0145 0.0106 0.0273 100 0.0373 0.0044 0.0043 0.0177 0.0316 150 0.2555 0.0237 0.0232 0.0555 0.0087 200 0.1664 0.0528 0.0536 0.0676 0.0281 250 0.1439 0.0388 0.0331 0.0606 0.0282 300 0.1624 0.0319 0.0382 0.0149 0.1463

Mean 0.1308 0.0280 0.0278 0.0378 0.0451

126

bromide concentrations from all monitoring island locations at each depth along with

the simulated results from Cases VII and VUI. At most depths, both cases predicted the

mean behavior of the measured bromide and yielded predictions that are difRcult to

distinguish from each other. Only at late times can the predictions from the two cases

be delineated. At the deeper depths, the numerical solutions failed to accurately predict

the bromide concentrations at the SMI and NMI, west locations because of diverging

effects. At the SMI west location, the measured bromide breakthrough curves had a

sharp interface that indicates primarily advective transport with little or no dispersion.

At this location the numerical solutions under predicted the magnitude of the bromide

breakthrough as well as over predicted the arrival time of the solute front. At the NMI,

west location, the solute front followed a very dispersed pattern and the numerical

solutions over predict the bromide concentrations. The MSE values (Table 4.10)

supported the observation that the model without hysteresis in the soil hydraulic

functions (Case VII) yielded very similar results as compared to the model

incorporating hysteresis into the soil hydraulic functions (Case VIII).

The predicted bromide concentration depth profiles also support the conclusion

that hysteresis does not play a major role in the transport of bromide (Figure 4.10 -

Figure 4.12). No significant effect from incorporating hysteresis into the soil hydraulic

functions could be detected in the predicted concentration profiles from Cases VII and

VIII. Both solutions yield good predictions with respect to the position of the measured

solute front as well as the shape of the bromide concentration profiles. These results

127

0 0.2 Relative concentration

0.4 0.6 0.8 1.2

SMI, west

SMI, east

NMI, west

NMI, east

— —Case VII

Case Vin

Figure 4.10. Measured bromide concentrations and model predictions for day 16, irrigation day 16.

128

0 0.2

Relative concentration

0.4 0.6 0.8 1.2

SMI, west SMI, east NMI, west NMI, east

— — Case VII Case vm

Figure 4.11. Measured bromide concentrations and model predictions for day 24, the last day of irrigation.

129

0 0.2 Relative concentration

0.4 0.6 0.8 1.2

c o

a. u Q

SMI, west • SMI, east • NMI, west • NMI, east

"Case vn 'Case Vni

Figure 4.12. Measured bromide concentrations and model predictions for day 93, the last measured day of redistribution.

130

hold even for late time predictions (Figure 4.12). These results are supported by similar

studies conducted by others [Mitchell and Mayer, 1998; Pickens and Gillham, 1980].

4.5.2.3.2 Preferential Transport

Numerical predictions for a nonsorbing, nonreactive, solute (/? = 1.0, ks = 0.0,

Case IX) were compared to the results from Case VIII {R = 0.87) to determine the

effects of ignoring potential mechanisms such as preferential transport or anion

exclusion. These mechanisms, preferential transport and anion exclusion, are used here

to describe accelerated solute transport. Because the cause of the accelerated transport

is unknown the retardation coefficient is used as an effective parameter to capture the

average preferential transport behavior rather than a specific process. As mentioned

previously, the transport parameters used in the numerical models represent the

properties fi-om the forward analytical models that had the lowest MSE's. The mean

values from the global approach yielded the best results in the forward analytical

models as compared to mean transport properties from the local approach.

Case VIII yielded the best overall results in terms of the MSE's with respect to

predicting the average bromide concentrations at all the locations (Table 4.10).

However, the predictions from the numerical models yielded mixed results in terms of

the specific locations. At the 50 cm depth, all of the models accurately predicted the

measured bromide concentrations (Figure 4.13). However, at eight of the remaining 20

locations. Case IX yielded better predictions than Case VIII (Figure 4.14 -Figure 4.17).

131

c o

c u u c o CJ u >

<u o£.

NMI, west NMI, east

p Q o p j

SMI, west

20 40 60 80

Time (Days)

iFfirnnriuianu'ft iS'u'^—; SMI, east i

grniarea

20 40 60 80 100

Time (Days)

Figure 4.13. Comparison of measured bromide data and the predicted bromide concentrations at the monitoring island locations, 50 cm depth. The solid line with triangles represent results from Case VI (analytical model, R = 0.87), the solid line represents results from Case VIII (R ~ 0.87), the dashed line represents results from Case IX (/? ~ 1.0), the solid line with solid circles represents results from Case VIII (R ~ 0.8).

132

NMI, east

c o

u C o o o >

0^

NMI, west

SMI, west SMI, east

20 40 60

Time (Days)

20 40 60 80 100

Time (Days)

Figure 4.14. Comparison of measured bromide data and the predicted bromide concentrations at the monitoring island locations, 100 cm depth. The solid line with triangles represent results from Case VI (analytical model, R = 0.87), the solid line represents results from Case VIII (R ~ 0.87), the dashed line represents results from C a s e I X ( R ~ 1 . 0 ) , t h e s o l i d l i n e w i t h s o l i d c i r c l e s r e p r e s e n t s r e s u l t s f r o m C a s e V I I I ( R ~ 0.8).

133

c .0

Urn c CJ r— o u >

oNMI, west

SMI, east SMI, west

20 40 60

Time (Days)

20 40 60

Time (Days)

100

Figure 4. IS. Comparison of measured bromide data and the predicted bromide concentrations at the monitoring island locations, 150 cm depth. The solid line with triangles represent results from Case VI (analytical model, R = 0.87), the solid line represents results from Case VIII (R ~ 0.87), the dashed line represents results from Case IX (/? ~ 1.0), the solid line with solid circles represents results from Case VIII {R ~ 0.8).

134

c o

o o c o u o > "5 u

o NMI, east fi NMI, west

o o

SMI, east SMI, west

20 40 60 80 0

Time (Days)

20 40 60 80 100

Time (Days)

Figure 4.16. Comparison of measured bromide data and the predicted bromide concentrations at the monitoring island locations, 200 cm depth. The solid line with triangles represent results from Case VI (analytical model, R = 0.87), the solid line represents results from Case VIII (R ~ 0.87), the dashed line represents results from C a s e I X ( / ? ~ 1 . 0 ) , t h e s o l i d l i n e w i t h s o l i d c i r c l e s r e p r e s e n t s r e s u l t s f r o m C a s e V I I I ( R ~ 0.8).

135

NMI, west NMI, east

§) SMI, west SMI, east

20 40 60

Time (Days)

20 40 60 80 100

Time (Days)

Figure 4.17. Comparison of measured bromide data and the predicted bromide concentrations at the monitoring island locations, 250 cm depth. The solid line with triangles represent results from Case VI (analytical model, R = 0.87), the solid line represents results from Case VIII (R ~ 0.87), the dashed line represents results from C a s e I X ( / ? ~ 1 . 0 ) , t h e s o l i d l i n e w i t h s o l i d c i r c l e s r e p r e s e n t s r e s u l t s f r o m C a s e V I I I ( R ~ 0.8).

136

Six of these locations are at the NMI, west location where measured bromide

concentrations adhere to a more dispersed pattern than the other locations (Figure 4.19).

Predictions from the conservative solute model (/? = 1, Case IX) also yielded better

results at the 150, 200, and 250 cm depths with regard to the average bromide behavior.

At the deeper depths (below 250 cm) Case IX failed to accurately predict the arrival

time of the solute front as well, and predicted a much more dispersed breakthrough

curve. This is obvious at the 300 cm depth (Figure 4.18). The retardation factor of

Case VIII (R ~ 0.87) was adjusted toR~ 0.8 to establish whether or not a better fit

could be achieved. Case VIII provided better results at all depths, except at the 300 cm

depth, using an /? ~ 0.87.

The fact that using an /? ~ 0.80 in Case VIII provided better results at the 300 cm

depth indicates that solutes are transported faster than the average pore-water velocity

above this depth. These results suggest that at the deeper depths, a mechanism such as

preferential transport or anion exclusion (or a combination of mechanisms) play a more

significant role in the transport of bromide. This may be attributed to the

heterogeneities of the soil profile due to layering or spatial variability in the velocity

field. The SMI, west location in particular exhibited transport significantly faster than

that predicted using an average pore-water velocity (Figure 4.21). Predictions clearly

show that it is necessary to use an /? < I although it is not clear what mechanism causes

this preferential solute transport. Adams and Gelhar [1992] attribute incomplete mass

recovery on solute transport that occurs at a rate greater than the average pore-water

velocity resulting in the solute traveling farther than would be predicted. This

137

_o rt c u o o o <u >

u cd

NMI, west NMI, east q O o o O

CO/ a

^ o SMI, west Q cP ̂ o o o o

o ^ o

SMI, east

o o

&

20 40 60 80 0

Time (Days)

20 40 60 80 100

Time (Days)

Figure 4.18. Comparison of measured bromide data and the predicted bromide concentrations at the monitoring island locations, 300 cm depth. The solid line with triangles represent results from Case VI (analytical model, R = 0.87), the solid line represents results from Case VIII (R ~ 0.87), the dashed line represents results from Case IX (/? ~ 1.0), the solid line with solid circles represents results from Case VIII (/? ~ 0.8).

138

c o

c <u u o u o >

o

o o c o u o >

o a:

c .2 eS u. C u c c u o >

<u

200 cm 50 cm

^iWooOo ^ _ o o o o

250 cm 100 cm

7 ' O •/ ̂ ponOO O O

300 cm 150 cm

0 20 40 60 80

Time (Days)

20 40 60 80 100

Time (Days)

Figure 4.19. Comparison of measured bromide data and the predicted bromide concentrations at the NMI, west location. The solid line represents model predictions from Case VIII (R ~ 0.87), the dashed line represents model predictions from Case IX (R = 1.0, Young et al., 1999), and the solid line with solid circles represents model predictions from Case VIII (R ~ 0.80).

139

c o

c o o c o

c o C3

(U o c o u u >

c o a

o u c o o >

(D

50 cm 200 cm

o ^ O o

•I '

I'

1.2 i—

K-^rr- rr^n—Q ^-O

100 cm 250 cm

°150 cm 300 cm

o O no 0°

20 40 60 80

Time (Days)

20 40 60 80 100

Time (Days)

Figure 4.20. Comparison of measured bromide data and the predicted bromide concentrations at the NMI, east location. The solid line represents model predictions from Case VIII (R ~ 0.87), the dashed line represents model predictions from Case IX (R = 1.0, Young et al., 1999), and the solid line with solid circles represents model predictions from Case VIII (R ~ 0.80).

140

c _o « k-c o u c o u u >

u Qi

c _o b. c u u c o u o > w u

Qi.

c o

c u u o u u >

u Qi

200 cm 50 cm

250 cm 100 cm

° oioo o o o 'o n o !o 300 cm 150 cm

0 20 40 60 80 0

Time (Days)

20 40 60 80 100

Time (Days)

Figure 4.21. Comparison of measured bromide data and the predicted bromide concentrations at the SMI, west location. The solid line represents model predictions from Case VIII {R ~ 0.87), the dashed line represents model predictions from Case IX (/? = 1.0, Young et al., 1999), and the solid line with solid circles represents model predictions from Case VUI {R ~ 0.80).

141

explanation is convenient in that it can describe both the observed accelerated transport

at the deeper depths as well as the incomplete bromide mass recovery. Another

explanation that would explain the observations of incomplete bromide recovery as well

as the accelerated transport is described by Roth etal. [1991] as preferential flow. They

attributed incomplete bromide mass recovery to preferential flow where several smaller

solute pulses of varying velocities split from the main solute pulse. There may be some

evidence of this preferential transport at the NMI (west) and SMI (west) locations

where a dual bromide breakthrough can be detected (Chapter 4.3, Measured Bromide

Concentrations) although, as Vanderborght et al. [2000] points out, transport through

macro pores is barely apparent in time series measured in-situ. However, whatever the

mechanism, it is clear from model predictions that it is impossible to predict the

breakthrough of bromide at the deeper depths without using a retardation coefficient

less than one.

The results of the analytical solution (Case VI) are also shown and compared to

the numerical solutions (Case VII - VIII) at the monitoring island locations (Figure 4.13

- Figure 4.18). At the 50 cm depth the analytical solution yielded results similar to that

of the numerical solution (Table 4.10). This is supported by the MSE that was

computed using the average measured bromide concentrations for each depth against

the simulated bromide concentrations. It should be noted that the results of the

analytical model (Case VI) compare favorably with the measured bromide data at the 50

and 100 cm depths although the solution is only valid for times within the irrigation

period. As expected, at the 150 and 200 cm depths, the predictions of the analytical

142

model provided good results only at early times. For the 250 and 300 cm depths, as

well as the mid to late time solutions for the 150 - 200 cm depths, the analytical

solutions were not valid and failed to accurately predict the bromide concentrations.

This is because of the inability of the analytical model to account for solute transport

due to drainage and displacement processes.

Figure 4.19 through Figure 4.22 show the measured and predicted breakthrough

of bromide at each of the monitoring island locations. Viewing the data in this manner

more clearly shows the effect of dispersion at the individual locations. The SMI, west

side location clearly shows the strongest anion exclusion or preferential transport with a

sharp breakthrough and the bromide breaking through at all depths by day 20. The

simulated bromide breakthrough curves closely match the observed data at the SMI,

east side and the NMI, west side locations.

Varying the input bromide concentrations, instead of using an average bromide

concentration of 31.6 mg/1, did not improve model predictions with respect to the

average bromide behavior. Figure 4.23 shows the predicted bromide breakthrough

curves for the model using an average bromide concentration of 31.6 mg / 1 for the

upper boundary condition (Case VIII) and the model using a variable bromide

concentration (Case X, Figure 2.4) for the upper boundary condition. Defining the

bromide concentrations for the upper boundary explicitly did not improve the

predictions with respect to capturing the details of the preferential transport.

143

0 20 40 60 80 0 20 40 60 80 100


Figure 4.22. Comparison of measured bromide data and the predicted bromide concentrations at the SMI, east location. The solid line represents model predictions from Case VIII (R ~ 0.87), the dashed line represents model predictions from Case IX (R = 1.0, Young et al., 1999), and the solid line with solid circles represents model predictions from Case VIII (R ~ 0.80).

144

0 20 40 60 80 0 20 40 60 80 100 Time (Days) Time (Days)

Figure 4.23. Comparison of all measured bromide data from around the monitoring islands and the predicted bromide concentrations. The solid line represents model predictions using a uniform input concentration (C© = 31.6 mg / 1, Case VIII); the dashed line represents model predictions using variable input concentrations (Figure 2.4, Case X).

145

Predictions actually worsened with respect to the average measured bromide

concentrations with percent difference between the measured and predicted bromide

concentrations increasing from 15.9 percent for Case VII (average bromide

concentration) to 21.5 percent for the model that explicitly define the bromide

concentrations for each irrigation day (Case X).

4.6. Conclusions

Numerical inversion techniques were used with measured bromide concentrations

at the monitoring island locations to estimate the transport parameters, R and a. The

transport of bromide was then simulated using analytical and numerical models and the

results compared to measured bromide concentrations at the monitoring island

locations.

Numerical inversion was utilized to estimate the transport properties using

measured bromide concentration data from the monitoring island locations. The

properties were estimated using two approaches introduced by Porro et al. [1993]: a

local approach where the measured concentration data are "fit" at each individual

location, and a global approach where the measured concentration data from six depths

at a location are "fit" simultaneously. These estimated transport parameters were then

used in a forward analytical model to assess which approach yielded the best results.

Examination of the correlation coefficients (r^) reveal that the local approach produced

the best results with respect to the "fit" of the data (Table 4.7). The estimated transport

146

properties from the SMI, west location were also used in an analytical model to assess

the two approaches. As expected, the local approach clearly offered superior results

compared to the global approach. These results held for other locations as well.

The parameters estimated fi'om these two approaches were then averaged and

incorporated into analytical models to investigate how averaging affects the previous

results. Based on previous results, it would appear reasonable to assume that the

estimated transport properties averaged from the local approach would yield superior

results. However, the analytical models using average transport properties from the

global approach yielded better results than averaging the transport properties obtained

from the local approach at all locations except the SMI, west location (Table 4.8). At

the SMI, west location the results were slightly better with an 11.3 percent difference in

the MSB values. At the other locations the results of the analytical model using average

transport properties from the global method yielded more significant differences with

the MSE's of the two methods differing by 28 to 77 percent.

Based on the results of the averaging schemes, the average transport properties

from the global approach were used in the numerical models. Numerical models were

developed to investigate the effects of hysteresis and anion exclusion on the transport of

bromide. In addition, the results from the numerical models were compared to the

results obtained from the best analytical model (Case VI) and used to provide insight to

how well the average transport properties represent the measured bromide behavior and

to compare the solutions. Incorporating hysteresis into the soil hydraulic functions had

little effect on the predicted bromide breakthrough curves. The models incorporating

147

hysteresis only yielded marginally better results than the models with no hysteresis

(Table 4.10). At most depths, both models predict the mean behavior of the measured

bromide and yield predictions that are difficult to distinguish from each other. Only at

late times can the predictions from the two cases be delineated. The predicted bromide

concentration profiles also support the conclusion that hysteresis does not play a major

role in the transport of bromide. No significant effect from incorporating hysteresis into

the soil hydraulic functions could be detected in the predicted concentration profiles

from the two models. Both solutions yield good predictions with respect to the position

of the measured solute front as well as the shape of the bromide concentration profiles.

These results also hold for late time predictions. These results are supported by similar

studies conducted by others [Mitchell and Mayer, 1998; Pickens and Gillham, 1980].

The results of the models using an /? < 1 demonstrate that while the mechanisms

which cause the solutes to travel faster than the average pore-water velocity catmot be

delineated, the process or processes must be accounted for and are lumped into the

retardation coefficient (Table 4.10). At the deeper depths ( below 250 cm), the

importance of using an /? < 1 becomes obvious as the model that uses R = 1 completely

fails to accurately predict the arrival time of the solute front and predicts a much more

dispersed breakthrough curve. Adjusting the retardation factor toR~ 0.8 failed to yield

better results compared to numerical models using a ~ 0.87, except at the 300 cm

depth. This result may indicate that the system experiences enhanced variations in the

velocity fields above this depth interval. At the deeper depths faster velocity fields play

a more significant role in the transport of bromide. The results of the analytical solution

148

(Case VI) were compared to the numerical solutions at the monitoring island locations.

The analytical solution yields results similar to those of the numerical solution at the 50

cm depth (Table 4.10). It should be noted that the results of the analytical model (Case

VI) are only valid for times within the irrigation period because of the assumption of

steady-state flow . As expected, at the late times and the deeper depths, the analytical

solutions are not valid and fail to accurately predict the bromide concentrations. This is

because of the inability of the analytical model to account for solute transport due to

drainage and displacement processes.

149

5. CONCLUSIONS

The objective of this dissertation was to determine how changes to the

parameterization of the conceptual model affects the flow and transport predictions.

The sub-objective of this study was to simulate the water flow and the transport of a

solute through a variably saturated heterogeneous field soil.

The infiltration and redistribution of water into a large (50 m by 50 m), controlled

and monitored field plot was modeled and the results compared with measured data.

Effects of the inclusion of hysteresis in the retention and hydraulic conductivity

functions were determined, and the ability of laboratory derived hydraulic parameters

from core samples to accurately predict the propagation of the wetting front under a

field setting was examined. Both the wetting front arrival and the changes in water

content using laboratory derived hydraulic properties incorporating hysteresis were

modeled. The arrival of the wetting front was simulated and compared to observed data

from two successive field infiltration events. Several models were developed using

hydraulic properties derived from drying and wetting experiments. These models were

then compared and the parameters adjusted if necessary, against data taken from the

first infiltration experiment. A post-audit of the final models from Experiment I were

conducted using data from a second experiment. Using the adjusted hydraulic

properties from Experiment I, simulations were performed and the results compared to

the measured data from Experiment II to assess the quality of the final model as well as

the assumption regarding using a homogeneous representation of the soil profile.

150

Simulations using hydraulic properties estimated in the laboratory with core

samples as first approximations yielded poor results with regards to estimating the

arrival of the wetting front at various depths as well as predicting the drainage phase of

the experiment until adjustment was made to the Ks parameter. The satmated hydraulic

conductivity, Ks, was adjusted to correctly predict the time of the wetting front arrival

and the changes in water content observed in the field during and after infiltration.

Without increasing Ks tenfold from the value of 46 cm d"', determined in the laboratory,

to 450 cm d ' acceptable predictions could not be made using the given set of hydraulic

properties and /Tj as a fitting parameter. The Ks adjustment is justified by computing

unsaturated hydraulic conductivity values determined in the field from tensiometer

observations at a range of depths from 0.5 to 3 m from around the monitoring islands

and average water content values from neutron probe data in a modified version of the

scaled-predictive method. Thus Ks became an effective saturated hydraulic

conductivity, Ks.eff, which incorporates uncertainties not included in the laboratory

determined Ks. The modified version of the scaled-predictive method introduced by

Mace et al. [1998] offered a valuable tool for determining how much to adjust Ks to

adjust the predictive hydraulic conductivity relationship. The adjustments lead to

reasonably good results for estimating the arrival of the wetting front and changes in

water content. The results also support the use of a homogeneous vertical soil profile

for this particular field site.

Laboratory derived hydraulic properties provided a much better first

approximation to the field properties than hydraulic properties based on soil texture

151

taken from an internal, general database in HYDRUS. It was not possible to adjust

either of the two models using hydraulic properties taken from the internal database as a

first approximation to the same degree of quality as the models using the laboratory

derived properties. Predictions based on properties taken from a database were unable

to capture the behavior of the changes in the water content in terms of the magnitude of

the water contents behind the wetting front and the redistribution phase of the

experiment. These results may, in part, stem from the use of a homogeneous profile.

The laboratory derived hydraulic properties are, in effect, based on a lumped parameter

profile where, although the soil core represents a small volume (or point measurement)

of the entire profile, they capture the average behavior in terms of the properties.

Models with hydraulic properties based on textural considerations used in a soil profile

with properties not conforming to a particular texture would be unable to capture the

average behavior. Capturing more distinct characteristics of the system by delineating

more layers of the system may correct this. Based on these results the laboratory-

derived parameters provide a unique and superior first approximation for predicting the

wetting front arrival and the shape of the curves as compared to predictions using

hydraulic properties from the internal database.

The simulations utilizing properties taken from wetting experiments and the case

incorporating hysteresis into the retention and hydraulic conductivity functions yielded

the best results as compared to the results from utilizing hydraulic properties taken from

drying experiments. Comparison of the results from these two cases indicates that

although hysteresis was not a dominant mechanism during these experiments the model

152

incorporating hysteresis does provide only marginally better results for predicting water

content changes. These results may be because the soil profile remained in the "wet"

region of the retention curve during most of the experiment. Incorporation of hysteresis

into the soil hydraulic functions, however, yielded superior predictions of the soil water

content profile as compared to predictions without hysteresis a finding which is

supported by similar observations by Pickens and Gillham [1980]. In addition,

incorporation of hysteresis resulted in the use of a more realistic value for the saturated

hydraulic conductivity as compared to the case without hysteresis (Case II). Another

factor affecting these results is that while the model incorporating hysteresis follows a

separate main drying curve fi-om the non-hysteretic model (Figure 3.18), the maximiun

difference between the drying curve for these two cases is approximately 7 percent at

100 cm of suction; this would indicate that a large difference should not be expected

between the two cases.

A post-audit of the adjusted parameters conducted by simulating a second

irrigation event in the same plot, yielded good results, with the MSE (Table 3.5) of the

same order as the results obtained fi'om the non-hysteretic and hysteretic models fi-om

Experiment I. In addition, using the results fi-om the models collectively, it would

appear that the assumption regarding the use of a homogeneous soil profile is supported

when trying to capture the average field behavior of processes such as the wetting fi-ont

arrival and the drainage behavior. However, it is very clear that the use of a

homogeneous profile to represent the real system fails when looking at detail orientated

processes such as water content changes at a specific point.

153

The transport of a solute through a variably saturated field soil was simulated

using analytical and numerical models. Location specific and spatially integrated

inversion methods were compared using analytical and numerical models, to assess

their ability to characterize the flux and transport properties. The effects of spatial

averaging of point measurements {9, R, D, a) on the transport predictions were

investigated. And finally, numerical models were used to investigate the effects of

hysteresis and the retardation coefficient on solute transport.

Transport properties were estimated using two approaches, a local and global

method. In the local approach the measured concentration data are "fit" at each

individual location, whereas in the global approach the measured concentration data

from six depths at a location are "fit" simultaneously. The local approach produced the

best results with respect to the correlation coefficients. The estimated transport

parameters from the two methods were then used in a forward analytical model to

assess which approach yielded the best results. The transport properties estimated at the

SMI, west location was used in an analytical model to assess the two approaches. As

expected, the local approach clearly offered superior results compared to the global

approach. These results held for other locations as well.

The parameters estimated from these two approaches were then averaged and

incorporated into analytical models to investigate how averaging affects the previous

results. The analytical models using average transport properties from the global

approach yielded better results than models using average transport properties from the

local approach at all locations except the SMI, west location. This is counter-intuitive

154

based on the previous results since the analytical models using transport properties

estimated from the local approach yielded superior results for specific locations. At the

other locations the results of the analytical model using average transport properties

from the global method yielded predictions that were 28 to 77 percent better in terms of

the MSE's than the models using properties from the local method.

The average transport properties from the global approach were used as first

approximations in the numerical models. Transport properties from the global approach

were chosen because predictions from analytical models using these properties yielded

better results in terms of the MSE's as compared to models using average properties

from the local approach.

Incorporating hysteresis into the soil hydraulic functions had little effect on the

predicted bromide breakthrough curves. The models incorporating hysteresis only

yielded marginally better results than the models with no hysteresis. At most depths,

both models predict the mean behavior of the measured bromide and yield predictions

that are difficult to distinguish from each other. Only at late times can the predictions

from the two cases be delineated. The predicted bromide concentration profiles also

support the conclusion that hysteresis does not play a major role in the transport of

bromide. No significant effect from incorporating hysteresis into the soil hydraulic

functions could be detected in the predicted concentration profiles from the two models.

Both solutions yield good predictions with respect to the position of the measured solute

front as well as the shape of the bromide concentration profiles. These results also hold

155

for late time predictiotis. These results are supported by similar studies conducted by

others {Mitchell and Mayer, 1998; Pickens and Gillham, 1980].

The results of the models using an /? < 1 demonstrate that while the mechanisms

which cause the solutes to travel faster than the average pore-water velocity cannot be

delineated, the process or processes must be accounted for and are lumped into the

retardation coefficient (Table 4.10). Numerical models using an /? ~ 0.87 yielded the

best results compared to numerical models that used retardation factors of 0.80, and 1.0

with respect to the MSE's. At the deeper depths ( below 250 cm), the importance of

using an /? < 1 becomes obvious as the model that uses R = 1 completely fails to

accurately predict the arrival time of the solute front and predicts a much more

dispersed breakthrough curve. Adjusting the retardation factor to R ~ 0.8 failed to yield

better results as compared to numerical models with ~ 0.87 with regard to the arrival

time of the bromide breakthrough except at the 300 cm depth. This result may indicate

that the system experiences enhanced variations in the velocity fields above this depth

interval. A possible explanation for this result is that at the deeper depths the local

pore-water velocity is greater due to some mechanism such as preferential flow or anion

exclusion and plays a more significant role in the transport of bromide. The results of

the analytical solution were compared to the numerical solutions at the monitoring

island locations. The analytical solution yields results similar to that of the numerical

solution at the 50 cm depth. It should be noted that the results of the analytical model

are only valid for times within the irrigation period because of the assumption of steady-

state flow . As expected, at the late times and the deeper depths, the analytical solutions

156

are not valid and fail to accurately predict the bromide concentrations. This is because

of the inability of the analytical model to account for solute transport due to drainage

and displacement processes.

In conclusion, for this field site, and under these conditions, the use of a

relatively simple one-dimensional model is suitable for predicting processes such as

wetting front advance and the transport of a solute at the scale of tens of meters. The

results also show that although laboratory derived hydraulic properties may be limited

in their applicability to field settings, for this field setting they clearly offer a superior

first approximation as compared to hydraulic properties based on texturai considerations

taken from a database. However, the laboratory derived hydraulic properties needed to

be adjusted in order for the numerical model to yield good predictions of the wetting

front arrival and changes in water content. These adjustments were made following an

iterative approach where the results of the numerical model reveal inconsistencies of the

hydraulic properties and the field data are used to adjust the conceptual model. This

iterative approach is used to achieve many of the objectives outlined above.

157

APPENDIX: CHARACTERIZATION

A variety of approaches were applied to characterize the MAC site. Most of

these approaches provided some quantitative information of varying quality with

respect to deriving hydraulic properties. However, these approaches did provide

valuable information with respect to the hydraulic and transport properties and observed

field processes. This section outlines some of these approaches to provide for a clearer

understanding of why some of the later approaches were taken.

Deriving hydraulic properties using the measured field data was an important

goal at the onset of the project. The primary types of data available for this task were

neutron probe data that yielded calculated water contents, tension data from installed

tensiometers, and textural data (sand, silt, clay, and gravel) at selected locations within

the plot. Ideally, water retention curves are generated from the observed data and soil

hydraulic properties are estimated from these curves for use in a soil hydraulic model.

The following sections outline the various approaches taken, as well as the processes

examined, to characterize the site's hydraulic properties at the preliminary stage of the

project. The approaches outlined are: development of field based water retention

curves, the assessment of variability in the measured neutron probe data in support of

deriving field based water retention curves, and examination of the unsaturated

hydraulic conductivity using the internal drainage method. In addition, it should be

recognized that what the data may lack in resolution it makes up for in volume (number

of point measurements) and the synergistic manner in which the data are examined!

158

Analysis of the Neutron Probe Data

Many of the approaches and methods used to estimate hydraulic properties, such

as the instantaneous profile method and use of field derived water retention curves

require that the in-situ water contents and potentials are defined. Because of variability

in the neutron probe measurements (hence variability in the calculated water contents),

various mechanisms were examined to account for this variability and various methods

were examined to reduce the variability the neutron probe data.

Water content values for infiltration experiments conducted at the MAC field

site were indirectly determined using a neutron probe. The neutron probe (neutron

source and detector) was placed in the soil in access tubes and high-energy neutrons

were emitted fi-om a Ra-Be or Am-Be source. Neutrons then collide with nuclei of

atoms in the surrounding soil. When the mass of the nuclei the neutron collides with is

much larger than the neutron mass, the neutron does not lose any appreciable energy

and the neutrons' velocity is retained. When the neutrons strike nuclei of a similar mass

(such as that of hydrogen nuclei), much of the neutrons' energy is lost. After a number

of these collisions, the velocity of the neutron becomes characteristic of the thermal

motion of hydrogen atoms in the soil [Jury et al., 1991]. This velocity is referred to as

"thermal velocities" (velocities characteristic of the hydrogen atoms in the soil). The

neutron-probe detector is sensitive only to neutrons moving at these thermal velocities.

The thermalized neutron count is proportional to the density of hydrogen atoms in the

159

vicinity of the source. A calibration curve can be developed "giving the number of

counts per unit time received by the detector versus the amount of hydrogen present"

[Jury etal., 1991]. The plotted neutron readings are not absolute counts but instead

count ratios {CR), which are a ratio of absolute counts to a shield count.

A polynomial equation is used to fit the data collected and calculate the

volumetric water content:

<51 = Co + C,(C/?) (A.I)

where Ov is the percent moisture content, Co and C/ are constants, and CR is the count

ratio determined as the count divided by the standard count (5C).

Volumetric water contents for the infiltration experiments conducted at the

MAC site were determined as follows. A standard count was taken in a vertical neutron

probe access tube isolated from the irrigated plot, approximately 20 m to the west,

before the actual count was taken in the irrigated plot. The standard count was taken at

a 2 m depth. The standard count for each day was then used to calculate the CR for that

day and then subsequently used in Equation (A. I).

The resulting calculated water contents were somewhat variable. This

variability can be attributed to the methodology underlying the determination of the

constants (Co andC/) in Equation (A.I), and a possible temperature dependence in

neutron probes.

The neutron probe used in this study was calibrated utilizing a steady-state

method. A small plot (12.2 by 6.1 m) containing 3 access tubes was irrigated 6 days

and then allowed to redistribute. Neutron probe readings were taken in 25 cm depth

160

increments during the data collection period. Following the data collection period, a

Giddings probe was used to collect soil core samples for water content analysis. The

calibration curve was constructed by correlating the neutron probe counts to the water

content determined by direct method and the constants, Co andC/ were subsequently

derived from the curve. Co andC/ were calibrated as -0.05830 and 0.21853,

respectively. Because the polynomial equation constants were developed for a plot

located off the experimental plot, and because they represent averaged values for the

calibration plot (taking into account heterogeneities for the entire calibration plot) they

1) carmot account for heterogeneity's on a very localized scale and 2) may not be

representative of the plot because the plot's physical properties may have been altered

during site preparation and installation of instnmients. No attempt was made to address

these complications.

Personal communication with Dr. Wierenga (Professor, Department of Soil,

Water and Environmental Science, University of Arizona, 1999) indicated that there

may be some temperature dependence associated with neutron probes. To explore

temperature dependence, the C/?'s, thus the water contents, were recalculated using

different techniques to determine the standard counts. Three approaches were used to

adjust the standard counts: a mean standard count value was calculated for each

individual experiment, a mean standard count was calculated representing both

experiments, and a regression was applied to the standard counts. Each approach was

evaluated by recalculating the water contents using the "new" standard count and then

161

quantifying whether there was an improvement in the "fit" of a regression applied to the

water content versus time curve.

The water contents were recalculated using four methods: the experimental day

SC (using a SC for the specific day), a mean standard count for the specific experiment,

a mean lumped SC (mean SC is computed using all experimental data), and a SC based

on a regression applied to the SC versus time curves. The "new" water contents were

then plotted versus time and regressions applied to them to check if the correlation

between the points had improved.

In every case, the correlation coefficients of the regressed water contents versus

time improved marginally for the water contents that were computed using either the

experimental mean, the lumped mean, or the regressed SC, as compared to the original

method. Also in every case, the method using the regressed SC resulted in marginally

better correlation coefficients than the methods using the means. This is surprising

considering the regressed SCs correlation coefficient for Experiment II was very low

(0.0001). Because of the very low regressed correlation coefficients, the improved

results were observed as being artificial and the method abandoned. It should also be

noted that despite the elaborate methods by which a "new" SC, was derived the end

result on the actual water content values was minimal. Based on these findings a closer

look was taken at the data used to calibrate the neutron probe.

Analysis of Field Derived Water Retention Curves

162

The field derived parameters (FDP), specifically van Genuchtens' curve fitting

parameters alpha and m(n = l/(l-m)), were determined by correlating the water content

to the tension data through time and processing the resulting tension versus water

content data with the code RETC [van Genuchten et al., 1991]. The residual water

content, saturated water content, and saturated hydraulic conductivity were estimated by

examining the raw data. Because of the questionable reliability of the tension data in

the 300-400 cm dry range (Wierenga, Personal Communication, 1999), only data fi-om

the wet range was input into RETC. The measured tension data fi-om the monitoring

islands was used. RETC was used to solve the inverse problem and generated an alpha

and n parameter for each depth (50 - 300 cm, 50 cm intervals) for seven locations

within the irrigated plot. Basic statistics were then performed on the parameters to

determine a mean value and examine the variability. The parameters were normally

distributed, however it should be noted the sample size was small. The residual and

saturated water contents were estimated by examining the raw data, the derived core

values, and the expected range of values given by the textural composition. Because of

a lack of reliable in-situ K values, the mean saturated hydraulic conductivity value was

taken fi-om laboratory experiments conducted on the core samples collected fi-om the

plot.

As indicated in the Analysis of Neutron Probe Data, the variability in the

calculated water contents resulted in highly variable water retention curves. In addition,

when fitting only two (a and m) of the four parameters defined in the inverse problem

{Or, 6s, a and m), the correlation coefficients were poor. This is attributable to the

163

variability of the calculated water contents and the limited range over which the

measured data extended. Because of these results, it was decided to use hydraulic

properties estimated in the laboratory from soil cores collected from the field site.

Estimation of the Unsaturated Hydraulic Conductivity Relationship

The internal drainage method as described by Hillel et al. [1972] was applied to

field data collected from the MAC site to determine the imsaturated hydraulic

conductivity relationship. The internal drainage method is derived from the

instantaneous profile method developed by Watson [1966], a method originally

developed for application to soil columns. Much of the following information is

summarized or abbreviated to allow the approach of the analysis to be understood.

Detailed descriptions of the experimental setup, procedures, and data collected can be

found in Young et al., [1999].

Application of the internal drainage method to a soil profile provides a means to

measure the unsaturated hydraulic conductivity function and other hydraulic

characteristics in situ. According to Hillel et al. [1972], the lot (irrigated plot) should be

large enough so that boundary effects are not experienced at the center of the plot. A

vertical neutron probe is installed within the plot to a depth usually exceeding two

meters to provide water content data. In proximity to the neutron probe (near enough to

measure the same soil mass), a series of tensiometers are installed at intervals not

exceeding 30 cm to provide tension data. The plot is then irrigated until effective

164

saturation is achieved, at which time irrigation stops and the plot is covered to prevent

evapotranspiration. As the redistribution process commences, measurements of water

content and tension are taken throughout the soil profile. Water content data can be

gathered using either time domain reflectometry (TDR) or neutron probe measurements.

Tensiometers are typically used to provide tension data. The water content and tension

measurements should be taken concurrently and frequently during the drainage period.

The resulting data are used to determine instantaneous potential gradients and fluxes

with in the soil profile.

The water content data for numerous locations throughout the irrigated plot were

graphed to see if there were any trends in the data. While the water content data

followed an overall trend of decreasing through time (at any given depth) during the

drainage period, there are specific points where the water content increases. These

variations were invariant with location and depth of measurement. Because of this

invariance, the trends were not attributed to heterogeneities in the material properties

but rather to calibration and measurement technique of the neutron probe, which would

affect the constants in the calibration polynomial. In addition, the manner in which the

standard counts are handled in computing the water contents can affect the variability in

the water content (see Analysis of Neutron Probe Data). An effort was made to

determine if some of this "noise" in the data could be removed by adjusting the

calibration values (i.e. averaging the standard counts). This resulted in marginally

better "fits" of regressions applied to the water content versus time data. No effort was

made to smooth the data by the process of elimination because there is no way to

165

ascertain which data points are "correct" or "incorrect." Following the advice of Ahuja

et al. [1980], regressions were applied to the water content and tension data to allow

values to be interpolated at specific times (i.e. to allow the tension and water contents to

be correlated at common points in time for calculating fluxes and gradients from the

regression curves). Regressions were applied to generate best-fit equations. The

equation with the highest correlation coefficient and a continuous first derivative was

chosen to interpolate the needed data.

The tension data for the NMI and SMI, east and west sides. Experiments I and

II, was plotted versus time to determine the most suitable data set to use in the method.

Experiment I data from the east side of the SMI was utilized for the internal drainage

method.

The flux for each depth and the cumulative flux for the entire drainage period

was calculated from the generated moisture content curves. The unsaturated hydraulic

conductivity for each depth through time was then calculated by dividing the fluxes by

the gradient. To evaluate whether the entire profile could be represented by a single

hydraulic conductivity curve, and to determine the functional relationship of the

hydraulic conductivity, the unsaturated hydraulic conductivity and the natural log of the

unsaturated hydraulic conductivity values was plotted against water content. A

regression was applied to the hydraulic conductivity values for all depths yielding

calculated saturated hydraulic conductivity's of 43.9 and 26.0 cm per day for two

locations within the plot. Regressions were also applied to the hydraulic conductivity

values for individual depths as well as smaller subsets of the entire data set with no

166

improvements in the fit. Examination of the functional relationship of hydraulic

conductivity revealed that it followed an exponential relationship as given by K(6) =

ae*^. These values are within the ranges foimd from laboratory tests run on soil cores

collected from the site. It should be recognized that these values are somewhat artificial

because of the large amount of smoothing of the measured data. The effect of

smoothing on the calculated hydraulic conductivity values is also observed and

considered by Ahuja et al., [1980].

167

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