Application of Model 

Abstraction Techniques to 

Simulate Transport in Soils

Office of Nuclear Regulatory Research 

NUREG/CR-7026
Application of Model

Abstraction Techniques to

Simulate Transport in Soils 

Manuscript Completed: June 2010 

Date Published: March 2011 

Prepared by

Y. Pachepsky1, T. Gish1, A. Guber1 

A. Yakirevich2, M. Kouznetsov2 

M. Van Genuchten3, 

T. Nicholson4, R. Cady4

1United States Department of Agriculture 

Agricultural Research Service

Environmental Microbial and Food Safety Laboratory 

Hydrology and Remote Sensing Laboratory 

Beltsville, MD 20705

2Department of Environmental Hydrology & Microbiology

Zuckerberg Institute for Water Research

Blaustein Institutes for Desert Research

Ben-Gurion University of the Negev

Sede Boqer Campus, 84990, Israel

3Department of Mechanical Engineering, COPPE/LTTC

Federal University of Rio de Janeiro, UFRJ

Rio de Janeiro, RJ CEP 21945-970, Brazil

4U.S. Nuclear Regulatory Commission

Office of Nuclear Regulatory Research

Washington, DC 20555-0001

T.J. Nicholson, NRC Project Manager 

NRC Job Code N6235

Office of Nuclear Regulatory Research

NUREG/CR-7026
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ABSTRACT

Successful understanding and modeling of contaminant transport in soils and groundwater is a

precondition of risk-informed predictions of the subsurface contaminant transport. Exceedingly 

complex models of subsurface transport are often inefficient. Model abstraction is a

methodology for reducing the complexity of a simulation model while maintaining the validity 

of the simulation. The objective of this work was to use model abstraction techniques to 

characterize and understand flow and transport in soils in the presence of shallow groundwater. 

We developed two case studies by carrying out two types of field tracer experiments at the 

USDA-ARS OPE3 Beltsville field site, and applying a sequence of model simplifications based 

on the HYDRUS software family and MODFLOW. Soil moisture, soil water potential, tracer 

concentrations in groundwater, groundwater levels, and weather data, along with ground 

penetration radar surveys, electric resistivity monitoring, and dilution tests complemented 

borehole log data and laboratory hydraulic measurements to characterize soil heterogeneity. The 

invoked series of model abstractions showed the important role of subsurface heterogeneity in 

the vadose zone and groundwater, and substantial improved the conceptualization of the 

subsurface. Results of this study provide techniques to aid the NRC licensing staff in their review 

of a licensee‟s abstraction of complex transport models, and to help confirm the acceptability of 

model abstraction assumptions used in performance assessments.
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CONTENTS

ABSTRACT. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . iii

EXECUTIVE SUMMARY. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . xiii

ACKNOWLEDGMENTS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . xix

ABBREVIATIONS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . xxi

SYMBOLS

1 INTRODUCTION . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 

xxiii

1

2 MODEL ABSTRACTION IN SUBSURFACE HYDROLOGY . . . . . . . . . . 3

2.1 Background . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3

2.2 Abstraction of model structure . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3

2.3 Abstraction of parameter determination . . . . . . . . . . . . . . . . . . . . . . . . . . . 9

2.4 Systematic model abstraction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11

 2.4.1 Model abstraction .................................................................. 11

 2.4.2 Model abstraction design and example ......................................... 13

2.5 Model abstraction vs. arbitrary selection of a “simple” model. . . . . . . . . . 15

3 EXPERIMENTS TO TEST AND CONFIRM MODEL ABSTRACTION

FOR FLOW AND TRANSPORT IN SOILS . . . . . . . . . . . . . . . . . . . . . . . . . . . 17

3.1 Outline of experiments to test and confirm model abstraction in soils . . . 17

3.2 OPE3 experimental site at Beltsville Agricultural Research Center . . . . . 21

 3.2.1 General description................................................................ 21

 3.2.2 Existing information relevant to flow and transport in soils.................. 25

 3.2.2.1 Small scale structural units and heterogeneities............................ 25

 3.2.2.1.1 Soil basic properties...................................................... 25

 3.2.2.1.2 Soil hydraulic properties................................................. 25

 3.2.2.2 Field scale heterogeneities................................................... 28

 3.2.2.2.1 Hydrologically active zones and subsurface flow pathways........ 28

 3.2.2.2.2 Soil cover structural units ............................... ............ 36

 3.2.3 Survey, monitoring and preliminary modeling to design site-specific flow

 and transport experiments........................................................... 41

 3.2.3.1 Fine-scale ground penetration radar survey................................ 41

 3.2.3.2 Location selection and site instrumentation................................ 41

 3.2.3.3 Soil basic properties at the lateral flow experimental site................ 47

 3.2.3.4 Soil electrical resistivity survey............................................. 52

 3.2.3.5 Soil moisture and groundwater monitoring................................ 61

 3.2.3.6 Dilution test.................................................................... 67

 3.2.3.7 Preliminary coupled surface-subsurface flow modeling.................. 68

 3.2.3.8 3D subsurface flow and transport modeling............................... 72

 3.2.4 Experimental setups, schedule and results...................................... 82

 3.2.4.1 Flux measurement experiment............................................... 82

 3.2.4.2 Lateral flow experiment...................................................... 89

4 BASE FLOW AND TRANSPORT MODELS . . . . . . . . . . . . . . . . . . . . . . . . . 101

4.1 Base model for the flux measurement experiment. . . . . . . . . . . . . . . . . . . . 101

 4.1.1 Model description .................................................................. 101

 4.1.2 Model calibration and simulations........................................ . ....... 103

 4.2 Base model for the lateral flow experiment . . . . . . . . . . . . . . . . . . . . . . . . . 114
vi

 4.2.1 Model description .................................................................. 114

 4.2.1.1 Geometry of the simulation domain and soil material distribution ...... 114

 4.2.1.2 Finite element mesh and observation nodes................................. 114

 4.2.1.3 Initial and boundary conditions................................................ 118

 4.2.2 Model calibration ................................................................... 118

5 MODEL ABSTRACTION APPLICATIONS . . . . . . . . . . . . . . . . . . . . . . . . . 135

5.1 Flux measurement experiment. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 135

 5.1.1 Abstraction by reducing the dimension of the flow domain .................. 135

 5.1.2 Abstraction by using an approximate analytical flow model ............... 135

5.2 Lateral flow experiment. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 139

 5.2.1 Abstraction by ignoring vadose zone ............................................ 139

 5.2.1.1 2D transport in groundwater................................................... 139

 5.2.1.2 1D transport in groundwater................................................... 146

 5.2.2 Abstraction with a change in scale: profile aggregation ....................... 151

 5.2.3 Abstraction of required parameters: using pedotransfer functions.......... 151

5.3 Summary and conclusion. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 156

6 REFERENCES . . . . . . .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 161

APPENDICES

A. REVIEWING THE MODELING PROBLEM CONTEXT. . . . . . . . . . . . . A-1

 A1.1 Reviewing the key output ........................................................... A-1

A1.1.1 Key output use .................................................................... A-1

A1.1.2 Key output type and scale ...................................................... A-1

A1.1.3 Accuracy of the key output ..................................................... A-2

A1.1.4 Evaluating model performance ................................................ A-2

 A1.2 Reviewing assumptions made in the base model development and 

 grounds for those assumptions...................................................... A-3

A1.2.1 Subsurface structural units ...................................................... A-3

A1.2.2 Dimension of the problem ...................................................... A-4

A1.2.3 Simulation domain, initial and boundary conditions ........................ A-4

A1.2.4 Estimated model parameters ................................................... A-5

A1.2.5 Data available for calibration ................................................... A-6

A1.2.6 Calibration procedure and results ............................................. A-7

A1.2.7 Software properties .............................................................. A-8

A1.2.8 Model documentation ............................................................ A-8

B. FIELD CALIBRATION OF MULTISENSOR CAPACITANCE 

 PROBES. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . B-1

C. FIELD-SCALE COUPLED SURFACE-SUBSURFACE FLOW 

 MODELING. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . .. . . . C-1

C1.1 Equations of the model............................................................... C-1

C1.1.1 Flow model ....................................................................... C-1

C1.1.2 Transport model ................................................................. C-2

C1.2 Coupling surface and subsurface flow and transport in the numerical 

Solution ................................................................................. C-2
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List of Figures

2-1 Categories of model abstraction techniques relevant to flow and transport 

modeling in subsurface hydrology ......................................................... 4

2-2 Hierarchy of models to simulate water flow and solute transport in structured soils 

or in unsaturated fractured rock (Pachepsky et al., 2006)............................. 5

2-3 Spatial and temporal operational scales in hydrology (Pachepsky et al., 2006).... 7

2-4 Design of model abstraction via model structure and parameter determination...... 14

3-1 The flux experiment schematic............................................................. 19

3-2 The lateral flow experiment schematic.................................................... 20

3-3 The USDA-ARS OPE3 research watershed; a – aerial view, b – instrumentation. A, 

B, C, D – research fields......................................................................... 22

3-4 Location of groundwater wells soil moisture sensors, and the runoff flume at the 

Field B......................................................................................... 23

3-5 Soil basic properties at the field B of the OPE3 watershed. Different colors and 

symbols refer to different sampling points. Hollow symbols show data for depths 

larger than 60 cm.............................................................................. 26

3-6 Figure 3-6. Soil water retention of samples at locations 1 and 2 near well w52 at 

field B; a) 2-5 cm depth, b) 20-23 cm depth, and c) 47-50 cm depth (●,○ –

location 1, , - location 2)................................................................... 27

3-7 Probability distributions of the saturated hydraulic conductivity for 20 cm2

support areas; a – field falling head measurements; - location 1, depth 25 

cm , - location 1, depth 45 cm, - location 2, depth 25 cm, 

- location 2, depth 40 cm; b – constant head measurements of vertical 

(●) and horizontal (○) conductivities of undisturbed samples with 20 cm2support 

area in the laboratory (error bars show standard deviations).................................... 29

3-8 Water seepage from the wall above the restrictive soil layer enriched with clay.... 30

3-9 Layout of the 7. 5-ha watershed overlaid with the 25- by 25-m sample grid. 

Blocks with alphanumeric designations and infiltration capacity designations 

make up the stratified random sample of grid cells selected for soil moisture 

monitoring probes. The shaded rectangle in the southeast corner of the field site 

shows the 0.5-ha subsection that was used for soil moisture observation and flow 

verification (after Gish et al, 2002. Permission to use this copyrighted material is 

granted by Soil Science Society of America Journal).................................... 31

3-10 Ground-penetrating radar image with a digital trace of the first restricting layer 

shown as the dotted line (after Gish et al, 2002. Permission to use this copyrighted 

material is granted by Soil Science Society of America Journal)........................ 33

3-11 Interpolated depth to the first continuous restricting layer for Block C03. (after 

Gish et al, 2002. Permission to use this copyrighted material is granted by Soil 

Science Society of America Journal)........................................................ 34

3-12 Potential subsurface flow pathways (blue lines) identified with Arc/Info 

hydrologic tools (after Gish et al, 2002. Permission to use this copyrighted 

material is granted by Soil Science Society of America Journal)..................... 35

3-13 Changes in soil water storage in 0-80 cm soil layer during the period of 

observations..................................................................................... 37

3-14 Spatial distribution of corn yields in field B in 2001. The red to yellow colors 

represent low corn yield areas and the dark blue colors represent high corn yield 
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areas.......................................................................................... 38

3-15 Corn yields and color infrared image of corn biomass taken in August 1999 (in a 

relatively dry growing season). Green stars designate moisture probe locations, 

while the red, pink and light blue lines designate subsurface flow pathway 

locations. The red color indicates regions with high biomass and the white regions 

low biomass, each reflecting extremes in the vegetative cycle of the corn plant. 

Corn grain yields greater than the mean are inside the black polygons, whereas 

areas outside the black polygons denote regions with yields below the mean......... 39

3-16 Spatial corn yield variation from 1998 to 2002. Note that 1998 and 1999 were 

drought, 2000 was wetter than normal, 2001 was normal, and 2002 was dry........ 40

3-17 Depth to the restrictive layer, subsurface flow pathways (brown polylines), 

locations of existing multi-sensor capacitance probes ( ), groundwater 

observation wells ( ), and runoff flume ( ) in the vicinity of the lateral flow 

experimental site at the Field B............................................................. 43

3-18 Lateral flow experimental setup ............................................................ 44

3-19 Schematic of the data acquisition and collection system................................ 45

3-20 Multi-sensor capacitance probes and groundwater wells locations at the 

experimental plot............................................................................. 46

3-21 Soil texture measured at 10 depths in 12 locations....................................... 48

3-22 Measured clay, silt, sand and organic carbon distributions in the soil profiles ...... 49

3-23 Soil bulk density distribution with the depth at locations 1-4........................... 50

3-24 Laboratory-measured saturated hydraulic conductivity................................. 51

3-25 Laboratory-measured soil water retention................................................. 53

3-26 The laboratory (left) and field (right) setup to measure soil electrical resistivity.... 54

3-27 Relationship between volumetric soil water content and electrical resistivity 

measured in samples from 10 depths at 12 locations.................................... 55

3-28 Performance of the model (602) to simulate the dependence of the soil electric 

resistivity on soil water content. (a) model parameters do not depend on soil 

properties, (b) model parameters depend on soil properties............................ 57

3-29 Soil temperature distribution in soil profile measured at 7 dates on the ER 

measurement time. The average temperature from locations 6 and 8 is shown...... 58

3-30 Electrical resistivity measured in 2-m soil profile along 24-m transect. Locations 

of groundwater wells and MCO (multiple capacitance probes) are shown with 

arrows........................................................................................... 59

3-31 Volumetric water content distributions in 2-m soil profile along 24-m transect for 

7 dates.......................................................................................... 60

3-32 Monthly (a) and cumulative values (b) of evapotranspiration and precipitation 

measured at the experimental site during the monitoring period (during July 2006 

– September 2007)............................................................................ 62

3-33 Soil water content and soil pressure head time series measured during July 2006 –

September 2007...............................................................................

63

64

3-34 Relationships between measured in locations 1 through 4 soil pressure head and 

volumetric water content..................................................................... 65

3-35 Groundwater depths measured at the experimental site during the monitoring 

period (November 2007 – March 2008)................................................... 66

3-36 Soil surface topography and the finite element mesh in coupled surface-
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subsurface flow and transport simulations. The blue rectangle shows the 

boundaries of the irrigated area............................................................................ 69

3-37 Subsurface representation and the finite element mesh in the coupled surfacesubsurface flow and transport modeling; a –restricting layer parallel to the 

daylight surface, b- restricting layer surface from the ground penetrating radar 

survey. Vertical bars show locations of the observation wells......................... 70

3-38 Development of the overland flow in preliminary coupled surface-subsurface 

simulations..................................................................................... 73

3-39 Tracer concentrations in the overland flow from the preliminary coupled surfacesurface solute transport simulations......................................................... 74

3-40 Simulation domain for solving the flow and transport problem with the 

HYDRUS-3D model. ........................................................................ 76

3-41 Boundary conditions definition............................................................. 77

3-42 Simulated distribution of (a) pressure head, and (b) concentration after 30 days 

(layer 1.5 m depth)............................................................................ 78

3-43 Location of (a) observation nodes and (b) the simulated breakthrough curves....... 79

3-44 Depth to GPR-identified clay lens and location of observation well and moisture 

capacitance probes (after Gish and Kung, 2007. Permission to use this 

copyrighted material is granted by Geoderma).................................................... 83

3-45 Schematic of observation well installation and instrumentation. Schematic is not 

to scale, i.e., the PVC well is only 3.8 cm in diameter, but 3 m in length (after 

Gish and Kung, 2007. Permission to use this copyrighted material is granted by

Geoderma)................................................................................................ 84

3-46 Averaged water flow rates pumped from the observation well as a function of 

time (after Gish and Kung, 2007. Permission to use this copyrighted material is 

granted by Geoderma).................................................................................... 87

3-47 Water table heights in the observation well. Error bars represent one standard 

deviation (after Gish and Kung, 2007. Permission to use this copyrighted material 

is granted by Geoderma).................................................................................. 88

3-48 Soil water content time series (after Gish and Kung, 2007. Permission to use this 

copyrighted material is granted by Geoderma)........................................................ 90

3-49 Tracer breakthrough curves for chloride, bromide and PFBA (after Gish and 

Kung, 2007. Permission to use this copyrighted material is granted by

Geoderma)............................................................................................. 91

3-50 Tracer mass recovery (after Gish and Kung, 2007. Permission to use this 

copyrighted material is granted by Geoderma)..................................................... 92

3-51 Cumulative water fluxes measured at the experimental site during the Lateral 

flow experiment............................................................................... 94

3-52 Groundwater depths measured at the experimental site during the lateral flow 

experiment..................................................................................... 95

3-53 Soil water content measured at 12 locations during the lateral flow experiment.... 97

3-54 Chloride content in the groundwater measured at 12 locations during the lateral 

flow experiment............................................................................... 98

4-1 Simulation domain with the boundary conditions specified (not to scale). 

Different textures and numbers represent the profile layers. CT are tracer 

concentrations in infiltrating water, Cir is the tracer concentration in the irrigation 
x

water............................................................................................. 102

4-2 Observed (circles) and simulated (lines) soil water contents............................ 106

4-3 Observed and simulated breakthrough curves of the tracers: (a) Br, (b) Cl and (c) 

PFBA. Circles – experimental, solid line – simulated with the seepage face 

boundary, dashed line - simulated without accounting for the seepage face 

boundary........................................................................................ 108

4-4 Cumulative water fluxes to the well. ...................................................... 110

4-5 Cumulative solute fluxes of (a) Br, (b) Cl and (c) PFBA to the well.................. 112

4-6 The simulated distribution of (a) pressure head, (b) water velocity vectors, and (c) 

Br concentration after 3 days the irrigation started....................................... 113

4-7 Simulation domain for solving the flow and transport problem with the 

HYDRUS-3D ode: a) whole domain; b) upper sub-layer; c) lower sub-layer......... 115

4-8 Finite element mesh; top –side view, bottom – bird view............................... 116

4-9 Locations of the observation nodes.......................................................... 117

4-10 Boundary conditions for simulations (refer to text for details).......................... 119

4-11 Location of observation wells (blue dots) in the vicinity of simulation domain (red 

rectangle) and hydraulic head distributions at different times in 2006-2007.......... 121

4-12 Simulated (lines) and observed (circles) chloride breakthrough curves. 

Simulations for the initial set of parameters listed in Table 4-2. L1 through L9 

denote observation wells 1-9, ○, ○, and ○ are color codes for L5 through L9 at the 

depths of 1.65, 1.35 and 1.05 m, respectively; ○ is the color code for the depth of 

1.1 m in L1 through L4....................................................................... 122

4-13 Simulated (lines) and observed (circles) chloride breakthrough curves. 

Simulations for the Ks=1. 0, 0.6 and 0.2 m/day for SL, SCL and L, respectively; 

aL=0.5 m, aL/ aT=5. Symbols are the same as in Fig. 4-12.............................. 126

4-14 Simulated (lines) and observed (circles) chloride breakthrough curves. 

Simulations for the Ksat=1.0, 0.6 and 0.2 m/day for SL, SCL and L, respectively; 

aL=0.15 m, aL/ aT=5. Symbols are the same as in Fig. 4-12............................. 127

4-15 Simulated (lines) and observed (circles) chloride breakthrough curves. 

Simulations for the Ksat=1.0, 0.6 and 0.2 m/day for SL, SCL and L, respectively; 

a) aL=0.5 m and b) aL=0.15 m. Symbols are the same as in Fig. 4-12.................. 128

4-16 Simulated distributions of the pressure head at the lowest model depth z=0 

(corresponds to the altitude of 35 above sea level); DOY is the day of the year...... 129

4-17 Simulated Darcy velocity vectors at the depth of around 1 m below surface; DOY 

is the day of year............................................................................... 130

4-18 Simulated distribution of Cl concentration at the depth of 0.5 m below the surface; 

DOY is the day of year, pink dots represent location of observation wells........... 131

4-19 Simulated distribution of Cl concentration at the depth of 1 m below the surface; 

DOY is the day of year, pink dots represent location of observation wells............ 132

4-20 Simulated distribution of Cl concentration at the depth of 1.4 m below the surface; 

DOY is the day of year, pink dots represent location of observation wells........... 133

5-1 Breakthrough curves of Br observed in the pumping well (open circles) and 

simulated at the groundwater level with two 1D models; solid line - equilibrium 

model, dashed line – non-equilibrium model.............................................. 136

5-2 Schematics of unconfined radial flow with infiltration.................................. 137

5-3 Well capture radius (r*) and pumping disc (Qr0) as a function of hydraulic 
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conductivity (Ksat) for a given set of parameters (r0=2. 5 cm, R=3000 cm, a=2000 

cm, i=0.41 cm/h, h0=90 cm, hR=82 cm).................................................... 138

5-4 Conversion of the subsurface material distributions from the HYDRIS3D model 

grid to the MODFLOW model grid. Top left – locations of artificial boreholes 

with properties defined in HYDRUS3D, top right – material distribution in 

artificial boreholes, bottom – cross-sections of material distributions in the 

MODFLOW simulation domain............................................................. 142

5-5 Measured and simulated groundwater levels for the period of soil saturation with 

water............................................................................................ 143

5-6 Figure 5-6. Measured ( ) and simulated tracer breakthrough in observation wells 

with the same values of dispersivity aL and effective porosity ne across the 

simulated transport domain; aL=1 cm, ne=0.2 cm3cm-3; aL =1 cm, ne=0.3 

cm3cm-3; aL =10 cm, ne=0.2 cm3cm-3.................................................... 144

5-7 Tracer transport simulations with three subdomains (top) having different 

parameters for the dispersivity aL (cm) and effective porosity ne. Measured ( ) 

and simulated ( ) Cl breakthrough curves are shown for five different 

observation wells (bottom). .................................................................. 145

5-8 A conceptual scheme for simulating 1D transport in groundwater during tracer 

transport experiment.......................................................................... 147

5-9 Observed (red circles) and fitted (blue lines) breakthrough curves in 

wells 1 through 12............................................................................. 148

5-10 The observed and simulated chloride breakthrough curves for the homogeneous 

sandy loam profile. Symbols are the same as in Fig. 4-12............................... 152

5-11 The observed and simulated chloride breakthrough curves for the homogeneous 

silt loam profile. Symbols are the same as in Fig. 4-12.................................. 153

5-12 The observed and simulated chloride breakthrough curves for the homogeneous 

profiles: a) sandy loam, and b) silt loam. Symbols are the same as in Fig. 4-12...... 154

5-13 The observed and simulated chloride BTCs curves for the abstracted model in 

which Ksat values were determined using pedotransfer functions developed by 

Rawls et al., (1998). Symbols are the same as in Fig. 4-12............................... 155

B-1 Soil water contents measured in the plots (symbols) and calculated using 

SENTEC (solid lines) and the laboratory measured (dotted lines) multi-sensor 

capacitance probes calibrations vs. multi-sensor capacitance probes scaled 

frequency........................................................................................ B-3

B-2 Plot-averaged vs. multi-sensor capacitance probes estimated soil water contents 

for the mesic Typic Hapludult soil. Solid symbols and hollow symbols show 

estimates with SENTEC calibration and the laboratory calibrations developed by

Starr and Paltineanu (1997), respectively. Solid and dash trend lines show the 

general relationship between plot average and MCP-estimated water contents for 

SENTEC and the laboratory calibrations. The 1:1 line is the dotted one.............. B-4

B-3 Average differences between plot-averaged water contents and measured with 

multi-sensor capacitance probes water contents as a function of texture in the 

upper 50-cm soil layer expressed with the regression tree. ε is the average

deviation for the group, N is the total number of samples in the group................ B-10
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List of Tables

3-1 Soil cover of the OPE3 crop production area............................................. 24

3-2 Soil properties used in preliminary simulations of coupled surface-subsurface 

flow and transport............................................................................. 71

3-3 Unsaturated soil hydraulic parameters..................................................... 80

4-1 Unsaturated soil hydraulic parameters inversely estimated using HYDRUS-1D. ... 107

4-2 Initial values of unsaturated soil hydraulic parameters................................. 120

4-3 The values of the coefficient determination (R2) and the Modified Index of 

Agreement (MIA) for two simulation scenarios with aL=0.5 m and aL=0.15 m.... 125

5-1 Calibrated aquifer parameters................................................................................... 149

5-2 Parameters found by solving the inverse of 1D transport in groundwater using 

CXTFIT. ....................................................................................... 150

B-1 Soil texture at locations of the multisensor capacitance probes installation.......... B-5

B-2 Soil bulk density around the multisensor capacitance probes.......................... B-6

B-3 Original and corrected for different depths multi-sensor capacitance probe 

calibration equations......................................................................... B-7

B-4 Root-mean-squared differences of plot average water contents (cm3cm-3) for the 

original and corrected multi-sensor capacitance probe calibration equations........ B-8
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EXECUTIVE SUMMARY

This study was designed and performed to demonstrate the applicability of model 

abstraction techniques to subsurface flow and contaminant transport problems. The study 

focused on future applications of modeling to contingency planning and management of potential 

and actual contaminant release sites within the scope of the US NRC operations. Our main 

objective was to use modeling along with field and laboratory observations to optimize the 

characterization of flow and transport processes in the subsurface. A systematic model 

abstraction methodology was developed and tested in previous work on flow in soils. This study 

aims to test and confirm the application of model abstraction to pollutant transport processes in 

soils and shallow groundwater systems. 

Two test cases were developed that included field tracer experiments and subsequent 

modeling with a series of sequentially simplified models. Modeling is generally only one 

component of subsurface characterization that may, as in this study, also include the use of 

borehole data, laboratory measurements of the soil hydraulic properties, application of 

geophysical methods, monitoring of soil moisture and the pressure head, groundwater 

monitoring, field hydrogeological tests, and tracer studies. The important role of modeling in 

characterizing the subsurface is to describe the prevailing flow and transport conditions. Given 

the non-uniqueness of interpretations of geophysical data, the often small scale of borehole and 

laboratory data as well as of most groundwater samples and tests, and the limitation of soil 

moisture monitoring in revealing the hydraulic conductivity of soils, development of alternative 

conceptual subsurface transport models, and distinguishing between these models, should be part 

of any overall modeling effort. 

The OPE3 experimental field site near Beltsville, MD, has been extensively studied for 

more than 10 years using geophysical, biophysical, remote sensing, and soil and groundwater 

monitoring methods. Available data are analyzed using a systematic procedure based on a broad 

vadose zone modeling context developed in this study. A major focus was on the existence of 

subsurface structural units and features that may drastically change the fate and transport of 

contaminants in the vadose zone, as well as of projected trajectories of the contaminant plume in 

groundwater. We found that solute transport in soils and shallow groundwater at the site is 

potentially affected by such features as the presence of a restrictive fine-textured layer that is not 

fully continuous laterally, the complex topography of the restrictive layer favoring preferential 

flow and transport along preferred pathways along its surface relief, the presence of natural 

capillary barriers, possible funnel flow in a coarse-textural layer between more fine-textured 

layers, and local high-conductivity parts of the soil pore space. 

An extensive field survey and monitoring program had to be initiated as part of this work in 

spite of the existence of a large database of soil and groundwater properties at the site. The main 

reason for this was the difference in scale at which the site was characterized previously, and the 

scale at which flow and transport processes are of a concern in contaminant release applications. 

Specifically, our 20 x 20 m research site required additional characterization since the site 

presented only a single pixel in the characterization of the entire 300 x 300 m OPE3 site. 

The employed geophysical methods provided essential information about transportcontrolling subsurface features. A 2x2 m ground penetrating radar survey showed the existence 

of a mostly continuous restrictive layer with complex topography. Soil electric resistivity 

monitoring furthermore revealed the existence of narrow hydrologically active vertical zones. 

The obtained data indicate that large parts of subsurface soils may not fully participate in the 
xiv

prevailing flow and transport processes. Biophysical monitoring of the research area allowed 

delineation of relatively large structural units in the soil cover that provided distinctly different 

conditions for plant growth. The size of those units exceeded the scale of investigation in this 

work. 

Borehole log data and laboratory hydraulic measurements both confirmed the potential for 

subsurface preferential solute transport, while at the same time indicating that an exact definition 

of a representative elementary volume for the subsurface may be difficult, if at all possible. 

Measurements of the water content and pressure head produced information about the hydraulic 

properties of the unsaturated soils. Field water retention was well defined using these 

measurements. This suggests that the Richards model did provide an appropriate 

conceptualization of the prevailing flow processes at the field site. 

Two field experimental studies, both of original design, were carried out and analyzed using 

model abstraction. One study, referred as the solute flux experiment, was meant to imitate a soil 

column experiment at the plot scale. The experiment involved the application of a conservative 

tracer around a well and subsequent irrigation with simultaneous pumping of ground water. This 

experiment should provide insight into the significance of zones in the soils having a high 

vertical conductivity. A second study was designed to observe the lateral transport of a surfaceapplied conservative tracer pulse when transport was controlled by regular irrigation pulses and 

natural precipitation. This second experiment should demonstrate the effect of the topography 

and continuity of the restrictive layer, as well as the significance of funnel flow due to the 

presence of a coarse layer between the finer-textured layers. The vadose zone during both 

experiments was monitored for soil water content and pressure heads, while groundwater levels 

and the groundwater chemical composition were also recorded. Groundwater compositions were 

monitored at three different depths. 

Two preliminary modeling projects preceded the lateral transport experiment. One was 

undertaken to estimate the potential importance of runoff and the need to intercept this runoff. 

This study required developing a new model and software to simulate coupled surfacesubsurface flow and transport at the plot scale for the 30x30 m study area. The software coupled 

the FEMWATER and 2DSOIL codes, the former simulating subsurface flow and the latter 

overland flow using a diffusive flow approximation. For the second modeling project we used 

the new software, HYDRUS-3D, to simulate flow and transport in the three-dimensional 

subsurface domain at the site. The purpose was to estimate the required duration of the 

experiment and the frequency of sampling needed to capture in detail the solute breakthrough 

curves in a number of observation wells. Both preliminary modeling studies were found useful in 

terms of improving the experiment setup and the schedule of the experiment. 

The solute flux experiment comprised approximately 7 days, whereas the lateral flow 

experiment continued for four months. About 10,000 analyses were made of the tracer 

concentration in order to develop the breakthrough curves. A preliminary analysis of the 

experimental results was used to obtain a conceptual representation of the prevailing subsurface 

transport processes. We hypothesized that preferential transport of solutes occurred in both 

experiments. Vertical transport in the unsaturated zone seemed to occur much faster than 

suggested by the observed water fluxes. The tracer breakthroughs in the lateral transport 

experiment occurred at substantially different times in the wells at similar distances from the 

application area. The differences in times to some extent corresponded to soil textural 

differences. 
xv

There were no indications in the solute flux experiment results that the Buckingham-Darcy 

flow model and the corresponding Richards equation were not applicable to the data. Therefore, 

water flow in both the unsaturated zone and in groundwater was simulated with the Richards 

equation using the HYDRUS2D software package. The seepage face along the observation well 

was found to be an important feature of the experimental setup of the solute flux experiment. 

Transport occurred both in groundwater as well as in the capillary fringe. The Richards equation 

for flow and the convection-dispersion model for transport were both successfully calibrated and 

provided good representations of the experimental results. No assumption about preferential 

solute transport in highly conductive parts of the soil pore space was needed. 

The 2D model for flow and transport in the variably-saturated zone was abstracted to a 1D 

model for vertical water flow and solute transport to groundwater. While ignoring the presence 

of a seepage face, the 1D model allowed preferential transport of solutes to occur. It appeared 

that this model was able to provide only approximate qualitative and quantitative predictions of 

solute breakthrough. The invoked abstraction demonstrated that ignoring the actual geometry of 

the flow and transport domain and the essential features of the flow process in the field can 

create a distorted conceptualization of transport in the subsurface. 

One more abstraction step was considered for 2D solute transport to demonstrate that a 

simple analytical model sometimes may be sufficient for certain modeling application. This 

abstraction was used to investigate the ability of the pumping well to intercept all of the surfaceapplied tracer, which is a critical aspect of the solute transport experimental setup. For this to 

occur, the tracer application zone must remain within the groundwater depression cone around 

the well. We showed that a simple analytical model evaluated the depression cone size with the 

same degree of accuracy as the more refined 2D saturated-unsaturated flow model. 

Results of the lateral flow experiment were relatively more complex than those of the solute 

flux experiment. Some relatively small temporal scale (1 to 2 day) phenomena were observed in 

several wells that could not be explained well. We ignored these fine-scale phenomena and 

concentrated on conceptualizations of the flow and transport processes at larger temporal scales. 

The fine-textured low-permeability layer was found to divert the tracer according to the 

topography of the layer. There were no indications that the Buckingham-Darcy flow model and 

corresponding Richards equations were inapplicable at the larger scale, likely because flow and 

transport at that scale seemed to be driven mostly by the hydraulic gradients in groundwater. The 

complexity of the flow and transport domain required the use of a full 3D representation. For this 

reason we used the HYDRUS3D software to simulate flow and transport in the lateral flow 

experiment. 

No attempt as yet has been made to calibrate the 3D flow/transport model assuming a 

layered profile. Since HYDRUS3D does not have a calibration option, only trial and error 

calibration could be applied. Given that 2 days of computation were needed for each simulation 

run with this code, we streamlined the calibration procedure by calibrating the model directly to 

the breakthrough curves, and not to groundwater levels. This created a dilemma in terms of 

selecting an appropriate conceptual model for transport. Solutes could be delivered to a well via 

two different transport mechanisms: (a) transport via a network of well-connected pathways that 

comprise only part of the bulk soil porosity at the field scale, thus assuming that part of the 

domain does not participate in the transport process, or (b) transport through all of the domain. 

To deliver solute to a well at approximately the same time, average water fluxes should be 

smaller in case (a) as compared to the case (b). We selected case (b) and used several model

abstractions to justify this selection. 
xvi

The trial-and-error calibration based on zonation of the flow and transport domain was 

reasonably successful. The maximum concentration levels and the 50% concentration arrival 

times were described satisfactory. However, we could not accurately reproduce the shape of the 

breakthrough curves. 

A dimension reduction abstraction considered only 2D flow in groundwater. MODFLOW 

and MT3D were used for this purpose. A special effort was undertaken to use in this abstraction 

the same zonation and layering as in the complete 3D representation. MODFLOW calibration 

capabilities were used successfully to reproduce the groundwater levels, while dispersivity and 

effective porosity values were estimated by trial and error from the breakthrough curves. The 2D 

abstraction process showed that the assumption of part of the soil not significantly participating 

in the solute transport process created a better representation of the breakthrough curves. A 

reasonable representation of solute transport was achieved with an effective porosity of 60-70% 

of total soil porosity. Thus, the model abstraction step helped to substantially improve the 

conceptualizaton of the subsurface transport conditions. 

A 1D abstraction step allowed efficient assessment of intrinsic groundwater velocities and 

the hydrodynamic dispersion parameters in different directions. The results also suggested the 

location of preferential flow pathways. Using pedotransfer functions to estimate saturated 

hydraulic conductivities and/or to substitute the heterogeneous soil profile by an equivalent 

homogeneous medium indicated that this kind of model abstraction may lead to incorrect 

estimates of tracer front arrival times at some locations. Actually, results depended on the 

complexity of the heterogeneity being abstracted. Since small-scale heterogeneities may control 

flow and transport at the larger scale, a careful profile aggregation and analysis of the results is 

required. 

The data analyses in this study permit several observations. First, our detailed studies 

revealed considerable soil heterogeneity at a very small site. We do not know how common such 

a degree of heterogeneity is since studies at this level of detail are relatively rare. It is important 

to recognize that the scale of our experiment was comparable the scale of solute release. 

Exclusion of a substantial part of the soil from the active solute transport process appears to be 

an important consequence of soil heterogeneity at the field scale. 

Second, calibration of vadose zone models is much more trying than calibration of 

groundwater models. This because of nonlinearity of the governing flow processes and the large 

number of parameters involved. Substantial changes in soil water contents and flow rates must 

occur to reliably calibrate a vadose zone model. 

Third, the use of models that assume the presence of mobile and immobile zones was 

avoided in this work. Such models are undoubtedly important when breakthrough tails are of 

interest. However, measuring tails takes time that is often impractical for field scale tracer 

studies where transport is controlled by weather conditions rather than by regional groundwater 

flow rates. And even when the tail is known, severe correlations are usually observed between 

the many parameters needed in this type of modeling. Assuming an effective porosity allowed us 

to characterize the subsurface so as to obtain the correct arrival times, and to obtain a reasonable 

approximation of the concentration maximum and the center of the mass position. 

Fourth, results of this study have implications for solute monitoring transport in 

heterogeneous formations. Well data generally represent a fairly small scale. In our experiments 

we encountered distinctly different breakthrough curves in wells that were approximately in 

similar positions relative to the source along the tracer plume propagation direction. A more 
xvii

general representation of solute transport in terms of integrated properties may be needed in 

order to provide a more reliable and accurate representation with models. 

Overall, this study demonstrated the usefulness of model abstraction in simulations of flow 

and transport in a variably-saturated subsurface. Whereas multidimensional and multi-process 

representations leaves room for several competing conceptual models for flow and transport, 

simpler models that retain the most essential features of those representations could provide 

meaningful alternatives. 
xviii
xix

ACKNOWLEDGMENTS

This work was partially supported via Interagency Agreement RES-02-008 between the U. S. 

Nuclear Regulatory Commission and USDA Agricultural Research Service. 

The authors acknowledge with thanks contributions by the following individuals:

Dr. Robert Hill and Mr. Zane Hadzick of the University of Maryland for their work in the 

electric resistivity survey, Mr. Randy Rowland and Mrs. Lynn McKee of USDA-ARS-Beltsville 

for their exceptional support of field and laboratory work; Dr. Daniel Gimenez and Dr. Dennis 

Timlin for their thoughtful comments of a draft version of this manuscript. 
xx
xxi

Abbreviations

1D, 2D, 3D One-dimensional, Two-dimensional, Three-dimensional

2DSOIL Modular simulator of soil and root processes

ANN Artificial neural networks

BTC Breakthrough curves

C Clay

CV Coefficient of variation

DGPS Differential global positioning system

EM Electromagnetic induction 

ET Evapotranspiration

FAO Food and Agriculture Organization of the United Nations

FEMWATER Finite element model for groundwater

GMS Groundwater Modeling System

GWD Groundwater depth

HPLC High performance liquid chromatography

HYDRUS Software package for simulating the movement of water, heat and multiple 

solutes in variably-saturated media. 

IC Ion chromatography

L Loam

MA Model Abstraction

MCP Multi-sensor capacitance probes

MODFLOW Three-dimensional finite-difference ground-water flow model

MT3D Modular 3-D Solute Transport model

MWBUS Model of Water Budget of Unsaturated Soil

NRC U. S. Nuclear Regulatory Commission

OPE3 Optimizing Production Inputs for Economic and Environmental Enhancement

PEST A nonlinear Parameter Estimation and optimization package

PFBA Perfluorobutyric acid

PTF Pedotransfer function

PVC Polyvinyl Chloride

RES2DINV Software designed to interpolate and interpret field data of electrical 

geophysical prospecting (2D sounding) of electrical resistivity (conductivity) 

and induced polarization. 

REV Representative elementary volume

ROSETTA Windows-based program that implements artificial neural network to soil 

hydraulic parameters

SCL Sandy Clay Loam

SiltCL Silt Clay Loam

SiltL Silt Loam

SL Sandy Loam

STANMOD STudio of ANalytical MODels software designed for evaluating solute 

transport in porous media using analytical solutions

SURFER Environmental software designed to produce contouring maps and surface 

plots in 2D

TDR Time Domain Reflectometry
xxii
xxiii

SYMBOLS

Roman symbols

A cross-sectional area of the well 

a empirical parameter

aL longitudinal dispersivity

aT longitudinal dispersivity

B empirical parameter

BD soil bulk density

C solution concentration

c0 initial concentration

cb background concentration in the groundwater

Clay percent clay

cR concentration of water in rain

csorb surface density of the attached solute

cw concentration in the well

 i

obs

w C t

observed concentrations of a tracer in pumped water

obs Cw

mean observed concentration

  w i C t

simulated concentrations of a tracer in pumped water

D hydrodynamic dispersion tensor

D

surface diffusion-dispersion tensor

dm molecular diffusive component

Dsoil solute dispersion coefficient in soil

dw well diameter

ER electrical resistivity

ERref reference electrical resistivity

g the acceleration due to gravity

h flow depth on soil surface

H(r) the Heaviside step function

h0 water table height at r=r0

hR water table height at r=R

i recharge rate

J rate of solute loss from runoff to soil with infiltration

K hydraulic conductivity tensor

k



corrected hydraulic conductivity in surface boundary nodes

KF parameters of the Freundlich equation for the mass-exchange isotherm

Ksat saturated hydraulic conductivity

ksurf surface conductivity

1/ 2

z

k

conductivity between two nodes

m a parameter of van Genuchten‟s water retention model

m Manning roughness coefficient

M rate of the solute mass influx from rain

MIA modified index of agreement 
xxiv

n a parameter of van Genuchten‟s water retention model

nF parameters of the Freundlich equation for the mass-exchange isotherm

p pressure head

q Darcy-Buckingham flux vector

q tracer dilution rate

l1

q



corrected flux at surface boundary nodes in x or y directions

Q radial water flux to well

Qc(SF) mass fluxes of the tracers to the well trough the seepage face

Qc(VB) variable flux boundaries

qd apparent flow rate caused by molecular diffusion of the solute

qf velocity of the undisturbed ground water flow

qh apparent flow rate caused by density convection

qm apparent flow rate caused by the mixing device

qs apparent flow rate caused by vertical currents in the well screen

qz water flux in the vertical direction

r radial coordinate

R rainfall rate

R radii of the outer boundary

r0 radii of the well

RMSD root-mean-square difference 

S0 surface slope in x-direction

Sand percent sand

Se soil water saturation

SF multi-sensor capacitance probe scaled frequency

Silt percent silt

T temperature

t time

Tref reference temperature

u velocity components in x-direction

v velocity components in y-direction

V water-filled well volume

z gravitational head

zs land surface elevation

Greek symbols



dispersivity tensor

α a parameter of van Genuchten‟s water retention model

z

distance between two nodes

(h)

Heaviside function

θ volumetric water content

θmax maximum volumetric water content

θmin minimum volumetric water content

θr residual water content

θs saturated water content
xxv l





corrected water content of surface boundary nodes

λ decay or biodegradation rate coefficient

τ parameter of Genuchten-Mualem model

ω spread parameter in a step function approximation
xxvi
1

1 INTRODUCTION

U.S. NRC staff reviews of performance assessments of nuclear facilities (e.g.,

decommissioning of the facilities, management of low-level and high-level radioactive waste 

disposal sites) frequently involve assessing models for subsurface water flow and solute transport 

in the vicinity of a nuclear facility (U. S. NRC, 1993, 1994). These models seek to represent 

complex and highly transient subsurface systems. Representations of those complex systems in 

existing models ranges from very simple to extremely sophisticated formulations (Davis et al.,

2004; Meyer et al., 1997; Neuman and Wierenga, 2003; Reily and Harbaugh, 2004; Hill and 

Tiedemen, 2007). 

Soluble contaminants are typically expected to be released into a variably-saturated

subsurface (or vadose) zone, which may include soils and fractured rocks. The vadose zone is 

made up of soils in many or most practically important cases. Soil properties of the vadose zone 

control contaminant travel times to groundwater, the actual locations where contaminant will 

reach groundwater, and the chemical, and biological transformations that contaminants are 

subjected to while moving through soils. A successful understanding and modeling of 

contaminant transport in soils is hence a precondition of risk-informed predictions of subsurface 

contaminant transport. 

Many mathematical models of subsurface flow and transport may be formulated for the 

same site. One reason for this is the inherent complexity of vadose zone layering and the 

properties of soil layers, lenses and other structural units that are generally resent. This 

complexity needs to be grossly simplified to be expressed in mathematical terms, with different 

sets of simplifying assumptions leading to different models (Neuman and Wierenga, 2003). And 

even when the kinds and relative positions of the structural units are selected, knowledge is never 

certain about the locations of the boundaries of these units, and about the flow and transport 

properties of the soils making up those units. This creates substantial uncertainty in the 

parameters of the models. 

The existence of several candidate models for the same observation site or for the same 

phenomenon is common in the environmental sciences and their applications, as well as in other 

disciplines. Making use of several models has been shown to be more beneficial than looking for 

the “single best” model. One approach, called multimodeling, uses outputs from several models, 

and assigns weights to those outputs to obtain the best fit to data. Multimodeling has been widely 

used in atmospheric sciences (Barnston et al., 2003; Palmer et al., 2000, 2004), and is now

increasingly accepted also in groundwater modeling (Ye et al., 2004; Poeter and Anderson; 

2005) as well as vadose zone flow modeling (Guber et al., 2006, 2008). The use of simpler 

modes to complement a complex model is another approach to utilize the multiplicity of models 

(Bigelow and Davies, 2003; Van Ness and Scheffer, 2005). Simple models have advantages 

regarding the collection of data, the computations involved, the interpretation of the simulation 

results, and conveying the simulation approach to both technical and lay audiences. On the other 

hand, the explicit description of mechanisms in more complex models may cause their better 

performance outside of conditions for which the simple models have been developed and tested. 

Currently, different research fields have been using different approaches to the selection or 

derivation of simple models for use along with more complex models. One of the methods 

consists in a systematic derivation of simpler models from the original complex model. This 

method has been termed “model abstraction”. In subsurface hydrology, this systematic model 

simplification was first suggested by Neuman and Wierenga (2004) in their work for the U. S. 
2

Nuclear Regulatory Commission. Examples of useful simplifications of ground water models 

were presented by Hill (2006). For soils, the model abstraction methodology, including 

techniques and examples of using model abstraction to simulate water flow, was developed in a

recent interagency study by Pachepsky et al. (2006). We viewed the application of model 

abstraction to solute transport in soils as the next logical step. 

The objective of this work was to develop a test example of the application of model 

abstraction to solute transport in a field soil. The work was designed to be an intensive study that 

should include a variety of advanced methods for characterizing, monitoring, and modeling flow 

and transport processes in the vadose zone. We benefitted in this study greatly from using the 

USDA-ARS OPE3 research site in Beltsville, MD, where the subsurface hydrologic and solute 

transport processes have been studied for more than a decade before this particular study began. 
3

2 MODEL ABSTRACTION IN SUBSURFACE HYDROLOGY

2.1 BACKGROUND

Model abstraction is a methodology for reducing the complexity of a simulation model 

while maintaining the validity of the simulation. Model abstraction techniques stem from a need 

to improve the reliability and to reduce the uncertainty of simulations, to make modeling and its 

results more explicable and transparent to end users, and to enable more efficient use of available 

resources in data collection and computations. 

An important feature of model abstraction is the explicit treatment of model structure 

uncertainty. Model structure, along with data uncertainty and scenario uncertainty, is known to 

introduce uncertainty in the modeling results. Unlike uncertainty in input data, model parameters 

and scenarios, the effect of model structure uncertainty on the uncertainty in simulation results is 

usually impossible to quantify in statistical terms. Using model abstraction, a series of models 

with feasible structures can be built and evaluated in a systematic manner. Each of the models is 

evaluated from results of an ensemble of simulations by its accuracy to measurement data, and 

by its predictions with respect to scenarios that have not been observed. 

Earlier collaborative work of ARS and NRC staff resulted in the definition of several

categories of model abstraction techniques relevant to subsurface flow and transport modeling 

(Pachepsky et al., 2006). These categories included abstractions of model structure and model 

parameter determination, and were based on a comprehensive review of model simplification 

techniques developed for subsurface flow and transport (Fig. 2-1). A brief review of available 

model abstraction techniques is given below for clarity and reference purposes; more detailed 

descriptions are in the above cited NUREG report. 

2.2 ABSTRACTIONS OF MODEL STRUCTURE

Hierarchies of models. An example of the hierarchy of models available to simulate water 

flow in variably-saturated porous subsurface media is presented in Fig. 2-2. A pre-defined 

hierarchy of models has been suggested previously for flow and transport in structured media 

(Altman et al., 1996). Fig. 2-2 shows a schematic representation of increasingly complex models 

that may be used to simulate preferential flow and transport in macroporous soils or unsaturated 

fractured rock. The simplest water budget model describes the accumulation of water in the soil 

matrix and its discharge when the water content exceeds the field water capacity, or during 

evaporation periods (Fig. 2-2a). The classical approach of simulating flow/ transport processes in 

a vadose zone devoid of macropores or fractures is to use the Richards equation for variablysaturated water flow and the advection-dispersion equation for solute transport (Fig. 2-2b). The 

simplest situation (Fig. 2-2c) for a fractured medium arises when the Richards and advectiondispersion equations are still used in an equivalent continuum approach, but now with composite 

(double-hump type) hydraulic conductivity (permeability) curves of the type shown by Mohanty 

et al. (1997), rather than the classical smooth curve for the relative permeability shown in Fig. 

2b. More involved dual-porosity type models (Fig. 2-2d) result when the medium is partitioned 

into fracture and matrix pore regions, with water and/or solutes allowed to exchange between the 

two liquid regions (e.g., Ventrella et al., 2000). Different formulations of this type are possible. 

For example, one could permit transient variably-saturated flow in the fractures only, while 

allowing water to exchange between the fracture and matrix domains. The latter situation leads 

to both advective and diffusive exchange of solutes between the fractures and the matrix but still
4

Figure 2-1. Categories of model abstraction techniques relevant to flow and transport modeling 

in subsurface hydrology. 

Abstraction of the model structure Abstraction of parameter determination

Hierarchy Metamodeling

of models

Limited

input 

domain

Scale

change

Upscaling Aggregation

Discretization

Scaling

Pedotransfer

Model abstraction

Abstraction of the model structure Abstraction of parameter determination

Hierarchy Metamodeling

of models

Limited

input 

domain

Scale

change

Upscaling Aggregation

Discretization

Scaling

Pedotransfer

Model abstraction
5

Figure 2-2. Hierarchy of models to simulate water flow and solute transport in structured soils or 

in unsaturated fractured rock (Pachepsky et al., 2006). 

Single 

continuum

Equivalent

matrix and

fracture

continuum

Dual porosity

Matrix Fracture Matrix Fracture

Dual 

permeability

Discrete

fractures

without

matrix

Discrete

fractures

with

matrix

Water

budget Relative permeability Pressure head

Complexity

Model abstraction

a b c d e f g

Single 

continuum

Equivalent

matrix and

fracture

continuum

Dual porosity

Matrix Fracture Matrix Fracture

Dual 

permeability

Discrete

fractures

without

matrix

Discrete

fractures

with

matrix

Water

budget Relative permeability Pressure head

Complexity

Model abstraction

a b c d e f g
6

without vertical flow in the matrix (e.g., Zurmühl and Durner, 1996; Zurmühl, 1998). Dualpermeability models (Fig. 2-2e) arise when water flow occurs in both the fracture and the matrix 

domains. Examples are models by Pruess (1991), Gerke and van Genuchten (1993) and Jarvis 

(1999). These models use different formulations for the exchange of water between the fracture 

and matrix regions. In some models (e.g., Wilson et al., 1998) more than two domains are 

considered, each one having its own hydraulic properties. The modeling approach can be refined 

further by considering transient flow and/or transport in well-defined discrete fractures without 

(Fig. 2-2f) or with (Fig. 2-2g) interactions between the fractures and matrix. The latter approach 

is based on the assumption that the flow and transport equations of the fracture network can be 

solved in a fully coupled fashion with the corresponding equations for the matrix (e. g., Therrien 

and Sudicky, 1996). 

Limited input domain. Model abstraction techniques based on delimiting the input domain 

rely on the notion that some feature or process may not be relevant for a given class of scenarios 

or for a given set of model outputs. A reduction in the spatial dimensionality is one application of 

this technique. Two-dimensional representations of the subsurface are sometimes redundant and 

1D representation may suffice as shown by Wang et al. (2003). In another example, Guswa and 

Freyberg (2002) explored the possibility of using a 1D model to characterize solute spreading in 

a medium containing low-permeability lenses; they found that the 1D macroscopic advectiondispersion equation matched results of the 2D model well when the equivalent conductivity of 

the domain was less than the geometric mean conductivity. This example shows that one should 

expect a change in parameter values when the dimensionality is reduced. 

Scale change. Scale is a complex concept having multiple connotations. The notion of 

support is important to characterize and relate different scales in subsurface hydrology. Support 

is the length, area, or volume for which a single value of a porous medium property is defined 

and no variations in this or other properties are taken into account. The size of an individual 

sample, or the size of a discrete spatial element in the flow model, are typical examples of 

support. The terms "resolution," "pixel size," "grid size,” and “voxel size" are used often to 

define the resolution in terms of length, area, or volume. An area or a volume that is sampled 

with given support determines the extent of measurements. Distances between sampling 

locations define the spacing, which is also a function of scale. Blöschl and Sivapalan (1995) 

suggested using the triplet of numbers support-spacing-extent, rather than a single value of 

support, spacing or extent, to characterize the scale of a hydrologic study. 

In practice, vadose zone investigations generally define the supports of core scale, soil 

profile or “pedon” scale, field scale, and watershed scale operationally, i.e. based on the

measurement setup and available equipment. Increasing the linear size by about two orders of 

magnitude generally corresponds to a transition from one of these scales to the next one, as 

shown schematically in Fig. 2-3. Changes in the spatial scale are usually reflected by changes in

the temporal scale as shown in this figure. 

Scale change with upscaling. This category of model abstraction recognizes the need to

alter model structure when the spatial scale changes. Model equations, variables and parameters 

change as the scale changes. A key premise of upscaling is the possibility to derive parameters of 

a coarser-scale model from parameters of a finer-scale model. 

To be effective, all upscaling techniques must use the correct statistical representations of

relatively rare but essential features at the finer scale since these features often govern relevant 

media properties or processes at the coarser scale. For example, if the hydraulic conductivity is 

distributed lognormally, then five percent of a fine-scale representative elementary volume
7

Figure 2-3. Spatial and temporal operational scales in hydrology (Pachepsky et al., 2006). 
8

(REV) will conduct 95% of all flow, which implies that relatively rare features at the smaller 

scale will control flow at the coarser scale. Macropores (i.e. relatively large pores) provide

another example of the importance of relatively rare fine-scale features. Relative to smaller 

matrix pores, macropores are rare in soils and are easy to miss during sampling. Yet, continuous

macropores largely control rates of water flow and solute transport in a soil profile. Similarly, 

lateral preferential flow pathways in the subsurface are fine-scale features at the field or 

watershed scale, and relatively difficult to locate. Yet, lateral preferential flow pathways may 

well control lateral flow and solute transport often at the larger scale. 

Scale change with aggregation. Aggregation also leads to a change in the governing 

equations and model parameters. However, unlike with upscaling, no relationship is assumed 

between the model parameters at the fine and coarse scales. Parameters of the coarser-scale 

model are deemed to be lumped, which suggests that field data are needed to calibrate the coarse 

scale models. An example is the use of a water budget soil flow model (Fig. 2-2a) at the field 

scale, while the Richards equation is used at the soil profile scale (Fig. 2-2b). Soil water retention 

is then parameterized in terms of field capacity at the coarse scale, whereas soil water retention 

curves are used at the fine scale. No reliable relationship exists between the water content at field 

capacity and the soil water content at a specific value of the pressure head, and therefore no 

relationship exists between the coarse- and fine-scale soil water retention parameters. 

Aggregation can be also implemented without a change in the model equations by 

combining several soil horizons or geologic strata. For flow and transport in vadose zone, one 

common application is to replace a heterogeneous soil profile with an equivalent homogenous 

profile while retaining the Richards equation as the flow model (Zhu and Mohanty, 2002). In 

such case, flow and transport parameters are still lumped. Attempts to determine the effective 

hydraulic properties of the equivalent soil profile from the layer properties have shown that the 

effective properties depend not only on layer properties as such, but also on the type of 

predominant water regime (infiltration or evaporation). 

Many examples of distributed watershed modeling with various degree of sub-watershed 

aggregation have recently been developed in surface hydrology. In general, excessive 

aggregation worsens model performance. For example, Boyle et al. (2001) showed that the 

aggregation from eight to three sub-watersheds did not worsen model performance, whereas 

aggregating all sub-watersheds in only one watershed did. 

Metamodeling. Metamodeling is a group of abstraction methods that uses results of multiple 

simulation runs to extract information helpful for simplifying a complex model. Metamodeling 

literally means modeling a model. Also known as the repromodeling (Meisel and Collins, 1973) 

or response surface modeling, Metamodeling creates a relatively simple empirical model 

intended to mimic the performance of a large complex model in order to reproduce the object 

model‟s input-output relationships (Davis and Bigelow, 2003). A common way to develop a 

metamodel is to generate “data” from a number of large-model runs and then to use statistical 

methods to relate model input to model output without attempting to understand the model‟s 

internal working. 

Machine learning methods have become a popular means to build metamodels. Artificial 

neural networks (ANNs) are the most popular among these since they are powerful 

approximators and, as such, are popularly used to relate multiple input variables to outputs from 

the complex model (Hecht-Nielsen, 1990). Examples of the application of artificial neural 
9

networks to mimic MODFLOW output for a range of scenarios for particular remediation sites 

were published as early as 10 years ago (Kron and Rosberg, 1998; Masket et al., 2000). The use 

of ANNs requires development of a large number of training datasets covering the range of 

possible scenarios of forcing variables. Generating such datasets requires extensive computing 

efforts, but after the ANN is trained, computations with the derive ANN are several orders of 

magnitude faster than simulations with the original model. An example involving regional 

wastewater planning in which, for reasons of computational efficiency, an artificial neural 

network was employed is given by Wang and Jamieson (2002). The ANN replicated the processbased model in multiple evaluations of the model output during optimization aimed at

determining both the best sites and individual discharge standards. Other machine learning 

methods such as support vector machines, classification and regression trees, and genetic 

programming are increasingly being appreciated in subsurface hydrology. 

Machine learning methods can be used to simulate not only the model output of interest, but 

also the results of any part of the computations performed during a model run. For example, 

Hassan and Hamed (2001) demonstrated the use of ANNs to predict particle trajectories in a 

particle-tracking algorithm simulating plume migration in heterogeneous media. Their

metamodeling approach substantially improved the computational efficiency of the entire 

algorithm. 

2.3 ABSTRACTION OF PARAMETER DETERMINATION

Discretization. Using a set of discrete parameter values, instead of continuous functions,

can sometimes lead to substantial simplifications. This simple but very important abstraction 

approach is commonly used in flow and transport modeling by employing soil and geological 

textural maps to define soil or sediment structural units that have the same hydraulic properties, 

even though real-world hydraulic properties may more gradually change from one unit to 

another. Zonation of the hydraulic conductivity was found to be efficient when geophysical and 

hydrogeological data were combined (Chen et al., 2001, 2004; Hubbard et al., 2003). Automated 

zonation is now also feasible (Tsai, 2003), which has the advantage of not needing a specific 

equation to simulate the dependence of parameters on the spatial coordinates. 

Abstraction by temporal discretization is often used to create soil surface boundary 

conditions or discharge values. The temporal support of precipitation and evaporation or 

discharge is then coarsened to time intervals of months or years to speed up computations or to 

avoid generating synthetic weather patterns. Unfortunately, this type of abstraction can 

potentially also introduce substantial errors. For example, McLaren et al. (2000) studied the 

transport of 35Cl in fractured tuff at Yucca Mountain and showed that changing the infiltration 

regime from a constant value of 5 mm y-1to a pulsing regime with the same annual average 

value greatly enhanced the transport of the radioactive isotope. The effect of infiltration pulsing 

was model dependent; low rates of mass exchange between preferential flow zones and the 

matrix further enhanced transport to make the predictions more consistent with observations 

(Bandurraga and Bodvarsson, 1999). Relationships between flow properties and water contents 

are highly nonlinear in the vadose zone. Temporal coarsening for this reason may cause 

simulated plumes to move much slower and to become much more compact from they would 

have been otherwise. 

Pedotransfer functions. Parameters of models for flow in variably-saturated porous media 

are nonlinear functions of the pressure head or water content. The parameters in these hydraulic 

functions are notoriously difficult to measure. Accurate measurement of water and solute fluxes 
10

in unsaturated soils remains a major research issue; no routine methods have been devised todate. Therefore, defining parameters using inverse methods is often problematic. Substantial 

efforts have been made to estimate the hydraulic parameters from data available from soil 

surveys or borehole logs. Empirical functions used for this purpose are often called pedotransfer 

functions (PTFs). Extensive work has been carried to develop PTFs. The proceedings of two 

international conferences (van Genuchten et al., 1992, 1997) and a book on this topic (Pachepsky 

and Rawls, 2004) provide a panoramic view of these fast-developing studies. 

The performance of pedotransfer functions can be evaluated in terms of their accuracy, 

reliability, and utility. In broad terms, the accuracy of a PTF can be defined as the

correspondence between measured and estimated data for the data set from which a PTF has 

been developed. The reliability of a PTF may be viewed as the correspondence between 

measured and estimated data for data set(s) other than the one used to develop the PTF. Finally, 

the utility of a PTF in model applications can be assessed in terms of the correspondence 

between certain measured and simulated environmental variables. 

PTFs developed from regional databases have been shown to be more reliable in regions 

with similar soil and landscape histories. For example, PTFs developed from the country-wide 

US database by Rawls et al. (1982) appear to be more robust than PTFs developed from regional 

databases. However the accuracy of any PTF outside of its development dataset is essentially 

unknown, and using multiple PTFs instead of relying on a single PTF may well be preferred. Ye 

et al. (2004) suggested averaging spatial variability models for unsaturated fractured tuff in

situations where standard information criteria provide an ambiguous ranking of the models such 

that it was not justified to select one model and discarding all others. Guber et al. (2006, 2008) 

likewise used an ensemble of pedotransfer functions to simulate water flow in variable saturated 

soils. 

Recent developments in pedotransfer technologies have focused on the use of spatially 

dense physical information related to soil cover. Using topographic information is based on the 

hypothesis that some relationship may exist between the soil hydraulic properties and 

topographic variables (Pachepsky et al., 2001) since (a) the basic properties of soil are known to 

be related to landscape position, and (b) soil hydraulic properties are related to basic soil 

properties. Soil water retention was found to exhibit a strong dependence upon terrain attributes 

in the work by Rawls and Pachepsky (2002) who used U. S. soil survey data from the National 

Resources Conservation Service (NRCS). Terrain attributes were also used by Romano and 

Palladino (2002) to improve PTFs. 

The use of hydrogeophysical, remote sensing, and crop yield data is based on a similar 

premise as using topography. The basic soils data should affect both the sensor readings and the 

soil hydraulic properties. Therefore, some relationship between the dense data and the hydraulic 

properties should be expected. A recent first book on hydrogeophysics (Rubin and Hubbard, 

2005) summarized the rapid progress in this field. Cross-borehole resistivity measurements are 

now also showing promise in improving estimates of flow and transport properties of the vadose 

zone (Looms et al., 2008; Deiana et al, 2008). One recent example involved the use of airborne 

gamma radiometric sensing to estimate the clay content of surface soils and using a simple 

pedotransfer function to convert this information into a spatial representation of soil water 

retention parameters (Smettem et al., 2004). In another example, Timlin et al. (2002) related 

biophysical information from yield maps to the soil field capacity. 

The use of dense auxiliary data in PTFs reflects an attempt to trade data quality for data 

quantity. Since dense coverage can be treated as an image, image analysis techniques may be 
11

used for segmentation and classification, as well as for delineating the structural units of soils. 

Data assimilation techniques may be suited also for combining soil survey and sensor 

information (McLaughlin, 1995). PTFs developed with auxiliary data are probably highly sitespecific and, therefore, useful mostly only for sites for which they were developed. Nevertheless, 

the availability of sensor data can make such PTFs a viable component of supplying parameters 

of models for water flow in the vadose zone. 

2.4 SYSTEMATIC MODEL ABSTRACTION

Earlier collaborative work between ARS and NRC staff resulted in the development of a

systematic and objective approach for model abstraction (MA) relevant to subsurface flow and 

transport modeling (Neuman and Wierenga, 2003; Pachepsky et al., 2006). The approach 

included (a) justifying the need for model abstraction, (b) reviewing the context of the modeling 

problem, (c) selecting applicable MA techniques, and (d) determining alternative MA directions 

and simplifying the base model in each direction. 

We emphasize here that model abstraction is always site-specific. Appendix A provides 

details of the model abstraction process. In this section we give only a brief description. 

2.4.1 MODEL ABSTRACTION STEPS

The MA process starts with an existing base model that can be calibrated and used in the 

simulations. The key output of the model is defined in this first step. The output provides the 

necessary and sufficient information required to make decisions about a certain issue of interest. 

The model abstraction process includes the following steps. 

1. Justify the need for the envisioned model abstraction

2. Review the context of the modeling problem

3. Design the model abstraction using selected techniques

4. Perform model abstraction

Model abstraction justification. Any model simplification requires calibration of the 

abstracted simpler model and its confirmation with multiple model runs. This is a separate 

modeling project that demands resources, and may be used later to justify the need for model 

abstraction. The base model may need abstraction for one or more of the following reasons:

 The base model includes a complex description of processes that cannot be 

observed well, but still needs to be calibrated; the calibrated values of parameters of those 

processes may be very uncertain. 

 The base model propagates uncertainty in the initial distributions, the parameters, 

and the invoked boundary conditions (forcing) in a manner that creates unacceptable 

uncertainty in the key output. 

 The base model produces inexplicable results in terms of the key output. 

 The base model requires an unacceptable amount of resources for the 

computations, data preprocessing, or data post-processing (e.g., the base model is not 

suited to be part of an operational modeling system that requires real-time data 

processing). 

 The base model lacks transparency to make the model and its results explicable 

and believable to users of the key output. 
12

The lack of transparency of the base model is often a result of abstraction motivated by the 

perception of potential users or critics of the simulation results. Incomprehensible simulation 

results with the base model or the unacceptable resource demand of the base model are often 

reasons that preclude the completion of a modeling project. 

The need for abstraction may stem also from uncertainty in the calibrated parameter values 

because of the limited observation ability or uncertainty in the simulation results. The decision to 

carry out the model abstraction may be based on the statistics of parameter estimates and the key 

output, as discussed by Pachepsky et al. (2006). 

Context of the modeling problem. The context of a modeling project has to be reviewed to 

assure the objectiveness and comprehensiveness of the selected model abstraction. One must

realize which details and features of the problem are to be omitted or de-emphasized when 

abstraction is performed. Neuman and Wierenga (2003) list the following issues that constitute 

the context:

1. What is (are) the question(s) that the base and abstracted models are to address? The answer 

should consider (a) the existing or potential problem in which modeling is one of the solution 

instruments, (b) the existing or potential causes of the problem, (c) the issues needing 

resolution, and (d) the criteria to be used for deciding the level of resolution. The key output 

has to be provided with the spatial and temporal scale at which model abstraction is 

evaluated. Acceptable criteria for accuracy and uncertainty of the model output must to be 

established by the end users. In some cases mandatory regulations exist on performance 

measures that articulate the statistics to use in a particular case. If there are no such 

regulations, then the statistics have to be selected and defined; they should describe simple 

and clear ideas about the correspondence between the data and the simulations, such as how 

variability in the model errors compares with variability in the data, if the model residuals 

have trends, or if systematic relative or absolute errors exist in the predictions. 

2. What type of data is available to calibrate the base and abstracted models and to test them 

with respect to the key output? An essential prerequisite is to have a database that is as broad 

as possible. The database must include data from public and private sources, cover both 

quantitative and qualitative (expert) information, and encompass both site-specific and 

generic information. A list of base model inputs and outputs would provide a convenient 

template for the necessary parts of the database. It is imperative to have statistics of all 

available model inputs and measurable model outputs, including (a) the initial distributions 

of water contents and/or pressure heads, and the concentrations of solutes of interest, (b) 

surface and subsurface soil properties including horizon or layer thicknesses, porosities, bulk 

densities, adsorption parameters, and in some cases redox conditions, (c) the forcing that 

provides the boundary conditions and the source/sink terms, and (d) the model parameters 

typical for the site. The latter can be inferred from an ensemble of pedotransfer functions,

provided the necessary soil survey and/or borehole log data are available to serve as 

pedotransfer inputs. Statistics includes the type of statistical distribution used, median values 

and variability measures, information about observed outliers, and correlations between 

parameter values. 

3. To make sure that the abstracted models are sound, additional information may have to be 

collected to ensure that the abstracted models include descriptions of all essential processes 

of flow and transport at a given site. This information may be of lower quality compared with 

the necessary part of the database. For example, one must be sure to not ignore certain small-
13

scale internal heterogeneities that may have a dominant effect on flow and/or transport at the 

scale of interest. 

2.4.2 MODEL ABSTRACTION DESIGN AND EXAMPLE

The design of a model abstraction project should include selection of the model abstraction 

techniques, definition of uncertainties that have to be simulated using Monte Carlo or other 

methods, and selection of the software to be used (Pachepsky et al., 2006). The selection of 

model abstraction depends on the reasons for the model abstraction. In general, model 

abstraction can lead to simplifications via:

 the number of processes being considered explicitly,

 simpler process descriptions,

 coarsening the spatial or temporal support

 the number of measurements to be used for reliable parameter estimation,

 reduced computational burden,

 simplified data pre-processing and post-processing. 

An example of model abstraction design and implementation was developed in a study 

focusing on infiltration in a variably-saturated soil subject to natural rainfall (Pachepsky et al.,

2006). The base model for this study was previously developed by Jacques et al. (2002) who 

simulated water flow in a layered soil using a single-continuum pore space model (media b in 

Fig. 2-2). Parameters were estimated by calibration using measured water content and pressure 

head time series. The key output was the soil water flux at three depths. The base model 

provided an excellent fit to the soil water contents but failed to simulate measured soil water 

fluxes. The results could not be explained well (Jacques et al., 2002). 

Fig. 2-4 shows the selected model abstraction techniques, the uncertainty treatment, and the 

software selected (Pachepsky et al., 2006). Four abstraction techniques were used. Two 

techniques simplified the base model via (1) a simpler process description, i. e., by changing the 

porous media model from a single-continuum (Fig. 2-2b) to a water budget model (Fig. 2-2a), 

and (2) by aggregating soil layers into a single layer with effective hydraulic properties. Two 

other techniques simplified the parameter determination by using only laboratory data, or by 

using an ensemble of pedotransfer functions. Fifty Monte-Carlo simulations were performed 

with each abstracted model using data on variability of calibrated, measured, or estimated

hydraulic properties. The HYDRUS 2D and MWBUS software packages were used to simulate

water flow in the single-continuum medium and with the water budget model, respectively. 

The model abstracted from the hierarchy of models correctly simulated fluxes and showed why 

inexplicable results had been obtained with the more complex model. Simultaneous calibration 

of a large number of parameters in the base model caused unrealistic flow simulations that 

included substantial runoff generation, whereas no runoff was observed during the experiments. 

The model abstraction via pedotransfer functions showed that an ensemble of pedotransfer 

functions produced a satisfactory representation of field uncertainty in the soil hydraulic 

properties. 
14

Figure 2-4. Design of model abstraction via model structure and parameter determination
15

2.5 MODEL ABSTRACTION VS. ARBITRARY SELECTION OF A “SIMPLE” MODEL

Models used in performance assessments of waste disposal sites generally ignore smallscale heterogeneities in space and time. Preferential pathways are typically ignored when a

single-continuum pore space representation is used. Observed strongly asymmetrical 

distributions of the pore water velocity are then often represented by an average velocity. 

Similarly, strongly asymmetrical temporal distributions of actual rainfall or discharge are

represented by rates averaged across long periods of time. Thus, the often-used models are 

actually abstractions of more realistic models that explicitly account for spatial and temporal 

heterogeneities. 

One argument for using a simplified model based on averaging is that locating and 

quantifying small-scale spatial and temporal heterogeneities has substantial conceptual and 

resource limitations. However, the magnitude of errors caused by ignoring the small-scale 

heterogeneities is never known a priori. Recent research shows that heterogeneities are common, 

and that even slight reductions in soil texture may lead to flow barriers and associated lateral

flow. These lateral flow paths may lead to solute mass losses, reduced vertical fluxes, and 

increased longitudinal dispersivities (Looms et al., 2008). This shows that it is imperative to 

evaluate possible prediction errors when the “simple” model is used. Deriving the simple model 

from the more complex base model provides opportunities for such an evaluation. 
16
17

3 EXPERIMENTS TO TEST AND CONFIRM MODEL ABSTRACTION

FOR FLOW AND TRANSPORT IN SOILS

In this study we apply a systematic abstraction process to base models accounting for 

heterogeneities in subsurface flow and transport. The abstraction will lead to often-used 

simplified models, with as overall objective the estimation of pattern and magnitudes of possible 

errors obtained with the simplified models. The purpose of this section is to provide an analysis

of the exhaustive ARS OPE3 vadose zone flow and transport database within the context of

model abstraction, and to describe the experiments and measurements carried out to develop the 

base flow and transport model. This model was developed and then subjected to abstraction as 

described in the following sections. 

3.1 OUTLINE OF EXPERIMENTS TO TEST AND CONFIRM MODEL ABSTRACTION IN SOILS

A century-long history of experimentation on solute transport in soils has resulted in a 

multitude of advanced experiment setups and procedures, as well as methods of data analysis. 

Experiments may be carried out at different scales as shown in Fig. 2-3. Currently no singlesource compendium of experimental methodologies exists to study flow and transport in soils,

and to characterize the ability of soils to transmit and retain chemicals. One exception may be a 

recent monograph by Dane and Topp (2002). Applying a model to infer soil properties from 

experimental results is still the standard method of data analysis. 

Generally, there are three sources of information about solute transport in soils: outflow 

breakthrough sampling, destructive soil sampling after transport has occurred, and monitoring of 

pore solution concentrations within the soil during the observed solute transport event. The 

applicability and relative reliability of those sources depends on the scale of the study. 

Outflow breakthrough sampling is probably the most reliable methodology since it 

effectively integrates solute transport for the given support area or volume. However, its 

applicability is limited when no or little breakthrough is present. Such situations are typical for 

strongly absorbed chemicals, colloids and microorganisms, and generally for all solutes if the 

soil is unsaturated and transport is slow. Even if considerable breakthrough occurs, the presence 

of several transport and retention processes may complicate the interpretation of results. This 

because multiple parameters describing those processes cannot be simultaneously inferred from a 

single breakthrough curve. 

Destructive post-experiment sampling is a useful complement to breakthrough data in that 

this may help to diminish or eliminate ambiguity in parameterization of the retention processes in 

soil column experiments. As the scale coarsens, the resource demand may become daunting and 

sample cross-contamination may become an issue, while field variability may increasingly 

compromise data reliability. A destructive sample may not contribute much to understanding the 

physical or chemical heterogeneity of a soil. 

Monitoring the pore solution composition is in principle the best approach for obtaining 

data. Unfortunately, monitoring devices tend to distort the concentration field within a soil. It is 

often not clear what part of the soil solution affects the sensor reading, or what part of the pore 

solution is extracted. As the observation scale coarsens, field variability introduces additional

uncertainty in the data. 

Although the ambiguity of data and/or their analysis undoubtedly creates difficulties in 

solute transport experiments at the field scale, the importance of the vadose zone in controlling 
18

chemical fate and transport in the subsurface requires the development and application of fieldscale predictive models. These field-scale models require field data for their calibration and 

testing. A list of structural heterogeneities that are important to consider within the context of

vadose zone modeling is given in Appendix A1. 2. Experimental setups in general should

addresses two types of heterogeneities: differences in water mobility in different parts of the soil 

pore space, and the effects of restricting layers and the capillary fringe on lateral transport. 

Two field experimental setups were implemented as part of this study. The first setup was 

meant to quantify solute dispersion in unsaturated soil and to evaluate the need for explicit 

simulation of prevailing soil physical heterogeneities. This setup exploited the ability of 

breakthrough concentrations to serve as integrators of transport at the support scale. A schematic 

of this first experiment is shown in Fig. 3-1. A tracer was applied to a relatively small area 

around a pumping well, with the irrigated area being substantially larger than the tracer 

application area. Ground water was pumped from the well, while the pumped water volume and 

the tracer concentration were continuously monitored. 

The second experimental setup was meant to evaluate the potential contribution of the 

variably-saturated zone and the capillary fringe to lateral chemical transport along a restrictive 

fine-textured layer. The lateral flow and transport processes were found to be relatively complex 

since the perched groundwater table fluctuated substantially in time. A schematic of this 

experiment is shown in Fig. 3-2. The tracer application area during the experiments was 

continuously irrigated, leading to a gradually expanding groundwater mound. The groundwater 

composition during the experiment was monitored using observation wells located within the 

projected plume. 

In both experiments the chemical application area had a radius of several meters to 

accommodate the scale of possible releases of contaminants from waste storage facilities. A 

conservative tracer was used. No soil solution sampling during the experiments was envisioned. 

The irrigation rate was selected such that the soils remained unsaturated. Soil moisture sensors 

had been installed to monitor the soil moisture content. Groundwater depths were measured, 

while surface runoff was monitored and, if found significant, intercepted and measured. All 

vegetation was eliminated from the chemical application area. A base model was developed for 

each experiment to accommodate the encountered complexities. Application of the model 

abstraction process will be illustrated for different key outputs. 
19

Figure 3-1. Schematic of the flux experiment. 

Irrigation 

area

Groundwater

pumped out Tracer 

application 

area

Groundwater

Unsaturated soil
20

Figure 3-2. Schematic of the lateral flow experiment. 

Tracer application area

Groundwater

Unsaturated soil

Observation well
21

3.2 THE OPE3 EXPERIMENTAL SITE AT THE BELTSVILLE AGRICULTURAL RESEARCH CENTER 

3.2.1 GENERAL DESCRIPTION

The study area was the 22-ha USDA-ARS “Optimizing Production Inputs for Economic and 

Environmental Enhancement,” or OPE3, experimental watershed in Beltsville, MD. An aerial 

view of the watershed is shown in Fig. 3-3. The watershed drains into a riparian wetland forest 

that contains a first-order stream (Gish et al., 2002, 2005; Chinkuyu et al., 2006). The vadose 

zone at the site was formed in fluvial deposits. Soils are mostly sandy loams and coarse sands on

a clay layer with surface slopes ranging from 1 to 4%. A description of the soil cover is given in 

Table 3-1. The watershed is in agricultural use and has been under corn since 1998. Tillage 

practices were the same each year, with fields typically being disked about one month prior to a 

second disking operation, followed by planting. 

OPE3 is a small watershed that is intensively instrumented, and where all data are

geolocated with a differential or kinematic global positioning system. Data collection included:

• Over 40 km of ground penetrating radar (GPR) data have been collected and analyzed. 

• Every two years, soil cores were extracted to determine the spatial correlations and 

distributions of organic matter, pH, and sand, silt, and clay percentages. 

• Electromagnetic induction (EM-31 and EM-38) data were collected for two of the 

watersheds. 

• 36,000 volumetric water content measurements at 48 locations were collected daily. 

• Micro-meteorological stations with eddy covariance systems monitored climatic 

conditions. 

• Multiple pesticide vapor flux towers were operational after pesticide application. 

• Water and chemical (N, P, and pesticides) runoff fluxes were collected from each 

watershed. 

• Watershed B (Fig. 3-3) was instrumented with 52 groundwater observation wells. 

• Corn grain yields were measured using a grain yield monitoring device. 

• Aircraft and satellite remote sensing imagery were collected. Ground- and tower-based 

reflectances were collected as needed. 

• Plant growth and development were measured periodically during the growing season. 

• 180 observation wells in the riparian wetland were monitored for anions and pesticides. 

• Stream flows and chemical fluxes in the stream were measured at five stations within the 

riparian wetland. 

• Wetland soil cores were extracted up to one-meter depth and analyzed for grain size, bulk 

density, carbon content, hydraulic conductivity, water content, and denitrification potential. 

• Dissolved gas was measured in groundwater samples throughout the wetland for evidence 

of denitrification and methanogenesis. 

• Dissolved oxygen, dinitrogen, nitrous oxide, and methane were measured. 

The experimental site of this particular work is located at the 3-ha field B of the OPE3 

experimental watershed. The field is currently instrumented with 64 soil moisture sensors 

(EnviroSCAN, SENTEK Pty Ltd., South Australia) distributed among 12 capacitance probes 

(Fig. 3-4) that measure soil water content at depths from 10 to 180 cm every 10 min year-round. 

Table 3-2 shows sensor depths and durations of the continuous observations. 
22

Figure 3-3. The USDA-ARS OPE3 research watershed; a – aerial view, b – instrumentation. A, B, C, 

D – research fields. 
23

Figure 3-4. Locations of groundwater wells and soil moisture sensors at the Field B shown at the 

false color aerial image. 
24

Table 3-1. Soil cover of the OPE3 crop production area. 

Soil 

associations 

and soil series

Coverage

%

Topsoil

texture

Description

DownerMuirkirkMatawan49 Sandy 

loam

 Downer Coarse-loamy, siliceous, semiactive, mesic Typic Hapludults

 Muirkirk Clayey, kaolinitic, mesic Arenic Paleudults

 Matawan Fine-loamy, siliceous, semiactive, mesic Aquic Hapludults

Bourne 23 Fine 

sandy 

loam

Fine-loamy, mixed, semiactive, thermic Typic Fragiudults

MatawanHammonton23 Loamy 

sand

 Hammonton Coarse-loamy, siliceous, semiactive, mesic Aquic Hapludults

DownerIngleside5 Loamy 

sand

 Ingleside Coarse-loamy, siliceous, semiactive, mesic Typic Hapludults
25

Field B was equipped with 52 groundwater monitoring wells, 41 of which are still active 

(Fig. 3-4). Some of the wells were instrumented with Divers (Van Essen Instruments, Giesbeek, 

The Netherlands) to measure groundwater levels every 30 min. 

Other monitoring equipment at Field B included an automated Sigma 980 runoff flow 

meter (Hach Company, Loveland, CO) that measured water flow every 10 min and periodically 

collected surface runoff samples so that water and chemical fluxes could be determined. The 

flume was installed at the field surface outlet (Fig. 3-4). The automated runoff sampler 

monitored fluxes on an event basis. An energy balance meteorological station with an eddy 

covariance tower was installed 20 m south of the boundary between Fields A and B (Fig. 3-3b). 

3.2.2 EXISTING OPE3 INFORMATION RELEVANT TO FLOW AND TRANSPORT IN SOILS

Results of surveys, monitoring, and hydrologic experiments at OPE3 were reviewed 

according to the outline in Appendix A to develop assumptions for constructing the base model. 

3.2.2.1 SMALL SCALE STRUCTURAL UNITS AND HETEROGENEITIES

The focus here was on heterogeneities that could be revealed at the core scale and could 

control the behavior of flow and transport at the field scale. The following information was used:

 Borehole data of soil texture and composition

 Soil water retention measurements on undisturbed samples,

 Field and laboratory soil hydraulic conductivity measurements. 

3.2.2.1.1 BASIC SOIL PROPERTIES

Data on soil texture, organic matter content, and pH had been collected during a soil survey 

performed by the USDA-NRCS in 1997 using samples representing distinct genetic horizons. 

Selected data are shown in Fig. 3-5. The organic matter content demonstrated a typical decrease 

with depth (Fig. 3-5a), indicating the absence of recent substantial changes in soil stratification 

caused by floods or erosion. The sand content exhibited large variations from horizon to horizon. 

Although the soils were characterized as having a coarse texture (Table 3-1), sand content varied

in the range between 50 and 90 % (Fig. 3-5b), with often drastic changes from one horizon to 

another in some profiles. Soil clay content near the soil surface tended to increase with depth, but 

more deeper decreased to a depth of about 90 cm as shown in Figs. 3-5c,d. Clay content varied 

substantially at depths below 90 cm. The relationship between soil clay and sand content was 

linear below 60 cm (Fig. 3-5e) which indicates a potential for having isolated lenses of

predominantly coarse and predominantly fine material. Soil pH tended to have higher values at 

places where the clay content was lower. Values of the pH smaller than 4. 5 were encountered at 

greater depths. This indicates a potential for aluminum mobility and soil mass cementation that 

would restrict the mobility of water and solutes in some parts of the soil profile. 

3.2.2.1.2 SOIL HYDRAULIC PROPERTY MEASUREMENTS

To evaluate possible effect of the macroporosity on the soil hydraulic properties, undisturbed 

samples having 20 cm2support area were taken for hydraulic conductivity measurements at the 

same support size in both the laboratory and the field. An example of water retention data from

three depths with increasing clay content is shown in Fig. 3-6. Samples taken close to soil 

surface showed well-defined macroporosity. A small decrease in the pressure head close to zero 

caused a substantial decrease in the water content of these samples. This decrease is a result of 
26

Figure 3-5. Basic soil properties at the OPE3 watershed. 
27

Figure 3-6. Soil water retention of samples at locations 1 and 2 near well w52 at field B; a) 2-5 

cm depth, b) 20-23 cm depth, and c) 47-50 cm depth (●,○ – location 1, , - location 2). 
28

macropores being emptied. The effect is almost absent at 50 cm depth where the clay content is 

larger than close to the surface, and where root activity is also lower. Macropores may be less 

developed or at this depth and hence are more difficult to detect here because of their infrequent 

appearance. 

Data for the saturated hydraulic conductivity corroborated the water retention data in terms 

of a decrease in macroporosity with an increase in clay content and a decrease in root activity. As 

shown in Fig. 3-7a, the maximum values of the hydraulic conductivity were similar at depths of 

25 and 40 or 45 cm. However, a substantial part of the soil, about 25% at location 1 and 50% at 

location 2, did not conduct water at a measurable rate at a depth of 40-45 cm where the effects of 

macroporosity on water retention were observed. 

Anisotropy in the saturated hydraulic conductivity is another consequence of changes in soil 

structure. Fig. 3-7b shows that the horizontal hydraulic conductivity was smaller than the vertical 

conductivity at a depth of 25 cm, whereas the reverse is true at a depth of 45 cm where all 

conductivity values were essentially zero of undisturbed samples taken to laboratory, with about 

half of the samples showing distinct non-zero horizontal conductivities. The data are in 

agreement with visual observations of seepage along the walls of a soil pit where the 

measurements were taken (Fig. 3-8). Seepage can be seen at a depth of 60 cm where the lateral 

conductivity was substantially higher than the vertical conductivity. 

3.2.2.2 FIELD SCALE HETEROGENEITIES

Considerable field-scale heterogeneity was evidenced by observed groundwater levels and 

chemical compositions, measured soil water contents, ground-penetration radar surveys, remote 

sensing imagery, and maps of measured corn yield. 

3.2.2.2.1 HYDROLOGICALLY ACTIVE ZONES AND SUBSURFACE FLOW PATHWAYS

Initially two sets of independent data were collected to determine optimal locations for 

subsequent soil core sampling. Photogrammetric and geophysical techniques were first used to 

provide a general characterization of the experimental watershed. Because surface slope and 

aspect influence both surface and subsurface hydrology, a 0. 25-m contour interval topographic 

map was derived from a stereo pair of aerial photographs and ground control points located with 

a submeter, a differential global positioning system (DGPS) receiver (Trimble 4000-SE, 

Sunnyvale, CA). 

Electromagnetic induction (EM-38) was used to estimate relative clay contents near the soil 

surface in order to estimate infiltration rates (Doolittle et al., 1994). The results showed EM-38 

values from 5 to 30. The EM data were divided into three equally sized populations, low (EM < 

12), intermediate (17 >EM > 12), and high (EM >17) values. 

The entire 7.5-ha site was next divided into different hydrologic groups based on surface 

topographic features and EM data. We assumed that areas with EM > 17 and a slope >2% would 

have a relatively low infiltration capacity, whereas areas with EM <12 and a slope < 1% would 

have relatively high infiltration capacities. All other areas were assumed to have medium 

infiltration capacities. Within each hydrological region of potential infiltration, 7 or 8 plots 

having dimensions of 25 x 25 m2each were randomly selected for higher resolution surveys (Fig. 

3-9). 

Ground-penetrating radar data were acquired for the entire 7. 5-ha field B along parallel 

north-south transects 25-m apart using a 150 MHz antenna. Within selected 25 by 25 m plots, 

additional GPR data were collected by towing the 150-MHz antenna along north-south transects 
29

Figure 3-7. Probability distributions of the saturated hydraulic conductivity for 20 cm2support 

areas; a – field falling head measurements; - location 1, depth 25 cm , - location 

1, depth 45 cm, - location 2, depth 25 cm, - location 2, depth 40 cm; b –

constant head measurements of vertical (●) and horizontal (○) conductivities of undisturbed 

samples with 20 cm2support area in the laboratory (error bars show standard deviations). 
30

Figure 3-8. Water seepage from the wall above restrictive soil layer. 
31

Figure 3-9. Layout of the 7. 5-ha watershed overlaid by a 25 by 25 m sample grid. Blocks with 

alphanumeric and infiltration capacity designations make up the stratified random sample of grid 

cells selected for soil moisture monitoring probes. The shaded rectangle in the southeast corner 

of the field site shows the 0. 5-ha subsection that was used for soil moisture measurements and

flow verifications (after Gish et al., 2002. Permission to use this copyrighted material is granted 

by Soil Science Society of America Journal). 
32

that were 2 m apart. GPR data were acquired in digital form so that a trace of the subsurface 

reflections could be produced using RADAN software (Geophysical Survey Systems, Salem, 

NH). The GPR data were distance-normalized and low-pass filtered prior to data interpretation. 

The GPR trace followed the shallowest contrasting dielectric discontinuity. Strong dielectric 

reflections were considered to be manifestations of water holding capacity differences due to 

textural discontinuities such as the presences of a clay lens below a sandy soil. Generally, the 

clay lens (high dielectric) occurred below the C horizon, which frequently contained much gravel 

(low dielectric). Depths to the strongest reflection were as shallow as 0.9 m and as deep as 3.4 m, 

but the majority of the data gave the strongest reflection at depths of 1.3 and 2 m. A GPR image 

profile is shown in Fig. 3-10. The first continuous restricting layer in this figure is situated 

immediately above the first continuous strong reflection, shown as a dotted line between depths 

of 1 and 2 m. The reflection of the restricting layer was not registered in about 5% of the total 

transect length. The topography of the first restricting layer was constructed using kriging 

assuming an omnidirectional variogram. We used the software packages GEO-EAS (EPA, Las 

Vegas, NV) and GS_ (Gamma Design Software, Plainwell, MI) for this purpose. An example of 

the obtained topography is given in Fig. 3-11. A first approximation of the subsurface flow 

pathways was constructed by subtracting the depth to the first continuous restricting layer from 

the surface elevation. The Arc/Info GIS hydrologic modeling tools FLOWDIRECTION and 

FLOWACCUMULATION were applied to a raster grid of the elevation-corrected subsurface 

topography to determine potential flow pathways (Fig. 3-12). The FLOWDIRECTION routine 

provided a grid of flow directions from one cell to its steepest downslope neighbor, while 

FLOWACCUMULATION determined the accumulated water from all cells that flowed into a 

particular downslope cell. 

The location of the restrictive layer was verified using multisensor capacitance probes 

installed at the blocks using a 2-m GPR survey, remote sensing imagery and a yield map (Gish et 

al., 2004, 2005). Sensors above the restrictive layer demonstrated the accumulation of water 

above the layer Gish et al., 2002). Patterns of high crop density during water limited growing 

seasons were observed with remote sensing imagery using the Airborne Imaging 

Spectroradiometer for Applications (AISA) for areas corresponding to the GPR-identified 

subsurface flow pathways that could accumulate limited subsurface water at the site (Gish et al., 

2004). During mildly dry years, corn yields decreased significantly (P<0.01) as the distance from 

the pathways decreased (Gish et al., 2004). 
33

Figure 3-10. Ground-penetrating radar image with a digital trace of the first restricting layer, 

indicated by the dotted line (after Gish et al., 2002. Permission to use this copyrighted material is 

granted by Soil Science Society of America Journal). 
34

Figure 3-11. Interpolated depth to the first continuous restricting layer for Block C03. (after Gish 

et al., 2002. Permission to use this copyrighted material is granted by Soil Science Society of 

America Journal). 
35

Figure 3-12. Potential subsurface flow pathways (blue lines) identified with Arc/Info hydrologic 

tools (after Gish et al., 2002. Permission to use this copyrighted material is granted by Soil 

Science Society of America Journal). 
36

3.2.2.2.2 SOIL COVER STRUCTURAL UNITS

The multi-sensor capacitance probe (MCP) network at the site revealed the existence of 

areas where the soil was either consistently wetter or consistently dryer than the average of the 

study area. The different areas defined large spatial structural units in the top part of the vadose 

zone constituting the soil cover of the site. There was a noticeable similarity in the soil water 

storage time series measured at different locations (Fig. 3-13). Time series from different 

locations appeared to be vertically shifted relative to each other. Such temporal stability of soil 

water storage can be used to select monitoring sites and estimate missing data as shown by 

Guber et al. (2007). 

The dense spatial coverage provided by remote sensing and yield mapping supported the 

existence of a spatial organization in soil cover at the site. Differences in soil water retention and 

hydraulic conductivity manifested themselves in either by spatially different biomass values or 

yield variability, or both. Areas that produced low corn yields in 2001 (e.g., BL4, BM2, BH3 and 

BM3 in Fig. 3-14) supposedly experienced either more intensive water logging or higher soil 

water losses to infiltration and/or evapotranspiration as compared to other locations. The spatial 

organization can be seen in Fig. 3-15, which shows an infrared image of corn biomass, 

superimposed on adjusted corn yields for 1999 (having a relatively dry growing season). Yields 

were greater than the mean inside the black polygons and less than the mean outside the black 

polygons. Therefore, areas with high biomass (inside the black polygons/red colors) will likely 

produce higher evapotranspiration rates than the low biomass areas. Multiyear mapping of the 

yields supported the existence of a spatial organization in soil cover, which manifested itself 

differently depending upon the weather conditions in a specific year (Fig. 3-16). 

We note that biophysics-based spatial units are in most cases relatively large. By 

comparison, contaminants are typically being released within a single unit. Still, it seems 

important to track such an organization since observations made for a different unit may give 

erroneous values of the infiltration and groundwater recharge rates, i.e., those variables that drive 

contaminant transport in the vadose zone. 
37

Figure 3-13. Changes in soil water storage of the 0-80 cm soil layer during the period of 

observations. 
38

Figure 3-14. Spatial distribution of 2001 corn yields in field B. The red to yellow colors 

represent low corn yield areas and the dark blue colors high corn yield areas. 
39

BH4

BM4

BM3

BH3

BL3

BH2

BL2

BL1

BM2

BM1

BH1

BL4

Figure 3-15. Corn yields and color infrared image of corn biomass taken in August 1999 (in a 

relatively dry growing season). Green stars designate moisture probe locations, while the red, 

pink and light blue lines designate subsurface flow pathway locations. The red color indicates 

regions with high biomass and the white regions low biomass, each reflecting extremes in the 

vegetative cycle of the corn plant. Corn grain yields greater than the mean are inside the black 

polygons, whereas areas outside the black polygons denote regions with yields below the mean. 
40

Figure 3-16. Spatial corn yield variation from 1998 to 2002. Note that 1998 and 1999 were 

relatively dry, 2000 was wetter than normal, 2001 was close to normal, and 2002 was dry. 
41

3.2.3 SURVEYING, MONITORING AND PRELIMINARY MODELING TO DESIGN SITE-SPECIFIC 

FLOW AND TRANSPORT EXPERIMENTS

The experiments as outlined in Section 3.1 envisaged tracer applications and monitoring in

areas of 10x10 to 20x20 m2. However, the OPE3 site had been surveyed in the past mostly at a 

much coarser scale. The flux measurement experiment used a location where more detailed 

surveys had been carried out in previous years. 

An additional set of measurements was made for selection and characterization of the lateral 

flow experiment. We decided to use for this experiment the intensively equipped South-Eastern 

part of Field B. Having a large number of groundwater wells (W18, 19, 20, 22, 23, 24, 25, 26, 

36, 37, and 38) in this area was a major argument for selecting this location. However, the area

had not been characterized at the fine scale during the ground penetration radar survey described 

in section 3.2.2.2.1. Therefore, an additional fine-scale ground penetration radar survey was 

conducted, thus allowing selection of the 30x30 m2site as described in the next section. 

3.2.3.1 FINE-SCALE GROUND PENETRATION RADAR SURVEY

A fine-scale GPR survey was conducted in April 2006 to obtain detailed information about 

the topography of the restrictive soil layer and the spatial structure of subsurface preferential 

pathways. An area of 16,617 m2in the South-Eastern part of the Field B (Fig. 3-17) was 

surveyed with a subsurface interface radar system-2 (Geophysical Survey System, Inc., North 

Salem, NH). Ground-penetrating radar data were acquired for the entire site along parallel eastwest transects 2-m apart. The GEO-EAS (EPA, Las Vegas, NV) and GS (Gamma Design 

Software, Plainwell, MI) geostatistical software packages were used to determine the spatial 

autocorrelation of the depth to the first continuous restricting layer. These two programs were 

used to produce omnidirectional semivariograms from point data derived from digitized traces 

(i.e., depth to the first continuous restricting layer and the associated geographic coordinates). 

Semivariogram models, which were fit using a least-squares approach, provided the necessary 

kriging parameters (i.e., nugget, range, and sill) for subsequent spatial interpolations. As a result, 

contour and three-dimensional surface maps of the depth to the first continuous restricting layer 

were produced. Results of the survey showed high spatial variability in the depth of the 

restrictive layer (Fig. 3-17). The depth varied within a range from 0.3 to 4.0 m, and did not 

correlate with the elevation of the soil surface. 

As before, the ArcGIS 9.3 hydrologic modeling tools FLOWDIRECTION and 

FLOWACCUMULATION were applied to a raster grid of the elevation-corrected subsurface 

topography to determine potential flow pathways. The fine resolution used in the new survey 

revealed smaller branches in the subsurface flow network, although the new subsurface flow 

pathways resembled in general the pathways identified in the 1999 survey. Four main subsurface 

pathways were detected, all with a flow direction from West to East (Fig. 3-17). This direction 

corresponded in general to the mean surface slope direction. 

3.2.3.2 LOCATION SELECTION AND SITE INSTRUMENTATION

The location for the experimental site was selected to meet the following specific conditions: 

(a) The experimental area must be large enough to show spatial variability in soil properties;

(b) The size of the irrigation plot should be reasonable for both a short-duration tracer 

application and a continuous uniform irrigation lasting several months;
42

(c) The number of observation wells, and their spacing, should be large enough to reduce the 

influence of neighboring wells, while still capturing subsurface preferential fluxes within 

reasonable time intervals;

(d) The site should exclude transit runoff and subsurface preferential pathways;

(e) The site should not interfere with other ongoing long-term studies. 

An experimental 10x10 m2site was selected in the intensively equipped South-Eastern part 

of Field B. Ground penetration radar data of this site indicated considerable variability in the 

depth to the restrictive soil layer (varying between 0.5 to 4.0 m), which was highest within the 

surveyed site (Fig. 3-17). Two large branches of preferential subsurface pathways as identified 

by GPR survey started in this area, which potentially could be used for the field tracer 

experiment. The beginning of the main preferential surface flow pathway was found along the 

Southern boundary of the site on May 11 2006 after intensive rainfall. This suggests that

preferential runoff would not affect the tracer study at the selected plot. Analysis of multi-sensor 

capacitance probe (MCP) monitoring data at locations BM2, BM3, BM4, BL3 and BH3 showed 

high spatial variability in water content at different depths. The site was located 30 m from a 

nearby road, which did not interfere with the long-term ongoing studies at Field B. 

Four plots (l-1, l-2, l-3 and l-4), each of 1 m2and 10 m apart, were instrumented in the 

spring of 2006 to monitor soil water contents, pressure heads, and groundwater depths (Fig. 3-

18). MCPs (EnviroSCAN, SENTEK Pty Ltd., South Australia) and soil tensiometers were 

installed at depths from 0.1 to 1.0 m at 0.1 m increments to monitor soil water content and 

pressure heads, respectively (Fig. 3-19). The MCP and tensiometers were connected to a CR10X datalogger (Campbell Scientific, Inc., Logan, Utah) to collect data every 15 minutes. Two 

AM416 Relay Multiplexers (Campbell Scientific, Inc., Logan, Utah) controlled datalogger 

communication with 40 pressure transducers (PX26-005GV, Omega, Stanford, CT) installed in 

tensiometers. Collected data were acquired from the Redwing 100 Airlink modem (Campbell 

Scientific, Inc., Logan, Utah) once a week (Fig. 3-19). Five additional locations 7 m 

downgradient from the site, as well as three locations 14 m downgradient, were equipped with 

observation wells and MCPs for monitoring water contents and groundwater depths (Fig. 3-20). 

Groundwater depths were measured at each location using Cera-Diver (Van Essen Instruments, 

Delft, The Netherlands) sensors installed in wells at a depth of 2.0 m. Barometric pressures were

recorded using a Baro-Diver sensor (Van Essen Instruments, Delft, the Netherlands). Volumetric 

water contents were measured periodically at locations l-1 to l-4 to correct MCP factory 

calibration (see Appendix B). 

A drainage line was constructed at distance of 1-m to the South and 1 m to the East of the 

plot boundary to collect runoff water. A 1⁄2‟ H-type flume was installed at the outlet of the 

drainage line and equipped with a 75 kHz Ultrasonic sensor connected to a Sigma 980 Flow 

meter (Hach Company, Loveland, CO) for continuous water level measurements. 
43

Figure 3-17. Depth to the restrictive layer, subsurface flow pathways (brown polylines), 

locations of existing multi-sensor capacitance probes ( ), groundwater observation wells ( ), 

and runoff flume ( ) in the vicinity of the lateral flow experimental site at Field B. 
44

Figure 3-18 Lateral flow experimental setup. 

MCP

Groundwater 

well

Soil tensiometers

Soil tensiometers

Runoff flume 

tensiometers

Sprinklers 

flume 

tensiomete

rs MCP

Runoff collector

Runoff collector

Multiplexer

Sprinclers 

flume 

tensiometers
45

Figure 3-19. Schematic of the data acquisition and collection system. 

Modem

Tensiometers

MCP

Tensiometers

MCP

MCP

Tensiometers

MCP

Tensiometers

Datalogger

Multiplexer

Multiplexer

Location 1 Location 3

Location 2 Location 4

Modem

Tensiometers

MCP

Tensiometers

MCP

MCP

Tensiometers

MCP

Tensiometers

Tensiometers

MCP

Tensiometers

MCP

MCP

Tensiometers

MCP

Tensiometers

Datalogger

Multiplexer

Multiplexer

Location 1 Location 3

Location 2 Location 4
46

Figure 3-20. Locations of multi-sensor capacitance probes and groundwater wells at the 

experimental plot Depth to the RL (m)

Irrigated 

area

10 m 7 m 7m 10 m 6 m 6 m 6 m 6 m 11 m 12 m

Loc-2

Loc-1

Loc-4

Loc-3

Loc-5

Loc-6

Loc-7

Loc-8

Loc-10

Loc-11

Loc-12

Loc-9 Depth to the RL (m)

Irrigated 

area

10 m 7 m 7m 10 m 6 m 6 m 6 m 6 m 11 m 12 m Depth to the RL (m)

Irrigated 

area

10 m 7 m 7m 10 m 6 m 6 m 6 m 6 m 11 m 12 m

Loc-2

Loc-1

Loc-4

Loc-3

Loc-5

Loc-6

Loc-7

Loc-8

Loc-10

Loc-11

Loc-12

Loc-9
47

3.2.3.3 BASIC SOIL PROPERTIES AT THE LATERAL FLOW EXPERIMENTAL SITE

Soil samples were taken from the soil surface to a depth of 2.0 m at each location during 

MCP and groundwater well installation. Soil texture was measured with the pipette method (Gee 

and Or, 2002) after dispersion with sodium pyrophosphate Na4P2O7. Values of soil pH were 

measured at a solid to liquid ratio of 1:1 (Page et al., 1982). Organic carbon content was 

measured in the upper 0.6-m soil layer using the dry combustion method (Page et al., 1982). 

Spatial variability in soil texture was found to be surprisingly high for the relatively small 

site. Soil texture was represented by six textural classes within the range from sandy loam to silty 

clay loam (Fig. 3-21). The particle size distribution generally did not change noticeably in the 

upper 1.3 m of the soil profile, where sand dominated over clay and silt. A distinct decrease in 

sand content and an increase in silt content can be seen below 1.3-m depth (Fig. 3-22), thus

indicating a gradual transition in soil texture from sandy loam to loam and then silty clay loam. 

The horizontal variability in soil texture was of the same order of magnitude as the vertical 

variability. Coefficients of variation for sand and silt content increased with depth and were in 

the range from 0.06 to 0.92 and from 0.15 to 0.48, respectively. One could expect much

variability in the soil water content at the studied site, since spatial variability in soil texture 

affects substantially the soil hydraulic properties. 

The organic carbon content of the upper 0.6 m of the soil profile did not vary much at each 

depth; values decreased gradually from 0.4-1.2 % at 0.1 m, to 0.03-0.13% at 0.6 m depth. The 

soil pH was highest in the upper 0.2-m soil layer; average pH values gradually decreased with 

the depth from 5.9 near the soil surface to 4.5 at 2.0-m depth. Coefficients of variation for pH 

were within the range from 0.04 to 0.10, indicating less horizontal variability in pH as compared 

to variability in the soil particle size distribution. 

The soil bulk density was measured on undisturbed samples taken from the upper 1.0-m soil 

layer at 0.1-m increments during MCP calibration at location 1-4. The bulk density generally 

increased with depth from 1.3-1.6 to 1.6-1.9 g cm-3 in the upper 0.3 m of the soil profile, but did 

not change noticeably with depth in deeper layers (Fig. 3-23). Coefficients of variation for the 

bulk density were in the range of 0.05 to 0.09 at different depths, and did not correlate with

average soil bulk density values and/or sampling depths. 

Soil hydraulic properties were measured on undisturbed soil samples (5 cm ID, 5.1 cm 

height) taken from depths of 0 to 1.0 m in 0.1 m increments at locations 1, 2, 3, and 4. Soil 

samples were gradually saturated from the bottom. A constant head soil core method (Reynolds

and Elrick, 2002) with a water head of 0.5 m was used to measure the saturated hydraulic 

conductivity of the soil samples. The samples subsequently were placed into 1400 Tempe 

pressure cells (Soil Moisture Equipment Corp., Santa Barbara, CA) to measure soil water 

retention as described by Dane and Hopmans (2002). Results of the soil hydraulic properties 

measurements are presented in Figs. 3-24 and 3-25. 

Measured saturated hydraulic conductivities (Ksat) varied greatly vertically and laterally; 

they were mostly in the range from 0.003 to 27.1 cm d-1. Generally smaller values were obtained 

at locations 1 and 3 compared to locations 2 and 4 (Fig. 3-24). Soil samples taken from depths of 

0.2-0.4 m at location 1 and from depths of 0.12-0.40 m and below 0.8-m at location 3 did not 

conduct water at 0.5 m pressure head. Low Ksat values measured on 5-cm diameter samples 

presumably characterized the hydraulic conductivity of the soil matrix, while higher values could 

be measured on large undisturbed soil samples. 
48

Figure 3-21. Soil texture measured at 10 depths in 12 locations. 

Depth:

Silt %

0

10

20

30

40

50

60

70

80

90

100

Clay %

0

10

20

30

40

50

60

70

80

90

100

Sand %

100 90 80 70 60 50 40 30 20 10 0

10 cm

30 cm

50 cm

70 cm

90 cm

110 cm

130 cm

150 cm

170 cm

190 cm

C

sC siC

scL

cL

S

lS sL

L siL

sicL

Si
49

Figure 3-22. Measured clay, silt, sand and organic carbon distributions in the soil profiles. 

Clay (%)

0 20 40 60 80 100

Depth (cm)

0

50

100

150

200

Sand (%)

0 20 40 60 80 100

Depth (cm)

0

50

100

150

200

Silt (%)

0 20 40 60 80 100

Quantile

OC (%)

0.0 0.2 0.4 0.6 0.8 1.0

25%

50%

75%
50

Figure 3-23. Measured soil bulk density distributions versus depth at locations 1 through 4. 

Location-1

Depth (cm)

0

20

40

60

80

100

120

Location-2

Location-3

Soil bulk density (g cm-3)

1.2 1.4 1.6 1.8 2.0 2.2

Depth (cm)

0

20

40

60

80

100

120

Location-4

1.4 1.6 1.8 2.0 2.2
51

Figure 3-24. Laboratory measured saturated hydraulic conductivities, Ksat. 

Ksat (cm d-1)

0.001 0.01 0.1 1 10 100

Depth (cm)

0

20

40

60

80

100

Loc-1

Loc-2

Loc-3

Loc-4
52

Soil water retention was found to vary with depths. Generally, the saturated water content 

decreased and the slope of the water retention curve increased with depth. We did not observe 

high lateral variability in soil water retention, except for the 30-40 cm soil layer (Fig. 3-25), 

where the variability could be attributed to high variability in the bulk density (Fig. 3-23). 

Summarizing the basic soil properties, one could expect considerable variability in the spatial 

and temporal patterns of the soil water content during the experiments, primarily because of high 

spatial variability in the saturated hydraulic conductivity. 

3.2.3.4 SOIL ELECTRICAL RESISTIVITY SURVEY

Soil electrical resistivity measurements have recently gained popularity as an expedient 

method for studying the spatial and temporal variability of many soil physical properties (i.e.,

soil structure, water content, or fluid composition). Because the method is non-destructive and 

very sensitive, it offers a very attractive tool for describing the subsurface properties without 

excavating. Soil electrical resistivity measurements have already been used in many applications,

such as: groundwater exploration, landfill and solute transfer delineations, agronomic 

management by identifying areas of excessive compaction, soil horizonization or depths to

bedrock, and assessing the soil hydraulic properties (Samouëlian et al., 2005). In this study we

used resistivity measurements as a monitoring tool to evaluate the degree of soil heterogeneity 

based on soil water content distributions. 

Water content distributions in the vadose zone were studied after the tracer experiment. The

apparent soil electrical resistivity of 2-m soil layers was measured 7 times when the soil water 

contents differed substantially. Soil temperature was measured at locations 6 and 8 at depths 

from 0.1 to 1.0 m using 0.1 m increments. 

A preliminary study was conducted to obtain a relationship between the volumetric water 

content (θ) and the soil electrical resistivity (ER). Disturbed soil samples for this purpose were 

taken immediately after the lateral tracer experiment at 12 locations in close proximity

(approximately 0.5 m) to the MCPs at depths of 0-2.0 m in 0.2 m increments, and used for the 

soil water content and ER measurements. The electrical resistivity was measured at the field 

water content using LandMapper ERM-2 (Landviser, LLC, League City, TX) in 4-electrode cells 

(9.6 cm length, 2.7 cm width, 2.3 cm height) especially designed for this experiment (Fig. 3-26) 

at a temperature of 22 ̊C. Results were plotted as pairs (θ, ER) measured for samples from 

different depths (Fig. 3-27). Generally ER decreased and approached a minimum faster with an 

increase in water content at depths of 10 and 30 cm, than at deeper soil layers. 

A regression tree algorithm (Venables and Ripley, 1996; S-PLUS 2000 Software) was used 

to identify soil parameters affecting the ER-water content relationships. To reduce the effect of 

soil structure on splitting variables, the dataset was subdivided into two datasets referred as 

topsoil (0-40 cm where soil structure could be affected by the root activity from previous years 

and by relatively high organic matter contents) and subsoil (40-200 cm) layers. The regression 

tree technique was applied to the two datasets separately. Soil bulk density (BD), and silt and 

clay content were found to be influential parameters for the topsoil, whereas BD and sand 

content were the influential parameters for the subsoil layer. A power function was fitted to the 

measured pairs (θ, ER) separately for each layer as follows:

ER = aθ-b(3-1)

where a and b are empirical parameters defined in terms of linear regressions of soil bulk density 

and/or the percentage of the soil textural fraction affecting the ER- θ relationship 
53

Figure 3-25. Laboratory-measured soil water retention curves. 

80-90 cm

Water content (cm3 cm-3)

0.10 0.15 0.20 0.25 0.30 0.35 0.40

-0

-200

-400

-600

-800

-1000 90-100 cm

0.10 0.15 0.20 0.25 0.30 0.35 0.40 0.45

60-70 cm

-0

-200

-400

-600

-800

-1000 70-80 cm

40-50 cm

Pressure head (cm)

-0

-200

-400

-600

-800

-1000 50-60 cm

20-30 cm

-0

-200

-400

-600

-800

-1000 30-40 cm

0-10 cm

-0

-200

-400

-600

-800

-1000 10-20 cm

Loc-1

Loc-2

Loc-3

Loc-4
54

Figure 3-26. Laboratory (left) and field (right) setups to measure soil electrical resistivity. 
55

Volumetric water content (cm3 cm-3)

0.05 0.10 0.15 0.20 0.25 0.30 0.35 0.40 0.45

ER (ohm m)

0

200

400

600

800

1000

1200

1400

1600

10 cm

30 cm

50 cm

70 cm

90 cm

110 cm

130 cm

150 cm

170 cm

190 cm

Figure 3-27. Relationship between volumetric soil water content and electrical resistivity 

measured on samples taken from 10 depths at 12 locations. 
56

The fitted parameters were:

 topsoil (0 – 40 cm) subsoil (40 – 200 cm)

a = 977.0 -25.1·Clay – 237.6·BD a = 32.2 + 0.176·Sand (3-2)

b = 0.316 + 12.5·Clay – 3.97·Silt b = 2.58 – 0.920·BD

Fig. 3-28 shows significant improvement in predictions of ER from the water content data 

when the empirical parameters a and b were calculated in this way from soil bulk density and 

soil texture. 

To perform the field survey, 50 electrodes were manufactured from stainless steel. 

Electrodes were installed on the soil surface at 0.5-m increments along a transect connecting 

wells 5, 6, 7, and 8 (Fig. 3-20). Soil temperature profile distributions were measured at locations

6 and 8 synchronously with the ER survey using Campbell 107 Soil Temperature Probes 

(Campbell Scientific, Inc., Logan, Utah). Apparent ER values were calculated from ER values

measured with a Wenner-Schlumberger array (Samouëlian et al., 2005), and processed using the 

RES2DINV software (GEOTOMO SOFTWARE SDN. BHD., Penang, Malaysia). 

Soil temperature generally decreased over time at all depths, was relatively constant versus

depths in October 2008, and increased with depth in November 2008 and March 2009 (Fig. 3-

29). Soil temperature data were used to correct field ER values to the same standard reference 

temperature. We used for this an equation derived recently by Besson et al. (2008) for 

unsaturated soils:

0.3

ref

ref T

T

ER ER





















(3-3)

where ER is the field-measured electrical resistivity at temperature T, and ERref is the electrical 

resistivity measured in the laboratory at temperature Tref =22 ̊C. 

The 2-D electrical resistivity survey was conducted twice a month during September –

November 2008, as well as on March 7, 2009. Results at different times are shown in Fig. 3-30. 

The high spatial variability in ER observed at all times indicates considerable soil heterogeneity 

across the 24-m transect. Relatively high ER values were observed at depths from 0.3 to 1.0 m 

along the first 16 m of the transect in September – October, 2008. Both high and low ER values 

were observed above and below these depths. The data do not suggest the existence of strict 

vertical soil stratification at the study site. Although the observed resistivities showed substantial 

temporal fluctuations, some similarities in the ER distributions can be seen in the 2-D images of

October 17, 31 and November 7, as well as of September 17 and November 21. 

Once corrected for temperature, the ER values were converted into volumetric water 

content using equation (3-1). The parameters a and b were calculated separately for the topsoil 

and subsoil (eq. (3-2)) using data from locations 5-8, and with soil texture and bulk density

averaged for each depth. Equation (3-1) was subsequently applied with constrains on the water 

content range θmin ≤ θ ≤ θmax, where θmin and θmax are the minimum and maximum water content 

observed at locations 5, 6, 7, and 8 during the monitoring period. 

The 2-D water content images revealed high spatial variability in the soil water content 

(Fig. 3-31), including distinct vertical fingers representing relatively dry soil zones. While not

spatially and temporally persistent, these fingers often joined a laterally extended relatively dry 

layer at depths between 0.3 and 1.0 m. The formation of fingers and associated dry and wet 

regions implies the presence of hydraulically inactive and active zones at those locations. 
57

Figure 3-28. Performance of the model (Eq. 3-2) to simulate the dependence of the soil electric 

resistivity on soil water content. (a) model parameters do not depend on soil properties, (b) 

model parameters depend on soil properties. 

Depth:

log(ER) measured

1.8 2.0 2.2 2.4 2.6 2.8 3.0 3.2

0-0.40 m R2=0.87

0.4-2.0 m R2=0.88

Depth:

log(ER) measured

1.8 2.0 2.2 2.4 2.6 2.8 3.0 log(ER) calculated

1.8

2.0

2.2

2.4

2.6

2.8

3.0

3.2

0-2.0 m R2=0.59

(a) (b)
58

Figure 3-29. Soil profile temperature distributions measured at 7 dates at the ER measurement 

time. Shown are average temperatures from locations 6 and 8. 

Date

Soil temperature oC

2 4 6 8 10 12 14 16 18 20 22 24

Depth (cm)

0

20

40

60

80

100

120

9/17/08

10/3/08

10/17/08

10/31/08

11/7/08

11/21/08

3/7/09
59

Figure 3-30. Electrical resistivity measured in a 2-m deep soil profile along a 24-m transect. 

Locations of groundwater wells and MCOs (multiple capacitance probes) are shown by arrows. 

3/07/09

10/31/08

9/17/08

10/03/08

10/17/08

11/07/08

11/21/08

Location 5 Location 6 Location 7 Location 8

- groundwater well - MCP

3/07/09

10/31/08

9/17/08

10/03/08

10/17/08

11/07/08

11/21/08

Location 5 Location 6 Location 7 Location 8

- groundwater well - MCP
60

Figure 3-31. Volumetric water content distributions in a 2-m soil profile along the 24-m transect 

at 7 dates. 

2 4 6 8 10 12 14 16 18 20 22

2

1.5

1

0.5

2

1.5

1

0.5

2

1.5

1

0.5

2

1.5

1

0.5

2

1.5

1

0.5

2

1.5

1

0.5

2

1.5

1

0.5

0 0.04 0.08 0.12 0.16 0.2 0.24 0.28 0.32 0.36 0.4

Distance (m) Volumetric water content 

Depth (m)

9/17/08

10/03/08

10/17/08

10/31/08

11/07/08

11/21/08

3/07/09

Location 5 Location 6 Location 7 Location 8

- groundwater well

- MCP

2 4 6 8 10 12 14 16 18 20 22

2

1.5

1

0.5

2

1.5

1

0.5

2

1.5

1

0.5

2

1.5

1

0.5

2

1.5

1

0.5

2

1.5

1

0.5

2

1.5

1

0.5

0 0.04 0.08 0.12 0.16 0.2 0.24 0.28 0.32 0.36 0.4

Distance (m) Volumetric water content 

Depth (m)

9/17/08

10/03/08

10/17/08

10/31/08

11/07/08

11/21/08

3/07/09

Location 5 Location 6 Location 7 Location 8

- groundwater well

- MCP
61

3.2.3.5 SOIL MOISTURE AND GROUNDWATER MONITORING

Soil moisture was monitored at the experimental site from July 1, 2006 through November 

1, 2007. A weather station located about 80 m from the site collected meteorological data at short 

time intervals (10 minutes). These data included: soil temperature, soil heat flux, air temperature,

relative humidity, 3-D wind speed profile, rainfall, long and short wave solar radiation, net solar 

radiation, saturation and actual vapor pressure, evapotranspiration, and CO2 fluxes. Daily 

evapotranspiration (ET) rates were computed using the Penman-Monteith method as documented 

by FAO (Allen et al., 1998). The daily ET and rainfall rates were integrated over time to obtain 

cumulative ET and precipitation values as a function of time from the beginning of the 

observation period. 

Monthly and cumulative ET and rainfall rates are shown in Fig. 3-32. Daily rainfall and ET 

values were in the range from 0 to 6.7 cm and from 5·10-3 to 0.4 cm respectively. The total 

amount of precipitation was two times larger than the total ET during the observation period. The 

rainfall and ET distributions were not uniform over the year. Relatively high rates of 

precipitation were observed in the months of April, September, October and November, and low 

rates in June and July. Contrary to precipitation, ET values were higher in the summer and lower

in the winter. 

Tensiometer and MCP readings were converted to volumetric water contents and pressure 

heads. The MCP factory calibrations were corrected separately for topsoil and subsoil to improve 

the accuracy of the water content measurements (see Appendix B). Tensiometer reading 

exhibited noise, which was removed using a multilevel 1-D wavelet decomposition with a 

Daubechies filter (db4). We used the Wavelet toolbox of the MATLAB 6.5 Software for this. 

Depending upon data quality, the multilevel parameter in the wavelet decomposition was fixed at 

values between 4 and 6. 

The non-uniform distribution of precipitation and ET affected the dynamics of the water 

content and the pressure head in the vadose zone during the experiments. Periods of deep soil 

drying followed rainfall events when water content almost approached saturation. Extremely low 

water contents were observed in September 2006, and August and October 2007 at practically all 

depths (Fig. 3-33). The low water contents corresponded to pressure heads close to or below the 

ceramic's air entry value. For this reason, tensiometers installed at depths less than 0.8 m did not 

work properly in August and September 2007. 

Temporal changes in the soil water content varied with depth. Water contents in the topsoil 

(0-0.4 m) generally increased rapidly during and after the rainfall events, while relatively small 

changes occurred in the subsoil (0.4-1.0 m). Water contents in deeper soil layers were less 

sensitive to precipitation and evapotranspiration as compared to the upper layers. This was also 

true for the pressure head. There always was a delay in response of the deeper soil layers to 

change sin the flux at the soil surface. 

Water contents at similar depths varied considerably among the four locations. The

differences were most pronounced at depths between 20 and 50 cm, where water contents were 

consistently higher at locations 2 and 4 as compared to locations 1 and 3. Consistently low water 

contents were observed at a depth of 70 cm at location 2 during the whole monitoring period. 

Spatial differences in soil water content dynamics were reflected by different field soil 

water retention curves, obtained by plotting field-measured pressure heads versus water contents

for 6 depths at 4 locations (Fig. 3-34). We present here only data measured during continuous 

soil drying (drainage water retention curves). The data in Fig. 3-34 in general resembled the 

laboratory-measured water retention curves (Fig. 3-25). Similarly as the laboratory data,
62

Figure 3-32. Monthly (a) and cumulative values (b) of evapotranspiration and precipitation 

measured at the experimental site during the monitoring period (during July 2006 – September 

2007). 

(b)

2006 2007

7/1 9/1 11/1 1/1 3/1 5/1 7/1 9/1 11/1

Cumulative flux (cm)

0

20

40

60

80

100

120

Evapotranspiration

Precipitation

(a)

Monthly amount (cm)

0

4

8

12

16

20
63

Location 1 Location 2

Figure 3-33. Time series of the measured soil water content and pressure heads during July 2006 – September 2007.

Pressure head (cm)

-0

-200

-400

-600

-800

-1000 Water content (cm

3 cm-3

)

0.1

0.2

0.3

0.4

2006 2007

7/1 9/1 11/1 1/1 3/1 5/1 7/1 9/1 11/1

Precipitation (mm)

0

20

40

60

80

100

Depth:

-0

-200

-400

-600

-800

-1000

7.5 cm

22.5 cm

37.5 cm

52.5 cm

67.5 cm

82.5 cm

97.5 cm

Depth:

0.1

0.2

0.3

0.4

10 cm 

20 cm

30 cm

40 cm 

50 cm

60 cm

70 cm

80 cm

90 cm 

2006 2007

7/1 9/1 11/1 1/1 3/1 5/1 7/1 9/1 11/1

0

20

40

60

80

100

63
64

Location 3 Location 4

Figure 3-33 continued. Time series of the measured soil water content and pressure heads during July 2006 – September 2007.

Pressure head (cm)

-0

-200

-400

-600

-800

-1000 Water content (cm

3 cm-3

)

0.1

0.2

0.3

0.4

2006 2007

7/1 9/1 11/1 1/1 3/1 5/1 7/1 9/1 11/1

Precipitation (mm)

0

20

40

60

80

100

Depth:

-0

-200

-400

-600

-800

-1000

7.5 cm

22.5 cm

37.5 cm

52.5 cm

67.5 cm

82.5 cm

97.5 cm

Depth:

0.1

0.2

0.3

0.4

10 cm 

20 cm

30 cm

40 cm 

50 cm

60 cm

70 cm

80 cm

90 cm 

2006 2007

7/1 9/1 11/1 1/1 3/1 5/1 7/1 9/1 11/1

0

20

40

60

80

100

64
65

Figure 3-34. Plots of measured soil water pressure heads versus volumetric water contents at 

locations 1-4. 

Depth 0-15 cm

-200

-400

-600

-800

-1000

Depth 15-30 cm

Depth 30-45 cm

Pressure head (cm)

-200

-400

-600

-800

-1000

Depth 45-60 cm

Depth 60-75 cm

Water content (cm3 cm-3)

0.1 0.2 0.3 0.4

-0

-200

-400

-600

-800

-1000

Depth 90-105 cm

0.1 0.2 0.3 0.4

Loc-1

Loc-2

Loc-3

Loc-4
66

Figure 3-35. Groundwater depths measured at the experimental site during the experiments (November 2007 through March 2008).

Location: Depth to the groundwater (cm)

0

50

100

150

200

1

2

3

4

0

50

100

150

200

5

6

7

8

9

10

11

12

2008 Daily precipitation (mm)

4/1 5/1 6/1 7/1 8/1 

0

2

4

6

8

(a)

(b) 66
67

saturated water contents gradually decreased with depth, whereas the slope of the water retention 

curve increased with depth. The slopes of the laboratory-measured retention curves were steeper 

compared to the field-measured data, resulting in lower water contents at the same pressure 

heads for the field measurements. The field-measured water retention curves at similar depths 

differed among the 4 locations. The maximum differences occurred at depths between 60 and 75 

cm between locations 2 and 3 and locations 1 and 4, with the water retention curves for locations 

2 and 3 shifted to lower water contents (Fig. 3-34). 

Groundwater depths (GWDs) were monitored at 12 locations starting November 1st, 2007. 

GWD values varied between 0.0 and 200 cm during the monitoring period (Fig. 3-35). The 

values were consistently smaller at locations 1, 3, 6, 9 and 11, and greater at locations 7, 8, 10 

and 12, particularly during continuous drying periods. Maximum seasonal variability in the 

GWD was observed at location 5, 8 and 12, while variability was minimal at locations 1 and 3. 

The GWD decreased rapidly after intensive rainfalls at all locations. Changes in the GWD were 

more pronounced at locations 7, 8, 10 and 12 compared to other locations during drying periods. 

3.2.3.6 DILUTION TEST

A relatively simple, routinely implemented single-well tracer test is the “point-dilution” 

test. This test was designed to estimate the hydraulic conductivity of aquifer material. In this 

study we used the point-dilution test to evaluate the spatial variability of the hydraulic 

conductivity across the assumed tracer plume path. The test assumes that a tracer is introduced 

into a well and its concentration measured with time. The differential equation describing the 

dilution rate of the solute, ∂cw/∂t, within the water-filled well volume, V, can be written as 

follows:

  w b

w

q c c

t

c

A

V

  





(3-4)

where cw and cb are the concentration in the well and the background concentration in 

groundwater, respectively [ML-3]; q represents the groundwater flux [LT-1] through some vertical 

cross-sectional area, A [L2], in the center of the saturated well segment; and V is the volume of 

water in the well [L3]. 

A general definition for q describing the different factors causing dilution of a solute is 

given by (e.g., Halevy et al., 1967): 

q = qf + qh + qs + qm + qd (3-5)

where qf is the velocity of undisturbed ground water flow (i.e., the undisturbed Darcy flux), qh is 

the apparent flow contribution caused by density convection, qs is the apparent flow rate caused 

by vertical currents in the well screen, qm is the apparent flow rate caused by the mixing device 

and qd is the apparent flow contribution caused by molecular diffusion of the solute. The factor 

is defined by Halevy et al. (1967) as a “borehole effect” to account for the distortion of flow 

lines due to the presence of the well. A detailed definition of this factor is given in a study of 

Drost et al. (1968), among others. Another effect that can cause a disturbance of the flow regime 

may occur as a consequence of a skin created around a well. The influence of this effect on 

point-dilution tests was examined by Bidaux and Tsang (1991). Halevy et al. (1967) suggested

that when the advective flux is relatively high compared to the diffusive flux (i.e., when qf>>qd ), 
68

the diffusion effect may be negligible. The lower limit of the measurable velocity, as suggested 

by Halevy et al. (1967), is in the order of diffusion (about 1 cm/day). 

It is frequently assumed that the dilution rate of a solute within the injection well is simply a 

consequence of ground water flow only (i.e., q=qf). Such an assumption is in many cases 

justified. Using this assumption, equation (3-4) for steady-state flow conditions (such that V, A

and q are constant in time) may be integrated to produce a dilution curve that follows an 

exponential trend as follows (Freeze and Cherry, 1979):

  e

f

q At

V

w b 0 b c c c c



  

(3-6)

where c0 is the initial concentration in the well [ML-3]. Solving for the qf leads to 

ln w b

f

0 b

V c c

q

At c c

  

      

(3-7)

which shows that the Darcy flux (qf) can be obtained immediately from the slope of a linear 

curve of the logarithm of the concentration versus time

Prior to the tracer experiment we carried out dilution tests for wells L10, L11 and L12. For 

the data analysis we used equation (3-7) and the following measured parameters: well diameters 

(dw) of 0.05 m; vertical cross-sectional areas (A) of 570, 885 and 465 cm2for wells L10, L11 and 

L12, respectively; water volumes (V) of 2826, 3474 and 1825 cm3 for the three wells,

concentrations cb=270 Sm/cm and c0=1750 Sm/cm, and an average gradient of the water table 

in the area of 0.045. Using these data we obtained saturated hydraulic conductivities (Ksat) of 

0.05, 1.34 and 2.46 m/day for the three locations (L10, L11 and L12, respectively). These 

numbers reflect the relatively high degree of heterogeneity of the site. They also indicate a need 

for substantial calibration of the flow model. 

3.2.3.7 PRELIMINARY COUPLED SURFACE-SUBSURFACE FLOW MODELING

The purpose of our preliminary coupled surface-subsurface flow modeling was to estimate 

possible losses of water and solute to runoff. Although soils at the site are predominantly sandy, 

runoff had been observed in the spring and early summer. A stable runoff pathway (Fig. 3-17) 

was observed for three consecutive years. This indicates that the experimental site needed

drainage to intercept runoff and that we needed to account for this runoff in the modeling efforts. 

No software to simulate coupled surface-subsurface flow and transport was readily 

available when we carried out this study. We therefore developed our own modeling tool by 

merging the publicly available codes FEMWATER and 2DSOIL. The approach is detailed in 

APPENDIX C. Preprocessing and postprocessing were done in the GMS 6.0 environment. 

A topography map used for the simulations is shown in Fig. 3-36. The irrigated rectangular 

area was located in the center of the simulated area. Rainfall was applied to this area at the rate 

of 0.5 m d-1for 0.04 d. The tracer concentration was set to one for 0.04 d, and to zero afterwards. 

An initial hydrostatic distribution was assumed for the soil water content. Soil layering and soil 

values for the hydraulic properties were selected in accordance with the measured basic soil data 

(Table 3-2). Two subsurface material distributions shown in Fig. 3-37 were used in the

simulations. One distribution assumed the presence of a restricting layer parallel to the soil 

surface, while the second distribution assumed that the restricting layer had the microtopography 

obtained from the ground penetration radar survey. Two initial groundwater depths (0.7 and 1.5 
69

Figure 3-36. Soil surface topography and assumed finite element mesh at the surface for the

coupled surface-subsurface flow and transport simulations. The blue rectangle shows the 

boundaries of the 10x10 m irrigated area. 
70

Figure 3-37. Subsurface representation and the finite element mesh in the coupled surfacesubsurface flow and transport model; a –restricting layer parallel to the soil surface, b- restricting 

layer surface as estimated from the ground penetrating radar survey. Vertical bars show locations 

of the observation wells. 

a b
71

Table 3-2. Soil properties used in the preliminary simulations of coupled surface-subsurface flow 

and transport. 

Horizon Depth Bulk density Texture Vertical Ksat Lateral Ksat

m g cm-3 m d-1 m d-1

Ap1 0.12 1.56 Loamy sand 0.1 0.01

Ap2 0.25 1.56 Loamy sand 0.1 0.01

B1 0.42 1.56 Sandy loam 0.1 0.01

B2 0.75 1.56 Sandy loam 0.1 0.01

BC Variable 1.51 Sand 0.1 0.01

C variable 1.64 Loam (60%) 10-810-8
72

m) were simulated, while the initial tracer concentration in the soils was set to zero. The elapsed 

time of the simulations was one day. The lateral boundaries of the simulation domain were 

assumed to be impervious. 

Simulated surface flow contours are presented in Fig. 3-38. Overland flow started at 

t=0.0048 d and developed according to the surface topography (Fig. 3-36). Both ponding fronts

and drying fronts formed during the surface runoff process. The assumed impervious lateral 

boundaries obviously distorted the simulated overland flow patterns. The runoff plume reached 

the lower (south) boundary at about 0.036 d, and then moved along this boundary. Simulated 

tracer concentrations in the surface water and upper soil layer are shown in Fig. 3-39. 

Concentrations decreased with distance from the irrigation area due to mixing with the initial soil 

solution and exchange between soil and surface water. 

The simulations of coupled surface-subsurface flow and transport indicated that the

predicted tracer concentrations in the surface water were very sensitive to grid refinement 

adjacent to the land surface. Very small vertical nodal spacings were required to resolve sharp 

concentration gradients and to control the volume of porous medium with which the surface 

water interacted. The lateral grid spacing was about 1 m and the vertical spacing about 0.1 m. 

Using smaller vertical grid sizes (~1 cm) for the surface nodes, while assuming the same 

horizontal mesh as before, was not successful as FEMWATER failed to run. Still, the 

simulations were useful in that they showed that substantial runoff was to be expected during the 

irrigation, and hence that surface drainage was important in order to intercept and account for the

runoff. 

3.2.3.8 3D SUBSURFACE FLOW AND TRANSPORT MODELING

Preliminary modeling of the planned tracer experiment was carried out using the HYDRUS3D code simulating variably-saturated water flow and solute transport (Šimůnek et al., 2007). 

The model is based on the Richards equation for flow and the advection-dispersion equation for 

transport. Assuming a conservative tracer (no sorption and decay), these equations are, 

respectively,

   1





K h

t



(3-8)

 C C

t

C

  D  q





(3-9)

where θ is the volumetric water content (L3/L3), t is time (T), h is the pressure head (L), K is the 

hydraulic conductivity tensor (L/T), C is the solution concentration (M/L3), D is the 

hydrodynamic dispersion tensor (L2/T), and q is the Darcy-Buckingham flux vector (L/T). 
73

Figure 3-38. Development of the overland flow as obtained with the preliminary coupled 

surface-subsurface simulations. 

t=0. 036 d t=0. 040 d

t=0. 800 d t=1. 000 d

Runoff

depth
74

Figure 3-39. Tracer concentrations in overland flow or the upper soil layer as obtained with the

preliminary coupled surface-surface solute transport simulations. 

t=0. 036 d t=0. 040 d

t=0. 800 d t=1. 000 d
75

The soil water retention and unsaturated hydraulic conductivity functions needed for 

solution of Eq. (3-8) were described using the van Genuchten (1980) relationships:

1  

m

n

r

e

s r

S p  

 

 

    

  

(3-10)

   

2

1

1 1

m

m K S K S S e sat e e         

(3-11)

respectively, where Se is relative saturation, θr is the residual water content (L3/L3), θs is the 

water content at saturation (L3/L3), Ksat is the saturated hydraulic conductivity (L/T), α (L) and n

(-) are shape parameters, m=1-1/n, and τ=0.5. 

Application of equations (3-8) to (3-11) to the field tracer experiment using HYDRUS-3D 

requires definition of the domain boundaries, the initial and boundary conditions, a numerical 

finite element mesh, and soil hydraulic and solute transport parameters. Based on experimental 

data that included the locations of the tracer application plot and observation (sampling) wells, 

the topography of the soil surface, and the low-permeability lower boundary, we considered a 3D 

layered hexahedral flow domain having 50x30 m lateral dimensions and being 4 m in height 

(Fig. 3-40), and having with slopes of -1.35oand 1.05oin x and y directions, respectively. The 

domain was discretized into a structured (triangular prisms) finite element mesh consisting of 

120,000 3D elements. The finite element mesh sizes were 0.1 m and 1 m in the vertical and 

horizontal directions, respectively. 

As initial condition for the water flow equation we used an equilibrium hydrostatic

distribution of the pressure head with depth. On a horizontal plane, this distribution corresponded 

to a groundwater gradient of -0.045 along the x-axis such that the water table in the center of the 

irrigated plot was at a depth of 1.55 m. The initial concentration for the transport simulations was 

taken to be zero.

The boundary conditions for water flow were as follows (see also Fig. 3-41): along the side 

boundaries, the pressure head corresponded to the initial distribution; along the soil surface a

water flux of 0.1 m/day was imposed on the irrigation plot area; the remainder of the soil surface 

was considered to be a zero-flux boundary. We further assumed a pulse duration of 0.5 day for a 

conservative tracer applied with the infiltrating water at a concentration of 1000 mg/l. 

Table 3-3 presents the hydraulic parameters used in simulations of a layered soil profile. 

The parameters were obtained by calibrating the flow model to the flux experiment (section 4.1. 

2), but with the saturated hydraulic conductivity values being decreased 10 times. The 

longitudinal and transversal dispersivities were assumed to be 0.5 and 0.1 m, respectively. 

Fig. 3-42 shows simulated distributions of the pressure head and the concentration at 1.5 m depth 

after 30 days. A groundwater mound developed due to intensive irrigation in the plot area. This 

irrigation influenced the transport of the tracer, which acquired a toroid (donut)-like distribution

with higher concentrations downstream. Fig. 3-42a shows the effect of the imposed constant 

pressure head boundary condition on the pressure head distribution within the domain. The 

influence of the boundaries was quite strong since they were relatively close to the irrigation plot 

(10 m, except for the downstream boundary). 
76

Figure 3-40. Assumed simulation domain for solving the flow and transport problem with

HYDRUS-3D. 
77

Figure 3-41. Definitions of the invoked boundary conditions. 
78

a) 

 

b)

 

Figure 3-42. Simulated distribution of (a) pressure head, and (b) concentration after 30 days 

(layer 1.5 m depth). 
79

Figure 3-43. Location of (a) observation nodes and (b) the simulated breakthrough curves. 

1. 5 m 

depth

a) b)
80

Table 3-3. Unsaturated soil hydraulic parameters. 

N Layer

cm

Parameters

 s  r 

, m-1 N Ks, m d

-1

1 0-30 0.327 0 4.6 1.62 2.4

2 30-50 0.351 0.024 5.5 1.46 2.7

3 50-80 0.260 0 5.4 1.33 4.5

4 80-150 0.315 0 6.9 1.76 3.6

5 150-250 0.330 0 4.4 3.00 1.2

6 250-400 0.410 0.095 1.9 1.31 0.01
81

Sixteen observation nodes (8 at the depth of 1.5 m and of 2 m) were assigned along 2 rows 

at distances of 7 m (5 nodes at each depth) and 14 m (3 nodes at each depth) from the edge of the 

irrigation plot in the downstream groundwater flow direction. Fig. 3-43b shows the simulated 

breakthrough curves at the observation nodes at 1.5 m depth (concentrations at a depth of 2 m 

were nearly identical). The simulations indicated that the tracer should arrive at the first and 

second rows of observation nodes after approximately 8 and 15 days, respectively. The 

maximum concentrations along the first row of observation nodes were observed after 18-25 

days, depending upon the location of the node in the plane, but with values that were diluted 

about 40-50 times relative to the initially applied tracer concentration. By comparison, the 

maximum concentration along the second row of observation nodes occurred after 38-43 days. 

A significant amount of runoff was observed after the tracer experiment started. Actually, 

most of the applied water turned into overland flow. We therefore decided to change the 

irrigation schedule by apply water only from 8:00 to 10:00 h in the morning and from 4:00 to 

6:00 h in the afternoon. Consequently, a simulation was performed to account for this change in 

the soil surface boundary condition. The saturated hydraulic conductivity was decreased by a 

factor of 10 to increase runoff. The calculations suggested that for this scenario one could expect 

the tracer to arrive at the first row of observation nodes 30 to 45 days after starting the 

experiment, which actually happened. 
82

3.2.4 EXPERIMENTAL SETUPS, SCHEDULES, AND RESULTS

3.2.4.1 FLUX MEASUREMENT EXPERIMENT

Experimental setup. 

The flux experiment was set up as shown in Fig. 3-1. The flow and concentration 

measurements of the pumped water were supplemented with measurements of the water content 

using the soil moisture capacitance probes (MCPs). Fig. 3-44 shows the depth to the subsurface 

restricting layer at and near the experimental area, and the location of the observation wells and 

soil moisture capacitance probes. The MCPs were located about 11 m west of the well used for 

measuring solute fluxes. They monitored soil water contents every 10 minutes. The probes were 

centered 0.1, 0.3, 0.5, 0.8, 1.2, 1.5, 1 and 1.8 m below the soil surface. Details of the setup are 

given by Gish and Kung (2007). Here we give only a brief overview to provide a good 

understanding of the full context of the experiments. 

A schematic of the well configuration is shown in Fig. 3-45. The observation well consisted 

of a 0.3-m wide hole in the top 0.3 m, while from 0.3 m to 3.0 m the well size was reduced to 5-

cm. Since wet sand can collapse, the hole (especially for the bottom of the 5-cm hole) jettable 

well points were used so that the wells could be pushed to the desired depths just above the 

underlying clay lens (2.5 to 3 m). Once the slotted well was inserted and well extensions were 

attached, blow sand was poured into the gaps between the observation well and the surrounding 

soil (for only the 5-cm hole). Since slots in the well can become clogged upon soil insertion, a 

positive water pressure was applied to the top of the observation well to clean out the well slots 

and activate the well. Once the sand had settled from the 0.3 to 3.0 m depths, a 0.2-m 

polyurethane (PU) disk was tightly fitted around the well at a depth of 0.3 m depth, while the 

original soil from 0 to 0.3 m was placed around the well. The purpose of the PU disk was to 

minimize water and solute flow down along the observation well, thus forcing water and solutes 

to move into the soil matrix. To minimize disturbance, the observation well was configured with 

two extensions. The lower extension was connected to the slotted well just above the 

polyurethane collar (about 0.30 m below the soil surface). For tillage and planting operations the 

well was capped at this juncture so that tillage implements would not disturb the well while the 

area around the well could receive the same tillage treatment as the rest of the field. The second,

more shallow extension was connected to the well just below the soil surface. This configuration 

allowed the above surface portion of the well to be removed for field operations. 

The average depth to the water table during the week prior to this study was 1.68 m. The depth 

of water table was continuously monitored with a submergible pressure transducer (Eijkelkamp, 

Agrisearch Equipment, Giesbeek, The Netherlands) located 2.9 m below the soil surface. A line 

for pumping water from the observation well was inserted 0.15 cm below the water table and 

attached to a portable pump which ran throughout the duration of the experiment. Water flow 

rates exiting the well were monitored by manually capturing the water in graduated cylinders. 

Since water flow rates from the pumped well could vary over short time durations (seconds),

three consecutive outflow volumes, each over a 1-minute duration, were collected at each 

observation time. To ensure that the entire solute breakthrough curve was accurately monitored,

observation times for the manual collection and for monitoring the flows were scheduled every 

15 minutes initially and then gradually increased to every hour. In between the water flow 

measurements, well water was pumped into a drainage pipe that carried the water 200-m off-site. 
83

Figure 3-44. Depth to the GPR-identified clay lens and location of observation wells and soil 

moisture capacitance probes (after Gish and Kung, 2007. Permission to use this copyrighted 

material is granted by Geoderma).
84

Figure 3-45. Schematics of observation well installation and instrumentation. Schematic is not 

to scale, i.e., the PVC well is only 3.8 cm in diameter, but 3 m in length (after Gish and Kung, 

2007. Permission to use this copyrighted material is granted by Geoderma).
85

No tracers were applied within a radius of 0.1 m of the observation well. Three tracers 

were manually sprayed between 0.1 to 3.0 m around the well, resulting in a treated area of about 

28.2 m2(Fig. 3-45). Bromide (0.1064 kg Br m-2) was applied 1.5 days before irrigation was 

initiated, and allowed to diffuse into the coarse-textured soil matrix at the soil surface. No 

precipitation other than irrigation was observed at this site, nor for the duration of the entire 

study. To ensure that water reaching the water table would be collected, we began pumping 

water continuously from the observation well two weeks before Br was applied. This would also 

establish and maintain a steady drawdown cone around the well. About 1.5 days after the Br 

application, but immediately before irrigation was initiated, a Cl pulse (0.052 kg Cl m-2) was 

surface applied. Pentafluorobenzoic benzoic acid (0.17 kg PFBA m-2) was applied 7 h after the 

experiment began. This tracer was used to determine any changes in chemical transit times after 

the soil profile had became wetter and possibly more hydrologically active. According to Jaynes 

(1994) and Kung et al. (2000b), PFBA is as conservative as Br and Cl, and has almost identical 

breakthrough patterns. As a result, three mobile chemical conservative tracers were used in this 

study, and monitored as they arrived in the observation well

While taking the water flow measurements, a single 30 ml water samples were collected 

and stored in a refrigerator until its chemical composition could be determined. These samples, 

as well as subsequent solution samples during the experiments, were split and eventually 

analyzed by high performance liquid chromatography (HPLC) for PFBA and by ion 

chromatography (IC) for Br and Cl. Within 12 hours of their collection in the field, the samples 

were being analyzed for Cl and Br while the remainder of the samples were stored in a 

refrigerator. Analysis of PFBA did not begin until a week after the experiment was terminated. 

Since Cl and Br were applied first, their breakthrough curves were used to determine when to 

terminate the experiment. The IC conditions were: mobile-phase, Sodium Borate-Gluconate 

(2%), n-Butanol (2%), acetonitrile (12%); flow rate, 1.2 ml min-1; guard column, Waters 

Corporation (Milford MA) IC-Pak Anion Guard-Pak; analytical column, Waters Corporation 

(Milford MA) IC-Pak Anion (50 mm x 4.6 mm i.d. ); and injection volume, 50 μL; and 

conductivity detection. The detection limits for of Br, and Cl were 0.1, 0.2 mg L-1, respectively. 

Calibration curves generally had r

2

values greater than 0.99. The HPLC conditions were as 

follows: mobile-phase, acetonitrile (40%), 15 mM KH2PO4 (titrated to pH 2.6 with phosphoric 

acid) (60%); flow rate, 1.8 ml min-1; guard column, Spherisorb SAX (10 mm x 4.6 mm i.d., 5-

μm, Sigma-Aldrich, St. Louis, MO); analytical column, Supelcosil SAX1 (25 cm x 4.6 mm i.d.,

5-μm, Sigma-Aldrich, St. Louis, MO); injection volume, 50 μL; and UV detection, 205 nm. The 

detection limit for PFBA acid was 1 μg L-1. Calibration curves generally had r

2

values greater 

than 0.999. 

Cl measured in the observation well could eventually come from three sources: 1) Cl 

already in the groundwater, which had been measured weekly for several months prior to Br 

application; 2) Cl from city irrigation water, which was measured throughout study by sampling 

the irrigation water, and 3) the Cl pulse itself that was to be monitored. The average Cl 

concentration of groundwater prior to irrigation was 7.3 mg Cl L

-1

, while the average 

concentration of city water was 8.75 mg Cl L

-1

. To separate the various sources of Cl, the 

averaged concentration observed in groundwater immediately before the study, was subtracted 

from all well water samples after Br application. At the time when Cl levels began to rise 

relatively sharply, the Cl concentration of the city irrigation water was subtracted from the 

remaining well water samples. The remaining Cl was assumed to be from the Cl pulse applied 

around observation well. Unfortunately, there was some ambiguity in determining exactly when 
86

the rapid increase in Cl occurred. Cl (from the tracer as well as from city irrigation water) will 

interact with the soil matrix resulting in a diffuse front (a gradual change in Cl), rather than in a 

sharp front (an abrupt change in Cl). As a result, Cl concentrations from city irrigation water 

may not have been subtracted as soon as they should have been. On the other hand, the entire 

8.75 mg Cl L-1 was subtracted instead of only a portion. Fortunately, flows and concentrations 

were being taken about every 30 min at this time, so the shift should not be more than one hour 

(two readings). 

A 4.1 mm h-1irrigation rate was applied to the research area (30 m by 40 m) using 7 rows of 

4 solid-state sprinklers, all set at a 6.4 m spacing. The sprinkler nozzles used were Weather Tec 

G50 (WCG5W with 23 degrees, Roberts Irrigation Company, Inc, Plover, WI). Christiansen 

coefficients of uniformity measured at 2 am (when winds were negligible) were 85%. Average 

daily wind speeds during the study typically ranged from 0.34 to 0.96 m s-1; however, there were 

three days with wind speeds exceeding 1 m s-1. On these three days, the average daily wind 

speed ranged from 1.38 to 2.5 m s-1, with corresponding maximum wind speeds (for 10 minute 

durations) ranging from 4.8 to 5.9 m s-1. Although no measurements of uniformity were taken at 

those times, we believe that they decreased during the periods of high wind. 

Water samples from the well were collected about every 4 hours during the time period 

between Br application and the irrigation. The pump intake line was located 0.15 m below the 

water table. The pump used for our study had a capacity of more than 0.34 L s-1. The background 

flow rates from the well before the irrigation were about 0.03 L s-1, but reached a maximum of

0.18 L s-1at the end of the study. Immediately following Cl application, the irrigation system 

was turned on and well samples were collected manually every 15 minutes for the first 24 hours. 

From 24 to 72 hours after irrigation began, well samples were manually collected about every 30 

min, and each hour afterwards. At one point, about two days into the irrigation, the pump failed 

and had to be replaced. 

The investigation was conducted in November when air temperatures ranged from 1 to 7 ̊ C. 

Samples were collected from the field every 6 hours and immediately prepared for the chemical 

Br and Cl analyses. From each 30 ml well sample, 15 ml was refrigerated for analysis of PFBA 

by HPLC. When most of the Br and Cl breakthrough curves appeared to be completed, the study 

was terminated. 

Experimental results. 

Flow rates from the observation well were approximately 0.03 L s

-1

for the first 12 hours 

after irrigation began, but then slowly increased until the study was terminated 7 days later (Fig.

3-46). Three consecutively measured 1-min flow volumes at each observation time were used to 

estimate coefficients of variation (CV). Values were about 5%, ranging from 1 to 10% regardless 

of the flow volume. 

Average water table depths, along with their temporal variability over each 24-h period, are 

shown in Fig. 3-47. At the beginning of the study, the water table height was 1.68 m and 

remained near that value for the duration of the experiment. Although the standard deviation

generally increased as the study progressed, there was no significant change in the average water 

table depth with time. 
87

Figure 3-46. Averaged water flow rates pumped from the observation well as a function of time 

(after Gish and Kung, 2007. Permission to use this copyrighted material is granted by

Geoderma). 
88

Figure 3-47. Water table heights in the observation well. Error bars represent one standard 

deviation (after Gish and Kung, 2007. Permission to use this copyrighted material is granted by

Geoderma). 
89

The soil water sensors indicated a sudden increase in soil water contents at about 1.5 days 

after Br application, which coincided with the onset of irrigation (Fig. 3-48). The relatively low 

water contents observed just prior to irrigation (about 0.10 cm3cm-3at the 0.1 m depth) reflected 

the low water holding capacity of the coarse-textured surface soil. Soil water contents in the top 

0.5 m remained well below saturation throughout the study. 

The real-time soil moisture profile data also showed a lag in the rapid rise in soil water 

contents with depth as the infiltrating water in time reached a given depth, with the 0.1 m sensor 

rising first and the 0.5 m sensor rising last. Soil water contents at 0.8 m rose sharply from 0.07 

cm3cm-3to about 0.15 cm3 water cm-3two days after Br application (or about 12 hours after 

irrigation was initiated), but lagged slightly behind the water contents at 0.5 m. The water 

contents at 0.8 m remained low, near 0.15 cm3cm-3throughout most of the study and then 

suddenly increased to 0.28 cm3cm-3during the last few hours of the experiment. Saturation at 

this depth corresponded to a water content of 0.33 cm3cm-3. Meanwhile, water contents 1.2 m 

below the soil surface started to rise such that 3 days after Br application (1.5 days after 

irrigation started) this soil layer began to reach saturation. The soil moisture sensor at 1.5 m 

showed the highest water contents even though the water table at the observation well was being 

maintained at 1.68 m. The soil water contents at 1.8 m were less than those at 1.5 m even though 

saturation was reached there. The lower water contents at 1.8 m were probably due to the 

presence of gravel, which in general has a lower porosity. Soil textures at 1.2 and 1.5 m were the 

same (although they showed slightly different maximum water contents), thus suggesting that the 

1.2-m water contents were likely due to capillary fringe effects. The rapid rise in water contents 

at 0.8 m nearly 8 days after Br was applied (6.5 days of irrigation) indicated that the 1.2 and 1.5 

m depths may have been saturated by the end of the study 11 m away from the observation well. 

Solute breakthrough curves (BTC) as a function time after irrigation started are shown in 

Fig. 3-49. To accommodate direct comparisons, each observed concentration was divided by the 

mass applied. Early increases in Cl before 1.5 days after application were not known, but 

accounted for << 1% of the total applied Cl. The rapid increases in solute concentration between 

days 1.5 and 2 were well quantified, as were the solute tails which began about three days after 

application. The rapid rise in concentration for each tracer reflected the front of the solute pulses 

arriving at the well. The rapid rise appeared to occur first for PFBA, which was applied 7 hours 

after application. However, there was no difference in the rapid rise of Cl or Br, which suggests 

that for this coarse-textured soil Br and Cl were transported initially through similar pore 

systems, while on average slightly larger pores may have contributed to the transport of PFBA. 

Cumulative tracer masses pumped out of the well are shown in Fig. 3-50. The recovery was 

excellent in this experiment. Percent recoveries were 100% for PFBA, 102% of bromide, and 

97% for chloride (after correction of the chloride contents from ground and city water). 

3.2.4.2 LATERAL FLOW EXPERIMENT

Experimental setup. 

The lateral flow experiment was set up as shown in Fig. 3-18 – Fig. 3-20. A windshield (160 cm

height) was constructed around locations 1-4 to minimize wind impact on irrigation uniformity. 

Four sprinkler nozzles (Olson Red Mini Rotor Style Drip Emitter by Olson Irrigation Systems, 

Santee, CA) were installed at heights of 1 m in the corners of the irrigation plot. One additional 

sprinkler nozzle (Olson Green Mini Rotor Style Drip Emitter) was installed at a height of 10 cm 

above the soil surface in the center of the plot (Fig. 3-18). The system was designed to provide 

continuous irrigation at a rate of 9.6 cm d-1, with a uniformity coefficient of 0.86, to the
90

Figure 3-48. Time series of the soil water content (after Gish and Kung, 2007. Permission to use 

this copyrighted material is granted by Geoderma). 
91

Figure 3-49. Observed tracer breakthrough curves for chloride, bromide and PFBA (after Gish 

and Kung, 2007. Permission to use this copyrighted material is granted by Geoderma).
92

Figure 3-50. Tracer mass recovery (after Gish and Kung, 2007. Permission to use this 

copyrighted material is granted by Geoderma).
93

13x14 m study area. The sprinklers were connected to a water hose equipped with a DLJSJ50 

water meter (Daniel L. Jerman Co., Hackensack, NJ) to measure the amount of applied water. 

The observation wells at locations 1-12 were equipped with samplers to collect water from 

3 different depths. The samplers consisted of a plastic 16-mm OD tubes containing 4 rubber 

packers installed into the wells. The packers separated three 30-cm long sections inside of the 

wells. A 2-mm ID plastic tubing connected the center of each section with the sampler outlet. 

Water samples were taken from each section with a 50-ml syringe. The sample volume typically 

ranged between 10 and 14 ml. The samplers were installed such that the samplings were taken at 

depths of 1.1 m at locations 1-4, and 1.05, 1.35 and 1.65 m at locations 5-12. 

A total of 42 kg KCl was dissolved in two 2.1-ton tanks with 4050 L of tap water to provide 

a Clconcentration of 4940 ppm. The KCl solution was applied to the experimental site using the 

irrigation system. The application started at 10:30 am and ended at 5:05 pm on March 25, 2008. 

A total of 3861 liters was applied to the site within 6.6 hr. The irrigation system was reconnected 

to the tap water hose immediately after the application. 

The irrigation was interrupted at 10:30 am on March 27 because of runoff at the site. Runoff 

losses were 39% of the irrigation water. The irrigation regime was adjusted to minimize runoff 

losses and to provide a nearly steady-state infiltration rate into the soil. Starting March 28, the 

site was irrigated twice a day, from 6 to 8 am and from 4 to 6 pm. Irrigation times were

controlled by an irrigation timer and set such that well water could be sampled twice a day for 

Cl-. Runoff amounts from the experimental site were recorded continuously. Irrigation was 

interrupted only after intensive rainfalls. The irrigation regime was corrected one more time on 

June 1 because of an increase in evapotranspiration that caused a decrease in the groundwater 

levels at locations 1-4. New times were set up for three irrigations each day: from 5 am to 7 am, 

from 1 pm to 3 pm, and from 9 pm to 11 pm. This schedule was followed until the end of 

experiment. 

Water samples were taken from three depths at 12 locations one hour prior to the KCl 

application. Samples were taken twice a day within the first 40 days after application, and then 

once a day (at 5 pm) until the end of the experiment. Within 24 hours of their collection in the 

field, the samples were analyzed for Clby ion chromatography as described in chapter 3.2.4.1. 

Irrigation and rainfall water was also periodically analyzed for Cl-. Soil water contents and 

groundwater depths were monitored using MCPs and Cera-Divers at 12 locations as described in 

chapter 3.2.3.2. The study was terminated when the groundwater levels decreased below the 

water sampling depths at most locations. 

Experimental results. 

Cumulative irrigation, precipitation, evapotranspiration and runoff data are shown in Fig. 3-

51. The daily irrigation rate was 9.5 cm d-1during the first two days, 1.5 cm d-1during the next 

64 days, and 1.8 cm d-1during the following 65 days. The first portions of runoff usually 

approached the flume 30-40 min after irrigation started. Runoff amounts were found to be in the 

range from 21 to 38% of the irrigation volumes. A total of 59 rainfall events were recorded 

during the 132-day experiment. The mean daily precipitation depth was 3.0 mm, which did not 

affect the soil water contents. Several events, however, did affect the water contents, the 

groundwater levels, as well as Clconcentrations in the wells. Rainfall events on April 22-23 

(54.6 mm), on May 10-14 (159 mm), on June 5-6 (43.4 mm), and on July 25 (50.0 mm) 

exceeded the daily irrigation rates considerably, and as such affected the soil water regime as 
94

Figure 3-51. Cumulative water fluxes measured during the lateral flow experiment. 

Date

4/1 5/1 6/1 7/1 8/1

Cumulative flux (cm)

0

50

100

150

200

250

Evapotranspiration

Irrigation

Runoff

Precipitation
95

Figure 3-52. Groundwater depths measured during the lateral flow experiment. 

Location: Depth to the groundwater (cm)

0

50

100

150

200

1

2

3

4

0

50

100

150

200

5

6

7

8

9

10

11

12

2008 Daily precipitation (mm)

4/1 5/1 6/1 7/1 8/1 

0

2

4

6

8

(a)

(b)
96

will be shown below. The average ET values were 0.5, 0.8, 1.0 and 1.1 mm d-1in April, May, 

June and July, respectively, which did not affect the soil water content dynamics. 

Fig. 3-53 illustrates the water table dynamics. Groundwater levels remained relatively high 

at locations 1-4 during the lateral flow experiment (Fig 3-53a). Minimum groundwater depths 

(GWDs) were observed at location 3, and the maximum levels at location 2 where they 

exhibited severe oscillations. Severe oscillations were also observed at location 4, but the water 

table there was closer to the soil surface as compared to location 2. Peaks in the GWD at 

locations 2 and 4 generally corresponded to the more intensive rainfall events. The GWD at 

location 1 was less affected by rainfall as compared to locations 2 and 4. Observed differences in 

the water content and GWD dynamics at locations 1 through 4 implied different hydrological 

regimes in different parts of the irrigated site. The same is obviously true for locations 5 through 

12. However, GWD differences between those locations remained between 5 cm after rainfalls 

and 119 cm after continuous soil drying. These differences were largest between the wells at 

adjacent locations 11 and 12. Considerable temporal variably in the GWD was also observed at 

locations 5 through 12. Average GWDs varied from 5 to 161 cm during the lateral flow 

experiment. Spatial and temporal variability in the GWD created unsteady subsurface flow from 

the irrigated plot toward locations 5-9 and locations 10-12. 

A plot of the soil water dynamics during the experiment is shown in Fig 3-53. Soil water 

contents before the experiment were in the range from 0.148 to 0.403 cm3cm

-3

and gradually 

decreased with depth. Three days after the experiment started, water content approached 

maximum values at practically all depths at locations 1 and 3, and below 25 cm depth at location 

4, while remaining relatively constant until the end of the experiment. The water contents

oscillated noticeably in the upper 20 cm at location 4 and at all depths at location 2. 

Considerable water content oscillations were observed also at non-irrigated locations 5-12 

in the upper 40-cm soil layer. Sharp increases and gradual decreases were observed in this soil 

layer immediately after the rainfall events (Fig. 3-53). Water contents at depths of 50 and 60 cm 

showed different behavior at these locations. Sharp increases were followed by sharp decreases

at locations 7-9, whereas water contents at locations 11 and 12 did not change noticeably with 

time. Differences in the soil moisture dynamics were caused by different soil texture and changes 

in the groundwater depth at these locations. Soil texture at depths of 50-60 cm was sandy loam at 

locations 7-9, and loam at locations 11-12. Water contents in sandy loam soils near saturation 

tend to decrease faster with an increase in the absolute value of the pressure head, compared with 

loamy soils. Rapid changes in the GWD, as well as transitions from saturation to unsaturated 

conditions and vice-versa, likely caused abrupt water content changes at locations 7-9. 

Differences in soil properties, hydraulic regimes and unsteady subsurface flow at the 12 

locations affected Cltransport. Clconcentrations in groundwater prior to irrigation varied 

within the range from 6 to 24 ppm and did not differ significantly between the different depths 

and locations. Because of small spatial variability in the initial Clconcentration at the different 

locations, we did not expect any effect of the initial Cldistribution on the results of the lateral 

flow experiment. Clconcentrations in the irrigated water were 10.2±3.0 ppm, whereas rainfall 

Clconcentrations (0.6±0.6 ppm) were one order of magnitude less than the irrigation water and 

the groundwater concentrations. Hence, the effect of rainfall on the groundwater concentrations 

could be quite pronounced, especially after intensive rain events. 

The Cltime series measured in 12 wells are shown in Fig. 3-54. We observed two distinctly 

different breakthrough curves at the irrigated site. A fast increase in Clconcentration was 

observed in wells 1 and 4 at the initial stage of the breakthrough curve soon after the tracer was 
97

Figure 3-53. Soil water content measured at 12 locations during the lateral flow experiment. 
98

Figure 3-54. Chloride content in the groundwater measured in 12 wells during the lateral flow 

experiment. 

Well 7 Cl

- concentration in ground water (ppm)

20

40

60

80 Well 8

Well 1

10

100

1000 Well 2

Well 11

4/1 5/1 6/1 7/1 8/1 

0

20

40

60

80 Well 12

4/1 5/1 6/1 7/1 8/1 

1.05 m

1.35 m

1.65 m

Well 3

10

100

1000 Well 4

Well 5

20

40

60

80 Well 6

Well 9

20

40

60

80 Well 10

Depth:
99

applied. A gradual decrease and another increase in Clconcentration followed the initial stage. 

Contrary to wells 1 and 4, a relatively slow increase was followed by a gradual decrease in Clin 

wells 2 and 3. These dramatic differences in the vertical transport rates of Clat the irrigated site 

were likely caused by different transport conditions. The water contents were relatively constant 

and groundwater was closer to the soil surface at locations 1 and 3 compared to locations 2 and 4 

where GWDs and the water content in the upper 0.50-m soil layer varied significantly during the 

later flow experiment. The water content and GWD data indicated that flow conditions were 

close to saturated at locations 1 and 3, but far from saturation in the topsoil layer at locations 2 

and 4. 

The tracer arrived at locations 5 through 9 at different times. It took approximately 60 days 

for the Clto appear in noticeable amounts at three depths at location 7, and 80 days at locations 

5 and 6. The distance between the irrigation site and locations 5 through 9 was 7 m, which means 

that the flow velocity should be within the range from 9 to 12 cm d-1. The tracer arrived at 

locations 5 and 7 at higher concentrations than at location 6. Surprisingly, we did not observe Clbreakthrough at locations 8 and 9, which were also located 7 m downgradient from the irrigation 

site. Locations 5 through7 were probably closer to location 4, where vertical Cltransport was 

faster than transport at location 3. 

An increase in the Clconcentration was observed at a depth of 1.65 m at locations 10,11 

and 12 at the end of the experiment. However, the increases were not so pronounced as those at 

locations 5, 6 and 7 where the concentrations remained within the range observed at locations 8 

and 9. 

The Clconcentration time series differed at three depths at locations 5 through 12. Clconcentrations were generally higher at depth of 1.6 m, than at the 0.5-m and 0.8-m depths, 

except at locations 8 and 12 where the Clconcentrations did not change with depth, and location 

7 where the highest Clconcentrations were observed at a depth of 1.35 cm. Noticeable 

differences in the Clbreakthrough curves were observed at three depths at locations 5, 6 and7. 

The peak concentrations at location 6 did not differ among three depths. At location 5, larger 

values were observed at depths of 1.05 and 1.35 m, whereas at location 7 the peak Clconcentrations at a depth of 1.35 m were smaller than those at depths of 1.05 and 1.65 m. 

Differences in the arrival times and the Clconcentration at three depths and 12 locations implies 

that the tracer was transported preferentially in hydraulically active soil zones. 

An interesting phenomenon we observed was the synchronous dilution of groundwater at 

different depths during rainfall. This follows from the oscillations in the Clconcentration time 

series at locations 7, 8, 10, 11 and 12. These oscillations corresponded to the GWD oscillations 

caused by fast decreases in the GWD after intensive rainfalls (Fig. 3-54). Smaller Clconcentrations were measured when the GWDs were smaller. An increase in the GWD always 

caused an increase in the Clconcentration. The decrease in Clconcentration can be explained as 

being the result of ground water dilution by infiltrated precipitation (CCl=0.6 ppm), while an 

increase could be caused partly by evaporation. However, it remains to be explained why Clchanges occurred synchronously at three different depths without changes in the concentration 

with depth. 
100
101

4 BASE FLOW AND TRANSPORT MODELS

4.1 BASE MODEL FOR THE FLUX MEASUREMENT EXPERIMENT

4.1.1 MODEL DESCRIPTION

Model equations. 

The tracer experimental data were analyzed using the HYDRUS-2D software package 

simulating variably-saturated water flow and solute transport (Šimůnek et al., 1999). The model

is based on the Richards equation for flow and the advection-dispersion equation for transport, 

given by equations (3-8) and (3-9), respectively. The soil water retention and unsaturated 

hydraulic conductivity functions were described using the van Genuchten (1980) relationships

given by equations (3-10) and (3-11), respectively. 

Simulation domain and boundary conditions. 

Application of Eqs. (3-8) to (3-11) to the field tracer experiment using HYDRUS-2D 

requires definition of the numerical finite element mesh, the initial and boundary conditions, and 

the soil hydraulic and solute transport parameters. The simulation domain and the initial and 

boundary conditions were defined in accordance with the experimental conditions as described in

Section 3.2.4.1. We considered an axisymmetrical flow field of 250 cm height and a radius of 30

m (Fig. 4-1). The finite element mesh size was 5 cm in the vertical direction and 10 cm in the 

horizontal direction everywhere, except near the soil surface and the well boundary where we 

used a mesh size of 2.5 cm. The bottom boundary was considered as a no-flux boundary for both 

water flow and solute transport. Along the right boundary, 20 m from the pumping well, we 

assumed that the water table depth (1.68 m) was not affected by the irrigation, and as such

imposed an equilibrium pressure head distribution versus depth for flow and a zero gradient 

concentration for transport. 

The soil surface boundary was divided into four concentric rings (Fig. 4-1). A constant 

water flux of 4.1 mm h

-1 was imposed between radii of 2.5 to 2,000 cm, and a zero flux 

elsewhere. A solute flux with a concentration equal to the concentration of the irrigation water 

(Cir) was assigned between radii of 2.5 and 10 cm, and between 300 and 2000 cm. Water and 

solute fluxes were assumed to be zero for radii larger than 2,000 cm. Flux concentrations 

between 10 and 300 cm near the well where the tracers were applied, were calculated such that 

they were consistent with the total tracer application rates. We assumed pulse durations of one 

hour (related to the dissolution times of the solutes) for all tracers, leading to concentrations of 

the infiltrating water of 26,000, 12,700 and 4,073 g L-3for Br, Cl and PFBA, respectively. The 

Cl concentration of the irrigation water was 8.75 μg cm-3(Section 3.2.4.1), while no Br and 

PFBA were present in the irrigation water. 

Along the left boundary (at a radius r of 2.5 cm) representing the well, a system-dependent 

seepage flux boundary was applied through which water can leave the saturated part of the flow 

domain. Although the model stipulated a potential seepage boundary from the soil surface to 170 

cm the “active seepage” zone occurred only near the water table (see Fig. 4-1), depending upon 

the transient flow conditions during the experiment. This type of boundary condition assumes a 

zero flux as long as the local pressure head at the soil-well interface is negative (Fig. 4-1). 

However, a zero pressure head is used as soon as the soil at a point along the boundary becomes 

saturated. Additionally, a variable flux (Neumann) boundary condition was specified between 

depths of 175 (the pump installation depth) and 23 cm. The total value of the imposed variable 
102

Figure 4-1. Simulation domain and specified boundary conditions (not to scale). Different 

textures and associated numbers represent the various profile layers. CT and Cir are the solute 

concentrations of the infiltrating water. 

r (cm)

300 cm

2000 cm

3000

z (cm)

1

2

3

4

5

0

Boundary Conditions legend 

No flux

Variable flux

Seepage face

Constant flux 4.1 mm/h

C=CTduring 1h

Constant flux 4.1 mm/h 

C=Cir

Equilibrium head

Well boundary

Active

Seepage

Face

250

r (cm)

300 cm

2000 cm

3000

z (cm)

1

2

3

4

5

0

Boundary Conditions legend 

No flux

Variable flux

Seepage face

Constant flux 4.1 mm/h

C=CTduring 1h

Constant flux 4.1 mm/h 

C=Cir

Equilibrium head

Boundary Conditions legend 

No flux

Variable flux

Seepage face

Constant flux 4.1 mm/h

C=CTduring 1h

Constant flux 4.1 mm/h 

C=Cir

Equilibrium head

Well boundary

Active

Seepage

Face

250
103

flux through this boundary was adjusted iteratively during the numerical calculations until the 

simulated total flow volume to the well matched the measured total volume of pumped water at 

the end of the simulation period. Finally, a zero concentration gradient was assumed along the 

left and right boundaries of the transport domain. 

As initial condition for the pressure head we used an equilibrium distribution in the profile 

corresponding to the observed initial water table depth of 1.68 m. The initial concentrations for 

the transport simulations were zero for Br and PFBA, and 7.3 mg/L for Cl, being the average 

measured Cl concentration in the saturated zone prior to irrigation. 

Calculation of tracer concentrations in the pumping well. 

Solute concentrations of the pumped water (Cw) were calculated from a mass balance 

equation assuming full mixing in the pumping well as follows

     

2

( ) ( )

w

w w c SF c VB p w

dC r h Q t Q t Q t C

dt

   

(4-1)

where rw is the well radius (L), hw is the mean water level in the well (L),Qc(SF) and Qc(VB) are the 

mass fluxes (M T-1) of the tracers to the well through the seepage face and variable flux 

boundaries, respectively, as calculated with HYDRUS-2D, and Qp is the pumping rate (L3T

-1

). 

Model performance. 

The goodness-of-fit of the model was evaluated using the coefficient of determination (R

2

) 

and the modified index of agreement (MIA) as given by Legates and McCabe (1999):

   

     



 



  



  n

i

n

i

obs

i w

obs

w

obs

w i w

n

i

i

obs

w i w

C t C C t C

C t C t

MIA

1 1

1

1 , (4-2)

where 

 i

obs

w C t

and 

 i

obs

w C t

represent the simulated and observed concentrations of the tracer in 

the pumped water at time ti, and 

obs Cw

is the observed mean concentration. While there is no 

statistical basis to decide exactly which MIA value is a good threshold characterizing the use of 

an "accurate" model, following Köhne et al. (2005) we assumed simulations with MIA>0.75 as 

being “accurate”. 

4.1.2 MODEL CALIBRATION AND SIMULATIONS

Inverse solution procedure for the soil hydraulic properties. 

Soil hydraulic parameters needed for the calculations were estimated using a combination 

of one-dimensional and two-dimensional inverse simulations carried out with the HYDRUS-1D 

(Šimůnek et al., 2005) and HYDRUS-2D (Šimůnek et al., 1999) software packages, respectively, 

as well as using laboratory measurements of the saturated water content (θs) of the various soil 

horizons. During a first step we used HYDRUS-1D to estimate the hydraulic parameters from 

observed water contents values that were monitored at different depths in the soil profile 11 m 

away from the pumping well. By using HYDRUS-1D we assumed that flow in the unsaturated 

zone this far (11 m) from the pumping well was mainly in the vertical direction, thus 

considerably minimizing computational times as compared to using HYDRUS-2D. During a 

second step we used HYDRUS-2D to perform additional calibrations of the saturated hydraulic 
104

conductivity (Ksat) of layers 3 to 5 (Fig. 4-1) where water presumably flowed both vertically and 

horizontally. 

For the HYDRUS-1D simulations we assumed a 250-cm deep soil profile consisting of 5 

layers consistent with the described lithology of the site: loamy sand (0-28 cm), sandy loam (28-

48 cm), sandy loam (48-78 cm), coarse sand (78-140 cm), and gravely sand (142-250 cm). The 

clay loam horizon (250–350 cm) had an extremely low conductivity and as such was considered 

to be impermeable and hence not included in the simulations. The sandy loam horizon (30-80 

cm) was subdivided into two layers based on the fact that markedly different water contents were 

observed during steady infiltration at depths of 30 and 50 cm (Fig. 3-49), thus indicating 

different hydraulic properties. The MCP measured water content at depths of 10, 30, 50, 80, 120 

and 150 cm were used to calibrate the flow model, which in total contained 25 hydraulic 

parameters (the five parameters θr, θs, α, n and Ksat for each of the five layers). To minimize 

issues of uniqueness in the inverse solution we decreased the number of optimized parameters by 

using experimentally measured values of the water content at saturation (θs), and zero values of 

the residual water content (θr) for all coarse-textured layers (except sandy loam). Thus, we 

needed to determine three parameters (Ksat, α, n) for each of five layers and one θr value (for the 

sandy loam horizon). 

The evaporation rate was relatively low, while no rain or irrigation occurred a week prior to 

the experiment. We therefore assumed that the initial pressure head profile was close to 

equilibrium with the water table at 1.68 m. The boundary condition at the soil surface defined a 

water flux of 4.1 mm h-1during the irrigation period. Since the bottom boundary at 250 cm was 

considered to be impermeable, the water table was likely to rise in some region around the well 

after irrigation started. As a result, some lateral water flow in the saturated zone occurred, which 

had to be accounted by a flux through the lower boundary in the one-dimensional HYDRUS-1D 

simulations. This flux varied with time depending on the position of the water table. To simulate 

this processes we used the HYDRUS-1D horizontal drain boundary condition with a drain 

spacing of 22 m (twice the distance from the MCP location to the pumping well). Although this 

boundary condition does not describe the physical 2D flow system exactly, it was the boundary 

condition available in HYDRUS-1D that most closely represented our field conditions. 

Initial estimates of the α and n parameters for the inverse procedure were based on the 

assumed initial equilibrium distribution of the pressure head and the observed water contents 

prior to the experiment, while Ksat values were initially estimated from soil textural class and 

particle size distribution information. We used a sequential inverse procedure by starting the 

parameter search with the first layer, while assuming that the other parameters were known (the 

initial estimates) and using observed water contents of the 10 cm depth only. The next step was 

to find parameters of the second layer by fitting water contents at depths of 0.1 and 0.3 m, and 

using the parameters of the first layer found at the previous step. The third step was to adjust 

parameters of layers 1 and 2 simultaneously by fitting measured water contents at depths of 0.1 

and 0.3 m. We continued this sequential procedure by gradually increasing the number of layers 

and hence the number of parameters that were simultaneously estimated. During the final step, 

the HYDRUS-1D code searched simultaneously for 15 parameters (θr for the sandy loam horizon 

was not changed after the third run). 

Soil hydraulic parameters from calibration. 

Fig. 4-2 compares MCP-measured water contents at different depth with simulated values 

obtained with HYDRUS-1D. Good agreement was obtained between the observed and simulated 
105

water contents for all depths except at 0.8 m, where the lowest value of the coefficient of 

determination (R

2

) of 0.877 was obtained. The fluctuations in observed water contents at the four 

upper observation points may have been caused by non-uniform irrigation during several windy 

days (Sect. 3.2.4.1). The calculated water content time series clearly describe the propagation of 

the moisture front into the profile. 

Table 4-1 presents the fitted hydraulic parameters obtained using the invoked inverse 

procedure. A relatively high value of 10 was obtained for the van Genuchten hydraulic parameter 

n for the fifth layer (gravely sand), which implies very steep water retention curve and an 

unsaturated hydraulic conductivity curve in which the conductivity decreases very rapidly with 

decreasing pressure head. While some slight changes in the minimized objective function 

occurred when the parameter n varied between 8 and 12, the simulated water contents were 

found not to be sensitive to these changes. We therefore accepted a value of n = 10 for the very 

coarse-textured gravelly sand layer. 

Additional calibrations were carried out with the complete two-dimensional axisymmetrical 

flow model against observed water contents. As a result, we obtained values for the saturated 

hydraulic conductivity, Ksat, of 185, 149 and 52 cm/h for layers 3, 4 and 5, respectively. The 

maximum difference of these Ksat values from those obtained for the 1D problem was for the 

fifth layer. The calibrated Ksat for the 2D problem here was approximately three times smaller 

than that of 1D problem. The difference likely was a consequence of using an imperfect lower 

boundary condition in the one-dimensional case. The simulated water contents obtained with 

HYDRUS-2D were essentially identical to those shown in Fig. 4-2. The coefficient of 

determination, R2, for the 2D calibration was 0.858, being slightly smaller than the value of 

0.877 obtained with the HYDRUS-1D calibration. 

Despite the achieved good fit to the experimental data, we realize that the obtained set of 

parameters may not be unique and that additional experiments would be helpful to reduce 

uncertainty in the parameters. Nevertheless, we accepted these values and used them for our 

simulations for the two-dimensional case. The objective of our study was to obtain an accurate 

description of the experimental field data (water contents, flow rates, concentrations of the well 

water), rather than unique soil hydraulic parameters. This since no attempts were made to 

extrapolate observed data beyond the experimental time period. 

2D simulations of water flow and solute transport

Solute transport simulations were carried out for 4 different values of the longitudinal 

dispersivity, aL (i.e., 5, 15, 25, and 40 cm). We used the same value for all layers, while 

assuming in most cases a ratio of 10 between the longitudinal (aL) and transversal (aT) 

dispersivities. This ratio is well within the range of values (5 to 20) reported in previous studies 

(e.g., Anderson, 1979; Domenico and Schwartz, 1998). Fig. 4-3 compares observed and 

calculated (using Eq. (4-5) solute breakthrough curves (BTCs) of the tracers in the well. Results 

are shown for simulations with and without accounting for a seepage face. Neglecting the 

seepage face boundary caused a delay of a few hours in the arrival of the solute fronts as well as 

of the maximum concentration. The peak concentrations decreased somewhat, except perhaps for 

Cl (Fig 4-3b). Since overall agreement with the experimental data was better when the seepage 

face was included in the simulations, we discuss in what follows only results obtained for 

simulations with the seepage face boundary. 
106

Figure 4-2. Observed (circles) and simulated (lines) soil water contents. 

0 1 2 3 4 5 6 7

Time (days)

0.05

0.10

0.15

0.20

0.25

0.30

0.35

Water content (cm3/cm3)

Irrigation started

0.1 m

0.3 m

0.5 m

0.8 m

1.2 m

1.5 m
107

Table 4-1. Unsaturated soil hydraulic parameters inversely estimated using HYDRUS-1D. 

N Layer

cm

Parameters

 s

†

 r 

, cm-1

n Ks, cm h

-1

1 0-30 0.327 0 0.046 1.62 100

2 30-50 0.351 0.024 0.054 1.46 115

3 50-80 0.260 0 0.054 1.33 113

4 80-150 0.315 0 0.069 1.76 161

5 150-250 0.330 0 0.044 10.00 167

†

Experimentally determined. 
108

Fig. 4-3. Observed and simulated breakthrough curves of the tracers: (a) Br, (b) Cl and (c) 

PFBA. Circles – experimental, solid line – simulated with the seepage face boundary, dashed 

line - simulated without accounting for the seepage face boundary. 

0 1 2 3 4 5 6 7

Time (days after irrigation started)

0

50

100

150

200

250

Br concentration, mg/L

0 1 2 3 4 5 6 7

Time (days after irrigation started)

0

40

80

120

Cl concentration, mg/L

0 1 2 3 4 5 6 7

Time (days after irrigation started)

0

10

20

30

40

PFBA concentration, mg/L

(a)

(b)

(c)
109

The best agreement between observed and simulated BTCs of the tracers in the well was 

obtained when we used a value of 15 cm for aL (Fig. 4-3). R2values were 0.909, 0.899, and 

0.930, and the MIA criterion (Eq. 4-6) 0.883, 0.857 and 0.896, for Br, Cl and PFBA, 

respectively. The model provided a good description of the tracer arrival in the well, but 

overestimated the arrival time of the maximum concentration by around 8.7%. Simulations with 

a dispersivity of 5 cm improved the description of the front part of the solute BTCs (especially 

the initial slope), but caused much lower tails. On the other hand, simulations with a dispersivity 

of 40 cm described the tails quite well, but resulted in much earlier arrival times and lower 

maximum concentrations as compared with observed values. Decreasing the ratio aL/aT from 10 

to 5 did not have an appreciable impact on the simulated BTCs. 

The steeper arrival fronts, the more pronounced asymmetrical shape, the earlier 

concentration peaks, and the longer tails of the observed BTCs as compared with the simulated 

curves (Fig. 4-3) may indicate enhanced preferential flow or an underestimation of the soil 

heterogeneity in the simulations (Kung et al., 2000; Buczko and Gerke, 2006). Some of these 

features probably could be accounted for by invoking a scale-dependent dispersivity in the 

model. The simulations were conducted with strictly horizontal soil horizons since the extent and 

spatial distribution of soil heterogeneity were not well known. The variability in the observed 

concentrations at about the time when the peak concentrations were detected (Fig. 4-3) may have 

been caused by an unsteady pumping rate (the pumping rate variability was fairly low, but 

generally increased with time) and because the pump had to be replaced at some point during the 

experiment (Gish and Kung, 2007). 

The sensitivity of the model to the assumed dissolution times of the tracers at the soil 

surface was tested next. A four-fold decrease or increase in the pulse duration (0.25 or 4 h, 

respectively), and consequently a four times increase or decrease in the surface boundary 

concentration (to preserve the injected tracer masses), were found to produce similar results. We 

additionally tested the effect of having a different thickness of the fifth layer (where most of the 

well screen was located) by moving the lower boundary of the flow domain up to 2.3 m or down 

to 2.7 m below the soil surface (Fig. 4-1). Simulation results showed that this did not affect the 

arrival time of the tracers. The front and back (receding) parts of the BTCs were slightly steeper 

while the maximum concentration in the well was about 10% larger for the thicker fifth layer 

(bottom boundary at 2.7 m) as compared with the 2.3-m deep bottom boundary. 

Water and solute fluxes at the well boundary

Using HYDRUS-2D we were able to estimate the different water and solute fluxes 

through the soil-well boundary. Good agreement (R2 = 0.944, MIA = 0.961) was obtained 

between the cumulative water volume flowing to the well (the sum of the cumulative seepage 

flux and the variable flux at the bottom of the well) and the cumulative pumping volume (Fig. 4-

4) during the experiment. The flux through the seepage face in these simulations started 

approximately 1.2 days after initiating irrigation. The cumulative seepage volume first exceeded 

the cumulative variable flux (groundwater) after 4.7 days, and at the end of the experiment was 

about 20% larger than the variable flux. The time period from 1.5 to 3 days when the seepage 

flux increased mostly, corresponds roughly with the time period when the water content at 

depths below 0.8 m increased as registered with the MCP probes (Fig. 4-2). 
110

Figure 4-4. Cumulative water fluxes to the well. 

0 2 4 6 8

Time (days after irrigation started)

0

20000

40000

60000

80000

Cumulative water flux, L

Actual cumulative pumping

Total water flux to the well

Variable flux

Seepage face flux

Simulated:
111

The estimated thickness of the seepage face at the time of the peak concentrations was 

about 35 cm. Thus, if a seepage zone exists it should have a substantial impact on the solute mass 

flux (Fig. 4-5). Good agreement was obtained between the calculated cumulative fluxes and the 

mass recoveries of Br (R2=0.930, MIA = 0.964) and PFBA (R2 = 0.950, MIA = 0.969), while the 

actual mass recovery of Cl significantly exceeded the simulated value after 4 days. This may 

have been caused by the presence of Cl sources in the unsaturated zone that were not accounted 

for in the model. All tracers showed much larger simulated mass fluxes through the estimated 

seepage face than through the variable boundary at the bottom of the well. Hence, solutes 

appeared to be moving mostly along flow paths close to the water table and then entered the well 

from the saturated region near the water table. The seepage face is part of the saturated zone 

(Fig. 4-6a) where most of the flow is horizontal (Fig. 4-6b) and where the tracers first reach the 

water table (Fig. 4-6c). 

Fig. 4-6 shows that the flow patterns in the capillary fringe just above the phreatic surface 

are also predominantly horizontal, thus shortening solute transport to the well boundary. These 

findings are consistent with both recent laboratory (Silliman et al., 2003) and field observations 

(Abit et al., 2008). Still, calculated first arrival times of the tracers to the well were around 40% 

and 30% earlier (for Br and PFBA, respectively) through the variable flux boundary than through 

the active seepage face, which became active 1.2 days after irrigation started (Fig. 4-4). 

Calculated cumulative mass fluxes through the seepage face at the end of simulation period were 

8, 4 and 11 times those through the saturated zone, for Br, Cl and PFBA, respectively. The 

highest ratio between these fluxes was for PFBA since this tracer was applied 7 hours after 

irrigation was initiated and the Cl was applied. As a result, PFBA arrived at the water table later 

than the other tracers (i.e., at times when the seepage face was developing and the seepage flux 

increased). The smallest ratio between the seepage solute flux and the variable flux was for Cl 

due to its immediate input from the saturated zone having a background concentration of 7.3 

mg/L. Our results are very much in agreement with sand box experimental and modeling results 

by Li et al. (2007) who studied the impact of a seepage face at the unconfined aquifer-lake 

interface. They found that most of the groundwater and pollutants discharged through a narrow 

portion near the top of seepage face. 
112

Figure 4-5. Cumulative solute fluxes of (a) Br, (b) Cl and (c) PFBA to the well. 

0 2 4 6 8

Time (days after irrigation started)

0

1000000

2000000

3000000

4000000

Cumulative Br flux, mg

Br actual mass recovery

Total flux of Br to the well

Variable flux of Br

Seepage face flux of Br

Simulated:

(a)

0 2 4 6 8

Time (days after irrigation started)

0

100000

200000

300000

400000

500000

Cumulative PFBA flux, mg

PFBA actual mass recovery

Total flux of PFBA to the well

Variable flux of PFBA

Seepage face flux of PFBA

Simulated:

(b)

0 2 4 6 8

Time (days after irrigation started)

0

500000

1000000

1500000

2000000

2500000

Cumulative Cl flux, mg

Cl actual mass recovery

Total flux of Cl to the well

Variable flux of Cl

Seepage face flux of Cl

Simulated:

(c)
113

Fig. 4-6. Simulated distributions of (a) pressure head, (b) flow velocity vectors, 

and (c) Br concentration three days after irrigation started. 

Active

Seepage Face

Variable 

Flux

-0.5

1

50

100

150

200

250

0

0.5

1

z, m

z, m

z, m

x, m

x, m

x, m

0

0

0

2.5

2.5

2.5

4

4

4

8

8

8

(a) Pressure head (m)

(b) Water velocity vectors

(c) Br- concentration (mg/L) Well

2

2

2

6

6

6

Active

Seepage Face

Variable 

Flux

Active

Seepage Face

Variable 

Flux

Active

Seepage Face

Variable 

Flux

-0.5

1

50

100

150

200

250

0

0.5

1

z, m

z, m

z, m

x, m

x, m

x, m

0

0

0

2.5

2.5

2.5

4

4

4

8

8

8

(a) Pressure head (m)

(b) Water velocity vectors

(c) Br- concentration (mg/L) Well

2

2

2

6

6

6

Active

Seepage Face

Variable 

Flux

Active

Seepage Face

Variable 

Flux
114

4.2 BASE MODEL FOR THE LATERAL FLOW EXPERIMENT 

4.2.1 MODEL DESCRIPTION

The HYDRUS-3D software (Šimůnek et al., 2007) was used to simulate three-dimensional 

subsurface water flow and solute transport in the lateral flow tracer experiment. 

4.2.1.1 GEOMETRY OF THE SIMULATION DOMAIN AND SOIL MATERIAL DISTRIBUTION

Based on experimental data that included the location of the tracer application plot, 

observation (sampling) wells, the topography of the soil surface and of the low permeability 

bottom (GPR data), we considered a 3D layered domain that extended laterally for 100 m in the x

direction and for 70 m in the y direction. The thickness (z direction) of the domain varied from 

2.15 m to 5.72 m. The domain was larger than the domain used for the preliminary simulations 

(50x30 m, see section 3.2.3.7) to diminish the influence of the imposed constant head boundary 

conditions on flow and transport within the domain. The domain (Fig. 4-7) was composed of 2 

major sub-layers: an upper layer representing soil formations characterized by relatively high 

hydraulic conductivities, and a lower sub-layer composed of materials with predominantly lower

permeabilities. 

The distribution of soil materials with different texture within the domain was set manually 

based on logs obtained during installation of observation wells L1-L12. We used a zonation 

method (Chen et al., 2001, 2004; Hubbard et al., 2003) to assign model parameters within the 

domain. Six soil materials were considered: Sandy Loam (SL), Sandy Clay Loam (SCL), Loam 

(L), Silt Loam (SiltL), Silt Clay Loam (SiltCL) and Clay (C). For the SL two different hydraulic 

conductivities were prescribed: one value for the upper 10 cm soil surface layer (corresponding 

to the first layer of the finite element mesh in the numerical model), whose conductivity was 

lower than the conductivity of the rest of the SL domain as a consequence of Ksat changes due to

soil structural alteration caused by intensive irrigation. 

4.2.1.2 FINITE ELEMENT MESH AND OBSERVATION NODES

The unstructured (triangular prisms) finite element mesh consisted of 54, 180 nodes and 

100, 156 3D elements (Fig. 4-8). The simulation domain was subdivided into 15 layers (12 layers 

in the upper sub-layer and 3 layers in the lower sub-layer). The vertical size of the finite element 

prisms varied depending upon location, with the elements following the surface of the soil 

surface and the surface of the lower sub-layer. In the upper layer the vertical size of the prisms 

was 5 cm near the surface, and 15-20 cm near the bottom. In the lower sub-layer the vertical size 

of the prism varied from 0.3 to 1.5 m (Fig. 4-8, top). The horizontal mesh size decreased from 5 

m near the downgradient domain boundary to 0.3 m close to the irrigation plot where most of the 

transport processes were expected (Fig. 4-8, bottom). Using this geometry and finite element 

mesh, a 125-day long simulation generally took between 36 to 48 h with a DELL PC Optiplex 

755, Intel CoreTM2 DUO CPU E8400 @3.00 GHz. Further refinement of the finite element mesh 

required longer simulation times. 

Twenty two observation nodes (Fig. 4-9) were assigned to record the simulated

breakthrough curves at specific sampling locations in observation wells L1 through L12. 

Although groundwater was sampled at three depths in all observation wells, only two 

observation nodes were set for wells L5 and L6 and only one for wells L7 through L12. This

because the grid was too coarse in the lower sub-layer. 
115

a)

b)

c)

Figure 4-7. Simulation domain used for solving the flow and transport problem with the 

HYDRUS-3D code: a) whole domain; b) upper sub-layer; c) lower sub-layer. 

Sandy Loam

Sandy Loam

Sandy Clay Loam

Loam

Silt Loam

Silt Clay Loam

Clay

Sandy Loam

Sandy Loam

Sandy Clay Loam

Loam

Silt Loam

Silt Clay Loam

Clay

Sandy Loam

Sandy Loam

Sandy Clay Loam

Loam

Silt Loam

Silt Clay Loam

Clay
116

Figure 4-8. Finite element mesh used for the HYDRUS-3D simulations; top –side view, bottom –

bird view. 
117

Figure 4-9. Locations of the observation nodes. 

L1

L2

L3

L4

L5 L6

L7

L8

L9

L10

L11

L12

L1

L2

L3

L4

L5 L6

L7

L8

L9

L10

L11

L12
118

4.2.1.3 INITIAL AND BOUNDARY CONDITIONS

As initial condition for the water flow simulations we used an steady-state pressure head 

distribution. This distribution was obtained by running the flow problem with constant pressure 

heads along the lateral boundaries (as described below) and zero fluxes along the remaining 

boundaries of the domain. Simulations ran for about 200 days of elapsed time until steady state 

flow conditions were reached. The initial Cldistribution varied from 10 to 30 mg L-1depending 

upon location as measured in observation wells prior to the experiment. 

The boundary surfaces with the different boundary conditions are shown in Fig. 4-10). 

Spatially variable, but constant in time pressure head profiles were specified along the lateral 

boundaries. Atmospheric boundary conditions were used at the soil surface. These conditions

simulated a variable flux due to irrigation, precipitation and evapotranspiration within the 

irrigated plot area, and a variable flux due to precipitation and evapotranspiration along the 

remaining part of the soil surface. Along the bottom of the domain we used a zero flux boundary

condition. The imposed flow rate during each irrigation event was decreased by 28% to account 

for the amount of water that was lost to overland flow that was collected, and as such had not 

interacted with the subsurface flow and transport processes. 

The distributions of the pressure head along the lateral boundaries were obtained from 

pressure head values observed during 2006-2007 (Fig. 4-11). Data from wells located in the 

vicinity and within the simulation domain were used for this purpose. Interpolation was done 

with the SURFER software. We note that the distributions obtained in this way were very similar 

for different periods of time. 

A third type (Cauchy) boundary condition was used along soil surface to simulate solute 

transport. Cl concentrations of the water during the tracer application was 4940 mg/l. Cl 

concentrations of the rainwater and the irrigation water were 8 ppm, while Cl concentrations of 

groundwater along the lateral boundaries were set to the average observed value of 15 ppm. 

Table 4-2 presents hydraulic parameters for different soil materials accepted as initial values 

for the simulations. These parameters (except for clay) were obtained as an average of those

determined with the ROSETTA software using data for soil texture and bulk density. The initial 

value of the longitudinal dispersivity was 0.5 m, while the ratio of longitudinal to transversal 

dispersivity was assumed to be 5 in all simulations. 

4.2.2 MODEL CALIBRATION AND SIMULATIONS

The HYDRUS-3D software in its current version does not have an option for automatic 

model calibration. Such an optimization would take an unreasonable amount of time for the fully 

3D variably-saturated field scale problem. Therefore, model calibration was performed using a

trial-and-error method. Our approach involved the sequential fitting of flow and transport models 

to available data. At the first step we estimated the velocity field by varying the saturated 

hydraulic conductivities of the various soil materials. The second step was the calibration of the 

transport parameters (dispersivities for the conservative tracer) through a series of trial-end-error 

runs. Much of our attention focused on observation wells L5, L6, and L7 where a well-defined 

breakthrough curve (BTC) was observed, and where both the arrival front and receding (tailing)

part of the breakthrough curve had been recorded. 

We started simulations with the hydraulic parameter values listed in Table 4-2. Simulated 

and observed breakthrough curves for the wells L1 through L9 are compared in Fig. 4-12. We 

note that the simulated BTCs for L5 through L7 exhibited much later arrival of the tracer than 
119

Figure 4-10. Boundary conditions used for the HYDRUS-3D simulations (refer to text for 

details). 
120

Table 4-2. Initial values of the unsaturated soil hydraulic parameters used in the simulation. 

N Material

Cm

Parameters

 s  r 

, m-1

n Ks, m d-1

1 Sandy Loam 0.387 0.053 2.57 1.40 0.26

2 Sandy Clay Loam 0.393 0.066 2.31 1.35 0.13

3 Loam 0.412 0.067 1.20 1.47 0.11

4 Silt Loam 0.450 0.080 0.65 1.56 0.12

5 Silt Clay Loam 0.466 0.087 0.78 1.52 0.12

6 Clay 0.410 0.095 1.90 1.31 0.01
121

Figure 4-11. Location of observation wells (blue dots) in the vicinity of simulation domain (red 

rectangle) and hydraulic head distributions at different times in 2006-2007. 

w02

w04

w06

w08

w10

w15w12

w18

w21

w33

w36

w39

w42

w43

w44

w47

w50

w52

W11

413450 413500 413550 413600

151300

151350

151400

151450

3/15/2006 3/31/2006 4/15/2006

4/30/2006 5/15/2006 5/31/2006

6/15/2006 6/30/2006 7/15/2006

7/31/2006 8/15/2006 8/31/2006

9/15/2006 3/15/2007 3/31/2007
122

Figure 4-12. Simulated (lines) and observed (circles) chloride breakthrough curves. Simulation

results are for the initial set of parameters listed in Table 4-2. L1 through L9 denote observation 

wells 1-9, ○, ○, and ○ are color codes for L5 through L9 at the depths of 1.65, 1.35 and 1.05 m, 

respectively; ○ is the color code for the depth of 1.1 m in L1 through L4.

80 100 120 140 160 180 200 220

Time (DOY)

0

20

40

60

80

100

Cl concentration (mg/l)

L5

L6

L7

L8

L9

80 100 120 140 160 180 200 220

Time (DOY)

0

20

40

60

80

100

Cl concentration (mg/l)

80 100 120 140 160 180 200 220

Time (DOY)

0

20

40

60

80

100

Cl concentration (mg/l)

80 100 120 140 160 180 200 220

Time (DOY)

0

20

40

60

80

100

Cl concentration (mg/l)

80 100 120 140 160 180 200 220

Time (DOY)

0

20

40

60

80

100

Cl concentration (mg/l)

Ln-1

Ln-2

Ln-3

Computed Observed

80 100 120 140 160 180 200 220

Time (DOY)

1

10

100

1000

Cl concentration (mg/l)

80 100 120 140 160 180 200 220

Time (DOY)

10

100

1000

Cl concentration (mg/l)

80 100 120 140 160 180 200 220

Time (DOY)

1

10

100

1000

Cl concentration (mg/l)

80 100 120 140 160 180 200 220

Time (DOY)

1

10

100

1000

Cl concentration (mg/l)

L1

L2

L3

L4

Ln-1

Computed Observed
123

was observed. We assumed that the reason for this was our use of too low hydraulic 

conductivities of the sandy loam, sandy clay loam and loam materials composing the upper sublayer of the domain. Hence for the next run we increased the saturated hydraulic conductivity 

(Ksat) values to 2.0, 0.4 and 0.3 m d

-1

for the sandy loam, sandy clay loam and loam soils, 

respectively. We further decreased the longitudinal dispersivity (aL) of these materials from 0.5 

to 0.2 m, while the ratio of longitudinal to transversal dispersivity was kept at aL/ aT=5. The 

agreement between the simulated and observed BTCs for wells L1through L4 became worse, 

whereas for L5 through L7 we noted much earlier arrival times of the simulated BTC fronts as 

compared to the observations. Wells L8-L9 now showed only slight higher concentration. The 

slope of the simulated BTC increased compared to the case of aL=0.5 m. Hence more parameter 

adjustments were clearly needed. 

The trial-and-error procedure continued for two months until a better fit for L5 through L8 

was obtained. During these runs we also slightly moved the boundaries between the SL, SCL and 

L soil layers to further improve the fit. The resulting values of Ksat were 1.0, 0.6 and 0.2 m d

-1

for 

the SL, SCL and L soils, respectively. Results of the simulations for wells L1 through L9 are 

presented in Fig. 4-13 and 4-14 for the scenarios with aL=0.5 m and aL=0.15 m, respectively. The 

agreement in terms of the magnitude of the concentrations was reasonable. However, the BTC 

shape was not simulated well. We note that the agreement is better for wells L1-L4 when aL=0.5 

m compared to a dispersivity of 0.15 m, while the opposite is true for wells L5-L8. The receding 

part of the BTCs in L5 through L7 was not simulated. It seemed that the width of the simulated 

plume was larger than the actual plume. A quantitative comparison between the latter two 

scenarios was performed using the coefficient determination (R2) and the Modified Index of 

Agreement (MIA) (Table 4-3). Calculated values of these criteria suggest a fair agreement for 

wells L5, L6, and L7 as well as for L2 and L3 at their lowest sampling depth. 

Fig. 4-15 shows the simulated and observed BTCs of wells L10-L12 for the scenarios of 

aL=0.5 m and aL=0.15 m. The results for these two cases are practically identical. The model was 

not able to simulate the observed oscillations in the measured concentrations at early times and 

the increase in concentration towards the end of the experiment. According to the model 

predictions, the plume did not reach wells L10, L11, and L12 by the end of simulation period. 

Calculated distributions of the pressure head along the lower (z=0) boundary (which 

corresponded to an altitude of 35 m above sea) at different times is shown in Fig. 4-16. A 

groundwater mound was found to develop under the irrigation plot, causing water to spread in all 

direction. This can be observed in Fig. 4-17 which shows a distribution of the flow velocity at a 

depth of approximately 1 m. At early times of the experiment between DOY (days of year) 90

and 110) when the groundwater level in the eastern part of the simulation domain was lower than 

this depth of1 m, preferential flow path may have developed due to particular topography of the 

restrictive bottom and the distribution of hydraulic properties (Fig. 4-17). Later on (after DOY 

130), the flow regime became quasi steady-state and changes were mainly due to variations in 

precipitation with time. 

Fig. 4-18, 4-19, and 4-20 show the simulated tracer plume at different times. The applied 

tracer initially was pushed to deep soil layers by the incoming fresh water. After some period of 

time, the plume had a bagel-like shape with concentration in the center of the plume being lower 

than at the peripheral part (except for concentrations at the lowest depth of 1.4 m). The migration 

of the plume and its expansion in different directions was controlled by the spatial distribution of 

the hydraulic properties. By the end of simulation period only the advancing front plume had 
124

reached the observation wells L5-L7. This explains why we were not able to simulate the 

residing part of BTCs in those two wells. 

To assess the effect of the capillary fringe on tracer transport, we performed a simulation 

with the parameter 



in the van Genuchten-Mualem equation (3-11) set at -3. Changing this 

parameter from 0.5 (the standard value) to -3 leads to higher unsaturated hydraulic conductivity, 

and presumably more flow and, consequently, transport in the capillary fringe. Our simulations

indicated practically no difference in the BTCs for these two values of 

 . The reasons are as 

follows: 1) after application, the tracer was flushed to the deeper horizons by the infiltrated fresh 

water (i.e., transport occurred mainly in groundwater); 2) the domain in the vicinity of the plot 

was close to saturation (i.e., practically no capillary fringe had developed there). 

Overall, the calibrated model reproduced the most important features of the lateral flow 

experiment. The model gave satisfactory levels of peak concentrations and was able to capture 

arrival times. However, some qualitative differences between simulated and measured 

concentrations were observed. Because experimentation with the HYDRUS 3D was extremely 

time-consuming, model abstractions were undertaken as shown in Section 5.2.1 to gain more 

insight into the effect of subsurface media properties on transport in the soils of this experiment. 
125

Table 4-3. Values of the coefficient of determination (R2) and the Modified Index of Agreement 

(MIA) for two simulation scenarios using aL=0.5 m and aL=0.15 m

BoreholeObs. 

Node

R

2 MIA R2 MIA

aL=0.5 m aL=0.15 m

L1

3 0.198 0.060 0.165 0.032

2 0.042 0.338 0.001 0.221

1 0.150 0.433 0.096 0.193

L2

3 0.888 0.431 0.349 0.253

2 - - - -

1 0.532 0.730 0.912 0.635

L3

3 0.130 0.440 0.151 0.475

2 0.558 0.527 0.730 0.748

1 0.573 0.574 0.003 0.393

L4

3 0.301 0.028 0.256 0.006

2 0.054 0.081 0.117 0.035

1 0.000 0.100 0.038 0.052

L5

3 - - - -

2 0.874 0.703 0.886 0.754

1 0.842 0.798 0.816 0.853

L6

3 0.505 0.583 0.698 0.742

2 0.700 0.693 0.494 0.615

1 - - - -

L7

3 0.821 0.708 0.833 0.803

2 - - - -

1 - - - -

L8

3 0.011 0.189 0.071 0.214

2 - - - -

1 - - - -

L9

3 0.01 0.327 0.007 0.347

2 - - - -

1 - - - -

L10

3 - - - -

2 0.126 0.379 0.088 0.411

1 - - - -

L11

3 - - - -

2 0.078 0.276 0.078 0.272

1 - - - -

L12

3 - - - -

2 0.009 0.320 0.011 0.319

1 - - - -
126

Figure 4-13. Simulated (lines) and observed (circles) chloride breakthrough curves. Simulations 

are for Ks values of 1.0, 0.6 and 0.2 m d

-1

for SL, SCL and L, respectively; aL=0.5 m, aL/ aT=5.

Symbols are the same as in Fig. 4-12. 

80 100 120 140 160 180 200 220

Time (DOY)

0

20

40

60

80

100

Cl concentration (mg/l)

L5

L6

L7

L8

L9

80 100 120 140 160 180 200 220

Time (DOY)

0

20

40

60

80

100

Cl concentration (mg/l)

80 100 120 140 160 180 200 220

Time (DOY)

0

20

40

60

80

100

Cl concentration (mg/l)

80 100 120 140 160 180 200 220

Time (DOY)

0

20

40

60

80

100

Cl concentration (mg/l)

80 100 120 140 160 180 200 220

Time (DOY)

0

20

40

60

80

100

Cl concentration (mg/l)

Ln-1

Ln-2

Ln-3

Computed Observed

80 100 120 140 160 180 200 220

Time (DOY)

1

10

100

1000

Cl concentration (mg/l)

80 100 120 140 160 180 200 220

Time (DOY)

1

10

100

1000

Cl concentration (mg/l)

80 100 120 140 160 180 200 220

Time (DOY)

1

10

100

1000

Cl concentration (mg/l)

80 100 120 140 160 180 200 220

Time (DOY)

1

10

100

1000

Cl concentration (mg/l)

L1

L2

L3

L4

Ln-1

Computed Observed
127

Figure 4-14. Simulated (lines) and observed (circles) chloride breakthrough curves. Simulations 

are for Ks values of 1.0, 0.6 and 0.2 m d

-1

for SL, SCL and L, respectively; aL=0.15 m, aL/ aT=5.

Symbols are the same as in Fig. 4-12. 

80 100 120 140 160 180 200 220

Time (DOY)

0

20

40

60

80

100

Cl concentration (mg/l)

L5

L6

L7

L8

L9

80 100 120 140 160 180 200 220

Time (DOY)

0

20

40

60

80

100

Cl concentration (mg/l)

80 100 120 140 160 180 200 220

Time (DOY)

0

20

40

60

80

100

Cl concentration (mg/l)

80 100 120 140 160 180 200 220

Time (DOY)

0

20

40

60

80

100

Cl concentration (mg/l)

80 100 120 140 160 180 200 220

Time (DOY)

0

20

40

60

80

100

Cl concentration (mg/l)

Ln-1

Ln-2

Ln-3

Computed Observed

80 100 120 140 160 180 200 220

Time (DOY)

1

10

100

1000

Cl concentration (mg/l)

80 100 120 140 160 180 200 220

Time (DOY)

1

10

100

1000

Cl concentration (mg/l)

80 100 120 140 160 180 200 220

Time (DOY)

1

10

100

1000

Cl concentration (mg/l)

80 100 120 140 160 180 200 220

Time (DOY)

1

10

100

1000

Cl concentration (mg/l)

L1

L2

L3

L4

Ln-1

Computed Observed
128

Figure 4-15. Simulated (lines) and observed (circles) chloride breakthrough curves. Simulations 

for for Ks values of 1.0, 0.6 and 0.2 m d

-1

for SL, SCL and L, respectively; a) aL=0.5 m and b) 

aL=0.15 m. Symbols are the same as in Fig. 4-12. 
129

Figure 4-16. Simulated distributions of the pressure head at the bottom of the simulated flow 

domain (z=0), corresponding to an altitude of 35 m above sea level); DOY is the day of the year. 
130

Figure 4-17. Simulated Darcy velocity vectors at a depth of around 1 m below the soil surface; 

DOY is the day of year. 
131

Figure 4-18. Simulated distribution of Cl concentration at the depth of 0.5 m below the surface; 

DOY is the day of year, pink dots represent location of observation wells.
132

Figure 4-19. Simulated distribution of Cl concentration at a depth of 1 m below the surface; 

DOY is the day of year, pink dots represent the locations of the observation wells. 
133

Figure 4-20. Simulated distribution of Cl concentration at a depth of 1.4 m below the surface; 

DOY is the day of year, pink dots represent the location of the observation wells. 
134
135

5 MODEL ABSTRACTION APPLICATIONS

5.1 FLUX MEASUREMENT EXPERIMENT

5.1.1 ABSTRACTION BY REDUCING THE DIMENSION OF THE FLOW DOMAIN

A 1D simulation of water flow and Br transport in the unsaturated zone was carried out to 

assess the effect of reducing the dimension of the flow domain on tracer transport to the well. We 

calculated the breakthrough curve (BTC) of Br at a depth of 1.68 m, which corresponds to the 

initial groundwater level and as such could be considered a well (a sink) in the 1D 

approximation. The simulations were performed with two transport models: 1) a 1D equilibrium 

model; and 2) a dual-porosity (mobile-immobile water) transport model assuming physical nonequilibrium. In both cases the longitudinal dispersivity (aL) was fixed at 15 cm, while the 

immobile water content (θm) for the nonequilibrium model was assumed to be 0.09 (fitted such 

that the simulated and observed peak concentration arrival times at the well were the same). 

Results are presented in Fig. 5-1. The equilibrium transport model exhibited relatively late 

arrival of both the BTC front and the maximum concentration at the groundwater level. The nonequilibrium model, which simulates preferential flow, correctly predicted the arrival of the 

maximum concentration; however, the simulated BTC front arrived much earlier than the 

observed front. Thus, we can conclude that this abstraction would lead to the wrong conclusion 

about the existence of preferential flow in the soil, and that the arrival of the solute at the well 

may well have been controlled by lateral (multi-dimensional) flow in the subsurface and the 

presence of a seepage face. 

5.1.2 ABSTRACTION BY USING AN APPROXIMATE ANALYTICAL FLOW MODEL

Narrowing the purpose of a modeling project sometimes allows one to considerably 

simplify the model, including making a change in the key output variables. We consider here the 

case where modeling may be used to estimate the radius of the tracer application area beyond 

which no losses would occur because of lateral subsurface flow away from the well. The 

recovery of an applied tracer is an important factor in a field tracer experiment to assess the 

solute mass balance. 

In a radially convergent saturated flow field the recovery depends on the tracer application 

radius and the capture well zone. To avoid losses of the tracer with lateral flow, the application 

radius must be less than the radius of the water table divide where the radial flow velocity is zero 

(Fig. 5-2). The radius of the water table divide can be estimated in an approximate manner from 

a solution of the Boussinesq equation for steady-state radial unconfined flow towards a well, 

subject to Dirichlet boundary conditions as follows

1

( )

s

h

K rh iH a r

r r r

        

   

, r0≤a≤R (5-1)

0 0

r  r : h  h

(5-2)

R h hRr  : 

(5-3)

where h is the water table height above the impermeable layer (L), r is the radial coordinate (L),

Ksat is the hydraulic conductivity of the aquifer, i is the recharge rate (L/T), 

H(r)

is the 

Heaviside step function, a is the radius of the infiltration area (r0≤a≤R), r0 and R are the radii of 

the well and the outer boundary (L), respectively, and h0 and hR are the water table heights at 

r=r0 and r=R, respectively. 
136

Figure 5-1. Breakthrough curves of Br observed in the pumping well (open circles) and 

simulated at the groundwater level with two 1D models; solid line - equilibrium model, dashed 

line – non-equilibrium model. 

0 2 4 6 8

Time, day

0

200

400

600

Br concentration, mg/l
137

Figure 5-2. Schematic of unconfined radial flow with infiltration. 

r

0

R

Infiltration, i

a

hR

h

0

h

r

r

*

Q

Wel

l
138

Figure 5-3. Well capture radius (r*) and pumping discharge (Qr0) as a function of the saturated 

hydraulic conductivity (Ksat) for a given set of parameters (r0=2.5 cm, R=3000 cm, a=2000 cm, 

i=0.41 cm/h, h0=90 cm, hR=82 cm). 

0 40 80 120 160

K (cm/h)

0

200

400

600

800

r

* (cm)

0

0.04

0.08

0.12

0.16

Qr

0

(L/s)

r

*

Qr

0
139

Assuming a constant hydraulic conductivity, Ksat, and integrating Eq. (5-1), we obtained an 

analytical expression for the radial water flux, Q (LT-3), towards the well as a function of the 

radial position, r, as follows 







 

r

h

Q 2Ksatrh  





















































     

0

2

2

0

2

2

0

2 2 2

ln ln

2

( ) ( )

r

R

a

R

a

a r

ir H a r ia H r a h h K i  R sat

 (5-4)

For the limiting case when a=R (application radius equals the radius of the outer boundary), this 

solution coincides with an equation derived previously by Aravin and Numerov (1965). 

An equation for the radius of the water table divide (r

*

) may be obtained by solving the 

equation for Q=0 to obtain for the case when r

*

<a

 

2 2

* 2 2 2 0

0

0

ln ln

2

sat

R

K a r R R r h h a

i a r

    

           

. (5-5)

The discharge rate from the pumping well is now given by 

 

0 0 0 0

2 2

2 2 2 2 0

0 0

0

2

ln ln

2

r sat r r

R s

h

Q r K h

r

a r R R ir h h K i a

a r









 



        

                  

(5-6)

Results of simulations with the HYDRUS-2D code indicated that the water table divide was 

located at about 660 cm from the well. An approximate estimate of the well capture radius can be 

obtained also with Eq. (5-5), which assumes steady-state flow conditions. Such conditions likely 

occurred during days 3 to 5 of the experiment when the pumping rate varied very little around a 

mean value of 0.12 L/s. The assumption of steady-state flow was further confirmed by the 

HYDRUS-2D simulations. Using Eqs. (5-5) and (5-6), we estimated the well capture radius (r*) 

of our field tracer experiment to be 580 cm, and the pumping discharge rate (Qr0) to be 0.12 L/s 

for our field experiment. For the calculations we used r0=2.5 cm, R=3000 cm, a=2000 cm, K=52 

cm/h, i=0.41 cm/h, h0=90 cm, and hR=82 cm. The values of both r* and Qr0 decreased with 

increasing values of the hydraulic conductivity (Fig. 5-3). 

The analytical solutions for r* (Eq. 5-5) and Qr0 (Eq. 5-6) were obtained with several 

simplifying assumptions such as having steady flow, a homogeneous aquifer, and no seepage 

face. This caused Eq. (5-5) to underestimate the well capture radius as compare to the more 

comprehensive HYDRUS-2D variably-saturated flow simulations. Nevertheless, this example 

demonstrates that for practical purposes the analytical solution can provide a useful first 

approximation of system parameters needed for the design of these type of tracer experiments. 

5.2 LATERAL FLOW EXPERIMENT

5.2.1 ABSTRACTION BY IGNORING VADOSE ZONE 

5.2.1.1 2D FLOW AND TRANSPORT IN GROUNDWATER

A first abstraction step considered here is a reduction in the dimension of the problem from 

three to two dimensions. Specifically, the fully 3D saturated-unsaturated flow and transport 
140

problem as described in the Section 4.2 was replaced by a 2D problem in which flow and 

transport occur only in groundwater. The effect of the vadose zone on retention and transport 

hence was ignored in this abstraction. The MODFLOW and the MT3D models were used 

consecutively for the approximate flow and solute transport simulations, respectively, while data 

preprocessing and postprocessing were implemented using the GMS software. 

For the simulations we used a rectangular flow domain of 10,000 x 7,000 cm. The lower 

boundary of the simulated domain was a horizontal plane at an elevation of 35 m. The upper 

boundary was the soil surface with elevations as shown in Fig. 3-36. The domain used previously 

for the HYDRUS-3D simulations was discretized laterally using a telescopic refinement grid 

with the center coinciding with the center of the irrigated area. The base size of the finite 

elements was 50 cm, and increased with a bias of 1.05 to the maximum size of 500 cm as the 

distance to the irrigated area increased. Each one-layer spatial grid had 4940 nodes. 

The automated interpolation and material distribution in GMS created a stratigraphy that 

was substantially different from the stratigraphy used in the base 3D model using HYDRUS 3D. 

Therefore a special effort had to be made to obtain a material distribution that was as close as 

possible to the distribution used in the HYDRUS 3D base model. The procedure consisted of the 

following steps:

- the lateral material distribution was imaged for each of 14 layers of the HYDRUS 3D grid;

- a 3D grid was built in GMS that had the same geometry as the layers in HYDRUS 3D;

- the “Boreholes” module of GMS was used to introduce 87 boreholes (Fig. 5-4, top left);

- vertical coordinates of all 14 layers were defined as in the HYDRUS 3D base model;

- a table of material distributions was built for each borehole (Fig. 5-4, top right);

- locations of material boundaries were defined using the “Auto assign horizons” option of 

the “:Boreholes” module;

- The MODFLOW HUF (Hydrological Unit Flow) module was used to define hydraulic 

properties of each cell of the 3D grid, while the “horizons to HUF” option was used to 

interpolate the borehole data to the grid nodes (inverse distance weighting was used for 

this interpolation). 

The above procedure resulted in 14 hydrologic units within the simulation domain. 

Examples of material distributions along various domain cross-sections are shown in Fig. 5-4, 

bottom. 

Dirichlet boundary conditions were defined along the vertical boundaries of the simulation 

domain. The initial distribution of groundwater levels in the domain was obtained by fitting the 

solution of the stationary flow problem to initial groundwater levels in the observation wells. 

The fitting was accomplished by varying the groundwater recharge separately within the 

irrigation area and outside this area. The model performance indicators obtained for this solution 

were: a Root Mean Square Error of 26 cm, a Mean Absolute Error of 21 cm and a Mean Error of 

3 cm. 

Groundwater recharge during the experiment was computed from a surface water balance 

using available rainfall data, evapotranspiration rates calculated with the Penman-Monteith 

equation, measured runoff data, and the applied irrigations and their schedule. 

The following setup was adopted for the numerical solution procedure. All cells were 

convertible, and the option “prevent cell drying and assign bottom elevation to dry cells” was 

used. The simulated experimental period of 112 days was divided into 481 stress period of 

varying durations depending upon the rainfall and irrigation rates. A minimum time step of 0.1 d 
141

was used. This time step was not allowed to exceed any of the stress period durations. The 

PCG2 (Pre-condition Conjunctive Gradient module with Modified Incomplete Cholesky matrix 

preconditioning methods) module was used as the matrix solver. As convergence criteria we

used a head change of 1 cm and a residual of 1 m3. Cells along the irrigated area periodically 

flooded, which caused some oscillations during the numerical solutions. Using the ”Cell wetting 

parameter” module did not improve the convergence (i.e., less oscillations or a computationally 

more efficient solution). The overall global mass balance error for the cumulative volume was a 

modest 0.47%, which further caused up to believe that the solution was reasonable. 

The MODFLOW calibration was carried out using the PEST software package. The 

MODFLOW solution for this purpose was fitted to the observed groundwater depths. Estimated 

hydraulic conductivity and specific yield values are shown in Fig. 5-4. The model performance 

indicators with the calibrated parameters were: a Root Mean Square Error of 44 cm, a Mean 

Absolute Error of 32cm, and a Mean Error of 3 cm. The accuracy the transient flow calibration 

was lower than the accuracy of initial ground water calibration. A likely reason for this is the 

difficulty of handling fully saturated soil layers in MODFLOW. The Fig. 5-5 illustrates this with 

a comparison of simulated and measured groundwater levels during a period with complete

saturation. Simulated groundwater values appear to be higher than 1 m above the soil surface, 

which caused large model errors. 

The MODFLOW calibration was evaluated using criteria outlined by Reilly and Hardbaugh 

(2004). The conceptual model of the system under investigation corresponded to our preliminary 

survey and monitoring data, and hence seemed to be reasonable. The mathematical 

representation of the boundaries were also reasonable since the flow domain boundaries were 

relatively far from the irrigation area, as was confirmed by preliminary simulations (data not 

shown). Simulated head and flow distribution were found to mimic important aspects of the flow 

system, such as magnitude and direction of the head contours. Except for periods of full soil 

profile saturation, quantitative measures of head differences between the simulated and observed 

values seemed acceptable in view of the objectives of our study. Noting that MODFLOW was 

not fully capable of simulating flow in the system under study, we nevertheless, proceeded with 

simulating transport in the lateral flow experiment using the MT3D model. The average of 

concentrations at three observation depths was used for our comparisons of simulated and 

measured values. 

The first set of simulations was carried out assuming the same values of the dispersivity and the 

effective porosity for all materials. An example of the type of results we obtained is shown in 

Fig. 5-6. The field data and simulations indicate that tracer concentrations at different wells 

reflected different subsurface transport conditions. For example, wells 5 and 7 seem to receive 

the tracer from a subsurface channel having the lowest dispersivity and the lowest effective 

porosity compared with other wells. Well 6 reflected transport conditions with a low effective 

porosity but a relatively high dispersivity. Wells 8 and 9, on the other hand, are most probably 

within a subdomain having a relatively high effective porosity. To confirm these conjectures, the 

simulation domain was separated into three subdomains, each one having its unique transport 

parameters as shown in Fig. 5-7. Simulated results using this approach provided a better match 

with the well tracer data.

Overall, the abstraction of the full 3D model to a 2D groundwater flow and transport model 

provided important insights into the subsurface transport properties. Values of the effective 

porosity (ne) generally increased with clay content (e.g., Fig. 5-4, top right). However, the values 

were substantially smaller than the porosity of the soil materials. This indicates that field scale 
142

Figure 5-4. Conversion of the subsurface material distributions from the HYDRUS 3D model 

grid to the MODFLOW model grid. Top left – locations of artificial boreholes with properties 

defined in HYDRUS3D, top right – material distribution in artificial boreholes, bottom – crosssections of material distributions in MODFLOW.
143

Figure 5-5. Measured and simulated groundwater levels during a period of full soil saturation 

with water.
144

Figure 5-6. Measured ( ) and simulated tracer breakthrough in observation wells with the same 

values of dispersivity aL and effective porosity ne across the simulated transport domain; 

aL=1 cm, ne=0.2 cm3cm-3; aL =1 cm, ne=0.3 cm3cm-3; aL =10 cm, ne=0.2 cm3cm-3

0

50

100

Cl concentration (ppm)

0

50

0 40 80

0

50

0 40 80

Observation day

0 40 80 0 40 80 0 40 80

Well 5 Well 6 Well 7 Well 8 Well 9
145

Figure 5-7. Tracer transport simulations with three subdomains (top) having different parameters 

for the dispersivity aL (cm) and effective porosity ne. Measured ( ) and simulated ( ) Cl 

breakthrough curves are shown for five different observation wells (bottom). 
146

transport at the study site occurred preferentially and that a substantial part of the soil profile 

conducted very little water and solute. The field heterogeneity as described in Sections 3.2.3.3, 

3.2.3.4, 3.2.3.5, and 3.2.3.8 created the essential prerequisites for such preferential transport to 

occur. 

5.2.1.2 1D TRANSPORT IN GROUNDWATER

Simulations of 1D transport in groundwater were carried outusing the windows-based 

STANMOD software package (Šimůnek et al., 1999). Specifically, we solved the inverse 

problem to determine transport parameters using the CXTFIT code, which is a part of the 

STANMOD software. As input for the simulations we used the observed breakthrough curves at 

wells L1 through L12. The conceptual scheme is presented in Fig. 5-8. We started simulations at 

the time the tracer was applied to the soil surface. Subseqent leaching to groundwater by fresh 

irrigation and rain water created a toroid- (or donut-) like concentration distribution in the 

horizontal plane around the pumping well. For the 1D transport problem we assumed a stepwise 

initial distribution along the flow direction as shown in Fig. 5-8. 

The maximum concentration C

*

of the initial step function resulting from leaching of the 

applied tracer and subsequent mixing with groundwater was estimated from the observed 

concentrations in wells L3 and L4 at the edge of the tracer application area. A least-squares 

optimization with CXTIFT allowed us to estimate the flow velocity (v) and the dispersion 

coefficient (D) from the breakthrough curves. In addition, to obtain a better fit between the 

observed and simulated BTCs, the length of the concentration step 

x

and concentration C*

(Fig. 5-9) were adjusted by trial and error. Despite the fact that this affected the uniqueness of 

the optimization, we used this procedure to solve the inverse problem. The estimated parameters 

are presented in Table 5-2, while the observed and fitted BTCs are shown in Fig. 5-9. 

Fair agreement between simulated and observed concentrations was obtained for wells 

L5 through L7, whereas a worse fit was obtained for wells L9 through L12 because of 

oscillations versus time. These oscillations were especially pronounced for L8. We believe that 

this behavior is a result of fast vertical preferential flow during infiltration following highintensity precipitation events, which cannot be modeled by CXTFIT. 

The groundwater flow velocity between the tracer application plot and first line of the wells 

(L5 through L9) was found to vary from 0.030 to 0.077 m d

-1

. Dispersivity (aL) values were in 

the range of 0.30-1.16 m, which are reasonable values for a field-scale tracer simulation in which 

a highly heterogeneous medium is represented by an equivalent homogeneous porous medium. 

Estimated flow velocities obtained for the second line of wells (L10, L1, and L12) were larger 

than those of L5 though L9, whereas the dispersivities had the same order of magnitude.

A noticeable increase in Clconcentration was observed at the deepest sampling points 

(1.65 m depth) of wells L10 through L12 of the second row of observation wells, starting at 

approximately day 60, while the concentrations in wells L5, L6, L7 and L9 of the first row of 

wells started to increase somewhere between 40 and 60 days after the experiment started. If we 

assume that the increase of concentrations of wells L10 through L12 was associated with the 

same source as for L5, L6, and L9, then the obtained results suggest a much higher flow velocity 

between the first and the second rows of the wells. This could be due to preferential flow through 

a thin conductive layer in the lower soil horizons. Another possible cause could be the presence 

some unknown source of high salinity in the study area, something that may need further testing. 
147

Figure 5-8. A conceptual scheme for simulating 1D transport in groundwater during 

 tracer transport experiment. 

Initial 

concentration

x

L1

L2

L3

L4

L5

L6

L7

L8

L9

L10

L11

L12

C*

Flow

Initial 

concentration

x

L1

L2

L3

L4

L5

L6

L7

L8

L9

L10

L11

L12

C*

Flow
148

Figure 5-9. Observed (red circles) and fitted (blue lines) breakthrough curves in 

wells 1 through 12. 

0

10

20

30

40

50

60

70

80

0 20 40 60 80 100 120 140 Time [days]

Resident Concentration L5

5

10

15

20

25

30

35

40

45

0 20 40 60 80 100 120 140 Time [days]

Resident Concentration L6

10

20

30

40

50

60

70

0 20 40 60 80 100 120 Time [days]

Resident Concentration

L7

5

10

15

20

25

30

35

40

45

0 20 40 60 80 100 120 140 Time [days]

Resident Concentration

L8

0

10

20

30

40

50

0 20 40 60 80 100 120 140 Time [days]

Resident Concentration

L9

0

10

20

30

40

50

0 20 40 60 80 100 120 140 Time [days]

Resident Concentration

L10

0

10

20

30

40

50

0 20 40 60 80 100 120 Time [days]

Resident Concentration

L11

0

5

10

15

20

25

30

35

0 20 40 60 80 100 120 140 Time [days]

Resident Concentration

L12

0

10

20

30

40

50

60

70

80

0 20 40 60 80 100 120 140 Time [days]

Resident Concentration L5

0

10

20

30

40

50

60

70

80

0 20 40 60 80 100 120 140 Time [days]

Resident Concentration

5

10

15

20

25

30

35

40

45

0 20 40 60 80 100 120 140 Time [days]

Resident Concentration L6

5

10

15

20

25

30

35

40

45

0 20 40 60 80 100 120 140 Time [days]

Resident Concentration

10

20

30

40

50

60

70

0 20 40 60 80 100 120 Time [days]

Resident Concentration

L7

10

20

30

40

50

60

70

0 20 40 60 80 100 120 Time [days]

Resident Concentration

5

10

15

20

25

30

35

40

45

0 20 40 60 80 100 120 140 Time [days]

Resident Concentration

L8

5

10

15

20

25

30

35

40

45

0 20 40 60 80 100 120 140 Time [days]

Resident Concentration

0

10

20

30

40

50

0 20 40 60 80 100 120 140 Time [days]

Resident Concentration

L9

0

10

20

30

40

50

0 20 40 60 80 100 120 140 Time [days]

Resident Concentration

0

10

20

30

40

50

0 20 40 60 80 100 120 140 Time [days]

Resident Concentration

L10

0

10

20

30

40

50

0 20 40 60 80 100 120 140 Time [days]

Resident Concentration

0

10

20

30

40

50

0 20 40 60 80 100 120 Time [days]

Resident Concentration

L11

0

10

20

30

40

50

0 20 40 60 80 100 120 Time [days]

Resident Concentration

0

5

10

15

20

25

30

35

0 20 40 60 80 100 120 140 Time [days]

Resident Concentration

L12

0

5

10

15

20

25

30

35

0 20 40 60 80 100 120 140 Time [days]

Resident Concentration
149

Table 5-1. Calibrated aquifer parameters

Material Parameter Value Relative

sensitivity

95% 

confidence

interval

Sandy Loam Horizontal conductivity (cm d-1

) 101 0.00009 36.7

Specific yield 0.11 0.021 0.0027

Sandy Loam Horizontal conductivity (cm d-1

) 138 0.0016 3.86

Specific yield 0.11 0.021 0.0027

Sandy Clay Loam Horizontal conductivity (cm d-1

) 53 0.00052 5.15

Specific yield 0.05 0.0047 0.000265

Loam Horizontal conductivity (cm d-1

) 4 0.000093 1.8

Specific yield 0.14 0.085 0.0011

Silt Loam Horizontal conductivity (cm d-1

) 18 0.00018 5.35

Specific yield 0.14 0.00011 3.3

Silty Clay Loam Horizontal conductivity (cm d-1

) 102 0.0029 1.5

Specific yield 0.1 NA§-

Clay Loam Horizontal conductivity (cm d-1

) 11 0.00016 5.7

Specific yield 0.1 NA -

§Was not estimated
150

Table 5-2. Parameters found by solving the inverse of 1D transport in groundwater using 

CXTFIT. 

Borehole v, m d

-1 D, m2

d

-1

aL, m

x

, m C

*

, mg l

-1 R2

L5 0.077 0.079 0.97 1.5 150 0.954

L6 0.058 0.042 0.72 0.5 150 0.707

L7 0.077 0.023 0.30 3.0 100 0.931

L8 0.030 0.011 0.37 0.5-4.0 150 0.331

L9 0.054 0.063 1.16 3.0 100 0.528

L10 0.121 0.025 0.21 1.0 150 0.384

L11 0.081 0.093 0.87 3.0 150 0.560

L12 0.111 0.079 0.71 3.0 150 0.221

(aL=D/v is the dispersivity, R2is determination coefficient)
151

5.2.2 ABSTRACTION WITH A CHANGE IN SCALE: PROFILE AGGREGATION

To assess the effect of the soil profile aggregation on the simulation results, we abstracted 

the model and converted the heterogeneous profile of the upper sub-layer to into an equivalent 

homogeneous medium. Two scenarios were considered: a profile composed of sandy loam (SL), 

and a profile consisting of a silt loam (SiltL). The saturated hydraulic conductivities were set 

according to Rawls et al. (1998) as 1.360 and 0.346 m/day, for SL and SiltL textural classes, 

respectively. The longitudinal dispersivity was assumed to be 0.2 m in both simulations. Results 

are presented in Fig. 5-10 to 5-12. Profile homogenization had only a minor effect on the 

simulated BTCs of wells L1 through L4 where vertical transport prevailed; however, the 

influence was very significant for wells L5 through L9 (Fig. 5-10 and 5-11). 

Introducing a homogeneous SL profile did lead to a delay of the tracer arrival time at well 

L5, and in early appearance in wells L6-L9 (Fig. 5-10). The simulated maximum concentrations 

in L6-L9 were at the same time were also significantly higher than the observed concentrations. 

Assuming a homogeneous SiltL profile with much lower hydraulic conductivity caused a delay 

in the tracer arrival times at wells L5-L7 compare to the calibrated model (Fig. 5-11). The effect 

of profile homogenization using SiltL on the BTCs of wells L8 and L9 was relatively minor. 

This was expected since the logs of these wells indicated the presence of low-permeability layers 

in this part of the study area. A comparison of simulations obtained with the homogeneous SL 

and SiltL profiles is shown in Fig. 5-13a and b, respectively, for wells L10-L12. Notice that the 

homogeneous SL simulations produced increases in the tracer concentration of wells L10, L11, 

and L12, but not for the other observation wells. 

5.2.3 ABSTRACTION OF REQUIRED PARAMETERS: USING PEDOTRANSFER FUNCTIONS

In this section we present the results of model abstraction scenario where we used 

pedotransfer functions (Rawls et al., 1998) to estimate the saturated hydraulic conductivities of 

the various soil materials from soil texture. The following Ksat values were used in the 

simulations: 1.36, 0.18, 0.094, 0.346, 0.09 and 0.048 m/day for SL, SCL, L, SiltL, SiltCL and C, 

respectively. Results are presented in Fig.5-14.

Substituting the calibrated Ksat with values determined using pedotransfer functions had 

minor effect on the BTCs of wells L1-L4 and L10-L12. The flow paths between the tracer 

application plot and L5 followed mainly a layer having a SL texture whose PTF Ksat value was 

very close to the calibrated value. Hence, the influence of the PTF abstraction was not significant 

for L5 either. However, for wells L6 through L9 we observed a delay in the simulated BTCs 

since the PTF estimated Ksat values of SCL and L were more than two times lower than the 

values obtained by the trial-and error. 
152

Figure 5-10. Observed and simulated chloride breakthrough curves for the homogeneous sandy 

loam (SL) profile. Symbols are the same as in Fig. 4-12. 

80 100 120 140 160 180 200 220

Time (DOY)

0

20

40

60

80

100

Cl concentration (mg/l)

L5

L6

L7

L8

L9

80 100 120 140 160 180 200 220

Time (DOY)

0

20

40

60

80

100

120

140

Cl concentration (mg/l)

80 100 120 140 160 180 200 220

Time (DOY)

0

20

40

60

80

100

120

140

Cl concentration (mg/l)

80 100 120 140 160 180 200 220

Time (DOY)

0

20

40

60

80

100

120

140

Cl concentration (mg/l)

80 100 120 140 160 180 200 220

Time (DOY)

0

20

40

60

80

100

120

140

Cl concentration (mg/l)

Ln-1

Ln-2

Ln-3

Computed Observed

80 100 120 140 160 180 200 220

Time (DOY)

1

10

100

1000

Cl concentration (mg/l)

80 100 120 140 160 180 200 220

Time (DOY)

1

10

100

1000

Cl concentration (mg/l)

80 100 120 140 160 180 200 220

Time (DOY)

1

10

100

1000

Cl concentration (mg/l)

80 100 120 140 160 180 200 220

Time (DOY)

1

10

100

1000

Cl concentration (mg/l)

L1

L2

L3

L4

Ln-1

Computed Observed
153

Figure 5-11. Observed and simulated chloride breakthrough curves for the homogeneous silt 

loam (SiltL) profile. Symbols are the same as in Fig. 4-12. 

80 100 120 140 160 180 200 220

Time (DOY)

0

20

40

60

80

100

Cl concentration (mg/l)

L5

L6

L7

L8

L9

80 100 120 140 160 180 200 220

Time (DOY)

0

20

40

60

80

100

Cl concentration (mg/l)

80 100 120 140 160 180 200 220

Time (DOY)

0

20

40

60

80

100

Cl concentration (mg/l)

80 100 120 140 160 180 200 220

Time (DOY)

0

20

40

60

80

100

Cl concentration (mg/l)

80 100 120 140 160 180 200 220

Time (DOY)

0

20

40

60

80

100

Cl concentration (mg/l)

Ln-1

Ln-2

Ln-3

Computed Observed

80 100 120 140 160 180 200 220

Time (DOY)

1

10

100

1000

Cl concentration (mg/l)

80 100 120 140 160 180 200 220

Time (DOY)

1

10

100

1000

Cl concentration (mg/l)

80 100 120 140 160 180 200 220

Time (DOY)

1

10

100

1000

Cl concentration (mg/l)

80 100 120 140 160 180 200 220

Time (DOY)

1

10

100

1000

Cl concentration (mg/l)

L1

L2

L3

L4

Ln-1

Computed Observed
154

 a) b)

Figure 5-12. Observed and simulated chloride breakthrough curves for homogeneous profiles:

a) sandy loam, and b) silt loam. Symbols are the same as in Fig. 4-12. 
155

Figure 5-13. The observed and simulated chloride BTCs curves for the abstracted model in which Ksat values were determined using

pedotransfer functions developed by Rawls et al., (1998). Symbols are the same as in Fig. 4-12.

80 100 120 140 160 180 200 220 Time (DOY)

0

20

40

60

80

100

Cl concentration (mg/l)

L5

L6

L7

L8

L9

80 100 120 140 160 180 200 220 Time (DOY)

0

20

40

60

80

100

Cl concentration (mg/l)

80 100 120 140 160 180 200 220 Time (DOY)

0

20

40

60

80

100

Cl concentration (mg/l)

80 100 120 140 160 180 200 220 Time (DOY)

0

20

40

60

80

100

Cl concentration (mg/l)

80 100 120 140 160 180 200 220 Time (DOY)

0

20

40

60

80

100

Cl concentration (mg/l)

Ln-1

Ln-2

Ln-3

Computed Observed

80 100 120 140 160 180 200 220 Time (DOY)

1

10

100

1000

Cl concentration (mg/l)

80 100 120 140 160 180 200 220 Time (DOY)

1

10

100

1000

Cl concentration (mg/l)

80 100 120 140 160 180 200 220 Time (DOY)

1

10

100

1000

Cl concentration (mg/l)

80 100 120 140 160 180 200 220 Time (DOY)

1

10

100

1000

Cl concentration (mg/l)

L1

L2

L3

L4

Ln-1

Computed Observed

155
156

5.3 SUMMARY AND CONCLUSION

This study was designed and performed to demonstrate the applicability of model 

abstraction techniques to subsurface flow and contaminant transport problems. The study 

focused on future applications of modeling to contingency planning and management of potential 

and actual contaminant release sites within the scope of the US NRC operations. 

Subsurface flow and transport modeling may have various purposes including site 

characterization, explaining the existing subsurface contamination pattern, and projecting the 

contaminant release results under various environmental and management scenarios. 

Contributing to the characterization the subsurface flow and transport domain was the purpose of 

modeling in this work. 

Modeling was only one component of characterization of the subsurface in this work that 

also included using the borehole data, laboratory studies of soil hydraulic properties, applying 

geophysical methods, monitoring soil moisture and soil pressure head, groundwater monitoring, 

field hydrogeological tests, and tracer studies. The important role of modeling in characterizing 

the subsurface was to describe the transport conditions. Given the non-uniqueness of 

interpretations of geophysical data, the small scale of borehole and laboratory data as well as of 

most groundwater samples and tests, and the limitation of soil moisture monitoring in revealing 

the hydraulic conductivity of soils, development of alternative conceptual subsurface transport 

models, and distinguishing between these models, was the essential part of the modeling effort. 

The OPE3 experimental field site near Beltsville, MD, has been extensively studied for 

more than 10 years using geophysical, biophysical, remote sensing, and soil and groundwater 

monitoring methods. Available data are analyzed using a systematic procedure based on a broad 

vadose zone modeling context developed in this study. A major focus was on the existence of 

subsurface structural units and features that may drastically change the fate and transport of 

contaminants in the vadose zone, as well as of projected trajectories of the contaminant plume in 

groundwater. We found that solute transport in soils and shallow groundwater at the site is 

potentially affected by such features as the presence of a restrictive fine-textured layer that is not 

fully continuous laterally, the complex topography of the restrictive layer favoring preferential 

flow and transport along preferred pathways along its surface relief, the presence of natural 

capillary barriers, possible funnel flow in a coarse-textural layer between more fine-textured 

layers, and local high-conductivity parts of the soil pore space. 

An extensive field survey and monitoring program had to be initiated as part of this work in 

spite of the existence of a large database of soil and groundwater properties at the site. The main 

reason for this was the difference in scale at which the site was characterized previously, and the 

scale at which flow and transport processes are of a concern in contaminant release applications. 

Specifically, our 20 x 20 m research site required additional characterization since the site 

presented only a single pixel in the characterization of the entire 300 x 300 m OPE3 site

The employed geophysical methods provided essential information about transportcontrolling subsurface features. A 2x2 m ground penetrating radar survey showed the existence 

of a mostly continuous restrictive layer with complex topography. Soil electric resistivity 

monitoring furthermore revealed the existence of narrow hydrologically active vertical zones. 

The obtained data indicate that large parts of subsurface soils may not fully participate in the 

prevailing flow and transport processes. Biophysical monitoring of the research area allowed 

delineation of relatively large structural units in the soil cover that provided distinctly different 
157

conditions for plant growth. The size of those units exceeded the scale of investigation in this 

work. 

The borehole log data showed surprisingly high spatial variability for the relatively small 

sites. For example, soil texture was represented by six textural classes in the range from sandy 

loam to silty clay loam. This underscored the possibility of the existence of the subsurface 

preferential solute transport, and at the same time indicated that the defining a representative 

elementary volume for the subsurface may be difficult if at all possible. 

Laboratory water retention data clearly indicated the presence of macroporosity in soils that 

potentially could case the fine-scale high-conductivity part of the soil pore space. Hydraulic 

conductivity measurements at the same scale showed that, in actuality, such high conductivity 

would require not only the presence of macropores but also the connectivity between these pores, 

could be found only in a relatively small percentage of locations. 

Soil moisture and soil pressure head monitoring data provided the information about field 

hydraulic properties of unsaturated soils. The field water retention was well defined by those 

measurements. This indicated that the Richards model could be an appropriate conceptualization 

of the flow processes in soils under study. It appeared necessary to develop a site-specific 

calibration of capacitance probes, and the method was developed for that purpose in this work. 

Two field experimental studies, both of original design, were carried out and analyzed using 

model abstraction. One study, referred as the solute flux experiment, was meant to imitate a soil 

column experiment at the plot scale. The experiment involved the application of a conservative 

tracer around a well and subsequent irrigation with simultaneous pumping of ground water. This 

experiment should provide insight into the significance of zones in the soils having a high 

vertical conductivity. A second study was designed to observe the lateral transport of a surfaceapplied conservative tracer pulse when transport was controlled by regular irrigation pulses and 

natural precipitation. This second experiment should demonstrate the effect of the topography 

and continuity of the restrictive layer, as well as the significance of funnel flow due to the 

presence of a coarse layer between the finer-textured layers. The vadose zone during both 

experiments was monitored for soil water content and pressure heads, while groundwater levels 

and the groundwater chemical composition were also recorded. Groundwater compositions were 

monitored at three different depths. 

Two preliminary modeling projects preceded the lateral transport experiment. One was 

undertaken to estimate the potential importance of runoff and the need to intercept this runoff. 

This study required developing a new model and software to simulate coupled surfacesubsurface flow and transport at the plot scale for the 30x30 m study area. The software coupled 

the FEMWATER and 2DSOIL codes, the former simulating subsurface flow and the latter 

overland flow using a diffusive flow approximation. For the second modeling project we used 

the new software, HYDRUS-3D, to simulate flow and transport in the three-dimensional 

subsurface domain at the site. The purpose was to estimate the required duration of the 

experiment and the frequency of sampling needed to capture in detail the solute breakthrough 

curves in a number of observation wells. Both preliminary modeling studies were found useful in 

terms of improving the experiment setup and the schedule of the experiment. 

The solute flux experiment comprised approximately 7 days, whereas the lateral flow 

experiment continued for four months. About 10,000 analyses were made of the tracer 

concentration in order to develop the breakthrough curves. A preliminary analysis of the 

experimental results was used to obtain a conceptual representation of the prevailing subsurface 

transport processes. We hypothesized that preferential transport of solutes occurred in both 
158

experiments. Vertical transport in the unsaturated zone seemed to occur much faster than 

suggested by the observed water fluxes. The tracer breakthroughs in the lateral transport 

experiment occurred at substantially different times in the wells at similar distances from the 

application area. The differences in times to some extent corresponded to soil textural 

differences.

There were no indications in the solute flux experiment results that the Buckingham-Darcy 

flow model and the corresponding Richards equation were not applicable to the data. Therefore, 

water flow in both the unsaturated zone and in groundwater was simulated with the Richards 

equation using the HYDRUS2D software package. 

The seepage face along the observation well was found to be an important feature of the 

experimental setup of the solute flux experiment. Transport occurred both in groundwater as well 

as in the capillary fringe. The Richards equation for flow and the convection-dispersion model 

for transport were both successfully calibrated and provided good representations of the 

experimental results. No assumption about preferential solute transport in highly conductive 

parts of the soil pore space was needed. 

The 2D model for flow and transport in the variably saturated zone was abstracted to a 1D 

model for vertical water flow and solute transport to groundwater. While ignoring the presence 

of a seepage face, the 1D model allowed preferential transport of solutes to occur. It appeared 

that this model was able to provide only approximate qualitative and quantitative predictions of 

solute breakthrough. The invoked abstraction demonstrated that ignoring the actual geometry of 

the flow and transport domain and the essential features of the flow process in the field can 

create a distorted conceptualization of transport in the subsurface. 

One more abstraction step was considered for 2D solute transport to demonstrate that a 

simple analytical model sometimes may be sufficient for certain modeling application. This 

abstraction was used to investigate the ability of the pumping well to intercept all of the surfaceapplied tracer, which is a critical aspect of the solute transport experimental setup. For this to 

occur, the tracer application zone must remain within the groundwater depression cone around 

the well. We showed that a simple analytical model evaluated the depression cone size with the 

same degree of accuracy as the more refined 2D saturated-unsaturated flow model. 

Results of the lateral flow experiment were relatively more complex than results of the 

solute flux experiment. Some small temporal scale (1 – 2 days) phenomena were observed in 

some wells that could not be explained. We ignored these fine scale phenomena and 

concentrated on conceptualization of the flow and transport at larger temporal scale. 

The fine-textured low-permeability layer was found to divert the tracer according to the 

topography of the layer. There were no indications that the Buckingham-Darcy flow model and 

corresponding Richards equations were inapplicable at the larger scale, likely because flow and 

transport at that scale seemed to be driven mostly by the hydraulic gradients in groundwater. The 

complexity of the flow and transport domain required the use of a full 3D representation. For this 

reason we used the HYDRUS3D software to simulate flow and transport in the lateral flow 

experiment. 

Since HYDRUS3D does not have a calibration option, only trial and error calibration could 

be applied. Given that 2 days of computation were needed for each simulation run with this code, 

we streamlined the calibration procedure by calibrating the model directly to the breakthrough 

curves, and not to groundwater levels. This created a dilemma in terms of selecting an 

appropriate conceptual model for transport. Solutes could be delivered to a well via two different 

transport mechanisms: (a) transport via a network of well-connected pathways that comprise 
159

only part of the bulk soil porosity at the field scale, thus assuming that part of the domain does 

not participate in the transport process, or (b) transport through all of the domain. To deliver 

solute to a well at approximately the same time, average water fluxes should be smaller in case 

(a) as compared to the case (b). We selected case (b) and used several model abstractions to 

justify this selection

The trial-and-error calibration based on zonation of the flow and transport domain was 

reasonably successful. The maximum concentration levels and the 50% concentration arrival 

times were described satisfactory. However, we could not accurately reproduce the shape of the 

breakthrough curves. 

A dimension reduction abstraction considered only 2D flow in groundwater. MODFLOW 

and MT3D were used for this purpose. A special effort was undertaken to use in this abstraction 

the same zonation and layering as in the complete 3D representation. MODFLOW calibration 

capabilities were used successfully to reproduce the groundwater levels, while dispersivity and 

effective porosity values were estimated by trial and error from the breakthrough curves. 

The 2D abstraction process showed that the assumption of part of the soil not significantly 

participating in the solute transport process created a better representation of the breakthrough 

curves. A reasonable representation of solute transport was achieved with an effective porosity of 

60-70% of total soil porosity. Thus, the model abstraction step helped to substantially improve 

the conceptualizaton of the subsurface transport conditions. 

A 1D abstraction step allowed efficient assessment of intrinsic groundwater velocities and 

the hydrodynamic dispersion parameters in different directions. The results also suggested the 

location of preferential flow pathways. 

Using pedotransfer functions to estimate saturated hydraulic conductivities and/or to 

substitute the heterogeneous soil profile by an equivalent homogeneous medium indicated that 

this kind of model abstraction may lead to incorrect estimates of tracer front arrival times at 

some locations. Actually, results depended on the complexity of the heterogeneity being 

abstracted. Since small-scale heterogeneities may control flow and transport at the larger scale, a 

careful profile aggregation and analysis of the results is required. 

Several observations have been made during the data analysis in this work. 

First, our detailed studies revealed considerable soil heterogeneity at a very small site. We 

do not know how common such a degree of heterogeneity is since studies at this level of detail 

are relatively rare. It is important to recognize that the scale of our experiment was comparable 

the scale of solute release. Exclusion of a substantial part of the soil from the active solute 

transport process appears to be an important consequence of soil heterogeneity at the field scale. 

Second, calibration of vadose zone models is much more trying than calibration of 

groundwater models. This is because of the nonlinearity of the governing flow processes and the 

large number of parameters involved. Substantial changes in soil water contents and flow rates 

must occur to reliably calibrate a vadose zone model. 

Third, the use of models that assume the presence of mobile and immobile zones was 

avoided in this work. Such models are undoubtedly important when breakthrough tails are of 

interest. However, measuring tails takes time that is often impractical for field scale tracer 

studies where transport is controlled by weather conditions rather than by regional groundwater 

flow rates. And even when the tail is known, severe correlations are usually observed between 

the many parameters needed in this type of modeling. Assuming an effective porosity allowed us 

to characterize the subsurface so as to obtain the correct arrival times, and to obtain a reasonable 

approximation of the concentration maximum and the center of the mass position.
160

Fourth, the available software was generally adequate for simulations. However, both 

HYDRUS3D and MODFLOW packages encountered difficulties when soil became fully 

saturated during the intensive rainfall. 

Fifth, results of this study have implications for solute monitoring transport in 

heterogeneous formations. Well data generally represent a fairly small scale. In our experiments 

we encountered distinctly different breakthrough curves in wells that were approximately in 

similar positions relative to the source along the tracer plume propagation direction. A more 

general representation of solute transport in terms of integrated properties may be needed in 

order to provide a more reliable and accurate representation with models. 

This work demonstrated the usefulness of model abstraction in simulations of flow and 

transport in variably-saturated subsurface. Whereas multidimensional and multi-process 

representations leaves room for several competing conceptual models for flow and transport, 

simpler models that retain the most essential features of those representations could provide 

meaningful alternatives. 
161

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Šimůnek, J., Vogel, T., and van Genuchten, M.Th., The SWMS2D Code for Simulating Water 

Flow and Solute Transport in Two-dimensional Variably Saturated Media, Version 

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A-1

APPENDIX A. REVIEWING THE MODELING PROBLEM CONTEXT

The decision to perform model abstraction is made from considerations of the base model 

and the key output (see section 2.2). Therefore, reviewing the base model and the key output is 

the first step of any model abstraction.

A1.1 REVIEWING KEY OUTPUT

Subsurface hydrologic models simulate complex systems and as such may generate a large 

number of output variables describing such systems. Which part of the model-generated 

information presents key output depends upon the purposes of the modeling project. 

A1.1.1 Key output use

The purpose of subsurface flow and transport modeling may include:

 Improve the understanding of the vadose zone to optimize future 

monitoring or for planning a specific experiment

 Evaluating the effects of past management practices or previous events on 

vadose zone chemistry and hydrology

 Understanding the current state of the vadose zone to define possible 

sources of contamination and their interaction with groundwater systems

 Predicting changes in the vadose zone resulting from existing or 

alternative management scenarios, and quantifying the role of the vadose zone in 

determining groundwater recharge rates and contaminating groundwater. 

Each of these purposes involves different key output that could be used to resolve specific 

regulatory, budgetary, societal or other issues. A single model could be used for several 

purposes, but the key output and boundary and initial conditions appear to be specific for a 

particular modeling project. 

A1.1.2 Key output type and scale

Various types of transformation or parts of the modeling results may be used to derive the 

key output. Specifically, 

 data filtering, e.g. concentrations and fluxes at specific times and/or 

locations

 boundary water fluxes such as 

- ground water recharge rates

- runoff losses

- losses to the lateral through boundaries

 boundary contaminant fluxes such as 

- fluxes to the water table

- projection of the known source area to the water table

- lateral fluxes in the capillary fringe to susceptible water sources and

wetlands

 maximum contaminant concentrations across various boundaries of the

simulation domain
A-2

 average concentrations of solute fluxes across various boundaries 

 contaminant arrival times to various boundaries

 cumulative masses of contaminant transported through or stored in the

vadose zone

The key output scale defines the temporal and spatial intervals over which the model output can 

be averaged to address the questions being asked. Daily, monthly, seasonal and yearly averages 

may be of interest depending upon the regulatory practices regarding the specific contaminant. 

Both a single maximum or total cumulative amounts may be used depending upon the 

contaminant involved and the accepted dose model. Similarly, spatial averaging of the pollution 

footprint in the vadose zone may yield sources as small as a borehole sample or as large as an 

agricultural field or an entire hydrologic response unit. Whatever the adopted scales, a review of 

output type and scale has to articulate and document the procedures used to derive the key output 

from the modeling results. 

A1.1.3 Accuracy of the key output 

The acceptable accuracy and uncertainty of the key output has to be requested from the end 

users. The acceptable accuracy relates to the performance of the model with respect to existing 

observations. The uncertainty relates to variations in the key output due to quantifiable variations 

in model parameters, external forcing, and scenarios. 

In some cases, mandatory regulations are in place that articulate the statistics to be used for 

evaluating model performance. Sometimes the regulatory criteria list threshold values that are 

established in certain risk assessment guidelines. It is necessary to verify whether these threshold 

values appear within or outside realistic ranges of the predicted key output variables, given their 

uncertainty. 

If the requirements for model accuracy are not established, characterizing the uncertainty in 

the key output becomes a part of the revew of the base model. As the model abstraction is 

applied, changes in the accuracy and uncertainty of the key output may be used to decide upon 

the applicability of a particular model abstraction technique. 

A1.1.4 Evaluating model performance

One is generally not able to directly estimate the accuracy of the key output since output is a 

derived value and simply cannot be measured. The performance of the model per se must then be 

evaluated. A large number of statistical tests has been proposed and may be used for this purpose 

(e.g. Belocchi et al., 2004; Hill and Tiedeman, 2007). It is preferable to use statistical tools that 

evaluate simple and clear ideas about the correspondence between data and the simulations, e.g., 

 how variability in model errors compares with variability in the data?

 do model residuals have spatial or temporal trends?

 is there a systematic relative or absolute error in the predictions? 

 how reliable are parameters derived from calibrations?

 how realistic are parameter derived values from calibrations?

 does the model tend to magnify errors in the inputs?
A-3

The performance of a model in terms of the adopted statistics must be compared with the 

performance of other models developed for similar purposes and having a similar complexity. 

Also, small model error measures usually do not guarantee that the model will perform well also 

when used for predictions. Simpler models with larger errors against observations can be more 

robust and perform better for some forecasts. Therefore, correct assumptions about the vadose 

zone, the boundaries of the simulation domain, and possible sources, sinks, and chemical and 

biological transformations within the simulation domain are often more important than the model 

error. 

A1.2 REVIEWING ASSUMPTIONS MADE DURING DEVELOPMENT OF THE BASE MODEL AND 

JUSTIFICATIONS FOR THOSE ASSUMPTIONS

A1.2.1 Subsurface structural units

The vadose zone typically consist of various horizons and connected or disconnected lenses. 

The profile may contain massive, cross-bedded, and horizontally-bedded units, both poorly and 

well sorted. All of these structural units may conduct water differently, with chemical transport

and transformation similarly varying among the different units. Even with significant advances 

recently in hydrogeophysical techniques, precise delineation of the various units remains a 

challenge in many practical situations. Borehole-based stratification often cannot provide the 

type of exhaustive coverage generally needed for the simulation domain. Measurements of 

pollutant concentrations are point based and depend upon the interaction of the measurement 

device (e.g. suction lysimeters) with the soil at different levels of water contents. 

Because of the great uncertainty in characterization, many often question the feasibility of 

performing vadose zone flow and transport simulations. While uncertainty definitely is an issue, 

such simulations are likely to become increasingly more popular, and essential, because of the 

importance of the vadose zone in terms of storing, transforming and redirecting pollutants 

entering this zone from the soil surface. In such simulations, the pertinent challenge is not to 

obtain a full-fledged three-dimensional description of the locations and properties of structural 

units. The relevant challenges are answers to such questions as

 Does a specific site have subsurface structural units and features that may 

drastically change the fate and transport of pollutants in the vadose zone along the 

projected trajectory of a contaminant plume?

 If a restrictive fine-material layer is expected, does it have dikes or faults; can the 

layer have gaps?

 If a restrictive layer is expected, can it have a topography causing flow and 

transport via preferential pathways along it upper surface?

 Are there natural capillary barriers (i.e., boundaries between finer material 

overlaying the coarse sediments)? If yes, are gaps in these barriers expected?

 Can funnel flow in coarse-textural soils develop due to presence of a layer of 

coarse materials between two fine-textured layers?

 Can geochemical conditions of saturated or perched zones in the vadose zone 

cause changes in pollutant transformations or retention?

 Can well-conducting layers contain fine-scale high-conductivity parts of the pore 

space that will facilitate transport through large pores during episodic infiltration events? 

 Is the lateral conductivity of the capillary fringe large enough to allow substantial 

contribution of the capillary fringe to lateral transport above the water table? 
A-4

An essential condition here is to obtain answers to these questions from an available 

database that is as broad as possible. The database has to include information from public and 

private sources, cover both quantitative and qualitative (expert) information, and encompass both 

site-specific and generic information. The geological, hydrogeologic, and hydrogeophysical 

assessment can gain benefit greatly from complementary sources as types of stream hydrographs, 

the presence and hydrology of springs, the presence of paleosoils, documented fragipans, 

experience during well construction, occurrence and concentrations of agricultural chemicals in 

well water, and crop yield variability in dry years. 

A1.2.2 Dimension of the problem

Most vadose zone flow and transport simulations are currently carried out in only one 

dimension (i.e., only vertical transport is considered). This is not sufficient for sites where 

unsaturated flow and transport pathways may be altered substantially due to presence of 

redirecting structural units mentioned in the previous section. A two dimensional representation 

is needed when 

 lateral transport can be substantial, 

 restrictive layers, if present, are well defined, 

 flow in the vadose zone is controlled by infiltration. 

A three-dimensional representation is needed when

 the contaminant release source is providing also a substantial amount of 

infiltration, 

 substantial lateral transport in the vadose zone is expected, both along and across 

the main groundwater flow direction. 

A1.2.3 Simulation domain, initial and boundary conditions

The simulation domain must be selected such that it reflects the dimension of the problem 

and allows one to set justifiable boundary conditions along all boundaries. One-dimensional 

(1D) problems require boundary conditions along the soil surface and the bottom of the vadose 

zone. Either a free drainage condition, or a zero pressure head condition at the ground water level 

(if the latter is monitored in time), is generally sufficient to simulate flow in this case. 

1D simulations likely will not provide correct simulations if substantial transport in the 

capillary fringe is expected, or if a restrictive layer exist that not only can cause perched water to 

develop but also may contain gaps that allows rising groundwater to move upward through gaps 

in the restrictive layer. In such cases 2D or 3D simulations are necessary. Multi-dimensional 

vadose zone flow and transport simulations are best simulated when 

 the simulation domain includes both a vadose zone and an aquifer, and 

 flow and transport need to be considered jointly, without assuming some rule of 

fluid and mass exchange between the vadose zone and groundwater. 
A-5

Boundary conditions in the groundwater subdomain have to be established according to 

existing guidelines for groundwater modeling. Boundary conditions for flow in the vadose zone 

must be established either from vadose zone monitoring data, or from preliminary 1D 

simulations of the vadose zone at the lateral boundaries of the flow domain. Alternatively, they 

can be defined in a more arbitrary fashion to provide continuity in the pressure head along a 

vertical direction from the water table to the soil surface. In the latter case, however, the 

boundaries should be placed far enough from the contaminant plume, so that the boundary 

conditions would not affect flow and transport within the domain of interest. This has to be 

verified by preliminary simulations using realistic values for the flow and transport parameters. 

Daylight surface boundary conditions have to be 

 harmonized with the time step accepted in the model. 

 set with proper attention to runoff from and run-on to the soil surface simulation 

domain;

 reflect water and chemical uptake. 

The representation of initial conditions depends on the purpose of the modeling. For 

exploratory and forecast purposes it is customary to run the model with realistic boundary 

conditions for relatively simulated periods (up to one year), and to use the results of this run as 

initial conditions for the flow model. For parameter estimation and understanding the current 

situation at the field site, measured initial values of the vadose zone state variables should be 

used. 

A1.2.4 Estimated model parameters 

The estimated parameter values must be obtained and reviewed irrespective if calibration 

applied or not. The estimated parameters for flow and transport either 

 are used directly in the simulations; 

 serve as initial estimates for model calibration; 

 used in evaluations of the results of a calibration

A list of estimated flow and transport parameters for each subsurface structural unit 

typically includes

 soil water retention parameters

 uunsaturated soil hydraulic conductivity parameters

 molecular diffusion coefficient of the contaminant

 dispersivity

 dual-porosity parameters

 chemical transformation parameters 

 biological transformation parameters

Additional parameters are used if the pollutant experiences colloid-facilitated transport, 

volatilization, or is represented by nanoparticles. 

General requirements of the parameter estimation include

 using several sources,

 matching scales
A-6

 correcting for field conditions

 defining uncertainty

Using several sources is recommended since a similarity in soil type (e.g., soil texture) by 

no means guarantees a comparable similarity in the flow and transport parameters. For example, 

soils of similar texture may exhibit up to two orders of magnitude differences in hydraulic 

conductivity. A compendium of literature flow and transport parameters in soils is given by 

Pachepsky and Rawls (2004).

A match in the scale of an experimentI is important when selecting literature values of 

hydraulic conductivity and dispersivity parameters since they are known to depend on the 

support or extent of the experiment in which they have been measured. A rule of thumb 

recommendation is to use parameters from experiments in which the support or extent is close to 

the vertical size of the cell used in numerical simulations. 

A correction is often needed when relying on laboratory-measurements of the hydraulic 

conductivity, the dispersivity, and dual-porosity parameters since they depend on the spatial 

scale of an experiment. Methods to account for this change in scale can be found in both the 

soils (Pachepsky et al., 2003) and groundwater (Neuman, 1990, 1995) literature. Corrections to 

field conditions are more difficult for chemical and biological transformation because they are 

specific to the type of pollutant. However, the anticipated differences in adsorption, dissolution, 

and transformation rates have to be articulated and taken into account in uncertainty-based 

modeling projects. 

Defining uncertainty in the estimated parameters is necessary for

 performing multiple simulations to evaluate the prediction uncertainty if no 

calibration is envisaged;

 determining the prior distributions of parameters to determine the posterior 

distributions of calibrated parameters if Bayesian methods are used in the calibrations;

 evaluating the calibration results. 

Obtaining parameter estimates from multiple sources provides the necessary information for 

uncertainty characterization. It is imperative to use estimates not only of average values found in 

the literature, but also of the uncertainty in the average values that are reported in many (but not 

all) literature sources. An alternative method is to use probability distributions developed for 

soils from a large international database (Meyer et al., 1997). 

A1.2.5 Data available for calibration 

Data needed for calibration of a vadose zone flow and transport model may include, in 

particular, monitoring data of 

 the soil water content, 

 the soil pressure head, 

 soil water fluxes, 

 concentrations of pollutants in soils, 

 tracer concentrations if a tracer test has been run, 

 hydrogeophysical data from cross-borehole monitoring of infiltration events, 

hydrogeophysical data from surface monitoring of soil water contents, 

 groundwater levels, 
A-7

 concentrations of pollutant or tracers in groundwater. 

In spite of the fact that flow and transport processes in the vadose zone are slow, tracer tests 

are desirable for evaluating the possibility of rapid pollutant transport in dual-porosity soils. 

Calibration data must be available if the purpose of modeling is to analyze results of current or 

future management scenarios of contingencies. One may argue that running a model with all 

parameters within their variability ranges may provide an exhaustive characterization of the 

uncertainty in predictions. This is true provided the structural units are conceptualized in a 

correct way, but that cannot be guaranteed in absolute terms. The credibility of a model increases 

if the calibration returns physically meaningful parameter values. 

All vadose zone measurements are to some extent indirect, and are affected by interactions 

between the measuring device and the medium being studied. Therefore, all data used for 

calibration have to be reported with expertly or directly estimated errors. This is needed to 

evaluate the calibration results in terms of their accuracy. 

The type of data, number of data points, and the frequency of data collection for reliable 

calibration is site-specific and depends on the method of calibration (see below). An optimal 

methodology of defining the best monitoring strategy for calibrating a vadose zone model 

presents an avenue of future research. 

A1.2.6 Calibration procedure and results 

Two calibration methods are used most often in vadose zone flow and transport modeling: 

trial-and-error (manual) calibration and automated calibration. Automated calibration does not 

change locations and dimensions of structural units; it only varies material properties within 

these units to match simulated and measured values. Trial-and-error calibrations usually change 

both the locations and the dimensions of the structural units until a better fit is obtained. 

An advantage of automated calibration is the objectivity in which the parameters are 

obtained. A disadvantage is that it may end up supporting an incorrect conceptualization of the 

flow and transport processes embedded in the model. Trial-and-error methods mirror automated 

calibration in terms of these advantages and disadvantages. If automated calibration is used, the 

statistics of parameters should be analyzed in the same way as recommended in groundwater 

modeling projects (Hill and Tiedeman, 2007). 

Vadose zone simulations are notoriously slow because of the nonlinearity in the governing 

flow equations. Therefore, automated calibration is usually implemented only for onedimensional simulations. Calibration in two- and three-dimensional simulations is usually 

achieved using trial-and-error process. 

The calibration process should include

 normalization of measurements to exclude the effect of the measurement unit on 

the calibration results,

 justified removal of non-sensitive parameters from calibration,

 assignment of different and explicable weights to measurements of different 

types. 
A-8

A1.2.7 Software properties

Because of the nonlinearities involved, numerical solutions of coupled vadose zone and 

groundwater problems often show unstable behavior, or produce unacceptable errors in the mass 

balances for water and solutes. This behavior, including the software used for the simulations, 

has to be documented and reported. 

A1.2.8 Model documentation

Reviewing the documentation of a model is an essential component of the base model 

review. Reily and Harbaugh (2004) indicate in their guidelines for evaluation of groundwater 

models that “because models are embodiments of scientific hypotheses, a clear and complete 

documentation of the model development is required for individuals to understand the 

hypotheses, to understand the methods used to represent the actual system with a mathematical 

counterpart, and to determine if the model is sufficiently accurate for the objectives of the 

investigation”. The same is true for vadose zone modeling. Clarifications on all of the topics 

addressed in appendices A1 and A1.2.1 through A1.2.7 have to be included in the

documentation.
B-1

APPENDIX B. FIELD CALIBRATION OF MULTISENSOR CAPACITANCE 

PROBES

Multisensor capacitance probes (MCPs) are used in field soil water content monitoring for 

various applications, such as for irrigation scheduling, estimating soil hydraulic properties, and 

evaluating water uptake by plants. It is desirable to know how representative data are from 

multisensor capacitance probes for a small plot surrounding the sensor. For example, such 

information may be needed if a plot is used for an infiltration experiment and soil water is 

monitored with the sensor to characterize the infiltration rate (Shukla and Jaber, 2007). Such 

upscaling may result in both random and systematic errors. Random errors may arise from smallscale variations in soil water contents and from variability of soil properties since capacitance 

probes are sensitive to soil bulk electrical conductivity (Baumhardt et al., 2000; Evett et al., 

2006; Kelleners et al., 2004) and soil mineralogy (Fares et al., 2004). Systematic upscaling errors 

may results from deficiencies in the calibration. In most cases, MCPs have been calibrated in the 

laboratory (Paltineanu and Starr, 1997; Baumhardt et al., 2000; Polyakov et al., 2005). 

Baumhardt et al. (2000) reported that the manufacturer-supplied MCP calibration equations were 

applicable to estimate soil water contents in Ap and calcic horizons of an Olton soil when the 

soil was air dried, but not when near saturation. They concluded that MCP calibration should be 

soil-specific. Morgan et al. (1999) came to the same conclusion when they tested manufacturer 

and laboratory (Paltineanu and Starr, 1997) calibrations on three fine sandy soils of Florida, 

while Evett et al. (2006) concluded the same for three other soils. 

Since MCP sensors provided a very important stream of information for both site 

characterization and monitoring during the experiment, we assessed the magnitude and variations 

in the difference between MCP-measured and plot-averaged gravimetrically measured water 

contents across 1 m2plots at the site , and searched for ways to modify the MCP calibration to 

better represent plot-averaged water contents. Multisensor capacitance probes (EnviroSCAN, 

SENTEK Pty Ltd., South Australia) were installed for this purpose in the spring of 2006 to 

monitor the soil water content and provide data for validation of a water flow model. Four plots 

(each 1 m2 and 10 m apart) were instrumented with MCPs located at 10 cm depth increments 

from 10 to 60 cm. Reference readings were taken for each sensor in air and water before 

installation. Undisturbed soil cores were taken with a 100 cm3soil auger at 50 cm distance from 

the MCPs at the vertices of an equilateral triangle in triplicate at three dates with distinctly 

different water contents at depths corresponding to the MCPs installation. The triangle was 

rotated by 40 before the second and third samplings. Soil water contents and soil bulk densities 

were measured gravimetrically. Soil texture was measured with the pipette method (Gee and Or, 

2002) after dispersion with sodium pyrophosphate Na4P2O7 of soil samples taken when the MCP 

access tubes were installed. 

To compare the MCP measurements with observed water content, the sensor scaled 

frequency (SF) was converted to volumetric water content using the SENTEK (1995) factory 

calibration equation:

 = (0.792SF – 0.0226)2.4752 (B-1)

as well a laboratory calibration for a mesic Aquic Hapludult silt loam soil as obtained by 

Paltineanu and Starr (1997): 

 = 0.490SF2.1674 (B-2)

The root-mean-square difference RMSD between plot-averaged θa,i and MCP-estimated 

water contents θMCP,i
B-2

  n

n

i

a i MCP i RMSD /

1

 , ,



  

(B-3)

was used to characterize the MCP measurements. Here n is the total number of compared water 

contents. 

Substantial variability in soil texture and soil bulk density with depth was observed at the 

four locations (Tables B-1 and B-2). Clay content was generally less in the topsoil (0-25 cm) 

than in the subsoil (25-65 cm) layer. Silt content was relatively constant (17-25%) at all depths, 

while sand content was less in the subsoil compared to the topsoil. Soil bulk density was less in 

the topsoil (1.34-1.69 g cm-3) than in the subsoil (1.69-1.95 g cm-3). The variation coefficient of 

soil bulk density ranged from 1 % to 14 %. 

Soil samples were taken at three dates when the soil was not excessively hard or soft for 

sampling, resulting in different soil water content ranges at different soil depths. Generally the 

water content range was wider in the top layer compared to that in the subsurface layers. Soil 

water contents were in the range from 0.10 to 0.51 m3 m

-3

in the topsoil, from 0.10 to 0.42 m3 m

-3

at depths of 25-55 cm, and from 0.09 to 0.38 m3 m

-3

in the 55-65 cm soil layer of four plots (Fig. 

B-1). Spatial variability in the soil water content measured at each of the four plots changed with 

soil depth. The standard deviations of the water content ranged from 0.02 to 0.12 cm3 cm-3, while 

the average water content ranged from 0.16 to 0.39 cm3cm-3in topsoil (data not provided here). 

The variability in soil water contents was in the range from 0.02 to 0.07 cm3cm-3and did not 

correlate with the soil water content in the subsoil. Deviations of MCP data from the measured 

water contents were observed at all depths in the four plots (Fig. B-1). 

The MCP data obtained with the SENTEK factory and laboratory calibrations are compared 

with plot-averaged soil water content measurements in Fig. B-2. Both random and systematic 

errors can be observed, resulting in root-mean-squared differences (RSMDs) in the range from 

0.037 to 0.058 cm3 cm-3for the SENTEK factory, and from 0.036 to 0.063 cm3 cm-3for the 

laboratory calibrations, respectively. Both MCP calibrations overestimated soil water contents at 

the low water contents and underestimate at the high water contents (Fig. B-2). We concluded 

that a calibration correction was needed to minimize the MCP errors of plot-averaged water 

content measurements. 

To correct the MCP performance, the coefficients a and b of linear regression between 

MCP-measured and plot-averaged water contents:

θa,i = aθMCP,i + b (B-4)

were calculated for data from all depths pooled together, for the topsoil (0-25 cm) data, the 

subsoil (25-65 cm) data, and for each observation depth separately. The calibration equations 

were transformed by combining equations (B-1), (B-2) with equation (B-3). The corrected 

equations are shown in Table B-3. Differences in coefficients of the MCP calibration equations 

indicate that the correction is depth-specific for both the SENTEC factory and the laboratory 

calibrations. 

Although the correction obtained with all pooled data reduced RMSD values for the entire 

depth range of 0-65 cm, smaller RMSDs were observed when corrections were applied to each 

depth or each soil horizon separately (Table B-4). This implies that depth or horizon specific 

corrections may be helpful to further reduce errors in the MCP measurements. 
B-3

Figure B-1. Soil water contents measured in the plots (symbols) and calculated using the 

SENTEC (solid lines) and laboratory measured (dotted lines) MCP calibrations vs. MCP scaled 

frequency. 

5-15 cm

0.1

0.2

0.3

0.4

0.5 15-25 cm 25-35 cm

35-45 cm

0.5 0.6 0.7 0.8 0.9

Volumetric water content (cm

3 cm-3

)

0.1

0.2

0.3

0.4

0.5 45-55 cm

MCP scaled frequency

0.5 0.6 0.7 0.8 0.9

55-65 cm

0.5 0.6 0.7 0.8 0.9 1.0

Plot 1

Plot 2

Plot 3

Plot 4
B-4

Figure B-2. Plot-averaged vs. MCP estimated soil water contents for the mesic Typic Hapludult 

soil. Solid and hollow symbols show estimates with the SENTEC calibration and laboratory 

calibrations developed by Starr and Paltineanu (1997), respectively. Solid and dash trend lines 

show the general relationship between plot average and MCP-estimated water contents for the 

SENTEC and laboratory calibrations, respectively. The dotted line shows the 1:1 line. 

10 cm

Measured water content (cm

3 cm-3

)

0.0

0.1

0.2

0.3

0.4

0.5

0.6

20 cm 30 cm

40 cm

0.0 0.1 0.2 0.3 0.4 0.5

0.0

0.1

0.2

0.3

0.4

0.5

50 cm

Volumetric water content from MCP (cm3 cm-3)

0.0 0.1 0.2 0.3 0.4 0.5

60 cm

0.0 0.1 0.2 0.3 0.4 0.5 0.6
B-5

Table B-1. Soil texture at locations of the multisensor capacitance probes installation. 

Depth Clay Silt Sand

cm % % %

0-15 15 ± 6#24 ± 9 61 ± 4

15-25 17 ± 4 23 ± 7 60 ± 3

25-35 22 ± 3 22 ± 5 56 ± 7

35-45 23 ± 4 21 ± 4 56 ± 7

45-55 24 ± 4 22 ± 4 54 ± 6

55-65 21 ± 6 21 ± 3 58 ± 2

#

The „±‟ separates the average from the standard deviation
B-6

Table B-2. Soil bulk density around the multisensor capacitance probes. 

Depth Location 1 Location 2 Location 3 Location 4

cm g cm-3g cm-3g cm-3g cm-3

0-15 1.344±0.029#1.516±0.033 1.557±0.031 1.455±0.007

15-25 1.691±0.112 1.649±0.020 1.689±0.130 1.674±0.038

25-35 1.822±0.040 1.722±0.058 1.843±0.046 1.831±0.019

35-45 1.741±0.109 1.694±0.009 1.787±0.079 1.828±0.031

45-55 1.764±0.097 1.731±0.023 1.828±0.038 1.805±0.019

55-65 1.782±0.099 1.726±0.044 1.952±0.062 1.885±0.062

#

The „±‟ separates the average from the standard error. 
B-7

Table B-3. The original SENTEC and laboratory MCP calibration equations. 

Depth

cm

SENTEC calibration Beltsville laboratory calibration

Original calibration equations

All depths  = (0.7920SF - 0.0226)2.4752  = 0.490SF 2.1674

Corrected calibration equations

0-65  = (0.8051SF - 0.0230)2.4752 + 0.0063  = 0.6247SF 2.1674

- 0.0704

0-25  = (0.8373SF - 0.0239)2.4752 + 0.0219  = 0.4996SF 2.1674

- 0.0140

25-65  = (0.7601SF - 0.0217)2.4752

- 0.0300  = 0.5690SF 2.1674- 0.0495

0-15  = (0.8292SF - 0.0237)2.4752 + 0.0084  = 0.6109SF 2.1674 

- 0.0530

15-25  = (0.8499SF - 0.0243)2.4752 + 0.0375  = 0.6466SF 2.1674

- 0.0919

25-35  = (0.7906SF - 0.0226)2.4752 + 0.0078  = 0.5512SF 2.1674

- 0.0535

35-45  = (0.8530SF - 0.0243)2.4752 +0.0465  = 0.6668SF 2.1674

- 0.1120

45-55  = (0.7942SF - 0.0227)2.4752 + 0.0002  = 0.5579SF 2.1674

- 0.0465

55-65  = (0.6495SF - 0.0185)2.4752

- 0.1779  = 0.3405SF 2.1674 + 0.0801
B-8

Table B-4. Root-mean-squared differences of plot-averaged water contents (cm3cm-3) for the 

original and corrected MCP calibration equations. 

Depth range

cm

SENTEC calibration Beltsville laboratory calibration

Original

Corrected 

for specific 

depth range 

Corrected for 

soil texture Original

Corrected for 

specific 

depth range 

0-65 0.0458 0.0455 0.0446 0.0474 0.0459

0-25 0.0505 0.0478 0.0429 0.0535 0.0491

25-65 0.0431 0.0428 0.0454 0.0436 0.0427

5-15 0.0542 0.0488 0.0402 0.0561 0.0505

15-25 0.0464 0.0447 0.0456 0.0506 0.0451

25-35 0.0344 0.0332 0.0284 0.0390 0.0333

35-45 0.0360 0.0349 0.0354 0.0392 0.0350

45-55 0.0357 0.0356 0.0375 0.0370 0.0355

55-65 0.0616 0.0563 0.0702 0.0580 0.0560
B-9

An exploratory analysis with regression trees (Rawls and Pachepsky, 2002) was used to 

evaluate the possible effect of basic soil properties on apparently random deviations of plotaveraged from MCP-measured water contents at depths from 5 to 55 cm. Sand, silt, and clay 

contents along with bulk density and depth were introduced as potential input variables. The

resulting regression tree is shown in Fig. B-3. The group of plots and depths with sand content 

greater than 62.2% showed on average the largest difference between the plot-averaged and 

MCP measured water contents (-0.030 cm3 cm-3). Where sand content was less than 62.2%, the 

silt content was the splitting variable. The average deviation was negligible at depths and 

locations where silt content was greater than 20.5%. An average difference of 0.021 cm3 cm-3

was found for samples with sand content less than 62.2% and silt content less than 20.5%. 

Neither soil bulk density nor depth was included in the list of splitting variables of the regression 

tree. However, the effect of bulk density could be masked by its correlation with textural 

components along the soil profile (Table B-1). Using high frequency capacitance probes, 

Gardner et al. (1998) concluded that differences in dry bulk density were important, while clay 

and organic matter content were not. 

We attempted to use the average deviations for the texture-based groups in Fig. B-3 to 

correct MCP measured water contents by subtracting group average deviations from the MCP 

measurement results. Improvements were observed in the RMSD values, which decreased from 

0.0458 cm3 cm

-3

to 0.0446 cm3 cm

-3 for the whole soil profile, and from 0.0505 cm3 

cm

-3

to 

0.0429 cm3 cm

-3

for the topsoil (Table B-4). However, corrections for soil texture did not reduce 

the RMSD for the subsoil. Similar results were obtained for the laboratory calibration (data not 

shown). These results imply that correction for texture is possible and desirable if a site-specific 

MCP calibration is to be developed. Since texture was dependent upon depth in our case (Table 

B-1), it actually might have been feasible to develop depth-dependent calibration corrections. 

Overall, both bias and random errors were observed when the differences between plot 

average and MCP-estimated soil water contents were analyzed for the top 65 cm of the coarseloamy, siliceous, mesic Typic Hapludult. Developing a site specific calibration to remove the 

bias appeared to be important. However, random variations apparently dominated the differences 

between plot-averaged and MCP-measured water contents. A linear correction of the calibration 

equation improved the estimates of the plot average water contents from the MCP data, but only 

by 0.7 percent on average, while leaving the RMSD at 0.046 m3 m

-3

overall. Relationships 

between the water content differences and soil texture were observed. Using these relationships 

to correct the MCP measurements increased their similarity to plot-averaged water contents, and 

reducing the RMSD to 0.045 m3 m

-3

overall. A site-specific MCP calibration correction appears 

to be desirable before using a single MCP in soil water monitoring at the plot scale, but the 

methods used here were not adequate for such a calibration. 
B-10

Figure B-3. Average differences between plot-averaged water contents and MCP-measured 

water contents as a function of texture in the upper 50-cm soil layer as expressed with a 

regression tree. ε is the average deviation for the group, and N is the total number of samples in 

the group. 

% Sand < 62. 2

 = 0. 02110

N = 21

 = -0. 03023

N = 12

 = 0. 00049

N = 27

% Silt < 20. 5 

Yes No

Yes No
C-1

APPENDIX C. FIELD-SCALE COUPLED SURFACE-SUBSURFACE FLOW AND 

TRANSPORT MODELING

C1.1 EQUATIONS OF THE MODEL

C1.1.1 Flow model

Overland flow may be simulated using the Saint-Venant conservation equations as (Tseng, 

1999):

Q E G F

t x y

  

  

  

(C-1)

where 

T Q  (h,hu,hv) ,

























 

huv

hu gh

hu

E

2 2

2

1

 





































2 2

2

1

hv gh

huv

hv

G 

















































( )

( )

4 / 3

2 2 2

0

4 / 3

2 2 2

0

h

m v u v

gh S

h

m u u v

gh S

R I

F

y

x

in which h is the flow depth on the soil surface [L]; u and v are the velocity components in the x

and y directions, respectively [LT-1], m/s; g is the acceleration due to gravity [L2T

-1

]; 

x

S0

and 

y

S0

are the surface slope in the x and y directions, respectively, t is time [T], m is Manning‟s 

roughness coefficient [L-1/3T], R is the rainfall rate [LT-1]; and I is the infiltration rate [LT-1]. If 

the local and convective inertial terms and the momentum term owing to rainfall excess are 

neglected, equation (C-1) reduces to its diffusive-wave (DW) approximation (e.g.,Weill et al., 

2009):

g R I

t

h

   



 



(C-2)

where 

( , )

x y







 



is the gradient operator in x-y space. The surface flux 

g



is calculated 

utilizing the two-dimensional form of the empirical Manning equation:

g k (h z)   surf 





(C-3)

where 





2

7 / 3

m

h

ksurf

is the surface conductivity, 

1/ 2

2 2

( ) ( )



































 

 













 

 

y

h z

x

h z s s

and zs is the land surface elevation [L]. 
C-2

The three-dimensional Richards equation as described and implemented in FEMWATER 

(Richards et al., 1997) was used to simulate water flow in variably-saturated soil. The water 

depth on the soil surface water depth was assumed to be equal to the pressure head p if p>0, 

otherwise p≤0. The flux boundary condition on the soil surface is

0

0

( ) ( )

( ) ( ) 0

0

surf surf n

s

n

n

h p z p z K K R p h

t x x y y

p z h K p R p h

n t

R h

      

          

  

     

  

 





(C-4)

where n is the vector normal to the soil surface boundary, 

R Rcos(z,n) n

is the projection of 

rain on the normal n, and n0 is a small parameter. Equations (C-4) can be condensed to the 

computationally more efficient form

0 0

( ) ( ) ( ) ( ) ( ) ( ) ( ) s

surf surf n

h z h h h z h z K p h h K h h K R

n t x x y y



 

        

      

     

(C-5)

where 













0, 0

1, 0

( )

h

h

 h

is the Heaviside function. 

C1.1.2 Transport model

Surface and subsurface solute transport is simulated with the three-dimensional advectivedispersive equation subject to decay, adsorption, and biodegradation in the liquid and solid 

phases (Richards et al., 1997). Overland transport of solutes can be described by the equation

q c D c hc J M

t

c

t

ch

s s

sorb

      











( ) 

( )

 

(C-6)

Here c is the solute concentration in the runoff [M L-3], 

nF

sorb F

c  K c

is the surface density 

of the attached solute [M L-2], KF and nF parameters of the Freundlich equation for the massexchange isotherm, 

D  hdm q

is the surface diffusion-dispersion tensor [L3T

-1

], dm is the 

molecular diffusive component [L2T

-1

], 



is the dispersivity tensor [L], λ is the decay or 

biodegradation rate coefficient [T-1], 

n

c

J cI Dsoil 



  is the rate of solute loss from runoff to 

soil with infiltration [L-2T

-1

], Dsoil is the solute dispersion coefficient in soil [L2T

-1

], M=cRRn is 

the rate of the solute mass influx from rain [ML-2T

-1

], and cR is the concentration of water in rain 

[ML-3]. The solute concentration in soil water on the soil surface is assumed to be equal to the 

concentration in runoff. 

C1.2 COUPLING SURFACE AND SUBSURFACE FLOW AND TRANSPORT IN THE NUMERICAL 

SOLUTION

We combined the public domain three-dimensional FEMFLOW code for saturatedunsaturated subsurface flow and transport with the two-dimensional 2DOIL (Pachepsky et al., 

1993) code for modeling runoff. The 2DSOIL code as coupled with FEMWATER used to alter 
C-3

the matrix coefficients of the boundary surface nodes in the flow and transport numerical 

equations as follows. 

For the 3D mesh, the Richards equation at the surface boundary nodes was integrated using 

the finite element approximation:

0

2( )

1 1

1

1

 





  





 





F

z

q U

A q

t

l l

l z

l l

 

(C-6)

where A is the finite element approximation of the gradient operator 





, and

l

 = ( , , , )

l

i j k  x y z t

and 

( , , , )l

i j k p x y z t

are the water content and pressure heads at node ijk, z=z(xi,yj,zk) is the 

gravitational head for node ijk, q  k( p  z)



is the water flux in the horizontal direction, 

( 1)

1

1/ 2







 



z

p

q k

l

z z

is water flux in the vertical direction, 

z

p

l





1

is pressure gradient in the 

vertical direction between the top surface boundary node and the next node in the vertical 

direction, 

z

and 

1/ 2

z

k

are the distance and the conductivity between these two nodes; 

n

l

l l

l

g R

t

h h

U   











 1

1

1



is a surface boundary flux (which is an approximation from 

surface flow equation (C-6)) and 













0 0

0

p

p p

h

is surface flow depth. Equation (6) can be 

rewritten as 

0

2( )

1 1

1

1

 





  





 





F

z

q U

A q

t

l l

l z

l l



   

(C-7)

where 

p p z

l l l





  2( ) /

is the corrected water content at the surface boundary nodes and 

( )

1 1 1 1 1

q q g k p z

l l l l l

     

    





 is the corrected flux at the surface boundary nodes in the x or 

y directions; 

k k k z

   surf 2/

is the corrected hydraulic conductivity of the surface boundary 

nodes; and 

(h)

is the Heaviside function. A similar approach was used for the transport 

simulations. 

Ponding did not generally occur simultaneously at all surface nodes, but the ponding front 

moved along the slope until all nodes were ponded. Similarly, the drying front (i.e., the front 

where runoff ceased to exist) also was moving from one node to another. Advances in the 

ponding and drying fronts were simulated by using upwind schemes for the nodes bracketing the 

front. The surface flow pressure gradient in the horizontal x and y directions could not be greater 

than the surface water layer gradient in those direction since the gradient is determined only of 

the depth of the surface water layer. For the wet or dry front for surface flow we used the 

limitation of surface horizontal gradient and upwind scheme for surface conductivity. 

Specifically, we used the control volume finite-element method for approximating the twodimensional surface flow and mass transport equation (Baliga and Patankar, 1980, 1983). For a 

rectangular surface mesh with two neighboring surface nodes, horizontal surface flow g

l+1,s+1 and 

conductivity

s

surf k

1/ 2

during iteration process on s+1 iteration is determined as

z

e

z z

e

p p

p p

p p

g k

l S l s

l S l S

l S l S

l S

surf

l s 





























 

 

  

   

 

 

  

/

max( ,0) max( ,0)

1

1, 1 1, 1

1

1, 1,

1

1, 1,

1, 1

1/ 2

1, 1







(C-8) 
C-4

where 





 

 

 

 

l S l S

l S l S

p p

p p

1, 1,

1

1, 1,

1 max( ,0) max( ,0)

automatically limits the value of the pressure gradient 

and 



















  

  

  



  

  

   



otherwise

k P P z z

k P P z z

k k P P

k

l S l S l S

surf

l S l S l S

surf

l S l S l S

surf

l S

surf

l S

surf

0

/ 2 0& ( )

/ 2 0& ( )

( ) / 2 0& 0

1

1, 1, 1,

1

1,

1

1,

1

1,

1

1,

1

1, 1,

1

1,

1,

1/ 2



(C-9)

In which 

l S

surf k

1,

1/ 2

  determines the possible direction and rate of surface flow front movement,

e

is the step in x or y direction. Using this approximation limits the surface pressure gradient 

prevents the erroneous computation of the flow from dry sells. This procedure provides the 

numerical stability and mass conservation in the surface flow. Overall, the surface flow equation 

was approximated only in surface boundary nodes and was solved simultaneously with the 

Richards equation in subsurface. The matrix of nonlinear system algebraic Richards equations 

had to be modified only in boundary nodes 

Two small parameters were introduced to prevent oscillations and to save the computation 

time. First, runoff was deemed to be formed and solution of the equations (C-7) began when the 

soil pressure head on the surface exceeded a small positive number h0 that could be viewed as an 

initial thickness of the water film on the surface. The value of h0 was set to 10-4 m. Second, the 

discontinuous Heaviside function and its derivative, the Dirac function, were replaced with their 

continuous approximations:

2 2

1

( )

arctg( / )

1

( )

h

h

h h h



 

 















(C-10)

where ω is the spread parameter. This allowed avoiding iterations to find the ponding time in 

each of surface nodes. The value of ω was 0.01m. 

Because of relatively poor mass balances observed in the flow and transport simulations, we 

changed the numerical scheme and used the control volume finite-element method (Baliga and 

Patankar, 1983) in FEMWATER and upstream weighing in 2DSOIL as implemented in the 

SWMS2D model (Simunek et al., 1994). These changes provided a satisfactory mass balance.
BIBLIOGRAPHIC DATA SHEET

(See instructions on the reverse)

NRC FORM 335

(9-2004)

NRCMD 3.7

U.S. NUCLEAR REGULATORY COMMISSION 1. REPORT NUMBER

 (Assigned by NRC, Add Vol., Supp., Rev.,

 and Addendum Numbers, if any.)

NUREG/CR-7026

3. DATE REPORT PUBLISHED

MONTH

March

YEAR

2011

4. FIN OR GRANT NUMBER

N6235

2. TITLE AND SUBTITLE

Application of Model Abstraction Techniques to Simulate Transport in Soils

5. AUTHOR(S)

Y. Pachepsky, T. Gish, and A. Guber (USDA/ARS); A. Yakirevich and M. Kouznetsov (BGU),

M. Van Genuchten (UFRJ), T. Nicholson and Ralph Cady (NRC)

(ARS- Agricultural Research Service, BGU - Ben-Gurion University of the Negev, UFRJ -

Federal University of Rio de Janeiro)

6. TYPE OF REPORT

Technical

7. PERIOD COVERED (Inclusive Dates)

September 2005 - October 2009

8. PERFORMING ORGANIZATION - NAME AND ADDRESS (If NRC, provide Division, Office or Region, U.S. Nuclear Regulatory Commission, and mailing address; if contractor,

Agricultural Research Service

9. SPONSORING ORGANIZATION - NAME AND ADDRESS (If NRC, type "Same as above"; if contractor, provide NRC Division, Office or Region, U.S. Nuclear Regulatory Commission, 

Division of Risk Analysis

provide name and mailing address.)

and mailing address.)

10. SUPPLEMENTARY NOTES

T.J. Nicholson, NRC Project Manager

11. ABSTRACT (200 words or less)

Successful understanding and modeling of contaminant transport in soils and groundwater is a precondition of risk-informed

predictions of the subsurface contaminant transport. Exceedingly complex models of subsurface transport are often inefficient.

Model abstraction is a methodology for reducing the complexity of a simulation model while maintaining the validity of the

simulation. The objective of this work was to use model abstraction techniques to characterize and understand flow and

transport in soils in the presence of shallow groundwater. We developed two case studies by carrying out two types of field tracer

experiments at the USDA-ARS OPE3 Beltsville field site, and applying a sequence of model simplifications based on the

HYDRUS software family and MODFLOW. Soil moisture, soil water potential, tracer concentrations in groundwater, groundwater

levels, and weather data, along with ground penetration radar surveys, electric resistivity monitoring, and dilution tests

complemented borehole log data and laboratory hydraulic measurements to characterize soil heterogeneity. The invoked series

of model abstractions showed the important role of subsurface heterogeneity in the vadose zone and groundwater, and

substantial improved the conceptualization of the subsurface. Results of this study provide techniques to aid the NRC licensing

staff in their review of a licensee's abstraction of complex transport models, and to help confirm the acceptability of model

abstraction assumptions used in performance assessments.

12. KEY WORDS/DESCRIPTORS (List words or phrases that will assist researchers in locating the report.)

field tracer experiment

flow and transport modeling

ground water

model abstraction

model simplification

pedotransfer function

soil water 

subsurface contaminant transport

uncertainty

vadose zone

14. SECURITY CLASSIFICATION

13. AVAILABILITY STATEMENT

unlimited

(This Page)

unclassified

(This Report)

unclassified

15. NUMBER OF PAGES

16. PRICE

NRC FORM 335 (9-2004) PRINTED ON RECYCLED PAPER

Beltsville Agricultural Research Center

10300 Baltimore Boulevard

Beltsville, MD 20705

Office of Nuclear Regulatory Research

U.S. Nuclear Regulatory Commission

Washington, DC 20555-0001