NUREG/CR-7221

Integrating Model Abstraction 

into Subsurface Monitoring 

Strategies

Office of Nuclear Regulatory Research

NUREG/CR-7221

Integrating Model Abstraction 

into Subsurface Monitoring 

Strategies

Office of Nuclear Regulatory Research

Manuscript Completed: December 2012

Date Published: March 2017

Prepared by:

Y. Pachepsky1, A. Guber1, A. Yakirevich2, 

F. Pan1, T. Gish1, M. Kouznetsov2,

M. Van Genuchten3, R. Cady4, T. Nicholson4

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

4Division of Risk Analysis

Office of Nuclear Regulatory Research

U.S. Nuclear Regulatory Commission

Washington, DC 20555

T.J. Nicholson, NRC Project Manager

NRC Job Code N6730

iii 

ABSTRACT 

NUREG/CR-7221 reports on integrating modeling abstraction techniques into subsurface 

monitoring strategies. This research is the culmination of many field and modeling studies 

conducted by the USDA/Agricultural Research Service (ARS) at their Beltsville Area Research 

Center. The research design was to identify and examine near-surface water flow pathways by 

monitoring performance indicators within the unsaturated zone and local water-table system. The 

peak tracer concentration and the time to peak concentration at several monitoring locations 

served as the performance indicators. The objective was to apply model abstraction techniques in 

designing monitoring networks such as those used at nuclear waste and decommissioned 

facilities. The level of spatial and temporal detail in characterizing soil properties (e.g. water 

contents and hydraulic conductivities) is based upon the model abstraction considerations. 

Simplifications may omit significant processes and conditions that control the water and 

contaminant migration. The ARS field studies provided detailed databases for modeling water 

and chemical tracer movement in 2- and 3- dimensions to facilitate understanding of what 

processes and properties could be simplified (abstracted). Model abstractions included using 

pedotransfer functions for hydraulic conductivity, soil profile homogenization, and unsaturated 

zone omission. This latter abstraction proved to be the most accurate in generating a monitoring 

network that reflected the calibrated model. A comprehensive sensitivity analysis was performed 

to identify possible directions of model simplification in the model abstraction process. The 

integration of model abstraction into monitoring strategies based upon the ARS field and modeling 

findings was documented and reviewed by international soil scientists. The studies were jointly 

funded by NRC and USDA/ARS. 

v 

FOREWORD 

This technical report was prepared by the USDA’s Agricultural Research Service (ARS), under a 

follow-on to Interagency Agreement 05-005 (RES-05-005, JCN N6730) with the Office of 

Nuclear Regulatory Research. The objective was to characterize how groundwater model 

abstractions (simplifications) within conceptual site models impact subsurface monitoring 

strategies. These monitoring strategies are used to confirm the performance of nuclear waste 

and decommissioned facilities. Numerical models which assess environmental impacts rely on 

both the conceptual site model simplifications (abstractions) and the monitoring data. The 

monitoring networks should incorporate the significant processes and conditions of the model 

abstraction, and be compatible with the performance indicators of the numerical models. 

The findings in this report represent the culmination of efforts presented in NUREG/CR-6884 and 

NUREG/CR-7026. These reports were previously developed under Interagency Agreement 02-

008 (RES-02-008), “Model Abstraction Techniques for Soil Water Flow and Transport.” The 

research presented in this document builds upon the previous work by characterizing the 

accuracy of ground-water monitoring networks derived from abstracted subsurface models. 

NRC licensees and NRC licensing staff routinely develop and assess numerical models of 

subsurface transport based upon conceptual site models. Simplifications in these models are due 

to uncertainties in identifying the significant flow and transport processes, parameter estimations 

and soil structure as reflected in the model framework. Examples of these simplifications include: 

soil profile homogenization, unsaturated zone omission, and pedotransfer function usage to 

estimate hydraulic conductivities. This report directly addresses how such simplifications impact 

ground-water monitoring networks. NRC staff can use the information presented here to review 

licensees’ monitoring and modeling programs, and assess the use of more compact, efficient 

ground-water models. 

This report is not a substitute for NRC regulations, and compliance is not required. Consequently, 

the approaches and methods described in this report are provided for information only, and 

publication of this report does not necessarily constitute NRC approval or agreement with the 

information contained herein. Similarly, the use of product or trade names in this report is intended 

for identification purposes only and does not constitute endorsement by either the NRC or 

USDA/ARS. 

________________________________ 

Michael F. Weber 

Director of Nuclear Regulatory Research 

________________________________

vii 

TABLE OF CONTENTS 

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

FOREWORD............................................................................................................................. v

LIST OF FIGURES................................................................................................................ xi

LIST OF TABLES............................................................................................................... xvii

EXECUTIVE SUMMARY.................................................................................................. xix

ACKNOWLEDGMENTS................................................................................................. xxiii

ABBREVIATIONS AND ACRONYMS....................................................................... xxv

1 INTRODUCTION......................................................................................................... 1-1

1.1 Background ............................................................................................................. 1-1

1.2 Objectives............................................................................................................... 1-2

1.3 Approach................................................................................................................. 1-2

2 MONITORING AND MODEL ABSTRACTION IN SUBSURFACE 

HYDROLOGY.............................................................................................................. 2-1

 2.1 Model Abstraction in Subsurface Hydrology .................................................. 2-1

2.1.1 Background ..................................................................................................... 2-1

2.1.2 Abstraction of Model Structure ..................................................................... 2-2

2.1.3 Abstraction of Parameter Determination ..................................................... 2-6

2.1.4 Systematic Model Abstraction ...................................................................... 2-8

2.1.5 Model Abstraction vs. Arbitrary Selection of a “Simple” Model ..................... 2-12

2.2 Approaches to Modeling-Based Monitoring Optimization ............................... 2-13

 2.2.1 Background .................................................................................................... 2-13

 2.2.2 Components of a Groundwater Monitoring Network Design ......................... 2-14

2.2.3 Methods of Groundwater Monitoring Network Design ................................... 2-15

2.2.4 Groundwater Monitoring Network Design Based on Flow and 

 Transport Models ........................................................................................... 2-18

2.3 Integrating Model Abstraction into Monitoring Design ..................................... 2-25

3 EXPERIMENT TO TEST AND CONFIRM MODEL ABSTRACTION 

FOR MONITORING FLOW AND TRANSPORT IN SOILS...................... 3-1

3.1 Outline of Lateral Flow and Transport Experiment............................................. 3-1

3.2 The OPE3 Experimental Site at the Beltsville Agricultural Research 

Center...................................................................................................................... 3-2

3.2.1 General Description ......................................................................................... 3-2
viii 

3.2.2 Existing OPE3 Information Relevant to Flow and Transport in Soils ................3-4

3.2.3 Surveying, Monitoring and Site-Specific Transport Experiments ................... 3-23

4 DETAILED FLOW AND TRANSPORT MODELS OF THE OPE3 

WATERSHED SITE................................................................................................... 4-1

4.1 Description of Models............................................................................................. 4-1

4.1.1 The HYDRUS-3D Code ................................................................................... 4-2

4.1.2 Modified TOUGH2 Code .................................................................................. 4-3

4.1.3 FULL-3D and QUASI-3D Models ..................................................................... 4-4

4.2 Model Calibration.................................................................................................... 4-9

4.2.1 Geometry of the Simulation Domain and Soil Material Distribution ................. 4-9

4.2.2 Initial and Boundary Conditions ..................................................................... 4-10

4.2.3 Model Calibration ........................................................................................... 4-18

5 SYSTEMATIC APPROACH FOR SIMPLIFYING THE OPE3 SITE 

MODEL........................................................................................................................... 5-1

5.1 Sensitivity Analysis to Direct Model Simplification ............................................. 5-1

5.1.1 Analysis of Subsurface Flow and Transport Processes .................................. 5-2

5.1.2 Performance Assessment Indicators ................................................................ 5-9

5.1.3 Transport Parameters ....................................................................................... 5-9

5.1.4 Subsurface Textural Units............................................................................... 5-18

5.1.5 Boundary Conditions ...................................................................................... 5-18

5.1.6 Sampling Frequency ....................................................................................... 5-22

5.1.7 Soil Material Elimination.................................................................................. 5-25

5.2 Model Abstraction Applications........................................................................... 5-29

5.2.1 Geometry of the Simulation Domain and Soil Material Distribution ............... 5-29

5.2.2 Initial and Boundary Conditions ..................................................................... 5-36

5.2.3 Simulation Scenarios ..................................................................................... 5-36

5.2.4 Performance Indicators .................................................................................. 5-37

5.2.5 Abstraction of Parameter Determination: Using Pedotransfer 

 Functions ........................................................................................................ 5-44

5.2.6 Abstraction of Profile Aggregation ................................................................. 5-50

5.2.7 Abstraction by Ignoring Unsaturated Zone .................................................... 5-51

5.2.8 Abstraction of Parameter Determination: Pedotransfer Functions and 

Hydraulic Conductivity Scaling ................................................................... 5-60

6 APPLICATIONS OF MODEL ABSTRACTION IN MONITORING 

NETWORK DESIGN................................................................................................. 6-1
ix

6.1 Selecting Monitoring Locations to Decrease Prediction Uncertainty ............... 6-1

6.1.1 A Linear Statistical Inference Method to Assess Data Importance to 

 Model Predictions, Sensitivity and Model Abstraction .................................... 6-1

6.1.2 Observation-Prediction Statistics Application ................................................. 6-3

6.1.3 Selecting Monitoring Locations Based on Statistical Analysis of the 

 Performance Indicators ................................................................................. 6-13

6.1.4 Model Abstraction Applicability for Selection of Monitoring Locations .......... 6-15

6.2 Selecting Monitoring Locations for Model Discrimination................................ 6-23

6.2.1 Kullback-Himmelblau Sequential Design Method ......................................... 6-23

6.2.2 Applications of the Kullback-Himmelblau Method ......................................... 6-26

7 SUMMMARY AND CONCLUSIONS.................................................................. 7-1

8 REFERENCES ............................................................................................................ 8-1

APPENDIX A REVIEWING ASSUMPTIONS MADE DURING 

 DEVELOPMENT OF THE BASE MODEL AND 

 JUSTIFICATIONS FOR THOSE ASSUMPTIONS.............. A-1

APPENDIX B THE QUASI-3D CODE BENCHMARKING ............................ B-1

xi

LIST OF FIGURES 

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

modeling in subsurface hydrology. ......................................................................... 2-2

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

or in unsaturated fractured rock (after Altman et al., 1996)..................................... 2-3

Figure 2-3 Spatial and temporal operational scales in hydrology (after Blöschl and Sivapalan, 

1995). ...................................................................................................................... 2-4

Figure 2-4 Relationships between the scale of measurement and the saturated hydraulic 

conductivity of soils and sediments; a – saprolite, North Carolina; measurements 

on cores, columns, and at the drain field scale (Vepraskas and Williams, 1995); 

b – Kokomo clay soil, Ohio; measurements with a permeameter, on cores, and 

on soil blocks (Zobeck et al., 1985); c – aquifer in a stream alluvium, Columbus, 

Ohio; measurements with a permeameter, flow meter, and using a slug test 

(Zlotnik et al., 2000); d – aquifer in glacial outwash, Cape Cod, MA (Zlotnik et al., 

2000); e, f, g, h – aquifers in Wisconsin (Schulze-Makuch et al., 1999), e –glacial 

outwash sediments, f – carbonate aquifer, g – high magnesium limestone with 

shale, h – finely crystalline dolomite,  - permeameter tests,  - piezometer 

tests,  - packer tests, - single well pumping and specific capacity tests; 

oversized symbols show averages over a large number of replications. .............. 2-10

Figure 2-5 Design of model abstraction via model structure and parameter 

determination ........................................................................................................ 2-13

Figure 2-6 Classification of groundwater monitoring network objectives (after Loaiciga et al, 

1992). .................................................................................................................... 2-17

Figure 2-7 Classification of groundwater monitoring design approaches .....................................

(after Hassan, 2003). ............................................................................................ 2-17

Figure 3-1 The USDA-ARS OPE3 research site; a – aerial view, b – instrumentation. A, B, 

C, D – research fields. ............................................................................................ 3-3

Figure 3-2 Locations of groundwater wells (brown circles) and soil moisture sensors (green 

circles) at field B. .................................................................................................... 3-5

Figure 3-3 Basic soil properties at the OPE3 site based on data of soil survey conducted in 

1999........................................................................................................................ 3-8

Figure 3-4 Soil texture at the OPE3 site based on data of soil survey conducted in 1999. ...... 3-9

Figure 3-5 Soil water retention data of samples collected at locations near wells w50 and 

w52 of field B; 2-5 cm depth, b) 20-23 cm depth, and c) 47-50 cm depth (●,○ –

well w50, ,- well w52). ......................................................................................3-10

Figure 3-6 Probability distributions of the saturated hydraulic conductivity for 20 cm2 

support areas; a – field falling head measurements; - well w50, depth 25 

cm , - well w50, depth 45 cm, - well 52, depth 25 cm, - 

well 52, depth 40 cm; b – constant head measurements of vertical (KSV) and

horizontal (KSH) conductivities of undisturbed samples with 20 cm2 support

area in the laboratory (error bars show standard deviations). ..............................3-11

Figure 3-7 Water seepage from the wall above a locally restrictive soil layer near well 

w50. ...................................................................................................................... 3-12

Figure 3-8 Layout of the 7.5-ha site overlain by a 25x25 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, with permission)..............................................................3-14
xii 

Figure 3-9 Ground-penetrating radar image with a digital trace of the first restricting layer, 

indicated by the dotted line (after Gish et al., 2002, with permission). .................. 3-15

Figure 3-10 Interpolated elevation of the first continuous restricting layer with potential 

subsurface flow pathways (blue lines) identified using Arc/Info hydrologic 

tools. ..................................................................................................................... 3-16

Figure 3-11 Time series of groundwater depths measured in field B in 2006-2007................3-18

Figure 3-12 Changes in soil water storage of the 0-80 cm soil layer measured at 8 locations 

of field B from May 1, 2001 through January 1, 2003. ..........................................3-19

Figure 3-13 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. ...3-20

Figure 3-14 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 yellow, green and light blue lines designate subsurface flow pathway 

locations. The yellow 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 having 

yields below the mean. ......................................................................................... 3-21

Figure 3-15 Spatial corn yield variations 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......................................................................................................... 3-22

Figure 3-16 Setup of the lateral flow experiment. .....................................................................3-24

Figure 3-17 Schematic of the data acquisition and collection system. ....................................3-26

Figure 3-18 Locations of multi-sensor capacitance probes and groundwater wells (indicated 

by “Loc-” number) at the experimental plot. ......................................................... 3-26

Figure 3-19 Soil texture measured at 10 depths in 12 location . .............................................3-27

Figure 3-20 Measured clay, silt, sand and organic carbon distributions in the soil profiles. ...3-28

Figure 3-21 Measured soil bulk density distributions versus depth at locations 1 through 4.. 3-30

Figure 3-22 Soil texture measured in logs w01-w52 at field B. ...............................................3-32

Figure 3-23 Laboratory measured saturated hydraulic conductivities, Ks. .............................3-32

Figure 3-24 Laboratory-measured soil water retention curves. .............................................. 3-33

Figure 3-25 Monthly (a) and cumulative values (b) of evapotranspiration and precipitation 

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

2006 – September 2007). .....................................................................................3-35

Figure 3-26 Examples of soil water content and pressure head time series measured at 

locations 1 and 2 in July 2006 September 2007. .................................................3-36

Figure 3-27 Groundwater depths measured at the experimental site during the period 

November 2007 - March 2008. ............................................................................ 3-38

Figure 3-28 Plots of measured soil water pressure heads versus volumetric water contents 

at locations 1-4......................................................................................................3-39

Figure 3-29 Example of ground-penetrating radar images used to delineate hydrological soil 

layers. ...................................................................................................................3-40

Figure 3-30 Plots of (a) the vertical water content distribution measured at locations BH3, 

BH4, BL3, BL4, BM2, BM3, and BM4 during the GRP survey, (b) the dielectric 

constant computed from average water contents among locations, and (c) the 

minimum, average and maximum time of GPR wave propagation computed 

from the soil dielectric constant profiles at seven locations. ................................. 3-43

Figure 3-31 Depths to six out of seven soil hydrological layers delineated using the fine-scale 

GPR survey at the experimental part of field B in 2006. The color scale in the 

legend indicates depths in cm. .............................................................................. 3-44
xiii 

Figure 3-32 Plots of (a) the irrigated plot equipped with tensiometers, MCPs and a flume for 

runoff collection, (b) the tracer application tanks, (c) the observation wells with 

the tracer sampling outlets, and (d) the windshield around the tracer application 

area. ...................................................................................................................... 3-45

Figure 3-33 Cumulative water fluxes measured during the lateral flow experiment. ................ 3-47

Figure 3-34 Groundwater depths measured at the experimental site during the period 

November 2007 - March 2008. ............................................................................. 3-48

Figure 3-35 Soil water content measured at 12 locations during the lateral flow experiment.3-49

Figure 3-36 Chloride contents of groundwater measured in 12 wells during the lateral flow 

experiment. ........................................................................................................... 3-50

Figure 4-1 Modeled variably-saturated subsurface system with a section of the finite 

difference (FD) grid (dashed lines). ........................................................................ 4-5

Figure 4-2 Mesh generated for HYDRUS-3D simulations. Observations nodes are shown 

in yellow. ............................................................................................................... 4-11

Figure 4-3 Vertical distribution of clay, silt and sand contents measured at 12 locations.....4-12

Figure 4-4 Soil texture groups obtained with cluster analysis. ............................................... 4-13

Figure 4-5 ROSETTA estimated soil water retention curves for selected soil texture groups.4-14

Figure 4-6 Material distribution used for the HYDRUS-3D simulations. ................................. 4-15

Figure 4-7 Initial and boundary conditions used for HYDRUS-3D simulations. ..................... 4-16

Figure 4-8 Daily irrigation, precipitation and evapotranspiration data used for the 

HYDRUS-3D simulation. .......................................................................................4-17

Figure 4-9 Observed (dots) and HYDRUS-3D simulated (continuous lines) groundwater 

depth time series. ..................................................................................................4-20

Figure 4-10 Observed (dots) and HYDRUS-3D simulated (continuous lines) Clconcentrations in wells L1-L12..............................................................................4-22

Figure 4-11 Mesh generated for the TOUGH2 simulations. ..................................................... 4-23

Figure 4-12 Observed (dots) and TOUGH2 simulations of groundwater depth time series. ..4-25

Figure 4-13 Depth-averaged observed (dots) and TOUGH2 simulated (continuous lines) Clconcentrations of wells 1-12. ................................................................................4-26

Figure 5-1 HYDRUS-3D simulated soil water contents at 12 locations. Constant values are 

where soil remains saturated. .................................................................................5-4

Figure 5-2 HYDRUS-3D simulated Cl- concentrations at 12 locations. ..................................5-5

Figure 5-3 Total water (a-d) and Cl- (e-h) fluxes obtained in HYDRUS-3D simulations during 

132 days at three depths in 12 monitoring locations. .............................................. 5-7

Figure 5-4 Relationships between total Cl- and water fluxes for four depths. Observation well 

numbers are shown above the symbols. ................................................................ 5-8

Figure 5-5 Time series of the sensitivity index Si along with its components obtained for 

HYDRUS-3D simulations using two levels of the saturated hydraulic conductivity 

of the SL1 soil material. ........................................................................................ 5-11

Figure 5-6 Time series of the sensitivity index Si obtained in HYDRUS-3D simulations with 

two levels of the saturated hydraulic conductivity for eight soil materials. ............ 5-14

Figure 5-7 Time series of the sensitivity index Di obtained in HYDRUS-3D simulations with 

two levels of the saturated hydraulic conductivity for eight soil materials. ............ 5-15

Figure 5-8 Sensitivity of the HYDRUS-3D and TOUGH2 models to the hydraulic 

conductivity (a, d), longitudinal (b, e) and transversal (c, f) dispersivity assessed 

for eight soil materials using time-averaged Si indices and their standard 

deviations SDSi. .................................................................................................... 5-16

Figure 5-9 Sensitivity of the HYDRUS-3D model to the hydraulic conductivity Ks (a,d), 

longitudinal dispersivity αL (b,e) and transversal dispersivity αT (c,f) assessed at 

seven observation wells using Si and Di indices for simulated peak 

concentrations Cpeak and times Tpeak. .................................................................... 5-17
xiv 

Figure 5-10 Temporal variation of the sensitivity index Di obtained in HYDRUS-3D 

simulations with extended and truncated material boundaries. ............................ 5-19

Figure 5-11 Temporal variation of the sensitivity index Di obtained in the TOUGH2 

simulations with extended and truncated material boundaries. ............................ 5-20

Figure 5-12 Temporal variation of the sensitivity index Di obtained in the LSA of the 

HYDRUS-3D and TOUGH2 models to runoff (a,b), evaporation (c,d) and 

groundwater depth. ............................................................................................... 5-23

Figure 5-13 Errors of predicting Cl- concentrations (RMSE), peak Cl- concentrations 

(ΔCpeak) and peak times (ΔTpeak) obtained in the HYDRUS-3D and TOUGH2 

simulations for measurements taken at different time intervals. ........................... 5-24

Figure 5-14 Alternative soil texture for the HYDRUS-3D model simplification. ........................ 5-26

Figure 5-15 Root-mean-square errors (RMSE) of predicting Cl- concentrations obtained with 

two models using the original and modified properties for SCL2 soil material. ..... 5-27

Figure 5-16 Errors of peak Cl- concentrations (ΔCpeak) and peak times (ΔTpeak) obtained 

with the HYDRUS-3D using the original and modified properties for SCL2 soil 

material. ................................................................................................................ 5-28

Figure 5-17 Boundary of new simulation domain with old (brown circles) and new (green 

circles) groundwater wells. .................................................................................... 5-31

Figure 5-18 Material distribution for the HYDRUS-3D mesh. ................................................... 5-32

Figure 5-19 Mesh generated for HYDRUS-3D simulations (a) with coordinates for 100 

output locations (b). .............................................................................................. 5-34

Figure 5-20 Probability distribution of the decade precipitation (a) and cumulative 

precipitation for decades with 25%, 50% and 75% probabilities (b). .................... 5-35

Figure 5-21 Spatial distributions of log10(Cpeak[ppm]) performance indicator obtained in 

HYDRUS-3D simulations with the calibrated parameters during 10-year 

simulation period in two scenarios for contaminant source locations, two GWD 

scenarios and precipitation probabilities of 25%, 50% and 75%. ........................5-40

Figure 5-22 Spatial distributions of Tpeak [day] performance indicator obtained in 

HYDRUS-3D simulations with the calibrated parameters during 10-year 

simulation period in two scenarios for contaminant source locations, two 

GWD scenarios and precipitation probabilities of 25%, 50% and 75%. ...............5-42

Figure 5-23 Spatial distributions of log10(QC [ppm m day-1]) performance indicator obtained 

in HYDRUS-3D simulations with the calibrated parameters during 10-year 

simulation period in two scenarios for contaminant source locations, two GWD 

scenarios and precipitation probabilities of 25%, 50% and 75%. ........................5-43

Figure 5-24 Spatial distributions of log10(Cpeak[ppm]) performance indicator obtained in 

HYDRUS-3D simulations with the abstracted Ks parameters during 10-year 

simulation period in two scenarios for contaminant source locations, two GWD 

scenarios and precipitation probabilities of 25%, 50% and 75%. ........................5-45

Figure 5-25 Spatial distributions of Tpeak[day] performance indicator obtained in HYDRUS-3D 

simulations with the abstracted Ks parameters during 10-year simulation period 

in two scenarios for contaminant source locations, two GWD scenarios and 

precipitation probabilities of 25%, 50% and 75%. ................................................ 5-46

Figure 5-26 Spatial distributions of log10(QC [ppm m day-1]) performance indicator obtained 

in HYDRUS-3D simulations with the abstracted Ks parameters during 10-year 

simulation period in two scenarios for contaminant source locations, two GWD 

scenarios and precipitation probabilities of 25%, 50% and 75%. ........................5-47

Figure 5-27 Efficiency indices of the parameter determination abstraction. ........................... 5-49

Figure 5-28 Spatial distributions of log10(Cpeak[ppm]) performance indicator obtained in 

HYDRUS-3D simulations with profile aggregated parameters during 10-year 
xv

simulation period in two scenarios for contaminant source locations, two GWD 

scenarios and precipitation probabilities of 25%, 50% and 75%. ........................5-52

Figure 5-29 Spatial distributions of Tpeak[day] performance indicator obtained in HYDRUS-3D 

simulations with profile aggregated parameters during 10-year simulation period 

in two scenarios for contaminant source locations, two GWD scenarios and 

precipitation probabilities of 25%, 50% and 75%. ................................................5-53

Figure 5-30 Spatial distributions of log10(QC [ppm m day-1]) performance indicator obtained in

HYDRUS-3D simulations with the profile aggregated parameters during 10-year 

simulation period in two scenarios for contaminant source locations, two GWD 

scenarios and precipitation probabilities of 25%, 50% and 75%. ........................5-54

Figure 5-31 Efficiency indices of the profile aggregation abstraction. .....................................5-55

Figure 5-32 Spatial distributions of log10(Cpeak[ppm]) performance indicator obtained in 

HYDRUS-3D simulations with ignoring unsaturated zone during 10-year 

simulation period in two scenarios for contaminant source locations, two GWD 

scenarios and precipitation probabilities of 25%, 50% and 75%. ........................5-56

Figure 5-33 Spatial distributions of Tpeak[day] performance indicator obtained in HYDRUS-3D 

simulations with ignoring unsaturated zone during 10-year simulation period in 

two scenarios for contaminant source locations, two GWD scenarios and 

precipitation probabilities of 25%, 50% and 75%. ................................................ 5-57

Figure 5-34 Spatial distributions of log10(QC [ppm m day-1]) performance indicator obtained 

in HYDRUS-3D simulations with limiting input domain abstraction during 10-year 

simulation period in two scenarios for contaminant source locations, two GWD 

scenarios and precipitation probabilities of 25%, 50% and 75%. ........................5-58

Figure 5-35 Efficiency indices for ignoring the unsaturated zone abstraction. ....................... 5-59

Figure 5-36 Observed and simulated chloride concentrations in locations 5 through 9 with 

saturated hydraulic conductivity values obtained with different parameterization 

methods: CAL – manual calibration, PTF - using pedotransfer functions of Rawls 

et al. (1998), A1 through A6, PTF-estimated valued scaled to the size of the 

computational cells. .............................................................................................. 5-62

Figure 5-37 Root-mean-square errors (RMSE) and slopes of regressions ‘ simulated vs. 

observed chloride concentrations’ in locations 5 through 9 with saturated 

hydraulic conductivity values obtained with different parameterization methods: 

CAL – manual calibration, PTF - using pedotransfer functions of Rawls et al. 

(1998), A1 through A6 - PTF-estimated valued scaled to the size of the 

computational cells. Regressions were computed with the intercept set to 

zero. ...................................................................................................................... 5-63

Figure 6-1 Simulation domain with existing (red symbols) and new (hypothetical) observation 

wells. The numbers at the plot identify new well numbers. ..................................... 6-5

Figure 6-2 Examples of time series of the sensitivity index Si(Ks) for eight materials in well 5 

and well 38 locations. ..............................................................................................6-6

Figure 6-3 Number of days with nonzero Si values for each material (a) and Si variations in 

50 observation wells. .............................................................................................. 6-7

Figure 6-4 New observation locations selected based on maximum Si values (yellow 

triangles) and on averaged OPR statistics (green triangles)................................... 6-8

Figure 6-5 Percent of increased uncertainty caused by removal one existing observation 

well. New observation well numbers are shown in parenthesis on X-axis. ........... 6-10

Figure 6-6 Percent of decreased uncertainty caused by adding one new observation 

well ....................................................................................................................... 6-11

Figure 6-7 Ranks of new observation wells at two depths computed based on the percent 

of decreased uncertainty caused by adding one new well. ................................... 6-12
xvi

Figure 6-8 Frequency distributions for the Cpeak

max in 11 transects (a), and monitoring locations

selected based on the frequency distributions of 3 performance indicators (b) .... 6-14

Figure 6-9 Spatial distributions of the performance indicators at 3 probability levels 

obtained in HYDRUS-3D simulations with the calibrated parameters. ................. 6-16

Figure 6-10 Monitoring locations selected using the frequency (a) and probability 

(b) approaches for 3 performance indicators. ....................................................... 6-17

Figure 6-11 Spatial distributions of the performance indicators at 3 probability levels 

obtained in HYDRUS-3D simulations with the abstracted parameters. ................ 6-19

Figure 6-12 Spatial distributions of the performance indicators at 3 probability levels 

obtained in HYDRUS-3D simulations with the abstracted soil profile. .................. 6-20

Figure 6-13 Spatial distributions of the performance indicators at 3 probability levels 

obtained in HYDRUS-3D simulations with the discarded unsaturated zone. ........ 6-21

Figure 6-14 Monitoring locations selected for the calibrated model and two abstractions using 

the frequency (a, b, c) and probability (d, e, f) approaches. .................................6-22

Figure 6-15 Simulation setup for synthetic example. ............................................................... 6-28

Figure 6-16 Distribution of scaling factor of saturated hydraulic conductivity in the simulation 

domain. ................................................................................................................. 6-28

Figure 6-17 Simulated contaminant distribution after 60 days, at the layer of z=7.5 m. ........... 6-29

Figure 6-18 Comparison of the BTCs obtained in the HYDRUS simulations (a) and using the 

analytical model (b) with the observed in two observation wells. .......................... 6-31

Figure 6-19 Distribution of the calculated values of discriminant function, Kv. ......................... 6-32

Figure 6-20 Modeling domain with finite element mesh and observation locations. ................ 6-34

Figure 6-21 Soil materials in two subsurface structure models: a) Model 1 - Layered media, 

b) Model 2 - Layers and lenses media (shown layers 4-10) ................................. 6-34

Figure 6-22 Example of a stochastic realization for the hydraulic conductivity scaling factor 

(SF). ...................................................................................................................... 6-36

Figure 6-23 Spatial distribution of tracer concentration after 120 days in 5th layer (z=2.75 m): 

a) Model 1, b) Model 2. ......................................................................................... 6-36

Figure 6-24 Simulations of the tracer BTCs in locations 5-12: a) Model 1; b) Model 2. ........... 6-37

Figure 6-25 Discriminant function (Kv) distribution in five simulations: (a)-(e) scenarios of the 

nth experiment was performed in wells L5-L9, respectively. ................................ 6-38
xvii 

LIST OF TABLES 

Table 2-1 Selected studies proposing methods for model-based groundwater monitoring 

network design ...................................................................................................... 2-20

Table 3-1 Soil cover of the OPE3 crop production area. ....................................................... 3-5

Table 3-2 Installation depths of the soil moisture sensors at field B of OPE3 site. ............... 3-6

Table 3-3 Soil texture measured in soil cores taken during installation of the 

groundwater wells at field B. .................................................................................3-31

Table 4-1 Soil properties used in simulations of Cl subsurface transport. ............................ 4-14

Table 4-2 Statistics of observed and simulated subsurface Cl- transport ............................. 4-21

Table 5-1 Hydraulics conductivity values obtained by calibration, estimation with PTFs 

from Rawls et al. (1998) and scaling abstractions A1 through A6. ....................... 5-33

Table 6-1 Model parameters found by trial-and error method. .............................................. 6-35

xix 

EXECUTIVE SUMMARY 

This study was designed and performed to investigate the opportunities and benefits of integrating 

model abstraction techniques into subsurface monitoring strategies. The study focused on future 

applications of modeling in contingency planning and management of potential and actual 

contaminant release sites within the scope of US NRC operations. The main objective was to 

develop methods for incorporating model abstraction techniques into the design of subsurface 

hydrologic monitoring and performance assessment programs. This study is based on a 

systematic model abstraction methodology that was developed and tested in previous work on 

flow and transport in soils and shallow groundwater systems. 

A comprehensive review of groundwater monitoring network (GMN) design techniques was 

conducted first. The review demonstrated the recent increased use of physically-based pollutant 

fate and transport models in monitoring network designs. Since GMN designs are based on a 

conceptual model of the presumed subsurface flow and transport conditions, and since 

abstraction of the model structure leads to a range of conceptual models and their mathematical 

counterparts, an opportunity arises to design GMNs that decrease uncertainty in the predictions of 

individual abstracted models, or in weighted predictions from several models combined via model 

averaging. Another opportunity is to use model abstraction via parameter estimation to augment 

existing monitoring networks for discriminating between different conceptual and mathematical 

abstractions. These opportunities are pursued in this work and applied to models that are 

obtained via model abstraction for full three-dimensional (3D) flow and transport in variably 

saturated flow domains. 

The USDA-ARS OPE3 experimental field site near Beltsville, MD, has been studied extensively 

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

monitoring methods. Available data were analyzed using systematic procedures within a broad 

vadose zone modeling context developed in our previous work. A major focus was on subsurface 

structural units and features that could drastically change the fate and transport of contaminants in 

the vadose zone, as well as on projected trajectories of the contaminant plume in groundwater. 

Solute transport in soils and shallow groundwater at the site could potentially be 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 the more fine-textured layers, and localized high-conductivity 

parts of the soil pore space. 

The abstraction methodologies were applied to data from the originally designed field site showing 

lateral transport of a surface-applied conservative tracer pulse, with transport being controlled by 

regular irrigation pulses and natural precipitation. The vadose zone was monitored for soil water 

contents and pressure heads, while groundwater levels and tracer concentrations in groundwater 

at three depths were also recorded. Fine-scale ground-penetration radar and time-lapsed 

electrical resistivity surveys, along with the borehole logs, contributed to the development of the 

original conceptual model in which subsurface structures exerted strong controls on flow and 

transport. A cluster analysis of borehole data showed the presence of nine soil materials in the 

studied subsurface domain. 
xx

A comprehensive sensitivity analysis was performed to identify possible directions of model 

simplification in the model abstraction process. Two sensitivity indexes, a first-order sensitivity 

coefficient and a derivative-based measure of sensitivity (section 5.1), were used to reflect the 

effect of parameter variations on variations in simulated values. These indexes were first 

computed as daily values, with their time series providing insight into the spatio-temporal 

sensitivity of solute transport in the variably saturated heterogeneous domain. The sensitivity of 

the base HYDRUS-3D model to the transport parameters and soil materials depended upon both 

location and time. The HYDRUS-3D code was found to be more sensitive to the transport 

parameters than modified TOUGH2. Time series of first-order sensitivity coefficient were 

aggregated to obtain an average and standard deviation of daily value over the observation period 

for each of eight soil materials. Ranking soil materials according to the aggregated sensitivity 

indexes allowed identification of those soil materials most appropriate for model simplification by 

material elimination. 

The proposed approach to abstract a model by decreasing the number of soil materials consisted 

of replacing the eliminated soil material with one of the closest materials according to the cluster 

analysis used for the material definition. The simulations were run with the three closest soil 

materials as possible replacement for the eliminated material. Different replacement materials 

were selected when the HYDRUS-3D or modified TOUGH2 codes were used, possibly because 

of differences in averaging hydraulic conductivity procedures. 

Four examples of model abstraction were developed using the manually calibrated HYDRUS-3D 

code as a base model. The examples included using pedotransfer functions for the hydraulic 

conductivity, profile aggregation, ignoring the unsaturated zone, and combining the use of 

pedotransfer functions with scaling. The efficiency of a particular abstraction option was evaluated 

by comparing simulation results of the calibrated and abstracted models using three performance 

indicators, namely simulated peak concentration, time to reach the peak concentration, and total 

mass flow through observation nodes and transects at different distances from the release points 

based on simulations of 10 year-long tracer flow and transport. 

The simulation domain that mimicked an NRC site was set within the boundaries of the GPR 

survey, and included the tracer application plot and 56 groundwater observation wells. Forty eight 

scenarios were simulated, each one being different in terms of the location and depth of the tracer 

release, groundwater dynamics, and precipitation. Pedotransfer estimates of soil water retention 

and the saturated hydraulic conductivity were generated using the Rosetta software and the 

tabulated summary of the Rawls databases, respectively. Estimates were found for each of 

20,000 simulation nodes. 

Abstraction of parameter estimation using empirical pedotransfer functions was found not to be 

efficient in our study due to the considerable sensitivity of HYDRUS-3D modeling results on the 

saturated hydraulic conductivity. Pedotransfer predictions of the saturated hydraulic conductivity 

were relatively poor as compared to calibrated values. Therefore, pedotransfer-based simulations 

produced results that were quite different from the calibrated model results. Time to peak 

concentration and total mass were better discriminators between the calibrated and abstracted 

models than the peak concentration itself. 

The scale mismatch between measurements reflected in the pedotransfer database and the 

computational grid discretization was a plausible explanation of the low efficiency of the 

pedotransfer abstraction process. Pedotransfer abstraction for this reason was complemented 

with scaling abstraction. The increase in the saturated hydraulic conductivity with the size of grid 

cells was simulated assuming a power-law dependence of hydraulic conductivity on the ratio of 
xxi

characteristic lengths (section 5.2.8). The accuracy of simulations with the concurrent use of 

pedotransfer and scaling abstraction was very close to that of the calibrated model, thus 

confirming the efficiency of systematic model abstraction. 

Profile aggregation, i.e. assuming a single soil material for all depths was another model abstraction 

technique implemented in this study. A motivation for this abstraction technique is possible 

dominance of one soil material in the simulation domain. Profile aggregation had a major effect on 

tracer transport in our study. Introducing a homogeneous profile resulted in drastic changes in the 

spatial pattern of the performance indicators. The model that used profile aggregation performed 

the poorest. 

Ignoring the unsaturated zone implies ignoring the retardation of water and chemical fluxes due to 

the nonlinear decrease in hydraulic conductivity with a decrease of water content in the absence 

of preferential flow and transport in the vadose zone. However, ignoring the unsaturated zone did 

not lead to noticeable changes of the performance indicators. A systematic difference between 

abstracted and calibrated modeling results was found for the times to peak concentration, but not 

for the maximum concentration and the total mass transported. The abstraction scheme which 

ignored the unsaturated zone was acceptable if the key performance indicators were the peak 

concentration and the total contaminant flux which passed through a transect or observation well. 

This method of model simplification was found to be acceptable because of a relatively shallow 

vadose zone at our site. 

It should be used with caution at sites with deep phreatic surfaces where characteristic times of 

vertical transport in unsaturated zone and lateral transport in groundwater are comparable. The 

procedure of this work needs to be re-applied to make sure that the travel time in the unsaturated 

zone can be ignored which may be the case in semi-arid zone. 

Mathematical models developed with model structure abstractions should have different 

underlying conceptual hypotheses. Since a monitoring network is always designed based on a 

conceptual model, designs may need to be different for models that are abstracted differently. A 

monitoring network design could either jointly use the designs resulting from several conceptual 

models, or develop a particular design to discriminate between models with the goal of selecting 

the more plausible one. 

Two approaches were developed and implemented for situations in which monitoring network 

augmentation is envisaged for flow and transport in a variably saturated three-dimensional 

subsurface domain. 

A sensitivity-based statistical inference method has been proposed in steady-state groundwater 

studies to rank candidate monitoring locations by their potential to improve model predictions and 

the accuracy of parameter estimation. The method was expanded in this study for applications in 

variably-saturated 3D flow and transport domains by redefining parameter sensitivities for nonstationary conditions. The modified statistical inference method was tested first using simulated 

data of the tracer experiment as obtained with the calibrated model so as to rank the existing 

observation wells in terms of their importance for model calibration. The method provided stable 

results indicating that (a) one (deeper) observation depth rather than two would be sufficient in the 

calibration, and (b) that the relative importance of wells is defined by either their presence in 

subdomains where fast changes in flow and transport occur within small distances, or their 

presence in relatively large subdomains where flow is slow compared to other parts of the OPE3 

simulated field site. The sensitivity based statistical inference method was further used to 

augment the observation network with the aim of improving the HYDRUS-3D calibration. 
xxii 

Observations at the lower of the two depths appeared to be more important, and followed the 

previously noted trend of importance of observations in subdomains where fast changes in flow 

and transport occur within small distances. 

Performance indicators were used to compare monitoring locations selected for the base model 

and for models abstracted using pedotransfer, profile aggregation, and ignoring the vadose zone 

by placing the tracer into groundwater at the very beginning of the simulations. Locations selected 

for the pedotransfer abstraction were close to those for base model if the peak concentration was 

used as the performance indicator. Soil profile aggregation was the only abstraction technique 

that generated a monitoring network dissimilar to the network obtained using the calibrated 

HYDRUS model. This occurred primarily due to existence of preferential lateral flow paths in the 

heterogeneous simulation domain, which were entirely discarded in the homogeneous profile 

abstraction process. Soil profile aggregation abstraction in general may well be suitable for smallscale applications or when vertical soil stratification is not important hydrologically. However, for 

large-scale projects natural succession of soil genetic horizons producing different hydrological 

regimes at different depths cannot be ignored when water flow and chemical transport are 

modeled. 

Abstraction by ignoring the unsaturated zone appeared to be the most accurate in predicting the 

tracer concentrations and fluxes, and consequently generated essentially the same monitoring 

network as the calibrated model. This occurred because the unsaturated zone was very thin in our 

study, while vertical transport dominated at the release points. These hydrological conditions 

created a specific flow regime in which the tracer was transported preferentially in the vertical 

direction before approaching the groundwater. The results of this abstraction can differ for a 

deeper unsaturated layer, especially when the soil profile contains horizontal lenses with 

contrasting hydraulic properties. The presence of such structural factors, and their effects, need to 

be evaluated at the conceptual model development stage. Model abstraction then can help to 

quantify their possible role at the mathematical modeling stage of a project. 

Model discrimination can be one of several objectives of groundwater monitoring design. A 

simplistic search for a location where predictions using two models differ the most can give 

unsatisfactory results since both data and model predictions are uncertain. The novel method 

developed in this work method determines new monitoring locations where the total information 

gain is maximized. The latter is computed based on estimates of the uncertainty in modeling 

results and uncertainty in observations. The discrimination was sought for the original model and 

the model obtained with the soil profile aggregation abstraction. 

 Pedotransfer functions were used to develop the ensemble of models for estimating the 

uncertainty in modeling results obtained with the numerical 3D flow and transport model. Peak 

tracer breakthrough concentrations were used to define the information gains. The determination 

of the new locations to augment existing ones was conducted on a 2-D grid. The information gain 

peaked in small area, and additional observation locations were very well spatially defined. 

Overall, integrating model abstraction and monitoring strategies appears to be a logical step given 

that both the mathematical models and the groundwater monitoring network designs are based on 

conceptual site models of subsurface structural and geochemical conditions. Developments in the 

fields of monitoring data assimilation and geophysical data fusion will further help to interfacing of 

the two technologies. Since the use of mathematical fate and transport models in groundwater 

monitoring designs is expanding, one should expect further intertwining of modeling and 

monitoring based on common conceptual modeling. 
xxiii 

ACKNOWLEDGMENTS 

This work was partially supported via Interagency Agreement IA-RES-08-134 between the U.S. 

Nuclear Regulatory Commission and the USDA Agricultural Research Service. 

The authors acknowledge with thanks contributions by the following individuals: 

Dr. Robert Hill for his work on subsurface structure analysis; Mr. Randy Rowland and Mrs. Lynn 

McKee of USDA-ARS-Beltsville for their exceptional support of field and laboratory work; Dr. 

Alexandra Kravchenko of Michigan State University for her help with sensitivity and statistical 

analyses; Dr. Daniel Gimenez and Dr. Dennis Timlin for their thoughtful comments of a draft 

version of this manuscript; U.S. NRC staff members, Mr. Hans Arlt and Ms. Cynthia Barr for their 

comprehensive and constructive reviews and suggestions for improvement; NRC staff member 

Thomas Aird for the valuable help in revising and publishing the report. 

xxv

ABBREVIATIONS AND ACRONYMS 

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

ANN Artificial neural networks

BTC Breakthrough curve

C Clay

CV Coefficient of variation

DGPS Differential global positioning system

ET Evapotranspiration

FAO Food and Agriculture Organization of the United Nations

FTM Model of the subsurface flow and transport

EM Electromagnetic induction

FD Finite difference

GLUE-BMA Combined Generalized Likelihood Uncertainty Estimation (GLUE) 

and Bayesian Model Averaging (BMA) methods

GMN Groundwater monitoring network

GMS Groundwater Modeling System

GPR Ground penetrating radar

GWD Groundwater depth

L Loam

LS Loamy sand

LSA Local sensitivity analysis

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

multiple solutes in variably-saturated media

MA Model abstraction

MATLAB A programming environment for algorithm development, data 

analysis, visualization, and numerical computation

MCP Multi-sensor capacitance probe

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

OPR Observation-prediction statistic

PTF Pedotransfer function

RADAN GSSI's state-of-the-art post-processing software

REV Representative elementary volume

ROSETTA Windows based program that implements artificial neural network to 

soil hydraulic parameters

S Sand

SA Sensitivity analysis

SCL Sandy clay loam

SDSi Standard deviation of the sensitivity index

SiCL Silt clay loam

SiL Silt loam

SL Sandy loam

TDR Time Domain Reflectometry

TOUGH Numerical model for simulating the coupled transport of water, 

vapor, non-condensable gas, and heat in porous and fractured 

media
xxvi

Roman symbols 

A Sensitivity matrix

b Exponent

C Solute concentration

C speed of light

Cpeak Peak concentrations

D Index of agreement

D Hydrodynamic dispersion tensors

Dij

Components of the hydromechanical dispersion tensor

Di Derivative-based sensitivity index

E Efficiency index

Ε Soil dielectric constant

ET Daily average evapotranspiration

ET̅̅̅̅ Evapotranspiration over simulation period

GWD Groundwater depth

H Matric pressure head

H Hydraulic head

hcf Pressure head at the top of capillary fringe

I Kullback-Leiber divergence

J Total information gain

Kv Total information gain with prior probabilities of models being correct

Ks Saturated hydraulic conductivity

KS,R Saturated Hydraulic conductivity estimated from Rawls’ pedotransfer 

function

K Hydraulic conductivity tensor

l

Pore connectivity parameter

Lg Size of the soil cores used to determine KS,R

Ls Characteristic length of the numerical grid used to solve flow and 

transport problem.

M A parameter of van Genuchten’s water retention model

N A parameter of van Genuchten’s water retention model

O Measured values

Pr

(n) Posterior probability

P Predicted values

P Probability

Q Darcy flux vector

qr

Darcy flux vector components

Q Water flux soil hydraulic parameters

QC Chemical mass flux

R Retardation factor

r

2 Coefficient of determination

RMSE Root Mean Square Error

S Sink/source term

Se Relative saturation

Si Sensitivity measure

SY’ Prediction standard deviation
xxvii 

Slope X Phreatic surface slope in X direction

Slope Y Phreatic surface slope in Y direction

T Time

Tpeak Time of peak concentrations

V Variance

i

v

Components of flow velocity

V Groundwater velocity

Vm Volume of geological media

v GPR wave velocity

W Matrix of weights of observations

Xi Generic factor

Xi

Nominal value of factor X

x,y,z Coordinates

Y Model output 

i Y

Nominal value of factor Y

Z Depth

Greek Symbols 



A parameter of van Genuchten’s water retention model

aL

Longitudinal dispersivity

aT

Transverse dispersivity

δ Dirac delta function

 Increment



Accuracy parameter

E Expected value

σr

2 Variance

σY

2 Variance of the distribution of observations about the expected value

λ First order decay rate



Finite difference operator



Specific water capacity

Θ Volumetric water content

 r

Residual water content

s 

Water content at saturation

τ GPR signal travel time

1-1 

1 INTRODUCTION 

1.1 Background 

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 

range from very simple to extremely sophisticated formulations (Neuman et al., 2003; Reilly and 

Harbaugh, 2004; Hill and Tiedeman, 2007; Valocchi, 2012). One reason for this is the inherent 

complexity of the subsurface, which needs to be dramatically simplified to be expressed in 

mathematical terms. Different sets of simplifying assumptions can be used that lead to different 

models (Neuman et al., 2003). And even when the types and relative positions of subsurface 

structural units are selected, knowledge about the locations of the boundaries of these units, and 

about the flow and transport properties of the soils and fractured rocks making up those units is 

uncertain. This creates substantial uncertainty with regard to the assignment of parameter values 

in 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. The use of simpler modes to complement a complex model is a promising 

approach (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 were initially developed or 

tested. 

Currently, different research fields have been adopting various approaches for selecting or 

deriving simple models for use along with more complex models (e.g., Casteletti, 2011; Lawrie 

and Hearne, 2007; Raick et al., 2006). One of these methods consists of a systematic derivation 

of simpler models from the original complex model. This method has been termed “model 

abstraction”. The systematic model simplification in subsurface hydrology was first suggested by 

Neuman and colleagues (2003) in their work performed for the U.S. Nuclear Regulatory 

Commission. Examples of useful simplifications of ground water models were later presented by 

Hill (2006). For soils, the model abstraction methodology, including those techniques and 

examples used in simulating water flow, was developed in a recent interagency study by 

Pachepsky, et al. (2006). 

One essential application of subsurface modeling is the development of monitoring programs and 

strategies. Monitoring of subsurface processes has been expanded significantly in the past 

several decades to address soil, groundwater, and surface water contamination. A wide variety of 

monitoring design techniques has been proposed (Minsker, 2003; Quevauviller et al., 2009). Yet, 

the central conundrum of subsurface monitoring design--the struggle between subsurface 

complexity and available monitoring resources still presents a challenge at decommissioning and 

new reactor sites--as well as at other potential point source contamination sites. Ideally, 

subsurface environments at potential or actual contaminated sites should be described using 

state-of-the-art conceptual models in conjunction with extensive monitoring data collected at the
1-2 

site. While potentially very realistic, these models generally introduce large data requirements 

and often focus on parameters that have only minimal influence on the specific subsurface 

processes of concern to anticipated contaminant transport. Limited costs and resources, 

however, tend to make this approach an unlikely option. Instead, there is a tendency toward 

modeling complex and highly transient subsurface flow and transport processes with greatly 

simplified models that overlook fine-scale heterogeneities that may well control contaminant flow 

and transport at coarser scales (Neuman, et al., 2003). 

Model abstraction techniques can be utilized to reduce the complexity of a natural system to its 

essential components and processes through a series of conceptualizations, selection of 

processes, and identification of parameters and boundary conditions. The result of successful 

model abstraction is to simplify the representation of a complex, natural groundwater system to a 

manageable level while still capturing an acceptable level of detail and realism (Pachepsky et al., 

2006). The central hypothesis of this study is that models of intermediate complexity as 

developed using model abstraction can be useful for the design of feasible monitoring networks 

and schedules at actual and potential contaminated sites. The selection of a specific model should 

depend on the purpose of monitoring, such as obtaining calibration data, demonstration of 

compliance with a regulatory limit, or for obtaining information to remediate a plume. 

1.2 Objectives 

The objective of this research was to develop methods for incorporating model abstraction 

techniques into the design of subsurface hydrologic monitoring and performance assessment 

programs. The enhanced abstraction strategies and models needed to be tested using a sitespecific database on flow and transport of tracers from pre-defined sources. 

1.3 Approach 

The research effort utilized a unique, long-term monitoring data set from the ongoing 

environmental monitoring program at the ARS OPE3 site, along with datasets collected at that 

same site during subsequent tracer experiments (Pachepsky et al., 2011). Both the vadose zone 

and groundwater were sampled continuously, which should present an advantage given the 

importance of the vadose zone in evaluating groundwater recharge and contaminant transport to 

groundwater (Hunt et al., 2008; Harter and Hopmans, 2004.). As appropriate for the shallow 

groundwater site, the base conceptual model to be simplified was selected to be fully threedimensional. The highly nonlinear nature of flow in the unsaturated zone makes the modeling 

results dependent upon mathematical approximations needed for numerical solutions using a 

realistic temporal and spatial discretization. To evaluate this issue, two available codes 

(HYDRUS-3D and TOUGH 2) were used concurrently in this study. 

The following requirements were considered to be important: 

1. The model abstraction techniques should be selected to support the performance

assessment modeling and monitoring at the field/watershed scale; 

2. The research should recognize a variety of data aggregation methods used in

performance assessment; data abstraction should be considered along with model 

abstraction; 

3. The effect and efficiency of model abstraction must be characterized in statistical terms;

and

4. Monitoring should improve both the performance of the abstracted models and

discrimination between the abstracted models. 
1-3 

The following research questions were addressed to meet the above requirements: 

1. Do the analyses and evaluations produce a sufficient technical basis to designate the 

appropriateness of the abstractions as represented by the different models, depending 

upon the “complexity” of the results (all data, filtered data or derivative data) used for the 

comparisons? 

2. When does a simplification create significant error and/or uncertainty, and what 

monitoring data support that determination? 

3. For the various abstracted models using filtered data or derivatives of the data, what test 

methods could be used to predict where (or when) to sample for a) an optimal reduction 

of uncertainty in the model; and b) discriminating indicators (or criteria) between models 

of different abstraction? 

4. How can monitoring assist in determining which abstracted model and its assumptions 

are appropriate for estimating transport given the release scenario and site-specific 

subsurface flow conditions (e.g., presence of preferential pathways, perching units, 

fracture connectivity)? 

5. Given the goals stated in the voluntary EPRI/NEI Industry Ground-Water Protection 

Initiative (Kim, 2009), what monitoring densities (i.e., areal, depth and time determinants) 

for that magnitude of release at the OPE3 field site would be needed to assure a high (or 

absolute) probability that the release would be detected? 

6. How much uncertainty can be reduced by monitoring the unsaturated zone close to the 

release location, as opposed to monitoring at the water table, and which performance 

indicators could best be used and monitored in the unsaturated zone? 

7. How could model abstraction techniques be coupled with site attributes and conditions to 

select the proper monitoring strategy to provide confidence in the selection of an 

appropriate remediation technique or techniques? 

Monitoring network design issues includes (a) creating an initial monitoring network and (b) 

augmenting an existing network. The modeling-based initial monitoring design at the OPE3 site 

was described earlier (Pachepsky et al., 2011). Here the ARS study team concentrated on 

augmentation of an existing monitoring network, and two reasons for this approach are 

considered: 

- improving model performance by augmenting the network to include optimal locations to 

decrease uncertainty in the predictions, and 

- improving model discrimination by augmenting the network to include the best locations for 

distinguishing between two models. 

2-1 

2 MONITORING AND MODEL ABSTRACTION 

IN SUBSURFACE HYDROLOGY

This section provides an overview of the state-of-the art of model abstraction and model-based 

monitoring design, and outlines the interactions between these two components of environmental 

assessments and predictions. Modeling and monitoring have substantial potential to complement 

each other to improve studies of any contamination problem. This is because the mathematical 

model and the monitoring network both require a conceptual model of the contaminated site, with 

both at the same time providing information about the validity of the invoked conceptual model. 

Monitoring and modeling both should also recognize the non-uniqueness of possible conceptual 

models, and thus should foresee their possible application to several models, rather than singling 

out only one model, even if thought to be the best. 

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

maintaining the validity of the simulation. Model abstraction, if conducted in a systematic manner, 

generates a variety of both conceptual and mathematical models. Any one of the conceptual 

models could serve as a basis for the monitoring design. The monitoring design itself can be 

useful by allowing one to distinguish between the mathematical models and their conceptual 

counterparts, and by eliminating models that generate unacceptable results. On the other hand, 

an ensemble of simplified models can serve as a source of data about uncertainty in model 

predictions, which then can be incorporated implicitly or explicitly in the monitoring design 

process. 

2.1 Model Abstraction in Subsurface Hydrology 

2.1.1 Background 

Model abstraction techniques stem from a need to improve the reliability of simulations, and to 

reduce their uncertainty, 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 uncertainty in the simulation results is 

usually impossible to quantify in statistical terms. However, 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 ability to match observed 

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 

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

modeling in subsurface hydrology.

2.1.2 Abstraction of Model Structure 

Hierarchies of models. An example of the possible 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 with composite 

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

(1994) and 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 (Ventrella et al., 2000; Šimůnek et al., 2003). 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 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 

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
2-3 

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 closely matched results of the 2D model 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 given by 

the length, area, or volume of a sample or element for which a single value of a porous medium 

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

soils or in unsaturated fractured rock (after Altman et al., 1996). 

property is defined and no variations in this or other properties are taken into account. The size of 

an individual sample, and 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 often 

used to define the resolution in terms of length, area, or volume. An area or 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 characterizing scale not with a single value of support, extent, or spacing, but 

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
2-4 

with a position of a particular hydrological dataset in the 3D space of coordinates ‘supportspacing-extent’. Therefore, change(s) in one or more of the numerical values of support, spacing, 

or extent leads to a change in scale. 

In practice, vadose zone investigations generally define the support 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 the 

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. 

Figure 2-3 Spatial and temporal operational scales in hydrology (after Blöschl and 

Sivapalan, 1995). 
2-5 

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

relatively rare but essential features at the finer scale since those 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 

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

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

example of the importance of relatively rare fine-scale features. As compared 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 often 

control lateral flow and solute transport 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. The value of water content at field capacity cannot be attributed to a 

single value of the soil water potential, and therefore no relationship exists between the coarseand 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 the 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). The flow and 

transport parameters are still lumped in that case. Attempts to determine the effective hydraulic 

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

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

predominant water regime (infiltration or evaporation). 

Many examples of distributed watershed modeling with varying degrees 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 

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

aggregating all sub-watersheds into 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 repro-modeling (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 inputoutput 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.
2-6 

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

networks (ANNs) are the most widespread among these since they are powerful approximators 

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

model (Haykin, 2008). Examples of the application of artificial neural 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 process-based 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 

also 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 particletracking algorithm simulating plume migration in heterogeneous media. Their metamodeling 

approach substantially improved the computational efficiency of the entire algorithm. 

2.1.3 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 maps to define 

soil or sediment structural units that have the same hydraulic properties, even though the realworld hydraulic properties may change more gradually 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; Straface et al., 2011). Automated zonation is now also 

feasible (Tsai et al, 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-1 to 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 what 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 
2-7 

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

unsaturated soils remains a major research issue; no routine methods have been devised to-date. 

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. Regression equations used for this purpose are often called pedotransfer functions 

(PTFs). These regressions relate soil water retention and hydraulic conductivity to more readily 

available soil parameters, such as contents of textural fractions, bulk density and organic carbon 

content. Extensive work has been carried to develop PTFs. The proceedings of two international 

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

2004), and a recent review (Vereecken et al., 2010) provide a panoramic view of these fastdeveloping 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 geophysical data and the hydraulic 

properties should be expected. A recent book on hydrogeophysics (Rubin and Hubbard, 2005) 

summarizes 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. (2003) related biophysical information 

from yield maps to the soil field capacity. 
2-8 

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 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 site-specific 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. 

Scaling. Abstraction of scaling presumes the dependence of flow and transport parameters on the 

shape and dimensions of the domain over which these parameters are averaged. The saturated 

hydraulic conductivity and the dispersivity are most often viewed as scale dependent parameters, 

although parameters of geochemical kinetics are also shown to be subject to scale-dependency 

(Malmstrom et al., 2000; White and Brantley, 2003; Li et al., 2006). Evidence is accumulating that 

parameters of biological activity models show scale-dependencies, too. 

Examples of observed scale dependencies in the saturated hydraulic conductivity are shown in 

Fig. 2-4. Ks values tend first to increase as the cross-sectional area or volume of the reference 

area increases and then presumably stabilize. The increase in Ks is caused by a change in the 

type of structural heterogeneities that are encountered as the scale increases. Large 

heterogeneities that are rarely viewed at the finer scales dominate flow as the scale increases. 

The dispersivity shows a similar behavior. Different measurement techniques (e.g., slug, single 

well, and multiple well pumping tests) represent different scales, and integration of their results 

presumes application of scaling as discussed by Neuman (1991). 

The structure of surface soils in some cases can create the decrease in the value of hydraulic 

conductivity with the increase of the thickness of soil layers that is involved in flow (Lauren et al., 

1988). There reason for that is the number of well-conducting macropores connecting top and 

bottom boundary of soil sample decreased as the length of soil column increased. 

The scaling abstraction of parameter determination provides compatibility of the scale of 

measurement with the scale of model resolution. Neuman et al. (2003) suggested that this can be 

done by either rescaling the data to fit the scale of model resolution (which often entails averaging 

or upscaling over computational grid cells) or adapting model resolution to fit the scale of 

measurement (which often entails adapting the size of grid cells to the size of the data support). 

2.1.4 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 et al., 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. 

The ARS study team emphasized that model abstraction is always site-specific. Pachepsky et al. 

(2011) provides a detailed overview of the model abstraction process. In this section the ARS 

study team provides a brief description. 
2-9 

2.1.4.1 Model Abstraction Steps 

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

simulations. 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 the 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 parameter values of those processes may be 

very uncertain. 

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

invoked boundary conditions (forcings) 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. 
2-10

Figure 2-4 Relationships between the scale of measurement and the saturated hydraulic 

conductivity of soils and sediments; a – saprolite, North Carolina; 

measurements on cores, columns, and at the drain field scale (Vepraskas and 

Williams, 1995); b – Kokomo clay soil, Ohio; measurements with a 

permeameter, on cores, and on soil blocks (Zobeck et al., 1985); c – aquifer in 

a stream alluvium, Columbus, Ohio; measurements with a permeameter, flow 

meter, and using a slug test (Zlotnik et al., 2000); d – aquifer in glacial 

outwash, Cape Cod, MA (Zlotnik et al., 2000); e, f, g, h – aquifers in Wisconsin 

(Schulze-Makuch et al., 1999), e –glacial outwash sediments, f – carbonate 

aquifer, g – high magnesium limestone with shale, h – finely crystalline 

dolomite,  - permeameter tests,  - piezometer tests,  - packer tests, - 

single well pumping and specific capacity tests; oversized symbols show 

averages over a large number of replications.
2-11

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 timely completion of a modeling project. 

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

because of limited observation ability or uncertainty in the simulation results. The decision to 

carry out model abstraction may be based on the statistics of the 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 process. One must 

realize which details and features of the problem are to be omitted or de-emphasized when 

abstraction is performed. Neuman et al. (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) existing or potential causes of the problem, (c) issues requiring 

resolution, and (d) 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 such regulations do not exist, then the 

statistics must 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 input and measurable model output data, 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, sorption parameters, and in some cases redox conditions, (c) the 

forcings that provide 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. Statistic measures include the type of statistical distribution used, 

median values and variability estimates, 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, again, one must be sure to 

not ignore certain small-scale internal heterogeneities that may have a dominant effect on 

flow and/or transport at the scale of interest. 
2-12

2.1.4.2 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). Decisions about 

which model abstraction technique to use depend on the reasons for the model abstraction. In 

general, model abstraction can lead to simplifications via: 

 the number of processes being considered explicitly,

 adopting simpler process descriptions,

 coarsening the spatial or temporal support

 the number of measurements to be used for reliable parameter estimation,

 reduced computational burden, and

 simplified pre-processing and post-processing data.

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 that 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. 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 initially could not be explained well (Jacques et al., 2002). Fig. 2-5 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 singlecontinuum (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 parameter 

estimation by using only laboratory data, or an ensemble of pedotransfer functions. Fifty MonteCarlo simulations were performed, with each abstracted model using data on variability of the 

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 water budget 

model, respectively. 

The abstracted model 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 process via 

pedotransfer functions at the same site showed that an ensemble of pedotransfer functions 

produced a satisfactory representation of field uncertainty in the soil hydraulic properties (Guber et 

al., 2006). 

2.1.5 Model Abstraction vs. Arbitrary Selection of a “Simple” Model

Models used in performance assessments of waste disposal sites generally ignore small-scale 

heterogeneities in space and time. Preferential pathways are typically ignored when a singlecontinuum 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
2-13

averaged across long periods of time. Thus, the often-used models are actually abstractions of 

more realistic models that explicitly could 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 variations in soil texture may lead to flow barriers and associated lateral flow. These lateral 

flow paths may lead to solute mass losses, lowed vertical fluxes, and higher longitudinal 

dispersivities (Looms et al., 2008). This shows that it is imperative to evaluate possible prediction 

errors when the “simple” model is used. Deriving a simple model from a more complex base 

model provides opportunities for such an evaluation. 

Figure 2-5 Design of model abstraction via model structure and parameter determination 

2.2 Approaches to Modeling-Based Monitoring Optimization

2.2.1 Background 

Significant efforts have been invested in the development of techniques to design groundwater 

monitoring networks (GMN), particularly for groundwater quality monitoring. A range of state-ofthe art reviews and guidance documents have been published about GMNs during the last 

decade (Bloomfield, 2000; Hassan, 2003; Minsker, 2003; U.S. EPA, 2005; U.S. DOE, 2004; Kollat 

et al., 2011). It is generally agreed that there is no unique “best” way to conduct a long-term 

monitoring optimization project. Multiple guidance documents, tools, and standardized methods 

and approaches which utilize qualitative, temporal, and/or spatial-statistical methods have been 

applied successfully to a range of sites. The most significant advantage conferred by any 

optimization approach is the fact that they are used to apply consistent, well-documente 

procedures, which incorporate formal decision tools, to the process of evaluating and optimizing 

monitoring programs (U.S. EPA, 2005). 
2-14

2.2.2 Components of a Groundwater Monitoring Network Design 

The design of modern groundwater monitoring networks requires consideration of a range of 

factors that include having adequate spatial and temporal coverage of sampling sites, balancing 

potentially competing objectives within a monitoring program, considering the complex nature of 

geologic, hydrologic, and other environmental factors, accounting for the significant uncertainty 

about many parameters used in the design process, and considering the range of applicability of 

various methods in network design including their relative strengths and weaknesses (Bloomfield, 

2000). 

Implementation of a GMN always requires clearly stated objectives. Loaiciga et al. (1992) proposed 

a classification of objectives that forms the basis of Fig. 2-6. Specifically, the objective of ambient 

monitoring is to establish an understanding of characteristic regional groundwater trends with time. 

Detection monitoring is designed to identify the presence of targeted parameters, such as 

contaminants, as soon as they exceed background or established levels. Compliance monitoring is 

established to examine whether or not a set of specified groundwater-monitoring requirements, 

usually for chemical constituents, is met, for example near waste disposal facilities. Research 

monitoring on the other hand is a characteristically detailed spatial and temporal groundwater 

sampling effort designed to meet specific research goals. Objectives of the monitoring network 

define the monitoring scale. 

Phase-dependent classification of monitoring objectives includes four general categories (U.S. EPA 

2004): identification of changes in ambient conditions; detection of flow and transport of the 

environmental constituent of interest, demonstration of compliance with regulatory requirements; 

and demonstration of the effectiveness of a particular response activity or action. 

The dynamic nature of a groundwater monitoring network is an important factor in the design of an 

effective groundwater monitoring network. Network design may be an iterative process in which 

initial sampling programs are often revised or updated as a result of previously collected data. Thus 

network augmentation or reduction is a characteristic feature of dynamic GMNs. In addition, the 

objectives of the monitoring network may also change with time. 

A dynamic GMN design hence includes an iterative validation-monitoring-refinement cycle 

(Hassan, 2003). 

GMNs must be developed according to a conceptual model of the site that includes geological 

and hydrogeological boundaries; the physical structure of the aquifer; information about recharge, 

discharge, groundwater flow pattern and mechanisms, rock-groundwater interactions, and the 

effects of unsaturated zone processes. Central to conceptual site model development is the 

collection, fusion and integration of appropriate geological data. Neuman et al. (2003) noted that it 

is often possible to postulate hydrogeologic conceptual models or hypotheses for a site on the 

basis of a broad range of publicly available geologic and geographic information about its 

surroundings. 

Additional conceptualizations can be implemented on the basis of generic data about similar 

regions and the properties of similar materials elsewhere. Still, it is important to realize that each 

site is unique and very likely to reveal additional properties and features when characterized in 

some detail locally. Local characterization is hence essential for postulating acceptably robust 

conceptual hydrogeologic models for a particular site. The broader the available database, the
2-15

more robust the conceptualization likely becomes. Key data categories include site and regional 

physiography, topography, climate, meteorology, soils, vegetation, land use, geomorphology, 

geology, geophysics, surface and subsurface hydrology, inorganic and organic hydrochemistry, 

radiochemistry, natural and anthropogenic isotopes, and remotely sensed data. Of special 

relevance to hydrogeologic model development are regional and local site data that allow one to 

define the distribution of hydrostratigraphic units on a variety of scales; their geologic structure; 

rock and soil types; their textural, physical, flow and transport properties; fluid types; the states of 

fluid saturation, pressure, temperature and density; chemical constituents and isotopes; major 

contaminants in soil, rock and groundwater; and their sources. 

Common constraints on groundwater monitoring networks include budgetary limitations, including 

availability and stability of funding, opportunities for developing dynamic GMNs, access to 

appropriate sites, environmental impact from the monitoring setups, availability of staff with 

appropriate skills, and technical limitations such as remote data collection. 

2.2.3 Methods of Groundwater Monitoring Network Design 

Existing GMN design methods differ in terms of the objectives of the design, the invoked physical 

model, the methods and objectives of optimization, the use of statistical representations of data, 

and the dimensionality of the spatial domain. Various classifications of GMN design methods have 

been proposed. One of the earlier classifications of GMN design methods (Hassan, 2003) is 

shown in Fig. 2-7. The two main categories and their branches were identified earlier by Loaiciga 

et al. (1992). However, the different methodologies developed under each of the general themes 

of Loaiciga et al. (1992) have been added to each methodology associated with either a network 

design theme or a network augmentation theme (Hassan, 2003). The author noted that that many 

of the developed approaches belong to more than one of the categories in Fig. 2-6. For example, 

a probability-based approach may be cast within an optimization framework, a variance-reduction 

approach may be based on kriging or co-kriging, and a simulation approach may be linked to an 

optimization technique. Kollat et al. (2011) recently listed such categories of methodological 

approaches that include expert-based hydrogeologic judgments, deterministic physics based 

simulations, geostatistical interpolation approaches, Monte Carlo physics-based simulations, and 

statistical filtering/data assimilation. 

One of the primary distinctions among GMN design methods is whether the method uses a 

physics-based mathematical model of subsurface flow and transport (FTM), or employs 

geostatistics and statistical inference based on the past observations. Each of the two approaches 

has advantages and disadvantages. Grabow et al. (2000) noted that geostatistical methods as 

generally applied are essentially interpolation techniques and are most useful for siting wells to 

better define a plume once it is located and its boundaries are identified. However, these methods 

are not as good at extrapolating as they are at interpolating, and thus may be of limited help in 

predicting plume movement. On the other hand, flow and transport model-based (FTM-based) 

methods provide essential forecast information on plume movement, and thus can be 

instrumental in siting wells to characterize future plume development. The forecast skill of such 

models, however, depends on the conceptual model of the subsurface and can be seriously 

compromised if the conceptual model is flawed. 

Recent developments in geostatistical methods in GMN design have progressed well beyond the 

optimal interpolation approach. An advanced, purely geostatistical/statistical toolbox, MAROS, 

was introduced with much success in 2003 (Aziz, 2003, Ling et al., 2004). Additional work in the 

same period was done on redundancy reduction using geostatistics (Nunes et al., 2004; Wu et al., 

2005). Since then, geostatistics-based methods began to include FTM components for various 
2-16

reasons. For example, Rivest et al. (2012) noted that groundwater contaminant plumes often 

display a curvilinear anisotropy, which conventional kriging and geostatistical simulation 

approaches generally fail to reproduce. They proposed to use a FTM to relate the spatial 

concentration patterns in natural coordinates directly with simulated flow patterns. Shlomi and 

Michalak (2007) proposed two new geostatistical tools based on using spatial structures of 

simulated flow and transport extracted from a FTM for spatial interpolation and uncertainty 

estimation. The new tools yielded results that are superior to those obtained by kriging, with a 

better reproduction of the true plume shape and lower uncertainty. Kollat et al. (2011) further 

demonstrated advantages of using data assimilation in GMN design. Data assimilation assumes 

knowledge of uncertainties in both the measurement and the modeling results. To estimate 

uncertainties in the modeling results, Kollat et al. (2011) used the Ensemble Kalman filter, with 

uncertainties in the modeling results being estimated from the ensemble FTM. The trend of 

merging geostatistical methods and FTMs seems to be very productive and is expected to 

continue. 
2-17

Figure 2-6 Classification of groundwater monitoring network objectives (after Loaiciga et 

al, 1992). 

Figure 2-7 Classification of groundwater monitoring design approaches (after Hassan, 

2003). 
2-18

2.2.4 Groundwater Monitoring Network Design Based on Flow and Transport Models 

Developments in using flow and transport models (FTMs) in the design of groundwater modeling 

networks (GMNs) during the last 20 years are summarized in Table 2.1. The table shows that 

FTMs have been used most often within a Monte Carlo simulations framework. Random 

selections of flow and transport parameters, locations of the contaminant sources (leaks), and 

boundary conditions are then used to develop probability distribution functions (PDFs) of 

contaminant concentrations at predefined locations. In several cases it was sufficient to obtain 

statistical moments, rather than full PDFs. Less often FTMs have been used to determine 

sensitivities of simulated concentrations to the parameter values. Deterministic representations of 

plumes with a single set of subsurface media parameters were used most often in past, but not 

lately. 

FTMs have been implemented for both static and dynamic network designs. Proposed dynamic 

FTM-based designs mostly considered only augmentations of an existing network. For example, 

the assumption is generally made that wells in operation before network augmentation will 

continue to function after the expansion (Hudak and Loaiciga, 1992; Lee and Kitanidis, 1996; Dhar 

and Datta, 2007; Tonkin et al., 2007; Kim and Lee, 2007; Chadalavada and Datta, 2008; Datta et 

al., 2009). Some authors did not specify a trigger for the network expansion, while others 

assumed that the management stages were defined such that eventually the well network would 

be augmented (e.g. Grabow et al., 2000). The common assumption is that the period of additional 

well installation is much shorter that the period between network augmentation events. Potential 

locations for the new wells typically were set at the nodes of a predefined grid (e.g. Cieniawski et 

al., 1995). Use of a dynamic design emphasizes efficient use of collected information, such as 

allowing the past behavior of the plume to serve as a predictive model for placing future wells 

(Grabow et al., 2000). The term “sequential design” has been utilized seemingly interchangeably 

with the term “network augmentation.” Sequential GMN designs appear to be much more costeffective than static one-time setups such as used in the work of Kim and Lee (2007). 

Two-dimensional flow and transport domains have been used most often in the past. Threedimensional layered domains with wells located in different layers were investigated by Hudak and 

Loaiciga (1992), and more recently by Kollat et al. (2011). The computational load using 3D 

models in the past called for simplification of the solute transport simulations by using particle 

tracking methods (Storck et al., 1997). Evidence suggests that in some situations two-dimensional 

simulations are poor approximations of natural three-dimensional systems (Hassan et al., 1998). 

Based on a case study review, Montas et al. (2000) concluded that 2D models can be very useful 

tools to study and predict contaminant behavior in natural aquifers, and thus can be used to 

design monitoring well networks to detect and characterize plume spreading and evolution in 

regional aquifers. 

The objective of FTM-based GNM designs have been related mostly with the detection, 

delineation and characterization of contaminant plumes. The probability of detection associated 

with any GMN design can be expected to increase with increased density of the network and/or 

increased frequency of sampling. A sensitivity analysis by Meyer et al. (1994) showed that the 

predicted performance of a given number of wells can decrease significantly as the heterogeneity 

of the porous medium increases. Poor estimates of the hydraulic conductivity were further shown 

to result in too optimistic estimates of network performance. 

Model discrimination was addressed in early studies by Usunoff et al. (1992) and Nordquist and 

Voss (1996). The former authors noted that conceptual model uncertainties often are the main
2-19

source of prediction uncertainties. Orders of magnitude differences in peak concentrations and 

arrival times were found when performing long-term predictions with the two models used in their 

study. They emphasized that simulations of the proposed experiment with all models are 

necessary but not sufficient since data obtained from the experiment could be fitted with several of 

the models. Nordquist and Voss (1996) tested the hypothesis that measurements in regions 

where alternative models produce the most divergent predictions will give the best information 

possible for deciding which of the candidate models is the most appropriate. 

Until recently few if any studies have addresses the effects of uncertainty in observed data on 

GMN designs using FTMs. Datta et al. (2009) may have been the first by using explicitly treated 

measurement errors as normally distributed additive terms. They indicated that source

identification errors depend upon assumptions in the measurement error characteristics. 

A variety of optimization algorithms have been used to solve the extremely complex problem of 

well placement optimization under multiple constraints. Substantial progress has been achieved 

with the advent of evolutionary algorithms (Minsker, 2003). Comparison of results obtained with 

different algorithms showed potentially substantial differences between different multi-objective 

optimization approaches (Cieniawski et al, 1995; Kollat and Reed, 2006). The ARS study team 

note that monitoring designs for FTM parameter estimation are not considered in this report; 

reviews and summaries of progress can be found elsewhere (e.g., Tsai et al., 2003; Hill and 

Tiedeman, 2007). 

The need to monitor both the vadose zone and groundwater has been emphasized repeatedly in 

the literature. Hudak and Loaiciga (1999) provided a compelling argument that comprehensive 

subsurface monitoring programs should include contaminant detectors in both the vadose and 

saturated zones. This work demonstrated that vadose zone detectors can provide early warnings 

of an impending groundwater contamination problem, and also yield information relevant to 

placing groundwater monitoring wells. Ward (2006) reported that, at the Hanford site, fine-scale 

geologic heterogeneities, including grain fabric and lamination, were observed to have a strong 

effect on the large-scale behavior of contaminant plumes, primarily through increased lateral 

spreading resulting from anisotropy. To our knowledge, no studies on optimization of FTM-based 

coupled monitoring of vadose zone and groundwater have been reported to date. Although 

conceptually the purposes and constraints for monitoring flow and transport in a coupled 

groundwater and vadose zone system may be similar in some aspects to monitoring flow and 

transport in groundwater only, the process rates in groundwater can be quite different from those 

in the vadose zone. Opportunities for sampling of dissolved contaminants hence are also 

different. 

Research on GMN optimization have only recently addressed uncertainties in the conceptual 

models that form the basis of the invoked FTM. These uncertainties are now increasingly 

acknowledged, and both model discrimination and model combination are viewed as potential 

directions to address these uncertainties (see e.g. Refsgaard et al., 2012). 

Overall, the steady progress in physical model-based optimization of groundwater monitoring has 

resulted in the development of a variety of powerful and robust optimization methods. Multiobjective criteria are now increasingly being used successfully in many studies. Multiple sets of 

model parameters have been used similarly in Monte Carlo simulations and sensitivity analyses. 

Furthermore, geostatistics-based GMN design methods are now starting to benefit FTM 

simulations. In particular, FTM-based GMN designs can be improved by incorporating information 

about uncertainties in both data and the model predictions. 
2-20

Table 2-1 Selected studies proposing methods for model-based groundwater monitoring network design 

No. Source Static

/Dynamic

§

Objective Optimization criteria Optimization 

algorithm

Model 

dimens

1 Usunoff et al., 

1992

S Model 

discrimination

If distances between 

simulation vector results 

obtained for all model 

pairings are large enough, 

then the proposed 

experiment can be used 

most effectively to select 

one of the models (provided 

'reality' is closely reproduced 

by that model).

None Simula

concep

each m

with me

then w

and sim

the oth

2 Hudak and 

Loaiciga, 1992

DA Plume 

characterization

Maximize coverage Location 

problem, 

linear 

programming

Determ

plume 

3 Hudak and 

Loaiciga, 1993

D Detection Maximize coverage Location 

problem, 

linear 

programming

Determ

plume 

(layere

4 Hudak, 1994 S Plume 

characterization

Cover a maximum number 

of siting horizons, and 

allocate wells to the single 

most effective horizon

Linear 

programming

Define 

section

3D (lay

5 Meyer et al., 

1994

S Detection Maximize the number of 

realizations in which the 

plume is detected given the 

maximum number of wells. 

Simulated 

annealing

Monte 

compu

detecti

above 

location

6 Cieniawski et 

al., 1995

S Detection Minimize number of 

undetected plumes and the 

average area of 

contamination of detected 

plumes.

Genetic 

algorithm

Monte 

compu

detecti

above 

location
2-21

7 Lee and 

Kitanidis, 1996

DA Groundwater 

quality monitoring

Minimize pumping and 

measurement cost

Dual Control Monte-Ca

calibrated 

uncertain

prediction

extended 

updates; 

8 Nordquist and 

Voss, 1996

S Model 

discrimination

Where results from different 

models differ the most

Ranking 

locations

Sensitivity

simulation

conceptu

and maxi

paramete

all meani

2D

9 Storck et al., 

1997

S Detection Maximize detection probability, 

minimize cost, minimize 

volume of contaminated 

groundwater at the time of 

detection.

Simulated 

annealing

Monte-Ca

calibrated 

a list of po

wells that 

contamin

the conta

volume w

detected 

monitorin

10 Grabow et al., 

2000

DP Plume 

characterization

None None Simulatio

direction 

the plume

expansion

the conta

distributio

11 Montas et al., 

2000

S Plume 

characterization

Minimize errors in contaminant 

concentration moments given 

the maximum number of wells 

selected from the original large 

set. 

Partial 

enumeration

Monte Ca

flow for ra

fields; ran

simulation

ensemble
 

2-22

12 Bierkens, M. F. 

P., 2006

S Detection Minimize total monitoring 

strategy calculated by adding 

the risk of pollution to the costs 

of installing and maintaining 

monitoring wells and 

conducting routine chemical 

analyses.

None Monte-Ca

calibrated 

probabilit

contamin

2D

13 Dhar and Datta, 

2007 

DP Groundwater 

quality monitoring

Maximize probability of 

detecting contamination at 

locations where a given 

pollution standard is exceeded, 

and minimize installation cost

Mixed 

integer 

programming

Monte-Ca

calibrated 

probabilit

contamin

2D

14 Tonkin et al., 

2007

DP Groundwater 

quality monitoring

Minimize predictive variance Ranking Sensitivity

simulation

simulated 

the obser

prediction

respect to 

paramete

15 Kim and Lee, 

2007

DA Plume 

characterization

Minimize existing uncertainty 

due to well installation

Genetic 

algorithm

Monte-Ca

calibrated 

probabilit

functions 

concentra

16 Chadalavada 

and Datta, 2008

DP Groundwater 

quality monitoring

Minimize probability of not 

monitoring pollutant 

concentrations at those 

locations where probable 

concentrations are large. 

Minimize estimation variances 

of pollutant concentrations at 

unmonitored locations.

Genetic 

algorithm

Monte-Ca

calibrated 

probabilit

contamin

2D
 

2-23

17 Datta et al., 

2009 

DP Source 

identification + 

groundwater 

quality monitoring

Minimize normalized error of 

flux estimates; maximize the 

sum of trimmed means given a 

set of potential monitoring well 

locations, and a maximum 

number of monitoring wells to 

be installed.

Sequential 

quadratic 

programming

Monte-Ca

perturbed 

generate 

contamina

2D

18 Bashi-Azghadi 

and Kerachian, 

2010

S Groundwater 

quality monitoring

Minimize monitoring costs 

(number of monitoring wells), 

maximize the reliability of 

contaminant detection and 

maximize the probability of 

detecting an unknown pollution 

source.

Genetic 

algorithm

Monte-Ca

calibrated 

probability 

contamina

19 Kollat et al., 

2011

S Plume 

characterization

Minimize monitoring costs, 

maximize information provided 

to the ensemble Kalman filter, 

minimize failures to detect the 

tracer, maximize detection of 

tracer fluxes, minimize error in 

quantifying tracer mass, and 

minimize error in quantifying the 

centroid of the tracer plume

Genetic 

algorithm

Monte-Ca

calibrated 

uncertaint

prediction

Ensemble 

updates; 

20 Melles et al. 

2011

S Detection Combined kriging-predicted 

error variance and populationweighted detection capability

Simulated 

annealing

Monte Ca

based on 

distributio

weather d
 

2-24

21 Reed and 

Kollat, 2012

S Plume 

characterization

Minimize monitoring costs, 

maximize information provided 

to the ensemble Kalman filter, 

minimize failures to detect the 

tracer, maximize detection of 

tracer fluxes, minimize error in 

quantifying tracer mass, and 

minimize error in quantifying 

the centroid of the tracer plume

Genetic 

algorithm

Monte-Ca

calibrated 

uncertain

prediction

Ensemble 

updates, 

¶Studies in which modeling was used to develop a synthetic example for the optimization process have not been 

§S – static network; DA - dynamic network with a single augmentation; DP – dynamic network with augmentatio

predetermined phases of the project.
2-25

2.3 Integrating Model Abstraction into Monitoring Design 

Systematic model abstraction can lead to a variety of conceptual models of potential use for 

optimization of the monitoring efforts. A conceptual model is always needed to address any of 

GMN objectives shown in Fig. 2-6. Therefore, as a result of the model abstraction process, 

multiple GMNs can be designed for purposes of aquifer characterization, parameter estimation, 

characterization of the background concentration, contaminant detection, compliance 

assessment, plume characterization, source identification, and model discrimination. Because 

each conceptual model has a flow and transport model associated with it, most of the above GMN 

optimization tasks can be approached with one of the methods shown in Fig. 2-1. 

Abstraction of the model structure can, in particular, be used in GMN design efforts that address 

the model discrimination problem. The specific objective then will be to augment an existing well 

network for the purpose of optimizing model discrimination. It is generally accepted that the 

traditional approach of model uncertainty analysis, which considers only a single conceptual 

model, may fail to adequately sample the full space of plausible conceptual models. As such, the 

traditional approach is prone to modeling bias and underestimation of predictive uncertainty. The 

purpose of model discrimination is not to identify the best model but rather to provide insight into 

the behavior of the different models, thereby adding important information about subsurface 

properties controlling or affecting flow and transport. A reduction in the prediction uncertainty 

resulting from model discrimination can be expected in three categories of uncertainty as defined 

by Refsgaard et al. (2012): (a) the geological structure; (b) the effective model parameters; and (c) 

model parameters including local scale heterogeneity. Two approaches to GMN design for model 

discrimination have been used in subsurface contaminant hydrology so far. Knopman and Voss 

(1989) postulated that points of greatest difference in predictions can contribute the most 

information to the discriminatory power of a sampling design. They suggested the use of three 

objective functions in the design optimization: the sum of squared differences in predicted 

concentrations, the squared scaled difference, and the minimum squared difference. This 

approach has been successfully used in several field cases (Knopman et al., 1991; Nordquist and 

Voss, 1996). Another approach was proposed by Usunoff et al. (1992). They formulated the 

optimization problem within a maximum likelihood framework and defined the performance of 

each model in terms of its ability to fit existing experimental data as well as data predicted with 

other models at additional monitoring points. Both approaches do not impose any restrictions on 

model structure and hence can be applied with the abstracted models. 

Several GMN designs are possible if alternative conceptual models are proposed as a result of 

model abstraction. Monitoring design optimization may then rely on weighted simulation results 

from the corresponding mathematical models to provide the required input for the optimization 

algorithms as outlined in Table 2-1. Bayesian model averaging (Ye et al., 2004) can be 

instrumental in determining model weights. Rojas et al. (2010) recently used a combined GLUEBMA approach to analyze prediction uncertainties generated with eight different conceptual 

models. The models predicted substantially different flow processes outside of the studied area. 

Having an appropriate site-specific GMN design (or designs) is then important to decrease model 

uncertainty. If the scale of the prediction domain is substantially different from the scale of the 

domain of the initial observations, then the abstraction of scale change can provide additional 

conceptual and mathematical models to be included in the monitoring design using methods 

outlined in Table 2-1.
2-26

Metamodeling abstraction is currently already being used for GMN designs. As shown by Arndt et 

al. (2005), replacing time-consuming model runs with computations using regression equations 

appears to be very efficient in designing optimal monitoring schemes for contamination sources. 

Abstraction of parameter determination includes the application of pedotransfer functions that 

allow one to generate model ensembles for application to flow in variably saturated soils (Guber et 

al., 2006; Guber et al., 2008). Model-based GMN design methods include the use of ensemble 

modeling with Monte Carlo-based randomly generated hydraulic and transport parameters (Table 

2-1). It has been noted that such methods for generating parameters can be hampered by 

uncertainty about possible correlation between parameters and appropriate ranges of some 

parameter values. The use of pedotransfer functions may alleviate this problem since the 

parameters of water retention and (if available) the hydraulic conductivity are not randomly 

generated but fitted to measured data. Another abstraction of this type – zonation – has already 

been used successfully in the design of GMNs (Tsai et al., 2003). 

Most of the model-based GMN design methods have been developed using assumptions that 

numerical calibration of the models can be performed, that parametric sensitivities can be 

determined, that measurement errors can be neglected, that the vadose zone can be neglected, 

and that a one-dimensional solute transport model is fully acceptable. One or more of these 

assumptions may not be applicable in most practically important cases. In this study the ARS 

study team develop or modify heuristic techniques that will avoid the need to make these types of 

assumptions (Section 6). The techniques will be applied to models that are obtained via model 

abstraction for full 3D flow and transport in a variably-saturated flow domain. 
3-1 

3 EXPERIMENT TO TEST AND CONFIRM MODEL ABSTRACTION FOR 

MONITORING FLOW AND TRANSPORT IN SOILS 

In this study, the ARS study team applied 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 dataset and the comprehensive model of flow and transport. This model and its 

abstractions have been used to demonstrate the integrating model abstractions in developing 

monitoring designs for the ARS OPE3 site example. 

3.1 Outline of Lateral Flow and Transport Experiment 

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 illustrated 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 alternative 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, however, the resource demands may become 

daunting and sample cross-contamination may become an issue, while field variability may 

further 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. 
3-2 

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 

chemical fate and transport in the subsurface requires the development and application of fieldscale predictive models. These field-scale models require 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 A. 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. 

The field experimental setup was implemented in this study 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 the 

experiment is shown in Fig. 3-18. The tracer application area during the experiments was 

continuously irrigated, leading to a gradually expanding groundwater mound. The composition of 

groundwater during the experiment was monitored using observation wells located within the 

projected plume. 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. Data obtained from soil surveys, water content 

measurements and the tracer experiment itself provided information for a base model that was 

developed to accommodate the encountered complexities as explained in the following chapter. 

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 site in Beltsville, MD. An aerial view of the 

site is shown in Fig. 3-1. The watershed in the area drains into a riparian wetland forest that 

contains a first-order stream (Gish et al., 2002, 2005; Chinkuyu et al., 2008). 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 site that is intensively instrumented, and where all data are 

geo-located with a differential or kinematic global positioning system. Data collection included the 

following: 

• Over 40 km of ground penetrating radar (GPR) data were collected and analyzed. 

• Every two years, soil cores were extracted to determine 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 sites. 

• 36,000 volumetric water content measurements at 48 locations were collected daily. 
3-3 

Figure 3-1 The USDA-ARS OPE3 research site; a – aerial view, b – instrumentation. A, B, 

C, D – research fields. 

• Micro-meteorological stations with eddy covariance systems to monitor 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 field. 

• Field B (Fig. 3-2) 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. 
3-4 

The experimental site of this particular study is located at the 3-ha field B of the OPE3 

experimental site. The field is currently instrumented with 64 soil moisture sensors (EnviroSCAN, 

SENTEK Pty Ltd., South Australia) distributed among 12 capacitance probes (Fig. 3-2) that 

measure soil water content at depths from 10 to 180 cm every 10 min year-round. Table 3-2 

shows installation depths of the soil moisture sensors. Field B was equipped with 52 groundwater 

monitoring wells, 41 of which are still active (Fig. 3-2). 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. 3-1b). 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. 3-1b). 

3.2.2 Existing OPE3 Information Relevant to Flow and Transport in Soils 

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 pH, organic matter content, Ca, Mg, K, P, sand, silt and clay contents had been collected 

during a soil survey performed by the USDA-NRCS at OPE3 site in 1997 using samples 

representing distinct genetic horizons. A detailed description of selected data is shown in Fig. 3-3. 

The soil pH was in a range between 4.3 and 7.5. The organic matter content varied from 0.12 to 

4.65% and demonstrated a typical decrease with depth, indicating the absence of recent 

substantial changes in soil stratification caused by floods or erosion. The sand, silt and clay 

content exhibited large variations at each depth. Although the soils were characterized as having 

a coarse texture (Table 3-1), sand content varied in the range between 34 and 97 % (Fig. 3-3), 

with often drastic changes from one horizon to another in some profiles. Loamy sand and sandy 

loam classes dominated in soil texture. Only 9% of the samples belonged to sand, sandy clay 

loam and loam texture classes according to the survey (Fig. 3-4a). The relationship between soil 

clay and sand content was linear below 60 cm (Fig. 3-4b), which suggests a potential for having 

isolated lenses of predominantly coarse and predominantly fine material. 
3-5 

Figure 3-2 Locations of groundwater wells (brown circles) and soil moisture sensors 

(green circles) at field B. 

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

Soil associations 

and soil series

Coverage

%

Topsoil

texture

Description

Downer-MuirkirkMatawan49 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

Matawan Fine-loamy, siliceous, semiactive, mesic Aquic 

Hapludults

Hammonton Coarse-loamy, siliceous, semiactive, mesic 

Aquic Hapludults

DownerIngleside5 Loamy sand

Downer Coarse-loamy, siliceous, semiactive, mesic 

Typic Hapludults

Ingleside Coarse-loamy, siliceous, semiactive, mesic 

Typic Hapludults
3-6 

Table 3-2 Installation depths of the soil moisture sensors at field B of OPE3 site. 

Location Depth (cm) 

10 30 50 80 120 150 180 

BH1 x x ns x ns ns ns 

BH2 x x ns x ns ns ns 

BH3 x x ns x ns ns ns 

BH4 x x ns x ns ns ns 

BL1 x x x x x x x 

BL2 x x x x x x x 

BL3 x x x x x x x 

BL4 x x x x x x x 

BM1 x x x ns x x x 

BM2 x x x ns x x x 

BM3 x x x ns x x x 

BM4 x x x ns x x x 

ns stands for no sensor.

3.2.2.1.2 Soil Hydraulic Property Measurements 

To evaluate possible effect of the macroporosity on the soil hydraulic properties, undisturbed 

samples having a 20 cm2 support 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. 3-5. Samples taken close to the 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 

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 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. 3-6a, 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 well w50 and 50% at well 

w52, 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. 
3-7 

Anisotropy in the saturated hydraulic conductivity is another consequence of changes in soil 

structure. Fig. 3-6b shows that the horizontal hydraulic conductivity was smaller than the vertical 

conductivity at a depth of 25 cm, with about half of the samples showing distinct non-zero 

horizontal conductivities. At the depth of 45 cm, all samples had zero horizontal conductivity. The 

data are in agreement with visual observations of seepage along the walls of a soil pit where the 

measurements were taken (Fig. 3-7). 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. 
3-8

Figure 3-3 Basic soil properties at the OPE3 site based on data of soil survey conducted in 1999. 

pH

4.5 5.0 5.5 6.0 6.5 7.0 7.5 Depth, cm

0

20

40

60

80

100

120

OM%

1 2 3 4

Ca (lbs/A)

500 1000 1500 2000 2500 3000

Sand (%)

40 50 60 70 80 90 Depth, cm

0

20

40

60

80

100

120

Silt (%)

5 10 15 20 25 30 35

Clay (%)

5 10 15 20 25 30 35
3-9

Sand (%)

30 40 50 60 70 80 

Clay (%)

5

35

30

25

20

15

10

Figure 3-4 Soil texture at the OPE3 site based on data of soil survey conducted in 1999. 
3-10

Figure 3-5 Soil water retention data of samples collected at locations near wells w50 and w52 of field B; 

23 cm depth, and c) 47-50 cm depth (●,○ – well w50, - well w52).
3-11

Figure 3-6 Probability distributions of the saturated hydraulic conductivity for 20 cm2 

support areas; a – field falling head measurements; - well w50, depth 

25 cm , - well w50, depth 45 cm, - well 52, depth 25 cm, 

- well 52, depth 40 cm; b – constant head measurements of 

vertical (KSV) and horizontal (KSH) conductivities of undisturbed samples

with 20 cm2 support area in the laboratory (error bars show standard 

deviations). 
3-12

Figure 3-7 Water seepage from the wall above a locally restrictive soil layer near well 

w50. 
3-13

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 site. 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. The ARS study team 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 m2 each were randomly selected for higher resolution surveys (Fig. 

3-8). 

A ground-penetrating radar survey was conducted in 2000. 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 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 data gave the strongest reflection at depths of 1.3 and 2 m. A 

GPR image profile is shown in Fig. 3-9. The first continuous restricting layer in this figure was 

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. The ARS study team used the software packages GEOEAS (EPA, Las Vegas, NV) and GS_ (Gamma Design Software, Plainwell, MI) for this purpose. 

An example of the topography this obtained is given in Fig. 3-10. 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 elevationcorrected subsurface topography to determine potential flow pathways (Fig. 3-10). 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., 2003, 2005). Sensors above the restrictive layer 

demonstrated the accumulation of water above the layer (Gish et al., 2002). 
3-14

Figure 3-8 Layout of the 7.5-ha site overlain by a 25x25 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, with permission). 
3-15

Figure 3-9 Ground-penetrating radar image with a digital trace of the first restricting 

layer, indicated by the dotted line (after Gish et al., 2002, with permission). 
3-16

Figure 3-10 Interpolated elevation of the first continuous restricting layer with potential 

subsurface flow pathways (blue lines) identified using Arc/Info hydrologic 

tools. 
3-17

Variability in the depth to the first continuous restricting layer also affected seasonal dynamics of 

the perched water tables. Groundwater depths monitored using Cera-Diver (Van Essen 

Instruments, Delft, The Netherlands) sensors installed in wells at a depth of 2.0 m in 19 locations 

across field B revealed high spatial variability in perched water levels (Fig.3-11). In some locations 

(e.g. w10, w11, w33, w39, w42-w44), the perched water level was consistently higher compared 

to other locations (e.g. w02, w12, w15, w18, w21, w36, w47). The amplitudes of groundwater level 

oscillations observed at locations with a shallow perched water were generally greater than in 

wells with relatively deep groundwater, thus indicating fast response of the water levels to rainfall 

in those locations. Since no differences in the oscillation phases were observed for the 19 

observation wells installed at different locations across field B, one can conclude that the decline 

in groundwater level was controlled primarily by water permeability of the restrictive layer, and that 

locations with shallow groundwater were hydraulically more active, compared to the other 

locations. In other words water fluxes were greater in wells where the restrictive layer was close to 

the surface due to hydraulic connectivity between surface and groundwater. Preferential flow was 

also a factor, especially in the well 21. 

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., 2003). During mildly dry years, corn yields decreased 

significantly (P<0.01) as the distance from the pathways increased (Gish et al., 2003). 

3.2.2.2.2 Structural Units of Soil Cover 

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 8 locations of field B from May 1, 2001 through January 1, 2003 (Fig. 3-

12). Time series from different locations appeared to be vertically shifted relative to each other. 

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 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. 3-13) supposedly experienced either more intensive waterlogging or higher soil water losses 

as compared to other locations. The spatial organization can be seen in Fig. 3-14, 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 these 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 zones where water availability 

to plants was consistently better or consistently worse than average (Fig. 3-15).
3-18

Figure 3-11 Time series of groundwater depths measured in field B in 2006-2007.

50

100

150

w02 

w04 

w06 

w08 

w10 

w12 Groudwater depth, cm

0

100

200

w15 

w18 

w21 

w33 

w36 

w39 

3/1/06 4/1/06 5/1/06 6/1/06 7/1/06 8/1/06 9/1/06 10/1/06 11/1/06 12/1/06 1/1/07 2/1/07 3/1/07 4/1/07 5/1/07

0

50

100

150

200

250

w42 

w43 

w44 

w47 

w50 

w52 

w11 
3-19

Figure 3-12 Changes in soil water storage of the 0-80 cm soil layer measured at 8 locations of field B from 

through January 1, 2003. 
3-20

Figure 3-13 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. 
3-21

Figure 3-14 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 yellow, green and light blue lines designate subsurface 

flow pathway locations. The yellow 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 

having yields below the mean. 

BH4

BM4

BM3

BH3

BL3

BH2

BL2

BL1

BM2

BM1

BH1

BL4
3-22

 

Figure 3-15 Spatial corn yield variations 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. 
3-23

Contaminant release typically occurs over an area much smaller than the biophysics-based unit. 

Still, it seems important to determine locations of different biophysics-based units, since the 

differences between units may reveal differences in the infiltration and groundwater recharge 

rates that will affect the transport of contaminant released over smaller area within a biophysicsbased unit. 

3.2.3 Surveying, Monitoring and Site-Specific 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. The ARS study team 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 

conducted in 2000 and described in section 3.2.2.2.1. Therefore, an additional fine-scale ground 

penetration radar survey was conducted to delineate boundaries of the soil hydrologic horizons for 

subsurface transport simulations. 

3.2.3.1 Location Selection and Site Instrumentation 

The location of 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; 

(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 m2 site was selected in the intensively equipped South-Eastern part of 

Field B. Ground penetration radar data obtained in 2000 for this site indicated considerable 

variability in the depth to the restrictive soil layer (varying between 2.5 to 4.0 m), which was 

highest within the surveyed site. 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 (Fig.3-10). 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. Analyses of multisensor capacitance probe (MCP) monitoring data at locations BM2, BM3, BM4, BL3 and BH3 
3-24

Figure 3-16 Setup of the lateral flow experiment. 

MCP

Soil tensiometers

Soil tensiometers

Runoff flume 

tensiometers

Sprinklers 

flume 

tensiomete

rs MCP

Runoff 

Runoff collector

Multiplexer

Sprinclers 

flume 

tensiometers
3-25

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 (loc-1, loc-2, loc-3 and loc-4), each of 1 m2 and 10 m apart, were instrumented in the 

spring of 2006 to monitor soil water contents, pressure heads, and groundwater depths 

 (Fig. 3-16). 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 contents and 

pressure heads, respectively. The MCP and tensiometers were connected to a CR-10X 

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 the tensiometers 

(Fig. 3-17). Collected data were acquired from the Redwing 100 Airlink modem (Campbell 

Scientific, Inc., Logan, Utah) once a week. 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. 3-18). 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 loc-1 to loc-4 to correct MCP factory calibration. 

A drainage line was constructed at a distance of 1m 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. 

3.2.3.2 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 in 2006. 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. 3-19). 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. 3-20), 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. 
3-26

Figure 3-17 Schematic of the data acquisition and collection system. 

Figure 3-18 Locations of multi-sensor capacitance probes and groundwater wells 

(indicated by “Loc-” number) at the experimental plot.

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 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
3-27

Figure 3-19 Soil texture measured at 10 depths in 12 locations. 
3-28

Figure 3-20 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%
3-29

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 depth from 

5.9 near the soil surface to 4.5 at 2.0-m depth (Fig. 3-20). Coefficients of variation for pH were 

within the range from 0.04 to 0.10, indicating less horizontal variability in pH as compared to the 

soil particle size distribution. 

The ARS team also measured the soil bulk density on undisturbed samples taken from the upper 

1.0-m soil layer at 0.1 m increments during MCP calibration at locations 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. 3-21). 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. 

Detailed soil texture measurements carried out in 2006 during the MCP and groundwater well 

installations at 12 locations were supplemented with data obtained in logs (wells w01-w52) 

installed in 2002 across field B. The soil texture was measured using the hydrometer method 

(Gee and Or, 2002) on soil samples taken from selected depths. Soil texture of the soil horizons 

represented 9 texture classes indicating high heterogeneity of soil properties (Table 3-2). In spite 

of the observed variability, four classes dominated soil texture. They were in the order of their 

frequency order: sandy loam (SL), loamy sand (LS), and silt loam (SiL) in layer 46-61cm; SL, LS, 

sand (S) and SiL in layer 107-122 cm; LS, SL and loam (L) in layers 168-183 cm and 229-244 cm; 

and LS, S and SL in layers 290-305 cm (Fig. 3-22). 

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 within the 10x10 m2

experimental site. 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 undisturbed soil cores. The cores 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. 3-23 and 3-24. 

Measured saturated hydraulic conductivities (Ks) 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. 3-23). Soil samples taken from depths of 20-50 cm at 

location 1 and from depths of 15-40 cm and below 80 cm at location 3 did not conduct water at 0.5 

m pressure head. Low Ks 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. 

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. The ARS study team 

did not observe high lateral variability in soil water retention, except for the 30-40 cm soil layer 

(Fig. 3-24), where the variability could be attributed to high variability in the bulk density (Fig. 3-

21). Summarizing the basic soil properties, one could expect considerable variability in the 
3-30

Figure 3-21 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
3-31

Table 3-3 Soil texture measured in soil cores taken during installation of the groundwater 

wells at field B. 

Well 

ID

Depth, cm Well 

ID

Depth, cm

46-61 107-

122

168-

183

229-

244

290-

305

46-61 107-

122

168-

183

229-

244

290-

305

W01 SL SiL LS SL LS W27 SL SL

W02 SL SL LS SL LS W28 SiL SL LS LS LS

W03 LS S LS LS S W29 SL LS SL SL SL

W04 LS S S S LS W30 SL SL LS SiL

W05 SL S S SL SL W31 SL SL L SiL

W06 SL LS SL SL LS W32 SiL SL SiL L

W07 LS S LS S S W33 SL S S S S

W08 LS LS LS LS LS W34 SL LS S LS S

W09 LS LS LS S W35 LS LS LS LS

W10 SL S S S LS W36 SiL SiL SL LS S

W11 L LS S LS S W37 SL L SL

W12 SL SL LS LS W38 SiL SiL SL LS SL

W13 SL LS LS SL W39 SL SL LS SL

W14 SL SL SL LS W40 LS S LS LS SL

W15 SL SL SL SL LS W41 LS SL LS SL SL

W16 SL SiL SL SL SL W42 SL S S LS S

W17 SL LS SL LS LS W43 SL SL LS SL L

W18 SL SL LS LS LS W44 LS LS L SiL

W19 SiL SL SL LS W45 SL SL SL SL L

W20 SiL SL S LS LS W46 SL LS SL

W21 SiL SiL LS SL SL W47 CL SiL SL LS S

W22 SiL SL LS LS LS W48 SiL SiL SiL LS LS

W23 SL SiL LS LS SL W49 SiL SiL LS S S

W24 L L CL CL L W50 S LS S SL LS

W25 SL SiCL CL SCL W51 LS S S LS SL

W26 L SL SiC CL W52 LS S S S S

 Abbreviations used in the table: 

S - sand 

SL - sandy loam 

LS - loamy sand 

L - loam 

SiL - silt loam 

SiCL - silty clay loam 

SiC - silty clay 
3-32

Figure 3-22 Soil texture measured in logs w01-w52 at field B. 

Figure 3-23 Laboratory measured saturated hydraulic conductivities, Ks. 

0.0

0.1

0.2

0.3

0.4

0.5

0.6

46-61 107-122 168-183 229-244 290-305

Frequency

Depth, cm

S

LS

SL

SCL

L

CL

SiL

SiCL

SiC

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
3-33

Figure 3-24 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
3-34

spatial and temporal patterns of soil water content during the experiments, primarily because of 

high spatial variability in the saturated hydraulic conductivity. 

3.2.3.3 Soil Moisture and Groundwater Monitoring 

The monitoring equipment installed in 2006 at the experimental site was tested during July 1, 

2006 – March 1, 2008. Soil water contents and pressure heads were monitored at the 

experimental site. 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 for the monitoring period July 1, 2006 - November 1, 

2007 are shown in Fig. 3-25. 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 about 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 readings exhibited 

noise, which was removed using a multilevel 1-D wavelet decomposition with a Daubechies filter 

(db4). The ARS study team used the Wavelet toolbox of the MATLAB 6.5 Software for this 

purpose. 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 contents approached saturation. Extremely low water contents 

were observed in September 2006, and in August and October 2007, at practically all depths (Fig. 

3-26). 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 contents 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 

changes in the flux at the soil surface.
3-35

Figure 3-25 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
3-36

Figure 3-26 Examples of soil water content and pressure head time series measured at locations 1 and 2 

September 2007. 
3-37

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 entire monitoring period. 

Groundwater depths (GWDs) were monitored at 12 locations starting November 1, 2007. 

Observed values varied between 0.0 and 200 cm during the monitoring period (Fig. 3-27). The 

GWD 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 as compared to other locations during drying events. 

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. 3-26). The ARS study team shows only data measured during 

continuous soil drying (drainage water retention curves). The data in Fig. 3-28 in general 

resembled the laboratory-measured water retention curves (Fig. 3-24). Similarly as the laboratory 

data, 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 of 

locations 2 and 3 shifted to lower water contents (Fig. 3-28). 

Overall, 44-month intensive equipment testing showed that in spite of some technical issues with 

MCP sensors and tensiometers the installed equipment appeared to be reliable and appropriate 

for the subsurface transport experiment outlined in part 3.1 of this chapter. Results of the soil 

moisture monitoring supported soil hydraulic and soil texture data and confirmed that the studied 

area represents a high heterogeneous layered system. 

3.2.3.4 Fine-Scale Ground Penetration Radar Survey 

A fine-scale GPR survey was conducted in April 2006 to obtain detailed information about the 

stratification of soil hydrological layers at the field site. A polygon of 16,617 m2 in the SouthEastern part of 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 east-west transects 2-m apart. The RADAN (Geophysical 

Survey Systems, Inc) software was used to process the acquired information. A total of 60 

scanned images were processed. A horizontal scale adjustment was used first to correct 

horizontal distances based on markers installed every 20 m along the scanned transects. 

Subsequently the diffractions were removed and dipping layers were corrected using the 2-D 

variable velocity migration method. This type of correction was necessary for images in which the 

deeper objects were obscured by numerous shallower objects that appeared as constructively 
3-38

Figure 3-27 Groundwater depths measured at the experimental site during the period November 2007 - M

11/1 12/1 1/1 2/1 3/1 Depth to the groundwater (cm)

0

50

100

150

200

1

2 

3

4 

5 

6

Date

11/1/07 12/1/07 1/1/08 2/1/08 3/1/08 

0

50

100

150

200

7

8

9

10

11

12
3-39

Figure 3-28 Plots of measured soil water pressure heads versus volumetric water 

contents at locations 1-4.
3-40

Figure 3-29 Example of ground-penetrating radar images used to delineate hydrological soil layers. 
3-41

interfering hyperbolic reflectors. Zero depths on the images were corrected next to match the soil 

surface using the vertical scale adjustments, after which the reflective layers were digitized using 

the EZ tracker option of the RADAN software. Seven digitized layers from each GPR image were 

saved in ASCI format at 25-cm horizontal resolution. Depths to the reflective layers were expressed 

as two-way signal travel times in the digitized images (Fig. 3-29). 

To define true depths to the reflective layers the ARS study team computed the GPR signal travel 

time τ as a function of the travel depth z as follows:

τ = 2 ∫

dz

v(z) ⁄

300

0

(3-1)

where v is the GPR wave velocity in soil, which depends on the soil dielectric constant E. 

Topp et al. (1980) showed that at frequencies between 1 MHz and 1 GHz values of E for sandy 

loam, clay and clay loam soils can be estimated from the volumetric soil water content θ as:

Ε = 3.03 + 9.3θ + 146.0θ2 − 76.7θ3 (3-2)

The wave velocity U is then: 

U(Z) = c/√Ε (3-3)

where c is the speed of light (0.3 m ns-1).

Seven soil water content profiles measured at locations BH3, BH4, BL3, BL4, BM2, BM3 and BM4 

(Fig. 3-8) during the GPR survey were used to compute profile distributions of the soil dielectric 

constant. Measured θ values varied between 0.167 and 0.347 at different depths and locations, 

and tended to decrease with depth (Fig. 3-30a). Variability in the water content translated into 

variability in the soil dielectric constant. Values of E also decreased with depth, ranging from 8.3 to 

20.6 (Fig. 3-30b). The variability in soil water content and associated variability in the soil dielectric 

constant did not produce large differences in the signal travel time τ (Fig. 3-30b). The variability in 

τ increased with depth, but remained less than 8 ns at a depth of 200 cm. Although soil water 

contents were not measured at other locations during the GPR survey, the ARS study team 

assumed that the water content variability measured at the seven selected locations represented 

reasonably well the spatial variability in θ across field B. Since observed variability did not affect 

much the travel time τ, the average relationship τ(Z) was used. 

The data for seven digitized layers were converted into depths to the soil horizons. To do this the 

ARS study team assumed that the vertical variability in soil texture affected the soil hydraulic 

properties and produced abrupt vertical water content changes. The layers between two 

consecutive reflective lines hence can be represented by soil horizons having specific soil hydraulic 

properties. To compute boundaries of these horizons the ARS study team interpolated digitized 

data using the inverse of the average relationship τ(Z). Results of the interpolation for the first six 

soil layers are shown in Fig. 3-31. The thickness of the first soil layer varied from 28 to 50 cm. This 

depth corresponded to the plough depth. The deepest layer detected by the GPR survey at this 

frequency was in the depth range from 211 to 243 cm. 
3-42

3.2.3.5 Tracer Experiment Experimental Setup.

The lateral flow experiment was set up as shown in Figs. 3-16 – 3-18, and Fig 3-32. Four 

sprinkler nozzles (Olson Red Mini Rotor Style Drip Emitter, Olson Irrigation Systems, 

Santee, CA) were installed at heights of 1 m in the corners of the irrigation plot (Fig. 3.22a). 

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. 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 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. Two 2.1-ton water tanks were installed for the tracer application (Fig. 3-22b). 

The observation wells at locations 1-12 were equipped with samplers to collect water from 3 

different depths (Fig. 3-32c). The samplers consisted of a 16-mm plastic OD tubes containing 4 

rubber packers installed into the wells. The packers separated three 30-cm long sections inside 

of the wells. The 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 so that the samples were 

taken at depths of 1.1 m at locations 1-4, and depths of 1.05, 1.35 and 1.65 m at locations 5 - 

12. A windshield (160 cm height) was constructed around locations 1- 4 to minimize wind 

impacts on the irrigation uniformity (Fig. 3-22d). 

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, 2008, 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. 
3-43

Figure 3-30 Plots of (a) the vertical water content distribution measured at locations BH3, BH4, BL3, BL4, 

during the GRP survey, (b) the dielectric constant computed from average water contents am

(c) the minimum, average and maximum time of GPR wave propagation computed from the s

constant profiles at seven locations. 

Water content (cm

3

 cm

-3

)

0.18 0.20 0.22 0.24 0.26 0.28 0.30 0.32 Depth, cm

0

50

100

150

200

Time

0 10 20 

min

average

max

Dielectric constant

6 8 10 12 14 16 18 20 22
3-44

Figure 3-31 Depths to six out of seven soil hydrological layers delineated using the finescale GPR survey at the experimental part of field B in 2006. The color scale in 

the legend indicates depths in cm. 

Hydrological layer 1 Hydrological layer 2

Hydrological layer 3 Hydrological layer 4

Hydrological layer 5 Hydrological layer 6
3-45

Figure 3-32 Plots of (a) the irrigated plot equipped with tensiometers, MCPs and a flume 

for runoff collection, (b) the tracer application tanks, (c) the observation wells 

with the tracer sampling outlets, and (d) the windshield around the tracer 

application area. 
3-46

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 Cl- by ion chromatography as described in chapter 3.2.4.1. Irrigation, while 

rainfall water was periodically analyzed also for Cl-. Soil water contents and groundwater depths 

were monitored using MCPs and Cera-Divers at 12 locations as described in chapter 3.2.3.3. The 

study was terminated when the groundwater levels decreased below the water sampling depths at 

most locations. 

Cumulative irrigation, precipitation, evapotranspiration and runoff data are shown in Fig. 3-33. The 

daily irrigation rate was 9.5 cm d-1 during the first two days, 1.5 cm d-1 during the next 64 days, 

and 1.8 cm d-1 during 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 Cl- concentrations 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 shown below. The average ET values 

were 0.5, 0.8, 1.0 and 1.1 mm d-1 in April, May, June and July, respectively, which did not affect 

the soil water content dynamics. 

Figure 3-34 illustrates the water table dynamics. Groundwater levels remained relatively high at 

locations 1-4 during the lateral flow experiment (Fig 3-34a). 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 phreatic surface 

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 

affected less 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 rainfall events, 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. 

Plots of the soil water content during the experiment are shown in Fig 3-35. Soil water contents 

before the experiment were in the range from 0.148 to 0.403 cm3 cm-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. 
3-47

Figure 3-33 Cumulative water fluxes measured during the lateral flow experiment. 

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. 3-35). Water contents at depths of 50 and 60 cm 

showed different trends 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 contributed further to the abrupt water content changes at 

locations 7-9. 

Differences in soil properties, hydraulic regimes and unsteady subsurface flow at the 12 locations 

affected Cl- transport. Cl- concentrations in groundwater prior to irrigation varied within the range 

from 6 to 24 ppm, but did not differ significantly between the different depths and locations. 

Because of small spatial variability in the initial Cl- concentration at the different locations, the 

ARS study team did not expect any effect of the initial Cl- distribution on the results of the lateral 

flow experiment. Cl- concentrations 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. 

Date

4/1 5/1 6/1 7/1 8/1

Cumulative flux (cm)

0

50

100

150

200

250

Evapotranspiration

Irrigation

Runoff

Precipitation
3-48

Figure 3-34 Groundwater depths measured at the experimental site during the period November 2007 - M

Depth to the groundwater (cm)

0

50

100

150

200

0

50

100

150

200

2008

4/1 5/1 6/1 7/1 

Daily precipitation (mm)

8

6

4

2

0
3-49

Figure 3-35 Soil water content measured at 12 locations during the lateral flow 

experiment. 
3-50

Figure 3-36 Chloride contents of 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:
3-51

The Cl- time series measured in 12 wells are shown in Fig. 3-36. The ARS study team 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 applied. 

A gradual decrease and another increase in Cl- concentration followed the initial stage. Contrary to 

wells 1 and 4, a relatively slow increase was followed by a gradual decrease in Cl- in wells 2 and 

3. These dramatic differences in the vertical transport rates of Cl- at 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 saturation 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 

Cl- to 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, the ARS study team did not 

observe Cl- breakthrough 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 Cl- transport 

was faster than at location 3. 

An increase in the Cl- concentration 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 Cl- concentration 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 Cl- concentrations did not change with depth, and location 

7 where the highest Cl- concentrations were observed at a depth of 1.35 m. Noticeable differences 

in the Cl- breakthrough 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 Cl- concentrations 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 Cl- concentration at three depths and 12 locations imply that the tracer was 

transported preferentially in hydraulically active soil zones. 

An interesting phenomenon the ARS study team 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. 3-36). 

Smaller Cl- concentrations were measured when the GWDs were smaller. An increase in the 

GWD always caused an increase in the Cl- concentration. The decrease in Cl- concentration 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 

Cl- changes occurred synchronously at three different depths without changes in the concentration 

with depth. 

4-1 

4 DETAILED FLOW AND TRANSPORT MODELS OF 

THE OPE3 WATERSHED SITE 

4.1 Description of Models 

Two fully 3D numerical codes, HYDRUS-3D and TOUGH2, were used for the water flow and 

contaminant transport simulations in the subsurface at the OPE3 site. Advantages of these two 

codes are their built-in mass conservation and having the same data preprocessing and postprocessing through the entire flow domain. The codes are, however, computationally intensive 

and not attractive for parameter estimation, uncertainty, sensitivity evaluation, and monitoring 

optimization unless massive parallel computing is used (e.g., Coumou et al., 2008). 

The complexity of subsurface flow systems creates a need and various opportunities for 

conceptual simplifications leading to a multiplicity of flow models. One common simplification is 

based on the assumption that lateral flow and transport in the unsaturated zone is not significant, 

except for the capillary fringe (Abit et al., 2008) or when perched temporary saturated layers 

appear are present (Twarakavi et al., 2009). If lateral flow is ignored in the unsaturated zone are, 

flow and transport can be simulated as a one-dimensional (1D) process, while flow and transport 

in groundwater remains a fully 2D or 3D phenomenon. The scarcity of information on the 

anisotropy of hydraulic properties in the vadose zone also favors the 1D approximation above the 

groundwater table. Such anisotropy has been demonstrated (Zhang et al., 2007), but is very rarely 

characterized to the extent of providing accurate estimates of the lateral flow process. As soon as 

the relative insignificance of lateral flow and transport in the vadose zone is surmised for the 

expected hydrologic forcing, a more efficient computational scheme will result, which is important 

when multiple simulations are needed to evaluate uncertainty or sensitivity. 

Barthel (2006) discussed alternative integrated modeling approaches that are based on coupling of 

existing modeling concepts for the saturated and unsaturated zones. A problematic issue with 

coupling existing models is the question of how to tailor their output in a consistent manner. 

Twarakavi et al. (2008) noted that evaluation of interactions between near-surface and groundwater 

flow processes using coupled models has been a desirable but difficult goal. These authors coupled 

the HYDRUS-1D code for the vadose zone with the MODFOW code for groundwater zone. The 

two computer codes interact (i.e., exchange information about groundwater recharge and 

groundwater level) only at the end of each MODFLOW time step, during which HYDRUS may 

perform multiple time steps to simulate the unsaturated zone flow. The MODFLOW code receives 

the recharge flux from HYDRUS and evaluates a new water table depth for the next time step. A 

new water table depth is then estimated and assigned as the pressure head bottom boundary 

condition for the HYDRUS code at the next time step of the MODFLOW code. A similar method 

was applied by Facchi et al. (2004). This approach is known to create mass balance error. 

Twarakavi et al. (2009) noted that for cases where the coupled mass balance is not achieved 

satisfactorily, a version of the HYDRUS package is available that can attain complete mass balance 

between the saturated and unsaturated zones by suitably altering the unsaturated profiles for each 

zone at the end of each time step. The need for modifications of the profiles can create difficulties 

in using water flow simulation results in subsequent simulations of solute transport. 

In efforts to control mass balance errors, Stoppelenburg et al. (2005) used an iterative approach 

to gradually adjust the recharge rates, while Liang et al. (2003) searched iteratively for the 

groundwater level until the mass balance requirements were met. In the latter case, the amount 
4-2 

of water in the unsaturated zone was used to adjust the position of the groundwater table. Shen 

and Phanikumar (2010) further used the mass balance equation to provide a linkage between the 

unsaturated zone and groundwater. The saturated zone vertically was represented as a single cell 

extending from the bottom of the unconfined aquifer to the lower boundary of the first element (cell) 

in the unsaturated zone above the water table. In other work, Yakirevich et al. (1998) coupled a 2D 

Boussinesq-like equation for the saturated zone with the 1D Richards model for the unsaturated 

zone. Unlike the Boussinesq equation for a leaky phreatic aquifer, the developed model did not 

contain a storage term with specific yield and a source term for natural replenishment. Instead, the 

equation included a water flux in the phreatic surface term through which the Richards equation 

was linked with the groundwater flow equation. Xu et al. (2012) integrated the Soil–Water–

Atmosphere–Plant (SWAP) package into the MODFLOW groundwater flow model in such a way 

that the SWAP package calculates vertical fluxes for MODFLOW, while MODFLOW provides 

averaged water table depths to determine the bottom boundary condition for the SWAP zones. 

Instead of coupling different models for areas above and below the groundwater table, one can also 

formulate one model for the entire continuous flow domain including both groundwater and the 

unsaturated zone. An efficient approach would be to develop a modeling approach that would (a) 

use the same model for the entire flow domain and (b) ignore lateral flow in the unsaturated zone 

or outside of the capillary fringe. The ARS study team addressed this by developing in this chapter 

the QUASI-3D model based on the Richards equation assuming 1D vertical flow in the unsaturated 

zone above the capillary fringe, together with 3D flow in groundwater and the capillary fringe in the 

unsaturated zone just above the groundwater table. As a first step the ARS study team implemented 

the quasi-3D approach only for water flow; the QUASI-3D code hence was not used for simulations 

of flow and transport of the OPE3 field experiment. The ARS study team benchmarked the code for 

simulating flow problems; some results are presented in Appendix B. 

4.1.1 The HYDRUS-3D Code 

The HYDRUS software package consists of a computational module, and an interactive graphicsbased user interface. (Šimůnek et al., 2006). The package can be used to simulate a wide range of 

problems involving water, heat and solute movement in two- and three dimensional variablysaturated porous media. 

The mathematical model for simulating water flow and contaminant transport is based on the 

Richards equation for flow and the advection-dispersion equation for transport. Assuming a 

conservative tracer (no sorption and decay), the governing equations are, respectively, 

    Sh

t







K 1



(4-1)

  CC

t

C

 qD





(4-2)

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 solute concentration (M/L3), D is the hydrodynamic 

dispersion tensor (L2/T), q is the Darcy flux vector (L/T), S is a sink/source term accounting for water 

uptake by plant roots or the presence of wells (1/T), and t is time (T). The transport equation can be 

extended to include provisions for nonlinear nonequilibrium reactions between the solid and liquid 

phases, linear equilibrium reactions between the liquid and gaseous phases, zero- and first-order 

production and degradation reactions. In addition, physical nonequilibrium transport can be 

accounted for by assuming a two-region, dual-porosity type formulations. 
4-3 

The soil water retention and the unsaturated hydraulic conductivity functions needed for solution of 

Eq. (1) were described in this study using the van Genuchten (1980) relationships: 

   n m

rs

r

e S h









 





1 (4-3)

     

2

1

11

m m

e

l

ese

 SSKSK (4-4)

respectively, where Se is relative saturation, θr is the residual water content (L3/L3), θs is the water 

content at saturation (L3/L3), Ks is the saturated hydraulic conductivity (L/T), α (L-1) and n (-) are 

shape parameters, m=1-1/n, and 

l

=0.5. 

The components of the hydrodynamic dispersion tensor for the case of an isotropic porous medium 

are expressed as 

   i j

ij T ij L T

v v

D a v a a

v

    (4-5) 

where i,j = 1, 2, 3 correspond to the x, y, z coordinate directions, respectively, 

aL

and 

aT

 are 

longitudinal and transverse dispersivities (L), respectively, 

i

v

 are components of the flow velocity 

(L/T), and 

2

i

i

v v  

(L/T) 

The governing flow and transport equations in HYDRUS-3D were solved numerically using 

Galerkin-type linear finite element schemes. Application of equations (4-1) to (4-5) to the field tracer 

experiment requires definition of the domain boundaries, the initial and boundary conditions, a 

numerical finite element mesh, and soil hydraulic and solute transport parameters. 

4.1.2 Modified TOUGH2 Code 

 

The TOUGH2 code, developed by Lawrence Berkeley National Laboratory (Pruess et al., 1999), is 

a numerical model for multidimensional fluid and heat flow of multi-phase, multi-component fluid 

mixtures in porous and fractured media. TOUGH2 has been applied to a wide range of problems, 

including geothermal reservoir engineering, nuclear waste disposal, environmental assessment and 

remediation, and unsaturated and saturated zone hydrology (Pruess et al., 1999). An advantage of 

the TOUGH2 simulator is that it can simulate flow in fractured porous media using double-porosity, 

dual-permeability, and multiple interacting continua (MINC) formulations. 

Similarly as HYDRUS-3D, the physical processes of fluid flow and tracer transport in TOUGH2 are 

governed by Equations (4-1) and (4-2), respectively. An integral finite-difference method is used to 

discretize the governing equations in space. TOUGH2 provides multiple equation-of-state (EOS) 

modules to handle different fluid mixtures, which are described by their components and phases 

with related thermophysical properties. The EOS9 module of TOUGH2 is a saturated-unsaturated 

flow module applicable to variably saturated media (Wu et al., 1996). EOS9 only considers a single 

aqueous phase and a single water component for variably saturated flow (Pruess et al., 1999). Like 

HYDRUS-3D, the EOS9 model ignores any effect of the air phase on fluid flow. The module is very 
4-4 

efficient numerically and well-suited to simulate water flow in the very heterogeneous variably 

saturated subsurface of the OPE3 site. 

For tracer transport, the ARS study team used the T2R3D module of TOUGH2 code, which is based 

on Equation (4.2) assuming general multi-phase subsurface flow conditions (Wu et al., 1996). The 

current version of TOUGH2 did not have provisions for directly coupling the EOS9 module with 

T2R3D (only the numerically more cumbersome EOS3 multiphase module enabled this coupling). 

It was therefore necessary to develop a fully coupled EOS9 and T2R3D model to simulate fluid flow 

and tracer transport in 3D variably-saturated media. For this reason the ARS study team 

incorporated the T2R3D numerical solution for tracer transport directly into the original EOS9 code. 

The resulting scheme first numerically solved the governing flow equation for each grid block, 

followed by solution of the transport equation using simulated values for fluid flow obtained at the 

same time step. 

The newly coupled model was first tested for flow simulations using a case of the Yucca Mountain 

project as solved with the EOS9 module. The flow results obtained with the two models were very 

close, indicating that the new coupled model could be used reliably for more general flow 

simulation in variably saturated porous media. The model was tested next for tracer transport 

using an example provided by the coupled EOS3 and T2R3D modules of TOUGH2. Differences 

between simulated tracer concentrations using the two models were within 5%, thus 

demonstrating that the new coupled model is suitable for simulations of tracer transport in variably 

saturated media. 

4.1.3 FULL-3D and QUASI-3D Models 

In this section, the ARS study team describes the FULL-3D and QUASI-3D finite difference codes 

based on complete and approximate solutions of the Richards equation for 3D variably-saturated 

media. The ARS study team is especially interested in QUASI-3D since this code provides an 

attractive alternative via model abstraction of the computationally more demanding HYDRUS-3D 

and TOUGH2 codes. QUASI-3D assumes that flow in the unsaturated zone above the capillary 

fringe occurs only in the vertical direction, but is fully 3D elsewhere. FULL-3D is an extension of 

QUASI-3D in that flow in the entire domain is described using the Richards equation. 

Figure 4-1 shows a schematic of the modeled hydrologic system, which includes both the 

unsaturated zone and the underlying groundwater zone. The boundary zcf(x,y,t) between the two 

zones, referred to as the specific surface, is characterized by a prescribed pressure head hcf. Let 

us introduce the following simplifying assumptions: 1) Flow in the unsaturated zone is in the vertical 

direction only; 2) 3D flow is considered in the groundwater zone, which can include the capillary 

fringe; 3) Water is incompressible and its density does not depend on solute concentration or 

temperature; and 4) the porous matrix is rigid. 

Water flow in the unsaturated zone and in groundwater is governed by the general 3D Richards 

equation 

S

z

q

y

q

x

q

t

x y z 























(4-6)

where 



 is the volumetric water content [L3L

-3], t is time [T], S is a sink/source term [T-1], x and y

are horizontal coordinates [L], z is the vertical coordinate, directed upward [L] and, qy and qz are 

Darcy-Buckingham fluxes [LT-1] given by 
4-5 

Figure 4-1 Modeled variably-saturated subsurface system with a section of the finite 

difference (FD) grid (dashed lines). 

x x y y z z

H H H

q K q K q K

x y z

  

     

  

 

in which Kx, Ky and Kz are hydraulic conductivitites in the x, y, and z directions [L], H=h + z is the 

total hydraulic head [L], and h is pressure head [L]. 

Using the assumption that lateral water flow is negligible in the unsaturated zone above capillary 

fringe (qx = qy = 0), a series of 1D Richards equations can be used to describe vertical flow at 

selected points within an areal plane as follows 

z

q

S

t z

 

  

 

 (4-7)

Flow in groundwater and the capillary fringe is governed also by (4-6), but with ∂θ/∂t=0 assuming 

fully saturated flow. At the specific surface (4-6) and (4-7) are coupled subject to conditions of 

continuity for the hydraulic head and the vertical water fluxes, i.e., 

z

y

x

Specific surface:

Vadose Zone:

1D Flow

Groundwater and 

capillary fringe:

3D Flow

h=hcf

(xi,yj)

kcf
4-6 

 

 



cf cf zz zz

HH

(4-8)

 

 



cf cf zz

z zzz qq

(4-9)

respectively, where zcf is the coordinate of the moving specific surface evaluated as a height where 

the hydraulic head is equal to the prescribed value to give 

  cf zz

htzyxh

cf





,,,

(4-10)

in which hcf characterizes the thickness of the capillary fringe above the water table (phreatic 

surface). Lateral flow in the capillary fringe is not considered if hcf=0, in which case the specific 

surface coincides with the water table. 

The model given by (4-6) through (4-10) was solved numerically using a finite-difference (FD) 

approximation on a rectangular grid. While not mandatory, the ARS study team considers here for 

simplicity, a uniform grid with nodes xi=(i-1)Δx, i=1,2,...,Mx, yj=(j-1)Δy, j=1,2,...,My, and zk=(k-1)Δz, 

and k=1,2,...,Mz. 

The general FD approximation of (4-6) and (4-7) is 

1

,,

,, 1 1 1

1

,,

,, ,, ,,

   







 n

kji

n

z

n

y

n

n x

n

kji

n

kji

S

t

kji kji kji



(4-11)

where the superscripts n and n+1 denote old and new time steps, respectively, and 

x

qq

n

kji

n

n kji

x kji 











 

1

,,2/1

1

1 ,,2/1

,,

,

y

qq

n

kji

n

n kji

y kji 











 

1

,2/1,

1

1 ,2/1,

,,

,

z

qq

n

kji

n

n kji

z kji 











 

1

2/1,,

1

1 2/1,,

,,

 

  





















 

 

 



i,jkk

i,jkk

x

HH

K

q

cf

cf

n

kji

n

n kji

n kji

kji

 for0

 for

1

,,

1

1 ,,1

1 ,,2/1

,,2/1

 

  





















 

 

 



i,jkk

i,jkk

y

HH

K

q

cf

cf

n

kji

n

n kji

n kji

kji

 for0

 for

1

,,

1

1 ,1,

1 ,2/1,

,2/1,

z

HH

q K

n

kji

n

n kji

kji

n

kji







 

 







1

,,

1

1 1,,

2/1,,

1

2/1,,

in which kcf(i,j) refers to the first node on the vertical grid line (xi,yj) below the moving boundary 

defined by (4-6) (Figure 4-1). Values of the hydraulic conductivity (

1

,,2/1





n K kji

) are calculated as the

arithmetic mean of the hydraulic conductivities at the neighboring cells (i,j,k) and (i+1,j,k). The value 

of kcf(i,j) meets the conditions 

2/

,, kkji cf zhzH

cf cf



(4-12)
4-7 

The system of equations given by (4-11) is strongly nonlinear due to the nonlinearity of the θ(h) and 

K(h) functions). A common method to solve (4-11) is linearization of the equations leading to a linear 

set of equations at each iteration of the form (Celia et al. 1990) 

)(

,,

)1(

,,,

)1(

,,,

)1(

,,,

,,

)(

,,

)(

,,

)1(

)( ,,

,,

s

kji

s

kjiz

s

kjiy

s

n kjix

n

kji

s

kji

n

s

kji

s

s kji

kji S

t t

HH











   







(4-13)

where μ=dθ/dh is the soil water (or specific) capacity, s=0, 1, 2,.. is the iteration number in the 

iterative solution process, with H(0) = H

n and θ

(0) = θ

n

. 

The assumption that lateral water flow is negligible in the unsaturated zone above the capillary 

fringe can substantially decrease the number of computations needed to solve (4-13). Specifically, 

the system of the FD equations given by (4-13) can be decomposed into two simpler systems that 

are linked to each other at only one node on each vertical grid line. One possible decomposition is 

to use the following 1D equations for the unsaturated zone above the specific surface 

)(

,,

,, )1(

)(

,,

)(

,,

)1(

)( ,,

,,

,,

s

jki

s

n z

n

kji

s

kji

n

s

kji

s

s kji

kji S

t t

HH

kji











 





 , k>kcf(i,j) (4-14)

while the full 3D equations are used for the medium below the specific surface: 

)(

,,

)1(

,,,

)1(

,,,

)1(

,,,

,,

)(

,,

)(

,,

)1(

)( ,,

,,

s

kji

s

kjiz

s

kjiy

s

n kjix

n

kji

s

kji

n

s

kji

s

s kji

kji S

t t

HH











   





 , k ≤ kcf(i,j) (4-15)

Equations (4-14) and (4-15) can be rewritten as follows 

( 1) ( 1) ( 1) ( )

, , , , , , , , 1 , , , , 1 , ,

s s s s A H D H G H W i j k i j k i j k i j k i j k i j k i j k  

  

 

(4-16)

( 1) ( 1) ( 1) ( 1)

, , , , , , 1, , , , , 1, , , , , 1

( 1) ( 1) ( 1) ( )

, , 1, , , 1, , 1, , , , , 1 , ,

s s s s

i j k i j k i j k i j k i j k i j k i j k i j k

s s s s

i j k i j k i j k i j k i j k i j k i j k

A H B H C H D H

E H F H G H W

   

  

  

   

  

   

(4-17)

At internal nodes of a regular grid, the coefficients of (4-16) and (4-17) become 

n

s

kji

kjikjikjikjikjikjikji

t

GFEDCBA





)(

,,

,,,,,,,,,,,,,,



(4-18a)

2

)(

,,2/1

,,

x

k

B

s

kji

kji







2

)(

,2/1,

,,

y

k

C

s

kji

kji







2

)(

2/1,,

,,

z

k

D

s

kji

kji







(4-18b)

 BE  ,,1,, kjikji

; 

 CF  ,1,,, kjikji

; 

 DG kjikji 1,,,,

(4-18c) 

n

n

kji

s

s kji

n kji

s

s kji

kji

s

kji

t

H

t

SW











,,

)(

)( ,,

,,

)(

)( ,,

,,

)(

,,

 

(4-18d)
4-8 

The tridiagonal system of equations given by (4-16) are most easily solved using the standard 

Thomas algorithm: 

H  H   ,,,,,,1,, kjikjikjikji

(4-19)

for k=kcf, kcf+1, ... Mz-1, Mz. and 

( )/( )

/( ),

,,1,,,,

)(

,,,,1,,,,

,,1,,,,,,,,

kjikjikji

s

kjikjikjikji

kjikjikjikjikji

AWG G

AD G

 



  

 

 

 

(4-20)

Now consider the subset of equations given by (4-15) pertaining to the combined saturated and 

capillary fringe region below the specific surface. These equations also contain values of H

evaluated at nodes (i,j,kcf+1). The ARS study team used (4-14) with k=kcf, and substitute this equation 

into (4-15) to eliminate the variable

)1(

1,,





s

kji

cf

H

, thus obtaining 

 

( 1) ( 1) ( 1) ( 1)

, , , , , , 1, , , , , 1, , , , , 1

( 1) ( 1) ( 1) ( 1) ( )

, , 1, , , 1, , 1, , , , , , , , ,

, ,

cf cf cf cf cf cf cf cf

cf cf cf cf cf cf cf cf cf

s s s s

i j k i j k i j k i j k i j k i j k i j k i j k

s s s s s

i j k i j k i j k i j k i j k i j k i j k i j k i j k

A H B H C H D H

E H F H G H   W

   

  

   

  

  

    

(4-21)

The system of equations (4-21) allows one to obtain the pressure head values 

)1(

,,

s H kji

in the subdomain 

cf

 kk

. Having evaluated the

)1(

,,

s

kji

cf

H

, values of 

)1(

,,

s H kji

 for 

cf

 kk

are estimated using (4-

19) at each (i,j) node. The iteration step is completed by checking the condition stated in (4-7) and

determining the new position of the specific surface for each pair (i,j). Iterations for each time step 

end when the following conditions are fulfilled 

H

s

ijk

s

ijk HH  

 max( ))()1(

(4-22a)

max( 0for,)

)()1(

 



h

s

ijk

s

ijk 



(4-22b)

in which εH and εθ are prescribed error tolerances for the total head and the water content, 

respectively.

The numerical model above is complemented with initial and boundary conditions that prescribe 

heads and/or fluxes at the assumed domain boundaries. The algorithm given by (4-11) to (4-22) 

was implemented by modifying the MODFLOW code (Harbaugh et al., 2000), and applying the 

Groundwater Modeling Software (GMS 6.0, 2002) software for pre- and post-processing. The 

MODFLOW model was modified for this purpose in two ways. First, the composite 1D unsaturated 

zone and 3D groundwater flow model was combined into the QUASI-3D code. The ARS study 

team next solved the complete 3D Richards equation to yield the FULL-3D code using procedures 

very similar as implemented for the VSF model of Thoms et al. (2006). The FULL-3D was later used 

as a benchmark for testing the computationally more attractive QUASI-3D model. 

The ARS study team noted that the manner in which the saturated and unsaturated zones in 

QUASI-3D are coupled, including the invoked numerical solution algorithm, is different from the 
4-9 

methods presented by Yakirevich et al. (1998) and Twarakavi et al. (2008). QUASI-3D implicitly 

couples the vadose zone and groundwater flow equations, which implies that calculations of the 

phreatic surface water flux at each time step are not required as a source term for the groundwater 

flow equation. The QUASI-3D also does not require introducing the specific yield parameter, unlike 

HYDRUS-MODFLOW (Twarakavi et al., 2008). 

4.2 Model Calibration 

4.2.1 Geometry of the Simulation Domain and Soil Material Distribution 

Based on experimental data that include the location of the tracer application plot, observation 

(sampling) wells, the topography of the soil surface and of the low permeability bottom boundary 

(estimated from GPR survey data), the ARS study team considered for HYDRUS-3D simulations 

a 3-D layered domain that extended laterally for 55 m in the x (east-west) direction and for 50 m in 

the y (north-south) direction. The thickness (z direction) of the domain varied from 3.12 m to 5.18 

m. The domain was smaller than the domain used for the preliminary simulations (Pachepsky et 

al., 2011) to reduce the simulation time. The unstructured (triangular prisms) finite element mesh 

consisted of 24,780 nodes and 45,640 3D elements (Fig. 4-2). The simulation domain was 

subdivided into 15 layers. 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 1.65-m soil layer the vertical size of the prisms was about 20 cm, while the 

size was about 40 cm below this depth (Fig. 4-2). The horizontal mesh size decreased from 5 m 

near the downgradient domain boundary to 0.7 m close to the irrigation plot where most of the 

transport processes were expected. Using this geometry and finite element mesh, a 125-day long 

simulation generally took between 3 to 6 h with a Dell PC Dimension DXC061, Intel CoreTM2 Duo 

CPU 6700 @2.66 GHz. Further refinement of the finite element mesh required longer simulation 

times. 

Twenty observation nodes (Fig. 4-2) were used to record the simulated breakthrough curves at 

specific sampling locations in observation wells L1 through L12. Although groundwater was 

sampled at three depths in wells L5 through L12, only two observation nodes were located at 

these wells since the grid was very coarse in the lower soil horizon. 

The distribution of soil materials with different textures within the domain was set based on logs 

obtained during installation of observation wells L1-L12 (Fig. 4-3). First the ARS study team 

interpolated measured soil textures to depths corresponding to each computational layer. A 

cluster analysis (SPLUS 2000) was subsequently used to group the interpolated soil textures into 

9 classes so that each class was represented by soil texture averaged for the samples belonging 

to this class (Fig.4-4). These classes included: three sandy loam classes (SL1, SL2 and SL3), two 

sandy clay loam classes (SCL1 and SCL2), two loam classes (L1 and L2), and two silty clay loam 

classes (SiCL1 and SiCL2). The soil water retention and hydraulic conductivity parameters of the 

van Genuchten equations (4-3) and (4-4) were obtained for the 9 texture classes with the 

ROSETTA software using data for soil texture and bulk density (Fig. 4-5, Table 4-1). The 

boundaries between different soil materials of each computational layer were set at about equal 

distances from the observation wells where materials were measured (Fig. 4-6). Soil texture 

measured at a depth of 210 cm was mostly presented by the SiCL2 texture class. Since the ARS 

study team did not have measurements below this depth, the SiCL2 texture at this depth was 

extended to the bottom of the flow domain. Subdividing soil hydraulic properties into 9 groups was 

expected to reflect hydrological complexity of the simulated domain and to provide flexibility in the 

model calibration process. 

 
4-10

4.2.2 Initial and Boundary Conditions 

As initial condition for the water flow simulations the ARS study team used an equilibrium 

pressure head distribution. This distribution was obtained from groundwater depths measured in 

the observation wells at the beginning of the tracer experiment (Fig. 4-7a). Spatially variable, but 

constant in time, pressure head profiles were specified along the lateral boundaries based on 

groundwater monitoring data obtained in the summers of 2006-2007 (Fig. 4-7b). The initial Cldistribution varied between 10 to 25 mg/l depending upon location as measured in the observation 

wells prior to the experiment (Fig. 4-7c). A third type (Cauchy) boundary condition was used along 

the soil surface to simulate solute transport. Cl- concentrations of groundwater along the lateral 

boundaries were set to the initial concentrations observed before the tracer experiment. 

Daily-averaged atmospheric boundary conditions were used at the soil surface. These conditions 

simulated a variable flux due to evapotranspiration and prolonged infiltration observed after 

precipitation and intense initial irrigation within the irrigated plot area and along the remaining part 

of the soil surface (Fig. 4-8). The ARS study team used a zero flux boundary condition along the 

bottom of the domain. 

The imposed flow rate during each irrigation event was decreased by 28% to account for water 

lost to overland flow that was collected. This runoff water had no effect on the subsurface flow 

and transport processes. The Cl- concentration of the applied tracer solution was 4940 mg/l, while 

the Cl- concentrations of the rainwater and irrigation water were 8 mg/l. 
4-11

Figure 4-2 Mesh generated for HYDRUS-3D simulations. Observations nodes are shown 

in yellow. 

Plot size: 55 x 50 m

Nodes: 247,80 

3D elements: 45,640
4-12

Figure 4-3 Vertical distribution of clay, silt and sand contents measured at 12 locations. 

Clay%

0

20

40

60

80

100

120

140

160

180

200

220

0 10 20 30 40 Depth (cm)

Silt%

0

20

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120

140

160

180

200

220

0 20 40 60 80

0

20

40

60

80

100

120

140

160

180

200

220

0 20 40 
4-13

Figure 4-4 Soil texture groups obtained with cluster analysis. 

Silt %

0

10

20

30

40

50

60

70

80

90

100

Clay %

0

10

20

30

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60

70

80

90

100

Sand %

102030405060708090100 0

0 cm

21 cm

41 cm

62 cm

83 cm

104 cm

124 cm

145 cm

166 cm

Soil texture group

C

sC siC

scL

cL

S

lS sL

L siL

sicL

Si

Depth:
4-14

Figure 4-5 ROSETTA estimated soil water retention curves for selected soil texture 

groups. 

Table 4-1 Soil properties used in simulations of Cl subsurface transport. 

Texture θr θs α n Ks1 Ks2 L BD Disp-L DispT

cm3cm-3 cm3cm-3 m-1- m d-1 m d-1- g cm-3 m m

SL1 0.051 0.369 3.20 1.440 0.32 2.50 0.5 1.6 1.0 0.2

SL2 0.047 0.500 2.97 1.378 0.21 0.10 0.5 1.6 1.0 0.2

SL3 0.049 0.380 2.08 1.426 0.24 2.50 0.5 1.5 1.0 0.2

SCL1 0.048 0.320 3.34 1.204 0.04 0.45 0.5 1.8 1.0 0.2

SCL2 0.067 0.401 1.65 1.391 0.11 0.11 0.5 1.5 1.0 0.2

L1 0.053 0.341 1.85 1.309 0.04 2.00 0.5 1.7 1.0 0.2

L2 0.057 0.341 1.17 1.386 0.03 0.70 0.5 1.7 1.0 0.2

SiCL1 0.062 0.333 1.10 1.348 0.02 2.00 0.5 1.8 0.1 0.02

SiCL2 0.066 0.346 0.98 1.375 0.01 0.15 0.5 1.8 1.0 0.2

Ks1 and Ks2 are Rosetta-estimated and fitted values of saturated hydraulic conductivity. 

Water content (cm3 cm-3)

0.05 0.10 0.15 0.20 0.25 0.30 0.35 0.40 0.45

pF

0

1

2

3

4

5

sL1

sL2

sL3

scL1

scL2 

L1

L2

sicL1

sicL2

Soil texture group:
4-15

Figure 4-6 Material distribution used for the HYDRUS-3D simulations. 
4-16

Figure 4-7 Initial and boundary conditions used for HYDRUS-3D simulations. 
4-17

Figure 4-8 Daily irrigation, precipitation and evapotranspiration data used for the HYDRUS-3D simulatio

Irrigation less 

runoff (cm/day)

8

6

4

2

0 Precipitation less runoff (cm/day)

6

4

2

0

Day from the beginning of the experiment

0 20 40 60 80 100 120 ET (cm/day)

0.5

0.4

0.3

0.2

0.1

0.0
4-18

4.2.3 Model Calibration 

4.2.3.1 HYDRUS-3D Simulations

The HYDRUS-3D software in its current version does not have an easily implemented option for 

automatic model calibration. Such an optimization would take an unreasonable amount of time for 

the fully 3-D 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 

parameters to available data. At a first step the ARS study team 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-and-error runs. Much of our attention was focused on observation wells L5 through 

L7, where well-defined breakthrough curves (BTCs) were observed, and where both the arrival 

front and the receding (tailing) part of the breakthrough curve had been recorded. 

The ARS study team started HYDRUS-3D simulations using the hydraulic parameter values 

estimated with the ROSETTA software (Table 4-1). The initial values of the longitudinal 

dispersivity were set at 0.5 m, while the ratio of longitudinal to transversal dispersivity was fixed at 

5 for all simulations. The simulation results indicated that soil hydraulic conductivity was not 

sufficient to allow infiltration of the amounts of water precipitated during rainfall and irrigation 

events. Stable model performance and realistic groundwater depth fluctuations were achieved 

only after the Ks values were increased tenfold. The model reasonably well reproduced the 

phases of the groundwater fluctuations, but not their amplitudes (Fig. 4-9). This could be caused 

by the adopted coarse vertical discretization of the simulated domain, ignoring macropore flow, 

and imposing time-independent pressure heads along the domain boundaries in the simulations. 

The trial-and-error procedure continued until a better fit for L5 through L7 was obtained. During 

these runs the ARS study team varied the values of Ks, and the longitudinal and transversal 

dispersivities, to obtain more rapid vertical Cl- transport at the irrigated plot, and an increase 

followed by a decrease in Cl- concentrations in wells L5-L7.

Simulated and observed breakthrough curves are compared in Fig. 4-10. The ARS study team 

noticed that the simulated BTCs for wells L1 and L4 exhibited much later arrival times of the tracer 

than the observed BTCs. Simulated tracer arrived earlier or at about the same time with measured 

tracer in wells L2 and L3, respectively (Table 4-2). The vertical flow during ponded infiltration was 

not simulated properly. Simulated peak concentrations also deviated from the observed in L1-L4. 

Better agreement of simulated and measured peaks was obtained for wells L5-L9.

Partitioning soil texture into 9 classes provided flexibility for model calibration, particularly at 

depths from 100 to 180 cm. Introducing a higher value of the saturated hydraulic conductivity Ks

for materials L1 and SiCL1 caused HYDRUS-3D to predict more rapid tracer transport toward 

wells L5-L8 at depths 110 and 160 cm (Fig. 4-10). The applied tracer initially was pushed by the 

incoming fresh water through the high water conductive materials SL1 and SL3 to deeper soil 

layers. Unsaturated soil in the top 100-cm soil layer prevented lateral plume propagation beyond 

the irrigation plot. Vertical Cl- transport dominated at this stage. When the plume approached 

the saturated zone with the more permeable material L1 at a depth of 104 cm and SiCL1 at 

depths of 124 cm and 145 cm, vertical flow turned horizontal at these depths, also due to low Ks

values in material SiCL2 underlying the SiCL1 at depths of 145 cm and 166 cm (see Fig. 4-6 ).
4-19

Thus, the incoming irrigation water pushed the plume laterally in the highly permeable L1 and 

SiCL1 materials (see Fig. 4-6). Thus, the incoming irrigation water pushed the plume laterally at 

depths 110 and 160 cm. After some period of time, the plume had a toroid shape with the 

concentration in the center of the plume being lower than at the peripheral part. This shape 

developed due to due to the application of clean irrigation water after Cl- injection The migration of 

the plume and its expansion in different directions was controlled by the spatial distribution of the 

hydraulic properties. Near the end of the simulation the advancing front plume had passed 

observation wells L5-L7.

In spite of having different transport distances from the irrigated plot to the transects crossing 

wells L5-L9 and wells L10-12 the observed increase in Cl- concentration in the more distant wells 

(L10-L12) occurred almost synchronously with increases in the proximate wells (L5-L9). This 

indicated preferential transport toward wells L10-L12 through material SiCL2 at a depth of 166 cm. 

However, an increase in Ks for this layer resulted in earlier tracer arrival to wells L7-L9 at a depth 

of 145 cm. This explains why the ARS study team were not able to simulate the BTCs in those 

three distant wells. 

The simulated depths differed from the observation depths because of coarse vertical 

discretization of the simulated domain. To compare results of the simulation with measured Cldata, the BTCs were averaged at each location. Cl was measured in the wells at depths of 105 

cm, 135 cm and 165 cm. The computational observation HYDRUS 3d nodes were set at depths of 

110 cm and 160 cm, due to the vertical discretization used in the simulations. The ARS study 

team compared measured concentrations averaged across the three depths (105 cm, 135 cm and 

165 cm) with the simulated Cl concentrations averaged across the two depths (110 cm and 160 

cm). Results of the comparison are shown in Fig. 4-10. Overall, the model was not able to 

simulate fast Cltransport within the irrigation plot and early plume arrival in wells L10-L12. 

However, the calibrated HYDRUS-3D model did reproduce the most important features of the 

lateral flow experiment. The model gave satisfactory levels of the peak concentrations and was 

able to capture arrival times in the first line of the observation wells (L5-L7). 
4-20

Figure 4-9 Observed (dots) and HYDRUS-3D simulated (continuous lines) groundwater depth time series

0.0

0.5

1.0

1.5

loc-

loc-

loc-

loc-

GW depth (m)

0.0

0.5

1.0

1.5

loc-

loc-

loc-

loc-

Day from the beginning of the experiment

0 20 40 60 80 100 120 140

0.0

0.5

1.0

1.5

2.0

loc-9

loc-1

loc-1

loc-1
4-21

Table 4-2 Statistics of observed and simulated subsurface Cl- transport 

Well # Peak time (day) Peak concentration (ppm)

observed simulated observed simulated

1 4.7 16 205.6 109

2 27.3 9 180.3 129

3 7.9 9 316.4 210

4 1.6 12 284.0 145

5 98.3 110 68.8 59.1

6 108.3 110 46.8 47.3

7 90.3 87 67.0 59.9

8 120.3 - 39.3 -

9 105.3 - 33.0 -

10 98.3 - 30.5 -

11 105.3 - 46.2 -

12 122.3 - 33.8 -
4-22

Figure 4-10 Observed (dots) and HYDRUS-3D simulated (continuous lines) Cl- concentrations in wells L1

Well 1 Cl (ppm)

0

50

400

350

300

250

200

150

100

Well 2 Well 3 

Well 5 Cl (ppm)

0

80

60

40

20

100

Well 6 Well 7 

Well 9

0 20 40 60 80 100 120 Cl (ppm)

60

50

40

30

20

10

Well 10

Day from the beginning of the experiment

0 20 40 60 80 100 120

Well 11

0 20 40 60 80 100 1200 20 40 60 80 

depth averaged

110 cm

160 cm

depth averaged
4-23

4.2.3.2 TOUGH2 Simulations

The structure of simulated domain and the its boundaries for TOUGH2 model were set similar to 

those used for HYDRUS-3D simulations. The simulation domain was discretized into a 3D 

computational grid generated using the integral finite difference method for TOUGH2 (Fig. 4-11). 

The grid had an average of 28 computational layers in the vertical direction, and 1,337 columns 

(or grid blocks) per layer), resulting in 42,900 grid blocks (or elements) and 133,319 connections 

in the grid system. Fine lateral cells (1m x 1m) were implemented in the 

vicinity of the irrigation plot and observation wells, while coarse lateral cells (2m x 2m) were used 

beyond the irrigated area. The thickness of each element varied from 5 cm to 30 cm depending 

upon location and the soil material distribution, resulting in a varying number of vertical elements 

at different locations. The thickness of vertical elements in the upper 1.65-m soil layer was about 

10-15 cm, and about 20 cm below this depth. The EOS9 and T2R3D modules of the TOUGH2 

family were used to simulate flow and tracer transport at the OPE3 site. Based on this adopted 3-

D grid, one simulation took about 6 h with a Dell PC Precision 690, Intel® Xeon® CPU 5130

@2.00 GHz. 

The soil hydraulic properties, the distribution of soil materials within the domain, and the initial and 

boundary conditions were set similar to the calibrated HYDRUS-3D model. 

Figure 4-11 Mesh generated for the TOUGH2 simulations. 
4-24 

Twenty-eight observation nodes were assigned to record simulated breakthrough curves at 

depths corresponded to the sampling depths at the 12 locations. One observation node was set at 

each of four wells at the irrigation plot, while three observation nodes were placed at three depths 

in wells L5 through L12. Observation nodes corresponded closely to the observation depths used 

in the experiment. 

Water flow was simulated using the EOS9 module, which is a saturated-unsaturated flow module 

of TOUGH2. Extensive tests with the EOS3 module, which describes coupled air and water flow, 

indicated instability in the results caused by changing pore air pressures. The EOS3 module was 

therefore replaced with the EOS9 module, which solves the Richard’s equation for water flow only 

and does not consider the presence of an air phase. Results of the water flow simulations are 

shown in Fig. 4-12. Overall, the EOS9 module reproduced the dynamics of the groundwater depth 

slightly better than the HYDRUS-3D code. The model also appeared to be more sensitive to 

rainfall events and, as compared to HYDRUS-3D, produced more accurate simulations of the 

amplitudes of groundwater fluctuations and the receding groundwater levels observed in the 

summer months during the experiments. Root-mean-squared errors of groundwater levels were 

comparable for the two models. In wells 5 through 9, these RMSE were 0.43, 0.30, 0.40, 0.26, 

and 0.27 for HYDRUS 3D and 0.48,0.43, 0.36, 0.31, and 0.38 for TOUGH2 (all in m). 

To simulate the tracer transport, EOS9 was coupled with the T2R3D module, which simulates 

radionuclide transport based on mass conservation and advection-dispersion equations as 

described in section 4.1. Observed BTCs and simulations with the TOUGH2 model are shown in 

Fig. 4-13. The model adequately reproduced the BTCs of wells L2, L3, L6 and L8. However, 

TOUGH2 failed to correctly predict receding Cl- concentrations of wells L1 and L4 and the BTCs 

of wells L5 and L7. Similar to the HYDRUS-3D results, simulations of the plume did not reach the 

transect across wells L10-12 within the simulation time. 

Overall, predictions of tracer transport was much better with the calibrated HYDRUS-3D model 

compared to the calibrated TOUGH2. HYDRUS-3D was more accurate in reproducing observed 

peak concentrations and peak times of Cl- of wells L5-L8. The ARS study teamrealize that the 

obtained set of parameters may not have been unique and that additional simulations would be 

helpfull to reduce parameter uncertainty. Nevertheless, the ARS study teamaccepted the values 

and used them to evaluate the applicability of different model abstraction techniques to model 

simplification and monitoring strategy development.
4-25

Figure 4-12 Observed (dots) and TOUGH2 simulations of groundwater depth time series. 

0.0

0.5

1.0

1.5

GW depth (m)

0.0

0.5

1.0

1.5

Day from the beginning of the experiment

0 20 40 60 80 100 120 140

0.0

0.5

1.0

1.5

2.0
4-26

Figure 4-13 Depth-averaged observed (dots) and TOUGH2 simulated (continuous lines) Cl- concentration

Well 1 Cl (ppm)

0

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100

Well 2 Well 3 

Well 5 Cl (ppm)

0

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Well 6 Well 7 

Well 9

0 20 40 60 80 100 120 Cl (ppm)

0

60

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10

Well 10

Day from the beginning of the experiment

0 20 40 60 80 100 120

Well 11

0 20 40 60 80 100 1200 20 40 60 80 
5-1 

5 SYSTEMATIC APPROACH FOR SIMPLIFYING 

THE OPE3 SITE MODEL 

5.1 Sensitivity Analysis to Direct Model Simplification 

Conducting a sensitivity analysis (SA) is an efficient methodology for model simplification. The SA 

approach for model simplification was first proposed by Rose and Harmsen (1978), and has since 

proven its efficiency in various modeling fields (e.g., Confalonieri et al., 2010; Brooks et al., 2010, 

Do and Rothermel, 2008; Cariboni et al., 2007). The SA has a long history of use in radionuclide 

transport modeling, beginning with U.S. NRC-supported effort (e.g., McKay, 1995) and including 

research in various parts of the world (e.g., Volkova et al., 2008; Ohi et al., 2010; Iooss et al., 

2008; Helton et al, 2010). 

Overall, two types of SA are recognized (Saltelli et al., 2010): a local sensitivity analysis and a 

global sensitivity analysis. A local SA examines the local response of the output(s) by varying 

input parameters one at a time while holding other parameters at central values. A global SA 

examines the global response (averaged over the variation of all the parameters) of model 

output(s) by exploring a finite (or even an infinite) region. While easier to implement, a local SA 

can only inspect one point at a time, with the sensitivity index of a specific parameter depending 

on the central values of the other parameters. The approach uses a local SA technique (LSA) 

when the sensitivity index measures only the main effect of each input parameter on the output 

variance. The method does not account for interactions among parameters. 

In the study, the ARS team used two indices in a LSA: a first order sensitivity coefficient (Saltelli et 

al., 2010) and a derivative-based measure of sensitivity (Saltelli et al., 2005).First order sensitivity 

coefficients estimate the variance-based first order effect 

 )|( Xi ~ XYEV iiX

(5-1)

of a generic factor Xi for model prediction Y written in the form: 

,( ,... )  21 XXXfY k

(5-2)

where Xi is the i-th factor and X~i denotes the matrix of all factors except Xi, and k is the number of 

factors. The meaning of the inner expectation operator 

E

in Eq.(5-1) is that the mean of Y is 

taken over all possible values of X~i while keeping Xi fixed. The outer variance V in Eq.(5-1) is 

taken over all possible values of Xi. The associated sensitivity measure (the first-order sensitivity 

coefficient) is: 

 

)(

)|( ~

YV

XYEV

Si Xi iiX

(5-3) 

where V(Y) is the total variance of the model output computed as: 

    )|()( )|( 

Xi ~ iiX  Xi ~ XYVEXYEVYV iiX

(5-4)
5-2 

The first-order sensitivity coefficient Si is a normalized index varying between zero and one, as 

 )|( Xi ~ XYEV iiX

 varies between zero and V (Y ).

The second LS index used in this study is a derivative-based sensitivity index. This index is a 

straightforward implementation of the sensitivity concept: if the model output of interest is Y, its 

sensitivity to an input factor Xi is simply ∂Y/∂Xi. This measure shows how sensitive the output is to 

a perturbation of the input. If a measure independent from the units used for Y and Xi is needed, 

then the normalized value of the model sensitivity can be used:

ii

i

X

Y

Y

X

Di







(5-5)

where 

Xi

is the nominal value of factor Xi and 

Yi

 is the value of Y when all input factors are at 

their nominal values. 

5.1.1 Analysis of Subsurface Flow and Transport Processes 

The HYDRUS-3D and TOUGH2 model calibrations based on results of the tracer experiment 

revealed considerable hydrologic complexity of the flow system. To understand better the 

behavior of the system, water and Cl- fluxes were analyzed in both the saturated and unsaturated 

zones of the simulation domain. 

Ten new observation nodes were assigned at depths of 0.4-0.7 m in addition to the 20 nodes 

used for the HYDRUS-3D calibration and shown in Fig. 4-2 to represent both the saturated and 

unsaturated parts of the soil profiles at the 12 observation locations. The HYDRUS-3D model was 

run with the parameters, initial conditions, and boundary conditions used for the calibration (Table 

4-1). Soil water content ( ) dynamics obtained with HYDRUS-3D simulations indicated that the 

upper 0.5-0.7 m of the soil profiles were not saturated, while the soil was saturated below these 

depths during the entire simulation period (Fig. 5-1). Values of  were generally higher at a depth 

of 1.1 m at locations 1, 2 and 4 than at the same depth and deeper at locations 3, and 5 through 

12. Differences in  values were caused by the material distribution in the simulation domain. The

saturated water content θs among the soil materials was highest (0.5 cm3 cm-3) in SL2 that formed 

the soil layer at a depth of 1.1 m at locations 1, 2 and 4 (Table 4-1). Soil layers at the same depth 

at the other locations were formed by the SL3, L1, L2, SCL1 and SCL2 materials (Fig. 4-5), with 

θs values ranging from 0.32 to 0.38 cm3 cm-3 (Table 4-1). 

Differences in material properties forming the simulation domain resulted in differences in 

simulated concentrations of the Cl- tracer at locations with similar initial and boundary conditions. 

Within the irrigated plot (wells 1-4), the Cl- tracer arrived at a depth of 0.6 m in well 3 and well 4 at 

about the same concentration 24 hours after the tracer application (Fig. 5-2). Tracer transport 

through the SL3 layer at these locations occurred in unsaturated conditions, and both the water 

content and the saturated hydraulic conductivity (Ks) affected Cl- movement. The velocity of 

unsaturated vertical Cl- transport was four times smaller than the Ks value of this layer. The Clconcentration in well 3 was higher than in well 4 when the tracer reached a depth of 1.1 m. Water 

contents at this depth were close to saturation in both wells, with Cl- transport being controlled 

mostly by the saturated hydraulic conductivity, which was seven times higher in L2 (well 3) 

compared to the SL2 material (well 4) at these depths (Table 4-1). Therefore, the slower vertical 

Cl- transport rate between depths 0.6 and 1.1 m in well 4 as compared to well 3 was attributed to 

the difference in the saturated hydraulic conductivities of the SL2 and L2 materials at a depth of 
5-3 

1.04 m at these two locations (Fig. 4-6). The Cl- breakthrough curve at a depth of 1.1 m in well 2 

was similar to that of well 4. Cl- transport at this depth was controlled by the SL2 material, which 

had the lowest Ks value (0.1 m d-1) of the different soil profiles at both locations. 

Downward Cl- transport within the irrigated plot (wells 1-4) changed to lateral transport soon after 

the tracer approached the saturated zone with its highly conductive layers L1 and SL1. Lateral 

transport was relatively slow: it took from 9 to 16 days for the tracer to pass the 1.1-m depth at the 

irrigated plot and from 87 to 110 days to arrive at wells 5, 6 and 7 which were located at the 

distance of 7 m from wells 3 and 4 at the irrigated plot (Fig. 5-2). Based on the arrival time, the 

average flow velocity was about 0.12 m day-1 in the vertical direction and 0.08 m day-1 in the 

horizontal direction within and outside the irrigated plot, respectively. 

The difference in flow velocities occurred due to a combination of flow conditions and hydraulic 

properties of the materials in the transport domain. Lateral flow was driven by the smaller (about 

0.03) lateral hydraulic gradient as compared to the vertical gradient (about 1), but the saturated 

conditions for horizontal flow vs. the partly saturated conditions for vertical flow, and higher Ks

values of the SL1 and L1 material (2.0-2.5 m day-1) at locations 5-7 compared to SL2 (Ks=0.1 m 

day-1) at locations 3 and 4, partially compensated for the difference in the hydraulic gradient. The 

ratio between the vertical and horizontal flow velocities was less than 3:1 for these reasons. The 

saturated conditions and high Ks values were not sufficient for the tracer to approach wells 10-12 

within the simulation period of time. The ARS study teamdid not observe any increase in Clconcentrations at these wells during the 132-day long simulations. Based on the flow velocity, the 

tracer arrival time at the transect across wells 10-12 was expected to be about 175th day after 

initiation of the irrigation experiment. 

A decrease in Cl- concentrations with time was observed at the locations of wells 9, 11 and 12. 

The decrease was more pronounced at a depth of 0.6 m as compared to the deeper layers. Two 

processes could cause this decrease. One possible reason is that the 0.6 m depth layer was in 

the unsaturated zone (Fig. 5-1), with the infiltration from the top soil layer delivering precipitation 

with a Cl- concentration of 8 ppm, which diluted the 25 ppm Cl- concentration at this depth. 

Another possible reason was lateral flow from wells 3, 5 and 6 locations that may have decreased 

the Cl- concentration at both 0.6 m and 1.2 m depths. The initial concentration of Cl- was only 

about 10 ppm in the soil at these locations. The water flux from these locations hence may have 

had a diluting effect on the more concentrated solutions in wells 9, 11 and 12. 

Lateral (qx and qy), vertical (qz) and total (q) water fluxes and Cl- concentrations (C) computed with 

the HYDRUS-3D code for the 30 observation nodes were used to evaluate total vertical and 

horizontal water and tracer fluxes through 12 locations during the 132-day simulation period. The 

lateral (Qx, Qy, QCx and QCy) and vertical (Qz and QCz) components as well as the total water and 

Cl- fluxes in different parts of the simulation domain were computed as:
5-4

Figure 5-1 HYDRUS-3D simulated soil water contents at 12 locations. Constant values are where soil rem

Well 1

0.6

0.5

0.4

0.3

0.2

0.1

1.1 m

Well 2

1.1 m

Well 3

1.1 m

0.6 m

Well 5 Water content (cm

3 cm-3

)

0.45

0.40

0.35

0.30

0.25

0.20

1.7 m

1.3 m

0.6 m

Well 6

1.8 m

1.3 m

0.8 m

Well 7

1.6 m 

1.1 m

0.4 m

Well 9

0 20 40 60 80 100 120

0.40

0.35

0.30

0.25

0.20

0.15

1.6 m

1.1 m

0.4 m

Well 10

Day from beginning of the experiment

0 20 40 60 80 100 120

1.5 m

1.3 m

0.7 m

Well 11

0 20 40 60 80 100 120

1.6 m

1.2 m

0.6 m

0 20 40 60 
5-5

Figure 5-2 HYDRUS-3D simulated Cl- concentrations at 12 locations.

Well 1

0

400

300

200

100

1.1 m

Well 2

1.1 m

Well 3

1.1 m

0.6 m

1.1 m

0.6 m

Well 5 Cl (ppm)

0

80

60

40

20

100

1.7 m

1.3 m

0.6 m

Well 6

1.8 m

1.3 m

0.8 m

Well 7

1.6 m 

1.1 m

0.4 m

1.6 m

1.1 m

0.4 m

Well 9

0 20 40 60 80 100 120

0

60

50

40

30

20

10

1.6 m

1.1 m

0.4 m

Well 10

Day from beginning of the experiment

0 20 40 60 80 100 120

1.5 m

1.3 m

0.7 m

Well 11

0 20 40 60 80 100 120

1.6 m

1.2 m

0.6 m

0 20 40 60 

1.6 m

1.1 m

0.6 m
5-6 

i

n

i

j j   tqQ

1

(5-6)

i

n

i

j j QC   tCq

1

(5-7)

where qj are the computed water fluxes at the observation nodes (m day-1), the index j refers to 

the flow direction (x,y or z), and ti is the time increment in the HYDRUS-3D output (day). These 

fluxes can be viewed as total water and Cl- masses passing through 1 m2 area during the 

simulations. 

The computed water and tracer fluxes are shown in Fig. 5-3. The smallest total water fluxes (Q) 

within the irrigated plot were obtained at locations 1 and 2 at a depth of 1.1 m, while the largest Q

values occurred at locations 3 and 4 at depths of 1.1 m and 0.6 m respectively (Fig 5-3d). 

Relatively small Q values at locations 1 and 2 were caused by the low hydraulic conductivity of the 

unsaturated SL2 and SCL1 materials in the upper 0.4-m layer of the soil profile. Saturated flow 

conditions and relatively high Ks values of the textures throughout the soil profile at location 3 

resulted in the large total water fluxes at a depth of 1.1 m at this location (Fig 5-3d). Outside the 

irrigated plot, total water fluxes were generally larger in the first transect across locations 5-9 as 

compared to locations 10-12, except the well 9 where the total flux did not differ from the values of 

wells 10-12 (Fig. 5-3d). The differences in the total water fluxes observed for the two transects 

were caused by radial water flow from the irrigated plot. Figure 5-3 shows that the vertical 

component of the water flux Qz (Fig 5-3c) was much smaller than the two horizontal components 

Qx and Qz (Fig. 5-3a and Fig 5-3b) outside of the irrigation area. The contribution of the vertical 

component Qz to the total flux Q was hence negligible compared with the two horizontal 

components. Lateral water flow eventually did approach the second transect. The Q values in 

wells 10 through 12 were close to their Qx values (Fig. 5-3a and Fig. 5-3d), indicating prevalence 

of water flow from the irrigated plot in the x-direction towards the observation well compared to the 

y-direction. 

The observed patterns in the total water flux translated into simulated total Cl- fluxes, QC. Within 

the irrigated plot maximum QC values were obtained at locations 3 and 4 as a result of high Q

values (Fig. 5-3h). Beyond the irrigated plot, QC values were highest at locations 5 through 8 due 

to lateral flow in both the x and y directions. The ratio between the horizontal (QCx or QCy) and 

vertical (QCz) components differed for these wells. The QCy component for well 5 contributed 

more than 50% to the total Cl- flux QC, while locations 6 and 7 were more affected by the QCx

component. The reasons for this was the high heterogeneity manifested in the variability in the 

saturated hydraulic conductivity of the materials composing the simulation domain. 

Large values of the total water flux did not necessarily lead to high tracer fluxes. The correlation 

coefficient between QC and Q in wells 3 through 8 was statistically insignificant (Fig. 5-4). The 

total Cl- fluxes in these locations were likely a combined result of the tracer fluxes from the 
5-7 

Figure 5-3 Total water (a-d) and Cl- (e-h) fluxes obtained in HYDRUS-3D simulations 

during 132 days at three depths in 12 monitoring locations. 

a Total water flux Qx, m 2

4

6

8

10

0.4 m

1.1 m

1.6 m

b Total water flux Qy, m 2

4

6

8

10

c Total water flux Qz, m 2

4

6

8

10

d

Monitoring well locations

2 4 6 8 10 12 Total water flux Q, m

0

2

4

6

8

10

e Total tracer flux QCx, m ppm 100

200

300

400

500

f Total tracer flux QCy, m ppm 100

200

300

400

500

g Total tracer flux QCz, m ppm 100

200

300

400

500

h

Monitoring well locations

2 4 6 8 10 12 Total tracer flux QC, m ppm

0

100

200

300

400

500
5-8 

Figure 5-4 Relationships between total Cl- and water fluxes for four depths. Observation 

well numbers are shown above the symbols. 

irrigated plot at the different depths. The considerable heterogeneity in the simulation domain 

caused high variability in the water and Cl- fluxes. This was the case even in the relatively small 

10x10 m irrigated plot, which showed elevated QC values at depths of 0.4 and 1.1 m at location 3. 

The fluxes in the Northern locations (wells 5-7) were probably more affected by the tracer flux 

from location 3, while the Southern locations (wells 8 and 9) were affected by the flux initiated 

from location 4. This probably explains the relatively high QC values in the Northern locations as 

compared to those at the Southern side. 

Overall, our analyses of the simulated time series of the water content and Cl- concentrations at 

12 locations, along with total water and tracer fluxes and their components, revealed considerable 

hydrologic complexity in the simulation domain associated with spatial variability in soil properties. 

The presence of both saturated and unsaturated zones, fluctuating perched water tables, 

contrasting hydrological regimes in the irrigated and non-irrigated areas, and spatial variability in 

the soil properties, provided a unique opportunity to explore a range of model abstraction 

techniques, which will be demonstrated in the following chapters. 

Total water flux, m

0 2 4 6 8 10

Total tracer flux, m ppm

0

100

200

300

400

500

0.4 m 

1.1 m

1.6 m
5-9 

5.1.2 Performance Assessment Indicators 

Sensitivity analyses were conducted to evaluate the applicability of different abstraction 

techniques to the model simplification. The simplifications refer to having distinct structural/textural 

units within the simulation domain and the fluxes on its boundaries. The goal of the sensitivity 

analyses was to simplify the model to a level where simulations still can depict key features of the 

modeled domain. To do this, the features should be defined explicitly. Standard Review Plan 

2.4.13 (NUREG-0800) specifies pathways and travel times as the critical parameters for 

assessment of ground and surface water radionuclide contamination. For this reason the ARS 

study team used as performance indicators in their sensitivity analysis, peak concentrations 

(Cpeak) and times to reach peak concentrations (Tpeak). Because the peak concentration was 

not observed at some locations in HYDRUS-3D simulations and in most TOUGH2 simulations, 

the ARS study team also included entire Cl- time series in the sensitivity analysis. 

5.1.3 Transport Parameters 

The sensitivity analysis was first used to evaluate applicability of the aggregation model 

abstraction technique. The ARS study team intended to reduce the number of the transport 

parameters by identifying materials which do not have a substantial effect on the HYDRUS 

simulations, and replacing them with materials having similar transport properties. To do this, the 

local sensitivity analysis (LSA) described in section 6.1 of this report was carried out. For the 

sensitivity analysis the ARS study team used the soil material distribution within the simulation 

domain, and the initial and boundary conditions obtained in the HYDRUS-3D calibration as 

described in detail in section 4.2. The local sensitivity analysis (LSA) was conducted first for the 

saturated hydraulic conductivity (Ks). Next, the effects of the longitudinal (αL) and transversal (αT) 

dispersivities on tracer transport were evaluated for 12 observation locations. Values of Ks, αL and

αT of the soil materials used in the LSA were set to ±50% of their nominal (calibrated) values. Note 

that all parameters of soil materials SiCL2 and SiCL3 were kept constant during the LSA. The 

SiCL2 and SiCL3 materials served as restrictive layers at the bottom of soil profile. Parameters 

for these materials were not used in the LSA analyses to eliminate the effects of variations in 

boundary fluxes on the SA results. 

As stated above, two values of each parameter were assigned (±50% of their nominal (calibrated) 

values) to eight soil materials (factors) resulting in 256 simulations using HYDRUS-3D and 256 

simulations using TOUGH2 (28 simulations in a multivariate sensitivity analysis). This was done 

for each of the three parameters studied, Ks, αL and αT for a total of 256 x 2 models x 3 

parameters = 1536 simulations. Results of the Cl-

 simulations obtained for the minimum and 

maximum values of each factor were different for the two models. These differences were typically 

greater in wells 1-7 as compared to wells 8-12, and were found to increase when the Cl- plume 

approached these wells. 

The first-order sensitivity coefficients Si were computed from the simulated Cl- time series to 

assess the sensitivity of both models to the transport parameters for the eight soil materials. To do 

this, Cl- transport was simulated using 256 combinations of Ks. Si values were computed 

subsequently for each of the eight soil materials and every output time. Specifically, for the 

minimum and maximum Ks values of material SL1 the ARS study team calculated the average 

concentration 

)|),(( Ks~i KsitzCE

 and variance 

)|),(( Ks~i KsitzCV

 at each output node for each output 

time t from the simulated Cl- concentration time series. The index i is used here to denote the soil 

material. The same computations were then repeated for SL2, SL3, SCL1, SCL2, L1 and L2. This 

produced estimates of the variance 

 )|),((  KsKs ~i Ksi

tzCEV

i

 and average variance 

 )|),((  Ksi Ks~i Ksi

tzCVE
5-10

from the average concentrations 

)|),(( Ks~i KsitzCE

 and the variances 

)|),(( Ks~i KsitzCV

computed for 

the two levels of Ks of each material. Finally, the first-order sensitivity coefficients Si and total 

variance V(

tzC ),(

) were calculated using Eqs. (5-3) and (5-4), respectively. 

An example of the Si computations for the sensitivity of HYDRUS-3D simulation results to Ks of 

soil material SL1 is shown in Fig. 5-5. The Si values varied in time and among locations. Generally 

the Si values were greater at locations where the material properties could affect the tracer 

transport process directly or indirectly. The direct effect of the SL1 material can be seen on the Si

time series for wells 1-5 in Fig. 5-5a. The SL1 soil material composed the soil layer at a depth of 

0.62 m at locations 1 and 3, the soil layer at a depth of 1.04 m at location 2, and the soil 

layers at depths of 0.21, 0.41 and 0.62 m at location 5, but was not present in the soil profile at 

location 4 (Fig. 4-5). The maximum Si values were for these reasons considerably greater for 

wells 1-3 and even for well 5 as compared to well 4, notwithstanding the cumulative tracer fluxes 

in well 4 being greater than in well 2 (Fig. 5-5). The indirect effect of material properties on the 

HYDRUS-3D sensitivity can be illustrated with Si values computed for wells 10-12. Note that the 

SL1 material was not presented in soil profiles at these locations. However Si values for simulation 

times between 60 and 100 days were significantly greater for well 11 compared to the other two 

wells (Fig. 5-5a). The reason for this was the high conductive layer L1 near well 11, which at 

location 3 was connected with the SL1 material at a depth of 0.62 m, thus providing preferential 

lateral flow from location 3 towards well 11. Materials at locations 10 and 12 were not connected 

directly with the SL1 material. The properties of this material hence had little effect on results of 

HYDRUS-3D simulations at these two locations. 
5-11

Figure 5-5 Time series of the sensitivity index Si along with its components obtained for 

HYDRUS-3D simulations using two levels of the saturated hydraulic 

conductivity of the SL1 soil material. 

(a)

Si

0.0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

(b)

VXi (EX~i (Y|Xi ))

0

2

4

6

8

10

12

14

16

well1

well2

well3

well4

well5

well6

well7

well8

well9

well10

well11

well12

(c)

Day from beginning of the experiment

0 20 40 60 80 100 120 140

V(Y)

0

5

10

15

20

25

30
5-12

The sensitivity of HYDRUS-3D to Ks was different for the eight soil materials. Values of the Si

index generally were larger for the SL1, SL2, SL3, L1 and SiCL1 materials, and smaller for SCL1, 

SCL2 and L2 (Fig. 5-6). The differences in the HYDRUS-3D sensitivities were caused by Ks

values used in the LSA. The Ks values of the first group of materials were greater than Ks values 

of the second group, except for SL2 (Table 4-1). The high HYDRUS-3D sensitivity to the relatively 

small Ks value (0.3 m day-1) of this material can be explained by its location. This material served 

as a restrictive flow layer at a depth of 0.41 m at locations 2 and 3, at a depth of 0.83 m at location 

2, and depths of 1.04 m and 1.24 m at locations 2 and 4, and thus controlled downward transport 

of the applied tracer within the irrigated plot. The effect of this material can also be seen in wells 5-

6, where SL2 was not present in the soil profile. These two wells received the dominant amount of 

mass of the applied tracer from the North-East corner of the irrigated plot (well 4), and therefore 

were affected indirectly by Ks of the SL2 material. 

The sensitivity of the HYDRUS-3D modeling results to the material properties was also assessed 

using the derivative-based sensitivity index (Di). Di values were computed using Eq. (6-5) from the 

same time series as used for the Si computations. The parameters obtained with the HYDRUS3D calibration and the Cl-

 concentrations simulated with these parameters were used in Eq. (6-5) 

as the nominal values of factors Xi and 

Yi

, respectively. Computed HYDRUS-3D model time 

series of the Di index for Ks of the eight soil materials are shown in Fig. 5-7. Overall variability of 

the Di index was greater compared with Si, with Di values over time changing signs from positive 

to negative and vice versa. This occurred due to acceleration of the tracer flux with an increase in 

Ks, resulted in a shift of the Cl- breakthrough curves along the time axis such that smaller Clconcentrations at Ks,min corresponded to higher concentrations at Ks,max in the rising limb, and vice 

versa in the declining limb of the Cl- breakthrough curves. 

The calculated values of Di indices confirmed the high sensitivity of HYDRUS-3D to Ks values of 

materials SL1, SL2, SL3, L1 and SiCL1 obtained in the analysis of Si values. The sensitivity to the 

materials was generally higher for soil types that directly or indirectly affected tracer transport. 

However, unlike the Si index, Di values changed signs from positive to negative, when an increase 

in the factor produced a decrease in the Cl- concentration. Some discrepancy existed between the 

data in Fig. 5-6 and Fig. 10a, and data in Fig. 5-7. Both indices (Si and Di) indicated a high 

sensitivity of the HYDRUS-3D calculations to Ks values of SL1 for well 2 and well 3, and a low 

sensitivity for well 4. However, unlike the Si index, Di values did not indicate high model sensitivity 

for well 1. 

The first-order sensitivity index (Si) is presumably a more informative measure of model sensitivity 

compared to the derivative-based sensitivity index (Di) since the term 

 )|( Xi ~ XYEV iiX

 in Eq. (6-3)

accounts for the combined effects of Xi and all other factors. Unlike Si, the Di index estimates the 

effect of Xi factor when all other factors are fixed at their nominal values. Therefore, the Di value 

for factor Xi may depend upon the nominal values of other factors. Nevertheless, Si can also 

mislead when the model sensitivity to all factors is low. In this case small values of the 

denominator in Eq. (6-3) may result in non-zero value of the Si index. Figures 5-5b and 5-5c 

illustrate this case. The variance of Ks of material SL1 did not affect results of HYDRUS-3D 

simulations. The Cl- concentrations in well 10 did not change during the simulation time (Fig. 5-2), 

thus leading to relatively small values of VXi for this parameter (Fig. 5-5b). However results of 

HYDRUS-3D simulations were about the same when Ks values of all materials varied, resulting in 

small values of V(Y) (Fig.5-5c). Division of a small VXi value by a small V(Y) gave Si a value about 

0.3 on day 130 of the HYDRUS-3D simulation (Fig. 5-5a), which indicated a moderate sensitivity 

of the model to Ks of material SL1. 
5-13

The Si time series computed with the HYDRUS-3D and TOUGH2 models were used to assess the 

sensitivity of both models to Ks, and the longitudinal (DL) and transverse (DT) dispersivities of the 

eight soil materials. To reduce the amount of information and simplify the data analysis, the Si time 

series were characterized by the mean, S̅ i, and the standard deviation, SDSi, of the Si index over 

the simulation time. The relationships between σ(S̅ i) and S̅ i are shown in Fig. 5-8. Generally SDSi

increased with increase in Si value for all materials. Based on data in Fig. 5-8 HYDRUS-3D model 

was more sensitive to Ks and L than TOUGH2 model (Fig. 5-8a,b,d,e). The sensitivity to was 

about the same in both models (Fig. 5-8c,f). The smallest values of Si and SDSi were obtained for 

SCL2 material in all locations indicating the low sensitivity of the HYDRUS-3D and TOUGH2 models 

to the transport properties in this material within the range of studied parameters. Therefore, based 

on Si index, the SCL2 material can be considered as a candidate for the model simplification. 

The LSA was performed above based on the tracer concentrations representing the whole 

simulation period of time. Two performance indicators: simulated peak concentrations (Cpeak) 

and time of the peak concentrations (Tpeak) at the tracer time series will be considered here as 

an alternative to the entire Cl- series. To evaluate the applicability of Cpeak and Tpeak

performance indicators the ARS study team analyzed the Cl- time series computed in the LSA of 

the HYDRUS-3D model. New indicators were not applicable for the data from wells 8-12 

simulated with both models and for wells 5-7 simulated with the TOUGH2 model due to absence 

of peaks on the Cl- curves. Therefore only the HYDRUS-3D results for wells 1-7 are used 

hereafter. The LSA was conducted using Si and Di indices computed both for the Cpeak and 

Tpeak data. The nominal values of factors Xi and 

Yi

for Di index were taken from the HYDRUS3D calibration data, similarly to the previous LSA. Results were presented as relationships 

between the sensitivity indices computed for Cpeak and Tpeak data in wells 1-7. General increase 

in Si(Cpeak) with increase in Si(Tpeak) with the slope close to one was observed in the 

simulations indicating approximately equal model sensitivity to both performance variables (Fig. 5-

9a,b,c). Depending on location, the model sensitivity to the soil materials differed, however the 

values of Si(Cpeak) and Si(Tpeak) were consistently smaller in SCL2 material for Ks, L and 

than in other soil materials. The Di values indicated high sensitivity of the HYDRUS-3D model to 

Ks, moderate sensitivity to and low sensitivity to L in soil materials (Fig. 5-9d,e,f). Unlike Si

index no relationship was found between Di(Cpeak) and Di(Tpeak). The values of Di for Ks were 

positive and negative indicating both an increase and decrease in Cpeak and Tpeak associated with 

increasing value of Ks. The Di(Cpeak) values were mostly negative, but Di(Tpeak) were close to zero 

for the αT parameter reflecting a decrease in the peak concentration with an increase in parameter 

of transversal dispersivity, while the peak time remained almost unchanged, which indicates a 

flattening of Cl- BTC. Based both on Si and Di indices computed for peak concentrations and peak 

times, material SCL2 can be selected for model simplification. 

Overall, introducing the peak concentration (Cpeak) and the time to peak concentration (Tpeak) as 

performance indicators for the LSA allowed us to reduce significantly the input information needed 

for the sensitivity analysis and to define the soil material that can be used for the model 

simplification example. One limitation of the new performance indicators is the need to have 

peaks in the simulated BTCs. 
5-14

Figure 5-6 Time series of the sensitivity index Si obtained in HYDRUS-3D simulations 

with two levels of the saturated hydraulic conductivity for eight soil materials. 

sL1

0.0

0.2

0.4

0.6

0.8

1.0

sL3

Si(Ks

)

0.0

0.2

0.4

0.6

0.8

scL2

0.0

0.2

0.4

0.6

0.8 Well-7

Well-8

Well-9

Well-10

Well-11

Well-12

L2

Day from beggining of the experiment

0 20 40 60 80 100 120

0.0

0.2

0.4

0.6

0.8

sL2

0.0

0.2

0.4

0.6

0.8

1.0

scL1

0.0

0.2

0.4

0.6

0.8

L1

0.0

0.2

0.4

0.6

0.8 Well-1

Well-2

Well-3

Well-4

Well-5

Well-6

sicL1

0 20 40 60 80 100 120

0.0

0.2

0.4

0.6

0.8
5-15

 

Figure 5-7 Time series of the sensitivity index Di obtained in HYDRUS-3D simulations 

with two levels of the saturated hydraulic conductivity for eight soil materials. 

sL1

Di(Ks)

-0.6

-0.4

-0.2

0.0

0.2

0.4

0.6

0.8

1.0

sL3

-0.8

-0.6

-0.4

-0.2

0.0

0.2

0.4

0.6

0.8

scL2

-0.10

-0.05

0.00

0.05

well-1 

well-2 

well-3 

well-4 

well-5 

well-6 

L2

Day from beginning of the experiment

0 20 40 60 80 100 120

-0.10

-0.05

0.00

0.05

0.10

0.15

sL2

-0.3

-0.2

-0.1

0.0

0.1

0.2

0.3

scL1

-0.10

-0.05

0.00

0.05

0.10

0.15

L1

-0.2

-0.1

0.0

0.1

0.2

sicL1

0 20 40 60 80 100 120

-4

-3

-2

-1

0

1

well-7 

well-8 

well-9 

well-10 

well-11

well-12 
5-16

Figure 5-8 Sensitivity of the HYDRUS-3D and TOUGH2 models to the hydraulic 

conductivity (a, d), longitudinal (b, e) and transversal (c, f) dispersivity 

assessed for eight soil materials using time-averaged Si indices and their 

standard deviations SDSi. 
5-17

Figure 5-9 Sensitivity of the HYDRUS-3D model to the hydraulic conductivity Ks (a,d), 

longitudinal dispersivity αL (b,e) and transversal dispersivity αT (c,f) assessed 

at seven observation wells using Si and Di indices for simulated peak 

concentrations Cpeak and times Tpeak. 

K s

0.0 0.2 0.4 0.6 0.8 Si(Cpeak)

0.0

0.2

0.4

0.6

0.8

1.0

DispL

Si(Tpeak)

0.0 0.2 0.4 0.6 0.8

DispT

0.0 0.2 0.4 0.6 0.8 1.0

(a) (b) (c)

-0.8 -0.6 -0.4 -0.2 0.0 0.2 -0.8 -0.6 -0.4 -0.2 0.0 0.2 0.4 Di(Cpeak)

-0.8

-0.6

-0.4

-0.2

0.0

0.2

0.4

sL1

sL2

sL3

scL1

scL2

L1

L2

sicL2

Di(Tpeak)

-0.8 -0.6 -0.4 -0.2 0.0 0.2

(d) (e) (f)
5-18

5.1.4 Subsurface Textural Units 

The spatial boundary between soil materials was also subjected to the LSA. The materials in the 

simulation domain were vertically distributed within the soil profiles based on soil texture 

measured at 10 depths at 12 locations as described in section 4.2.1 of this report. The lateral 

boundaries between different textural materials were equally spaced between neighboring wells. 

Since no information existed about the actual locations of the various lateral material boundaries, 

it seemed worthwhile to assess the effect of material delineation on results of the tracer 

simulations. To do this, the lateral boundary of each soil material was extended or truncated for 

about 1 m. Only one material boundary out of nine was changed in each model run, resulting in a 

total of 18 runs for the HYDRUS-3D and TOUGH2 models. The model sensitivities to the material 

distributions were assessed using the derivative-based sensitivity index Di. The first-order 

sensitivity coefficient Si was inapplicable for this LSA since boundary locations were not 

independent variables for the different materials. The nominal values of factors Xi and Y̅i in Eq. 5-

5 were taken from the HYDRUS-3D and TOUGH2 simulations using the calibrated parameters. 

The values of the sensitivity index Di for both models varied greatly in time (Fig. 5-10 and Fig. 5-

11). Modification of the material boundary caused at many locations an increase following by a 

decrease in the Cl- concentration, and vice versa, with time, resulting in the Di sign changing from 

positive to negative values and back. For some reason these changes were not seen in the 

TOUGH2 simulations, which produced Di values which were either consistently positive or 

negative during the entire simulation (Fig. 5-11). Common for the two models was the low 

sensitivity to modification in the SCL2 material boundary. A possible explanation for this is the 

location of SCL2 in the simulation domain. The SCL2 material was primarily located at depths of 

0.21 m and 0.41 m at locations 6 and 7. The ARS study team previously showed (section 5.1.1) 

that the tracer was transported from the irrigated plot towards wells 5-8 predominantly laterally in 

the upper layer of the saturated zone, while vertical water fluxes beyond the application area were 

insignificant. The SCL2 material was located far from the preferential fluxes and therefore did not 

affect their velocities and directions.. 

5.1.5 Boundary Conditions 

The ARS study team previously examined the properties of the soil as a possible option for model 

simplification. Another possible way for model abstraction is simplification of the flow conditions on 

the boundaries of the simulation domain. The ARS study team used thus far daily-averaged 

precipitation and evapotranspiration rates for the top boundary of the entire, and daily-averaged 

irrigation rates less runoff in addition to the atmospheric boundary conditions within the irrigation 

plot. A zero flux boundary condition was imposed along the bottom of the domain. Spatially 

variable but constant in time pressure head profiles were specified along the lateral boundaries 

based on groundwater monitoring data obtained in the summers of 2006-2007. To evaluate the 

role of the boundary conditions in the model and to identify variables for model simplification, the 

LSA was applied separately to the top and lateral boundaries of the domain. For simplicity the 

ARS study team used the one-factor-at-a-time approach, thus excluding the combined effect of 

several factors on the LSA results. The Di index was used as a measure of model sensitivity. 
5-19

 

Figure 5-10 Temporal variation of the sensitivity index Di obtained in HYDRUS-3D 

simulations with extended and truncated material boundaries. 

sL1

Di(Material distrubution)

-0.2

-0.1

0.0

0.1

0.2

0.3

sL3

-0.2

-0.1

0.0

0.1

0.2

scL2

-0.10

-0.05

0.00

0.05

L2

Day from beginning of the experiment

0 20 40 60 80 100 120

-0.15

-0.10

-0.05

0.00

0.05

0.10

0.15

sL2

-0.6

-0.4

-0.2

0.0

0.2

0.4

scL1

-0.10

-0.05

0.00

0.05

0.10

0.15

L1

-0.04

-0.02

0.00

0.02

0.04

0.06

0.08

0.10

0.12

0.14

sicL1

0 20 40 60 80 100 120

-0.8

-0.6

-0.4

-0.2

0.0

0.2

0.4

0.6

0.8 well1 

well2

well3 

well4

well5 

well6

well7

well8

well9

well10

well11

well12 
5-20

Figure 5-11 Temporal variation of the sensitivity index Di obtained in the TOUGH2 

simulations with extended and truncated material boundaries. 

sL1

Di(Material distrubution)

-0.4

-0.2

0.0

0.2

0.4

0.6

sL3

-0.2

0.0

0.2

0.4

0.6

0.8

1.0

scL2

-1.0

-0.5

0.0

0.5

1.0

1.5

L2

Day from beginning of the experiment

0 20 40 60 80 100 120

-2

0

2

4

6

8

sL2

-0.2

0.0

0.2

0.4

0.6

0.8

1.0

1.2

1.4

1.6

scL1

-2.0

-1.5

-1.0

-0.5

0.0

0.5

1.0

L1

-1.2

-1.0

-0.8

-0.6

-0.4

-0.2

0.0

0.2

well-7 

well-8

well-9

well-10 

well-11 

well-12 

sicL1

0 20 40 60 80 100 120

-0.2

-0.1

0.0

0.1

0.2

0.3

well1

well2

well3

well4

well5

well6
5-21

The LSA was first applied to the runoff data. Runoff was experimentally estimated as 28% of 

irrigation and precipitation in our previous study (Pachepsky et al., 2011). For the LSA the ARS 

study team used 20% and 40% of irrigation and precipitation as estimates for runoff in both 

HYDRUS-3D and TOUGH2. Soil properties and the other boundary conditions were set similar to 

the HYDRUS-3D calibration simulation. The changes in runoff values dramatically affected the 

simulated Cl- BTCs. A decrease in runoff resulted in a general increase in Cl- concentrations and a 

decrease in the tracer arrival times at wells 1-9. An increase in runoff had the opposite effect on 

the simulated Cl- BTCs. Minor changes in Cl- concentrations were observed in well 11 and well 

12. These changes were less pronounced for the TOUGH2 simulations, particularly for wells 5-8. 

The difference between results of the HYDRUS-3D and TOUGH2 simulations was mostly a 

general underestimation of the measured Cl- concentrations in wells 5-7, which originated from 

omitting any calibration of TOUGH2. In spite of differences in their prediction accuracy, both 

models were sensitive to the runoff changes. The Di indices ranged from -2 to 1 and from -0.5 to 

0.6 for HYDRUS-3D and TOUGH2, respectively (Fig. 5-12a,b), thus indicating high model 

sensitivity to inflow along the upper boundary of the domain. The LSA was not conducted with 

precipitation and irrigation since the results would be essentially the same. This is because the 

flux in both models was set as irrigation and precipitation less runoff. 

Next, the LSA was applied to the evapotranspiration data. Evapotranspiration ranged from 0 to 2.3 

mm with a variance of 63% during the observation period. The goal of the LSA was to replace 

daily-averaged ET values with those averaged over the entire simulation period (i.e. ). The 

HYDRUS-3D and TOUGH2 simulations were run with daily- and long-term averaged and 

values using parameters and boundary conditions obtained with the HYDRUS-3D calibration. The 

Cl- breakthrough curves simulated with differently averaged ET were very close to each (data not 

further shown). Values of the sensitivity index Di were of the same order of magnitude in both 

models, except for well 2 in HYDRUS-3D simulations (Fig. 5-12c,d). For some reason the Di

values for this well decreased in time, likely indicating the increase in Cl- concentrations at this 

location when daily-averaged ET were replaced with the longer-term values. Overall, small 

values of Di obtained in the simulations allowed model simplification using averaging 

evapotranspiration values over the full 132-day simulation period. 

Finally, the LSA was used also to estimate the effect of groundwater depth on the simulation 

results. The depth to groundwater as obtained with the HYDRUS-3D calibration was increased 

and decreased by 0.10 m. Both HYDRUS-3D and TOUGH2 were run with the modified lateral 

boundary conditions and parameter sets resulting from the HYDRUS-3D calibration. The changes 

in the groundwater depth affected the Cl-

 BTCs differently at 12 locations using HYDRUS-3D. 

Within the irrigation plot the changes affected mostly the shapes of the BTCs. Simulated BTCs 

flattened when the depth to groundwater increased. This increase caused an increase in the Clconcentrations of wells 5-8, most likely because of an increase in the hydraulic gradients 

controlling lateral flow from the irrigation plot towards the observation wells. Changes in Cl- were 

not significant in wells 10-12 since an increase in the gradient was not sufficient to deliver the 

tracer to these wells within the simulation period. Results of the TOUGH2 simulations revealed 

similar tendencies, except for smaller changes in the Cl- concentrations of wells 5-8 as compared 

to HYDRUS-3D simulations. The Di indices computed for both models are shown in Fig. 5-12e,f. 

HYDRUS-3D was generally more sensitive to changes in the groundwater depth compared to 

TOUGH2. The Di indices ranged from -1.3 to 0.5 and from -0.4 to 0.4 for HYDRUS-3D and 

TOUGH2, respectively. In spite of different sensitivities, the effect of the boundary conditions on 

the simulation results was significant for both models. This indicates that groundwater depth 

could not be subjected to model simplification. 
5-22

5.1.6 Sampling Frequency 

The impact of different data collection frequencies on the modeling results was studied also using 

the HYDRUS-3D and TOUGH2 models. The sampling frequency in the field experiment ranged 

from twice a day during the first 37 days to once a day afterwards. Over 4,500 water samples 

were taken from 3 depths at 12 locations and analyzed for Cl- content during the 132-day 

experiment. The intensive sampling scheme provided detailed information about tracer transport 

within and beyond the irrigated plot at different depths. The tracer was found to be transported 

preferentially beyond the irrigated plot in the upper layer of the saturated zone due to relatively 

high hydraulic conductivity of the soil material composing this layer (Pachepsky et al., 2011). 

Unfortunately, the adopted intensive sampling scheme is impractical for most application. Our 

study hence aimed at reducing the sampling frequency without significantly affecting model 

performance. 

Alternative Cl- sampling intervals were selected within the range from 1 to 10 days, with 1 day 

increments. Since sampling always started at the beginning of the experiment, the number of 

samplings ranged from 131 to 13. Model performance was evaluated using the root mean 

squared error (RMSE) for both models, as well as errors in predicting peak Cl- concentrations 

(ΔCpeak) and peak times (ΔTpeak) using the HYDRUS-3D software. Both models were run using the 

HYDRUS-3D calibration parameters. Values of RMSE obtained with the simulations using the 

calibrated parameters (the zero sampling time intervals in Fig. 5-13) were compared with RMSEs 

computed for the reduced number of samplings (i.e. 131 and 13 sampling dates were used for the 

RMSE computations with 1-day and 10-day frequencies, respectively). The computed RMSE 

values did not change noticeably with an increase in the sampling time interval for wells 5-13. 

Changes were noticeable only for wells 1 and 4, which were located within the irrigated plot. The 

RMSE value decreased about two times for well 4 when the sampling interval became greater 

than 2 days. This occurred because the highest Cl- concentrations in this well 

were observed within the first 3 days since the beginning of the experiment, with the model failing 

to reproduce the experimental data. Similar results were obtained from an analysis of errors in 

predicting the Cl- peak concentrations and peak times using the HYDRUS-3D model. 

Noticeable changes in the errors occurred only for well 4 after the sampling time interval 

exceeded 2 and 4 days for ΔCpeak and ΔTpeak, respectively. The discrepancy between these two 

time intervals for this well was caused by a fast decline in the Cl- BTC during the first 37 days of 

the experiment, followed by a slow increase in the Cl- concentration during the next 60 days, with 

a second peak time occurring at 96th day from beginning of the experiment. The increase in the 

sampling time interval caused a decrease in the peak concentration until this concentration 

became smaller than the second concentration peak. The sampling time interval was 5 days when 

the second peak became greater than the first peak (Fig. 5-13). 

Overall a sampling interval of 10 days was sufficient for collecting data in wells located beyond the 

irrigated plot. A 2-day sampling interval was more appropriate for wells within the irrigated plot 

where the higher water fluxes caused more rapid transport of the applied tracer. 
5-23

Figure 5-12 Temporal variation of the sensitivity index Di obtained in the LSA of the 

HYDRUS-3D and TOUGH2 models to runoff (a,b), evaporation (c,d) and 

groundwater depth. 

0 20 40 60 80 100 120

well7

well8

well9

well10 

well11

well12

Day from beginning of the experiment

0 20 40 60 80 100 120

Di(Groundwater depth)

-2.0

-1.5

-1.0

-0.5

0.0

0.5

1.0

well1

well2

well3

well4 

well5

well6

(e) (f)

0 20 40 60 80 100 120 0 20 40 60 80 100 120

Di(Evaporation)

-0.4

-0.3

-0.2

-0.1

0.0

0.1

0.2

0.3

(c) (d)

TOUGH2

0 20 40 60 80 100 120

well7

well8

well9

well10

well11

well12 

HYDRUS-3D

0 20 40 60 80 100 120

Di(Runoff)

-2.5

-2.0

-1.5

-1.0

-0.5

0.0

0.5

1.0

1.5

well1

well2

well3

well4 

well5

well6

(a) (b)
5-24

Figure 5-13 Errors of predicting Cl- concentrations (RMSE), peak Cl- concentrations 

(ΔCpeak) and peak times (ΔTpeak) obtained in the HYDRUS-3D and TOUGH2 

simulations for measurements taken at different time intervals. 
5-25

5.1.7 Soil Material Elimination 

The LSA local sensitivity analysis revealed different model sensitivities to the 8 soil materials that 

represented the soil properties of the simulation domain. The very small values of the sensitivity 

indices Di and Si for material SCL2 suggest that the simulation domain perhaps could be 

simplified by using fewer soil materials, and consequently fewer transport parameters for the 

HYDRUS-3D and TOUGH2 simulations. 

Three soil materials (SL3, SCL1, L1) were considered as possible replacements for SCL2. These 

three materials were selected since they were the nearest neighbors among the textural classes 

as obtained with the cluster analysis in Task II. The SL3, SCL1, L1 alternative soil materials (Fig. 

5-14) had DL and DT parameter values similar to SCL2, except for SL3 whose DL value was ten 

times smaller. The Ks values of the alternative materials were from 5 to 25 times higher than the 

Ks of SCL2 (Table 4-1). Three new simulations were carried out with the HYDRUS-3D and 

TOUGH2 models using the same initial and boundary conditions as for the calibration simulations, 

but with the modified parameters for SCL2. 

The BTCs computed using HYDRUS-3D were found to be very close to the original BTCs 

obtained for SCL2. The main difference was for the simulation using SL3 for well 2, which showed 

a BTC that was much closer to the observed Cl- curve. Unlike results of HYDRUS-3D simulations, 

the BTCs computed with TOUGH2 differed from the original curve of wells 1-8. The maximum and 

minimum differences were obtained with simulation using the SCL1 and L1soil materials, 

respectively (Fig. 5-15). 

In view of these findings, the transport domain could now be simplified based solely on results of 

the HYDRUS-3D and TOUGH2 simulations using the original (SCL2) and alternative materials 

(SL3, SCL1, and L1). Both SCL1and L1 could replace the SCL2 material when using the 

HYDRUS-3D model, while L1 material was the best alternative to SCL2 for TOUGH2. The 

observed Cl- data could provide additional information for model simplification. This information 

may include RMSE values of the simulated Cl- concentrations and prediction errors in the peak 

concentrations and the times to peak concentrations. Based on the RMSEs (Fig. 5-15) all three 

materials could be selected for simplification of both models, provided the Cl- concentrations of 

wells 1 and well 2 are not a concern. The ARS study team showed earlier in section 5.1.1 that the 

cumulative tracer fluxes did not affect Cl- transport toward the other wells. However, if the 

concentrations in those wells are important for decision making, then SL3 for HYDRUS-3D and 

SL3 or L1 for TOUGH2 would be the best alternatives to the SCL2 soil material. 

The same conclusions can be derived for the HYDRUS-3D code using other performance 

indicators, specifically the peak concentration (Cpeak) and the time of the peak concentration (Tpeak) 

of the tracer time series. Figure 5-16 illustrates the accuracy of HYDRUS-3D model in predicting 

Cpeak and Tpeak in wells 1-7. The errors for both performance indicators were smaller for the 

SL3 material, thus confirming the results of the RMSE analysis. 
5-26

Figure 5-14 Alternative soil texture for the HYDRUS-3D model simplification. 
5-27

Figure 5-15 Root-mean-square errors (RMSE) of predicting Cl- concentrations obtained 

with two models using the original and modified properties for SCL2 soil 

material. 
5-28

Figure 5-16 Errors of peak Cl- concentrations (ΔCpeak) and peak times (ΔTpeak) obtained 

with the HYDRUS-3D using the original and modified properties for SCL2 soil 

material. 
5-29

5.2 Model Abstraction Applications 

The model abstraction methodology, developed in this study, is comprised of the following steps: 

(i) site conceptualization, (ii) analysis of hydrological conditions, (iii) specifying accidental release 

scenarios, (iv) selecting performance indicators, (v) simulating contaminant transport for the 

assumed scenarios, and (vi) model simplification based on the performance indicators. The 

adopted abstraction techniques may differ and be specific for licensing NRC sites, depending 

upon hydrological complexity of a particular site. For the OPE3 site in Beltsville, MD, the ARS 

study team evaluated the applicability of three model abstraction techniques: (i) parameter 

abstraction, (ii) profile aggregation, and (iii) ignoring the unsaturated zone. To implement these 

three abstraction techniques and make the results transferable to other NRC sites the ARS study 

team assumed that: 

 The calibrated HYDRUS-3D model adequately reproduced subsurface contaminant

transport in the studied area.

 The hydrologic complexity of field B at the OPE3 site is commensurate with the complexity

of NRC sites.

 Variability in the ground water depths as measured in the observation wells during the

monitoring period (2006-2010) is similar to the variability at NRC sites.

 The irrigated area at the experimental site represents a decommissioning or licensing

NRC site; accidental release is equally probable at any point within the site area.

 The creek and observation wells at the eastern boundary of the OPE3 site represent

protected ground and surface water resources in the vicinity of the NRC site.

 Weather conditions at the decommissioning or licensing site are adequately represented

by the 60-year weather data collected by the Beltsville weather station.

The ARS study team realized that some these assumptions may not be applicable to all NRC 

sites, but believe that the proposed methodology can serve as a general guidance to simplify 

models predicting subsurface contaminant transport from a particular release point. 

5.2.1 Geometry of the Simulation Domain and Soil Material Distribution 

NRC regulation 10 CFR 100.20(3) specifies that factors important to hydrological radionuclide 

transport (such as soil, sediment, and rock characteristics, adsorption and retention coefficients, 

ground water velocities, and distance to the nearest surface body of water) must be obtained from 

on-site measurements (61 FR 65176, Dec. 11, 1996). These onsite measurements provide a 

basis for creating a conceptual site model that evaluates and provides a qualitative representation 

of the important features, events, and processes of the groundwater flow and transport system 

(Interim). In this study all available information obtained from soil surveys, groundwater 

monitoring and modeling was integrated into the conceptual model of the decommissioning or 

licensing NRC site. 

A new simulation domain that mimics a NRC site was defined within the boundaries of the GPR 

survey conducted in 2006. The domain included the tracer application plot, 44 old groundwater 

observation wells installed in 2000, and 12 new sampling wells installed in 2006 (Fig.5-17). The 

domain extended laterally for 190 m in the x (east-west) direction and for 118 m in the y (northsouth) direction, bordered by a first-order distributary in the eastern part. The thickness (z

direction) of the domain varied from 2.60 m in the east to 8.73 m in the west and was set so that it 

included a flow restrictive layer along the bottom boundary. This difference in the thickness was 

caused by a slope of the soil surface. The coordinate system in the HYDRUS-3D 
5-30

simulation assumed the origin to be at the bottom of the domain (the z-axis was assumed to be 

positive upward). 

The domain was subdivided vertically into ten hydrological layers based on data from the GPR 

survey conducted in 2006 (Fig. 3-31). The material in each layer was distributed based on soil 

texture measured in logs during installation of the observation wells. Soil properties within the 

irrigated plot were assigned similar to those used for the HYDRUS-3D calibration, while soil 

textures measured in 44 logs during well installation in 2000 (Table 3-2) were used outside that 

area. In all 12 texture classes/subclasses were needed to represent the soil materials within the 

transport domain (Fig 5-18). These classes included: Sand (S), Loamy sand (lS), two Sandy 

Loam classes (SL1, SL2), Sandy Clay Loam (SCL1), Clay Loam (CL), two Loam classes (L1 and 

L2), three Silt Clay Loam classes (SiCL1, SiCL2, SiCL3), and Silt Loam (SiL). Boundaries 

between different soil materials of each computational layer were set at approximately equal 

distances from the observation wells where the materials were measured. The soil below a depth 

of 4.03 m was considered to represent a flow restrictive layer, and was represented by the SiCL3 

texture which has a very low value of the saturated hydraulic conductivity (Ks=0.001 m day-1). 

Subdividing the soil hydraulic properties into 12 groups was expected to reflect hydrological 

complexity of the simulation domain, and to provide flexibility for model abstraction. 

Soil hydraulic parameters for the 12 materials are shown in Table 5-1. Within the irrigated area 

these properties were set equal to the parameters obtained in the HYDRUS-3D calibration. 

Beyond this area the ARS study team used ROSETTA estimated parameters of the vanGenuchten water-retention equation and Ks values estimated using the PTFs of Rawls et al. 

(1998). The dispersivity parameters αL and αT of all materials were set to 1.0 m and 0.2, 

respectively. 

The unstructured (triangular prisms) finite element mesh consisted of 11,770 nodes and 20,380 

3D elements. The vertical size of the finite element prisms varied depending upon location, with 

the elements following the soil surface and the surface of the lower sub-layer. The vertical size of 

the finite elements for the upper 2-m soil layer ranged from 0.2 to 0.3 m, while the size below this 

depth was about 0.3 m and 2-m at the eastern and western boundaries of the domain, 

respectively (Fig. 3-19a). The horizontal mesh size increased from about 1.3 m within the 

irrigation plot where the fastest fluxes were observed, to 5 m outside of that area. Using this 

geometry and associated finite element mesh, a 10-year long simulation generally took between 6 

and 8 h with a Computech Intel CoreTM i7 CPU 930 @2.80 GHz computer. Further refinement of 

the finite element mesh required longer simulation times. A total of 100 observation nodes (Fig. 5-

19b) spaced 10-m apart were used to record the simulated breakthrough curves at depths of 

approximately 2.3 m. Although the maximum lateral fluxes of the tracer during the sensitivity 

analysis of HYDRUS-3D were observed to occur at a depth of 1.1 m, the ARS study team 

increased the output depth since the 10-year simulations showed that the water table decreased 

to below 2 m during periods of low precipitation, which caused the long-term tracer fluxes to 

become larger at a depth of 2.3 m as compared to the 1.1 m depth. 
5-31

Figure 5-17 Boundary of new simulation domain with old (brown circles) and new (green 

circles) groundwater wells. 
5-32

Figure 5-18 Material distribution for the HYDRUS-3D mesh. 
5-33

Table 5-1 Hydraulics conductivity values obtained by calibration, estimation with PTFs 

from Rawls et al. (1998) and scaling abstractions A1 through A6. 

Soil

texture

Ls, m 0.05 0.2

b 0.3 0.5 0.7 0.3 0.5 0.7

Saturated hydraulic conductivity, Ks, m d-1

Calibrated Rawls 

et al. 

1998

A1 A2 A3 A4 A5 A6

SL1 2.50 1.339 5.331 13.390 33.634 3.517 6.695 12.745

SL2 0.10 0.307 1.222 3.070 7.711 0.806 1.535 2.922

SL3 2.50 1.339 5.331 13.390 33.634 3.517 6.695 12.745

SCL1 0.45 0.067 0.267 0.670 1.683 0.176 0.335 0.638

SCL2 0.11 0.017 0.068 0.170 0.427 0.045 0.085 0.162

L1 2.00 0.149 0.593 1.490 3.743 0.391 0.745 1.418

L2 0.70 0.149 0.593 1.490 3.743 0.391 0.745 1.418

SiCL1 2.00 0.118 0.470 1.180 2.964 0.310 0.590 1.123

SiCL2 0.15 0.118 0.470 1.180 2.964 0.310 0.590 1.123
5-34

Figure 5-19 Mesh generated for HYDRUS-3D simulations (a) with coordinates for 100 

output locations (b). 

280

300

320

340

360

380

400

420

400 450 500 550 600 650

Mesh nodes

Output nodes

Observation wells
5-35

Figure 5-20 Probability distribution of the decade precipitation (a) and cumulative 

precipitation for decades with 25%, 50% and 75% probabilities (b). 

0

20

40

60

80

100

8,000 8,500 9,000 9,500 10,000 10,500 11,000 11,500 12,000 12,500

Probability (%)

Total decade precipitation (mm)

0

2,000

4,000

6,000

8,000

10,000

12,000

0 365 730 1095 1460 1825 2190 2555 2920 3285 3650

Cumulative precipitation (mm)

Day

25%

50%

75%

ET
5-36

5.2.2 Initial and Boundary Conditions 

In this part of our study the ARS study team examined the subsurface transport of the tracer 

leaked from the irrigated area. The assumed initial spatial distribution of Cl- was found to affect the 

breakthrough curves calculated using HYDRUS-3D. The ARS study team observed that relatively 

high initial Cl- concentrations of wells 9, 11 and 12 (Fig. 5-2) decreased partly due to inflow of low 

concentrated Cl- solution from locations wells 5 and 3. To eliminate the influence of the initial 

concentration on the tracer distribution, and to better follow the subsurface migration of the 

applied chemical, the initial tracer concentration was set equal to zero across the simulation 

domain. A third-type (Cauchy) boundary condition was used along the soil surface to simulate 

solute transport. The tracer concentrations of precipitation and groundwater along the lateral 

boundaries were set to zero. 

As initial condition for the water flow simulations the ARS study team used equilibrium pressure 

head distributions. These distributions were assigned to four groundwater depth scenarios defined 

later in section 5.2.3. Ten-day averaged atmospheric boundary conditions were used at the soil 

surface. Evapotranspiration rates were computed using the Penman-Monteith method as 

documented by FAO (Allen et al., 1998) for weather data of year 2006 and repeated for each 

simulation year. Based on the flow velocities obtained in section 5.1.1, a 10-year simulation period 

was considered to be sufficient for the tracer to arrive at the eastern boundary of the simulation 

domain. The ARS study team discarded extra days in leap years, which allowed us to fix the total 

simulation period at 3650 days. Three precipitation scenarios were considered in the 10-year 

HYDRUS-3D simulations. To generate these scenarios, the precipitation data collected in 

Beltsville from 1949 to 2006 were summed for each 10 consecutive years and ranked in an 

increasing order (Fig. 5-20a). Ten-year precipitation rates at probability levels of 25%, 50% and 

75% were subsequently selected for HYDRUS-3D simulations. The selected decades were 1992-

2001, 1984-1993 and 1976-1985, with total precipitation rates of 9527 mm, 10,339 mm and 

10,659 mm for the 25%, 50% and 75% probabilities, respectively. Since the interdecadal 

distributions of precipitation were relatively uniform (Fig 5-20b), the ARS study team did not 

expect that temporal variability in the upper boundary conditions would affect results of the 10-

year HYDRUS-3D calculations. Daily variability in rainfall values affected the numerical stability of 

HYDRUS-3D simulations, which could be avoided by using 10-day averaged precipitation values 

in our simulations. Total decadal evapotranspiration was 4237 mm, less than half of the 

precipitation. A zero flux boundary condition was imposed along the bottom of the domain. 

5.2.3 Simulation Scenarios 

To model the accidental release of a tracer from a single holding tank outside of a containment 

structure, the ARS study team considered four scenarios. In the first two scenarios the release 

points were set on the soil surface at locations of wells 3 and 4 within the irrigated plot. The 

accidental release of a 1000 ppm spill was assumed to occur at rate of 0.2 m day-1 through a 1-m2

area within the first 10 days of the simulation. This translates to a total of 2 kg of tracer being 

released as a pulse with 2 m3 of water. The release points of the other two scenarios were in 

groundwater at depth of 2.3 m. The tracer fluxed for the third and fourth scenarios hence occurred 

in the saturated zone. The ARS study team expected much faster solute transport rates when 

released in the saturated zone as compared to the partly unsaturated conditions considered for 

the first two scenarios. 

Four different scenarios were developed also for the lateral boundary conditions. These conditions 

were set as equilibrium pressure head profiles for spatially variable, but constant in time, 

groundwater depths. The main reason for assuming a constant in time boundary condition 
5-37

was the considerable complexity of the shape at the lateral boundary of the simulation domain. 

Whereas technically HYDRUS-3D allows the implementation of time-variable pressure head 

boundary conditions, the transition between the physical boundaries of the simulation domain and 

temporally changing variable groundwater levels creates a problem of conjunction and often 

results in abrupt changes in the boundary conditions which hamper rapid convergence of the slow 

that numerical solution of the Richards equation. Another reason for using different boundary 

scenarios is uncertainty due to limited information about the spatial and temporal variability of 

groundwater levels. Long-term hydrological data are not available at many newly designed NRC 

sites. For these cases, indirect methods are recommended for determining annual average 

conditions (Interim SRP 2.412 and 2.4.13). Because of uncertainty in the indirect methods, it is 

necessary in these cases to conduct a consequence analysis assuming conservative hydrologic 

conditions and parameter estimates. The groundwater depths measured in the wells at field B in 

2006-2007 (Fig. 3-11) and 2007-2008 (Fig. 3-27) provided general information about the spatial 

and temporal variability of the water table in the flow domain. The ARS study team realized that 

the 10-year variability in groundwater levels may differ from the observed values. For this reason 

the ARS study team generated several scenarios with different slopes and depths to groundwater 

for HYDRUS-3D simulations. These were: (1) a slope in x direction (SlopeX) of 1.6%, a slope in 

the y direction (SlopeY) of 1%, and a groundwater level (GWD) of 5.5 m relative to the bottom of 

the simulation domain in Fig. 5-19, (2) the same slopes with GWD=6.0 m; (3) SlopeX=1.6%, 

SlopeY=0.4%,and GWD=5.5 m; and (4) SlopeX=1.6%, SlopeY=0.4%, GWD=6.0 m. Note that 

GWD is the level above the zero vertical coordinate, which served as the bottom boundary of the 

flow domain. These GWD levels corresponded to groundwater depths varying from 3.5 m to 1.5 m 

for GWD=5.5 m, and from 3.0 m to 1 m for GWD=6.0 m in the western and eastern parts of the 

domain, respectively. These levels of the groundwater were also used for the initial pressure head 

distributions in the domain as was described in section 5.2.2. 

Overall, 48 different scenarios were simulated with HYDRUS-3D, comprising the four release 

scenarios, four groundwater scenarios and three precipitation scenarios. These scenarios 

provided input for the model abstraction process described in the following sections. 

5.2.4 Performance Indicators 

The LSA was performed using tracer concentrations representing the entire simulation period. In 

practice different performance indicators can be used for decision making based on the model 

results. The American National Standard for evaluation of subsurface radionuclide transport at 

commercial nuclear power plants (ANSI/ANS-2.17-2010) recommends using radionuclide 

concentrations (either volume- or flux averaged), mass fluxes, travel times and predicted doses as 

performance indicators. For these reasons the ARS study team used in this study simulated tracer 

concentrations and fluxes to characterize chemical transport from the assumed accidental release 

locations. To characterize the direction and velocity of contaminant migration the ARS study team 

used the simulated peak concentration (Cpeak) and times to peak concentration (Tpeak) at the 

observation nodes and along transects at different distances from the release points. The spatial 

distributions of Tpeak were used to estimate the velocities and directions of the contaminant plume 

for all simulation scenarios. 

To evaluate the accuracy of each model abstraction technique, several efficiency criteria were 

used in this study. Model efficiency criteria were defined by Beven (2001) as mathematical 

measures of how well a model simulation fits observations. In hydrological modeling, efficiency 

criteria are typically based on the ratio between the prediction error and variability in the 

observations. In spite of apparent simplicity, there is no general agreement on how to use the 
5-38

error term and the observation variability. The simplest way to compute model efficiency was 

proposed by Nash and Sutcliffe (1970). They introduced the efficiency criterion E as the deviation 

from one of the absolute squared differences between the predicted and observed values, 

normalized by the variance of the observed values: 

ENS = 1 − ∑ (Oi−Pi

)

2

∑(Oi

-O̅)

2

(5-8)

where Oi and Pi are the measured and predicted values. Values of the efficiency index E are 

within the range from 0 to -∞ and increase in absolute value when the deviations between 

predicted and measured values increase. A deficiency of this criterion is in its sensitivity to large 

measured or predicted values, since squared values are used in both the numerator and 

denominator. 

Another efficiency criterion is the index of agreement d proposed by Willmot (1981). This criterion 

is defined as the ratio between the mean square error and the potential error as follows 

dW = 1 − ∑ (Oi

-Pi)

2

∑ (|Pi

-O̅|+|Oi-O̅|)

2 (5-9)

A third model efficiency index used in this study to evaluate model abstraction accuracy is the 

squared correlation coefficient: 

r

2 = ( ∑(Oi

-O̅)(Pi-P) ̅̅̅

√∑ (Oi

-O̅)

2√∑ (Pi

-P̅)

2

)

2

(5-10)

The power of the above efficiency indices for hydrological model assessment were examined by 

Krause et al. (2005). These authors showed that selection and use of specific efficiency criteria, 

as well as interpretation of the results, can be a challenge since each criterion places different 

emphasis on different types of simulated and observed results. The ARS study team believes that 

the use of multiple criteria for the abstracted models will reduce uncertainty in the result 

interpretation. Therefore all three criteria were applied to the performance indicators discussed 

earlier in this section. 

To assess the performance of the selected indicators 48 HYDRUS-3D runs were carried out for 

the scenarios defined in section 5.2.3 using parameters obtained in the HYDRUS-3D calibration. 

Required hydraulic parameters for the new materials beyond the calibration domain were 

estimated using the ROSETTA software (Table 5-1). These simulations will be referred to 

hereafter as “calibrated” to distinguish them from the abstraction simulations. Results of the 

simulations for the three weather, two source and two groundwater scenarios are shown in Figs. 

5-21 through Fig. 5-23. The ARS study team selected these 12 cases as the most representative 

of the 48 HYDRUS-3D simulations. Results showed that the shape of the contaminant plume as 

represented by the peak concentration was influenced most by the location of the release point. 

Overall, the release from locations 1 and 3 produced considerably wider plumes with larger tracer 

concentrations as compared to locations 2 and 4 (only locations 1 and 2 are shown in Fig. 5-21). 

Weather scenarios and the slope of groundwater had minor effects on the plume shape and the 

concentrations. Tracer concentrations generally decreased exponentially with distance from the 

release point (Fig. 5-21). This decrease was more pronounced for releases from locations 2 and 4 

rather than from locations 1 and 3, and more pronounced for a groundwater level of 5.5 m as 

compared to the 6.0-m scenario. 
5-39

The location of the release points also influenced the tracer peak concentration travel time, Tpeak. 

Spatial patterns of Tpeak were different for release locations 1 and 2, and were affected by 

groundwater depth scenario for location 1 (Fig. 5-22). The shapes of Tpeak distributions create an 

illusion of having preferential tracer pathways in x-direction from the source at locations 1 and 

location 2 for the 5.5-m groundwater level scenario. However, these pathways significantly differ 

from zones with high Cpeak values shown in Fig. 5-21 and no correlation was found between the 

simulated Tpeak and Cpeak values. Differences between the simulated Tpeak and Cpeak spatial 

patterns can be explained by flow diversity. Due to high heterogeneity of the simulation domain, 

the tracer arrived in many instances at the nodes within a short period of time, but in small 

concentrations. Soon after arrival, the tracer may become diluted by inflow from the upslope area 

and hence may not contribute further to plume propagation. The highly concentrated flux at other 

locations was moving slower than the less concentrated flux, which caused the Tpeak values to 

become smaller in the main flow path as to the branches. The Tpeak and Cpeak values were 

derived from the tracer breakthrough curves at each observation node and did not characterize 

the total mass of the transferred contaminant. Since the spatial pattern of mass is the only true 

measure of the migrating contaminant plume, the ARS study team supplemented the Tpeak and 

Cpeak analysis with the analysis of the contaminant mass distribution. 
5-40

Figure 5-21 Spatial distributions of log10(Cpeak[ppm]) performance indicator obtained in HYDRUS-3D simu

calibrated parameters during 10-year simulation period in two scenarios for contaminant sou

GWD scenarios and precipitation probabilities of 25%, 50% and 75%. (Cpeak) - 25% 10 log

400

380

360

340

320 (Cpeak) -50% 10 log

400

380

360

340

320

520 530 540 550 560 570 580 590 (Cpeak) - 75% 10 log

400

380

360

340

320

520 530 540 550 560 570 580 590 520 530 540 550 560 570 580 590 520 530 540 550 560 570 

Source 1, GWD=5.5 m Source 2, GWD=5.5 m Source 1, GWD=6.0 m Source 2, GWD=6.0
5-41

Standard HYDRUS-3D simulation results include time series of the tracer concentration C(t) and 

nodal water fluxes q(t). The ARS study team used these values to compute the tracer fluxes QC 

at the 100 output nodes according to Eq. 5-7. The flux values, shown in Fig. 5-23, represent the 

total tracer masses passing through a 1 m2 area during the simulations. The QC patterns closely 

resemble the Tpeak and especially the Cpeak patterns. The total tracer mass generally 

decreased more or less exponentially within the first 30-m travel distance from the release point. 

This shows that only a fraction of the total tracer mass passed through the observation wells and 

that this fraction decreased with distance due to the plume spreading beyond the monitoring 

network. Beyond the 30-m travel distance the total tracer mass remained somewhat constant. 

Similar to the Cpeak patterns, the QC spatial distribution was wider for the release from locations 

1 and 3 compared to locations 2 and 4, with considerably more mass being transported from 

locations 1 and 3 (Figs. 5-21 and 5-23). The major effects of source location and groundwater 

level on tracer transport, and the relatively minor effects of groundwater slope and the weather 

scenario, can be seen in Fig. 5-23. Different release locations produced different spatial 

distributions of the performance indicators, with the distributions being further altered by the flow 

conditions associated with the groundwater level. 

Overall, both release location and lateral boundary condition were major factors affecting the 

contaminant transport process in our study. The largest tracer concentrations and fluxes were 

observed when the tracer was released at locations 1 and 3 into shallow groundwater. Among the 

performance indicators, the total tracer flux QC was the most accurate, and the times to peak 

concentration Tpeak the least accurate, for assessing contaminant transport in this study. The 

ARS study team realized that the results may be site- and scenario-specific, and that further 

research may be needed to investigate the power of the performance indicators for different 

contaminant transport condition.
5-42

Figure 5-22 Spatial distributions of Tpeak [day] performance indicator obtained in HYDRUS-3D simulations 

parameters during 10-year simulation period in two scenarios for contaminant source locatio

scenarios and precipitation probabilities of 25%, 50% and 75%. Tpeak - 25% 400

380

360

340

320 Tpeak -50% 400

380

360

340

320

520 530 540 550 560 570 580 590 Tpeak - 75% 400

380

360

340

320

520 530 540 550 560 570 580 590 520 530 540 550 560 570 580 590 520 530 540 550 560 570 

0 

50

10

15

20

25

30

35

Source 1, GWD=5.5 m Source 2, GWD=5.5 m Source 1, GWD=6.0 m Source 2, GWD=6.0
5-43

Figure 5-23 Spatial distributions of log10(QC [ppm m day-1]) performance indicator obtained in HYDRUS-

the calibrated parameters during 10-year simulation period in two scenarios for contaminant 

two GWD scenarios and precipitation probabilities of 25%, 50% and 75%. (QC) - 25% 10 log

400

380

360

340

320 (QC) -50% 10 log

400

380

360

340

320

520 530 540 550 560 570 580 590 (QC) - 75% 10 log

400

380

360

340

320

520 530 540 550 560 570 580 590 520 530 540 550 560 570 580 590 520 530 540 550 560 570 580 

Source 1, GWD=5.5 m Source 2, GWD=5.5 m Source 1, GWD=6.0 m Source 2, GWD=6.0
5-44

5.2.5 Abstraction of Parameter Determination: Using Pedotransfer Functions 

The first model abstraction technique implemented in this study was abstraction of the soil hydraulic 

parameters. The purpose of this abstraction was to skip the time-consuming and computationally 

demanding model calibration process, but instead to work with estimated hydraulic parameters. 

The ARS study team showed earlier in section 4.2 that the calibrated parameters differed from the 

pedotransfer function (PTF) derived estimates. However, the obtained results could be scale and 

scenario-specific. The HYDRUS-3D calibration was based on application of the Cl- tracer to a 

relatively large plot (10x10m), followed by measurements in the vicinity (7 m) of the application area. 

A steady-state infiltration regime was artificially created and maintained within the application area. 

Water fluxes in reality are rarely at steady-state due to irregular rainfall events and groundwater 

fluctuations such that steady-state regimes may persist only for short periods of time. The ARS 

study team assumed that the model will be less sensitive to the hydraulic properties and boundary 

conditions if the release occurs over a small area (1 m2), and if the tracer is transported over a long 

distance with unsteady water flow. The ARS study team expected to see a scale and time effect 

on propagation of the contaminant plume caused by tracer dilution and dispersion. 

To test the parameter abstraction technique, 48 HYDRUS-3D runs were carried out with 

scenarios defined in section 5.2.3, water retention parameters used in the calibrated model, and 

saturated hydraulic conductivities of the entire flow domain estimated using the PTFs of Rawls et 

al. (1998). The estimated Ks values were 4.37, 2.95, 0.31, 1.34, 0.07, 0.02, 0.15, 0.15, 0.12, 0.12, 

0.001 and 0.35 m day-1 for S, LS, SL1, SL2, SCL, CL, L1, L2, SiCL1, SiCL2, SiCL3 and SiL, 

respectively. The Ks value of the SiCL3 material was not altered in this abstraction since SiCL3 

served as a flow restrictive layer at the bottom of the profile. Thus only the saturated hydraulic 

conductivity was abstracted in this section, while soil water retention parameters were kept 

unchanged in all simulations. The performance indicators Cpeak, Tpeak, and QC were derived from 

the simulated concentration time series at 100 output nodes and along 11 transects passing 

through the observation nodes and crossing the simulation domain in the y-direction. 

Iso-contours of the peak concentration, the time to peak concentration and the total solute flux 

over the 3650-day simulation for the three weather, two groundwater and two source location 

scenarios are shown in Fig. 5-24 - Fig. 5-26. Substituting the calibrated Ks values with values 

determined using the PTF estimates of Rawls et al. (1998) affected the spatial distributions of 

Cpeak, Tpeak and QC in the transport domain. Values of Cpeak for the abstracted model were in 

general larger than those for the calibrated model, with the shapes of the plume being more 

elongated in the x-direction. These changes can be attributed to the almost threefold increase in 

Ks of the loamy sand material at depths of 1.77 m and 2.35 m (Fig.5-18), which must have 

facilitated tracer transport. Increased Ks values noticeably reduced the tracer arrival times (Fig. 5-

22 and Fig. 5-25). Tpeak values computed were from 1.1 to 1.9 times smaller for the abstracted 

model compared to the calibrated model. The flow acceleration was not proportional to the 

increase in Ks, most likely due to a change in the pressure head gradient between the release 

points and the lateral boundaries of the simulation domain. The pressure heads were set constant 

in time along the lateral boundaries, while in the central part of the domain the pressure heads 

changed over time and were controlled mostly by the Ks values of the materials above the flow 

restrictive layer. Small values of Ks in the calibrated model created conditions for temporary 

increases in the groundwater level during periods with high precipitation, leading to larger 

hydraulic gradients between the central and outlying parts of the domain. Since the flux is a 

product of the conductivity and pressure gradient, an increase in Ks hence is partly compensated 

for by a lower pressure gradient in the abstracted model.
5-45

Figure 5-24 Spatial distributions of log10(Cpeak[ppm]) performance indicator obtained in HYDRUS-3D simu

abstracted Ks parameters during 10-year simulation period in two scenarios for contaminant 

two GWD scenarios and precipitation probabilities of 25%, 50% and 75%. (Cpeak) - 25% 10 log

400

380

360

340

320 (Cpeak) -50% 10 log

400

380

360

340

320

520 530 540 550 560 570 580 590 (Cpeak) - 75% 10 log

400

380

360

340

320

520 530 540 550 560 570 580 590 520 530 540 550 560 570 580 590 520 530 540 550 560 570 580 

Source 1, GWD=5.5 m Source 2, GWD=5.5 m Source 1, GWD=6.0 m Source 2, GWD=6.0
5-46

Figure 5-25 Spatial distributions of Tpeak[day] performance indicator obtained in HYDRUS-3D simulations 

Ks parameters during 10-year simulation period in two scenarios for contaminant source loc

scenarios and precipitation probabilities of 25%, 50% and 75%. Tpeak - 25% 400

380

360

340

320 Tpeak -50% 400

380

360

340

320

520 530 540 550 560 570 580 590 Tpeak - 75% 400

380

360

340

320

520 530 540 550 560 570 580 590 520 530 540 550 560 570 580 590 520 530 540 550 560 570 580 

0 

500 

1000 

1500 

2000 

2500 

3000 

3500 

Source 1, GWD=5.5 m Source 2, GWD=5.5 m Source 1, GWD=6.0 m Source 2, GWD=6.0
5-47

Figure 5-26 Spatial distributions of log10(QC [ppm m day-1]) performance indicator obtained in HYDRUS-

the abstracted Ks parameters during 10-year simulation period in two scenarios for contami

locations, two GWD scenarios and precipitation probabilities of 25%, 50% and 75%. (QC) - 25% 10 log

400

380

360

340

320 (QC) -50% 10 log

400

380

360

340

320

520 530 540 550 560 570 580 590 (QC) - 75% 10 log

400

380

360

340

320

520 530 540 550 560 570 580 590 520 530 540 550 560 570 580 590 520 530 540 550 560 570 580 

Source 1, GWD=5.5 m Source 2, GWD=5.5 m Source 1, GWD=6.0 m Source 2, GWD=6.0
5-48

Alteration of the soil hydraulic properties affected the sensitivity of the model to the upper 

boundary conditions. The spatial patterns of the performance indicators were different for years 

with 25%, 50% and 75% precipitation probabilities. The Cpeak and QC spatial distributions were 

narrower for the 50% probability in the source 1 release scenarios compared to 25% and 75% 

probability weather scenarios (Fig. 5-24 and Fig. 5-26). A possible reason for this is the interdecadal precipitation distribution (Fig. 5-20). 

Larger Cpeak values for the abstracted model translated into the larger QC values (Fig. 5-23 and 

Fig. 5-26). The QC values computed for the 11 transects were from 2 to 10 times larger for the 

simulations with abstracted parameters than with the calibrated model. The differences were 

found to increase with distance from the source of the release. The changes were relatively 

dramatic due to the strong nonlinearity of the advection-dispersion equation used to describe 

subsurface contaminant transport in this study. 

Values of the performance indicators obtained with HYDRUS-3D using the calibrated and 

abstracted Ks values were used to assess the applicability of the parameter abstraction technique. 

The ARS study teamcomputed the Nash-Sutliffe and Willmot efficiency criteria and the coefficients 

of determination using Eqs. (5-8) – (5-10). The performance indicators Cpeak, Tpeak and QC as 

obtained with the calibrated and abstracted parameters served as measured (O) and predicted 

(P) values in these equations. Values of the efficiency criteria computed for 100 output nodes are 

shown in Fig. 5-27 a,c,e. Generally, values of the efficiency indices were highest for Cpeak and 

lowest for Tpeak and/or QC, indicating better performance of the abstracted model in predicting 

peak concentrations as compared to peak times and total fluxes. The E values of QC computed 

for all scenarios, and of Tpeak for most scenarios were negative (Fig. 5-27a), which indicates that 

the mean value of the performance indicator would be a better predictor than the simulated 

values. Values of the index d and coefficients of determination for Cpeak ranged from 0.74 to 0.99 

and from 0.39 to 0.97, respectively (Fig.5-27 c,e), reflecting a potentially good agreement between 

the abstracted and calibrated models. High values of the computed indices do not always provide 

reliable estimate of model accuracy since they are not sensitive to systematic model over- and 

under-predictions. To test the abstraction results for the presence of systematic errors, the 

coefficients of linear regression P = a + bO were computed. The computed values of the intercept 

(a) and slope (b) ranged from -0.03 to 0.69 and from 0.67 to 1.79, respectively indicating the 

presence of systematic errors and poor correspondence between the abstracted and calibrated 

models. Systematic errors were also obtained for predicted Tpeak and QC values, indicating failure 

of the abstracted model to reproduce the calibrated model. 

Values of the efficiency criteria of the performance indicators computed for the transects differed 

from those computed for the 100 observation nodes. Generally better agreement was found 

between the calibrated and abstracted simulations when the Cpeak and QC performance indicators 

were used for assessing the accuracy of the abstracted model as compared to the Tpeak indicators. 

The E values computed for all scenarios for Tpeak and approximately half of the scenarios for the 

QC indicators were again negative (Fig. 5-27b), indicating poor performance of the abstracted 

model. The large negative E values computed for QC at the observation nodes became smaller 

along the transects, while small negative E values computed for Tpeak at the nodes became 

larger when computed for the transects (Fig. 5-27a and Fig.5-27b). This occurred due to bias of 

the Nash-Sutcliffe criterion towards large values. The tracer did not arrive at some locations or 

could arrive only in small amounts at distant nodes 5 to 10 years after the release event. Values of 

Tpeak for those locations were set to 3650 days or were close to this number. In the abstracted 

model the total number of nodes with large Tpeak values was less as compared
5-49

Figure 5-27 Efficiency indices of the parameter determination abstraction. 
5-50

to the calibrated model (Figs. 5-22 and 5-25). The difference (P-O) in the numerator of Eq. (5-2) 

was therefore significantly larger than the difference (O-) in the denominator, thus producing high 

negative E values. The Tpeak values for the transects were significantly smaller than at the 

observation nodes for both the calibrated and abstracted models since the tracer had passed 

through all 11 transects within the 10-year simulation period. Smaller Tpeak values produced 

smaller values of the E efficiency criterion shown in Fig. 5-27b. 

Similar to results obtained for the 100 observation nodes, values of the Willmot efficiency criteria 

and coefficients of determination for Cpeak were reasonably high along all transects, thus 

suggesting that the abstracted model adequately reproduced the original model (Fig. 5-27b,d,f). 

For instance, d values ranged from 0.805 to 0.995 and values of R2 were statistically significant 

(P<0.05) and ranged from 0.733 to 0.996. To confirm these statistics the ARS study team tested 

the results for the presence of systematic errors. Computed slope and intercept values varied 

from 0.76 to 1.86 and from 0.23 to 2.79, respectively, indicating the presence of a systematic error 

and poor performance of the abstracted model. 

Overall, the three performance indicators used in this study pointed to inappropriateness of the 

model parameter abstraction that would use PTF without the appropriate attention to scale effects. 

The high sensitivity of the HYDRUS-3D modeling results to the saturated hydraulic conductivity 

resulted in significant changes in flow velocities and concentrations, as well as in total mass fluxes 

of the tracer transported from the release points assuming different weather, groundwater and 

release scenarios. These changes were traced using the Cpeak , Tpeak and QC performance 

indicators and assessed using the Nash-Sutcliffe and Willmot efficiency criteria and the 

coefficients of determination for 100 output nodes and 11 transects. The Tpeak and QC 

performance indicators were better discriminators between the calibrated and abstracted models. 

Both efficiency criteria and the coefficients of determination failed to discriminate the models in 

terms of the Cpeak performance indicator due to insensitivity of these statistics to the systematic 

error. 

5.2.6 Abstraction of Profile Aggregation 

The second model abstraction technique implemented in this study was profile aggregation. A 

motivation for this abstraction was dominance of the SL2 material in the simulation domain. To 

assess the effect of soil profile aggregation on the simulation results, the ARS study team converted 

the heterogeneous profile of the upper sub-layer into an equivalent homogeneous medium having 

SL2 soil texture. Soil properties below the flow restrictive layer were kept unchanged. The transport 

parameters for both layers were taken from the calibrated HYDRUS-3D model. A total of 48 

scenarios were run again as described in section 5.2.5. Selected simulation results are presented 

in Figs. 5-28 - 5-30

Profile aggregation was found to have a major effect on tracer transport. Introducing a 

homogeneous SL2 profile produced changes in the spatial distribution of the performance 

indicators. The tracer flux turned approximately 30° to the South, while the shape of the Cpeak

distribution changed from infuser- to diffuser-like. This caused the narrowest part of the tracer 

plume to occur in the vicinity of the release point (Fig. 5-28). The abstraction also affected 

concentrations and flow velocities. Generally, the peak concentrations were higher and the travel 

times towards the output nodes were shorter for the abstracted model as compared to the calibrated 

model (Fig. 5-28 and Fig. 5-29). The plume spread even faster than in simulations with parameter 

abstraction discussed in the previous section. The main reason for this was the relatively high 

saturated hydraulic conductivity (Ks=2.5 m day-1) of material SL2, which provided conditions for fast 

flow in the entire simulation domain. 
5-51

Based on visual comparisons of the spatial patterns of the three performance indicators obtained 

with the abstracted (Fig. 5-28 - Fig. 5-30) and calibrated (Fig. 5-21 - Fig. 5-23) models, one should 

not expect good agreement between the two models. Indeed the values of the efficiency criteria 

for profile aggregation (Fig. 5-31) were smaller than those computed for parameter abstraction 

(Fig. 5-27). Tests for the presence of systematic errors are therefore, not really needed to 

conclude inadequacy of the model assuming a more homogeneous profile as compared to the 

calibrated heterogeneous profile model. 

5.2.7 Abstraction by Ignoring Unsaturated Zone 

The third abstraction technique implemented in this study involved ignoring the unsaturated zone. 

To do this, the tracer release sources were moved from the soil surface to the saturated zone at 

2.1 m depth. In general terms, unsaturated flow in the absence of preferential transport should 

retard water and chemical fluxes due to the nonlinear decrease in the hydraulic conductivity with 

decreasing of water content, and the associated long residence time in the vadose zone. 

Therefore, the ARS study team expected more rapid transport for the abstracted model compared 

to the original model. The 48 scenarios were run with parameters obtained in the HYDRUS-3D 

calibration. Results of the simulations are shown in Fig. 5-32 – Fig. 5-35. Surprisingly, ignoring the 

unsaturated zone did not lead to noticeable changes in the performance indicators. Values of 

Cpeak, Tpeak and QC obtained while ignoring of the unsaturated zone varied within the same ranges 

as the performance indicators in the original model. The plume shapes in Fig. 5-32 - Fig. 5-34 

closely resembled the shapes obtained in simulations with the calibrated parameters (Fig. 5-21 - 

Fig. 5-23). The similarities between two sets of simulations are quite remarkable, and were 

confirmed by the efficiency criteria. Values of the Nash and Sutcliffe efficiency coefficients ranged 

from 0.948 to 0.992, from 0.612 to 0.999, and from 0.956 to 0.994 for the peak concentration, time 

to peak concentration, and the total flux, respectively (Fig. 5-35). No negative values were 

obtained for this criterion. The Willmot efficiency coefficients and coefficients of determination 

were both close to one, which also indicates good agreement between the abstracted and original 

models. 

Values of the efficiency indices for both the observation nodes and the transects were greater for 

Cpeak and QC as compared to Tpeak for several scenarios. For this reason the ARS study team 

tested all performance indicators for the presence or absence of systematic errors. The tests 

showed the presence of systematic errors only for the Tpeak indicator at probability level P<0.01. 

This led us to conclude that there was a delay in the tracer transport in some scenarios and that 

abstraction by ignoring the unsaturated zone is applicable if the key performance indicators are 

the peak concentration and the total contaminant flux passing through a transect or observation 

well. Model simplification by ignoring the unsaturated zone seemed possible in our study because 

of the presence of perched water and relatively shallow water tables. However, eliminating the 

unsaturated zone should be done with caution at NRC sites having thicker unsaturated zones. 
5-52

Figure 5-28 Spatial distributions of log10(Cpeak[ppm]) performance indicator obtained in HYDRUS-3D simu

aggregated parameters during 10-year simulation period in two scenarios for contaminant so

GWD scenarios and precipitation probabilities of 25%, 50% and 75%. (Cpeak) - 25% 10 log

400

380

360

340

320 (Cpeak) -50% 10 log

400

380

360

340

320

520 530 540 550 560 570 580 590 (Cpeak) - 75% 10 log

400

380

360

340

320

520 530 540 550 560 570 580 590 520 530 540 550 560 570 580 590 520 530 540 550 560 570 580 

-6 

-4 

-2 

0 

2 

Source 1, GWD=5.5 m Source 2, GWD=5.5 m Source 1, GWD=6.0 m Source 2, GWD=6.0
5-53

Figure 5-29 Spatial distributions of Tpeak[day] performance indicator obtained in HYDRUS-3D simulations 

aggregated parameters during 10-year simulation period in two scenarios for contaminant so

GWD scenarios and precipitation probabilities of 25%, 50% and 75%. Tpeak - 25% 400

380

360

340

320 Tpeak -50% 400

380

360

340

320

520 530 540 550 560 570 580 590 Tpeak - 75% 400

380

360

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320

520 530 540 550 560 570 580 590 520 530 540 550 560 570 580 590 520 530 540 550 560 570 580 

0 

500 

1000 

1500 

2000 

2500 

3000 

3500 

Source 1, GWD=5.5 m Source 2, GWD=5.5 m Source 1, GWD=6.0 m Source 2, GWD=6.0
5-54

Figure 5-30 Spatial distributions of log10(QC [ppm m day-1]) performance indicator obtained in HYDRUS-

the profile aggregated parameters during 10-year simulation period in two scenarios for cont

locations, two GWD scenarios and precipitation probabilities of 25%, 50% and 75%. (QC) - 25% 10 log

400

380

360

340

320 (QC) -50% 10 log

400

380

360

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320

520 530 540 550 560 570 580 590 (QC) - 75% 10 log

400

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520 530 540 550 560 570 580 590 520 530 540 550 560 570 580 590 520 530 540 550 560 570 580 

0

2

4 

6 

Source 1, GWD=5.5 m Source 2, GWD=5.5 m Source 1, GWD=6.0 m Source 2, GWD=6.0
5-55

Figure 5-31 Efficiency indices of the profile aggregation abstraction. 
5-56

Figure 5-32 Spatial distributions of log10(Cpeak[ppm]) performance indicator obtained in HYDRUS-3D simu

unsaturated zone during 10-year simulation period in two scenarios for contaminant source 

scenarios and precipitation probabilities of 25%, 50% and 75%. (Cpeak) - 25% 10 log

400

380

360

340

320 (Cpeak) -50% 10 log

400

380

360

340

320

520 530 540 550 560 570 580 590 (Cpeak) - 75% 10 log

400

380

360

340

320

520 530 540 550 560 570 580 590 520 530 540 550 560 570 580 590 520 530 540 550 560 570 580 

Source 1, GWD=5.5 m Source 3, GWD=5.5 m Source 2, GWD=5.5 m Source 4, GWD=5.5 m
5-57

Figure 5-33 Spatial distributions of Tpeak[day] performance indicator obtained in HYDRUS-3D simulations 

unsaturated zone during 10-year simulation period in two scenarios for contaminant source 

scenarios and precipitation probabilities of 25%, 50% and 75%. Tpeak - 25% 400

380

360

340

320 Tpeak -50% 400

380

360

340

320

520 530 540 550 560 570 580 590 Tpeak - 75% 400

380

360

340

320

520 530 540 550 560 570 580 590 520 530 540 550 560 570 580 590 520 530 540 550 560 570 580 

0 

500 

1000 

1500 

2000 

2500 

3000 

3500 

Source 1, GWD=5.5 m Source 3, GWD=5.5 m Source 2, GWD=5.5 m Source 4, GWD=5.5 m
5-58

Figure 5-34 Spatial distributions of log10(QC [ppm m day-1]) performance indicator obtained in HYDRUS-3

limiting input domain abstraction during 10-year simulation period in two scenarios for conta

locations, two GWD scenarios and precipitation probabilities of 25%, 50% and 75%. (QC) - 25% 10 log

400

380

360

340

320 (QC) -50% 10 log

400

380

360

340

320

520 530 540 550 560 570 580 590 (QC) - 75% 10 log

400

380

360

340

320

520 530 540 550 560 570 580 590 520 530 540 550 560 570 580 590 520 530 540 550 560 570 580 

Source 1, GWD=5.5 m Source 3, GWD=5.5 m Source 2, GWD=5.5 m Source 4, GWD=5.5 m
5-59

Figure 5-35 Efficiency indices for ignoring the unsaturated zone abstraction. 
5-60

5.2.8 Abstraction of Parameter Determination: Pedotransfer Functions and Hydraulic 

Conductivity Scaling 

Systematic model abstraction can include the sequential or concurrent application of two or more 

categories of model abstraction. The ARS study team implemented this using pedotransfer 

functions and scaling, thus using two categories of parameter estimation abstraction (Fig. 2-1). 

Simulations were carried out for the smaller flow domain used for model calibration (Section 4.2). 

This enabled us to compare results of the parameter estimation abstraction with the model 

calibration results. 

Scaling abstraction strives to provide compatibility of the parameter estimation scale with the 

scale of model resolution. Neuman et al. (2003) suggested that this can be done by upscaling 

over computational grid cells. Accordingly, scaling abstraction for parameter estimation was 

implemented by upscaling PTF-estimated hydraulic conductivity values to the computational grid 

cells. A relatively minor effect of scale on soil water retention was observed (Pachepsky et al., 

2001) for soils having similar textures as those in this study, For this reason the ARS study team 

applied upscaling to the saturated hydraulic conductivity, Ks. 

Schulze-Makuch et al. (1999) suggested using a power-law relationship to correlate the 

increase in Ks with the volume Vm of tested aquifer material as follows 

KS = AVs

B

 (5.11) 

in which A and B are empirical parameters. The ARS study team reviewed the literature of data 

sources used by Rawls et al. (1998) to develop pedotransfer functions to estimate Ks as a function 

of scale and volume. The ARS study team noted a great variety of shapes of aquifer material. 

The shapes were also quite different from the shapes of computational cells in our numerical 

study. Direct application of the above volume-based scaling (5.11) was hence not possible. For 

this reason the ARS study team replaced the volume of affected media by the characteristic 

length of the medium and calculated the scaled hydraulic conductivity based on reference KsR

values estimated using the PTFs of Rawls et al. (1998) using the following relationship 

Ks

∗ = KsR (

Lg

Ls

)

b

 (5.12) 

where Lg is characteristic length of the numerical grid used to solve flow and transport problem, Ls

represents the size of the soil cores used to determine KsR, and b is an exponent. 

Substantial uncertainty exists in Eq. (5.12) stemming from variations in the lengths of samples 

used to measure Ks in the Rawls et al. (1998) database. The lengths mostly varied from 0.05 to 

0.2 m. The value of the exponent b was also uncertain; Schulze-Makuch et al. (1999) 

encountered values of B in Eq. (5-11) from 0.40 to 0.95 for homogeneous porous media, from 

0.62 to 0.96 for heterogeneous dual- porosity media, and from 0.82 to 1.13 in heterogeneous, 

fractured media. The ARS study team assumed six abstraction scenarios (Table 5.2) based on a 

single value for KsR for each soil material, one value (5 m) for Lg, two values (0.05 and 0.2 m) for 

Ls, and three values (0.3, 0.5 and 0.7) for b. The Ks value in the SiCL3 material was not altered in 

this abstraction since SiCL3 served as the flow restrictive layer at the bottom of the flow domain. 
5-61

Results of the simulations are presented in Fig. 5-36 as plots of simulated versus observed 

concentrations. The concurrent use of the PTF abstraction and scaling abstraction gave results 

that were very similar to those of the calibration. Visual inspection of Fig. 5-36 suggests that 

scaling cases A1, A4 and A5 produced relationships between the simulated and observed 

concentrations that were quite similar to the calibration (Fig. 5-36, CAL). The linear trend lines in 

Fig. 5-36 represent the correspondence between simulated and observed concentrations 

 Cobs=aCsim (5.13) 

where a is the slope of linear fit. This slope differed most significantly from unity for scaling 

scenarios A2, A3, and A6. 

Figure 5-37 shows values of the determination coefficient (R2) of the regressions and values of the 

slopes a in (5.13). Values of R2 for scenarios A1, A4 and A5 were relatively close to the calibration 

scenario, with slopes closest to 1. The ARS study team concluded that the Ks values of Rawls et 

al. (1998) must be scaled using (Lg/Ls)

b

 from the soil core size for which hydraulic conductivity was 

determined to the representative numerical grid size, with the exponent b varying between 0.3 and 

0.5 for small to large soil core sizes. 
5-62

Figure 5-36 Observed and simulated chloride concentrations in locations 5 through 9 with 

saturated hydraulic conductivity values obtained with different 

parameterization methods: CAL – manual calibration, PTF - using 

pedotransfer functions of Rawls et al. (1998), A1 through A6, PTF-estimated 

valued scaled to the size of the computational cells. 
5-63

Figure 5-37 Root-mean-square errors (RMSE) and slopes of regressions ‘ simulated vs. 

observed chloride concentrations’ in locations 5 through 9 with saturated 

hydraulic conductivity values obtained with different parameterization 

methods: CAL – manual calibration, PTF - using pedotransfer functions of 

Rawls et al. (1998), A1 through A6 - PTF-estimated valued scaled to the size of 

the computational cells. Regressions were computed with the intercept set to 

zero.

6-1 

6 APPLICATIONS OF MODEL ABSTRACTION IN 

MONITORING NETWORK DESIGN 

Models developed using abstractions based on model structure will have different underlying 

conceptual representations. Since a monitoring network is always designed based on a 

conceptual model, designs may be different for different abstracted models. As evidence is 

growing that conceptually different models can provide similar accuracy, developments in 

environmental modeling technologies is moving in two directions: (a) multimodeling in which 

several models are used simultaneously, in particular using ensembles of models, and (b) ranking 

models and selecting the most plausible model or models. Systematic model abstraction enables 

one to provide sets of models and ensembles of models for both of these modeling strategies. 

Integrating model abstraction in monitoring network design follows the same two strategies. 

Monitoring network design can either jointly use designs resulting from several conceptual 

models, or develop a design to discriminate models with the goal of selecting the more plausible 

one. This section describes two methods that the ARS study team developed to implement both 

strategies. 

6.1 Selecting Monitoring Locations to Decrease Prediction Uncertainty 

6.1.1 A Linear Statistical Inference Method to Assess Data Importance to Model 

Predictions, Sensitivity and Model Abstraction 

The purpose of conducting sensitivity analyses for model calibration is to assess the value of the 

data collected from monitoring wells in terms of their usefulness for model calibration and to 

identify new locations that could improve the reliability of the calibration. Generally threedimensional models require spatially distributed parameters that characterize transport properties 

of the materials composing the simulation domain. Ideally, the monitoring locations should be 

selected so as to provide sufficient and reliable information for determining the hydraulic and 

transport parameters of each soil material. To comply with these requirements, data collected at 

specific locations must vary temporally within a range that corresponds to the sensitivity of the 

model to the transport properties of the selected material, and have minimum interference with the 

parameters of other materials. Relatively small temporal variability typically can lead to high 

parameter uncertainty, while the interference produces correlation between the parameters of 

different soil materials. The best possible information therefore could be obtained from a dense 

monitoring network covering areas close to the tracer application point as well as wells and depths 

embracing all possible soil materials within the simulation domain. Unfortunately this implies a 

spatial density of the monitoring network that is impractical. Monitoring data are normally 

collected from a limited number of locations with soil properties generally not well known at the 

time of data collection. In this case a sensitivity analysis can be used to assess the value of the 

collected data for model calibration and to identify new locations that are most likely to produce 

information necessary for improving the calibration process. 

To evaluate the importance of observations for improving model predictions, Draper and Smith 

(1981), and Hill (1998) proposed the use of a linear statistical inference equation for calculating 

prediction standard deviations: 

SYl

′ = [S

2

(AY (A

TωA)

−1AY

T

)ll]

1/2

(6-1)

where 
6-2 

Yl

′

 is the l

th predicted value;

SYl

′ is the standard deviation of Yl

′

;

S

2

 is the calculated error variance from the model calibration; 

AY is the sensitivities of the predictions with respect to the model parameters; 

A is the matrix of sensitivities of the simulated equivalents of the observations (Yi

′

) with respect

to the model parameters; 

T indicates the transpose of the matrix; 

(A

TwA)

-1is a symmetric square linear approximation of the parameter variance-covariance matrix; 

Xj is the j

th parameter; ω is the matrix of weights on observations used in the calibration. 

Equation (6-1) was used to evaluate the importance of existing hydraulic-head observation 

locations to advective-transport predictions for the Death Valley regional flow system in California 

and Nevada (Hill et al., 2001) for the stationary flow regime. Elements of the matrix of sensitivities 

AY were calculated as derivatives: 

AY =

∂Yl

′

∂Xj

(6-2)

Standard deviations describing the precision of the water level measurements were used to 

calculate the weights in ω in that study. 

To evaluate the effect of omitting an observation location on the prediction uncertainty, Hill et al. 

(2001) used a modified version of equation (6-1) as follows: 

SYl(−i)

′ = [S

2

(AY (A(−i)

T w(−i)A(−i))

−1AY

T

)ll]

1

2

(6-3)

in which SYl(−i)

′ is the standard deviation of the l simulated value, Yl

′

, calculated without the i

th

observation location; (A(−i)

T w(−i)A(−i))

−1 is a symmetric, square parameter variance-covariance

matrix calculated with the information for the i

th observation omitted; 

AY(-i) is the matrix of sensitivities of the simulated equivalents of the observations (Yi

′

) with respect

to the model parameters, with the sensitivities for the i

th observation omitted; 

ω(-i) is the diagonal matrix of weights on observations used in the calibration, with the value 

for the i

th observation omitted. 

The relative importance of an observation for a prediction was defined as the percent increase in 

uncertainty caused by omitting an observation, and was termed the Observation-Prediction 

(OPR-) statistic: 

OPR− = [(SYl(−i)

′ SYl

⁄ ) − 1.0 ′ ] × 100 (6-4)

Similarly to equation (6-4) the relative importance of a new observation for a prediction can be 

calculated as: 

OPR+ = [(SYl(+i)

′ SYl

⁄ ) − 1.0 ′ ] × 100 (6-5)

where SYl(+i)

′ is the standard deviation of the l simulated value, Yl

′

, calculated with the i

th

observation location added; 
6-3 

For the case of adding observations, SYl(+i)

′ is calculated as: 

SYl(+i)

′ = [S

2

(AY (A(+i)

T w(+i)A(+i))

−1AY

T

)ll]

1

2

(6-6)

where index (+i) identifies the added location. 

The applicability of the linear statistic method (equations (6-1) through (6-6)) to evaluation of the 

importance of the existing and new water head and flow observations for a hypothetical 

groundwater flow system was demonstrated in Tonkin et al. (2007). 

The applicability of the linear statistic method given by equations (6-1) through (6-6) to evaluation 

of the importance of existing and new pressure head and flow observations for a hypothetical 

groundwater flow system was demonstrated in Tonkin et al. (2007). The approach could not be 

literally transferred to our work since it assumes flow stationarity, which is not the case in our 

study. Therefore, the ARS team used the first-order sensitivity coefficient (Eq. 6-3) as a substitute 

for the parametric sensitivity (6-2). Values of the first-order sensitivity coefficient were averaged 

over the observation period. 

6.1.2 Observation-Prediction Statistics Application 

The Observation-Prediction statistics (OPR) method described in section 6.1.1 was implemented 

to evaluate the importance of observations collected in the monitoring wells during the lateral flow 

experiment for the HYDRUS-3D calibration. HYDRUS-3D was run with the parameters and 

boundary conditions obtained with the model calibration. To evaluate the importance of the 

observation locations for the HYDRUS-3D calibration, and specifically for saturated hydraulic 

conductivity, values of Ks of 8 soil materials within the simulation domain were varied similarly as 

for the model sensitivity analysis in section 5.1.3. The only difference between the simulations in 

section 5.1.3 and the current HYDRUS-3D runs was the initial profile distribution of the tracer. 

Initial C0 values were set to zero to eliminate the influence of spatially variable initial 

concentrations on the sensitivity index values. A total of 256 simulations were carried out 

assuming two combinations of the Ks parameters of 8 materials. The computed tracer 

concentrations were recorded at 100 observation nodes to provide input for the sensitivity and 

OPR statistics. The observation (output) nodes were placed on the regular rectangular grid within 

a 27x14 m rectangular area at depths z of 2.07 and 2.49 m (Fig. 6-1). The eight locations (wells 5 

through 12) used for the model calibration and sensitivity analysis in section 5.1.3 constituted the 

existing observation network for the OPR analysis. 

Values of the sensitivity index Si(Ks) were found to be different for the same soil material at two 

depths and 50 locations, indicating different model sensitivities to Ks associated with the specific 

location of the observation node in the simulation domain. Generally, zero Si values were obtained 

for times smaller than the tracer arrival times at each location. For instance, nonzero Si values 

were observed starting from days 88 and 118 of the simulation in wells at distances of 3.5 and 14 

m from the irrigated plot, respectively (Fig. 6-2). This shows that the distance from the irrigated 

plot was the major factor influencing Si values at selected locations. Sensitivity values also 

changed with depth. Temporal persistence in the Si time series was observed at some locations. 

For example, the, Si values of well 38 decreased for 8 soil materials in the order L1, SiCL1, SCL2, 

SCL1, SL1, L2, SL1 and SL3 at both computational layers (i.e. z=2.07 and 2.49 m). Persistence 

with depth at other locations existed only for some materials. For example, Si values were 

persistent for 6 out of 8 soil materials at well 5 (Fig. 6-2). 
6-4 

The effect of depth and distance can be clearly seen in Fig. 6-3. Generally, the number of 

simulation days with nonzero Si values, and Si values averaged among the materials, were 

greater for the computational layers at 2.49 m as compared to 2.07 m layer (Fig. 6-3). The number 

of nonzero Si days, the range and the average Si values tended to decrease with distance from 

the irrigated plot, reflecting a general decrease in the model sensitivity with tracer travel distance. 

Notwithstanding this tendency, several points among the observation wells located at equal 

distances from the irrigated plot showed consistently high and low Si values. Since locations with 

high Si values are more informative and more important compared to locations having low Si

values, they could be included into the existing monitoring network for improvement of the model 

calibration. The potential locations selected solely based on the Si values are shown in Fig. 6-4.

The importance of existing observation locations for the HYDRUS-3D calibration was evaluated 

using the OPR- statistic. Averaged over time, the Si values obtained with HYDRUS-3D were used 

to calculate the matrix of sensitivities AY in Eq. 6-1. The standard deviations were computed 

separately for each well used for the HYDRUS-3D calibration (wells 5 through 12) based on Eq. 6-

1. The matrix of weights ω on the observations was represented by the proportion of days

showing nonzero Si values during the 131 day simulation. Consequently, wells with fewer nonzero 

Si values had higher weights in the computations. To evaluate the effect of omitting an 

observation location on the prediction uncertainty, the deviations SYl(−i)

′ were computed with

weights of the omitted location set equal to zero in Eq. (6-1). Finally, the ARS study team 

calculated the relative importance of each observation on the predictions using Eq. 6-4.

The percent of increased uncertainty OPR- ranged from 0 to 28.7%, and was greater for z=2.49 m 

than for the z=2.07 m layer (Fig. 6-5). Relatively high OPR-values were obtained at the locations 

of wells 6, 11 and well 12 (z=2.49 m layer) and at well 6 (z=2.07 m layer), indicating the 

importance of data collected at those places for model calibration. Data collected near wells 7 and 

8, and at all locations of the z=2.07 m layer, except well 6, were the least important value for 

model calibration. This result implies that it is not necessary to collect data at two depths for the 

model calibration, and emphasizes the overall importance of monitoring at the depth 

corresponded to the 2.49 m computational layer. 
6-5 

Figure 6-1 Simulation domain with existing (red symbols) and new (hypothetical) 

observation wells. The numbers at the plot identify new well numbers. 

340

350

360

370

380

390

400

410

455 465 475 485 495 505 515

simulation domain

irrigated plot

old observation wells

new output nodes
6-6

Figure 6-2 Examples of time series of the sensitivity index Si(Ks) for eight materials in well 5 and well 38 
6-7 

Figure 6-3 Number of days with nonzero Si values for each material (a) and Si variations 

in 50 observation wells. 

(b)

New observation well

0 10 20 30 40 50

Si (Ks 

)

-0.15

-0.10

-0.05

0.00

0.05

0.10

0.15

0.20

0.25

Z=2.49 m

Z=2.07 m

(a)

Number of simulation days with nonzero Si values

0

10

20

30

40

50
6-8 

Figure 6-4 New observation locations selected based on maximum Si values (yellow 

triangles) and on averaged OPR statistics (green triangles). 

340

350

360

370

380

390

400

410

455 465 475 485 495 505 515

Simulation domain

irrigated plot

old observation wells

new output nodes

Si index method

OPR method
6-9 

The importance of the new observation locations for the HYDRUS-3D calibration was evaluated 

using the OPR+ statistic. The Si values computed for two depths at 50 locations shown in Fig. 6-1 

were averaged over time periods showing nonzero values and used to calculate the matrix of 

sensitivities AY in Eq. 6-6. The matrix of weights ω on the observations was represented by the 

proportion of simulation days with nonzero Si values over the total simulation period (131 days). 

The standard deviations computed for locations at wells 5 through 12 for the OPR- statistics were 

used for the denominator in Eq. 6-5. The numerators SYl(+i)

′ in Eq. 6-5 were computed by adding

one output node at a time to the existing nodes. The OPR+ statistics computed for the added 

nodes for two computational layers at 50 locations ranged from 0% to 46.6% and from 0% to 

54.8% for the 2.49 m and 2.07 m computational layers, respectively (Fig. 6-1). The OPR+ values 

averaged across 8 existing observation wells did not change significantly with distance from the 

irrigated plot. However, they were noticeably smaller for some wells at z=2.49 m than at z=2.07 m, 

indicating that data collected from the z=2.49 m layer were less important. 

To identify new locations for improving the HYDRUS-3D calibration, the average OPR+ values 

were ranked in a descending order. The ranks of the new wells were different for the two 

computational layers (Fig. 6-7), with the percentage decrease in uncertainty generally being 

higher for the same rank for the z=2.07 m layer as compared to the 2.49 m layer. The locations of 

the new observations wells were therefor selected based on OPR+ values computed for z=2.07 m. 

The new monitoring locations selected on the basis of high Si values and using the OPR+ statistics 

along with the existing monitoring locations are shown in Fig. 6-4. The locations obtained using 

both methods were very close to each other and indicated the preferential flow direction of the 

tracer. Nevertheless, the locations selected using the OPR+ method were slightly northward from 

the locations having high Si values in the first three transects (wells 1-10, wells 11-20 and wells 

21-30) . These mismatches can be caused by differences in the approaches used in the two 

methods. The Si-based method analyses values of the sensitivity separately at each observation 

location and indicates the locations with the highest sensitivity. These locations were between 

wells 6 and 7 in the existing monitoring network, where the highest concentrations were calculated 

(Fig. 5-2). The OPR+ method examines the spatial distribution of Si values weighed by the number 

of nonzero values and selects the locations were Si values were not necessarily high, but were 

changing spatially. For instance, new observation location 16 between wells 7 (location 15) and 8 

(location 17) in the existing monitoring network was in a transitional zone from relatively high 

concentrations in well 7 to low concentrations in well 8, indicating considerable uncertainty in the 

Si values computed for location 17. 
6-10

Figure 6-5 Percent of increased uncertainty caused by removal one existing observation 

well. New observation well numbers are shown in parenthesis on X-axis. 

Z = 2.49 m

-5

0

5

10

15

20

Z = 2.07 m

Existing observation wells

4 5 6 7 8 9 10 11 12 13

Percent of increased uncertainty

-5

0

5

10

15

20

(11) (13) (15) (17) (19) (32) (36) (40) 
6-11

Figure 6-6 Percent of decreased uncertainty caused by adding one new observation well. 

Z = 2.49 m

-10

0

10

20

30

40

50

Z = 2.07 m

New observation wells

0 10 20 30 40 50

Percent of decreased uncertainty

-10

0

10

20

30

40

50
6-12

Figure 6-7 Ranks of new observation wells at two depths computed based on the percent 

of decreased uncertainty caused by adding one new well. 

New well for Z=2.07 m 

7 6 48 30 8 38 50 16 9 29 49 4 3 23 2 5 14 39 12 21 24 10 26 1 46 27 28 22 18 37 25 47 35 31 45 42 43 41 20 33 34 44 Percent of decreased uncertanty 

0

2

4

6

8

10

New well for Z=2.49 m 

7 6 8 22 34 30 5 44 4 3 38 21 9 49 33 2 14 31 43 24 16 29 39 42 12 48 46 10 1 23 27 26 25 47 35 37 41 28 45 18 20 50

Z=2.49 m

Z=2.07 m
6-13

Overall, both statistical methods provided useful additional information for optimization of the 

monitoring network, specifically for model calibration purposes. The method using the 

observation-prediction (OPR) statistic accounts for both model sensitivity to the parameters and 

their spatial structure. Based on results of this study, the ARS study team recommend using the 

OPR+ method for selecting monitoring locations to improve model calibration. 

6.1.3 Selecting Monitoring Locations Based on Statistical Analysis of the Performance 

Indicators 

To identify optimal locations for monitoring propagation of the contaminant plume from the source, 

the ARS study team used the results of 48 simulations for different weather, groundwater level 

and release scenarios as described earlier in section 5.2.3. Plume propagation was evaluated 

using again three performance indicators: Cpeak, Tpeak and QC computed for each of the 100 output 

nodes. Two approaches were used to select the monitoring locations. The first approach was 

based on the frequencies of appearance of extreme values of the performance indicators 

evaluated at different distances from the release points, while the second approach used the 

probability analysis. 

To implement the first approach the minimum values of Tpeak (Tpeak

min ), and maximum values of Cpeak

(Cpeak

max ) and QC (QCpeak

max ) were computed for each transect passing through the output nodes 

located at the same distance from the release points. These values were computed using the 

results of HYDRUS-3D simulations with the calibrated parameters separately for each scenario. 

One location within each transect with the minimum value of Tpeak

min , and maximum value of Cpeak

max

 

or QCpeak

max was chosen as a potential monitoring location for this transect. Locations were selected 

in the same manner for each performance indicator at all 11 transects and for all 48 scenarios. 

The ARS study team next analyzed the frequency of appearance of the selected locations at each 

transect using results of the 48 simulations. The frequency distributions for the Cpeak performance 

indicator at 11 transects is shown in Fig. 6-8a. The distributions typically had a sharp peak at one 

of the locations. The maximum frequency values were 0.68±0.17, 0.78±0.13 and 0.65±0.21 for 

Cpeak, Tpeak and QC, respectively, which indicates high probabilities of detecting the contaminant 

plume using the selected locations. 

Monitoring locations identified based on the frequency approach are mapped in Fig. 6-8b. Overall, 

the locations selected using the QC indicator were in good agreement with those selected using 

the Cpeak performance indicator, while Tpeak-based locations were shifted from 10 to 20 m to the 

north from the Cpeak- and QC-based locations. The shift between the locations selected using 

different performance indicators increased with the tracer travel distance (Fig. 6-8b). The 20 m 

shift is significant for a 100 m travel distance, and can be even more pronounced for large-scale 

simulations. 

To implement the second approach for selecting new monitoring locations, now based a 

probability analysis, the ARS study team analyzed the spatial distributions of performance 

indicators obtained with the 48 simulations using the calibrated HYDRUS-3D model. The ARS 

study team mapped for this purpose 
6-14

Figure 6-8 Frequency distributions for the Cpeak

max in 11 transects (a), and monitoring 

locations selected based on the frequency distributions of 3 performance 

indicators (b). 
6-15

mapped the values of 3 performance indicators at 25%, 50% and 75% probability level. These 

levels will specify for each output node the probability that the performance indicator obtained with 

the 48 simulation scenarios will not exceed the value of the performance indicator at that 

probability level. For instance, Cpeak

75% means that the Cpeak values computed for 36 scenarios at 

this node will be smaller than Cpeak

75% , while Cpeak values will be greater than Cpeak75% value at this 

node only for 12 scenarios. 

The spatial distributions of log10(Cpeak), Tpeak and log10(QC) for three probability levels are shown in 

Fig. 6-9. The spatial variability generally decreased for Cpeak and QC, and increased for the Tpeak

performance indicator with an increase in the probability level. For instance Cpeak varied within 7, 5 

and 4 orders of magnitude for the 25%, 59% and 75% probability levels, respectively (Fig. 6-9). 

High Cpeak variability translated into considerably variability in the QC values, which ranged within 

7.5, 6.5 and 5.5 orders of magnitude for the same probability levels. To identify potential locations 

for the monitoring network examined persistence of high PI values within each transect. The 

persistence was assessed as an interquartile range (PIpeak

75% − PIpeak25% ), while the values of the 

performance indicators were taken at 50% probability level. 

Generally, an increase in the interquartile range with the PIpeak

50% increase was observed in this 

study, which indicates variation in the flow direction associated with the source location and 

groundwater scenarios. Therefore very few locations with PI values smaller than PIpeak

50% were 

selected, while in most cases locations with maximum PIpeak

50% were chosen for Cpeak and QC PI 

within each transect. The locations with the smallest travel times Tpeak

5o% were selected for Tpeak 

performance indicator. The selected locations are shown in Fig. 6-10b. The selected locations are 

shown in Fig. 6-10b. The spatial position of the observation network was very similar to that 

obtained using the frequency approach (Fig. 6-10a), which confirms the reliability of the 

implemented approaches. 

Overall, both the frequency and probability of peak performance indicators appear to be 

appropriate statistics to identify monitoring locations with the highest probability of contaminant 

plume detection. The observed differences between the time-based (Tpeak) and concentration 

(Cpeak) or flux-based (QC) performance indicators can be attributed to the different nature of these 

indicators. The arrival time is not always a good predictor of plume propagation in highly 

heterogeneous media due to combined effect of the contaminant dispersion and dilution, which 

may lead to very rapid transport of relatively small amounts of contaminant. As such, the Cpeak and 

QC performance indicators appear to be more reliable for identifying monitoring locations. 

6.1.4 Model Abstraction Applicability for Selection of Monitoring Locations 

The applicability of the model abstraction techniques described in sections 5.2.5-5.2.7 is tested in 

this section for selection of monitoring locations. To do this the ARS study team examined the 

spatial distributions of the performance indicators obtained with HYDRUS-3D using the abstracted 

parameters (section 5.2.5), using profile aggregation (section 5.2.6) and using the abstraction of 

ignoring the unsaturated zone (section 5.2.7). Similar to section 6.2.1, values of the performance 

indicators at probability levels of 25%, 50% and 75% were plotted as contour maps. Spatial 

distributions obtained for the three model abstractions were found to be different. Patterns of the 

Cpeak and QC indicators obtained with parameter abstraction (Fig. 6-11) in general resembled the 

patterns of the calibrated HYDRUS-3D model. However, the absolute values of the performance 
6-16

Figure 6-9 Spatial distributions of the performance indicators at 3 probability levels 

obtained in HYDRUS-3D simulations with the calibrated parameters. 25% probability

320

340

360

380

400 -6 

-4 

-2 

0 

2 50% probability

320

340

360

380

400

520 530 540 550 560 570 580 590 75% probability

320

340

360

380

400

1000 

2000 

3000 

4000 

520 530 540 550 560 570 580 590

-4 

-2 

0 

2 

520 530 540 550 560 570 580 590

 log10 (Cpeak) Tpeak log10 (QC)
6-17

 

Figure 6-10 Monitoring locations selected using the frequency (a) and probability (b) 

approaches for 3 performance indicators. 

 domain boundary

x output nodes 

 release locations

 Cpeak

 Tpeak

 Flux QC

(b)

(a)
6-18

indicators were somewhat different. Specifically the abstracted model systematically 

underestimated peak concentrations and overestimated total fluxes (Fig. 6-9 and Fig. 6-11). Little 

or no similarities were found between the travel times of the calibrated and abstracted models. 

Abstraction to a homogeneous soil profile produced even greater differences with the original 

model. The shapes of the plume and absolute values of the performance indicators for the 

homogeneous profile model significantly deviated from the calibrated heterogeneous model (Fig. 

6-8). The flow direction, viewed as a line with the smallest gradient in the performance indicator, 

was shifted towards south in the abstracted model compared to the original one. 

No differences in the spatial patterns of the performance indicators between the original and 

abstracted model were found when the abstraction of ignoring the unsaturation zone was 

implemented. The spatial distributions of the three performance indicators were reproduced by the 

abstracted model with high accuracy at the 25%, 50% and 75% probability levels (Fig. 6-13). This 

result was expected since this abstraction adequately reproduced predicted concentrations and 

fluxes as was shown in section 5.2.7. To test the applicability of the three abstraction techniques 

to selecting monitoring locations, both the frequency and probability approaches were 

implemented to the spatial distributions of performance indicators. Peak values of the 

performance indicators were used for the frequency approach, while the peak and inter quartile 

range values were used both in the probability approach as described in section 6.2.1. 

Monitoring locations for the two abstractions, along with the original model, are shown in Fig. 6-

14. The parameter abstraction generated similar monitoring networks for the Cpeak and QC

performance indicators, while locations identified using Tpeak values were shifted 10 to 20 m to the 

north (Fig. 6-14b). This shift was not systematic, which indicates a weakness of the Tpeak indicator. 

Differences between the two approaches for location selection were minor for the Cpeak and QC 

indicators, but noticeable for Tpeak. This could be attributed to the different sensitivity of the 

different approaches to the shape of the performance indicator distributions. In spite of the 

observed differences between the absolute values of Cpeak and QC, the observation locations for 

the abstracted model were very close to those obtained with the calibrated model. For the 

frequency approach, 6 and 7 out of 10 locations for the Cpeak and QC indicators, respectively, 

were located 10 m to the north in the abstracted model as compared to the original model (Fig. 6-

14 a,b). These differences were even smaller for the probability approach. Only 3 and 4 out of 10 

locations for the abstraction model did not match the locations of the original model (Fig. 6-14 

d,e). The difference in all cases was 10 m, which is comparable with the output grid resolution. 

Interestingly, the locations selected on the basis of Tpeak values for the abstracted model were not 

systematically shifted from those of the calibrated model. The monitoring locations for the 

abstracted model oscillated around the network obtained for the calibrated model with a 10 m 

amplitude. Overall, in spite of inaccuracies in the parameter abstracted model for predicting 

contaminant concentrations and fluxes, this abstraction approach appeared to be appropriate for 

selecting monitoring location in our study. 

The abstraction by ignoring the unsaturated zone appeared to be the most accurate in predicting 

the tracer concentrations and fluxes, leading to essentially the same monitoring network as the 

calibrated model. Monitoring locations obtained using both the frequency and probability 

approaches for the abstracted model matches for 100% the locations generated by the original 

model (Fig. 6-14 c,f). As discussed in section 6.2.7, this was possible since the unsaturated zone 

was very thin in this study and since spatial heterogeneity in the soil properties caused vertical 

transport to dominate at the release points. These hydrologic conditions created a specific flow 

regime in which the tracer was transported preferentially in the vertical direction before reaching 
6-19

Figure 6-11 Spatial distributions of the performance indicators at 3 probability levels 

obtained in HYDRUS-3D simulations with the abstracted parameters. 25% probability

320

340

360

380

400 -6 

-4 

-2 

0 

2 50% probability

320

340

360

380

400

520 530 540 550 560 570 580 590 75% probability

320

340

360

380

400

1000 

2000 

3000 

4000 

520 530 540 550 560 570 580 590

-4 

-2 

0 

2 

520 530 540 550 560 570 580 590
6-20

Figure 6-12 Spatial distributions of the performance indicators at 3 probability levels 

obtained in HYDRUS-3D simulations with the abstracted soil profile. 25% probability

320

340

360

380

400 -6 

-4 

-2 

0 

2 50% probability

320

340

360

380

400

520 530 540 550 560 570 580 590 75% probability

320

340

360

380

400

1000 

2000 

3000 

4000 

520 530 540 550 560 570 580 590

-4 

-2 

0 

2 

520 530 540 550 560 570 580 590

 log10 (Cpeak) Tpeak log10 (QC)
6-21

Figure 6-13 Spatial distributions of the performance indicators at 3 probability levels 

obtained in HYDRUS-3D simulations with the discarded unsaturated zone. 25% probability

320

340

360

380

400 -6 

-4 

-2 

0 

2 50% probability

320

340

360

380

400

520 530 540 550 560 570 580 590 75% probability

320

340

360

380

400

1000 

2000 

3000 

4000 

520 530 540 550 560 570 580 590

-4 

-2 

0 

2 

520 530 540 550 560 570 580 590

 log10 (Cpeak) Tpeak log10 (QC)
6-22

Figure 6-14 Monitoring locations selected for the calibrated model and two abstractions using the freque

probability (d, e, f) approaches. 

 domain 

boundary

x output nodes

 release 

locations

 Cpeak

 Tpeak

 Flux QC

Calibrated model Parameter abstraction Abstraction discar

unsaturated zone 

(a

)

(b

)

(c

)

(d

)

(e

)

(f)
6-23

groundwater. The results of this abstraction may differ when a thicker vadose zone is present, or 

when horizontal lenses may slow down vertical transport. 

Using a homogeneous soil profile was the only abstraction technique that generated a monitoring 

network dissimilar to the network obtained with the calibrated HYDRUS model. The selected 

monitoring locations were systematically shifted to the south from those of the calibrated model, 

with the difference increasing with the distance from the source of release (data not further 

shown). This occurred primarily due to existence of preferential lateral flow within the 

heterogeneous simulation domain. These preferential flow path were completely discarded in the 

homogeneous profile abstraction process. Homogeneous soil profile abstraction generally may 

be more appropriate for small scale applications or for situations where vertical soil stratification is 

not important. The natural succession of soil genetic horizons of large scale field projects may 

produce different hydrological regimes at different depths that cannot be ignored when water and 

chemical transport is modeled. The results of this study provide a very remarkable illustration of 

this general concept. 

6.2 Selecting Monitoring Locations for Model Discrimination 

6.2.1 Kullback-Himmelblau Sequential Design Method 

Coupling of modeling and monitoring can be conducted for various purposes. One of the 

purposes can be selection of a better model from a set of models originating, for instance, from 

different conceptualizations of subsurface, from different levels of model complexity, from different 

lists of processes included, etc. The model comparison and discrimination can be improved if 

additional observations will be included. A new observaPtion points can be selected at the 

location where the maximum difference between model predictions is achieved. 

A fruitful approach to evaluate the usefulness of a measurement for distinguishing between two 

hypotheses was proposed in the seminal paper (Kullback and Leibler, 1951) in which the 

information in a measurement for discrimination between two hypotheses was first defined. The 

mean value of this Kullback-Leibler information represented the information gain that could be 

encountered if the true hypothesis were accepted rather than the wrong one. This mean value 

eventually was termed Kullback-Leibler divergence, information gain, relative entropy, or 

information divergence, and was computed for model predictions an estimate of the information 

loss when full truth is approximated by the model (Poeter and Anderson, 2005). This measure 

was proven to be useful in (a) evaluation of predictive capabilities of hydrological models when 

observations presented the ‘true’ distribution that was approximated by model predictions (Weijs 

et al., 2010) , (b) improving inverse solutions of groundwater flow models (Szucs et al, 2006), and 

(c) assessment of improvement in modeling results with data assimilation (Bulygina and Gupta, 

2009). Various approximations of the Kullback-Leibler divergence resulted in development of the 

family of model discrimination criteria, such as Akaike criterion AIC, and later AICc, (Burnham and 

Anderson, 2004) that were used in groundwater modeling to rank calibrated models (Poeter and 

Anderson, 2005; Foglia et al., 2007; Ye et al., 2008;), and in inverse groundwater modeling for 

hydraulic conductivity estimation using Bayesian model averaging (Tsai and Li, 2008). All 

applications of the Kullback-Leibler divergence to model discrimination, however, relied on the 

existing set of observations and did not attempt to seek additional measurements. 

Kullback (1959) showed that Kullback-Leibler information could be also applied for the selection of 

a new observation location to better discriminate between models without making an assumption 

that one of models generates the ‘true’ distribution whereas another one does not.
6-24

Himmelblau (1970) implemented this suggestion for the case of non-linear models. The method is 

as follows: 

Let Y be a random variable that is distributed with a probability density p1

(y ) when hypothesis H1

is true (Model 1) and distributed with a probability density p2

(y ) when hypothesis H2 (Model 2) is 

true. Then in some sense the quantity ln[p1

(y ) p2(y )⁄ ] can be said to be a measure of the odds 

in favor of choosing H1 over H2 or, from the information theory viewpoint, of the information in 

favor of hypothesis H1 as opposed to hypothesis H2. The expected information in favor of choosing 

either H1 or H2 respectively is given by Kullback-Leibler divergences 

I(1: 2) = ∫ p1

(y )

∞

−∞

ln p1

(y )

p2

(y )

dy (6-7)

I(2: 1) = ∫ p2

(y )

∞

−∞

ln p2

(y )

p1

(y )

dy (6-8)

Kullback (1959) proposed that the total information gain due to selecting one model instead of 

another, i.e. value 

J(1,2) = I(1: 2) + I(2: 1) = ∫ [p1

(y ) − p2

(y )]

∞

−∞

ln p1

(y )

p2

(y )

dy (6-9)

be maximized to distinguish between two states of nature. It means that the new monitoring point 

has to be selected where the J(1,2) value reaches maximum. 

From the linearized analysis, one can assume that the (n+1)st observation is normally distributed 

about the expected value for the model, E {Yr

(n+1)} = yr(n+1), with a variance of σY

2

 (Himmelblau, 

1970). Furthermore, yr

(n+1) is distributed in a local (linearized) region about a predicted value, 

Ŷ

r

(n+1), with a variance of σr

2

. Consequently, Y

(n+1) is distributed about Ŷ

r

(n+1) with a variance of 

σY

2 + σr

2

. Thus the probability density of Y

(n+1)

 for the rth model is 

pr(y

(n+1)

) =

1

σY

2+σr

2 exp [−

1

2

(Y

(n+1)−Ŷ

r

(n+1)

)

2

σY

2+σr

2

] , r=1, 2 (6-10)

The quantities Ŷr and σr

2

 represent the mean and variance of Y for the rth model. Kullback (1959) 

showed that substituting (6) into (3) and (4), after completing the integrations yields 

I(1: 2) =

1

2

ln σY

2+σ2

2

σY

2+σ1

2 +

1

2

ln σY

2+σ1

2

σY

2+σ2

2 −

1

2

+

1

2

(Ŷ

1

(n+1)−Ŷ

2

(n+1))

2

σY

2+σ2

2

 (6-11)

I(2: 1) =

1

2

ln σY

2+σ1

2

σY

2+σ2

2 +

1

2

ln σY

2+σ1

2

σY

2+σ1

2 −

1

2

+

1

2

(Ŷ

1

(n+1)−Ŷ

2

(n+1))

2

σY

2+σ1

2

 (6-12)

J(1,2) =

1

2

(σ1

2 − σ2

2

) (

1

σY

2+σ2

2 −

1

σY

2+σ1

2) (Ŷ

r

(n+1) − Ŷ

s

(n+1)

)

2

 (6-13)

Box and Hill (1967) described an improved version of Kullback (1959) discriminant function in 

which the prior probabilities are included. To make full use of prior information available about the 

validity of each model, in addition to computing the estimation coefficients used in Ŷ

r

(n+1)

, it would 

seem reasonable to weight I(1: 2) and I(2: 1) by the respective prior probabilities of Model 1 or 

Model 2 being the correct model, P1

(n)

 and P2

(n)

, respectively. 
6-25

Himmelblau (1970) extended the previous approach by assuming that several competing models 

exist, among which the (n+1)st experiment is to discriminate. A scalar discriminant function can be 

formed using the matrix of relative likelihoods and a vector of prior probabilities as follows: 

Kv = [P1

(n)

 ... Pv

(n)

] ∙ [

I(1: 1) ⋯ I(1: v)

⋮ ⋱ ⋮

I(v: 1) ⋯ I(v: v)

] [P1

(n)

⋮

Pv

(n)

] (6-14)

Each element on the main diagonal of the I(r: s) a matrix is zero so the discriminant function 

becomes: 

Kv =

1

2

∑ ∑ Pr

(n)

Ps

(n)

[

(σr

2−σs2

)

2

(σY

2+σr

2

)(σY

2+σs

2

)

+ (Ŷ

r

(n+1) − Ŷ

s

(n+1)

)

2

(

1

σY

2+σr

2 +

1

σY

2+σs

2)]

v

s=r+1

v

r=1 (6-15)

One way to obtain the posterior probability that model r is correct after taking n observations is to 

apply successively for each model Bayes’ theorem in the following form:

Pr

(n) =

Pr(y(n))

∑ Pr

(n−1)

pr(y(n))

v

r=1

 (6-16)

where pr

(n−1)

 is the prior probability associated with the rth model. The initial probabilities pr

(0)

 can 

be set equal to 1/v if not known. 

In general, neither σY

2

 nor σr

2

, r=1,...v, will be known; hence the values of these variances must be 

estimated. Himmelblau (1970) suggests obtaining the variance of Ŷ

r

 for a model, by using the 

intermediate values (variances and co-variances at the optimal point) obtained in least square 

estimates of the models’ parameters. 

The sequential procedure to discriminate among v models is summarized as follows (Himmelblau, 

1970): 

1. Based on experimental design selected in some arbitrary or suboptimal way, collect n data 

points. 

2. Estimate the parameters in the v models by linear or nonlinear regressions; estimate σY

2

and calculate each σr

2

. 

3. Calculate the prior probabilities for the (n+1)st run which are equal to the posterior 

probabilities for the nth run by using equations (6) and (12) with n substituted for (n+1) in 

the latter. The initial P’s can all be equal to 1/v if no better choice is available. 

4. Select the vector of experimental conditions for the (n+1)st run (the vector x

(n+1) by 

maximizing Kv using a numerical optimization routine. 

5. Run an experiment at x

(n+1) and repeat starting with step 2. 

The sequential procedure continues until one (or more) Pr

(n)

 reaches a value acceptance of the 

model by some criterion. Or the experimenter can just observe the trend of the changes in the Pr 

as the number of experiments increases, drop models with low values of Pr, and add models, if he 

wishes, terminating the experiments when he feels satisfied with the discrimination actually 

achieved. 

Limitations of applying the above procedures to subsurface flow and transport problems are that 

(1) the data are rarely sufficient to calibrate models, and (2) few if any numerical codes are 

available for calibrating 3D models if a variably-saturated subsurface is simulated (even if such 

codes exist, calibration procedure can consume enormous time). As mentioned above, the 

calibration is needed to estimate values of the means and variances for the simulated variables. 
6-26

The latter problem can be overcome by using the assumptions of the ensemble Kalman filter 

(EnKF) methodology. The centerpiece of the EnKF methodology is the hypothesis that the 

covariance matrix of predictions can be obtained by running an ensemble of models and 

computing statistics, including variances and covariances on the predictions. Models in the 

ensemble have the same system of equations (as such it is a single model) but differ in the initial 

conditions, parameter values, and forcings, which may vary in feasible ranges with realistic 

probability distributions to form an ensemble. Using this postulate, one can run ensembles for 

each model to obtain the required values of Ŷr and σr

2

. 

6.2.2 Applications of the Kullback-Himmelblau Method 

In this section the ARS study team presents two examples to demonstrate using the KullbackHimmelblau sequential design (KHSD) method for augmentation of a monitoring network for a 

contaminated aquifer based on data of (1) synthetic simulations, and (2) the OPE3 field tracer 

experiment carried out in 2008. It is assumed that n (≥1) observation locations are available where 

concentrations are measured to obtain breakthrough curves (BTCs) to be used for the model 

calibration. As independent variable, the ARS team selected coordinates (xi, i=n+1,..,N) of 

“imaginary” observation points that compose a grid covering some area downstream to the 

contaminant source location. As response function (Y), the ARS team selected the maximum 

concentration that can be reached at each observation point. The variance (σr

2

) and mean (Ŷ) for 

the rth model at each point is calculated by running models using randomly varying parameters 

within a certain range and computing statistics. The value of the discriminant function (Kv, Eq. (6-

17)) is subsequently calculated at each location. The maximum value of Kv specifies the location of 

the new observation point. 

6.2.2.1 Example of Synthetic Simulations

Consider the aquifer to be composed of relatively homogeneous sediment characterized by a 

loamy sand texture. The simulation domain is presented by a rectangular parallelepiped having 

the size of 50x30x10 m in the x, y and z directions, respectively (Figure 6-15). Flow in the 

saturated zone is essentially one-dimensional in the x-direction. Groundwater is very shallow. 

Constant total hydraulic head values of 9.5 m and 9 m are prescribed along the boundaries at x=0 

and x=50 m respectively; thus creating a hydraulic head gradient of 0.01 in the saturated zone. 

Hydraulic heads along the boundaries y=0 and y=50 m decrease linearly from 9.5 to 9.0 m with 

increasing x. The boundaries at z=0 and z=50 m were subjected to no flux conditions. Initially at 

t=0, the contaminant concentration in the aquifer is assumed to be zero. 

A total of 20 L of contaminated water with a concentration C0 of 100 mg L-1 was injected at the 

location of x0=5, y0=15 and z0=8 m during 0.01 day. Two observation wells were installed at 

Wo1(x=10m, y=13m) and Wo1(x=10m, y=18m) where groundwater was sampled from a depth of 

7.5 m. To create synthetic BTCs, the ARS study team performed simulations with the HYDRUS3D model by imposing the above initial and boundary conditions, as well as the contaminant 

injection. The porous medium hydraulic parameters characterizing loamy sand were taken from 

the HYDRUS database as: θs=0.41, θr=0.057, α=12.4 m-1, n=2.28, and Ks=3.5 m day-1. The 

longitudinal (aL) and transverse (aT) dispersivities were assumed to be 0.75 and 0.15 m, 

respectively. The hydraulic parameters of most or all field problems exhibit spatial variability. To 

account for this the ARS study team generated a lognormally distributed hydraulic conductivity 

field using by using linear scaling transformations (Simunek, et al. 2011) with a scaling parameter 

of 0.25 (Fig. 6-16). 
6-27

The finite element mesh consisted of 33,201 nodes and 60,000 3D elements with mesh sizes of 1 

m in the x- and y-directions, and 0.5 m in the z-direction. Contaminant transport was simulated 

with HYDRUS-3D for a time period of 60 days (the initial observation period). Simulated 

concentration distribution is shown in Figure 6-17.

To apply the KHSD method for augmentation of the monitoring network, one needs at least two 

models. As our first model the ARS study team used the same HYDRUS-3D model; however, 

unlike the synthetic forward simulation, the random hydraulic conductivity field was not introduced 

and the saturated hydraulic conductivity was assumed to be constant. The second model was 

selected based on the assumption that flow in the saturated zone is essentially one dimensional 

and uniform. Solute transport for such conditions can be described with the linear advectiondispersion equation 

R

∂C

∂t = Dx

∂

2C

∂x2 + Dy

∂

2C

∂y2 + Dz

∂

2C

∂z2 − v

∂C

∂x − RλC

+

M

θ

δ(x − x0

)δ(y − y0)δ(z − z0)δ(t − t0) (6-17)

subject to initial condition 

C(x, y, z, 0) = 0 (6-18)

and boundary conditions 

C(±∞, y, z, t) = C(x, ±∞, z, t) = C(x, y, ±∞, t) = 0 (6-19)

where C is contaminant concentration, R is retardation factor, Dx, Dy, Dz and are hydrodynamic 

dispersion coefficients in x, y and z directions, respectively, v is groundwater flow velocity, λ is 

the first order decay rate, M is the contaminant mass released instantaneously at point (x0, y0, z0) 

at time t0, θ is aquifer porosity and δ is the Dirac delta function.

 The analytical solution for the problem (6-17) - (6-19) is (Lenda and Zuber, 1970): 

C(x, y, z, t) =

M

θ

1

8π3 2⁄

1

√DxDyDz⁄R

1

tπ3 2⁄

exp[−λ(t − t0

)]

∙ exp [−

{(x−x0

)−v(t−t0

)⁄R}

2

4Dx(t−t0

)⁄R

] ∙ exp [−

(y−y0

)

2

4Dy(t−t0

)⁄R

] ∙ exp [−

(y−y0

)

2

4Dy(t−t0

)⁄R

] (6-20)
6-28

Figure 6-15 Simulation setup for synthetic example. 

Figure 6-16 Distribution of scaling factor of saturated hydraulic conductivity in the 

simulation domain. 

0

50 m

Wo1 Existing observation wells

Imaginary observation wells

Source of contamination

10 m

30 m

Water table

Wo1

Wo2
6-29

Figure 6-17 Simulated contaminant distribution after 60 days, at the layer of z=7.5 m. 

Wo1

Wo2

Concentration

mg/m3
6-30

Parameters of HYDRUS-3D and the above analytical model must be calibrated using the 

observed BTCs at the observation wells. A manual trial and error calibration procedure was used 

for HYDRUS-3D, while the Levenberg-Marquardt nonlinear optimization method (Marquardt, 

1963) was used to calibrate the analytical model. 

Parameters obtained for the HYDRUS 3D model were Ks=3.2 m day-1, aL=1.0 m and aT=0.17 m. 

These values were not much different from those used to generate the BTCs at observation wells, 

mostly because relatively moderate values of the scaling parameter for log(Ks) was used. Results 

of the HYDRUS trial and error fit for BTCs at the two wells are shown in Figure 6-18a. Transport 

parameters found for analytical solution (6-20) were v=0.123 m/day, Dx=0.202 m2 day-1, Dy=0.015 

m2 day-1 and Dz=0.002 m2 day-1. Results obtained with the analytical model are shown in Figure 6-

18b.

Ninety six imaginary observation wells at z=7.5 m, in the rectangular area bounded by (x,y) 

coordinates: (12,8) m and (34,22) m were chosen to calculate the discriminant function values, Kv

(equation (6-16). The distance between nodes was 2 m in both x- and y-directions (Fig. 6-15). To 

estimate variance (σr

2

) and mean (Ŷ

r

) of the maximum concentrations in those nodes, the ARS 

study team performed 25 runs for each model using randomly varying parameters within a range 

20% from the values found by the inversion. Simulations were executed for a period of 365 days. 

To calculate the Kv values, the ARS study team used the variance and mean of the concentrations 

of the first observation well (Wo1), i.e. =8.4 and =16.1, respectively, as a starting point (the nth 

experiment). The initial values of prior probability were 0.5. Calculated distribution of the 

discriminant function presented in Figure 6-19 indicate a clear maximum at x=22 m and y=16 m, 

which is supposed to become the location of a new observation point. 

Calculation of Kv using data from the second well (Wo2) with =0.85 and =3.4 as the starting point 

did not provide an apparent maximum value within the area of imaginary wells. The ARS team 

assumed that was because of the use of the maximum concentration in the response function. 

The mean maximum concentration in well Wo2 (3.4 μg L-1) was approximately 5 times smaller than 

in Wo1 (16.1 μg L-1).
6-31

 

Figure 6-18 Comparison of the BTCs obtained in the HYDRUS simulations (a) and using 

the analytical model (b) with the observed in two observation wells. 

(a)

(b)
6-32

Figure 6-19 Distribution of the calculated values of discriminant function, Kv. 
6-33

6.2.2.2 Application to the OPE3 Field Experiment

The Kullback-Himmelblau sequential design (KHSD) methodology was tested using data from the 

tracer experiment carried out in 2008 at the USDA-ARS OPE3 integrated research site (Fig. 3-18). 

A pulse of KCl solution was applied to an irrigation plot, and chloride concentrations were 

measured in groundwater at three sampling depths with 12 observations wells. 

The spatial distribution of soil materials was obtained from cores taken from depths of 0-200 cm at 

20 cm increment during installation of the observation wells. Soil texture measured at 12 locations 

between depths of 0.2 m and 2.0 m at 0.2 m increments was grouped into 9 clusters such that 

each class was represented by soil texture averaged over the samples belonging to this class 

texture (Fig. 4-3). These classes included: three sandy loam classes (SL1, SL2 and SL3), two 

sandy clay loam classes (SCL1 and SCL2), two loam classes (L1 and L2), and two silty clay loam 

classes (SiCL1 and SiCL2). 

A 3D conceptual flow and transport model was developed to simulate water flow and chloride 

transport for the tracer experiment at the OPE3 site. The ARS team considered a 3-D layered 

domain that extended laterally for 60 m in the x (east-west) direction and for 50 m in the y (northsouth) direction. The thickness (z direction) of the domain varied from 2.5 m to 4.3 m (Fig. 6-20). 

The finite-element mesh was composed of 6670 nodes and 11088 3D elements. 

The KHSD method was used to search for the optimal location of the augmentation wells on a 2D 

grid including 120 imaginary wells (Fig. 6-20). For the response function the ARS study team 

calculated the maximum observed concentration (Cmax) in each observation well during the 120 

day simulation using HYDRUS-3D. The initial and boundary conditions were prescribed as 

follows: 

- Equilibrium pressure head distributions relative to the groundwater levels measured in 

the observation wells at the beginning of the tracer experiment; 

- Spatially variable, but constant in time, pressure head profiles specified along the lateral 

boundary; 

- Variable initial Cl- distribution as measured in observation wells prior to the experiment; 

- Third type (Cauchy) boundary conditions for transport along the soil surface; 

- Cl- concentrations of groundwater along the lateral boundaries were set to the initial 

concentrations observed before the tracer experiment; 

- Daily-averaged atmospheric boundary conditions at the soil surface beyond the irrigated 

plot, and daily-averaged irrigation depth less runoff at the soil surface within the 

irrigated plot (Fig. 4-7); 

- A zero flux boundary condition along the bottom of the simulated domain; 

- Cl- concentrations of 4940 mg L-1 and 8 mg L-1 in the irrigation water during and after the 

tracer application, respectively. 

The ARS team considered discrimination between two models differing in terms of their 

subsurface structure lithology as follows (see also Fig. 6-21): Model 1 involving a layered medium 

containing 10 layers and 5 materials (every layer was assumed to be homogeneous), and Model 

2 involving a medium with 10 layers and lenses, and 7 soil materials. Locations of lenses were 

delineated manually. 
6-34

Figure 6-20 Modeling domain with finite element mesh and observation locations. 

Figure 6-21 Soil materials in two subsurface structure models: a) Model 1 - Layered media, 

b) Model 2 - Layers and lenses media (shown layers 4-10) 3.9 m

60 m

50 m

Irrigated

area

L1

L2

L3

L4

Existing monitoring well

x

y

z

Imaginary monitoring well

x

y

z

L8

L9

L12

L7

L6 L10

L11

L5 3.9 m

60 m

50 m

Irrigated

area

L1

L2

L3

L4

Existing monitoring well

x

y

z

Imaginary monitoring well

x

y

z

L8

L9

L12

L7

L6 L10

L11

L5
6-35

The hydraulic conductivities and dispersivities were calibrated manually, while pedotransfer 

functions were used to condition the calibration results to produce an ensemble of models. Model 

parameters are presented in Table 6-1. The ensemble modeling was used to estimate variances 

of the means of model response (Cmax) distributions. The ensembles of 25 realizations for each 

model were simulated by generating a lognormally distributed saturated hydraulic conductivity 

field with a prescribed standard deviation of log10(Ks) equal to 0.25. An example stochastic 

realization of the hydraulic conductivity scaling factor is shown in Fig. 6-22). 

Figure 6-23 shows the spatial distribution of the tracer concentration at the end of the simulation 

time. The ARS team noted that the distribution simulated using Model 2 exhibited a more definite 

preferential flow and transport patterns as compared to Model 1. Simulated BTCs at eight existing 

monitoring well (L5-L12) are presented in Fig. 6-24 for the two models. Values of the discriminant 

function, Kv, were evaluated at 120 locations of the imaginary monitoring wells (Fig. 6-20) on the 

5th grid layer. 

Five simulation scenarios were carried out by assuming that the nth experiment was performed in 

different existing monitoring well (those at locations L5 to L9). When using Bayesian estimates to 

calculate the discriminant function (Eq. 6-17), specific locations of max(Kv) were very different in 

each of the five simulations. The ARS team suggests that this was because of a lack of a good 

calibration of the model affecting the calculation of prior and posterior probabilities. Applying the 

simpler equation (6-13), which disregards Bayesian estimates, provided similar results for all five 

simulations as shown in Fig. 6-25. The maximum of Kv was located at x=498-500 m and y=370 m, 

east of well L8. The distinction between the BTCs simulated with two models was most significant 

at L8 (Fig. 6-17). Another local maximum was found between wells L6 and L10. The difference 

between the two BTCs was also considerable at well L6 (Fig. 6-24). 

Table 6-1 Model parameters found by trial-and error method. 

Parameter

Texture

 r

 s

 ,

m-1

n Ks

m/day

aL

m

aT

m

Material 1 0.049 0.361 2.31 1.37 0.3 0.25 0.05

Material 2 0.046 0.331 3.06 1.26 0.3 0.25 0.05

Material 3 0.0422 0.317 3.54 1.24 1.0 0.25 0.05

Material 4 0.044 0.313 3.30 1.22 0.2 0.25 0.05

Material 5 0.047 0.314 2.51 1.23 0.1 0.25 0.05

Material 6 0.060 0.328 1.22 1.32 0.01 0.25 0.05

Material 7 0.060 0.328 1.22 1.32 0.0001 0.25 0.05
6-36

Figure 6-22 Example of a stochastic realization for the hydraulic conductivity scaling 

factor (SF). 

Figure 6-23 Spatial distribution of tracer concentration after 120 days in 5th layer (z=2.75 

m): a) Model 1, b) Model 2. 

L

a) b)
6-37

Figure 6-24 Simulations of the tracer BTCs in locations 5-12: a) Model 1; b) Model 2. 

(a)

Random realization

Mean

Observed

(b)
6-38

Figure 6-25 Discriminant function (Kv) distribution in five simulations: (a)-(e) scenarios of 

the nth experiment was performed in wells L5-L9, respectively. 

a) b ) c) d ) e)

X, m X, m X, m Y, m

X, m X, m
7-1 

7 SUMMMARY AND CONCLUSIONS 

The objective of this project was to demonstrate applicability of model abstraction techniques for 

optimization of monitoring networks at US NRC licensing sites. The study focused on two aspects 

of network optimization: (1) identification of performance indicators providing reliable information 

about subsurface contaminant transport, and (b) defining monitoring locations that would improve 

model calibration and reduce risk of incorrect detection of contaminant releases. 

To accomplish the project goal, the ARS study team used data from the OPE3 experimental field 

site near Beltsville, MD. This site has been extensively studied for more than 10 years using 

physical, geophysical, biophysical, remote sensing, and groundwater monitoring methods. All 

available data were analyzed in a systematic way and used to construct a conceptual site model 

and simulation domain. Special attention was paid to the spatial heterogeneity and organization of 

soil structural units composing the OPE3 site. 

A complex set of methods was employed to study the heterogeneity. A ground penetrating radar 

survey was conducted with 2x2 m spatial resolution and a scanning depth of approximately 3 m. 

Results of the survey were analyzed jointly with the water content monitoring data to delineate soil 

hydrologic layers. Results of the soil surveys conducted within the 10-year study period revealed 

considerable heterogeneity at the site, and provided detailed information about spatial 

organization of the soil structural units. The spatial heterogeneity was confirmed by direct and 

remote measurements at different scales. At the soil core scale these methods included soil 

chemical analysis, soil texture analysis, and measurements of the soil bulk density, soil water 

retention and saturated hydraulic conductivity. At the soil profile scale the ARS team used soil 

water content, pressure head and groundwater monitoring. At the field scale, methods of 

electromagnetic induction, electrical resistivity, color infrared imaging and direct measurements of 

corn biomass were implemented. 

At the soil core scale laboratory water retention data clearly indicated the presence of soil 

macroporosity that potentially could cause fine-scale high-conductivities in parts of the soil pore 

space. Hydraulic conductivity measurements at the same scale showed that, in actuality, such 

high conductivity regions would require not only the presence of macropores but also of a 

connectivity between these pores, which could be found only in a relatively small percentage of 

locations. 

At the soil profile scale soil moisture and soil pressure head monitoring data provided the required 

information about field hydraulic properties of unsaturated soils. Field water retention was well 

defined by those measurements. This indicated that the Richards model would be an appropriate 

conceptualization of the flow processes in the soils under study. 

Soil electrical resistivity monitoring at the field scale further revealed the existence of narrow 

hydrologically active vertical zones. The obtained data indicated that some parts of the subsurface 

did 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 conditions for plant growth. The size of those units exceeded the scale 

of investigation of this project. 

To validate applicability of the model abstraction techniques for model calibration, a field 

experimental study was designed and carried out. The experiment involved the application of a 

pulse of conservative tracer on a 10x10 m plot equipped to monitor soil water contents, 
7-2 

pressure heads, groundwater depths and runoff. The tracer concentrations were monitored at 3 

depths in 5 and 3 wells installed at distances of 7 m and 14 m from the irrigated plot, respectively. 

The concentration measurements were supplemented with water content and groundwater depth 

data for all wells. The data collected within the 130-day monitoring period provided information for 

model calibration. The collected dataset included 28 breakthrough curves measured at 12 

locations (involving a total of 7,280 tracer concentrations). The data indicated the presence of a 

fine-textured, low-permeability layer diverting 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 model. For this reason, the ARS study team 

used the HYDRUS-3D and TOUGH2 software packages to simulate flow and transport in the 

lateral flow experiment. For the TOUGH2 simulations, the radionuclide/tracer transport module 

T2R3D was coupled with the EOS9 module describing a saturated-unsaturated water flow in a 

porous medium. 

Since both models do not have a calibration option, trial and error calibration was applied in this 

study. The calibration objective functions consisted of deviations of simulated groundwater depths 

and measured concentrations. The calibrated parameters were the saturated hydraulic 

conductivity and the longitudinal dispersivity of 8 soil materials composing the simulation domain. 

The ratio of longitudinal to transversal dispersivity was set to 5 in all simulations to reduce the 

number of fitting parameters. The water retention parameters were estimated from basic soil 

properties using the ROSETTA software for all materials. The trial-and-error calibration was 

reasonably successful for HYDRUS-3D, yielding satisfactory description of the peak 

concentrations and their arrival times. However, both models failed to reproduce accurately the 

shape of the breakthrough curves, while the peaks in concentration could not be predicted with 

the TOUGH2 simulations. 

A sensitivity analysis was conducted to evaluate applicability of the different abstraction 

techniques to simplify the calibrated model. Using modeling results, the ARS team examined the 

combination of the simulation domain composition with specific transport properties and fluxes on 

the domain boundaries. The variance-based first order sensitivity coefficient (Si) and the 

derivative-based sensitivity index (Di) were used in the sensitivity analysis. Four abstraction 

techniques were tested using HYDRUS-3D and TOUGH2: (1) parameter abstraction, (2) 

subsurface textural units, (3) boundary conditions, and (4) time influence. The accuracies of the 

abstraction techniques were evaluated in terms of three performance indicators: (1) the tracer 

time series, (2) the peak concentrations (Cpeak), and (3) the times to peak concentration (Tpeak). 

Results of the sensitivity analysis showed that introducing the peak concentration and the time to 

peak concentration as performance indicators for the LSA allowed a significant reduction in the 

input information for the sensitivity analysis, and definition of the soil material that could be used 

for model simplification. The results also revealed a limitation of the Cpeak and Tpeak performance 

indicators in that they needed having peaks on the simulated BTCs. Both parameter abstraction 

and alteration of the boundary between soil materials (abstraction of subsurface textural units) 

identified the same material as a candidate for model simplification. Further analysis showed that 

this material could be replaced with another material with similar soil texture. 

Among the boundary conditions, averaging evapotranspiration rates did not affect the 

performance indicators, while runoff and groundwater depth did have an effect and therefore were 

not a subjected to model simplification. The sampling time influenced the performance indicators 

when the sampling intervals were longer than 2 and 10 days within and beyond the irrigated plot, 
7-3 

respectively. Overall, the sensitivity analysis appeared to be a useful tool to identify the directions 

for model abstraction. 

Results of the sensitivity analysis were also used to evaluate the importance of observations 

collected in the monitoring wells during the lateral flow experiment, and to identify new locations to 

improve the HYDRUS-3D calibration. To do this, the ARS study team implemented the 

Observation-Prediction statistics (OPR) method, which computes the percent of changed 

uncertainty OPR caused by omitting or adding one observation node. The OPR method indicated 

that there was no need for data collection at two depths for model calibration, and emphasized the 

overall importance of monitoring at a depth corresponding to the z=2.49 m computational layer. 

The OPR method also appeared to be sensitive to values of the sensitivity parameters and their 

spatial structure. New monitoring wells identified using the OPR method were located in zones of 

transition from relatively high to low concentrations where the maximum model predicting 

uncertainty can be expected. Based on results of this study, the OPR method is recommended for 

selecting monitoring locations to improve model calibration. 

The applicability of different abstraction approaches was also evaluated at the scale of a 

decommissioning or license NRC site. The size of the simulation domain for this purpose was 

increased to 118x190 m to mimic the scale of a NRC site. Soil properties and boundary conditions 

of the extended domain were set based on a 10-year soil survey and groundwater monitoring 

data. Three precipitation scenarios were generated based on 60-year weather data in Beltsville, 

MD. These scenarios included decades with 25%, 50% and 75% probabilities of the precipitation. 

The ARS study team assumed that the 10-year simulation period was sufficient for the tracer 

travel distance between the irrigation plot and the eastern edge of the simulation domain, and that 

the three selected probabilities adequately represent the temporal variability of precipitation. 

Four release scenarios and four groundwater scenarios represented uncertainties associated with 

the source of the contaminant release and the subsurface flow conditions. The release was 

simulated as a 10-day contaminant pulse from either the east-north or east-south points within the 

irrigated plot located on the surface or at the depth of 2.3 m. A total of 48 different scenarios were 

generated for HYDRUS-3D simulations, which included: 4 release scenarios x 4 groundwater 

scenarios x 3 precipitation scenarios. These scenarios provided input for the model abstraction 

techniques. 

The simulated tracer concentrations and fluxes were chosen in this study to characterize the 

tracer spread from the potential points of accidental release, while the simulated peak 

concentration (Cpeak) and time to peak concentration (Tpeak) at the observation nodes and 

transects at different distances from the release points characterized the direction and velocity of 

the contaminant plume. The accuracy of the model abstraction techniques was evaluated using 

the Nash and Sutcliffe efficiency criterion, the Willmot efficiency criterion and the coefficient of 

determination. 

Three abstraction techniques were validated for this scale. They were: (1) abstraction using 

pedotransfer functions, (2) profile aggregation, and (3) abstraction by ignoring the unsaturated 

zone. In abstraction (1) the calibrated values of the saturated hydraulic conductivities were 

replaced by their PTF estimates, in abstraction (2) the heterogeneous soil profile was replaced 

with a homogeneous profile composed of the dominant soil material in the domain, while in 

abstraction (3) unsaturated contaminant transport was discarded by placing the release source on 

the groundwater table. Techniques (1) and (2) were found to be inappropriate for model 

abstraction. This was confirmed by all performance indicators. Technique (1) altered significantly 
7-4 

the contaminant concentrations, flow velocities and total mass transported, while technique (2) 

altered the flow direction. Ignoring the unsaturated zone appeared to be the only abstraction 

applicable for model simplification in our study. This result was attributed to the presence of 

perched water in our study and should be used cautiously at NRC sites with thick unsaturated 

zones. 

The same abstraction techniques were used to identify monitoring locations that had high 

probability to detect contaminant release and transport from a NRC decommissioning or licensing 

site. Results of HYDRUS-3D simulations for 48 scenarios were used to identify locations at 

different distances from the release points with (a) more frequent, and (b) more probable and 

persistent appearance of extreme values of the performance indicators, while the second 

approach involved a probability analysis. Overall, both the frequency and probability of the peak 

performance indicators appeared to provide appropriate statistics to identify monitoring locations 

with highest probability of contaminant plume detection. The observed difference between the 

time-based (Tpeak) and concentration- (Cpeak) or flux- (QC) based performance indicators were 

attributed to the different nature of the indicators. Arrival time did not appear to be a good 

predictor of plume propagation in high heterogeneous media due to the combined effect of 

contaminant dispersion and dilution on contaminant transport. The Cpeak and QC indicators were 

more reliable to identify the monitoring locations in this study. 

Validation of the three model abstraction techniques to identify monitoring locations confirmed 

applicability of the abstraction by ignoring the unsaturated zone for contaminant transport 

monitoring. However, the results of this abstraction may differ when a thicker vadose zone is 

present, or when horizontal lenses may slow down vertical transport. Monitoring locations 

obtained using the abstracted model matched the network identified by the calibrated model. In 

case of parameter abstraction, the abstracted model systematically underestimated peak 

concentrations and overestimated total fluxes. Little or no similarities were found between the 

travel times of the calibrated and abstracted models. Surprisingly, in spite of inaccuracies in the 

parameter abstracted model, the parameter abstraction approach appeared to be appropriate for 

monitoring location selection in this study. The homogeneous soil profile was the only abstraction 

technique which generated a monitoring network dissimilar to the network obtained with the 

calibrated HYDRUS model. The selected monitoring locations were systematically shifted to the 

south from the calibrated model, with the difference increasing with the distance from the source 

of release. This occurred primarily due to existence of the preferential lateral flow in the 

heterogeneous simulation domain, which was entirely discarded using homogeneous profile 

abstraction. 

Overall, this study demonstrated that model abstraction is an important component for 

development of monitoring strategies at NRC decommissioning or licensing sites. At the stage of 

data collection and analysis, model abstraction can identify sources of predictive uncertainty and 

optimize monitoring networks for the model calibration specific for the selected performance 

indicators. At the monitoring stage, model abstraction serves as a tool for model conceptualization 

and calibration. The calibrated model in turn provides most probable directions and velocities of 

contaminant transport from a potential release point under different scenarios, even when the 

source and the released mass are not well defined. Based on the model predictions some old 

locations can be excluded and new locations can be included into the monitoring network to 

provide more reliable information about potential contaminant transport from the release points. 

This multistep approach can be iterative since new monitoring data can provide important 

information for model conceptualization and improvement of the model calibration. 
7-5 

The Kullback-Himmelblau sequential design method was used for augmentation of the monitoring 

well network assuming that comparison and discrimination of models can be improved if additional 

observations are included. The method is based on (1) generalization of Kullback’s discriminant 

function and “weights of evidence” for the case of available prior probabilities, and (2) ensemble 

modeling to estimate the variance of the predicted values. The method was tested using data from 

(1) a synthetic example generated with HYDRUS-3D by simulating pulse injection of a 

conservative pollutant into an aquifer composed of relatively uniform sediments, and (2) the tracer 

experiment at the USDA-ARS OPE3 integrated research site, carried out in 2008. In each case 

two models were used for the simulations: a complex and an abstracted model. Models used for 

the synthetic example were the HYDRUS-3D model, and an analytical solution of Lenda and 

Zuber (1970) for 1D uniform flow and 3D transport. 

To simulate flow and chloride transport for the tracer experiment at the OPE3 site two threedimensional flow and transport models were used based on the HYDRUS-3D code: a model 

representing a layered medium; and a model accounting for many layers and lenses. Calibration 

of hydraulic conductivities and dispersivities was performed, and pedotransfer functions were 

conditioned to calibration results to build an ensemble of models. A search of the optimal location 

for augmentation wells was carried out on a 2D grid downstream of the tracer injection. A single 

response function of the maximum observed concentration was used to discriminate between the 

models. Results indicate that the KHSD method can be used to find the optimum location of 

additional observation wells. Well-calibrated models provide a single optimal location, but if 

models are not well calibrated the Bayesian estimates strongly depend on the sequence of 

observation wells. Generalization of the method is possible for multiple response cases, such as 

maximum concentrations and arrival times. The information theory-based KHSD method to 

augment the observation network shows promise for improving the monitoring of flow and 

transport for discrimination of conceptual models of the subsurface. Outcomes of this study can 

provide information for future data collection and monitoring efforts that further reduce the 

uncertainty. 

8-1 

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A-1 

APPENDIX A REVIEWING ASSUMPTIONS MADE DURING DEVELOPMENT 

 OF THE BASE MODEL ANDJUSTIFICATIONS FOR 

 THOSE ASSUMPTIONS 

Subsurface structural units 

The vadose zone typically consists 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 the water content. 

Because of 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 fullfledged 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?

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 sitespecific and generic information. The geological, hydrogeologic, and hydrogeophysical 

assessment could benefit greatly from complementary sources such as types of stream 

hydrographs, the presence and hydrology of springs, the presence of paleosoils, documented 
A-2 

fragipans, experience during well construction, occurrence and concentrations of agricultural 

chemicals in well water, and crop yield variability in dry years. 

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 the 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

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

 flow and transport need to be considered jointly, without assuming some rule of

fluid and mass exchange between the vadose zone and groundwater

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. 
A-3 

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 long simulation periods (e.g., 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. 

Estimated model parameters 

Estimated parameter values must be obtained and reviewed whether or now calibration is applied. 

The estimated parameters for flow and transport either: 

 are used directly in the simulations

 serve as initial estimates for model calibration

 are 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

 unsaturated 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

 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-4 

A match in the scale of an experiment is important when selecting literature values of the 

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). 

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

 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 
A-5 

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. 

Calibration procedure and results 

Two calibration methods are used most often in vadose zone flow and transport modeling: trialand-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 one-dimensional 

simulations. Calibration in two- and three-dimensional simulations is usually achieved using trialand-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 

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. 
A-6 

Model documentation 

Reviewing the documentation of a model is an essential component of the base model review. 

Reilly 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 this appendix have 

to be included in the documentation. 
B-1 

APPENDIX B THE QUASI-3D CODE BENCHMARKING 

B.1 Model Evaluation Procedure 

The QUASI-3D model described in section 4.3.1 was tested and benchmarked against the 

corresponding full numerical code, FULL-3D. At a first stage, the performance of the FULL-3D and 

the QUASI-3D codes were assessed against measured and simulated water flow through a sandy 

soil using the laboratory setup of Vauclin (1979). This experiment was simulated earlier with the 

VSF model (Thoms et al., 2006) and the HYDRUS-1D-MODFLOW model (Twarakavi et al., 

2008). At a second stage, the performance of FULL-3D and QUASI-3D was compared against 

simulations with synthetic data of 3D problems addressing infiltration, pumping and groundwater 

mound dissipation through soils with different hydraulic properties. Benchmarking against 

available analytical solutions was also performed. Comparisons were made with reference to the 

following metrics. 

 The maximum difference between simulated groundwater levels with the QUASI-3D 

(

Z 3DQ

) and the FULL3D (

Z 3DF

) codes, at the end of the simulation period: 

max( ) max 3 ZZ 3DFDQdZ   (B1) 

 The maximum relative difference between simulated groundwater levels at the end of the 

simulation period 

max[( ]/) max 3 3 3DFDFDQ

rel dZ   ZZZ

 (B2) 

 Mass balance error, Merr, assessed by 

err (fin ini

 QQWWM s*/) 100%

 (B3) 

where Wini and Wfin are the initial and final water storage in the investigated 

domain, Q is the difference between total amounts of injected and pumped water, 

and 

Qs

 is the sum of the absolute values of injected and pumped water volume. 

 The number of time steps, Nt, required for the simulation. 

 The total computation time, CPU. 

 The average number of iterations (accounting for the nonlinearity) within a time step, niter.

This refers to the total number of iterations Niter during a specific simulation divided by the 

number of time steps needed for this simulation. It characterizes the computations load 

needed to build the linearized matrix of the algebraic equations. 

 The average number of iterations per solution of the linear system of equations at one 

iteration, nlin, commencing from the original nonlinear system. This addresses the total 

number of iterations needed to solve the linear system of (8), for which Nlin, is divided by 

the total number of iteration Niter. This characterizes the proportion of computations needed 

to solve the linearized system of the FD equations, (8), using the PCG2-MODFLOW 

routines based on the modified incomplete Cholesky Preconditioned Conjugate Gradients 

method (Hill, 1990) 
B-2 

B.1.1 2-D Variably Saturated Transient Infiltration Observed in Laboratory Experiments 

Results obtained with several models are compared in this section, including against observed 

laboratory data by Vauclin et al. (1979), The laboratory experiment was conducted using a 6 m 

long, 2 m high box was filled with sandy soil. Two drainage outlets were set at the box walls at 

0.65 m from its bottom. Each outlet was connected to a reservoir in which a level of 0.65 m above 

the bottom of the box was maintained during the entire experiment. At the beginning, the 

experimental system was maintained in hydraulic equilibrium with soil in full saturation at and 

below the levels of the drainage outlets. Water was applied for 8 hours at a 2x1 m2 strip in the 

center of the soil surface at a rate Q of 3.55 m day-1. The remainder of the soil surface was sealed 

to prevent evaporation. The simulation was carried out using the following soil hydraulic 

parameters: θs=0.30 m3 m-3, θr = 0.01 m3 m-3, α= 3. 3 m-1, n = 4.1, and Ks=8.50 m day-1. 

To compare the performance of the FULL-3D code with VSF, The ARS team followed the same 

spatial discretization cited in Thoms et al. (2006), i.e. a grid spacing of 0.1 m laterally and 0.06 m 

vertically. The time step was 1 min. A domain of 3 m by 2 m was considered due to symmetry of 

the flow process. 

Results of the water table simulations with the VSF and FULL-3D codes (both were developed by 

modifying MODFLOW) are compared in Fig. B1a, which also shows the experimentally measured 

water table. Simulation results for VSF and FULL-3D codes coincides and yielded an acceptable 

fit with the measured data. This provided confidence about the FULL-3D code to serve as 

appropriate benchmark for evaluating the performance of the QUASI-3D code. Fig. B1b shows 

results of the water table simulations conducted with two quasi 3D models: HYDRUS-1D - 

MODFLOW (Twarakavi et al. 2008) and our QUASI-3D code which did not consider the capillary 

fringe. Both codes underestimates the water table depth. The most significant discrepancies 

occurred below the water application area. HYDRUS-1D - MODFLOW created a smoother water 

table profile as compared with QUASI-3D. The latter produced a flatter groundwater table under 

the irrigated area and a sharp decrease in the water level outside of the irrigated area. Differences 

between the two codes relative to the groundwater level are attributed to the constant specific 

yield term in HYDRUS-1D - MODFLOW, which appears to be a fitting parameter. Using the 

constant specific yield provides a smoothing of the solution close to the infiltration source. Unlike 

HYDRUS-MODFLOW, the specific yield is not used in QUASI-3D where the water table is 

considered to be a moving boundary with its position estimated by the coupled solution of the 

Laplace equation in the saturated domain and a series of 1D equations for vertical flow in the 

unsaturated zone. Xu et al. (2012) simulated the same experiment using the SWAP-MODFLOW2000 package. Results showed that the simulated water table elevations closely matched the 

observed levels, except during the first 2 hours when they were slightly higher than the observed 

levels, probably due to neglecting lateral flow in the unsaturated zone. 

The effect of introducing a capillary fringe is shown in Fig B1c. The increase in the thickness of the 

capillary fringe (a decrease in the value of hcf) leads to smaller differences between simulations 

with QUASI-3D and the observed elevation of the water table. Decreasing hcf to -0.5 m, improves 

the agreement between the QUASI-3D and FULL-3D simulations. The position of the specific 

surface was not affected by hcf for values of hcf<-1 m. At the beginning of the simulation, the water 

table rise in the center of the box strongly depended upon lateral flow in the unsaturated zone. At 

later stages, accounting for the capillary fringe with hcf < -0.5 m provided satisfactory 

correspondence between the benchmark solution using FULL-3D and the QUASI-3D codes 

across the entire simulation domain. 
B-3 

Figure B-1 A comparison of water table elevation calculated using the (a) VSF and FULL3D codes, (b) HYDRUS-MODFLOW and QUASI-3D (with hcf=0 m) codes, (c) 

QUASI-3D code (with hcf=-0.25 m and -0.50 m), with the experimental data of 

Vauclin et al. (1979). 
B-4 

B.1.2 3-D Transient Infiltration, Pumping and Groundwater Mound Dissipation Simulations. 

A comparison of the FULL-3D and QUASI-3D codes was carried out for simulations of 

infiltration/pumping events with synthetic data. The flow domain consisted of a rectangular 

parallelepiped with lengths L in both horizontal directions, and thickness D (Fig. B2). Simulations 

were performed for two sets of hydraulic parameters for a homogeneous porous medium at three 

scales: small (L=100 m, D=1 m), medium (L=1000 m, D=10 m), and large (L=10,000 m, D=100 

m). The initial water table depth was D/2. Auniform grid was introduced in the simulation domain. 

The number of grid points was 100 in each direction, with the total number of nodes being 106.

Hydraulic properties of the three sediments (sand, sandy loam and silt loam), expressed as in 

terms of the van Genuchten-Mualem model (Eqs. 4-3, 4-4), are presented in Table B1. 

Four simulation setups were considered. 

Simulation setup 1: Infiltration from the soil surface. Infiltration from square areas at the soil 

surface (10x10 m, 100x100 m, and 1000x1000 m for the small, medium and large spatial scales, 

respectively) located at the center of the surface domain would cause the water tables to rise. The 

bottom and lateral boundaries of the domain were subjected to no-flow conditions. An infiltration 

rate of 0.01 m day-1 during 15, 150 and 1500 days were ascribed to the spatial scales. Since 

simulations were performed for the aquifer composed of sandy material (Table B1), no capillary 

fringe was considered. 

Simulation setup 2: Groundwater pumping. A vertical well was located in the center of the 

simulation domain, with the well screen reaching the bottom of the aquifer bottom. The lengths 

were 0.2, 2.0 and 20 m for the small, medium and large scales, respectively. Constant pumping 

rates of 0.5, 50, and 5000 m3d

-1 during 15, 150 and 1500 days were assumed for the three space 

scales, respectively. All boundaries were subject no-flow conditions. Similar simulations with the 

same soil (Table B1) were also performed for the case of having constant head at the lateral 

boundary of the domain. Results for this latter case could be compared with the analytical solution 

of Neuman (1975) for pumping from an isotropic unconfined aquifer. Again, no capillary fringe was 

considered. 

Simulation setup 3: Sequential infiltration, redistribution (groundwater mound dissipation), 

and pumping. Infiltration over a square area 100x100 m at a rate of 0.01 m day-1 during 365 

days, was followed by a pause of 365 days allowing redistribution of the water (all boundary fluxes 

and internal sinks were set to zero), after which pumping occurred during 365 days at a rate of 50 

m3d

-1. Simulations were performed for the medium scale with parameters for sediment 2 (Table 

B1) corresponding to sandy loam, and for two hcf values (0 and -0.15 m). 

Simulation setup 4: Groundwater mound dissipation 

The mathematical formulation and analytical solution of the problem are presented in 

Poubarinova-Kochina (1977). The groundwater level at the initial time, t0, is given as a rectangular 

parallelepiped (height

h

) on top of flat surface (elevation h0) 















0 1 2

0 1 2

0

if , 

if , 

),,(

RyRxhh

RyRxh

tyxh

 (B4) 
B-5 

Figure B-2 A sketch of the domain for synthetic simulations of infiltration/pumping 

stresses. 

Table B-1 Hydraulic properties of porous media used in numerical experiments 

Setup Texture θr θs α, (m-1

) n Ks , (m/day)

1 and 2 Sand 0.070 0.400 0.145 2.68 5.0

3 Sandy loam 0.065 0.410 0.075 1.89 1.06

4 Silt loam 0.131 0.369 0.423 2.06 0.0496

Initial water table

Infiltration area

Pumping well

L

D 
B-6 

where R1 and R2 are initial extensions of the groundwater mound in x and y directions, 

respectively. The analytical solution of the linearized 2-D Boussinesq equation for this case is 

given by 

  









 















 



 



at

yR

at

yR

at

xR

at

h xR

htxh

2

erf

2

erf

2

erf

2

erf

4

,

1 1 2 2

0

 (B5) 

where 

  ys ShKa

~

 , Sy

 is the specific yield and 

2

~

0  hhh

 is the average groundwater 

level. 

The ARS study team carried out simulations for a silty loam soil (Table B1) at the medium spatial 

scale. The size of the initial groundwater mound was: R1=R2=55m, h=1 m. Specific yield for the 

analytical solution was taken to be 

Sy

=0.136. 

Fig. B3 compares results obtained with the QUASI-3D and FULL-3D models for the infiltration 

example (simulation setup 1). While Table B2 and Fig. B3 compares results for simulation setups 

1 (infiltration) and 2 (pumping). Overall, results of the simulated water table elevation with the 

FULL-3D and QUASI-3D codes are very close, showing a maximum relative difference (

rel dZmax

) 

that did not exceed the value of 0.004 for the infiltration simulations and 0.053 for pumping 

simulations. The maximum relative difference in groundwater levels for the two codes was larger 

for the small-scale experiments as compared to the larger domain. 

In the infiltration simulations, the QUASI-3D code formed a slightly taller and steeper groundwater 

mound as compared to the one simulated by the FULL-3D at all scales (Figure B3a, b, and c). 

The largest difference (

dZmax

) in groundwater levels simulated by the two codes was 0.02 m at 

the large scale, while the smallest 

dZmax

=0.002 m was obtained at the small scale. 

For the second setup (pumping) with no flow boundary conditions along the lateral boundaries, 

the cone of depression simulated with QUASI-3D code was shallower than that simulated with 

FULL-3D (Fig. B3a, b, and c). The largest absolute difference (

dZmax

) between the groundwater 

levels obtained with the two codes was 0.529 m for the larger scale. The smallest value at

dZmax

=0.019 m was for the small-scale simulated pumping with a constant head boundary condition at 

the lateral boundary. This exhibited practically identical solutions for the QUASI-3D and FULL-3D 

codes. The absolute maximum deviation in groundwater levels was 0.0016 m. Comparison of the 

QUASI-3D solution with the analytical solution of Neuman (1975), assuming a value of 0.3 for the 

specific yield of sand, provided a very good agreement between the simulated groundwater levels 

(not further shown here). Maximum absolute errors in the vicinity of the pumping well were 0.18, 

0.08 and 0.002 m for the large, medium and small scales, respectively. 

The mass balance of all simulations was satisfactory for all soil textures. For both models the 

mass balance errors did not exceed values of 0.21%, 0.06% and 0.04% for the small, medium 

and large scales, respectively. 

Results of simulations for setup 3 (sequential infiltration, mound dissipation, and pumping) are 

presented in Fig. B4 and Table B2. Simulations with the FULL-3D and QUASI-3D codes for 
B-7 

groundwater levels with hcf=-0.15 m were practically identical, with the maximum difference being 

less than 0.1 m. The maximum difference obtained for groundwater levels between the FULL-3D 

and QUASI-3D codes without a capillary fringe (hcf=0) varied from 0.07 m during infiltration to 0.7 

m during pumping. 

Figure B-3 Results of simulations of examples considering infiltration (setup 1) and 

pumping (setup 2) for (a) small, (b) middle and (c) large scales, with the 

QUASI-3D and FULL-3D codes. 
B-8 

The mass balance error was less than 0.01% in all simulations.. 

Results of the simulations of groundwater mound dissipation (setup 4) are shown in Fig. B5 and 

Table B2. The simulation with QUASI-3D for a groundwater level of hcf=0, was actually closer to 

the analytical solution of the linearized Boussinesq equation as compared to the FULL-3D 

solution. This is due to the fact that the QUASI-3D code accounts both for the specific features of 

the variably-saturated flow model and for the limitations of the Dupuit assumption. The maximum 

difference was 0.042 m at the groundwater mound summit, where QUASI-3D predicted higher 

groundwater levels than FULL-3D which did not account for horizontal flow in the capillary fringe. 

Introducing the capillary fringe into QUASI-3D with a value of -3.4 for hcf provided very good 

agreement between the QUASI-3D and FULL-3D models. The maximum deviation of the 

simulated groundwater levels was only 0.004 m. 

B.2 Computational Efficiency Of The Quasi-3d Code

The numerical efficiency was expressed in terms of CPU time, the number of time steps Nt, the 

number of nonlinear iterations Niter, and the number of iterations to solve the linearized set of finite 

difference (FD) equations Nlin (Table B2). In all simulations for setups 1 and 2 (infiltration and 

pumping, respectively), the CPU time for QUASI-3D code less than that of the FULL-3D code. 

However, only in two cases out of six simulations was the computational efficiency of QUASI-3D 

significantly higher (up to 300%) than that of the FULL-3D. For the infiltration simulations at the 

medium and large scales, the number of time steps and the number of nonlinear iterations were 

larger for QUASI-3D as compared FULL-3D (Table B2). For all other simulations, Nt and Niter

were approximately the same for both codes, which means a very similar rate of convergence 

(niter) when solving the set of non-linear FD equations. Yet, for setup 1 (infiltration), convergence 

was slower for the QUASI-3D code in comparison to FULL-3D, while the opposite was true for the 

setup 2 (pumping) simulations (Table B2). The number of iterations to solve the linearized set of 

the FD equations (Nlin) using the PCG2-MODFLOW code was smaller for QUASI-3D as compared 

to the FULL-3D code at the small scale. The number of iterations for QUADI-3D were, however, 

larger for the medium and large scales. 

For setup 3, the computations with QUASI-3D in terms of CPU time and the number of iterations 

were about 30% faster than those of the FULL-3D code. The better numerical efficiency of the 

QUASI-3D code was not only due to a decrease in the computations to form the matrix of FD 

equations and its solution, but also because of a lower total number of iterations by about 30%. 

For setup 4, the computational efficiency of QUASI-3D was only slightly better than that of FULL3D. 

The total computation time was partitioned between (1) the time needed to compose the FD 

matrix equations, including calculations of the non-linear soil hydraulic properties and various 

terms in the FD equations, and (2) the time needed to solve the final set of matrix equations. To 

assess this partitioning, the ARS study team built a linear regression relation for the total CPU 

time (TCPU) as a function of total number of nonlinear iterations (Niter) and total number of iterations 

to solve the linearized set of equations using PCG2-MODFLOW (Nlin):

CPU iteriter  NmNmT linlin

(B6) 
B-9 

Table B-2 Performance of the benchmark of FULL-3D and QUASI-3D models for the 

 setups 1, 2*, 3 and 4. 

Scale Setup Model Merr

%

CPU

min

Nt Niter Nlin

m

Small

1. Infiltration

QUASI-3D 0.06 3.29 138 311 359 0.002 0.004

FULL-3D 0.05 4.02 136 290 523

2. Pumping

QUASI-3D 0.21 3.11 136 272 407 0.019 0.053

FULL-3D 0.05 3.39 136 272 408

Medium

1. Infiltration

QUASI-3D 0.06 20.0 543 1743 6199 0.006 0.001

FULL-3D 0.02 23.33 535 1735 5028

2. Pumping

QUASI-3D 0.04 6.58 183 486 3224 0.067 0.020

FULL-3D 0.00 22.07 378 1315 7395

Large

1. Infiltration

QUASI-3D 0.01 75.12 1220 4984 43388 0.020 0.000

FULL-3D 0.02 78.15 1094 4329 29408

2. Pumping QUASI-3D 0.00 24.5 521 1454 15585 0.529 0.016

FULL-3D 0.04 63.05 887 2788 29387

Medium

3.Infiltration,

pause, 

pumping

QUASI-3D 

hcf=0 m 0.01 27.16 694 2450 6824 0.7 0.029

QUASI-3D 

hcf=-0.15 m 0.01 27.35 697 2493 6535 0.01 0.002

FULL-3D 0.01 43.11 930 3342 8151

Medium

4.Groundwater

mound 

dissipation

QUASI-3D 

hcf=0 m

0.00 13.41 603 1206 1635 0.042 0.007

QUASI-3D 

hcf=-3.4 m

0.00 14.43 603 1206 1639 0.004 0

FULL-3D 0.00 15.14 603 1206 1640

*Pumping simulations with no flow boundary condition at the lateral boundary.

dZmax

rel dZmax
B-10

Figure B-4 Results of simulations of the setup 3 example: (a) infiltration and mound 

dissipation and (b) pumping, with the QUASI-3D and FULL-3D codes. 
B-11

Figure B-5 Results of simulations with the analytical solution, QUASI-3D and FULL-3D 

codes of groundwater mound dissipation, for the setup 4 example. 
B-12

where 

miter

and 

mlin

 are the specific CPU times required to build matrices and to solve the 

linearized set of equations for one iteration, respectively. 

The ARS study team used the results presented in Table B2 to obtain estimated of the coefficients 

in Eq. (B6). Table B3 presents parameters of the linear regression. For setups 1 and 2, when 

using the QUASI-3D code, the number of nodes for the FD grid associated with 1D flow in the 

unsaturated zone was about half of the total number of nodes. When using FULL-3D, all FD grid 

nodes were associated with 3D flow process. The CPU time of the QUASI-3D code for one linear 

iteration (i.e., to solve linearized FD equation set using the PCG2-MODFLOW code) was found to 

be almost half of that of FULL-3D for both infiltration and pumping. This because of the 

significantly smaller number of nodes associated with the 3D flow process. Note that the 

computational expense to perform one iteration for solving the linear set of equations with positive 

definite matrix PGG2, is proportional to the total number of nodes. Most of the CPU time was 

spent to compute matrices of the FD equations, while the time required to solve this set of 

equations depended on the rate of convergence speed (10-40% of total CPU time). 

Table B-3 Linear regression parameters of (B6) to assess time performance efficiency of 

the FULL-3D and QUASI-3D codes. 

Code QUASI-3D FULL-3D

Coefficients

miter

min

mlin

min

miter

min

mlin

min

Values 0.0086 0.00073 0.0097 0.0013

R2 0.999 0.999

B.3 Effect of Capillary Fringe 

The QUASI-3D code was found to be efficient and accurate in comparisons with the benchmark 

FULL-3D code when the capillary fringe was considered. Numerical experiments presented in the 

sections 4.1 and 4.2 showed that horizontal flow of water in the unsaturated zone can have a 

noticeable effect on groundwater level in the vicinity of sources and sinks. Assigning a value of the 

pressure head (hcf) to define the position of the specific surface representing the capillary fringe, 

which is accounted for by a moving boundary between 1D flow in the unsaturated zone and 3D 

flow in groundwater, allows one to expand the zone of 3D flow to the capillary fringe and increase 

the accuracy of groundwater table simulations. The value of hcf can be estimated from the soil 

water curve or by comparing the QUASI-3D solution with the more accurate FULL-3D solution for 

prescribed conditions. The effect of the capillary fringe on water flow and solute transport is 

controversial. Experiments by Abit et al. (2008) showed that when Br was introduced in the 

capillary fringe, it was moving laterally above the water table. The role of the capillary fringe 

should depend on dependency of the hydraulic conductivity on the pressure head near saturation. 

The pore-connectivity parameter l in the van Genuchten-Mualem model (Eq. 4-4) and properties 

of the soil water retention curve both affect this dependency. The parameter l (median value of 0.5 

derived by Mualem, 1976) describes the tortuosity of the pore space and can significantly affect 

the rate at which the hydraulic conductivity decreases with the pressure head. However, values of 

l from a range of -10 to 10 have been encountered (van Genuchten et al. 1989). Yates et al. 

(1992) and Schaap and Leij (2000) reported an even wider range of l values. When this 
B-13

parameter is negative and has a large absolute value, the hydraulic conductivity of unsaturated 

soils in the capillary fringe remain close to the value of the saturated hydraulic conductivity as soil 

dries out (Pachepsky et al., 2000). On the other hand, if the parameter l is a large and positive, the 

hydraulic conductivity decreases fast as soil loses water, which happens most often in finetextured soils or in soils with well-developed macroporosity (Wösten and van Genuchten, 1988). 

The effect of the parameter l on the efficiency of accounting for the capillary fringe presents an 

interesting avenue for further research. 

The 1D approximation for flow in the unsaturated zone to estimating risks of groundwater 

contamination has been employed for various contaminants, e.g. PEARL (Leistra et al, 2001) for 

pesticides and RESRAD for radionuclides (Yu et al., 2001). No capillary fringe is considered in 

these codes. The QUASI-3D code may be used to assess potential errors caused by ignoring the 

capillary fringe. The code may be useful also for assessing the role of vertical heterogeneities that 

can cause accumulation of perched water. Approximation with and without a capillary fringe can 

also be applied to the QUASI-3D and with FULL-3D codes. This can facilitate further evaluation of 

the conceptual model behind the QUASI-3D approximations. 



NUREG/CR-7221

Y. Pachepsky1, A. Guber1, A. Yakirevich2, F. Pan1, T. Gish1, M. Kouznetsov2, 

M. Van Genuchten3, R. Cady4, T. Nicholson4

1United States Department of Agriculture

Agricultural Research Service

Environmental Microbial and 

Food Safety Laboratory

Hydrology and Remote Sensing 

Laboratory

Beltsville, MD 20705

T.J. Nicholson, NRC Project Manager

Division of Risk Analysis 

Office of Nuclear Regulatory Research

U.S. Nuclear Regulatory Commission 

Washington, DC 20555

NUREG/CR-7221 reports on integrating modeling abstraction techniques into subsurface monitoring strategies. This research 

is the culmination of many field and modeling studies conducted by the USDA/Agricultural Research Service (ARS) at their 

Beltsville Area Research Center. The research design was to identify and examine near-surface water flow pathways by 

monitoring performance indicators within the unsaturated zone and local water-table system. The peak tracer concentration 

and the time to peak concentration at several monitoring locations served as the performance indicators. The objective was to 

apply model abstraction techniques in designing monitoring networks such as those used at nuclear waste and 

decommissioned facilities. The level of spatial and temporal detail in characterizing soil properties (e.g. water contents and 

hydraulic conductivities) is based upon the model abstraction considerations. Simplifications may omit significant processes 

and conditions that control the water and contaminant migration. The ARS field studies provided detailed databases for 

modeling water and chemical tracer movement in 2 and 3 dimensions to facilitate understanding of what processes and 

properties could be simplified (abstracted). Model abstractions included using pedotransfer functions for hydraulic 

conductivity, soil profile homogenization, and unsaturated zone omission. This latter abstraction proved to be the most 

accurate in generating a monitoring network that reflected the calibrated model. A comprehensive sensitivity analysis was 

performed to identify possible directions of model simplification in the model abstraction process. The integration of model

abstraction into monitoring strategies based upon the ARS field and modeling findings was documented and reviewed by 

international soil scientists. The studies were jointly funded by NRC and USDA/ARS.

groundwater flow and transport 

modeling model abstraction 

model simplification 

monitoring strategies 

pedotransfer function 

sensitivity analysis 

soil water 

subsurface hydrology 

unsaturated zone 

March 2017

Technical

Integrating Model Abstraction into Subsurface Monitoring Strategies

3Department of Mechanical 

Engineering, COPPE/LTTC

Federal University of Rio de Janeiro, 

UFRJ

Rio de Janeiro, RJ CEP 21945-970, 

Brazil

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

4Division of Risk Analysis

Office of Nuclear Regulatory Research

U.S.Nuclear Regulatory Commission

Washington, DC 20555



NUREG/CR-7221 Integrating Model Abstraction into Subsurface Monitoring Strategies March 2017