Scientific Investigations Report 2008–5035

National Water-Quality Assessment Program

Transport of Anthropogenic and Natural

Contaminants (TANC) to Public-Supply Wells 

Simulations of Ground-Water Flow and

Particle Pathline Analysis in the Zone of

Contribution of a Public-Supply Well in

Modesto, Eastern San Joaquin Valley, California

U.S. Department of the Interior

U.S. Geological Survey

water table

MORE CONSOLIDATED DEPOSITS

ALLUVIAL

FAN DEPOSITS

Regional flow

FLOOD-PLAIN

DEPOSITS

Confining unit

AGRICULTURAL RECHARGE

Irrigation wells

River

Aquifer

URBAN RECHARGE

NOT TO SCALE

Simulations of Ground-Water Flow and 

Particle Pathline Analysis in the Zone of 

Contribution of a Public-Supply Well in 

Modesto, Eastern San Joaquin Valley, 

California

By Karen R. Burow, Bryant C. Jurgens, Leon J. Kauffman, Steven P. Phillips, 

Barbara A. Dalgish, and Jennifer L. Shelton

National Water-Quality Assessment Program

Transport of Anthropogenic and Natural Contaminants (TANC) 

to Public-Supply Wells

Scientific Investigations Report 2008–5035

U.S. Department of the Interior

U.S. Geological Survey
U.S. Department of the Interior

DIRK KEMPTHORNE, Secretary

U.S. Geological Survey

Mark D. Myers, Director

U.S. Geological Survey, Reston, Virginia: 2008

For product and ordering information:

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U.S. Government.

Although this report is in the public domain, permission must be secured from the individual copyright owners to 

reproduce any copyrighted materials contained within this report.

Suggested reference:

Burow, K.R., Jurgens, B.C., Kauffman, L.J. Phillips, S.P., Dalgish, B.A., and Shelton, J.L., 2008, Simulations of groundwater flow and particle pathline analysis in the zone of contribution of a public-supply well in Modesto, eastern San 

Joaquin Valley, California: U.S. Geological Survey Scientific Investigations Report 2008–5035, 41 p. Available at 

http://pubs.usgs.gov/sir/2008/5035
iii

Foreword

The U.S. Geological Survey (USGS) is committed to providing the Nation with credible scientific information that helps to 

enhance and protect the overall quality of life and that facilitates effective management of water, biological, energy, and 

mineral resources (http://www.usgs.gov/). Information on the Nation’s water resources is critical to ensuring long-term availability of water that is safe for drinking and recreation and is suitable for industry, irrigation, and fish and wildlife. Population 

growth and increasing demands for water make the availability of that water, now measured in terms of quantity and quality, 

even more essential to the long-term sustainability of our communities and ecosystems.

The USGS implemented the National Water-Quality Assessment (NAWQA) Program in 1991 to support national, regional, State, 

and local information needs and decisions related to water-quality management and policy (http://water.usgs.gov/nawqa). 

The NAWQA Program is designed to answer: What is the condition of our Nation’s streams and ground water? How are conditions changing over time? How do natural features and human activities affect the quality of streams and ground water, and 

where are those effects most pronounced? By combining information on water chemistry, physical characteristics, stream 

habitat, and aquatic life, the NAWQA Program aims to provide science-based insights for current and emerging water issues 

and priorities. From 1991–2001, the NAWQA Program completed interdisciplinary assessments and established a baseline 

understanding of water-quality conditions in 51 of the Nation’s river basins and aquifers, referred to as Study Units (http://

water.usgs.gov/nawqa/studyu.html).

Multiple national and regional assessments are ongoing in the second decade (2001–2012) of the NAWQA Program as 42 of 

the 51 Study Units are reassessed. These assessments extend the findings in the Study Units by determining status and trends 

at sites that have been consistently monitored for more than a decade, and filling critical gaps in characterizing the quality of 

surface water and ground water. For example, increased emphasis has been placed on assessing the quality of source water 

and finished water associated with many of the Nation’s largest community water systems. During the second decade, NAWQA 

is addressing five national priority topics that build an understanding of how natural features and human activities affect 

water quality, and establish links between sources of contaminants, the transport of those contaminants through the hydrologic system, and the potential effects of contaminants on humans and aquatic ecosystems. Included are topics on the fate of 

agricultural chemicals, effects of urbanization on stream ecosystems, bioaccumulation of mercury in stream ecosystems, effects 

of nutrient enrichment on aquatic ecosystems, and transport of contaminants to public-supply wells. These topical studies are 

conducted in those Study Units most affected by these issues; they comprise a set of multi-Study-Unit designs for systematic 

national assessment. In addition, national syntheses of information on pesticides, volatile organic compounds (VOCs), nutrients, 

selected trace elements, and aquatic ecology are continuing.

The USGS aims to disseminate credible, timely, and relevant science information to address practical and effective waterresource management and strategies that protect and restore water quality. We hope this NAWQA publication will provide you 

with insights and information to meet your needs, and will foster increased citizen awareness and involvement in the protection 

and restoration of our Nation’s waters.

The USGS recognizes that a national assessment by a single program cannot address all water-resource issues of interest. 

External coordination at all levels is critical for cost-effective management, regulation, and conservation of our Nation’s water 

resources. The NAWQA Program, therefore, depends on advice and information from other agencies—Federal, State, regional, 

interstate, Tribal, and local—as well as nongovernmental organizations, industry, academia, and other stakeholder groups. Your 

assistance and suggestions are greatly appreciated.

 Matthew C. Larsen

Acting Associate Director for Water
iv

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v

Contents

Abstract ..........................................................................................................................................................1

Introduction.....................................................................................................................................................2

Background on Public-Supply-Well Vulnerability...........................................................................2

Purpose and Scope ..............................................................................................................................4

Description of Study Area ............................................................................................................................4

Hydrogeologic Setting .........................................................................................................................4

Land and Water Use.............................................................................................................................5

Ground-Water Flow System................................................................................................................5

Ground-Water Quality in Modesto Public-Supply Wells................................................................6

Public-Supply Well Selection ......................................................................................................................6

Ground-Water Flow Model...........................................................................................................................6

Regional Ground-Water Flow Model ................................................................................................8

Local Ground-Water Flow Model ......................................................................................................8

Model Geometry and Discretization ........................................................................................8

Boundary Conditions, Model Stresses, and Initial Conditions ............................................9

Aquifer Hydraulic Conductivity................................................................................................11

Hydrofacies Classification ..............................................................................................11

Spatial Correlation Model of Hydrofacies ....................................................................12

Ground-Water Flow Model Calibration ...........................................................................................12

Sensitivity Analysis.............................................................................................................................17

Ground-Water Flow Model Results .................................................................................................17

Simulated Water Levels and Flows.........................................................................................17

Simulated Budget ......................................................................................................................17

Simulation of Advective Transport by Particle Tracking ......................................................................17

Methods and Model Parameters ....................................................................................................21

Particle Tracking Results and Comparison to Age Tracer Concentrations ..............................22

Comparison between Land Use in the Contributing Recharge Area (CRA) and 

Occurrence of Selected Constituents ..............................................................................25

Processes Affecting Nitrate and Uranium Concentrations in the Aquifer and the 

Public-Supply Well ...............................................................................................................29

Long-Term Concentrations of Nitrate and Uranium in the Public-Supply Well........................33

Model Uncertainties and Limitations .......................................................................................................36

Summary and Conclusions.........................................................................................................................36

Acknowledgments.......................................................................................................................................37

References Cited..........................................................................................................................................38
vi

Figures

Figure 1. Map showing study area near Modesto in the eastern San Joaquin Valley, 

California .................................................................................... 3

Figure 2. Map showing extent of local ground-water flow model nested within regional 

model of an area near Modesto, eastern San Joaquin Valley, California ............ 7

Figure 3. Map showing boundary conditions and distribution of recharge specified in the 

local ground-water flow model near Modesto, eastern San Joaquin Valley, 

California .................................................................................... 10

Figure 4. Graphs showing hydrofacies distribution used in the ground-water flow 

model near Modesto, eastern San Joaquin Valley, California ........................ 13

Figure 5. Graphs showing (A) simulated and measured water level and (B) weighted 

residuals for the calibrated local ground-water flow model near Modesto, 

eastern San Joaquin Valley, California ................................................... 16

Figure 6. Graph showing comparison between boundary flows in the regional model and 

boundary flows in the calibrated local ground-water flow model near Modesto, 

eastern San Joaquin Valley, California.................................................... 17

Figure 7. Graphs showing sensitivity of model parameters with respect to (A) sum of 

squared residuals of simulated and measured water levels, (B) net flow through 

upgradient (east) boundary, and (C) net flow through downgradient (west) 

boundary .................................................................................... 18

Figure 8. Map showing simulated water table elevation in local ground-water flow 

model near Modesto, eastern San Joaquin Valley, California ........................ 19

Figure 9. Map showing simulated water level in model layer 150 in local ground-water

flow model near Modesto, eastern San Joaquin Valley, California .................. 20

Figure 10. Graph showing simulated water level along vertical transect A-A′ in local 

ground-water flow model near Modesto, eastern San Joaquin Valley, 

California .................................................................................... 21

Figure 11. Map showing contributing recharge area and particle travel times to publicsupply well near Modesto, eastern San Joaquin Valley, California .................. 23

Figure 12. Graph showing simulated flow-weighted age of particles reaching the publicsupply well near Modesto, eastern San Joaquin Valley, California .................. 24

Figure 13. Graph showing simulated age and interpreted ground-water age from 

age-dating tracers, as compared with depth below water table in monitoring 

wells and the public-supply well near Modesto, eastern San Joaquin Valley, 

California .................................................................................... 25

Figure 14. Graph showing concentrations of tritium (3H) and sulfur hexafluoride (SF6) 

in recharge ................................................................................. 26

Figure 15. Graphs showing simulated and measured concentrations of (A) sulfur 

hexafluoride (SF6) and (B) tritium (3H) in monitoring wells and the public-supply 

well near Modesto, eastern San Joaquin Valley, California. ........................... 27

Figure 16. Graph showing simulated and measured tritium (3H) concentrations with depth 

in monitoring wells and the public-supply well near Modesto, eastern San 

Joaquin Valley, California. .................................................................. 27

Figure 17. Graph showing estimated concentrations of nitrate in recharge from nitrogen 

fertilizer applications over time and measured nitrate concentrations in 

monitoring wells ........................................................................... 31

Figure 18. Graph showing simulated and measured concentrations of nitrate in monitoring 

wells and the public-supply well near Modesto, eastern San Joaquin Valley, 

California .................................................................................... 32
vii

Figure 19. Graph showing alkalinity and uranium concentrations in monitoring wells at 

different depths and in the public-supply well near Modesto, eastern San 

Joaquin Valley, California .................................................................. 33

Figure 20. Graph showing simulated and measured alkalinity in monitoring wells and the 

public-supply well near Modesto, eastern San Joaquin Valley, California ......... 34

Figure 21. Graph showing simulated long-term concentrations of nitrate in the publicsupply well near Modesto, eastern San Joaquin Valley, California .................. 35

Figure 22. Graph showing simulated long-term alkalinity and inferred uranium 

concentrations in the public-supply well near Modesto, eastern San Joaquin 

Valley, California ........................................................................... 35

Tables

Table 1. Well depths and pumping rates assigned to wells in the local ground-water 

flow model near Modesto, eastern San Joaquin Valley, California .................. 11

Table 2. Embedded transition probability matrices and mean hydrofacies lengths in the 

geologic model near Modesto, eastern San Joaquin Valley, California ............ 12

Table 3. Hydraulic conductivity of hydrofacies used in the local ground-water flow 

model near Modesto, eastern San Joaquin Valley, California ........................ 15

Table 4. Volumetric budget of local ground-water flow model near Modesto, eastern 

San Joaquin Valley, California ............................................................ 21

Table 5. Summary statistics for the simulated contributing recharge area and the zone 

of contribution of the public-supply well near Modesto, eastern San Joaquin 

Valley, California ........................................................................... 24

Table 6. Well characteristics and simulated and interpreted ground-water ages from 

age-dating tracers in monitoring wells sampled in 2003–2005 near Modesto, 

eastern San Joaquin Valley, California ................................................... 26

Table 7. Nitrate concentrations, volatile organic compound and pesticide occurrence, 

and relation to land use in the contributing recharge areas of the public-supply 

well and monitoring wells in Modesto, eastern San Joaquin Valley, California ... 28

Table 8. Nitrate, alkalinity and uranium concentrations from monitoring wells and the 

public-supply well sampled in 2003–2005 near Modesto, eastern San Joaquin 

Valley, California ........................................................................... 30
viii

Conversion Factors, Spatial Datums, Abbreviations, and 

Acronyms

SI to Inch/Pound

Multiply By To obtain

Length

millimeter (mm) 0.03937 inch (in.)

meter (m) 3.281 foot (ft) 

kilometer (km) 0.6214 mile (mi)

Area

square meter (m2

) 0.0002471 acre 

square kilometer (km2

) 247.1 acre

Flow rate

cubic meter per day (m3

/d) 0.000264 million gallons per day (Mgal/d)

cubic meter per day (m3

/d) 35.31 cubic foot per day (ft3/d) 

cubic meter per minute (m3

/min) 264.2 gallon per minute (gal/min)

meter per day (m/d) 3.281 foot per day (ft/d)

meter per year (m/yr) 3.281 foot per year (ft/yr) 

Spatial Datums

Vertical coordinate information is referenced to the North American Vertical Datum of 1988 (NAVD 88).

Elevation, as used in this report, refers to distance above the vertical datum.

Horizontal coordinate information is referenced to the North American Datum of 1983 (NAD 83).

Concentrations of chemical constituents in water are given either in milligrams per liter (mg/L) or 

micrograms per liter (μg/L).

Abbreviations and Acronyms

CRA, contributing recharge area 3

H, tritium

MCL, maximum contaminant level

NAWQA, National Water-Quality Assessment Program

PSW public-supply well

SF6

, sulfur hexafluoride

TANC, transport of anthropogenic and natural contaminants

USGS, U.S Geological Survey

VOC, volatile organic compounds

ZOC, zone of contribution
Abstract 

Shallow ground water in the eastern San Joaquin Valley 

is affected by high nitrate and uranium concentrations 

and frequent detections of pesticides and volatile organic 

compounds (VOC), as a result of ground-water development 

and intensive agricultural and urban land use. A single publicsupply well was selected for intensive study to evaluate the 

dominant processes affecting the vulnerability of publicsupply wells in the Modesto area. A network of 23 monitoring 

wells was installed, and water and sediment samples were 

collected within the approximate zone of contribution of the 

public-supply well, to support a detailed analysis of physical 

and chemical conditions and processes affecting the water 

chemistry in the well. A three-dimensional, steady-state local 

ground-water-flow and transport model was developed to 

evaluate the age of ground water reaching the well and to 

evaluate the vulnerability of the well to nonpoint source input 

of nitrate and uranium. 

Particle tracking was used to compute pathlines and 

advective travel times in the ground-water flow model. The 

simulated ages of particles reaching the public-supply well 

ranged from 9 to 30,000 years, with a median of 54 years. The 

age of the ground water contributed to the public-supply well 

increased with depth below the water table. Measured nitrate 

concentrations, derived primarily from agricultural fertilizer, 

were highest (17 milligrams per liter) in shallow ground water 

and decreased with depth to background concentrations of 

less than 2 milligrams per liter in the deepest wells. Because 

the movement of water is predominantly downward as a result 

of ground-water development, and because geochemical 

conditions are generally oxic, high nitrate concentrations 

in shallow ground water are expected to continue moving 

downward without significant attenuation. Simulated longterm nitrate concentrations indicate that concentrations have 

peaked and will decrease in the public-supply well during the 

next 100 years because of the low nitrate concentrations in 

recharge beneath the urban area and the increasing proportion 

of urban-derived ground water reaching the well. The 

apparent lag time between peak input concentrations and peak 

concentrations in the well is about 20 to 30 years. 

Measured uranium concentrations were also highest 

(45 micrograms per liter) in shallow ground water, and 

decreased with depth to background concentrations of 

about 0.5 microgram per liter. Naturally-occurring uranium 

adsorbed to aquifer sediments is mobilized by oxygen-rich, 

high-alkalinity water. Alkalinity increased in shallow ground 

water in response to agricultural development. As groundwater pumping increased in the 1940s and 1950s, this highalkalinity water moved downward through the ground-water 

flow system, mobilizing the uranium adsorbed to aquifer 

sediments. Ground water with high alkalinity and high 

uranium concentrations is expected to continue to move deeper 

in the system, resulting in increased uranium concentrations 

with depth in ground water. Because alkalinity (and 

correspondingly uranium) concentrations were high in shallow 

ground water beneath both the urban and the agricultural 

land, long-term uranium concentrations in the public-supply 

well are expected to increase as the proportion of uraniumaffected water contributed to the well increases. Assuming 

that the alkalinity near the water table remains the same, the 

simulation of long-term alkalinity in the public-supply well 

indicates that uranium concentrations in the public-supply well 

will likely approach the maximum contaminant level; however, 

the time to reach this level is more than 100 years because of 

the significant proportion of old, unaffected water at depth that 

is contributed to the public-supply well.

Simulations of Ground-Water Flow and Particle Pathline 

Analysis in the Zone of Contribution of a Public-Supply 

Well in Modesto, Eastern San Joaquin Valley, California

By Karen R. Burow, Bryant C. Jurgens, Leon J. Kauffman, Steven P. Phillips, Barbara A. Dalgish, and 

Jennifer L. Shelton 
2 Simulations of Ground-Water Flow and Particle Pathline Analysis, Zone of Contribution of a Public-Supply Well, Modesto, Calif.

Introduction

In 2000, ground water provided 37 percent of the 

public drinking-water supplies used by 242 million people 

nationwide (Hutson and others, 2004). Withdrawals of ground 

water for public supply has increased five fold over the last 

50 years, causing increased concern about the quality of water 

pumped by public-supply wells. California withdraws more 

ground water for public supply than any other state in the 

nation, serving more than 30 million people and accounting 

for 18 percent of the total ground-water withdrawals for public 

supply in 2000 (Hutson and others, 2004). 

The use of ground water for public supply is threatened 

by compounds that have been introduced by human activities. 

Volatile organic compounds (VOC) were detected in 90 of 

98 aquifer studies completed across the nation; California 

led most other states in detection frequencies (Zogorski and 

others, 2006). Nationwide, pesticides were detected in more 

than 50 percent of wells in shallow ground water (Gilliom 

and others, 2006). Nitrate was detected in 71 percent of wells 

in shallow ground water, and concentrations were above the 

maximum contaminant level (MCL) of 10 mg/L, as N (U.S. 

Environmental Protection Agency, 2006) in at least one 

well out of 20 to 30 wells in nearly one-half of the 33 major 

aquifers studied (Nolan and Stoner, 2000). 

In the eastern San Joaquin Valley, California (fig. 1), 

agricultural withdrawals are the dominant water use; however, 

increased reliance on ground-water withdrawals for publicsupply will likely result from the rapid population growth 

and periods of drought. In shallow ground water, pesticides 

were detected in 69 percent of domestic wells, and nitrate 

concentrations were above the MCL in 24 percent of domestic 

wells sampled during 1993–95 (Dubrovsky and others, 1998). 

Low concentrations of VOCs were detected in more than 

70 percent of public-supply wells sampled in Fresno and 

more than 90 percent of wells in Modesto in 2001–02 (Wright 

and others, 2004). Concentrations of nitrate and detections 

of pesticides in the deep part of the aquifer system, where 

public-supply wells typically are screened, will likely increase 

as the proportion of young water contributed to these wells 

increases (Burow and others, 2007). Sustainability of groundwater quality for present and future public supply requires 

monitoring and understanding of the mechanisms controlling 

the vulnerability of public-supply wells to contamination. 

Background on Public-Supply-Well 

Vulnerability

Aquifer and public-supply-well susceptibility to 

contamination is a function of the intrinsic conditions of an 

aquifer, such as depth to water, flow-system confinement, 

recharge rate, hydraulic conductivity, porosity, pumping 

rate, and geochemical conditions (Focazio and others, 2002). 

Public-supply-well vulnerability is determined by assessing 

aquifer susceptibility and potential contaminant sources 

overlying or within the area contributing recharge to the well 

(Franke and others, 1998; Focazio and others, 2002). In this 

report, the word “contaminant” is defined as any natural or 

anthropogenic chemical or physical property of the groundwater resource in question that could threaten human health, 

interfere with water-treatment practices (Focazio and others, 

2002), or cause other problems. 

Several methods have been used to protect public water 

supplies by determining the susceptibility or vulnerability 

of an aquifer to contamination. Process-based methods 

attempt to predict contaminant transport paths at either 

regional or site-specific scales using model simulation 

techniques (National Research Council, 1993). The strength 

of process-based approaches is the ability to differentiate 

the effects of the underlying processes controlling transport, 

such as geochemical transformations, contaminant source 

loading, ground-water velocity, and diffusion and dispersion 

processes. In process-based studies of public-supply-well 

vulnerability, the land use above the contributing recharge 

area of a public-supply well, the travel times of ground water 

flowing to the well, and aquifer stresses such as well pumping 

rates are important factors affecting the sources and fate of 

contaminants reaching the wells (Reilly and Gibs, 1993; Reilly 

and Pollock, 1995; Johnson and others, 2000; Kauffman and 

others, 2001; Brown and others, 2002). However, lack of data, 

and the averaging of variables over scales that fail to capture 

the inherent physical and chemical heterogeneity of the system 

impair the ability of models to quantify contributing areas to 

wells (Reilly and Pollock, 1993; Barlow, 1997; Focazio and 

others, 2002; Harrar and others, 2003). Additionally, many 

models do not adequately represent alternative pathways for 

contaminants to reach wells, such as short-circuits through 

wellbores or unmapped layers of high hydraulic conductivity 

(Franke and others, 1998; Cole and Silliman, 2000). 

Additionally, natural contaminants such as trace elements, 

radionuclides, or salinity are rarely considered because of 

the difficulty in mapping the source areas and the subsurface 

volumes of these contaminants. 
Introduction 3

Figure 1. Study area near Modesto in the eastern San Joaquin Valley, California.

Hydrofacies model grid extent 

EXPLANATION

Boundary containing active area of local model 

Regional model 

0 5 10 Kilometers

0 5 10 Miles

River Joaquin San

River Merced

River

Stanislaus

River Tuolumne

Modesto

STANISLAUS COUNTY

MERCED COUNTY

SAN JOAQUIN COUNTY

CreekDry

Ranges Coast

San Joaquin 

Valley

Study area

Central

Valley

MREA core location 

132

120

108

33

165

5

5

99

99

CALIFORNIA

Sierra Nevada

Base from U.S. Geological Survey digital elevation data, 2006.

Urban area 
4 Simulations of Ground-Water Flow and Particle Pathline Analysis, Zone of Contribution of a Public-Supply Well, Modesto, Calif.

This study is part of the U.S. Geological Survey’s 

(USGS) National Water-Quality Assessment (NAWQA) 

program. To improve understanding of the interrelationship 

between sources of contaminants, their transport through 

hydrologic systems, and the effects of contaminants and 

physical alterations on the quality of drinking water, a processbased study of the transport of anthropogenic and natural 

contaminants to public-supply wells (TANC) was initiated 

in 2001 (Wilber and Couch, 2002). The TANC study was 

designed to assess the vulnerability of public-supply wells 

to contamination by answering the question: “What are the 

primary anthropogenic and natural contaminant sources, 

aquifer processes, and well characteristics that control 

the transport and transformation of contaminants along 

flow paths to public-supply wells in representative watersupply aquifers?” The TANC study incorporates field data 

on solid-phase and water chemistry, geochemical analysis 

and interpretation, and process-based models to determine 

the vulnerability of public-supply wells to anthropogenic 

and natural contaminants at multiple scales and in multiple 

hydrogeologic settings across the nation. Results from the 

TANC study will provide a better understanding of the most 

important factors controlling the vulnerability of the nation’s 

public-supply wells (Eberts and others, 2005). 

Seven regional-scale (hundreds to thousands of km2

) 

studies were completed in a range of settings using regional 

ground-water flow models and water-quality data from publicsupply wells (Paschke and others, 2007) to evaluate aquifer 

hydrogeologic processes, well characteristics, and potential 

contaminant sources affecting the vulnerability of publicsupply wells. Following the regional analysis, more detailed 

local-scale (less than 100 km2) studies were implemented in 

4 of the 7 study areas: the Central Valley Aquifer System in 

the eastern San Joaquin Valley near Modesto, California, the 

Floridan Aquifer System near Temple Terrace, Tampa Bay 

Region, Florida, the Glacial Aquifer System near Woodbury, 

Connecticut, and the High Plains Aquifer System near York, 

Nebraska. The local-scale studies incorporated nested local 

ground-water flow and transport models to enhance the 

understanding of specific physical and chemical processes 

affecting the vulnerability of public-supply wells in the 

regional aquifer.

Purpose and Scope

This report is one of two reports that document the local 

TANC study near Modesto in the eastern San Joaquin Valley, 

California (fig. 1). The results of the characterization of 

the hydrogeologic setting, water and solid-phase chemistry, 

and the geochemical analysis of processes affecting longterm concentrations of nitrate and uranium in a selected 

public-supply well will be presented in a future report. 

The report presented here documents the development and 

calibration of the steady-state local ground-water flow model 

used in the analysis of the transport of nitrate and uranium 

to the public-supply well, and documents the results of the 

transport analyses. The hydraulic conductivity distribution of 

the aquifer system was generated using a conditional indicator 

geostatistical method. The local flow model was calibrated to 

water-level measurements from multilevel monitoring wells 

and to inflows and outflows from the regional model. Particle 

tracking analysis was used to delineate the contributing 

recharge area and the zone of contribution of the selected 

public-supply well and the monitoring wells in the study 

area. Concentrations of tracers computed using particle 

pathlines and associated flow were compared with measured 

concentrations of age-dating tracers collected in the wells. 

Particle ages and land use in the contributing recharge areas 

of the wells were compared to measured concentrations to 

evaluate the effects of land use on measured concentrations. 

Simulated concentrations of nitrate and alkalinity were 

compared with measured concentrations to evaluate the 

downward movement of nitrate and uranium in the aquifer. 

Future long-term concentrations of nitrate and uranium 

concentrations in the public-supply well were estimated using 

the calibrated local flow and transport model.

Description of Study Area

The San Joaquin Valley occupies the southern two-thirds 

of the Central Valley of California (fig. 1), a large, northwesttrending, asymmetric structural trough filled with marine 

and continental sediments up to 10 km thick (Page, 1986; 

Gronberg and others, 1998). The San Joaquin Valley is a level 

depression more than 400 km long and 30 to 90 km wide. East 

of the valley, the Sierra Nevada rise to an elevation of more 

than 4,200 m; west of the valley are the Coast Ranges, a series 

of parallel ridges of moderate elevations (Mendenhall and 

others, 1916). 

Hydrogeologic Setting

Streams in the northern part of the San Joaquin Valley 

drain through the San Joaquin River northward; the southern 

part of the valley is hydrologically closed. The climate is 

semiarid, characterized by hot summers and mild winters, with 

rainfall primarily during late fall through early spring. Rainfall 

averaged 315 mm annually from 1931 to 1997 (National 

Oceanic and Atmospheric Administration, 2005). 
Description of Study Area 5

The TANC regional-scale study area is about 2,700 km2 

in the northeastern San Joaquin Valley bounded on the west by 

the San Joaquin River, on the north near the Stanislaus River, 

on the south near the Merced River, and on the east by the 

Sierra Nevada foothills (Phillips and others, 2007a) (fig. 1). 

The San Joaquin River is the central drainage for the northern 

San Joaquin Valley and is the only major surface-water outlet 

from the valley. The Stanislaus, Tuolumne, and Merced Rivers 

drain the Sierra Nevada and are tributaries to the San Joaquin 

River. All rivers in the study area have been significantly 

modified from natural conditions. Each has multiple reservoirs 

for irrigation and power generation, which effectively delays 

discharge of large amounts of snowmelt runoff and reduces the 

peak discharge. Imprinted over this hydrology is an extensive 

network of canals used to deliver water for irrigation. 

The local-scale study area that is the subject of this report 

is nested within the regional study area, occupying about 100 

km2

 on the north side of Modesto (fig. 1). The local study area 

is situated on a belt of coalescing fluvial fans of low relief that 

lie between the dissected uplands to the east and the nearly 

flat surface of the valley floor (Burow and others, 2004). The 

sediments were deposited by the Stanislaus and Tuolumne 

Rivers as a heterogeneous mixture of unconsolidated, 

interlayered lenses of gravel, sand, silt, and clay (Marchand 

and Allwardt, 1981; Burow and others, 2004). Most of the 

unconsolidated deposits in the study area are contained within 

the Pliocene-Pleistocene Laguna, Turlock Lake, Riverbank, 

and Modesto Formations. The Turlock Lake, Riverbank, and 

Modesto Formations form a sequence of overlapping terrace 

and alluvial fan systems (Davis and Hall, 1959; Marchand 

and Allwardt, 1981) indicating cycles of alluviation, soil 

formation, and channel incision that were influenced by 

climatic fluctuations and resultant glacial stages in the Sierra 

Nevada (Bartow, 1991; Weissmann and others, 2004). 

Land and Water Use

Irrigated crops are planted in about 65 percent of the 

regional study area. Dominant crops include almonds, walnuts, 

peaches, grapes, grain, corn, pasture, and alfalfa. The local 

study area contains about 54 percent urban land and 46 

percent agricultural land. The two most dominant crops are 

almond and fruit orchards. Agricultural irrigation began in the 

regional study area in the early 1900s and accounts for about 

95 percent of the total water use. Surface-water supplies from 

the Stanislaus and Tuolumne Rivers are managed by irrigation 

districts and delivered to agricultural users through hundreds 

of kilometers of lined canals. Most irrigation districts and 

private agricultural users pump ground water for irrigation. 

Private agricultural ground-water pumpage is not measured 

in the regional or local study area, but is estimated as about 

32 percent of total agricultural water use in water year 2000 

(Burow and others, 2004; Phillips and others, 2007b). 

During the last several decades, urban areas have 

expanded into the agricultural area as a result of increasing 

population. In Stanislaus County, the estimated population 

in 2005 was more than 500,000 people, an increase of more 

than 10 percent since 2000 (California Department of Finance, 

2006). Urban water demand is met by surface-water and 

ground-water supplies. Before 1995, the city of Modesto used 

ground water exclusively for public supply. In 1994, a surfacewater treatment plant was completed. About 55 percent of 

Modesto’s municipal and industrial water requirement was 

met with ground water in water year 2000 (Burow and others, 

2004; Phillips and others, 2007b). 

Ground-Water Flow System

Ground water in the local study area is unconfined, 

although water-bearing layers of sand and gravel become 

semi-confined with depth owing to numerous, overlapping, 

discontinuous clay lenses. Before development of the groundwater resource, most ground-water recharge occurred in the 

upper parts of the alluvial fans where streams entered the 

basin. Ground water generally moved southwest, toward the 

axis of the San Joaquin Valley and discharged primarily to 

the San Joaquin River and surrounding marshlands (Gronberg 

and others, 1998). However, the diversion of surface water 

from streams, and intensive ground-water pumping and 

recharge resulting from irrigated agriculture and growth of 

the urban areas, have significantly altered the natural flow 

system. Following development of the ground-water resource, 

percolating irrigation water became the primary form of 

ground-water recharge, and irrigation pumpage became the 

primary form of ground-water discharge (Davis and others, 

1959; Page and Balding, 1973; Londquist, 1981). As a 

result, ground water primarily moves downward within the 

regional and local flow systems. Water moving laterally may 

be pumped and reapplied at the surface multiple times. In 

addition, because ground-water recharge in the Modesto urban 

area is less than recharge in the agricultural areas, municipal 

ground-water withdrawals have created a water-level 

depression beneath the city (Burow and others, 2004).

The USGS installed several multi-depth monitoring 

wells in the regional study area near Modesto and near the 

Merced River (Phillips and others, 2007b). Monitoring wells 

were instrumented with pressure transducers that recorded 

hourly water-level measurements for periods typically ranging 

from 1 to 3 years. These data for the Modesto area show that 

vertical hydraulic gradients from the water table (about 10 m 

deep) to the deeper production zones of most municipal wells 

(about 40–100 m) were strongly downward during the spring 

and summer months (about 0.2–0.3). The downward gradient 

was weaker during the fall and winter. Seasonal water-level 

fluctuations are about 6 m in the deeper wells, and usually less 

than 1 m at the water table, in the Modesto area.
6 Simulations of Ground-Water Flow and Particle Pathline Analysis, Zone of Contribution of a Public-Supply Well, Modesto, Calif.

Ground-Water Quality in Modesto 

Public-Supply Wells

The chemistry of ground water in the regional study 

area has been affected by agricultural and urban activities. 

Nitrate concentrations in public-supply wells in the Modesto 

area ranged from 0.23 to 9.5 mg/L, with a median of 3.5 

mg/L during 1999–2000 (Wright and others, 2004). Nitrate 

concentrations were higher in public-supply wells on the 

periphery of the city than in wells near the center of the urban 

area. The wells containing higher nitrate concentrations 

were located in newer suburban developments, on previous 

agricultural land and closer to current agricultural areas 

where nitrogen fertilizers are used. Nitrate concentrations 

in shallow ground water beneath almond orchards, one of 

the dominant crops in the local study area, are typically 

high (Burow and others, 1998). In addition to anthropogenic 

nitrate concentrations, naturally-occurring trace elements 

and radionuclides in ground water, such as arsenic and 

uranium, are also of concern in the Modesto area. Uranium 

concentrations were above the MCL of 30 μg/L in several 

public-supply wells, causing the abandonment of these wells 

for use (City of Modesto, written commun., 2003). 

Public-Supply Well Selection

A single public-supply well was selected for study at 

the local scale to evaluate the dominant processes affecting 

the vulnerability of public-supply wells in the Modesto area. 

The selection of the public-supply well for the local study 

was based on previous work at the regional scale that defined 

baseline hydrologic data and typical ground-water chemistry 

within the regional ground-water flow model domain. 

The regional ground-water flow model was used to 

simulate the zone of contribution (ZOC) and the contributing 

recharge area (CRA) for 60 of 112 public-supply wells 

operating in the Modesto area (Phillips and others, 2007a). 

The CRA is defined as the areal extent at the water table 

(or top boundary) where water entering the ground-water 

flow system will eventually be removed by the discharging 

well. The ZOC is the three-dimensional volumetric part of 

the aquifer system through which ground water flows to the 

discharging well from the CRA (Focazio and others, 2002). 

Particle-tracking analysis was used to compute the extent and 

percentages of different land uses within the CRA of each well 

and to relate the contaminants in the wells to that land use. 

The public-supply well selected for this study is in 

northeast Modesto (fig. 2), and was selected from a subset of 

15 of the 60 wells for which CRAs were computed and for 

which water-quality samples were collected by the USGS 

in 2003. These 15 wells supplied the top 25 percent of 

annual pumpage in 2000, which ranged from 0 to 5,800 m3

/d 

(1.5 Mgal/d). The public-supply well selected for study is one 

of the highest in annual production (1.2 Mgal/d; top 5 percent 

of total supply) and pumps at a rate of 6.1 m3/min (1,600 gal/

min) during the summer season. In the winter, the well is 

pumped for a short duration every day, averaging 0.4 m3/min 

(110 gal/min) over a 24-hr period. The median well depth of 

public-supply wells in the Modesto area is 81.7 m (268 ft) and 

the median screened interval length is 27.7 m (91 ft), although 

many wells have no screened-interval information or have an 

open bottom. The public-supply well selected for this study 

is 120 m deep and is screened from 27.7 to 111.6 m below 

land surface and has an open bottom from 111.6 m to about 

115 m. Of the 60 public-supply wells for which CRAs were 

computed, 45 percent had a CRA consisting of mostly urban 

land, 28 percent had a CRA consisting of mostly agricultural 

land, and 27 percent had a CRA consisting of a mixture of 

agricultural and urban land. To select the single public-supply 

well for this study, preference was given to wells that had a 

CRA that allowed the differences between agricultural and 

urban land-use effects on ground-water quality to be studied 

and the influence of urbanization on the quality of ground 

water reaching public-supply wells to be evaluated. The CRA 

computed for the selected well had an areal extent of 96 km2

(fig. 2), containing about 65 percent agricultural land and 

32 percent urban land (Phillips and others, 2007a). The well 

was constructed in 1961. Residential development began near 

the well in the 1960s and has expanded outward to the north 

and east. 

The public-supply well selected for this study is deeper, 

has a longer screened interval, and is a larger producer than 

most wells in the Modesto area. This well was selected 

because it was screened across a large thickness of the aquifer 

system, and ground-water quality in the ZOC was expected 

to represent a transition from agricultural to urban land use. 

By characterizing the ground-water age and the processes 

affecting the water chemistry at different depths in the aquifer 

system, results can be extrapolated to other wells that are 

screened at shallow depth intervals. 

Ground-Water Flow Model

Movement of water and solutes from recharge areas to 

the public-supply well was evaluated using a steady-state, 

three-dimensional, ground-water flow and transport model 

(Pollock, 1994; Harbaugh and others, 2000). The local model 

developed for this study was nested within the regional model 

used for the TANC regional analysis in the northeastern San 

Joaquin Valley (fig. 2) (Paschke and others, 2007; Phillips 

and others, 2007a). Simulations of quantities of water of 

different ages and solute concentrations in the well provided 

information on ground-water velocities to complement the 

interpretation of water chemistry data from wells sampled 

for this study and provided estimates of long term nitrate and 

uranium concentrations in ground water in the study area. 
Ground-Water Flow Model 7

Figure 2. Extent of local ground-water flow model nested within regional model of an area near Modesto, eastern San Joaquin Valley, 

California. 

Particle density map and contributing recharge area computed using regional model.

62

52

32

42

72

22

12

02

91

82

92

92

Hydrofacies model grid extent

19

Public-supply well

EXPLANATION

Lines of equal particle density, in number of particles per

 model cell

less than or equal to 500

501 to 1,000

1,001 to 1,500

1,501 to 2,000

more than 2,000

Contributing recharge area for travel times less than or equal

 to 100 years; derived from regional model pathline analysis

0 1 2 Kilometers

0 1 2 Miles

Base from U.S. Geological Survey digital data, 2006.

Road or highway 

Boundary containing active area of local model 

Simulated water-table elevation from regional model—

 Contour interval 1 meter. Datum is North American Vertical

 Datum of 1988

Regional model grid

Agricultural land use area

Urban land use area
8 Simulations of Ground-Water Flow and Particle Pathline Analysis, Zone of Contribution of a Public-Supply Well, Modesto, Calif.

Regional Ground-Water Flow Model 

The regional ground-water flow model of the northeastern 

San Joaquin Valley used to provide stresses and boundary 

conditions for the local model was documented as part of the 

TANC regional-scale studies (Phillips and others, 2007a). 

The regional model grid is oriented parallel to the valley axis, 

37 degrees west of due north (fig. 2). The model area extends 

61.2 km along the valley axis and 54.8 km from the Coast 

Ranges to the Sierra Nevada foothills (fig. 1), though the area 

west of the San Joaquin River is inactive. Each model cell is 

400 m by 400 m, and the grid has 153 rows and 137 columns. 

The regional model layering is a series of wedges that 

generally represent the regional dip of the sediments toward 

the southwest. Sixteen model layers were defined. Above the 

Corcoran Clay (a regional confining unit west of the local 

model area), model layer thickness ranged from 0.5 to 16 m; 

below the Corcoran Clay, model layer thicknesses ranged 

from 20 to 74 m. Layer thicknesses generally were designed 

to increase with depth and decreasing availability of sediment 

texture data. The top of the uppermost model layer represents 

the land surface, and the bottom is a smoothed version of 

the land surface. The thicknesses of layers 2 through 7 were 

assigned as a percentage of the thickness of materials between 

layer 1 and the top of the Corcoran clay. Layer 8 represents 

the Corcoran Clay where present; the top surface of the 

Corcoran Clay was a smoothed rendition constrained by data 

from driller’s logs. The thickness of the Corcoran Clay ranged 

from 3 to 43 m. A thickness of 5 m was specified in layer 8 

in the eastern part of the regional model where the Corcoran 

Clay was not present. The thicknesses of layers 9-16 were 

assigned as a percentage of the thickness of materials between 

the bottom of the Corcoran Clay and the bottom of the model. 

The total thickness of the wedge-shaped model ranged from 

about 220 to 430 m. Hydraulic conductivity was distributed 

using a spatial correlation model of sediment texture (as 

percentage of coarse-grained texture). This method uses the 

estimated sediment texture for each model cell and a method 

of calibration which uses horizontal and vertical hydraulic 

conductivities to estimate each textural end member. A vertical 

gradient was imposed at the general head boundaries on the 

north, south, and eastern sides of the model. 

The regional model was refined during the development 

of the local model (Phillips and others, 2007b). Refinements 

included the following: (1) a three-dimensional model of 

percentage of coarse-grained texture to represent the spatially 

varying hydraulic conductivity field in the model domain 

(Burow and others, 2004) was incorporated, replacing the twodimensional version; (2) the top and bottom surface and the 

extent of the Corcoran Clay were refined with additional data; 

(3) recharge was reduced as a result of continued analysis 

of the water budget data; (4) continuous water-level data 

available from the local study were used to improve calibration 

results (Phillips and others, 2007b). 

Local Ground-Water Flow Model 

A three-dimensional, steady-state model of groundwater flow in the local study area was developed using 

MODFLOW-2000 (Harbaugh and others, 2000) to simulate 

movement of water in the contributing area of the publicsupply well and to support the transport modeling analysis. 

The local model simulates conditions that existed in water 

year 2000, the period simulated by the regional steady-state 

model. Measured ground-water levels in the regional study 

area suggest that the ground-water system has been in a quasisteady-state condition for many years (Phillips and others, 

2007a). Although water levels rose rapidly in the Modesto 

area in 1995 after surface water was imported to supplement 

ground-water supplies for drinking water, the rise slowed 

greatly by 2000 (Burow and others, 2004). For the purposes 

of this study, the quasi-steady-state condition of the aquifer 

system is adequately represented by a steady-state model. 

Model Geometry and Discretization 

The extent of the local ground-water flow model 

presented in this report encompasses the ZOC and CRA 

for travel times less than or equal to 100 years (fig. 2) as 

determined by particle pathline analysis using the regional 

model (Phillips and others, 2007a). As in the regional model, 

the local model grid is oriented parallel to the valley axis, 37 

degrees west of due north (fig. 2), aligned with the regional 

lateral ground-water flow direction. The nested, local model 

was discretized into a uniform grid of finite-difference cells 

consisting of 200 rows of 72-m-length-cells and 100 columns 

of 34-m-length-cells. 

The active area of the local model grid encompasses 

most of the CRA generated using the MODPATH particlepathline analysis of the regional model (Phillips and others, 

2007a) (fig. 2). In addition, a probabilistic method was used 

to evaluate the effect of parameter uncertainty on the CRA 

generated using the regional model. The probabilistic method 

uses a Monte Carlo technique which varies the hydraulic 

conductivity of geologic units in the model within the range of 

uncertainty. Nearly 700 parameter sets were generated using 

a covariance matrix for the optimal parameters, which were 

determined using a method of parameter estimation. Particles 

were tracked backward from the public-supply well for each of 

the 370 cases for which mass balance errors were less than 10 

percent (Jeff Starn, U.S. Geological Survey, written commun., 

2004). A larger number of model runs would provide more 

cases with lower mass balance error; however, computation 

time would be impractical. The local model was unaffected 

by the results of the probabilistic CRA, as it was generated 

primarily to determine the extent of the local model and help 

place monitoring wells for the local study. The combined 

particle endpoint distribution is mapped as contours of 

particle density (fig. 2). The CRA derived from the 

MODPATH particle-pathline analysis and the particle density 
Ground-Water Flow Model 9

contours indicated that most of the recharge contributing to the 

public-supply well was east and north of the well; the highest 

density of particles was due east of the public-supply well. 

The local model grid has 200 layers of uniform 0.6 m 

thickness. The active area of the model coincides with the 

water table at the top of the model and the bottom of the 

regional-scale model layer 10 at the bottom of the model, 

which is below the bottom of the public-supply well and below 

the dominant pumping zone in this area. 

Boundary Conditions, Model Stresses, and 

Initial Conditions 

A mixture of specified head and specified flux boundaries 

were used to constrain the local model using head and flux 

values from the regional model (fig. 3). A series of model 

runs using different combinations of specified head and flux 

boundaries determined the best combination of boundary 

conditions. The resulting combination of boundaries was 

selected on the basis of residuals between measured and 

simulated water levels, model mass balance, and flow through 

boundaries and multi-node wells. Conditions along the 

north and south boundaries of the local model, representing 

approximate flow lines, were simulated using specified flux 

cells. Although these lateral boundaries approximated flow 

lines at the water table, flow directions varied with depth; 

therefore, lateral boundary conditions in the local model 

were specified fluxes derived from lateral flows simulated 

in the regional model. Cell-by-cell boundary fluxes for the 

local model were calculated from adjacent larger cells in the 

regional model by using a hydraulic-conductivity-weighted 

distribution. Net flows specified along the north and the 

south boundaries were 3,773 and –2,159 m3/d, respectively, 

approximately an order of magnitude lower than the net flows 

through the upgradient and top (recharge) boundaries. The 

upgradient and downgradient lateral boundaries were specified 

head, using values from the regional model. Hydraulic head 

varied from 26 m near the water table to 16 m at depth along 

the upgradient boundary, whereas hydraulic head varied 

from 19 m near the water table to 13 m at depth along the 

downgradient boundary. The hydraulic head values were 

interpolated from the regional model onto the local model 

grid. The lower boundary of the local model was specified 

head from the regional model; hydraulic heads from the 

regional model were interpolated onto the local model grid in 

the same way as the lateral boundaries. The upper boundary of 

the local model was specified flux to represent the water table. 

Stresses in the local model include recharge and groundwater withdrawal from wells. Recharge in the local model was 

derived from agricultural and urban water budget subareas 

from the regional model (Burow and others, 2004; Phillips and 

others, 2007b). Recharge from agricultural return flow was 

estimated using the calculated crop demand in the regional 

water-budget analysis and an estimated consumptive use 

of applied water. Recharge in the urban area was estimated 

by accounting for landscape irrigation, leakage from water 

distribution lines, and precipitation recharge. Recharge rates 

from the regional model ranged from 0.6 to 0.7 m/yr in the 

agricultural areas, and were 0.3 m/yr in the urban areas. The 

recharge specified from the regional model was adjusted 

on a cell-by-cell basis during calibration of the local model 

to account for the heterogeneous hydraulic conductivity 

distribution used in the model, and limit mounding of 

hydraulic heads in low-permeability cells (fig. 3). In some 

cases, recharge applied to cells moved laterally and discharged 

from adjacent cells because of the local geometry of the 

hydraulic conductivity distribution. However, the total 

amount of recharge and the approximate ratio of agricultural 

(67 percent) to urban (33 percent) recharge specified in the 

regional model was maintained as much as possible. 

Total ground-water pumpage assigned in the local model 

was 49,822 m3/d, distributed among 22 wells (table 1). Private 

agricultural ground-water pumpage was not measured in the 

regional study area, but was estimated in the water budget 

analysis for the regional model (Burow and others, 2004; 

Phillips and others, 2007b). The locations of privately pumped 

wells also are unknown; therefore, agricultural pumpage 

was distributed areally within the agricultural water budget 

subarea by assuming an average well spacing of 1,200 m. 

The vertical distribution of private agricultural pumpage was 

estimated using the average screened interval of irrigation 

wells in each subarea. Wells operated by irrigation districts or 

for public supply were assigned known pumping rates across 

documented screened locations. Pumping in 15 of the wells 

in the local model area was simulated using the standard well 

package in MODFLOW-2000 (fig. 3). Pumping in each model 

layer within the screened interval for each well was assigned 

by weighting the total pumpage by the hydraulic conductivity 

of each layer along the well screen. To account for potential 

flow vertically through the wellbore, pumping in 7 of the wells 

in the local model was simulated using the multi-node well 

package in MODFLOW-2000 (Halford and Hanson, 2002). To 

minimize model computation time, only wells containing long 

screened intervals were simulated as multi-node wells: wells 

were simulated as multi-node wells if the top of the screened 

interval was less than about 35 m below the water table, the 

bottom of the screened interval was deeper than about 80 m 

below the water table, and the screen length was greater than 

50 m. 
10 Simulations of Ground-Water Flow and Particle Pathline Analysis, Zone of Contribution of a Public-Supply Well, Modesto, Calif.

EXPLANATION

Specified recharge, in meters per day

Boundary containing active area of local model 

Road or highway 

Agricultural land use area 

0.00081 to 0.097

0.00035 to 0.0008

0.0000011 to 0.00034

0 to 0.000001

Urban land use area 

Monitoring well location and identifier

Pumping well represented as multinode well in

ground-water flow model 

Pumping well 

FPB

0 0.5 1 1.5 Miles

0 0.5 1 1.5 Kilometers

WEIGHTED SPECIFIED FLUX

WEIGHTED SPECIFIED FLUX

SPECIFIED HEAD

SPECIFIED HEAD

Base from U.S. Geological Survey digital data, 2006.

PSW

FPA

FPB

FPC

FPD

FPE

OFPA

OFPB

SA SB

SC

Figure 3. Boundary conditions and distribution of recharge specified in the local ground-water flow model near Modesto, eastern San 

Joaquin Valley, California. 

PSW, public-supply well.
Ground-Water Flow Model 11

Aquifer Hydraulic Conductivity

The distribution of hydraulic properties used in the 

local model was estimated by model calibration using a 

three-dimensional spatial correlation model of hydrofacies. 

The spatial correlation model of hydrofacies was developed 

using a transition-probability-based geostatistical approach 

to explicitly evaluate the effects of dispersion on solute 

concentrations in the aquifer caused by macro-scale 

heterogeneity. A single realization (a plausible threedimensional representation of the hydrofacies distribution) of 

the distribution of hydrofacies was selected from a series of 

realizations and used to calibrate the flow model. Hydrofacies 

are defined here as sediments with similar hydraulic properties 

that were deposited in similar depositional environments. 

Using this approach, the three-dimensional character of the 

movement of water through primary channels is preserved, 

and more accurately represents transport pathways and 

dispersion of contaminants moving to the well. 

Hydraulic conductivity was specified for each model grid 

cell using a stochastically-generated hydrofacies distribution. 

The hydrofacies distribution was generated using a conditional 

indicator geostatistical method that uses a transitionprobability Markov-chain model to define the statistical 

correlation structure of discrete hydrofacies (Carle and Fogg, 

1996, 1997; Carle 1997; Carle and others, 1998). A matrix 

of transition probabilities was developed for the dip, strike, 

and vertical directions. From the transition rate matrices, a 

continuous lag Markov Chain model was developed, which 

was used with cokriging in a sequential indicator simulation 

to generate images of subsurface facies distributions. The 

hydrofacies distribution was generated using the software 

TProGS (Carle, 1999). 

Hydrofacies Classification

The alluvial sediments in the local study area consist 

primarily of interlayered lenses of gravel, sand, silt, and clay 

deposited in alluvial fans by the Stanislaus and Tuolumne 

Rivers (Jurgens and others, in press). The sediments were 

deposited in cyclic alluvial fan aggradation sequences linked 

to Pleistocene glacial episodes and the local base level of the 

San Joaquin River (Davis and Hall, 1959; Weissmann and 

others, 2002; Burow and others, 2004; Weissmann and others, 

2004). For this study, sediments were classified into four 

hydrofacies: gravel, sand, muddy sand, and mud. The term 

mud is defined here as undifferentiated silt and (or) clay. The 

gravel hydrofacies is characterized as cobbles and pebbles in 

a coarse sand matrix, representing channel lag deposits, and 

has the highest hydraulic conductivity. The sand hydrofacies 

is characterized as moderately-well sorted medium to coarse 

sand, deposited in primary channels of the Stanislaus and 

the Tuolumne Rivers or secondary tributary channels. The 

muddy sand hydrofacies is characterized as finely laminated 

fine-grained sand in a matrix of clay and silt, deposited in 

the floodplain proximal to channels. The mud hydrofacies is 

characterized as massive to laminated silt and mud, deposited 

in the floodplain farther from the channel than the muddy sand 

hydrofacies and has the lowest hydraulic conductivity. The 

hydrofacies categories were based on previous classification 

of deposits on the Kings River alluvial fan (Burow and 

others, 1997; Weissmann and Fogg, 1999). The sediments 

in the study area are similar to the Kings River alluvial fan 

sediments because they were derived from similar source 

rocks and deposited by similar processes. The Tuolumne 

River and Kings River fans have similar drainage basin sizes, 

stream gradients, and changes in elevation; the Stanislaus 

River fan has a smaller drainage-basin size. All three drainage 

basins were extensively glaciated. The Stanislaus and the 

Tuolumne River alluvial fans are smaller than the Kings River 

fan, however. The basin subsidence rates near the Stanislaus 

and Tuolumne Rivers are significantly lower and the basin 

width is significantly smaller than that near the Kings River 

(Weissmann and others, 2004). Therefore, the paleosol 

hydrofacies in the Kings River fan (Weissmann and Fogg, 

1999) is not well preserved in the study area and therefore was 

not included as a separate facies. 

Table 1. Well depths and pumping rates assigned to wells in 

the local ground-water flow model near Modesto, eastern San 

Joaquin Valley, California.

Local 

well 

name

Depth to top of 

screen below 

water table, 

in meters

Depth to 

bottom of 

screen below 

water table, 

in meters

Screen 

length, 

in meters

Pumping rate, 

in cubic 

meters per day

A-206 17.7 113.7 96.0 206 

A-3A 41.8 92.0 50.2 3,607 

A-3B 41.1 91.1 50.0 3,607 

A-3C 49.3 86.5 37.2 3,607 

A-3D 31.0 92.9 61.9 3,607 

A-3E 48.7 74.1 25.4 3,607 

A-6A 52.2 78.7 26.5 3,078 

B-24 14.0 95.7 81.7 1,238 

B-25 13.8 123.3 109.5 3,746 

B-37 13.5 60.9 47.4 3,306 

B-39 20.1 65.6 45.5 4,206 

B-46 24.5 66.8 42.3 2,714 

B-48 66.3 119.5 53.2 2,542 

B-50 44.1 94.7 50.6 2,163 

B-52 23.1 97.1 74.0 4,327 

B-54 39.5 129.4 89.9 1,460 

B-58 92.5 118.9 26.4 204 

B-259 11.8 91.5 79.7 505 

B-260 22.8 98.1 75.3 603 

B-262 69.2 95.3 26.1 692 

B-264 69.5 121.8 52.3 344 

B-269 41.7 91.6 49.9 453 

 Total pumpage from local model 49,822 
12 Simulations of Ground-Water Flow and Particle Pathline Analysis, Zone of Contribution of a Public-Supply Well, Modesto, Calif.

Spatial Correlation Model of Hydrofacies

To develop the three-dimensional spatial correlation 

model of hydrofacies, sediment descriptions derived from 

continuous core collected by the USGS at site MREA (fig. 1) 

and from cuttings and e-logs obtained during drilling for 

the TANC study were discretized into 0.3-m increments and 

assigned a hydrofacies category. The transition probability 

matrix for the vertical direction was developed by fitting 

a Markov Chain model to the discretized data and using 

the calculated proportions of each hydrofacies category. 

Calculated proportions were 0.01, 0.19, 0.31, and 0.49 for 

gravel, sand, muddy sand, and mud hydrofacies, respectively. 

Core and cuttings data were too sparse in the lateral 

directions to develop the Markov Chain model in the strike 

and dip directions by the same data fitting procedure. 

Transition probability matrices for the strike and dip directions 

were developed by using the calculated proportion of each 

hydrofacies and by modifying parameters used in Weissmann 

and Fogg (1999). Because the Tuolumne River alluvial fan 

is about half the area of the Kings River alluvial fan, the 

correlation lengths of the hydrofacies were reduced by a factor 

of about 2 to represent the difference in scale between the two 

fans. 

The Markov Chain model developed from the 

transition probability matrices (table 2) was used in a 

conditional sequential indicator simulation to generate 

multiple equiprobable realizations. Separate realizations 

of the hydrofacies distributions were generated for each of 

six aggradation sequences (Jurgens and others, in press) to 

reflect the unconformities produced by extensive periods 

of non-deposition or erosion (Weissmann and Fogg, 1999). 

The resulting realizations were combined to represent the 

three-dimensional hydrofacies distribution for use in the local 

ground-water flow model. 

Eleven sets of realizations were generated for each of the 

combined alluvial fan aggradation sequences. Each resulting 

hydrofacies distribution was used in preliminary ground-water 

flow simulations to determine which distribution best fit the 

measured water levels. None of the model simulations using 

the eleven sets of realizations matched the magnitude of the 

vertical hydraulic gradient of about 0.075 (annual average) 

measured between depths of about 35 and 55 m below land 

surface. This depth interval corresponded to a fine-grained 

zone observed in borehole cuttings and geophysical logs at 

this depth. Therefore, a more continuous mud layer about 6 

m thick was generated by increasing the correlation length of 

the mud hydrofacies at these depths. The ground-water flow 

model was run for each of the 11 realizations using 2 different 

mud layers, for a total of 22 model runs. The realization that 

best fit measured water levels was selected for subsequent 

ground-water flow model calibration and transport modeling 

(fig. 4A,B). 

Ground-Water Flow Model Calibration

The local flow model was calibrated using formal 

parameter estimation and systematic manual calibration 

techniques. Preliminary calibration was done using the 

parameter estimation process in MODFLOW-2000 (Hill and 

others, 2000) by comparing simulated and measured water 

levels. Because the estimated parameters were significantly 

correlated and because it was difficult to automate the 

updating of the hydraulic-conductivity-weighted flux 

boundaries during each parameter estimation run, the 

parameter estimation method was used to provide preliminary 

estimates of hydraulic conductivity of the hydrofacies. The 

hydraulic conductivity values were later refined through a 

systematic manual calibration. The head-based calibration 

was further evaluated by comparing fluxes in the regional 

model and comparing proportions of recharge in the urban and 

agricultural areas. 

Table 2. Embedded transition probability matrices and mean hydrofacies lengths in the geologic model near Modesto, eastern San 

Joaquin Valley, California.

[L, mean length of hydrofacies , in meters; s, symmetry assumed; b, background category; <, less than]

Vertical direction Horizontal strike direction Horizontal dip direction

Gravel Sand Muddy 

 sand Mud Gravel Sand Muddy  sand Mud Gravel Sand Muddy sand Mud

Gravel L = 1.2 0.45 0.54 0.01 Gravel L = 110 0.45 0.54 0.01 Gravel L = 370 0.45 0.54 0.01

Sand <0.01 L = 1.4 0.53 0.46 Sand s L = 300 0.53 0.38 Sand s L = 862 0.53 0.39

Muddy 

sand

0.06 0.4 L = 2.0 0.54 Muddy 

sand

s s L = 190 0.75 Muddy 

sand

s s L = 450 0.80

Mud 0.01 0.46 0.53 L = 3.3 Mud b b b b Mud b b b b
Ground-Water Flow Model 13

B

A

Hydrofacies category

Gravel

DISTANCE IN STRIKE DIRECTION (NORTHEAST),

IN METERS

DISTANCE IN STRIKE DIRECTION (NORTHEAST), IN METERS

DISTANCE IN DIP DIRECTION (NORTHWEST),

IN METERS

ELEVATION, IN METERS

Datum is North American

Vertical Datum of 1988

DISTANCE IN DIP DIRECTION (NORTHWEST),

IN METERS

Sand

Muddy sand

Mud

30,000

30,000 31,000 32,000

33,000 34,000 35,000

42,000

43,000

44,000

45,000

46,000

47,000

48,000

20

-20

-40

-60

-80

0

48,000

47,000

46,000

45,000

44,000

43,000

42,000

31,000 32,000 33,000 34,000 35,000

Figure 4. Hydrofacies distribution used in the ground-water flow model near Modesto, eastern San Joaquin Valley, California. 

(A) Three-dimensional model of hydrofacies and (B) two-dimensional view of clay 6 meters thick inserted at depths ranging from 35 to 

55 meters below land surface. 
14 Simulations of Ground-Water Flow and Particle Pathline Analysis, Zone of Contribution of a Public-Supply Well, Modesto, Calif.

Simulated water levels were compared to measured water 

levels in 18 monitoring wells screened at multiple depths 

at 7 sites (FPA, FPB, FPC, FPD, FPE, OFPA, and OFPB) 

(fig. 3). Measured water levels at sites SA, SB, and SC were 

not included in the calibration because these sites contained 

only water table wells, had a limited number of water-level 

measurements, and the water table elevation was represented 

at the other 7 sites. Water-level data for each well were 

averaged between the summer low period and the winter high 

period to determine the annual water-level observation. Water 

levels in the shallow part of the aquifer varied as much as 0.2 

m seasonally, whereas water levels varied by as much as 5.6 m 

seasonally in the deep part of the aquifer because of seasonal 

changes in water demand. Water levels in the deep part of 

the aquifer were as much as 10 m lower than water levels 

in the shallow system during the summer months, however, 

indicating that the difference between water levels at the 

water table and the deep part of the aquifer is greater than the 

difference in water levels caused by seasonal changes. 

Hydraulic conductivities were initially estimated 

using slug tests, aquifer tests, and results from previous 

investigations. Four hydraulic conductivity parameters were 

estimated during the calibration: the horizontal hydraulic 

conductivity of the sand hydrofacies (HK2), the horizontal 

and the vertical hydraulic conductivities of the muddy sand 

hydrofacies (HK3 and VK3, respectively), and the vertical 

hydraulic conductivity of the mud hydrofacies (VK4). 

Because the gravel hydrofacies represents only 1.4 percent 

of the modeled volume, simulation results were insensitive 

to changes in the hydraulic conductivity of that hydrofacies. 

Therefore, the initial estimate of hydraulic conductivity of 

the gravel hydrofacies was not adjusted. Similarly, the results 

were insensitive to the vertical hydraulic conductivity of the 

sand hydrofacies and the horizontal hydraulic conductivity of 

the mud hydrofacies, and therefore these values also were not 

further adjusted in the calibration process. 

Initial model runs using the parameter estimation 

package resulted in estimated hydraulic conductivity values 

for the sand (HK2), muddy sand (HK3 and VK3), and mud 

hydrofacies (VK4) of 98, 2, 1, and 0.001 m/d, respectively. 

These estimates were generally at the high end of the range of 

expected hydraulic conductivity values for these hydrofacies 

(Freeze and Cherry, 1979; Domenico and Schwartz, 1998). 

The simulations were most sensitive to the vertical hydraulic 

conductivity of the mud hydrofacies (VK4). Although the 

simulations were least sensitive to the muddy sand hydrofacies 

parameters (HK3 and VK3), the muddy sand hydrofacies 

was expected to have the largest range of possible values. 

Some of the sediments in this hydrofacies were moderately 

well sorted, whereas some contained interstitial or laminated 

silt and clay, depending on the relative proximity to the 

channel during deposition. For subsequent calibration, muddy 

sand hydrofacies parameters (HK3 and VK3) and vertical 

hydraulic conductivity of the mud (VK4) were adjusted 

through a manual calibration procedure. The hydraulic 

conductivity of the sand (HK2) was 98 m/d, within the range 

of values estimated in similar studies: the calibrated hydraulic 

conductivity for the 100-percent coarse-grained textural endmember in the regional model was 80 m/d (Phillips and others, 

2007b); the estimated hydraulic conductivity of the sand 

hydrofacies in a local model nested within the same regional 

model was 80 m/d (Phillips and others, 2007b); the estimated 

hydraulic conductivity of the sand hydrofacies in a local 

model in an area north of Modesto was more than 130 m/d 

(Fleckenstein and others, 2006). The local studies used the 

same hydrofacies approach. 

Because 7 of the 18 water-level measurements were in 

wells screened at the water table, the simulation results were 

primarily sensitive to hydraulic conductivity of the hydrofacies 

at the recharge boundary. Although the recharge flux applied 

from the regional model was weighted according to the 

hydraulic conductivity of the recharge cells, in some locations 

simulated water levels at the water table were highly variable 

and water mounded at cells insufficiently connected to high 

conductivity cells deeper in the model. In these cases, recharge 

applied to cells moved laterally and discharged from adjacent 

cells. To determine which recharge cells were best connected 

to high hydraulic conductivity cells in deeper parts of the 

model, the recharge boundary was specified as a constanthead boundary. The specified head approximated the water 

table from the regional model. Hydraulic conductivity values 

for the muddy sand hydrofacies (HK3 and VK3) were then 

systematically varied to obtain the best fit between simulated 

water levels and measured water levels while maintaining 

the approximate total flows derived from the regional model. 

A specified flux was then applied at the recharge boundary 

on the basis of the simulated fluxes from the specified head 

run. Resulting fluxes were distributed equally between the 

urban and the agricultural areas, which is inconsistent with 

relative recharge rates estimated from the water budget: about 

66 percent of the recharge occurs in the agricultural area and 

34 percent occurs in the urban area. Therefore, the recharge 

was redistributed by assigning a higher weight to the fluxes 

assigned in the agricultural area. The redistributed recharge 

was further refined by matching flows through the bottom, 

upgradient, and downgradient boundaries to flows from the 

regional model. Total recharge specified in the local model 

area was within 1.5 percent of the recharge from the regional 

model, with 58 percent of the recharge in the agricultural area 

and 42 percent in the urban area (fig. 3). Vertical hydraulic 

conductivity of the mud hydrofacies (VK4) was adjusted 

manually to obtain the best fit between simulated water levels 

and measured water levels for the given boundary conditions. 
Ground-Water Flow Model 15

The final estimates of horizontal (HK3) and vertical 

(VK3) hydraulic conductivity for the muddy sand were 2.2 

and 1.1 m/d, respectively (table 3). The final estimate of 

vertical hydraulic conductivity of the mud (VK4) was 0.0031 

m/d, which was similar to 0.008 m/d, the calibrated hydraulic 

conductivity for the 0-percent coarse-grained textural endmember (fine grained) in regional model (Phillips and others, 

2007b). These values are within the range of values from the 

literature (Bouwer, 1978; Freeze and Cherry, 1979; Domenico 

and Schwartz, 1998) and from the slug and aquifer test 

analyses. The resulting simulated water levels were generally 

similar to measured water levels, although they deviated at 

a few wells (fig. 5A), such as water table wells FPC-1 and 

FPD-1, intermediate-depth wells FPA-3, FPD-2 and OFPA-2, 

and the deepest monitoring well adjacent to the public-supply 

well, FPA-4. The sum of squared weighted residuals between 

simulated and measured water levels was 9.3 m2; the average 

residual was 0.25 m. Ten of the 18 water levels were within 

0.5 m of measured water levels. Weights were applied to 

measurements at site FPD because this site was influenced by 

an adjacent canal, and it was in the agricultural setting where 

the location of pumping wells was not known. The relation 

between simulated water levels and weighted residuals appears 

to be generally independent and normally distributed (fig. 5B), 

although the distribution appears slightly biased by the wells 

noted above. Simulated water levels were less than measured 

in 12 of 18 wells. 

Local differences between simulated and measured 

water levels was likely due to a lack of correspondence 

between the realization selected for simulation and the true 

distribution of hydrofacies around individual wells. The 

Table 3. Hydraulic conductivity of hydrofacies used in the local ground-water flow model near Modesto, eastern San Joaquin Valley, 

California. 

[ —, not enough data]

Hydrofacies

Horizontal 

hydraulic 

conductivity 

used in 

simulation

Vertical 

hydraulic 

conductivity 

used in 

simulation

Minimum 

hydraulic 

conductivity

 from slug tests

Maximum 

hydraulic 

conductivity 

from slug tests

Average 

hydraulic 

conductivity 

from slug tests

Hydraulic 

conductivity 

from aquifer test

Range of literature 

values1

In meters per day

Gravel 800 727 2 6 4 20 1 to 2,500

Sand 2

98 45 2 24 8 20 0.01 to 500

Muddy sand 2

2.2 21.1 0.3 6 3 2 0.0001 to 20

Mud 0.001 2

0.0031 0.0006 6 — 0.0004 1E-8 to 0.01 1

From Bouwer, 1978; Freeze and Cherry, 1979; Domenico and Schwartz, 1998. 

2

Estimated during calibration. 

hydrofacies distributions were conditioned on hydrofacies data 

at the boreholes, but the degree of interconnection between 

high permeability hydrofacies adjacent to individual wells 

varied among realizations and was expected to influence the 

simulation of water levels at the well. Because the publicsupply well is screened over a much greater thickness than the 

monitoring wells, the public-supply well was less affected by 

the local variations in hydrofacies distributions. The threedimensional character of the movement of water through 

primary channels was preserved using this hydrofacies 

approach to characterizing the three-dimensional hydraulic 

conductivity distribution, and more accurately simulates 

transport pathways and dispersion of contaminants moving to 

the well. 

Simulated vertical gradients were similar to measured 

vertical gradients. Simulated vertical gradients ranged from 

0.04 to 0.07 between the water table and the deepest wells at 

each site, and measured vertical gradients ranged from 0.04 to 

0.08. The simulated flows in the local model were similar to 

flows from the regional model (fig. 6). Net flow through the 

top (recharge) boundary and the upgradient (east) boundary 

was within 1.5 percent of the flow in the regional model. 

Net flow through the downgradient (west) boundary was 

lower than flow in the regional model, and net flow through 

the bottom boundary of the model was higher than the flow 

in the regional model, although the net flows through these 

boundaries were an order of magnitude less than flow through 

the upgradient and recharge boundaries. 
16 Simulations of Ground-Water Flow and Particle Pathline Analysis, Zone of Contribution of a Public-Supply Well, Modesto, Calif.

2.0

0

-0.5

-1.0

-1.5

-2.0

0.5

1.0

1.5

WEIGHTED RESIDUAL BETWEEN SIMULATED HYDRAULIC HEAD

AND MEASURED WATER LEVELS, IN METERS

SIMULATED HYDRAULIC HEAD, IN METERS

10 15 20 25

MEASURED WATER LEVELS, IN METERS

10 15 20 25

10

15

20

25

SIMULATED HYDRAULIC HEAD, IN METERS

FPD-1

FPA-3

FPA-4

OFPA-1

A

B

OFPA-2

FPD-2

FPC-1

FPA-3

FPA-4

FPD-1

FPC-1

FPD-2

OFPA-1

OFPA-2

Figure 5. (A) Simulated and measured water level and (B) weighted residuals for the calibrated local 

ground-water flow model near Modesto, eastern San Joaquin Valley, California. 
Simulation of Advective Transport by Particle Tracking 17

Sensitivity Analysis

To determine the influence of model parameters 

on model results, the horizontal and vertical hydraulic 

conductivity of the sand (HK2 and HK3), the vertical 

hydraulic conductivity of the muddy sand (VK3), and the 

vertical hydraulic conductivity of the mud (VK4) were each 

varied independently over a range of 0.2 to 5 times their 

calibrated value. Recharge fluxes were held constant for 

the set of sensitivity runs. Model sensitivity is reported in 

terms of the sum of squared residuals between simulated 

and measured water levels (fig. 7A). Simulated water levels 

are most sensitive to VK4. Heads are matched more closely 

with higher HK2 values, although the improvement becomes 

less significant after 2 times the calibrated value. Because 

the sum of squared residual statistic may be dominated by 

the water levels at the water table, however, flows through 

the upgradient (east) and downgradient (west) specified head 

boundaries were also compared (figs. 7B,C). Simulated flows 

through the boundaries are most sensitive to HK2, followed 

by VK4. Both simulated water levels and flows are generally 

insensitive to changes in HK3 and VK3. The hydraulic 

conductivity and anisotropy of the muddy sand facies (HK3 

and VK3) can vary widely, depending on whether the fine 

sands have interstitial or laminated silts and clay present, 

and the muddy sand facies is likely one of the least wellcharacterized hydrofacies (Dalgish, 2006). Sensitivity runs 

with constant anisotropy of 2 for HK3 and VK3 indicate that 

simulated water levels and flows were insensitive to changes 

in HK3 and VK3 (figs. 7A,B,C). FLOW , IN CUBIC METERS PER DAY

SPECIFIED HEAD OR FLUX MODEL BOUNDARY

EAST WEST TOP

(Recharge)

BOTTOM

20,000

30,000

40,000

Regional model

Local-scale model

10,000

0

-10,000

Figure 6. Comparison between boundary flows in the regional 

model and boundary flows in the calibrated local ground-water 

flow model near Modesto, eastern San Joaquin Valley, California.

In the local model, east, west, and bottom boundaries are 

specified head and top boundary is specified flux. 

Ground-Water Flow Model Results

Simulated Water Levels and Flows

The simulated water table (fig. 8) indicates that 

horizontal movement of ground water in the shallow part of 

the aquifer system generally is from north to south from the 

agricultural area toward the center of the urban area. The 

simulated horizontal hydraulic gradient was about 0.002. In 

contrast, horizontal movement of water at layer 150 (80–85 

m below land surface) was generally from the northeast to 

southwest and had a horizontal hydraulic gradient of about 

0.001 (fig. 9). The differences in horizontal flow direction 

between the shallow and the deep system are likely related to 

the distribution of pumping. Although only 14 percent of the 

total simulated withdrawals occurred in layers deeper than 

layer 150, 3 wells that each accounted for at least 10 percent 

and together totaled 59 percent of the withdrawals below layer 

150 are in the northwest part of the model. The simulated and 

measured vertical gradients in the study area indicate that most 

ground water moves downward toward pumping well screens 

(fig. 10). 

Simulated Budget

The steady-state volumetric ground-water flow budget 

indicates the importance of recharge and pumping stress on 

the aquifer system (table 4). Total flow through the model was 

about 98,000 m3/d. Inflow through the upgradient and recharge 

boundaries accounted for 40 and 26 percent of the total inflow, 

respectively, whereas outflow through the wells accounted 

for 51 percent of the total outflow. The model was partially 

calibrated to flows from the regional model at specified 

head boundaries (fig. 6), so the resulting flows are strongly 

controlled by boundary conditions generated from the regional 

model. 

Simulation of Advective Transport by 

Particle Tracking 

Particle tracking was used to compute pathlines and 

advective travel times in the local ground-water flow model. 

The CRA and ZOC were delineated for the public-supply well 

and used to characterize the age and source of water reaching 

the well. Simulated travel times and recharge rates for the 

public-supply well and the monitoring wells were combined 

with estimated input concentrations for various tracers to 

calculate simulated flux-weighted concentrations reaching 

the wells. The simulated concentrations were compared to 

measured concentrations in the wells to evaluate the adequacy 

of model parameters. Long term concentrations of nitrate and 

uranium in the public-supply well were estimated using input 

concentrations for nitrate and alkalinity concentrations.
18 Simulations of Ground-Water Flow and Particle Pathline Analysis, Zone of Contribution of a Public-Supply Well, Modesto, Calif.

10

0

10,000

15,000

20,000

25,000

30,000

35,000

40,000

45,000

20

30

40

50

60

0.1 1 10

0.1 1 10

0.1 1 10

MULTIPLIER OF CALIBRATED VALUE

EXPLANATION

A

B

C

Parameter varied in local model

SUM OF SQUARED RESIDUALS,

IN METERS SQUARED

NET FLOW THROUGH UPGRADIENT (EAST)

BOUNDARY, IN CUBIC METERS PER DAY

NET FLOW THROUGH DOWNGRADIENT (WEST)

BOUNDARY, IN CUBIC METERS PER DAY

10,000

5,000

0

-5,000

-10,000

-15,000

-20,000

15,000

Regional model value

HK2 (horizontal K of sand)

HK3 (horizontal K of muddy sand)

VK3 (vertical K of muddy sand)

VK4 (vertical K of mud)

HK3/VK3 = 2

Figure 7. Sensitivity of model parameters with respect to (A) sum of squared residuals of simulated and measured water levels, (B) net 

flow through upgradient (east) boundary, and (C) net flow through downgradient (west) boundary. 

HK2, horizontal hydraulic conductivity of sand hydrofacies; HK3, horizontal hydraulic conductivity of muddy sand hydrofacies; VK3, 

vertical hydraulic conductivity of muddy sand hydrofacies; VK4, vertical hydraulic conductivity of mud hydrofacies; HK3/VK3, ratio of 

horizontal to vertical hydraulic conductivity for muddy sand hydrofacies. 
Simulation of Advective Transport by Particle Tracking 19

EXPLANATION

13 to 15 

>15 to 17 

>17 to 19 

>19 to 21 

>21 to 23 

>23 to 25 

>25 to 27 

>27 to 29 

>29 to 31 

>31 to 33

Simulated water-table elevation, in meters. Datum

is North American Vertical Datum of 1988.

>, is greater than

Boundary containing active area of local model 

Road or highway 

Agricultural land use area 

Urban land use area 

Monitoring well location and identifier

Pumping well represented as multinode well in

ground-water flow model 

Pumping well 

FPB

PSW

FPA

FPB

FPC

FPD

FPE

OFPA

OFPB

SA SB

SC

0 0.5 1 1.5 Miles

0 0.5 1 1.5 Kilometers

Figure 8. Simulated water table elevation in local ground-water flow model near Modesto, eastern San Joaquin Valley, California. 

PSW, public-supply well.
20 Simulations of Ground-Water Flow and Particle Pathline Analysis, Zone of Contribution of a Public-Supply Well, Modesto, Calif.

A

A A'

A'

EXPLANATION

Boundary containing active area of local model 

Road or highway 

Approximate location of section

shown in figure 10 

Agricultural land use area 

Urban land use area 

Monitoring well location and identifier

Pumping well represented as multinode well in

ground-water flow model 

Pumping well 

FPB

0 0.5 1 1.5 Miles

0 0.5 1 1.5 Kilometers

<12

>12 to 13 

>13 to 14 

>14 to 15 

>15 to 16 

>16 to 17 

>17 to 18 

>18 to 19 

>19

Simulated water-level elevation of model

layer 150, in meters. Datum is North American

Vertical Datum of 1988. < is less than or equal to;

>, is greater than 

-

-

FPA

FPB

FPC

FPD

FPE

OFPA

OFPB

SA SB

PSW SC

Figure 9. Simulated water level in model layer 150 in local ground-water flow model near Modesto, eastern San Joaquin Valley, 

California. 

PSW, public-supply well.
Simulation of Advective Transport by Particle Tracking 21

Methods and Model Parameters 

Ground-water pathlines and advective travel times for 

the calibrated local ground-water flow model were calculated 

using the program MODPATH (Pollock, 1994). The travel 

times calculated using this method represent an average travel 

time for the advection of a “particle” of water or conservative 

solute, but also includes the effects of macro-scale mechanical 

dispersion caused by the three-dimensional distribution of 

hydrofacies. 

An effective porosity was specified for each active cell 

according to the hydrofacies category defined for that cell. An 

effective porosity of 0.20 was used for the gravel hydrofacies; 

0.25 was used for the sand hydrofacies; 0.30 was used for 

the muddy sand hydrofacies; 0.35 was used for the mud 

hydrofacies. Effective porosities were estimated at the low end 

of a range of total porosity values (Domenico and Schwartz, 

1998); the weighted-average effective porosity was 31 percent.

24

21

18

15

12

Simulated water-level elevation, in meters.

Datum is North American Vertical Datum of 1988. 

A A'

Public-supply

well

0

0 0.4 0.8 Mile

Screened interval of 0.4 0.8 Kilometer

pumping well 

EXPLANATION

100

50

0

L AYER 150 

METERS

Vertical exaggeration 26:1 

0

50

100

METERS

Figure 10. Simulated water level along vertical transect A-A′ in local ground-water flow model near Modesto, eastern San Joaquin 

Valley, California. Location of transect shown on figure 9. 

Table 4. Volumetric budget of local ground-water flow model 

near Modesto, eastern San Joaquin Valley, California.

Boundary or stress

In Out

In cubic meters per day

Constant head 63,381 39,989

Recharge 25,091 0

Specified flows 9,220 7,948

Wells 381 50,327

Total 98,073 98,264

Percent discrepancy -0.19
22 Simulations of Ground-Water Flow and Particle Pathline Analysis, Zone of Contribution of a Public-Supply Well, Modesto, Calif.

Simulated tracer concentrations in the public-supply well 

were computed using forward tracking from recharge areas to 

the screened interval of the public-supply well. The particles 

were uniformly distributed on the face of the model cells 

associated with the inflow to the model. The flow associated 

with each particle was computed by dividing the inflow at 

the source face by the number of particles started at that face. 

The subset of particles that terminated at the public-supply 

well was used to define the area contributing recharge to that 

well. The flow and travel times associated with those particles 

that discharged at the public-supply well were then used to 

estimate tracer concentrations. The tracer concentration was 

assigned to each particle on the basis of the travel time and 

by assuming an input concentration of the tracer over time. A 

flux-weighted average concentration for the public-supply well 

was determined by multiplying the sum of the concentrations 

of particles in each layer by the total flow associated with that 

layer, and summing all the layers. Some particles that reached 

the public-supply well did not originate at recharge cells in the 

local model; rather, they originated at the lateral boundaries 

of the local ground-water flow model. In these cases, particles 

were placed at recharge locations in the regional ground-water 

flow model and tracked to equivalent locations on the lateral 

boundary of the regional model. The resulting travel times for 

these particles are the sum of the travel times from the local 

and the regional ground-water flow models. These particles, 

which did not originate at the recharge boundary in the local 

model, accounted for less than 0.5 percent of the flow to the 

well. 

Simulated ages and CRAs also were computed for 23 

monitoring wells sampled in this study by backtracking 

particles from each well screen to their recharge area. 

Similar to the particle tracking for the public-supply well, 

some particles did not terminate at recharge cells but instead 

terminated at the lateral boundaries of the local model. 

Particles were placed at equivalent locations along the lateral 

boundary of the regional ground-water flow model and tracked 

backwards to recharge locations. 

Particle Tracking Results and Comparison to 

Age Tracer Concentrations 

The CRA and ZOC were computed for the public-supply 

well and the monitoring wells in the study area to evaluate 

particle travel times (hereinafter referred to as simulated 

age), and to relate ground-water quality to land use in the 

CRA. The computed CRA for the public-supply well covers 

about 45 km2 and extends from about 0.5 km to the south 

and southwest of the well to about 2 km to the north and 

northeast of the well (fig. 11), overlying both the urban and the 

agricultural areas. The age of particles recharged in different 

cells varies spatially within the CRA, influenced by the 

heterogeneous hydrofacies distribution used in the model. In 

general, particle ages are less than about 30 years immediately 

northeast of the well and in the northwestern part of the CRA, 

whereas ages exceed 90 years southeast of the well and on the 

northeastern edge of the CRA. Although the simulated CRA 

does not exactly represent the recharge area and age of ground 

water reaching the public-supply well, the ‘patchy’ appearance 

of recharge areas of young age adjacent to recharge areas of 

old age is probably a realistic feature of this aquifer system 

and is consistent with the conceptual understanding of the 

hydrogeology. 

The simulated ages of particles reaching the publicsupply well ranged from 9 to 30,000 years; the median was 54 

years (table 5). Particle ages were weighted according to the 

flow associated with each particle for each layer along the well 

screen. Simulated ages indicate that a large proportion of the 

water contributed to the public-supply well is less than about 

75 years old (fig. 12); however, 25 percent of the water is more 

than 100 years old, indicating that the well pumps water of a 

mixture of ages, spanning a wide range of hydraulic conditions 

in the aquifer system over time. 

The age of the ground water contributed to the publicsupply well increases with depth below the water table 

(fig. 13), reflecting a generally linear increase in age with 

depth in the shallow part of the well (less than 45 m below the 

water table) and a logarithmic increase in age with depth in 

the deeper part of the well. At depths of less than about 45 m 

below the water table, particle ages are less than 100 years. At 

depths of more than 60 m below the water table, the particle 

ages range from 140 to 1,300 years, constituting 25 percent 

of the flow to the well. The maximum weighted particle age 

of more than 30,000 years was calculated to be 75 m below 

the water table (not shown on figure 13). Flow to the well at 

this depth represents only 0.8 percent of the total flow to the 

well because of the fine-grained layers adjacent to the screen, 

which is consistent with a lack of measured wellbore flow in 

this interval during pumping (Jurgens and others, in press). 

Because the public-supply well did not exist 140 years ago 

and the intensity of pumping in the ground-water system 

did not increase until the 1940s or 1950s, the steady-state 

pumping conditions represented in the model likely represent a 

minimum age of ground water at depths more than 60 m below 

the water table. Prior to pumping, travel times to the deep part 

of the aquifer were likely much longer. Ground water entering 

the bottom of the well more than 60 m below the water table 

was expected to be generally unaffected by anthropogenic 

inputs at the land surface. 

The simulated ages of particles reaching the 23 

monitoring wells were similar to the simulated ages of 

particles reaching the public-supply well at similar depths in 

the aquifer (fig. 13). The median simulated age of particles 

reaching water table wells ranged from 0.4 to 7.3 years, and 

the median simulated age of particles reaching intermediatedepth wells ranged from 31 to 150 years. The median 

simulated age of particles reaching the deepest monitoring 

wells at depths equal to the deepest part of the public-supply 

well ranged from 1,100 to 1,700 years (table 6). 
Simulation of Advective Transport by Particle Tracking 23

Figure 11. Contributing recharge area and particle travel times to public-supply well near Modesto, eastern San Joaquin Valley, 

California. 

PSW, public-supply well.

EXPLANATION

Boundary containing active area of local model 

Road or highway 

Monitoring well location and identifier

Pumping well represented as multinode well in

ground-water flow model 

Pumping well 

FPB

0 0.5 1 1.5 Miles

0 0.5 1 1.5 Kilometers

8 to 10

>10 to 20

>20 to 30

>30 to 40

>40 to 50

>50 to 60

>60 to 70

>70 to 80

>80 to 90

>90 to 100

>100 

Travel time to public-supply well from

 contributing recharge area, in years.

 >, is greater than

FPA

FPB

FPC

FPD

FPE

OFPA

OFPB

SA SB

SC

PSW
24 Simulations of Ground-Water Flow and Particle Pathline Analysis, Zone of Contribution of a Public-Supply Well, Modesto, Calif.

Ground-water ages derived by interpreting samples of 

age dating tracers (Jurgens and others, in press) generally 

agree with simulated ages (tables 5 and 6; fig. 13). The median 

simulated age of 54 years for water in the public-supply 

well is similar to the interpreted age of 55 years from agedating tracers; however, the interpreted ages were more than 

50 percent older than the median simulated ages for water in 

2 water table wells (FPC-1 and FPD-1), 1 intermediate-depth 

well (FPD-2), and all 4 deep wells (FPA-4, FPB-3, FPC-3, and 

FPD-3). Simulated ages in the deep monitoring wells should 

differ from interpreted ground-water ages from the age-dating 

tracers because steady-state conditions that included pumping 

were simulated and the oldest interpreted ages pre-date 

pumping. The simulated age was older than the age interpreted 

from age-dating tracers only in the public-supply well and in 

monitoring well FPB-2. 

The ground-water age interpreted from age-dating 

tracers is not measured directly. Interpreted ground-water 

age is estimated using simple analytical models that describe 

age distributions for various combinations of recharge area 

and aquifer geometry (Cook and Böhlke, 1999). Although 

the comparison between simulated and interpreted groundwater ages is useful to generally evaluate whether simulated 

ages reasonably represent measured ages, direct comparison 

is difficult. The age interpreted from age-dating tracers does 

not directly account for the age and fraction of pre-traceraged water in the sample, and some simplifying assumptions 

about the age distribution of the flow system must be made 

in the interpretation. 

A more robust comparison between simulated 

ground-water age and interpreted age from age-dating 

tracers was made by comparing simulated and measured 

concentrations of the age-dating tracers rather than simulated 

and interpreted ages. Concentrations were assigned to 

particles on the basis of flow-weighted particle age and 

input concentration histories for sulfur hexafluoride (SF6) 

and tritium (3H) (fig. 14). Atmospheric concentrations of 

SF6 have increased since the 1950s, and SF6 concentrations 

have been used to date recently recharged ground 

water (Busenberg and Plummer, 2000; Böhlke, 2005). 

Concentrations of 3H in precipitation (Michel, 1989) peaked 

in the 1960s (fig. 14), indicating that the comparison 

to concentrations between simulated and measured 3H 

concentrations could be non-unique. 3H concentrations were 

adjusted for radioactive decay to 2004 assuming a 12.3 

year half-life. Ground-water samples were collected from 

the public-supply well and shallow monitoring wells, and 

were analyzed for dissolved SF6 gas and 3H concentrations 

(Jurgens and others, in press); concentrations measured in 

the wells were compared with simulated concentrations. 

Figure 12. Simulated flow-weighted age of particles reaching 

the public-supply well near Modesto, eastern San Joaquin Valley, 

California. 

0

0

0.005

0.010

0.015

0.020

0.025

100 200 300

SIMULATED PARTICLE AGE, IN YEARS

FRACTION OF FLOW TO WELL

400 500

Depth to top of screened interval

(m below land surface)

27.7

Depth to bottom of open interval 119.2

Depth to water 10.2

Ground-water age interpreted from age tracers (years)1 55

Simulated ground-water age (years)2

 Minimum 9

 Median 54

 Mean 420

 Maximum 30,000

Area contributing recharge (km2) 45

Mean velocity (m/d) 0.026

Median velocity (m/d) 0.017

Volume of ZOC (m3) 325,000,000

Pumping rate (m3/d) 3,746

 

Table 5. Summary statistics for the simulated contributing recharge area and the zone of 

contribution of the public-supply well near Modesto, eastern San Joaquin Valley, California. 

[ZOC, zone of contribution. m, meter; km2, square kilometer; m/d, meter per day; m3, cubic meter; m3/d, cubic 

meter per day]

1

Interpreted ground-water age is from Jurgens and others (in press).

2

Simulated ground-water age for public-supply well is flow-weighted average of particle travel times for each 

model layer at well screen.
Simulation of Advective Transport by Particle Tracking 25

The simulated SF6 concentration of 0.40 part per trillion 

by volume (pptv) in the public-supply well was lower than 

the measured concentration of 0.73 pptv (fig. 15A). Similarly, 

simulated concentrations of SF6 for the monitoring wells were 

lower than measured concentrations in the intermediate-depth 

monitoring wells (FPB-2, FPC-2, FPD-2) and higher than 

measured concentrations in the water table wells, especially in 

wells FPC-1 and FPD-1. Although simulated concentrations 

were not expected to exactly match measured concentrations 

because the hydraulic conductivity distribution did not reflect 

the true distribution, Jurgens and others (in press) noted 

that SF6 concentrations measured in shallow ground water 

were lower than expected, and measured concentrations in 

intermediate-depth ground water were higher than expected, 

for ages interpreted from other ground-water age tracers. 

The simulated 3H concentration of 5.8 tritium units 

(TU) in the public-supply well was slightly higher than 

the measured concentration of 4.6 TU (fig. 15B). Many 

of the simulated concentrations of 3H for the monitoring 

wells were similar to measured concentrations; however, 

simulated concentrations were much lower than measured 

concentrations in 6 wells (FPA-2, FPA-3, FPB-2, FPE-2, 

OFPA-2, and OFPB-2) and much higher than measured 

concentrations in 1 well (FPD-2). All of these wells are 

screened in the intermediate depths in the aquifer. The reasons 

for concentrations being lower could be because of possible 

differences in measured and calibrated hydraulic conductivity 

values (at each well), although results for only 3 of the 6 wells 

could be explained by differences in hydraulic conductivity. 

Also, simulated concentrations of 3H at intermediate 

depths are strongly sensitive to the particle ages because 3H 

concentrations peak (fig. 14) during the recharge dates of 

water contained in this zone. Overall, the trend for simulated 

3

H concentrations with depth in both the public-supply well 

and the monitoring wells generally corresponds with the trend 

in measured 3H concentrations with depth (fig. 16). 

Comparison between Land Use in the 

Contributing Recharge Area (CRA) and 

Occurrence of Selected Constituents 

The local ground-water flow model generally matches 

observed conditions in the ZOC of the public-supply well, 

and can be used to link sources of contaminants in the CRA 

with concentrations in the public-supply well. The CRA for 

the public-supply well lies predominantly beneath the current 

(2001) urban land use area (fig. 11). Analysis of recent 

land-use maps indicates that about 67 percent of the CRA 

is beneath urban land, whereas only 32 percent is beneath 

agricultural land (table 7). Both agricultural and urban 

contaminants are expected to exist at the water table beneath 

the CRA. The urban area has expanded north and west of 

the public-supply well since the 1960s, with residential and 

commercial development replacing agricultural land. 

Ground water within the ZOC older than about 40 

years was expected to contain primarily agricultural-related 

contaminants, whereas ground water younger than 40 

years was expected to contain both urban and agricultural 

contaminants. Elevated concentrations of nitrate and low 

concentrations of VOCs and pesticides have been measured 

in the public-supply well (table 7), which is consistent with 

both agricultural and urban sources. Although elevated 

concentrations of nitrate do not indicate exclusively 

agricultural input, previous monitoring of ground-water 

quality beneath agricultural land (Burow and others, 1998; 

Burow and others, in press) has increased expectations of 

elevated nitrate levels. 

1

0

10

20

30

40

50

60

70

80

10 100

GROUND-WATER AGE, IN YEARS

EXPLANATION

DEPTH BELOW WATER TABLE, IN METERS

1,000 10,000

Simulated age in public-supply well,

flow-weighted average for each model layer

Simulated age in monitoring well

Interpreted age from age-dating tracers

Figure 13. Simulated age and interpreted ground-water age from 

age-dating tracers, as compared with depth below water table 

in monitoring wells and the public-supply well near Modesto, 

eastern San Joaquin Valley, California. 

Simulated ages in the public-supply well are flow-weighted. 

Interpreted ground-water age from Jurgens and others, in press. 
26 Simulations of Ground-Water Flow and Particle Pathline Analysis, Zone of Contribution of a Public-Supply Well, Modesto, Calif.

The stable isotope composition of ground 

water from the public-supply well also is 

consistent with the composition of surface water 

used for irrigation (Jurgens and others, in press), 

further indicating that the nitrate concentration in 

the public-supply well may be derived primarily 

from previous agricultural inputs. However, the 

composition of ground water reaching the publicsupply well reflects urban inputs also. The VOCs 

detected in the public-supply well (chlorinated 

solvents, disinfection byproducts; Jurgens and 

others, in press) are likely derived from urban 

land-use practices because they were not detected 

in the agricultural monitoring networks and are 

typically detected in ground water beneath urban 

areas nationwide (Squillace and others, 2004). 

The pesticides detected in the public-supply well 

(simazine, atrazine, and desethyl atrazine) could 

be derived from either agricultural or urban use. 

Well name

Depth 

category/ Well 

type1

Depth to top 

of screened 

interval

Depth to 

bottom of 

screened or 

open interval

Depth to 

water

Ground-water 

age interpreted 

from age 

tracers2 

(years)

Simulated ground-water age 

(years)

In meters below land surface) Minimum Median Maximum

FPA-1 Water table 9.1 10.7 7.8 6 3.3 4.0 4.6

FPA-2 Shallow 35.1 36.6 7.9 32 19 21 44

FPA-3 Intermediate 65.5 67.1 10.1 81 74 80 86

FPA-4 Deep 104.5 106.1 10.5 4,600 1,100 1,100 1,100

FPB-1 Water table 9.1 10.7 7.8 10 4.8 6.1 7.4

FPB-2 Intermediate 57.0 58.5 10.9 53 59 80 100

FPB-3 Deep 100.0 101.5 11.5 9,300 1,300 1,400 1,500

FPC-1 Water table 11.9 13.4 8.5 15 3.2 3.8 4.3

FPC-2 Intermediate 61.9 63.4 11.8 32 32 32 32

FPC-3 Deep 105.8 107.3 12.2 8,300 1,600 1,700 1,800

FPD-1 Water table 8.5 10.1 9.3 12 0.3 0.6 1.0

FPD-2 Intermediate 50.9 52.4 13.0 90 31 31 32

FPD-3 Deep 101.8 103.3 13.5 7,100 1,200 1,200 1,200

FPE-1 Water table 9.1 10.7 8.8 — 0.8 0.9 2.0

FPE-2 Shallow 29.9 31.4 8.8 — 15 18 28

FPE-3 Intermediate 61.9 63.4 11.9 — 45 47 48

OFPA-1 Water table 9.1 10.7 9.2 — 2.1 2.1 2.7

OFPA-2 Shallow 29.0 30.5 9.2 — 72 78 90

OFPA-3 Intermediate 57.3 58.8 11.9 — 140 150 180

OFPB-2 Intermediate 50.6 52.1 11.3 — 36 56 64

SA Water table 9.1 10.7 8.7 — 1.9 2.3 12

SB Water table 9.1 10.7 9.3 — 0.2 0.4 0.7

SC Water table 9.1 10.7 10.2 — 5.1 7.3 9.5 1

Well depth zones are depth below land surface and were characterized by Jurgens and others (in press) for use in interpreting the geochemical data. 

2

Interpreted ground-water ages are from Jurgens and others (in press).

Table 6. Well characteristics and simulated and interpreted ground-water ages from age-dating tracers in monitoring wells sampled 

in 2003-2005 near Modesto, eastern San Joaquin Valley, California. 

[—, no data]

1940 1950 1960 1970

DATE RECHARGED

SULFUR HEXAFLUORIDE (SF6) CONCENTRATION,

IN PARTS PER TRILLION BY VOLUME

TRITIUM (3H) CONCENTRATION IN 2004,

IN TRITIUM UNITS

1980 1990 2000

0 0

10

20

30

40

50

60

70

80

90

100

1

2

3

4

5

6

7

3H

SF6

Figure 14. Concentrations of tritium (3H) and sulfur hexafluoride 

(SF6

) in recharge. 3

H concentrations are updated from Michel (1989) and corrected 

for decay to 2004; SF6

 concentrations are updated from Busenberg 

and Plummer (2000). 
Simulation of Advective Transport by Particle Tracking 27

Land use in the CRAs for the monitoring wells in the 

study area ranged from 100 percent urban land to 100 percent 

agricultural land; two wells were each in a CRA that had a 

mixture of urban and agricultural land use (FPA-2 and SA) 

(table 7). Most of the wells with CRAs containing 100 percent 

agricultural land use had concentrations of nitrate that were 

consistent with either agricultural or old, unaffected ground 

water. Three wells, FPA-4, FPC-2, and OFPB-2, had VOCs 

typically found in urban land-use settings, in spite of having 

a CRA containing 100-percent agricultural land use. FPA-4 

was affected by downward movement of contaminants through 

the adjacent public-supply well when the public-supply well 

was not in operation (Jurgens and others, in press). Both 

FPC-2 and OFPB-2 are in areas in transition from agricultural 

to urban land use, and might be influenced by newer urban 

development. 

Figure 15. Simulated and measured concentrations of (A) sulfur 

hexafluoride (SF6

) and (B) tritium (3H) in monitoring wells and the 

public-supply well near Modesto, eastern San Joaquin Valley, 

California.

A

B

0

0 5 10 15 20

0

0

5

10

15

20

1

2

3

4

5

6

1 2 3 4 5 6

FPD-1

FPD-2

FPD-2

FPC-1

EXPLANATION

FPC-2

FPC-2

FPB-2

FPB-2

FPE-2

FPA-2

OFPA-2

OFPB-2

FPA-3

MEASURED SF6 CONCENTRATION,

IN PARTS PER TRILLION BY VOLUME

MEASURED 3H CONCENTRATION,

IN TRITIUM UNITS

SIMULATED SF6 CONCENTRATION,

IN PARTS PER TRILLION BY VOLUME

SIMULATED 3H CONCENTRATION,

IN TRITIUM UNITS

1:1 correlation line

Monitoring wells

Public-supply well

1:1 correlation line

0

0 5 10 15 20

10

20

30

40

50

60

70

80

90

100

Measured in monitoring wells

Simulated in monitoring wells

Simulated in public-supply wells

DEPTH BELOW WATER TABLE, IN METERS

TRITIUM CONCENTRATION, IN TRITIUM UNITS

EXPLANATION

Figure 16. Simulated and measured tritium (3H) concentrations 

with depth in monitoring wells and the public-supply well near 

Modesto, eastern San Joaquin Valley, California.
28 Simulations of Ground-Water Flow and Particle Pathline Analysis, Zone of Contribution of a Public-Supply Well, Modesto, Calif. Well name Nitrate concen- tration (mg/L, as N) Number of VOCs detected Number of pesticides detected1 Median age of simulated groundwater (years) Recent general land use in contributing recharge area Recent detailed land use in contributing recharge area Urban Agricul- tural Urban: Low intensity residential Urban: Residential/ other Urban: Commercial/ industrial/ transportation Agriculture: Orchards/ vineyards/ other Agriculture: Row crops Agriculture: Pasture/hay Rangeland: Grasslands/ herbaceous (percent) (percent) PSW 5.5 5 3 54 67 30 50 4 13 4 4 22 2 FPA-1 1.5 3 4 (URB) 4.0 100 0 100 FPA-2 12 2 0 21 52 48 17 18 17 40 8 FPA-3 3.0 0 0 80 0 100 100 FPA-4 2.4 2 1 1,100 0 100 100 FPB-1 3.2 3 0 6.1 100 0 100 FPB-2 4.0 1 0 80 100 0 4 34 62 FPB-3 1.0 0 0 1,400 0 100 92 8 FPC-1 13 4 4 3.8 100 0 100 FPC-2 8.7 1 2 (AG) 32 0 100 100 FPC-3 1.5 0 0 1,700 0 100 100 FPD-1 17 0 4 (AG) 0.6 0 100 100 FPD-2 4.0 0 1 (AG) 31 0 100 100 FPD-3 1.8 1 0 1,200 100 0 100 FPE-1 1.8 1 3 (URB) 0.9 100 0 100 FPE-2 13 3 3 18 100 0 92 8 FPE-3 5.6 0 0 47 100 0 100 OFPA-1 3.1 5 2 2.1 100 0 64 36 OFPA-2 12 0 0 78 100 0 83 17 OFPA-3 4.4 0 0 150 100 0 96 4 OFPB-2 1.6 2 2 56 0 98 31 67 2 SA 2.4 4 1 (AG) 2.3 81 19 81 19 SB 6.5 3 2 0.4 100 0 100 SC 11 8 1 7.3 100 0 100 Table 7. Nitrate concentrations, volatile organic compound and pesticide occurrence, and relation to land use in the contributing recharge areas of the public-supply well and monitoring wells in Modesto, eastern San Joaquin Valley, California. [The land-use data set used for these classifications was an enhanced version of the U.S. Geological Survey 1992 National Land Cover Data (NLCD), which classified land use by each 30- by 20-meter area of land in the conterminous United States; the original and enhanced versions of the NLCD are described by Vogelmann and others (2001) and Nakagaki and Wolock (2005), respectively. Nitrate, VOC, and pesticide data are reported by Jurgens and others (in press). mg/L, milligrams per liter; N, nitrogen; —, no data; VOC, volatile organic compound, PSW, public-supply well]

1Pesticide use category in parentheses: URB, urban use only; AG, agricultural use only; no designation, pesticide is used in both urban and agricultural land-use settings.
Simulation of Advective Transport by Particle Tracking 29

Six of the 13 wells in a CRA where 100-percent of the 

land was urban had nitrate concentrations above 5 mg/L: 

FPC-1, FPE-2, FPE-3, OFPA-2, SB, and SC. Because 

many of the wells contain ground water that was recharged 

tens to thousands of years ago, concentrations of nitrate or 

other constituents may not be derived from recent land use. 

Therefore, the wells were also classified with respect to the 

most likely source of nitrate by evaluating the geochemistry 

of the ground water and determining the likely land use 

in the CRA at the time of recharge based on approximate 

dates of urban development (table 8). Nitrate concentrations 

in ground water reaching wells FPC-1, FPE-2, FPE-3 and 

OFPA-2 were elevated because of previous agricultural land 

use. However, elevated nitrate concentrations in ground water 

from SB and SC are likely due to septic inputs, on the basis 

of bromide-to-chloride ratios and the location of unsewered 

subdivisions (Jurgens and others, in press). The public-supply 

well, and 6 of the 12 wells containing nitrate derived from 

agricultural land use, contained VOCs also (FPA-2, FPB-2, 

FPC-1, FPC-2, FPE-2, and OFPB-2), suggesting that ground 

water from these wells could contain a mixture of urban and 

agricultural inputs. Most of these wells were screened at 

intermediate depths, from 20 to 50 m below the water table. In 

general, concentrations of nitrate in ground water dominated 

by agricultural inputs are high (median 7.2 mg/L), whereas 

concentrations in ground water dominated by urban inputs are 

low (median 3.1 mg/L) (table 8). 

Processes Affecting Nitrate and Uranium 

Concentrations in the Aquifer and the 

Public-Supply Well 

Nitrate concentrations in the ZOC of the public-supply 

well were highest near the water table beneath the agricultural 

land and at the shallow depth (table 8). Concentrations were 

above the MCL of 10 mg/L (U.S. Environmental Protection 

Agency, 2006) in 2 wells screened near the water table 

beneath the agricultural area and in 1 well beneath the urban 

area. The median nitrate concentration in wells screened near 

the water table beneath the agricultural area was 15 mg/L, 

whereas the median concentration in wells screened near 

the water table beneath the urban area was only 3.1 mg/L. 

Nitrate concentrations decrease with depth to background 

concentrations equaling about 2 mg/L or less in the deepest 

wells. Most of the aquifer is oxic (Jurgens and others, in 

press); therefore, nitrate was expected to be transported 

conservatively through the system. Nitrate concentration in 

the public-supply well (5.5 mg/L) was between concentrations 

in the shallow and the deep part of the ZOC because of the 

mixture of zones contributing ground water to the well. 

Wells were divided into water table (less than 5 m below the 

water table), shallow (up to 50 m below land surface), and 

intermediate (50 to 70 m below land surface), and deep zones 

(greater than 70 m below land surface) on the basis of depth 

and geochemistry of water reaching the wells (Jurgens and 

others, in press). Nitrate concentrations in the shallow depth 

zone are similar to concentrations at the water table beneath 

the agricultural area; concentrations are much lower in the 

intermediate depth zone (table 8). Because of the mostly 

downward movement of water in the study area, nitrate in 

shallow ground water is likely to continue moving downward. 

Long-term nitrate concentrations in the public-supply 

well will depend on the relative proportions of urban and 

agricultural land within the CRA of the well and the amount 

of nitrogen input within each of these settings. High nitrate 

concentrations derived from agricultural fertilizer and low 

nitrate concentrations near the water table from urban recharge 

will continue to move downward and contribute to the total 

nitrate concentrations in the well. If nitrate input beneath the 

urban area remains low, then nitrate concentrations in the 

public-supply well will level off and decrease. If nitrate input 

beneath the agricultural area increases significantly, nitrate 

concentrations could increase in the public-supply well, 

although urban development in the CRA would decrease the 

amount of agriculturally-derived water reaching the well. 

Fertilizers were the primary source of nitrate in the ZOC 

of the public-supply well. The generally high concentrations 

beneath the agricultural area, low concentrations beneath 

the urban area, and the decrease in nitrate concentrations 

below the shallow depth are consistent with the history of 

nitrogen fertilizer use. Estimates of nitrogen concentrations 

in recharge water from nitrogen fertilizer applied over time 

were used as input concentrations for the simulation of 

nitrate concentrations in the public-supply well (fig. 17). 

Nitrate concentrations in recharge water were estimated using 

a method outlined by Böhlke (2002) using ground-water 

recharge dates and county-based nitrogen fertilizer application 

data (Alexander and Smith, 1990; Ruddy and others, 2006). 

This method is described below.

On the basis of mean ground-water ages from age-dating 

tracers collected in the monitoring wells, a linear ground-water 

age gradient with depth was characterized (Cook and Böhlke, 

1999), indicating a constant vertical velocity with depth for 

ground water younger than about 60 years. The estimated 

recharge rate, r, was calculated using the equation, 

r nZ

n

Z

 

where

is the effective porosity,

is the saturated t

= / , τ

hickness of the aquifer, and

τ is the mean age of ground water in the aquifer 

(Cook and Böhlke, 1999; Böhlke, 2002).

(1)
30 Simulations of Ground-Water Flow and Particle Pathline Analysis, Zone of Contribution of a Public-Supply Well, Modesto, Calif.

An effective porosity of 0.3 and a saturated thickness of 

55 m were assumed. A mean ground-water age of 42 years 

was calculated by averaging the mean ages derived from the 

age-dating tracers. The resulting estimated recharge rate was 

0.4 m/yr. The nitrogen application was estimated by dividing 

the reported nitrogen fertilizer application for the county 

(Ruddy and others, 2006) by the area of fertilized land in that 

county and assuming that 50 percent of the nitrogen fertilizer 

reached the water table. Similar leaching fractions have been 

reported for agricultural recharge in other areas in the United 

States (Böhlke and Denver, 1995; Böhlke, 2002). Estimated 

nitrate concentrations in recharge within the CRA of the 

public-supply well were then calculated by assuming that the 

proportion of agricultural input in the CRA had decreased and 

the proportion of urban input had increased beginning in about 

1960, when urban development began in this area. The nitrate 

input in the urban area was assumed to be 3.1 mg/L, which 

is the median concentration in water table wells beneath the 

urban area (table 8). The median of expected concentrations 

in recharge caused by nonfarm fertilizer applications during 

1987–2001 (Ruddy and others, 2006) was 3.6 mg/L, which is 

consistent with the median concentrations measured in water 

table wells beneath the urban area. 

The concentration of nitrate in recharge consistently 

increased in the agricultural area between the 1940s and 1970s 

(fig. 17). The axes representing nitrate concentration and 

nitrogen fertilizer application in figure 17 are quantitatively 

related through the recharge rate, such that the application 

Well name Dominant land use affecting 

nitrate concentrations

Nitrate concentration, 

in mg/L as N

Uranium concentration, 

in μg/L

Alkalinity, dissolved 

(mg/L as CaCO3

)

Water table well depth zone1

FPA-1 Urban 1.5 32 363

FPB-1 Urban 3.2 11 308

FPC-1 Ag 13 23 376

FPD-1 Ag 17 23 232

FPE-1 Urban 1.8 4.8 246

OFPA-1 Urban 3.1 25 416

SA Urban 2.4 30 494

SB Urban 6.5 32 446

SC Urban 11 29 432

Median 3.2 25 376

Shallow well depth zone1

FPA-2 Ag 12 24 309

FPE-2 Ag 13 22 298

OFPA-2 Ag 12 45 380

Median 12 24 309

Intermediate well depth zone1

FPA-3 Ag 3.0 2.5 104

FPB-2 Ag 4.0 6.6 144

FPC-2 Ag 8.7 10 187

FPD-2 Ag 4.0 3.4 127

FPE-3 Ag 5.6 4.3 133

OFPA-3 Ag 4.4 3.7 129

OFPB-2 Ag 1.6 4.5 146

Median 4.0 4 146

Deep well depth zone1

FPA-4 Old 2.4 1.0 89

FPB-3 Old 1.0 0.3 80

FPC-3 Old 1.5 0.2 79

FPD-3 Old 1.8 0.6 90

Median 1.6 0.5 85

Public-supply well

PSW MIXED 5.5 11 174

Table 8. Nitrate, alkalinity and uranium concentrations from monitoring wells and the public-supply well sampled in 2003–2005 near 

Modesto, eastern San Joaquin Valley, California.

[Ag, agricultural; mg/L, milligram per liter; μg/L, microgram per liter; N, nitrogen; CaCO3, calcium carbonate; PSW, public-supply well]

1

Well depth zones are depth below land surface and were characterized by Jurgens and others (in press) for use in interpreting the geochemical data. 
Simulation of Advective Transport by Particle Tracking 31

amount on one axis corresponds to the expected concentration 

in recharge on the other axis. Estimated concentrations in 

recharge are similar to measured concentrations, although 

there are only 5 wells containing agriculturally-derived nitrate 

with corresponding ground-water recharge dates. A correlation 

between measured concentrations and estimated nitrate 

concentrations in recharge water from nitrogen fertilizer 

applications has been noted in other parts of the eastern San 

Joaquin Valley (Burow and others, 2007; Burow and others, in 

press). The low measured nitrate concentrations in the younger 

(1990s) water were from wells screened at the water table 

beneath the urban land-use setting and are not expected to 

have received agricultural fertilizer.

Results of the particle pathline analysis were used to 

compare simulated and measured nitrate concentrations in 

the public-supply well and monitoring wells. Using the same 

approach as that used for the SF6

 and 3H comparisons, nitrate 

concentrations were assigned to particles on the basis of flowweighted particle age and assuming an input concentration 

history for the agricultural and urban settings (fig. 17). 

Simulated nitrate concentrations were significantly correlated 

to measured nitrate concentrations in monitoring wells and 

to concentrations derived from historical data 

from regulatory compliance monitoring records 

for the public-supply well (p = 0.002, rho = 

0.47; Spearman’s rank correlation) (fig. 18). 

The simulated concentration of nitrate in the 

public-supply well was 6.0 mg/L, which is 

slightly higher than the measured concentration 

of 5.5 mg/L. Simulated concentrations in some 

monitoring wells were higher than measured 

concentrations (for example, FPD-1, FPD-2, 

FPC-2), and simulated concentrations in other 

monitoring wells were lower than measured 

concentrations (for example, SB, SC, OFPA-2). 

Some wells showed a similar discrepancy 

between simulated and measured tritium 

concentrations (FPD-2 and OFPA-2), suggesting 

that the simulated age distributions for these 

wells may not adequately reflect the actual age 

distribution. The measured nitrate concentration 

in FPD-1 was lower than simulated, likely the 

result of dilution by recharge of nearby canal 

water (Jurgens and others, in press). Measured 

nitrate concentrations in SB and SC were higher 

than simulated concentrations, probably a result 

of contributions from nearby septic systems. 

Other possible factors affecting measured 

nitrate concentrations included local variability 

in fertilizer management near the monitoring 

wells, other sources of nitrate such as manure, 

and the mixing of ground water of different ages 

in the ground-water samples. Manure was not 

expected to be a significant source of nitrate in 

the study area because of the absence of confined 

animal operations near the wells. The method 

Figure 17. Estimated concentrations of nitrate in recharge from 

nitrogen fertilizer applications over time and measured nitrate 

concentrations in monitoring wells. 

Measured concentrations of nitrate from ground water sampled during 

2003–2005 are plotted against corresponding interpreted ages from agedating tracers. The estimated concentrations of nitrate from fertilizer 

applications represents 50 percent of the nitrogen fertilizer applications 

divided by the area of fertilized land, dissolved in 0.4 meter per year of 

recharge. MCL, maximum contaminant level; % percent. Figure modified 

from Burow and others (in press). 

1940 1950 1960

Estimated nitrate concentration in recharge in urban area

Estimated nitrate concentration in recharge in agricultural area

Monitoring well in urban area

Monitoring well in agricultural area

1970

YEAR

EXPLANATION

NITRATE CONCENTRATION, IN MILLIGRAMS

PER LITER, AS NITROGEN

NITROGEN FERTILIZER APPLICATION,

IN KILOGRAMS PER HECTARE PER YEAR

1980 1990 2000

0

25

20

15

10

5

0

10

20

30

40

50

60

70

80

90

100

50% fertilizer N

MCL

used to compute estimated nitrogen fertilizer applications may 

over-estimate nitrate concentrations because of dispersion and 

mixing of ages in ground-water samples (Burow and others, 

2007). 

Measured uranium concentrations were highest near the 

water table (median 25 μg/L), and decreased in concentration 

with depth (median for deepest wells, 0.5 μg/L) (table 8). 

Uranium concentrations were higher than the MCL of 30 μg/L 

in 2 wells screened near the water table beneath the urban 

area. Uranium concentrations are similar beneath agricultural 

(median 23 μg/L) and urban (median 29 μg/L) areas. Uranium 

concentrations in the shallow depth zone are similar to 

concentrations at the water table. Uranium concentrations 

have been mobilized, and high concentrations near the water 

table have migrated to shallow depths along with nitrate. 

Concentrations are much lower in the intermediate depth zone 

than the shallow depth zone (table 8). Uranium concentration 

in the public-supply well (11 μg/L) was between those in 

the shallow and the deeper part of the system because of the 

mixture of zones contributing to the well. 
32 Simulations of Ground-Water Flow and Particle Pathline Analysis, Zone of Contribution of a Public-Supply Well, Modesto, Calif.

Uranium concentrations were strongly correlated 

(p < 0.01, rho = 0.95; Spearman’s rank correlation) to 

alkalinity (as CaCO3) (fig. 19). Because more alkalinity 

data was available than uranium data and because uranium 

concentrations are correlated to alkalinity, our analysis focused 

on alkalinity rather than uranium, and uranium concentrations 

in the public-supply well were inferred from alkalinity. 

Sediment cores and geochemical analysis indicated that 

naturally-occurring uranium adsorbed to aquifer sediments has 

been mobilized by oxygen-rich, high-alkalinity (dominantly 

bicarbonate anion) water moving downward through the 

flow system (Jurgens and others, in press). Alkalinity has 

increased in shallow ground water over time. Historic data 

on bicarbonate alkalinity of shallow ground water indicate 

that concentrations were about 110 mg/L (as CaCO3

) in 1910 

(Mendenhall and others, 1916), and the median concentration 

in wells screened near the water table sampled in 2003–2005 

was 376 mg/L (table 8). Similar to the decrease in nitrate 

and uranium with depth, alkalinity remains generally high 

(median 309 mg/L) in the shallow depth wells and decreases 

significantly to a median of 146 mg/L in the intermediate 

depth wells and a median of 85 mg/L in the deepest wells. 

The cause for increased alkalinity in shallow ground water 

is not known, although it is hypothesized that high-alkalinity 

water has moved downward through the unsaturated zone 

to the water table and subsequently moved downward 

through the ground-water flow system. High alkalinity may 

have developed above the water table as a result of natural 

evaporative processes through time. After the onset of 

intensive irrigation and replacement of natural vegetation 

with crops having high transpiration rates, high-alkalinity 

water in the vadose zone may have moved to the water table 

(for example, see Lico, 1992). As ground-water pumping 

increased in the 1940s and 1950s, this high-alkalinity water 

began moving downward through the ground-water flow 

system, mobilizing adsorbed uranium along the way. The 

concept that high-alkalinity water was recharged and moved 

downward as agricultural development intensified is supported 

by statistically significant correlations between uranium and 

nitrate concentrations and alkalinity and nitrate concentrations 

(p = 0.013, rho = 0.52 and p = 0.03, rho = 0.46, respectively; 

Spearman’s rank correlation). As noted previously, nitrate 

concentrations increased in recharge during this time and, 

like high-alkalinity water, moved downward through the flow 

system. 

Results of the particle pathline analysis were used to 

develop an input concentration history for alkalinity. Using 

the same approach as that used for the SF6, 3H, and nitrate 

comparisons, concentrations were assigned to particles on the 

basis of flow-weighted particle age and assuming an input 

concentration history based on the conceptual model described 

above. The input function developed that is consistent with 

measured concentrations assumes that alkalinity concentration 

before 1900 was 80 mg/L; this assumption was based on 

measured background concentrations in the deep monitoring 

wells. From 1900 to 1945, alkalinity was assumed to be 110 

mg/L, an assumption based on historic concentrations before 

intensive agricultural development (Mendenhall and others, 

1916). From 1945 to 2005, alkalinity was assumed to increase 

linearly with time from 110 mg/L to current concentrations 

of about 450 mg/L at the water table. Alkalinity of about 

450 mg/L correlates to a uranium concentration of about 30 

μg/L, which is the current MCL for drinking water. This input 

function assumes no carbonate reactions. 

Simulated alkalinity concentrations were significantly 

correlated to measured concentrations in the public-supply 

well and monitoring wells (p < 0.001; rho = 0.83; Spearman’s 

rank correlation) (fig. 20). The simulated alkalinity in the 

public-supply well (197 mg/L) was higher than the measured 

concentration (174 mg/L). Measured concentrations were 

lower than simulated for FPD-2 and measured concentrations 

were higher for OFPA-2. These differences between measured 

and simulated concentrations were also noted for simulated 

and measured nitrate and for simulated and measured tritium 

concentrations, further suggesting that the simulated age 

distributions for these wells may not adequately reflect 

the actual age distribution. Measured concentrations lower 

than simulated concentrations for wells FPD-1 and FPE-1 

is consistent with dilution by low-alkalinity recharge water 

(Jurgens and others, in press). 

1:1 correlation line

0

0

5

10

15

20

25

5 10 15 20 25

MEASURED NITRATE CONCENTRATION,

IN MILLIGRAMS PER LITER, AS NITROGEN

SIMULATED NITRATE CONCENTRATION,

IN MILLIGRAMS PER LITER, AS NITROGEN

FPC-2

SC

SB

FPD-2

FPD-1

OFPA-2

EXPLANATION

Monitoring wells

Public-supply well, U.S. Geological Survey data

Public-supply well, historical data

Figure 18. Simulated and measured concentrations of nitrate 

in monitoring wells and the public-supply well near Modesto, 

eastern San Joaquin Valley, California. 

Historical data from city of Modesto, written commun., 2003.
Simulation of Advective Transport by Particle Tracking 33

In summary, these results indicate that nitrate and 

alkalinity concentrations in recharge have increased over time. 

High concentrations of nitrate and alkalinity in the shallow 

part of the system have moved downward, and are expected 

to continue to move downward through the system with time. 

Downward movement of nitrate and alkalinity through the 

aquifer will continue to affect concentrations of nitrate and 

uranium in the public-supply well as an increasing proportion 

of young, affected water is contributed to the well. 

Long-Term Concentrations of Nitrate and 

Uranium in the Public-Supply Well

The vulnerability of the public-supply well to nonpoint 

source inputs of nitrate and high-alkalinity water causing 

elevated concentrations of uranium is evident from the 

water chemistry data (Jurgens and others, in press) and the 

modeling analysis presented in this report. Assuming the 

present ground-water flow conditions persist, long-term 

concentrations of nitrate and uranium in the public-supply well 

will depend on the concentrations of nitrate and uranium at 

the water table in the future. Continued downward movement 

of ground water that is high in both nitrate and uranium 

will increase concentrations in the public-supply well as the 

proportion of younger water contributed to the well increases 

over time. To evaluate potential long-term nitrate and uranium 

concentrations in the public-supply well during the next 

100 years, additional particle pathline analysis was done. 

0 100 200 300 400 500

10

0

20

30

40

50

ALKALINITY, IN MILLIGRAMS PER LITER,

AS CALCIUM CARBONATE

URANIUM CONCENTRATION,

IN MICROGRAMS PER LITER

Water table

Shallow

Intermediate

Deep

Public-supply well

Depth zone of monitoring wells—

URANIUM MCL

EXPLANATION

Figure 19. Alkalinity and uranium concentrations in monitoring wells at different depths and in the public-supply well near Modesto, 

eastern San Joaquin Valley, California. 

Depth zones for monitoring wells listed in table 8. MCL, maximum contaminant level. 
34 Simulations of Ground-Water Flow and Particle Pathline Analysis, Zone of Contribution of a Public-Supply Well, Modesto, Calif.

Long-term nitrate concentrations in the public-supply 

well will depend on the proportion of urban and agricultural 

land within the contributing recharge area of the well and 

the amount of nitrogen input within each of these settings. 

Assuming the proportion of agricultural and urban land use 

remains fixed at the current proportion of about 70 percent 

urban land and 30 percent agricultural land, and assuming that 

the nitrate input concentrations beneath these settings remain 

the same (3.1 mg/L in the agricultural area and 17 mg/L in the 

agricultural area), simulated long-term nitrate concentrations 

in the public-supply well indicate that concentrations have 

peaked, and will decrease slightly to near 5 mg/L over the 

next century (fig. 21). Concentrations in the public-supply 

well would remain below input concentrations for at least 100 

years because of the long time needed to travel to the deepest 

part of the public-supply well. If application rates of nitrogen 

fertilizer in the agricultural area increase significantly, 

nitrate concentrations in the public-supply well will increase. 

However, given the current population growth and expansion 

of the urban area, it is likely that this well will eventually 

capture water recharged entirely within the urban area. In 

this case, if nitrate concentrations in recharge beneath the 

urban area remain low, concentrations will likely continue to 

decrease to near 3 mg/L over the long term. 

The simulated long-term nitrate concentrations 

in the public-supply well reflect a difference of 20 to 

30 years between peak concentrations in recharge and peak 

concentrations in the well. This apparent time lag is the 

result of the wide range of ages of water reaching the 

public-supply well (as a function of the distance to the well 

and ground-water velocity) combined with the characteristics 

of the input concentrations over time. An understanding of the 

length of time between changes in input concentrations and 

resulting concentrations in the public-supply well is needed to 

predict the impact of changes in land-use management. 

Uranium concentrations do not depend on the proportion 

of urban and agricultural land within the CRA area because 

alkalinity (and uranium) concentrations are high beneath both 

types of land. Continued downward migration of oxygenated, 

high-alkalinity ground water is expected to mobilize uranium 

adsorbed on deeper sediments (Jurgens and others, in press). 

Assuming that the alkalinity near the water table remains 

the same (450 mg/L), simulated long-term alkalinity in the 

public-supply well indicates that alkalinity and uranium 

concentrations will increase gradually over the next 100 

to 200 years (fig. 22). Simulated alkalinity flattened out at 

about 400 mg/L, which generally corresponds to uranium 

concentrations between 25 and 30 μg/L (Jurgens and others, in 

press); exceptions were noted in 2 wells that had an alkalinity 

of less than 400 mg/L but had concentrations of uranium 

greater than the MCL. Although uranium concentrations 

would likely approach the MCL in the public-supply well over 

time, it will probably take more than 100 years because water 

with low uranium concentrations from deep in the aquifer 

will also contribute to the well. This allows time to evaluate 

management strategies and to alter well construction or 

pumping strategies to prohibit concentrations from exceeding 

the MCL. 

To the extent that the conditions affecting the 

vulnerability of the public-supply well investigated in this 

study are typical of conditions affecting other public-supply 

wells in the Modesto region, these results can be useful in 

evaluating the vulnerability of other wells to nonpoint-source 

input of contaminants. High nitrate concentrations have 

been measured in shallow ground water beneath agricultural 

land throughout the eastern San Joaquin Valley (Burow and 

others, 1998; Burow and others, 2007). Because of the mostly 

downward movement of water in the study area and generally 

oxic geochemical conditions, nitrate in shallow ground water 

will probably continue moving downward without significant 

attenuation. Wells beneath a high proportion of agricultural 

land or wells installed in recently converted agricultural 

land are likely to have higher concentrations of nitrate than 

the public-supply well in this investigation. High alkalinity 

and uranium concentrations have been measured in shallow 

ground water in other parts of the eastern San Joaquin Valley. 

Public-supply wells screened in these areas may be similarly 

affected by uranium concentrations. Public-supply wells with 

shallow screened intervals containing mostly young water will 

likely have higher concentrations of both nitrate and uranium 

because of the lack of mixing with old water having low 

concentrations. 

Figure 20. Simulated and measured alkalinity in monitoring wells 

and the public-supply well near Modesto, eastern San Joaquin 

Valley, California. 

Historical data from city of Modesto, written commun., 2003.

0

0

100

20

300

400

500

100 200 300 400 500

MEASURED ALKALINITY,

IN MILLIGRAMS PER LITER

SIMULATED ALKALINITY,

IN MILLIGRAMS PER LITER

EXPLANATION

Monitoring wells

Public-supply well, U.S. Geological Survey data

Public-supply well, historical data

1:1 correlation line

FPD-2 FPC-2

FPD-1 FPE-1

OFPA-2
Simulation of Advective Transport by Particle Tracking 35

Figure 21. Simulated long-term concentrations of nitrate in the public-supply well near 

Modesto, eastern San Joaquin Valley, California. 

MCL, maximum contaminant level. 

Simulated concentration in public-supply well

Estimated concentration in recharge

YEAR

1945 1965 1985 2005 2025 2045 2065

25

20

15

10

5

0

Nitrate MCL

2085 2105

NITRATE CONCENTRATION,

IN MILLIGRAMS PER LITER, AS NITROGEN

Simulated concentration in public-supply well 

Estimated concentration in recharge 

YEAR

ALKALINITY, IN MILLIGRAMS PER LITER,

AS CALCIUM CARBONATE 

1900 1940 1980 2020 2060 2100 2140 2180

500

350

300

250

200

150

100

50

0

400

450

Approximate equivalent

uranium concentration

at MCL

Figure 22. Simulated long-term alkalinity and inferred uranium concentrations in the 

public-supply well near Modesto, eastern San Joaquin Valley, California. 

MCL, maximum contaminant level.
36 Simulations of Ground-Water Flow and Particle Pathline Analysis, Zone of Contribution of a Public-Supply Well, Modesto, Calif.

Model Uncertainties and Limitations

The accuracy of the ground-water flow model was limited 

by the assumptions used in numerical modeling to characterize 

the flow system; assumptions included model boundary 

conditions, discretization, and the effectiveness of the model 

calibration. The ground-water flow model was developed to 

portray and test the conceptual understanding of the aquifer 

system. The model was not expected to reproduce the natural 

system in detail, but to represent its dominant characteristics. 

Models solve for average conditions within each cell, the 

parameters for which are interpolated or extrapolated from 

measurements and estimated during calibration. Results from 

this model should be interpreted generally and are best suited 

for comparative analysis rather than for prediction at this 

location, although the model can predict in general terms the 

long-term concentrations in the public-supply well. 

The accuracy of model results is related to the quality 

and spatial distribution of input data and of measurements 

used to constrain the calibration. All of the water-level 

data used to calibrate the local model were collected from 

USGS monitoring wells, which are distributed throughout 

the local model domain. High-quality chemical tracer data 

were available from a significant number of wells in the local 

model area to further demonstrate the ability of the model 

to represent overall transport through the aquifer. Stresses in 

the regional and local models were based on data for water 

year 2000, whereas detailed water levels used for calibration 

were for 2003–05. Longer-term water-level data indicate that 

climatic conditions did not change significantly between 2000 

and 2005. 

Estimated hydraulic conductivity values and rates of 

chemical transport were sensitive to the specified recharge 

boundary, lateral boundary conditions, and the distribution 

of hydrofacies. The boundary conditions for the local model 

relied entirely on the regional model. However, the local 

model area near Modesto was one of two locations in the 

regional model that had high-quality input data, including 

pumpage by well, sediment texture, and high-quality waterlevel measurements, so conditions in the local area were well 

represented in the regional model. The hydrofacies distribution 

was constrained by sediment texture from a significant number 

of wells in the local model area. The local model results were 

sensitive to the three-dimensional distribution of hydrofacies; 

however, using a similar hydrofacies approach within the 

domain of the same regional model, Phillips and others 

(2007b) determined that the estimated hydraulic conductivity 

values were more sensitive to changes in areal recharge and 

boundary fluxes than to the three-dimensional distribution of 

the four hydrofacies characterized in this region. 

The steady-state model assumes the aquifer system is 

in equilibrium. Measured ground-water levels in the regional 

study area suggest that the ground-water system has been in 

a quasi-steady-state condition for many years (Phillips and 

others, 2007a). Prior to intensive ground-water development, 

hydraulic conditions were likely much different. However, 

simulating post-development conditions is most appropriate 

to study anthropogenic influences on the quality of water in 

public-supply wells. 

Summary and Conclusions

A single public-supply well was selected for intensive 

study to evaluate the dominant processes affecting the 

vulnerability of public-supply wells in the Modesto area. 

The public-supply well, with a depth of 120 m, was selected 

from a set of 15 wells that represented the top 25 percent of 

annual pumpage in 2000. A regional ground-water flow model 

was used to simulate the zone of contribution (ZOC) and the 

contributing recharge area (CRA) for the selected well, and 

to choose locations for a network of 23 monitoring wells to 

support a detailed analysis of physical and chemical conditions 

and processes affecting the water chemistry in the well. 

A local-scale, three-dimensional, steady-state groundwater flow and transport model was developed for this study 

to evaluate the age of ground-water reaching the public-supply 

well, and to evaluate the vulnerability of the well to nonpoint 

source input of nitrate and uranium. The local model is nested 

within the steady-state regional model that was calibrated for 

water year 2000. The active domain of the local model was 

determined by the CRA and ZOC of the public-supply well 

simulated using the regional-scale model. 

Stresses used in the regional model were used in the local 

model, including discharge from ground-water pumping, and 

recharge from agricultural return flow, precipitation, landscape 

irrigation, and leakage from water distribution lines. Recharge 

and agricultural pumpage were determined in a water-budget 

analysis. The local model included both agricultural and urban 

land uses. Lateral boundary conditions in the local model 

were specified flux from the regional-scale model along 

approximate flow lines on the north and south boundaries 

and specified head from the regional-scale model on the 

upgradient and downgradient lateral boundaries. 

The hydraulic conductivity distribution used in the 

local model was developed using a transition-probabilitybased geostatistical approach. For this study, sediments were 

classified into four hydrofacies categories: gravel, sand, 

muddy sand, and mud. Separate realizations of the hydrofacies 

distributions were generated for each alluvial fan aggradation 

sequence to reflect the unconformities produced by extensive 

periods of non-deposition or erosion. The resulting realizations 

were combined to represent the three-dimensional hydrofacies 

distribution for use in the local ground-water flow model. 

Eleven realizations were generated for each set of sequences. 

The model was calibrated using parameter estimation and 

systematic manual calibration techniques. Model results were 

compared to measured water levels and concentrations of 

age-dating tracers.
Acknowledgments 37

Particle tracking was used to compute pathlines and 

advective travel times for solutes in the local ground-water 

flow model, which was used to compute a refined contributing 

recharge area (CRA) for the public-supply well. The CRA 

covers about 45 km2, extending from about 0.5 km to the 

south and southwest of the well to about 2 km to the north 

and northwest of the well; it overlies both the urban and the 

agricultural areas. The simulated ages of particles reaching 

the public-supply well ranged from 9 to 30,000 years with a 

median of 54 years. Particle ages were weighted according to 

the flow associated with each particle for each layer along the 

well screen. The age of the ground water contributed to the 

public-supply well generally increased logarithmically with 

depth below the water table. At depths less than about 45 m 

below the water table, particle ages were less than 100 years. 

At depths more than 60 m below the water table, the particle 

ages ranged from 140 to 1,300 years; water in this age range 

was 25 percent of the flow to the well. 

Most of the CRA for the public-supply well lies beneath 

the land area that is currently urban. Ground water within the 

ZOC older than about 40 years probably contains primarily 

agricultural-related contaminants, whereas ground water 

younger than 40 years probably contains both urban and 

agricultural contaminants because urban development began 

in the 1960s. Elevated concentrations of nitrate, and low 

concentrations of VOCs and pesticides, were measured in the 

public-supply well, which is consistent with concentrations in 

both agricultural and urban sources. 

Nitrate concentrations in the ZOC of the public-supply 

well were highest in shallow, agriculturally-impacted 

ground water. The median nitrate concentration in wells 

screened near the water table beneath the agricultural area 

was 15 mg/L, whereas the median concentration in wells 

screened near the water table beneath the urban area was 

3.1 mg/L. Nitrate concentrations decreased with depth to 

background concentrations of about 2 mg/L or less in the 

deepest monitoring wells. Nitrate concentration in the publicsupply well (5.5 mg/L) was between concentrations in the 

shallow and the deep part of the ZOC because of the mixture 

of zones contributing ground water to the well. Because of 

the downward movement of ground water and generally 

oxic geochemical conditions, nitrate will move downward 

through the system without significant attenuation. Estimated 

nitrate concentrations in recharge over time, represented by 

measured nitrate concentrations and corresponding groundwater age-dates, indicate increasing concentrations of nitrate 

in recharge over time in the agricultural area. Assuming the 

proportion of agricultural and urban land use in the CRA of 

the public-supply well remains fixed at current proportions, 

however, and assuming that the current input concentrations 

beneath these settings remain the same, simulated long-term 

nitrate concentrations in the public-supply well indicate that 

concentrations have peaked, and will decrease slightly to near 

5 mg/L during the next 100 years. 

The simulated long-term nitrate concentrations in the 

public-supply well also indicate a 20- to 30-year time lag 

between peak input concentrations and peak concentrations 

in the well. An understanding of the length of time between 

changes in input concentrations and resulting concentrations 

in the public-supply well is needed to predict the impact of 

changes in land-use management. 

Uranium concentrations in the ZOC of the public-supply 

well were also highest in shallow ground water (median of 

25 μg/L) and decreased with depth to background levels of 

about 0.5 μg/L. Sediment cores and geochemical analysis 

indicated that naturally-occurring uranium adsorbed to aquifer 

sediments is mobilized by oxygen-rich, high-alkalinity 

water moving downward through the flow system. Increased 

alkalinity at the water table in response to agricultural 

development resulted in increased uranium concentrations 

near the water table. As ground-water pumping increased in 

the 1940s and 1950s, this high-alkalinity water began moving 

downward through the ground-water flow system, mobilizing 

uranium along the way. On the basis of the modeling analysis, 

high-alkalinity, high-uranium water will likely continue 

to move deeper in the system. Because alkalinity (and 

uranium) concentrations are high beneath both the urban and 

agricultural land, long term uranium concentrations in the 

public-supply well are expected to increase as the proportion 

of uranium-affected water contributed to the well increases. 

Assuming that the alkalinity near the water table remains 

the same in the future, simulated long-term alkalinity in the 

public-supply well indicates that concentrations of uranium 

will increase gradually over the next 100 to 200 years. 

Uranium concentrations in the public-supply well will 

likely approach the MCL; however, it will take more than 

100 years because of the old water at depth contributed to the 

public-supply well.

Acknowledgments

The authors thank Lanora Hill at the city of Modesto for 

her consistent support and her knowledge of ground-water 

quality in the study area. Assistance and cooperation critical 

to the completion of this study were provided by numerous 

staff at the city of Modesto, including Jeremy Damas, William 

Wong, and Garner Reynolds. Thanks to Walt Ward, Joe 

Lima, and Mike Niemi at Modesto Irrigation District for 

assisting with land access and support in the installation of 

monitoring wells. Gary Weissmann at the University of New 

Mexico helped interpret core and cuttings samples, and helped 

develop a conceptual model of the sedimentary sequences in 

the subsurface. Graham Fogg at the University of California 

at Davis helped develop the spatial correlation model of 

aquifer hydrofacies and provided input on parts of the model 

calibration and sensitivity analysis. Sandy Eberts provided 

critical support and facilitated a transfer of knowledge among 

the TANC team and other scientists in the USGS. 
38 Simulations of Ground-Water Flow and Particle Pathline Analysis, Zone of Contribution of a Public-Supply Well, Modesto, Calif.

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Burow—Simulations of Ground-Water Flow and Particle Pathline Analysis in the Zone of Contribution

 of a Public-Supply Well in Modesto, Eastern San Joaquin Valley, California

Scientific Investigations Report 2008–5035

Study

Unit

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