Simulation of Multiscale Ground-Water Flow in Part of the 

Northeastern San Joaquin Valley, California

U.S. Department of the Interior

U.S. Geological Survey

SIR 2007–5009
Cover: Olive orchard near the Merced River, California. Joe Domagalski, 

U.S. Geological Survey.
Simulation of Multiscale Ground-Water 

Flow in Part of the Northeastern San 

Joaquin Valley, California

By Steven P. Phillips, Christopher T. Green, Karen R. Burow, Jennifer L. Shelton, 

and Diane L. Rewis

 

Scientific Investigations Report 2007–5009

U.S. Department of the Interior

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

DIRK A. KEMPTHORNE, Secretary

U.S. Geological Survey

Mark D. Myers, Director

U.S. Geological Survey, Reston, Virginia: 2007

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reproduce any copyrighted materials contained within this report.

Suggested reference:

Phillips, S.P., Green, C.T., Burow, K.R., Shelton, J.L., and Rewis, D.L., 2007, Simulation of multiscale ground-water flow 

in part of the northeastern San Joaquin Valley, California: U.S. Geological Survey Scientific Investigations 

Report 2007-5009, 43 p.
iii

Contents

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

Introduction.....................................................................................................................................................1

Purpose and Scope ..............................................................................................................................3

Study Area Descriptions......................................................................................................................3

Topography and Climate .............................................................................................................3

Surface-Water Hydrology ..........................................................................................................3

Land Use........................................................................................................................................3

Water Use .....................................................................................................................................3

Site Descriptions..........................................................................................................................4

Conceptual Understanding of Ground-Water System.............................................................................5

Geology...................................................................................................................................................6

Geohydrology.........................................................................................................................................6

Aquifer Hydraulic Properties .....................................................................................................6

Lithologic Distributions ...............................................................................................................8

Regional Study Area...........................................................................................................8

Local Study Area.................................................................................................................8

Ground-Water Occurrence and Movement..........................................................................10

Water Budget ......................................................................................................................................15

Ground-Water Age .............................................................................................................................19

Ground-Water Flow Simulations ...............................................................................................................19

Spatial Discretization .........................................................................................................................19

Regional Model ..........................................................................................................................19

Local Model ................................................................................................................................19

Boundary Conditions and Model Stresses.....................................................................................23

Regional Model ..........................................................................................................................23

Local Model ................................................................................................................................25

Estimation of Aquifer Hydraulic Properties....................................................................................25

Regional Model ..........................................................................................................................25

Local Model ................................................................................................................................27

Model Calibration and Sensitivity ....................................................................................................27

Regional Model ..........................................................................................................................27

Regional Simulated Hydraulic Heads............................................................................30

Local Model ................................................................................................................................30

Local Simulated Hydraulic Heads..................................................................................33

Evaluation of Fluxes in Local Model ..............................................................................34

Sensitivity of Local Model Parameter Estimates to Hydrofacies 

Distribution and Recharge.................................................................................35

Model Results......................................................................................................................................38

Limitations and Appropriate Use of the Models............................................................................40

Regional Model ..........................................................................................................................40

Local Model ................................................................................................................................40

Summary........................................................................................................................................................41

Acknowledgments.......................................................................................................................................41

References....................................................................................................................................................42
iv

Figures

Figure 1. Locations of San Joaquin regional and local study areas within the 

Central Valley, California .................................................................. 2

Figure 2. Land use and description of U.S. Geological Survey (USGS) wells in Modesto, 

San Joaquin regional study area, California ............................................. 4

Figure 3. Land use and description of U.S. Geological Survey (USGS) transect wells, 

San Joaquin local study area, California ................................................ 5

Figure 4. Selected geologic units, San Joaquin regional study area, California ............... 7

Figure 5. Two-dimensional slices through three-dimensional model of percentage 

coarse-grained sediments, San Joaquin regional study area, California ............ 9

Figure 6. Vertical transition probabilities used to constrain vertical sequences of 

hydrofacies, San Joaquin local study area, California ................................. 11

Figure 7. Conceptual diagram of (A) regional lateral ground-water flow and (B) vertical 

flow influenced by agricultural practices and natural discharge zones ............ 13

Figure 8. Contours of measured water-level altitudes in the unconfined to semiconfined 

aquifer, spring 2000, San Joaquin regional study area, California..................... 14

Figure 9. Hydrographs of measured water-level altitudes for selected irrigation wells 

from 1960 to 2001, San Joaquin regional study area, California ..................... 15

Figure 10. Hydrographs of water-level altitudes measured hourly in U.S. Geological 

Survey monitoring wells in urban Modesto from December 2003 to July 2005, 

San Joaquin regional study area, California ............................................. 16

Figure 11. Hydrographs of water-level altitudes measured hourly in U.S. Geological 

Survey monitoring-well transect from June 2003 to May 2005, San Joaquin 

local study area, California ............................................................... 17

Figure 12. Subareas of regional model used for water-budget calculations, San Joaquin 

regional study area, California ............................................................ 18

Figure 13. Estimated rates of recharge for subareas of regional model, water year 2000, 

San Joaquin regional study area, California. .......................................... 20

Figure 14. Estimated rates of ground-water pumping for subareas of regional model, 

water year 2000, San Joaquin regional study area, California ........................ 21

Figure 15. Model extent, boundary conditions, and extent of the downslope, midslope, 

and upslope areas for the regional model, San Joaquin regional study area, 

California .................................................................................... 22

Figure 16. Vertical discretization of regional model along row 73, San Joaquin regional 

study area, California ..................................................................... 23

Figure 17. Extent of active area and boundary conditions for the local model, San Joaquin 

local study area, California ............................................................... 24

Figure 18. Estimated rates of recharge for the local model, water year 2000, San Joaquin 

local study area, California ............................................................... 26

Figure 19. Frequency of estimated horizontal and vertical hydraulic conductivity for the 

upslope (eastern) and downslope (western) alluvial deposits, San Joaquin 

regional study area, California ............................................................ 28

Figure 20. Vertical section roughly parallel to the Merced River showing distribution of 

hydrofacies used in calibrated local model, San Joaquin local study area, 

California .................................................................................... 29

Figure 21. Error surfaces used to calibrate, and calibration results for, the regional model, 

San Joaquin regional study area, California ............................................. 31

Figure 22. Simulated hydraulic heads at the water table and in layer 9, and errors between 

measured water levels and simulated hydraulic heads at wells used to calibrate 

the regional model, San Joaquin regional study area, California ..................... 32
Figure 23. Relation between simulated hydraulic head and measured water levels for 

regional model, San Joaquin regional study area, California ........................ 33

Figure 24. Relative composite sensitivity of computed hydraulic head at calibration points 

to changes in the horizontal and vertical hydraulic conductivities of the defined 

hydrofacies, local model, San Joaquin local study area, California .................. 34

Figure 25. Relative sensitivity of computed hydraulic head at calibration points to changes 

in hydraulic parameters, local model, San Joaquin local study area, California ... 35

Figure 26. Relation between simulated hydraulic head and measured water levels for the 

local model, San Joaquin local study area, California ................................. 36

Figure 27. Simulated water-table altitudes for the local model, San Joaquin local study 

area, California .............................................................................. 37

Tables

Table 1. Proportions and mean lengths of hydrofacies used in local model, San Joaquin 

local study area, California ............................................................... 12

Table 2. Soft-conditioning probabilities assigned to hydrofacies for non-U.S. Geological 

Survey well log descriptions, San Joaquin local study area, California ............ 12

Table 3. Calibrated and specified hydraulic conductivity values for the local model, 

San Joaquin local study area, California ................................................ 29

Table 4. Measured concentrations of sulfur hexafluoride (SF6) along the U.S. Geological 

Survey well transect and concentrations estimated using simulated travel time 

and historical atmospheric concentrations of SF6, San Joaquin local study area, 

California .................................................................................... 38

Table 5. Changes in key hydraulic conductivity parameters with alternate threedimensional distributions of hydrofacies in the local model, San Joaquin 

local study area, California ............................................................... 38

Table 6. Simulated water budget for the regional model, San Joaquin regional 

study area, California ..................................................................... 39

Table 7. Simulated water budget for the local model, San Joaquin local study area, 

California .................................................................................... 39
vi

Datums Used

Vertical coordinate information is referenced to the North American Vertical Datum of 1988 

(NAVD 88).

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

83).

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

km, kilometer

km2, square kilometer

m, meter 

m/d, meter per day

m/km, meter per kilometer

m/yr, meter per year

m3/d, cubic meter per day

mg/L, milligram per liter

mm, millimeter

pptv, parts per trillion by volume

Kcoarse , coarse-grained lithologic end member

Kcorc , Corcoran Clay

Kfine , hydraulic conductivity of fine-grained lithologic end member

Kh , horizontal hydraulic conductivity 

Kv , vertical hydraulic conductivity between model layers 

NAWQA, National Water-Quality Assessment

SF6, sulfur hexafluoride

TProGS, Transition-Probability Geostatistical Software

RMSE, root mean square error

SANJ, San Joaquin-Tulare Basins study unit of NAWQA

USGS, U.S. Geological Survey
vii

Well-Numbering System 

Wells are identified and numbered according to their location in the rectangular system for the subdivision of 

public lands. Identification consists of the township number, north or south; the range number, east or west; 

and the section number. Each section is divided into sixteen 40-acre tracts lettered consecutively (except I 

and O), beginning with “A” in the northeast corner of the section and progressing in a sinusoidal manner to 

“R” in the southeast corner. Within the 40-acre tract, wells are sequentially numbered in the order they are 

inventoried. The final letter refers to the base line and meridian. In California, there are three base lines and 

meridians; Humboldt (H), Mount Diablo (M), and San Bernardino (S). All wells in the study area are referenced 

to the Mount Diablo base line and meridian. Well numbers consist of 15 characters and follow the format 

003S007E13A001. In this report, well numbers are abbreviated and written 3S/7E-13A1. The following diagram 

shows how the number for well 3S/7E-13A1 is derived.

R7E R8E R9E

nai dir e M

lo bai Dt nuo M

 T2S

 T3S

 T4S

RANGE

PI HS N W

OT

 R1W R1E

27

R7E

T3S

Well-numbering diagram

6 5 4 3 2 1

7

18 13

8 9 10 11 12

17 16 15 14

19 24

30 25

31 36

20 21 22 23

29 28 26

32 33 34 35

SECTION 13

D C A

E F G H

M L K J

N P Q R

B

3S/7E-13A1
This page intentionlly left blank.
Abstract

The transport and fate of agricultural chemicals in a 

variety of environmental settings is being evaluated as part of 

the U.S. Geological Survey (USGS) National Water-Quality 

Assessment Program. One of the locations being evaluated is a 

2,700-km2 (square kilometer) regional study area in the northeastern San Joaquin Valley surrounding the city of Modesto, 

an area dominated by irrigated agriculture in a semi-arid 

climate. Ground water is a key source of water for irrigation 

and public supply, and exploitation of this resource has altered 

the natural flow system. The aquifer system is predominantly 

alluvial, and an unconfined to semiconfined aquifer overlies 

a confined aquifer in the southwestern part of the study area; 

these aquifers are separated by the lacustrine Corcoran Clay. 

A regional-scale 16-layer steady-state model of ground-water 

flow in the aquifer system in the regional study area was 

developed to provide boundary conditions for an embedded 

110-layer steady-state local-scale model of part of the aquifer 

system overlying the Corcoran Clay along the Merced River. 

The purpose of the local-scale model was to develop a better 

understanding of the aquifer system and to provide a basis for 

simulation of reactive transport of agricultural chemicals.

The heterogeneity of aquifer materials was explicitly 

incorporated into the regional and local models using information from geologic and drillers’ logs of boreholes. Aquifer 

materials were differentiated in the regional model by the 

percentage of coarse-grained sediments in a cell, and in the 

local model by four hydrofacies (sand, silty sand, silt, and 

clay). The calibrated horizontal hydraulic conductivity values 

of the coarse-grained materials in the zone above the Corcoran 

Clay in the regional model and of the sand hydrofacies used in 

the local model were about equal (30–80 m/d [meter per day]), 

and the vertical hydraulic conductivity values in the same 

zone of the regional model (median of 0.012 m/d), which is 

dominated by the finer-grained materials, were about an order 

of magnitude less than that for the clay hydrofacies in the local 

model.

Data used for calibrating both models included long-term 

hourly water-level measurements in 20 short-screened wells 

installed by the USGS in the Modesto and Merced River areas. 

Additional calibration data for the regional model included 

water-level measurements in 11 wells upslope and 17 wells 

downslope from these areas. The root mean square error was 

2.3 m (meter) for all wells in the regional model and 0.8 m 

for only the USGS wells; the associated average errors were 

0.9 m and 0.3 m, respectively. The root mean square error for 

the 12 USGS wells along a transect in the local model area 

was 0.08 m; the average error was 0.0 m. Particle tracking 

was used with the local model to estimate the concentration 

of an environmental tracer, sulfur hexafluoride, in 10 USGS 

transect wells near the Merced River that were sampled for 

this constituent. Measured and estimated concentrations in the 

mid-depth and deepest wells, which would be most sensitive 

to errors in hydraulic conductivity estimates, were consistent. 

The combined results of particle tracking and sulfur hexafluoride analysis suggest that most water sampled from the 

transect wells was recharged less that 25 years ago.

Introduction

The U.S. Geological Survey (USGS) National WaterQuality Assessment (NAWQA) Program is studying the 

transport and fate of agricultural chemicals in a variety of 

hydrologic and agricultural settings across the nation. The 

agricultural chemicals studied include those associated with 

applied fertilizers, herbicides, and pesticides. One of these settings is in the northeastern San Joaquin Valley near Modesto, 

California (fig. 1). The regional-scale study area straddled the 

valley floor and the local-scale study area was focused on a 

small area along the Merced River south of Turlock (fig. 1). 

These study areas are hereinafter referred to as “regional” and 

“local.”

Simulation of Multiscale Ground-Water Flow in Part of the 

Northeastern San Joaquin Valley, California

By Steven P. Phillips, Christopher T. Green, Karen R. Burow, Jennifer L. Shelton, and Diane L. Rewis
EXPLANATION

Active area of local model

Regional model extent

Urban area

Basin deposits

Eastern fans

Western fans

Geologic provinces Locations of wells listed in figure 9

Represents unconfined zone

Represents semiconfined zone

Well depth unknown

regional model row 73

(shown in figure 16)

area shown in figure 2

area shown in 

figure 3

 San 

Francisco

Los

Angeles

Central

Valley

COAST RANGES

SIERRA

NEVADA

San Joaquin

Valley

Regional

study area

CALIFORNIA

20 KILOMETERS

0 8 16 MILES

0 10

6S/12E-12F1

6S/11E-27K1

5S/10E-24C1

4S/9E-19A1

3S/9E-7C1

2S/11E-19K1

3S/7E-13A1

121 15

37

45

37

30

37

15

121 120 45 120 30

Modesto

Turlock

Merced

Tuolumne River

San Joaquin River

Merced River

Stanislaus River

Turlock Lake

(Reservoir)

Turlock Lake

(Reservoir)

Modesto

Reservoir

Modesto

Reservoir

Woodward

Reservoir

Woodward

Reservoir

Figure 1. Locations of San Joaquin regional and local study areas within the Central Valley, California. 

 Simulation of Multiscale Ground-Water Flow in Part of the Northeastern San Joaquin Valley, California
Purpose and Scope

The purpose of this report is to summarize the hydrologic 

settings of the regional and local study areas and document 

the development and calibration of steady-state regional and 

local ground-water flow models. These models support future 

simulations and analyses of chemical mass balance, transport, 

and fate. Additional information on the regional hydrologic 

setting can be found in Burow and others (2004) and Gronberg 

and Kratzer (2006). The model described in this report is an 

updated version of the model described by Phillips and others 

(in press).

Study Area Descriptions

The San Joaquin Valley is more than 400 km long, 40 

to 90 km wide, and occupies the southern two-thirds of the 

Central Valley of California (fig. 1). The valley floor is underlain by a structural trough filled with marine and continental 

sediments up to 10 km thick (Gronberg and others, 1998). The 

Sierra Nevada rise east of the valley to an altitude of more than 

4,200 m; the Coast Ranges, having moderate altitude, form the 

western edge of the valley. The San Joaquin River drains the 

northern part of the San Joaquin Valley through San Francisco 

Bay; the southern part of the valley is a hydrologically closed 

basin.

 The regional 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 (fig. 1). Within the regional bounds is the 

local study area, about 17 km2, located south of Turlock along 

a reach of the Merced River (fig. 1).

Topography and Climate

The land surface in the regional study area slopes 

westward from the Sierra Nevada foothills to the San Joaquin 

River; gradients range from less than 1 m/km near the river to 

more than 5 m/km in places near the foothills and adjacent to 

streams and rivers, including the local study area (fig. 1). The 

climate is semi-arid, characterized by hot summers and mild 

winters; the rainfall averaged 315 mm annually from 1931 to 

1997 during late fall through early spring (National Oceanic 

and Atmospheric Administration, 2005).

Surface-Water Hydrology

The San Joaquin River is the central drainage for the 

northern San Joaquin Valley and is the only major surfacewater 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 their natural state. Each has 

multiple reservoirs for irrigation and power generation, which 

effectively delay discharge of large amounts of snowmelt 

runoff. An extensive network of canals is used to deliver water 

for irrigation.

Land Use

Agriculture is the primary land use, covering about 65 

percent of the regional study area and about 80 percent of the 

local study area. The primary crops in the regional study area 

are almonds, walnuts, peaches, grapes, grain, corn, pasture, 

and alfalfa. Modesto, Turlock, and a number of smaller urban 

areas covered about 6 percent of the regional study area in 

2000. The remaining area was predominantly natural vegetation near the foothills and in riparian areas (California Department of Water Resources, 2001a,b).

Water Use

Agricultural irrigation supplied by surface water and 

ground water currently accounts for about 95 percent of 

the total water use in the region (Burow and others, 2004). 

Surface-water supplies originate primarily from a series of 

reservoirs in the Sierra Nevada foothills. These supplies are 

managed by irrigation districts and delivered to agricultural 

users through hundreds of kilometers of lined canals.

Most irrigation districts and private agricultural users also 

pump ground water for irrigation; in addition, some districts 

pump ground water to lower the water table in areas where it 

has risen too close to the land surface to support agriculture 

without active management. Private agricultural ground-water 

pumpage is not measured in the regional study area but was 

estimated in a water-budget analysis (Burow and others, 2004) 

to be about 32 percent of total agricultural water use in water 

year 2000 (October 1, 1999, through September 30, 2000). 

Ground-water use is insignificant in the local study area, 

where most irrigation water is delivered by canal or pumped 

from the Merced River.

Urban water demand is met by surface-water and groundwater supplies. Before 1995, the city of Modesto, the largest urban area in the regional study area, used ground water 

exclusively for public supply. A surface-water treatment plant 

was completed in 1994, which now provides about one-half 

of Modesto’s municipal and industrial water supplies. About 

55 percent of urban water requirement was met by ground 

water in water year 2000 (Burow and others, 2004).

On the basis of information from local drillers’ logs, 

about 60 percent of wells in the study area are for domestic 

use, followed by 27 percent for irrigation, 4 percent for public 

supply, and 7 percent for test, stock, industrial, and other uses 

(Burow and others, 2004). Well depths range from 7 to 368 m 

below land surface; the median depth is 59 m. The median 

depths below land surface to the midpoints of perforated 

intervals in domestic, irrigation, and municipal wells are 47, 

63, and 68 m, respectively. Fewer wells exist in the older sediments and terraces east of Modesto and Turlock and along the 

San Joaquin River. The deepest wells are in the older sediments in the eastern part of the regional study area, and the 

shallowest wells are in the western part and along the rivers. 

Additional clusters of deep wells are in the urban areas.

Introduction 
Site Descriptions

Clusters of monitoring wells were installed by the USGS 

at two primary locations in the regional study area: urban 

Modesto and the local study area. The wells in urban Modesto 

were installed as part of a USGS national assessment of the 

vulnerability of public-supply wells to contamination from 

urban, agricultural, and natural sources (Eberts and others, 

2005). The Modesto-area wells used in this study for model 

calibration and the associated land use are shown in figure 2. 

There are four clusters of monitoring wells consisting of 3 

or 4 wells each; mid-screen depths ranged from about 10 m 

near the water table to about 100 m. All well screens in the 

Modesto area were 1.5 m. Twelve of these wells were instrumented using pressure transducers that recorded hourly waterlevel measurements for periods ranging from 1 to 2.5 years.

Clusters of monitoring wells installed in the local study 

area as part of this study were located at three sites along a 

transect (fig. 3) that is roughly oriented in the direction of 

ground-water flow toward the Merced River. The site at the 

upper end of the transect (northern, up-gradient end) was in 

an almond orchard. The middle site was between an upslope 

almond orchard and a corn field (feed corn), and the site at the 

lower end was in native vegetation at the edge of the riparian 

0 .75 1.5 KILOMETERS

0 0.5 1 MILE

USGS well cluster and depth to midpoint of 

screen, in meters, for shallowest and deepest 

wells in each cluster

FPA_10

FPA_105

FPD_9

FPD_103

FPC_12

FPC_107

FPB_10

FPB_101

FPB_10

120 58

37

42

37

40

121

EXPLANATION

Orchard, primary almond

Field crops

Native vegetation

Vinyard

Urban Modesto

Land use

Figure 2. Land use and description of U.S. Geological Survey (USGS) wells in Modesto, San Joaquin 

regional study area, California. 

 Simulation of Multiscale Ground-Water Flow in Part of the Northeastern San Joaquin Valley, California
zone (fig. 3) of the Merced River. Four to six wells at each site 

were used for this study; mid-screen depths ranged from about 

6 m near the water table to about 27 m for those screened 

above the Corcoran Clay. Screen lengths for this group of 

wells were 0.6 m except at the water table (1.5 m). One well at 

the lower end of the transect was screened below the Corcoran 

Clay at a depth of 53 m; the screen length was 3 m. Fourteen 

of these transect wells were instrumented using pressure 

transducers that recorded hourly water-level measurements for 

periods ranging from 1 to 1.6 years.

Conceptual Understanding of 

Ground-Water System

The aquifer system in the regional study area is composed 

of Tertiary and Quaternary alluvial deposits shed from the 

surrounding Sierra Nevada and Coastal mountain ranges. The 

basin-fill comprises coalescing alluvial fans, which tend to be 

coarse grained near the mountains and finer grained toward the 

center of the basin. The Corcoran Clay Member of the Tulare 

Figure 3. Land use and description of U.S. Geological Survey (USGS) transect wells, San Joaquin local study area, 

California.

0 450 900 METERS

0 1,500 3,000 FEET

upper_7

lower_5

lower_9

lower_15

lower_25

lower_29

lower_53

middle_5

middle_13

middle_19

middle_25

upper_7

upper_14

upper_20

upper_27

120 4836 120 48 120 4724

37

42

37

23

24

USGS well transect 

USGS well cluster with location along

transect (upper, middle, lower) and depth 

to midpoint of screen in meters

EXPLANATION

Orchard, primary almond

Feed corn

Native riparian vegetation

Native vegetation

Vinyard

Other

Land use

Merced River

Conceptual Understanding of Ground-Water System 
Formation is a lacustrine clay deposit that separates the basinfill deposits into an upper unconfined to semiconfined aquifer 

and a lower confined aquifer throughout much of the regional 

study area (Burow and others, 2004). The local study area is 

underlain entirely by the Corcoran Clay.

Ground-water flow directions have changed and rates 

have increased because of extensive development. Under 

natural conditions, recharge occurred in the upper alluvial fans 

where streams enter the basin, and ground water discharged to 

the San Joaquin River and surrounding marshlands. Groundwater pumping for irrigation and public supply combined 

with delivery of surface water for irrigation has greatly altered 

the distribution of recharge and discharge (Burow and others, 2004). Ground-water flow has become more complex as 

increased surficial recharge and ground-water withdrawal have 

increased vertical flow in the system; water on a lateral flow 

path may be repeatedly removed by pumping and reapplied at 

the surface.

Geology

The Central Valley is a northwest-trending structural 

trough between the Sierra Nevada and the Coast Ranges (Bartow, 1991). The Sierra Nevada Range lies on the eastern side 

of the valley, comprises primarily pre-Tertiary granitic rocks, 

and is separated from the Central Valley by a foothill belt of 

marine and metavolcanic rocks. The Coast Ranges lie on the 

western side of the valley and are a complex assemblage 

of rocks, including marine and continental sediments of 

Cretaceous to Quaternary age (Gronberg and others, 1998).

The San Joaquin Valley can be divided generally into 

three physiographic regions (fig. 1): the western alluvial fans, 

the eastern alluvial fans, and basin deposits (Burow and others, 1998). Alluvial fan deposits on both sides of the valley 

are composed predominantly of coarse-grained sediments 

near the head of each fan that become finer grained toward the 

valley trough. The sediments in the eastern alluvial fan region 

generally are more permeable than sediments in the western 

alluvial fan region because sediment-source rocks and watershed characteristics are different between the two areas. The 

basin deposits within the regional study area are a combination 

of coarse-grained channel deposits and fine-grained deposits 

from flood events.

Consolidated rocks and deposits exposed along the margin of the valley floor include Tertiary and Quaternary continental deposits (fig. 4), Cretaceous and Tertiary marine sedimentary rocks, and the pre-Tertiary Sierra Nevada basement 

complex (Piper and others, 1939; Davis and others, 1959). 

The Mehrten Formation, the youngest of the Tertiary rocks, 

is composed of volcanic-derived mafic rocks. Unconsolidated 

deposits in the study areas generally comprise gravel, sand, 

silt, and clay primarily derived from granitic sources, and most 

are contained within the Pliocene-Pleistocene Laguna (not 

mapped at the surface in study areas), Turlock Lake, Riverbank, and Modesto Formations, including the Corcoran Clay. 

These are interspersed with minor amounts of Holocene dune, 

stream-channel, and flood-basin deposits (Arkley, 1962; 1964; 

Davis and Hall, 1959). The Turlock Lake, Riverbank, and 

Modesto Formations form a sequence of overlapping terrace 

and alluvial fan systems (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).

The Corcoran Clay, a lacustrine deposit that is a key subsurface feature in the San Joaquin Valley, is a Member of the 

Tulare Formation (Croft, 1972). The Corcoran Clay has been 

correlated with the E-clay (Page, 1986), the diatomaceous clay 

(Davis and others, 1959), and the lacustrine clay within the 

Turlock Lake Formation in the regional study area (Marchand 

and Allwardt, 1981). Page (1986) used results of previous 

work and a limited number of well logs and geophysical logs 

to map the areal extent of this regional confining unit. Additional lithologic data were used recently to modify the mapped 

extent of this prominent unit in the regional study area (Burow 

and others, 2004). The eastern extent of the Corcoran Clay 

roughly parallels the San Joaquin River valley axis (fig. 4). In 

the regional study area, the top of the Corcoran Clay occurs 

between 26 and 80 m below land surface and the unit has 

a maximum thickness of 57 m. In the local study area, the 

Corcoran Clay is encountered 40 m below land surface and is 

about 18 m thick.

The Mehrten Formation is a key subsurface feature 

tapped by wells in the eastern part of the study area (fig. 4). 

The Mehrten Formation marks a change in lithology and 

texture from overlying sediments of primarily unconsolidated 

coarse-grained sediments of arkosic composition to primarily 

consolidated sediments of volcanic-derived mafic materials 

(Burow and others, 2004). The Mehrten Formation outcrops 

in the eastern part of the regional study area and lies at least 

120 m below land surface beneath Modesto.

Geohydrology

Aquifer Hydraulic Properties

Only limited information on the distribution and magnitude of aquifer hydraulic properties was available prior to this 

study. One available ground-water flow model was developed 

at a similar scale of investigation (Londquist, 1981), and it was 

highly generalized spatially.

 Simulation of Multiscale Ground-Water Flow in Part of the Northeastern San Joaquin Valley, California
Figure 4. Selected geologic units, San Joaquin regional study area, California.

Holocene

Pleistocene

Pliocene

Quaternary Tertiary

16 MILES

0 10 20 KILOMETERS

0 8

121 15 120

37

45

37

30

37

15

120 45 120 30

EXPLANATION

Dunes

Alluvium and dredge tailings

Stream channel deposits

Flood-basin deposits

Nonmarine terrace deposits

Modesto Formation

Riverbank Formation

Turlock Lake Formation

Mehrten Formation

Urban

Active area of local model

Regional model extent

Boundary of Corcoran Clay

Geology

Tuolumne River

San Joaquin River

Merced River

Stanislaus River

Modesto

Turlock

Merced

Conceptual Understanding of Ground-Water System 
Single-well hydraulic tests—slug tests—were done in 18 

shallow wells in the bed and on the banks of the Merced River 

down-gradient from the local well transect as part of this study 

(Zamora, 2006). The sediments tested ranged from silty sand 

to well-sorted coarse sand, and computed hydraulic conductivity values ranged from 15 to 250 m/d and had a mean of 

85 m/d. Slug tests done for a previous study in three wells 

above the Corcoran Clay along the eastern bank of the San 

Joaquin River within the regional study area were used to 

compute hydraulic conductivities of 2, 24, and 53 m/d (Phillips and others, 1992). The sediment types that these tests 

represent are unknown.

Permeameter tests of cores from the Corcoran Clay 

indicate vertical hydraulic conductivities ranging from 

1 × 10–6 to 3 × 10–6 m/d (Page, 1977). Previous investigations, 

however, indicate numerous wells screened across the Corcoran Clay have locally short-circuited the impedance to flow 

across the clay layer and significantly enhanced intraborehole 

flow through the clay (Williamson and others, 1989; Belitz 

and Phillips, 1995). The vertical hydraulic conductivity estimated by Belitz and Phillips (1995) for an area southwest of 

the regional model, where the Corcoran Clay is about 

100–240 m below land surface, is 1.6 × 10–4 m/d.

Lithologic Distributions

Because available data on the hydraulic properties of the 

aquifer system are scarce, material properties in this study 

were estimated on the basis of the distribution of sediment texture or hydrofacies derived from drillers’ logs, geologic logs, 

and geophysical logs. The regional texture distribution was 

estimated using the general approach of Laudon and Belitz 

(1991), which is easily applied to regional-scale problems. The 

local texture distribution was estimated using a geostatistical 

approach that incorporates factors related to the depositional 

environments (Carle, 1996). Although this method is more 

powerful than that of Laudon and Belitz (1991), it is difficult 

to apply to many regional-scale problems, owing to regional 

variability in depositional environments.

Regional Study Area

To facilitate this texture-based approach for the regional 

model, a database was constructed as part of a cooperative 

effort between the USGS and the Modesto Irrigation District 

to organize information on well construction and subsurface 

lithology in the study area (Burow and others, 2004). About 

10,000 drillers’ logs were examined. Because sediment 

descriptions on drillers’ logs can be ambiguous and widely 

variable, a rating scheme was developed to select a subset of 

about 3,500 logs for further use. The database contains lithologic and well-construction information, which was used to 

vertically distribute ground-water pumping in the flow model.

A geostatistical approach was used to generate a heterogeneous hydraulic-conductivity field for the regional 

flow model using the primary texture of sediments from the 

database (Burow and others, 2004). Lithologic descriptions in 

the database were expressed as a percentage of coarse-grained 

sediment for 1-m depth intervals. These percentages were 

then interpolated using three-dimensional kriging, with no 

lateral anisotropy, over a grid equivalent to that of the regional 

model in the horizontal dimension for successive 10-m thick 

intervals in the vertical dimension. These values were then 

interpolated over the variable-thickness model grid to obtain 

an estimated distribution of sediment texture throughout the 

regional model domain. A more detailed description of kriging 

parameters is provided by Burow and others (2004). Estimated 

texture distributions for depth slices below the land surface 

are shown in figure 5. The estimated texture distributions were 

well constrained by sediment texture data to a depth of about 

50 m, reasonably constrained to 100 m, and poorly constrained 

below 100 m. For the deeper parts of the aquifer system, for 

which no data were available, the texture value in the lowest 

layer estimated was duplicated in all underlying model cells. 

These cell-by-cell texture values were used to generate the 

distribution of hydraulic conductivity values as described 

in the section “Estimation of Aquifer Hydraulic Properties,” 

under “Ground-Water Flow Simulations.”

Local Study Area

The spatial distribution of sedimentary hydrofacies in the 

local model area was simulated using Transition-Probability 

Geostatistical Software (TProGS) (Carle, 1996; Carle, 1997; 

Carle and Fogg, 1996; Carle and Fogg, 1997; Carle and others, 1998). Using TProGS, probabilities of encountering one 

defined hydrofacies next to another are determined from borehole and (or) other raw data. Markov-chain models approximating these transition probabilities are used in sequential 

indicator simulation, and these results are smoothed with 

simulated annealing to generate three-dimensional realizations that honor the measured data points and transition probabilities. This method preserves cross-correlations between 

sediment types that can affect preferential flow through 

interconnected high-conductivity zones (Fogg and others, 

2001).

A single realization generated using TProGS represents 

one of many possible distributions of the defined hydrofacies. 

A key advantage of this method is that the same input can 

be used to generate hundreds of realizations, which provides 

the opportunity to explore a wide range of equally probable 

hydrofacies distributions.

 Simulation of Multiscale Ground-Water Flow in Part of the Northeastern San Joaquin Valley, California
Figure 5. Two-dimensional slices through three-dimensional model of percentage coarse-grained 

sediments, San Joaquin regional study area, California. 

Modified from Burow and others (2004). 

10,000

0

20,000

30,000

40,000

50,000

60,000

DISTANCE FROM ORIGIN IN X-DIRECTION (NORTHEAST), IN METERS

A B

C D

90

80

70

60

50

40

30

20

10

Percentage

coarse-grained

sediments

10 meter depth (33 ft) 25 meter depth (82 ft)

50 meter depth (160 ft) 100 meter depth (330 ft)

EXPLANATION

San

Joaquin River

Tuolumne River

Stanislaus River

Merced River

San

Joaquin River

Tuolumne River

Stanislaus River

San

Joaquin River

Tuolumne River

Stanislaus River

Merced RiverMerced River

San

Joaquin River

Tuolumne River

Stanislaus River

Merced River

San

Joaquin River

Tuolumne River

Stanislaus River

Merced River

San

Joaquin River

Tuolumne River

Stanislaus River

Merced River

DISTANCE FROM ORIGIN IN Y-DIRECTION (NORTHWEST), IN METERS

E 150 meter depth (490 ft) F 200 meter depth (660 ft)

0 10,000 20,000 30,000 40,000 50,000 0 10,000 20,000 30,000 40,000 50,000

10,000

0

20,000

30,000

40,000

50,000

60,000

10,000

0

20,000

30,000

40,000

50,000

60,000

Conceptual Understanding of Ground-Water System 
Geostatistical realizations of the local study area were 

bounded by or included three major geologic features of 

the unconfined to semiconfined aquifer: the Corcoran Clay, 

Pleistocene alluvial fan deposits, and incised Holocene river 

deposits (Marchand and Allwardt, 1981). The Corcoran Clay 

is a semi-permeable barrier to vertical flow between the 

unconfined to semiconfined aquifer and the confined aquifer, 

and was the lower boundary for the geostatistical realizations. 

Overlying the Corcoran Clay, Pleistocene alluvial fan deposits 

account for most of the permeable sediments. Adjacent to the 

Merced River, Holocene alluvium fills an incised river valley 

in the Pleistocene alluvial fan deposits. The lower boundary 

of Holocene alluvium along the Merced River was estimated 

using cores from the USGS well transect, and previous maps 

and reports on the surficial geology of the area (Marchand and 

Allwardt, 1978, 1981). These boundaries were used to specify 

the spatial extent of sedimentary sequences in geostatistical 

realizations.

Pleistocene alluvial fan deposits were characterized using 

geologic logs that describe the USGS transect wells. The logs 

had a maximum resolution of about 0.3 m for those boreholes 

drilled using an air hammer and about 1.5 m for those drilled 

using mud rotary. Clay, silt, silty sand, and sand were chosen 

as the representative hydrofacies on the basis of the frequency 

of observation of various sediment types in cores collected 

during drilling, Each lithologic description in the logs was 

assigned to one of these hydrofacies, and vertical transition 

probabilities (fig. 6), mean thicknesses, and volumetric proportions (table 1) were computed from this data set. Horizontal transition probabilities were estimated by multiplying the 

vertical mean lengths by factors of about 200 in the dip (X, 

toward the southwest) direction and about 100 in the strike (Y) 

direction (table 1). The scaling factors, which are greater along 

the depositional slope, were chosen on the basis of observations of horizontal continuity of sedimentary layers between 

wells and previous reports of the area’s sedimentary geology 

(Marchand and Allwardt, 1981).

Changes in stratigraphic orientation owing to the gradual 

downwarping of sediments after deposition, or areal variability in rates of deposition, were approximated by setting the 

dip parallel to the gently undulating surface of the Corcoran 

Clay at that interface, and to zero at the ground surface. In the 

interior of the alluvial fan sediments, dip values were assigned 

for each location (X, Y, and Z) by linear interpolation between 

the dip at the ground surface and at the surface of the Corcoran 

Clay. The dip direction was set parallel to the X axis.

For Holocene alluvium, sediments were assigned to 

hydrofacies containing silt, silty sand, or sand. Proportions 

and mean thicknesses were calculated from the upper part of a 

geologic log of a borehole at the lower end of the well transect 

(table 1). Available data were insufficient to characterize 

cross-correlations among sediment types; therefore, transition 

probabilities were derived using mean lengths and maximumentropy Markov chain models (Carle and Fogg, 1997). Mean 

lengths (table 1) were estimated from the dimensions of the 

Merced River channel and local floodplain areas as mapped 

by Marchand and Allwardt (1978). The azimuth of the dip of 

the Holocene alluvium was set parallel to the centerline of the 

mapped alluvium and the dip was set to zero.

Two hundred realizations of the three-dimensional 

distribution of hydrofacies were generated for the local study 

area. For these realizations, drillers’ logs and USGS geologic 

logs were used as conditioning data. Conditioning refers to 

the inclusion of information that will affect the realization; 

the degree to which the realization is affected depends on 

the user-specified accuracy of the information. In this case, 

drillers’ logs contain a variety of terminology used to describe 

sediments and typically are not very detailed; therefore, 

most observations were treated as “soft” conditioning data 

by assigning a probability, p, where 0 ≤ p ≤ 1 for each of 

the simulated hydrofacies on the basis of the specific well 

log description (table 2). USGS geologic logs were used as 

“hard” conditioning data, where p = 1. Separate realizations 

were generated for the Holocene alluvium and Pleistocene 

alluvial fans. The simulated stratigraphic sequences were then 

merged into composite realizations that incorporated sequence 

boundaries, conditioning data, and simulated hydrofacies for 

the Holocene alluvium and Pleistocene alluvial fans above the 

surface of the Corcoran Clay.

Hydrofacies distributions for the local model improved 

the regional model in that area. Boreholes used to estimate 

regional sediment texture were sparse in the local model area, 

and did not include the three drilling sites along the USGS 

well transect. Regional kriging results, which depicted the 

local study area as being very coarse-grained throughout, 

compared poorly to data from sites along the transect, and the 

regional model did not closely simulate measured local conditions. Therefore, regional sediment texture estimates were 

replaced with TProGS-generated hydrofacies distributions in 

the local model area. The hydrofacies were translated crudely 

to percent coarse-grained materials as follows: sand and silty 

sand were considered 100 percent coarse-grained, and silt and 

clay zero percent. These percentages were averaged for all 

local cells within each regional cell.

Ground-Water Occurrence and Movement

Ground water occurs in the unconfined to semi-confined 

aquifer above and east of the Corcoran Clay, within the Corcoran Clay, and in the confined aquifer beneath the Corcoran 

Clay. The thickness of the unconfined to semiconfined aquifer 

above the Corcoran Clay ranges from about 26 to 80 m in the 

regional study area. East of the Corcoran Clay, this aquifer 

comprises primarily unconsolidated alluvial sediments, but 

includes the upper part of the more-consolidated Mehrten Formation. Irrigation and public-supply wells were completed in 

coarse-grained units in the upper Mehrten. The confined aquifer comprises alluvial sediments and upper Mehrten Formation sediments from beneath the Corcoran Clay to the deepest 

occurrence of fresh water. The contribution of ground water 

from the consolidated rocks beneath the primary aquifers was 

assumed negligible and was not considered.

10 Simulation of Multiscale Ground-Water Flow in Part of the Northeastern San Joaquin Valley, California
Figure 6. Vertical transition probabilities used to constrain vertical sequences of hydrofacies, San Joaquin local study area, 

California. 

USGS, U.S. Geological Survey. 

EXPLANATION

Transition probability

Measured from USGS borehole data

Markov chain approximation

VERTICAL DISTANCE, IN METERS

VERTICAL TRANSITION PROBABILITY

Clay

0

0

.5

1.0

0

.5

1.0

0

.5

1.0

0

.5

1.0

1 2 0 1 2 0 1 2 0 1 2

Silt Silty sand Sand

Conceptual Understanding of Ground-Water System 11
Under natural conditions, ground water was primarily 

recharged at the upper parts of the alluvial fans where the 

major streams enter the valley (fig. 7). Ground-water flow 

followed the southwest slope of the basement complex and the 

dip of the overlying sedimentary deposits toward the southwest in the direction of the valley trough. Artesian conditions 

near the San Joaquin River indicated discharge to the river and 

surrounding marshlands (Davis and others, 1959).

Ground-water development in the basin changed groundwater flow patterns. Historically, water pumped for agricultural irrigation and irrigation return flows is much greater than 

natural discharge and recharge, which has caused an increase 

in vertical flow in the system (fig. 7B) (Page and Balding, 

1973; Londquist, 1981). Ground water generally flows toward 

the southwest, as occurred prior to development (fig. 8). However, ground water moving along a lateral flow path may be 

extracted by wells and reapplied at the surface multiple times 

before reaching the valley trough (fig. 7B), at which point it 

may flow beneath the river toward pumping centers on the 

west side of the valley rather than discharge to the river. South 

of the Tuolumne River is a centrally located ground-water 

flow divide (fig. 8), east of which water flows eastward toward 

irrigation wells in an agricultural area with no surface-water 

supplies. West of the flow divide, water generally flows westward toward the valley trough.

The western part of the study area along the San Joaquin 

River is an area of ground-water discharge where the water 

table is shallow, often within 3 m of the land surface. Water 

is pumped from this area to lower the water table so crop 

roots are not damaged; this water is added to irrigation canals. 

Depth to the water table increases eastward, particularly south 

of the Tuolumne River, where depths can exceed 40 m within 

the large cone of depression (fig. 8).

Geologic age Hydrofacies Proportion Mean length, in meters

X Y Z

Holocene Silt 0.24 80 100 1.26

Silty sand 0.46 60 100 1.18

Sand 0.31 40 160 0.93

Pleistocene Clay 0.37 395 184 1.78

Silt 0.20 185 116 0.92

Silty sand 0.23 274 137 1.37

Sand 0.21 191 72 0.96

Table 1. Proportions and mean lengths of hydrofacies used in local model, San Joaquin 

local study area, California. 

[Due to rounding, sum of proportions do not equal 1.0] 

Table 2. Soft-conditioning probabilities assigned to hydrofacies for non-U.S. Geological 

Survey well log descriptions, San Joaquin local study area, California.

[non-USGS, non-U.S. Geological Survey]

Description in nonUSGS well logProbability of hydrofacies occurrence

Clay Silt Silty sand Sand

Clay 0.75 0.25 0 0

Clayey sand 0 0 1 0

Clayey shale 0.5 0.5 0 0

Gravelly sand 0 0 0 1

Hard pan 0.5 0.5 0 0

Rock 0.5 0.5 0 0

Sand 0 0 0.25 0.75

Sandy clay 0.5 0.5 0 0

Sandy clayey shale 0.5 0.5 0 0

Sandy gravel 0 0 0 1

Sandy shale 0.5 0.5 0 0

Sandy silt 0 1 0 0

Sandy topsoil 0 0.4 0.4 0.2

Shale 0.5 0.5 0 0

Silty clay 0.6 0.4 0 0

Silty sand 0 0 1 0

Topsoil 0.3 0.3 0.3 0.1

Unknown 0.25 0.25 0.25 0.25

12  Simulation of Multiscale Ground-Water Flow in Part of the Northeastern San Joaquin Valley, California
Figure 7. Conceptual diagram of (A) regional lateral ground-water flow and (B) vertical flow 

influenced by agricultural practices and natural discharge zones. 

Modified from Burow and others (2004). 

Generalized direction of 

regional ground-water flow

water table

MORE CONSOLIDATED DEPOSITS

FLUVIALLY DEPOSITED ALLUVIAL FAN DEPOSITS

Regional flow

FLOOD-PLAIN

DEPOSITS

Confining unit

AGRICULTURAL RECHARGE

irrigation wells

river

NOT TO SCALE

Aquifer

B

A

20 KILOMETERS

0 8 16 MILES

0 10

37

15

37

45

121 15 120 120 45 120 30

Conceptual Understanding of Ground-Water System 13
Water levels near the city of Modesto generally decreased 

until the early 1990s (fig. 9). This decrease likely was caused 

by increased urban development and associated pumping for 

public supplies punctuated by drought conditions in 1976 

and 1987–92. A series of wet years in the mid-1990s and 

completion of a surface-water treatment plant in 1994, which 

provided additional surface-water supplies for public and 

industrial uses, resulted in a recovery of water levels (fig. 9).

Data from USGS wells in the Modesto urban area show 

that vertical hydraulic gradients from the water table (about 

10 m below land surface) to the deeper production zones of 

most municipal wells (about 40–100 m below land surface) 

are strongly downward and larger during spring and summer 

(about 0.2–0.3) than during fall and winter (fig. 10). Seasonal 

water-level fluctuations are about 6 m in the deeper wells and 

generally less than 1 m at the water table in the Modesto urban 

area.

30

20

15

15

20

20

35

25

25

30

30

20 KILOMETERS

0 8 16 MILES

0 10

San Joaquin River

Merced River

Tuolumne River

Stanislaus River

121 15 120 45 120 30

37

45

37

30

37

15

121

Urban

Lines of equal water level altitude, in meters; dashed

where approximated. Contour interval 5 meters. 

Datum is North American Vertical Datum of 1988.

Active area of local model

Regional model extent

Boundary of Corcoran Clay

Location of well used to map water levels

Direction of ground-water flow

Approximate location of ground-water flow divide 

EXPLANATION

Figure 8. Contours of measured water-level altitudes in the unconfined to semiconfined aquifer, spring 

2000, San Joaquin regional study area, California.

14  Simulation of Multiscale Ground-Water Flow in Part of the Northeastern San Joaquin Valley, California
Water levels measured in the transect wells in the local 

study area are shown in figure 11 (locations of wells shown in 

figure 3). These data show a weak downward gradient during 

the spring and summer below the almond orchard at the upper 

end of the well transect, and essentially no vertical gradient 

in this area the rest of the year. Measurements at the middle 

site show no vertical gradient year-round in the three deepest 

wells. The shallowest well at this site was screened in sandy 

silt and was not properly developed, but the hydrograph shows 

irrigation cycles in the adjacent corn field. Vertical gradients 

underlying natural vegetation near the Merced River at the 

lower end of the well transect were weakly upward, with the 

exception of several reversals when water levels were at their 

highest. Temporal variability of measured water levels was 

dominated by irrigation at the upper end of the well transect, 

the river stage at the lower end, and a combination of these 

influences in the middle. The hydrograph for the well below 

the Corcoran Clay at the lower end of the well transect (not 

shown in fig. 11) indicates a strong downward gradient across 

the unit during the irrigation season (average of about 0.3) and 

little or no vertical gradient the rest of the year.

Water Budget

Sources of recharge in the regional study area include 

agricultural return flow, infiltration of precipitation, reservoir 

leakage, and inflow from rivers. Ground-water discharges to 

pumping wells, rivers, transpiration, and evaporation. Information is available for some of these processes in the regional 

study area. Results from a recent 3-month study conducted 

by the Modesto Irrigation District, which manages the 

Modesto Reservoir, suggest a leakage rate of about 67,600 to 

84,500 m3/d (Walter Ward, Modesto Irrigation District, oral 

commun., 2002). The interaction of ground water and surface 

water is largely unknown, but some data are available. A previous study of a 19-mile reach of the San Joaquin River within 

the regional study area showed predominantly gaining conditions during an 11-month period of drought conditions during 

1988–89 (Phillips and others, 1991). Temperature and waterlevel measurements made within and below the Merced River 

as part of this study indicated predominantly gaining conditions within the local study area (Zamora, 2006). Additionally, 

a water-level map that includes the regional study area (fig. 8) 

suggests losing conditions in the upper reaches of the Stanislaus, Tuolumne, and Merced Rivers, and gaining conditions 

in the lower reaches.

Figure 9. Hydrographs of measured water-level altitudes for selected irrigation wells from 

1960 to 2001, San Joaquin regional study area, California. 

Well locations shown on figure 1. 

10

5

0

15

20

25

30

35

40

45

1960 1970 1980 1990 2000

WATER-LEVEL ALTITUDE, IN METERS ABOVE NAVD 88

YEAR

Well zone screened

Unconfined

3S/7E-13A1

3S/9E-7C1

4S/9E-19A1

Semiconfined

6S/12E-12F1

Unknown

2S/11E-19K1

5S/10E-24C1

6S/11E-27K1

Conceptual Understanding of Ground-Water System 15
Discharge to pumping wells was measured for urban 

wells and wells owned or used by irrigation districts. No data 

were available for pumpage from domestic wells. Although 

domestic wells are common in the study area, much of the 

water from these small-capacity wells is returned to the aquifer system by way of septic systems; therefore, the net use was 

assumed to be a small percentage of total pumping. Data on 

private agricultural pumping are not available; nor are data on 

evaporation from the shallow water table.

Estimates of many of the key components of recharge 

and discharge—agricultural return flow, infiltration of precipitation, transpiration, and private agricultural ground-water 

pumping—have been made using a water-budget approach 

(Burow and others, 2004) for water-year 2000 (October 1, 

1999, through September 30, 2000). This approach and minor 

modifications are described generally herein; for details, the 

reader is referred to Burow and others (2004). Surface water 

and ground water are used for irrigation in the agricultural 

areas. Surface-water delivery data were available for most 

of the regional study area, although private pumpage records 

were not. Ground-water use in agricultural areas and areal 

recharge estimates were well constrained by the regional water 

budget.

The water budget was delineated geographically by dividing the regional study area into subareas for which surfacewater deliveries could be obtained or estimated. A separate 

water budget was calculated for each of the resulting 47 subareas (fig. 12), which included agricultural and urban settings, 

foothill areas with natural vegetation, riparian areas having 

natural vegetation and (or) crops, and reservoirs.

Digital land-use data (California Department of Water 

Resources, 2001a,b) were used to estimate the water budget 

for subareas containing primarily non-urban land (Burow 

and others, 2004). The area of each crop or other vegetation 

type was determined using a geographic information system 

(GIS). A daily crop demand was calculated on the basis of 

crop or vegetation type and climate, and a total daily irrigation 

demand was estimated for each subarea. The total irrigation 

demand was met by a combination of surface-water deliveries, ground water pumped by irrigation districts, and private 

ground-water pumping. The total reported or estimated 

monthly surface-water and ground-water deliveries were 

subtracted from the estimated monthly irrigation demand 

to determine the monthly unmet irrigation demand. Private 

ground-water pumping was then assumed to equal this residual 

irrigation demand.

10

2003 2004 2005

0

15

20

25

W

ATER-LEVEL ALTITUDE, IN METERS ABOVE NAVD 88

DECEMBERJANUARYFEBRUARYMARCHAPRILMAYJUNEJULYAUGUSTSEPTEMBEROCTOBERNOVEMBERDECEMBERJANUARYFEBRUARYMARCHAPRILMAYJUNE

FPA_10

FPD_103

FPD_9

FPA_105

Figure 10. Hydrographs of water-level altitudes measured hourly in U.S. Geological Survey monitoring wells in urban Modesto from 

December 2003 to July 2005, San Joaquin regional study area, California.

Locations of FPA and FPD wells shown on figure 2.

16  Simulation of Multiscale Ground-Water Flow in Part of the Northeastern San Joaquin Valley, California
Recharge was estimated differently for areas containing native vegetation, irrigated crops, and urban land. The 

recharge for each of these areas estimated by Burow and others (2004) was reduced by 10 percent during calibration of the 

regional model. Recharge in areas with native vegetation was 

based on an assumed fraction of precipitation that did not run 

off and was not consumed (transpired). Because consumptive 

use for native vegetation was unknown, it was assumed that 

about 40 percent of precipitation runs off or is consumed in 

the foothill areas. This differs from the assumption in Burow 

and others (2004) of no runoff or consumption of precipitation 

in the foothills.

Recharge in irrigated agricultural areas was estimated as 

the portion of precipitation and irrigation not consumed by 

the crops (consumptive use). The consumptive use of applied 

water was estimated to be 63 percent for most of the regional 

study area on the basis of calculated values for two subareas 

receiving surface-water deliveries and having few known wells 

(among the 3,500 wells cataloged from drillers’ logs). This 

estimate was considered reasonable because crops are 

cultivated in sandy soils and irrigated by flooding and permanent sprinklers. Consumptive use of applied water was 

assumed to be 80 percent in the older fan deposits in the foothill areas, where sediments are more indurated and efficient 

irrigation methods such as micro-sprinkler and drip are used.

For the urban areas, recharge from delivered water was 

estimated using the minimum-month method to determine 

indoor and outdoor water use (California Department of Water 

Resources, 1994). Ten percent of the estimated outdoor use 

was subtracted from the total to account for leakage from 

water distribution lines (California Department of Water 

Resources, 1994). Fifty percent of the remaining outdoor 

water use was assumed to be consumptive use for landscape 

irrigation or runoff to streams, and the remainder was assumed 

to contribute to urban recharge (Burow and others, 2004). 

Recharge in the urban area from precipitation was assumed to 

be 50 percent of total precipitation because much of the runoff 

in Modesto and other urban areas is drained through largediameter boreholes backfilled with rock. These “rock wells” 

are direct conduits to the water table.

21

22

23

24

25

26

27

28

29

WATER-LEVEL ALTITUDE, IN METERS ABOVE NAVD 88

2003 2004 2005

upper_7

middle_5

upper_27

middle_25

lower_5 lower_29

river stage

JUNEJULYAUGUSTSEPTEMBEROCTOBERNOVEMBERDECEMBERJANUARYFEBRUARYMARCHAPRILMAYJUNEJULYAUGUSTSEPTEMBEROCTOBERNOVEMBERDECEMBERJANUARYFEBRUARYMARCHAPRIL

MAY

Figure 11. Hydrographs of water-level altitudes measured hourly in U.S. Geological Survey 

monitoring-well transect from June 2003 to May 2005, San Joaquin local study area, California.

Well locations shown on figure 3.

Conceptual Understanding of Ground-Water System 17
EXPLANATION

Boundary of water-budget subarea

Active area of local model

Regional model extent

Agricultural, native, or urban area represented by one or more water-budget subareas

Eastside Water District

Merced Irrigation District

Merquin Community Water District

Modesto Irrigation District

Oakdale Irrigation District

South San Joaquin Irrigation District

Stevinson Water District

Turlock Irrigation District

Foothills

Riparian and miscellaneous agricultural areas

Urban

20 KILOMETERS

0 8 16 MILES

0 10

121 15

37

45

37

30

37

15

121 120 45 120 30

Figure 12. Subareas of regional model used for water-budget calculations, San Joaquin regional study 

area, California. 

Modified from Burow and others (2004). 

18  Simulation of Multiscale Ground-Water Flow in Part of the Northeastern San Joaquin Valley, California
The estimated average areal recharge rate for the regional 

study area was about 0.54 m/yr; the highest recharge rates 

were for the agricultural areas in the southwestern part of the 

study area (fig. 13) and along the rivers in the northeastern 

part. The lowest estimated recharge rates were for the foothills 

and the urban areas. Similarly, the highest estimated pumping rates were for the agricultural areas in the southwestern 

part of the regional study area (fig. 14). The relatively high 

rates of pumping and recharge in the southwestern agricultural 

areas were related, in part, to the irrigation efficiency and the 

supplemental pumping required to manage the shallow water 

table.

Ground-Water Age

Samples collected from most of the USGS wells along 

the transect in the local study area were analyzed for sulfur 

hexafluoride (SF6), an environmental tracer that has been used 

to estimate ground-water age (Busenberg and Plummer, 2000). 

Atmospheric concentrations of SF6 were very low prior to 

1965 and have increased since then, making it a good means 

of dating young ground water. Concentrations of SF6 in water 

samples from the USGS well transect (Larry Puckett, U.S. 

Geological Survey, written commun., 2005) are compared in 

this report to concentrations estimated using simulated travel 

times from the water table to these wells and the historical 

atmospheric concentration of SF6 (Böhlke, 2005).

Ground-Water Flow Simulations

Steady-state models of ground-water flow in the regional 

and local study areas were developed using MODFLOW2000 (Harbaugh and others, 2000) to provide tools to help 

understand the flow system at both scales and the associated 

transport and fate of agricultural chemicals at the local scale. 

Lateral boundaries of the local model were defined by regional 

model results and assigned as specified flow rates.

Both models simulate water-year 2000, when the groundwater system was in a quasi-steady-state condition. Measured 

water levels in the regional study area suggest much of the 

system has been at equilibrium for many years, particularly 

the areas that have a shallow water table downgradient from 

Modesto and Turlock, including the local study area (fig. 9). 

The two areas where water levels have recently changed are 

Modesto and the agricultural area upslope from Turlock. Water 

levels recovered rapidly when surface water was imported to 

the Modesto area in 1995, but the recovery slowed by 2000. 

Upslope from Turlock, water levels declined for about 2 

decades because of increased ground-water use associated 

with new agricultural development. Although data for this area 

are sparse, they suggest water levels may have approached 

equilibrium.

Spatial Discretization

Regional Model

The regional model area is in the northeastern San Joaquin Valley extending from north of the Stanislaus River to 

south of the Merced River and bounded on the northeast by the 

Sierra Nevada foothills and the southwest by the San Joaquin 

River. The model grid is oriented parallel to the valley axis, 

37 degrees west of due north (fig. 15). The model area extends 

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

Ranges to the Sierra Nevada foothills, although the area west 

of the San Joaquin River is not simulated. Each model cell is 

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

The regional model layering was designed as a series of 

wedges to generally represent the regional dip of the sediments (fig. 16). Sixteen model layers were defined, ranging in 

thickness from 0.5 to 16 m above the Corcoran Clay (excluding the uppermost model layer) and from 20 to 74 m below 

the Corcoran Clay. 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 thickness ranges from 1 to 40 m. The thickest 

cells in the uppermost layer are near the foothills and generally 

are not saturated. 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 (10, 10, 15, 20, 20, 

and 25 percent of that thickness, respectively).

Layer 8 represents the Corcoran Clay, where present, the 

top surface of which was a smoothed rendition constrained by 

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

varies spatially as determined by Page (1986) and from analysis of logs, and ranged from 3 to 43 m. A thickness of 5 m was 

specified in layer 8 where the Corcoran Clay was not present. 

The thickness of layers 9–16 was assigned as a percentage of 

the thickness of materials between the bottom of the Corcoran 

Clay and the bottom of the model. Layers 9–16 were 10, 10, 

10, 10, 10, 15, 15, and 20 percent of that thickness, respectively. The bottom of the model was an artificial surface that 

loosely represented topographic variability and the general dip 

of the Corcoran Clay. The total thickness of the wedge-shaped 

model ranges from about 220 to 430 m.

Local Model

The local model is located within the regional model 

area, straddles the Merced River (fig. 17), and is oriented the 

same as the regional model (fig. 1). The active model area 

is about 17 km2. Each model cell is 40 m by 40 m, and the 

grid has 110 rows and 140 columns. There are 110 flat-lying 

layers, each 0.5 m thick, with a maximum altitude of 34.5 m. 

The layer thickness was the same as that for the TProGS grid, 

which was determined on the basis of the thickness of hydrofacies recorded in USGS geologic logs. The bottom of the 

model coincides with the top of the Corcoran Clay.

Ground-Water Flow Simulations 19
Active area of local model

Regional model extent

EXPLANATION

0.62 to 0.77 (2.03 to 2.52)

0.47 to 0.58 (1.54 to 1.90)

0.36 to 0.44 (1.18 to 1.44)

0.14 to 0.29 (0.46 to 0.95)

Estimated recharge rate, in meters per year

 (feet per year in parentheses)

0 8 16 MILES

0 10 20 KILOMETERS

121 15

37

45

37

30

37

15

121 120 45 120 30

Figure 13. Estimated rates of recharge for subareas of regional model, water year 2000, San Joaquin 

regional study area, California. 

Modified from Burow and others (2004). 

20 Simulation of Multiscale Ground-Water Flow in Part of the Northeastern San Joaquin Valley, California
Active area of local model

Regional model extent

EXPLANATION

0.65 to 0.96 (2.13 to 3.15)

0.51 to 0.64 (1.67 to 2.10)

0.22 to 0.50 (0.72 to 1.64)

0.0 to 0.17 (0.0 to 0.56)

Estimated pumping rate, in meters per year

 (feet per year in parentheses) 0 10 20 KILOMETERS

0 8 16 MILES

121 15

37

45

37

30

37

15

121 120 45 120 30

Figure 14. Estimated rates of ground-water pumping for subareas of regional model, water year 2000, San 

Joaquin regional study area, California. 

Modified from Burow and others (2004). 

Ground-Water Flow Simulations  21
Figure 15. Model extent, boundary conditions, and extent of the downslope, midslope, and upslope 

areas for the regional model, San Joaquin regional study area, California. 

EXPLANATION

Water table, free surface

Urban

Lateral general-head boundary

Lateral general-head boundary with vertical gradient imposed

General-head boundary representing lower river reaches

Specified-recharge boundary representing upper river reaches

No-flow boundary

Active area of local model

0 10 20 KILOMETERS

0 8 16 MILES

Area not simulated

upslope

area

midslope

area

downslope

area

San Joaquin River

121 15 121 120 45 120 30

37

45

37

30

37

15

22  Simulation of Multiscale Ground-Water Flow in Part of the Northeastern San Joaquin Valley, California
Boundary Conditions and Model Stresses

Regional Model

Lateral boundary conditions in the regional model are 

no-flow along the Sierra Nevada foothills and general-head 

elsewhere (fig. 15). The general-head boundaries were specified using a water-level map (fig. 8), typical vertical hydraulic 

gradients calculated from measured water levels, and hydraulic-conductivity estimates for each cell along the boundary. 

Initially, no vertical gradients were imposed along the lateral 

boundaries, but measured water levels in Modesto, where 

pumpage is known, could not be simulated using justifiable 

ranges of aquifer hydraulic parameters. Therefore, gradients 

were later imposed along the northwestern and southeastern 

edges of the regional model grid during model calibration. A 

downward hydraulic gradient of 0.05 was assigned from layers 

1 through 9, the latter being the approximate average location 

of well perforations in the region. Below layer 9, the same gradient was assigned in an upward direction; the maximum head 

below layer 9 was constrained to that of the water table in the 

same row and column of the model grid.

The southwestern boundary of the regional model 

coincides with the San Joaquin River, and was simulated as a 

lateral general-head boundary; all cells west of the river are 

inactive. This configuration allows for known cross-valley 

flow beneath the San Joaquin River (Belitz and Phillips, 1995; 

Phillips and others, 1991). Water-level data and production 

wells are sparse near this boundary; therefore, a vertical gradient was not specified. Heads in all cells below the river were 

set to 0.1 m above river stage on the basis of previous work 

in the upper 30 m of the aquifer system along the river, which 

showed predominantly gaining conditions during an 11-month 

period in 1988–89 (Phillips and others, 1991).

The upper boundary of the regional model was simulated 

as the water table, and the lower model boundary was simulated as no-flow. The lower model boundary was arbitrarily 

located far below the deepest wells, and significant vertical 

flow at that depth was considered unlikely.

Agricultural return flow, infiltration of precipitation, 

reservoir leakage, and inflow from rivers recharge the regional 

aquifer. Agricultural return flow, infiltration of precipitation, 

and private agricultural ground-water pumping were estimated 

in the water-budget analysis. The two recharge estimates from 

the water-budget analysis were summed for each waterbudget subarea, and this recharge was distributed evenly to the 

uppermost active model layer within each subarea.

-500

-400

-300

-200

-100

0

100

0 5,000 10,000 15,000 20,000 25,000 30,000 35,000 40,000

DISTANCE FROM SAN JOAQUIN RIVER ALONG MODEL ROW 73, IN METERS

ALTITUDE OF MODEL LAYER, IN METERS ABOVE NAVD 88

Top of layer 1 (land surface)

Bottom of layer 16 (artificial)

Corcoran Clay portion of layer 8

Figure 16. Vertical discretization of regional model along row 73, San Joaquin regional study area, California. 

Location of row 73 is shown on figure 1. 

Ground-Water Flow Simulations  23
Ground-water discharges to pumping wells, rivers, and 

evaporation were simulated. Private agricultural pumping was 

distributed laterally within water-budget subareas, assuming 

an average well spacing of 1,200 m (every 3 cells). Measured 

pumpage in urban areas and irrigation districts was withdrawn 

from cells that contained the pumping wells. The vertical 

distribution of private agricultural pumping was estimated 

using the average screened interval of irrigation wells in each 

subarea. Pumpage was distributed vertically by weighting 

transmissivity to layers intersected by a well screen. Measured 

pumpage also was distributed in this manner.

Interaction between ground water and surface water 

was simulated as reservoir leakage, gaining reaches, and 

losing reaches of the four rivers. There were three 

significant reservoirs along the northeastern boundary of the 

regional model: Woodward, Modesto, and Turlock, from 

north to south (fig. 1). These reservoirs were approximately 

equal in size, and an estimate of leakage rates (about 67,600 

to 84,500 m3/d) was available only for a 3-month period for 

the Modesto Reservoir (Walter Ward, Modesto Irrigation 

District, oral commun., 2002). Leakage rates for the other two 

reservoirs were assumed to be similar to that for the Modesto 

Reservoir. The Reservoir package (Fenske and others, 1996) in 

MODFLOW-2000 was used to simulate the reservoirs, which 

requires specification of reservoir stage, and information for 

calculating the conductance of the reservoir bottom. The stage 

was estimated from topographic maps, and the conductance 

terms were adjusted to approximate the assumed leakage rate.

EXPLANATION

Cells representing the Merced River

Specified-flux boundary based on regional model

USGS well cluster (fig. 3)

120 4930 120 48 120 4630

37

24

37

22

30

3,600 7,200 FEET

1,000 2,000 METERS

0

0

Merced River

Figure 17. Extent of active area and boundary conditions for the local model, San Joaquin local study 

area, California. 

24  Simulation of Multiscale Ground-Water Flow in Part of the Northeastern San Joaquin Valley, California
The four rivers in the study area were represented in 

the model as a combination of general-head and specifiedflux cells. General-head cells were used where the river was 

potentially connected to the water table; this allowed flow 

into and out of the river. The river stage was estimated using 

streamgage data and topography, and the riverbed 

conductance was calculated using the estimated vertical 

hydraulic conductivity by cell, the approximate river width, 

and an assumed riverbed thickness of 1 m. Recharge from the 

river was specified in model cells where the river was disconnected from the water table. This value (0.005 m/d per cell) is 

poorly constrained and was not adjusted during calibration.

Bare-soil evaporation from the water table was simulated 

where the water table was within 2.1 m of the land surface. 

The maximum evaporation rate of 1.6 m/yr was specified at 

the land surface, and a linear decrease to zero at 2.1 m below 

land surface was simulated on the basis of previous work in a 

nearby area (Belitz and Phillips, 1995).

Local Model

The location of the lateral boundaries was based roughly 

on flow lines associated with the water table. The northeastern 

boundary was at a shallow angle to a flow line, and the northwestern and southern boundaries approximated flow 

lines converging at the Merced River (fig. 17). Although 

two of these lateral boundaries approximated flow lines at 

the water table, flow directions vary with depth; therefore, 

lateral boundary conditions in the local model were specified 

fluxes derived from lateral flows simulated in the regional 

model. The estimated local distribution of sediment types 

was translated into sediment texture values for overlapping 

regional model cells, thus minimizing incompatible flux/sediment combinations at the regional/local interface. Cell-by-cell 

boundary fluxes for the local model were calculated from 

those for adjacent larger cells in the regional model by using a 

hydraulic-conductivity-weighted distribution.

The upper boundary of the local model was the water 

table, and the lower boundary was general-head, allowing 

vertical flow through the Corcoran Clay. The hydraulic head 

beneath the Corcoran Clay was specified at 19.9 m, which 

was the average value from 2004 to 2005 measured in a USGS 

well completed beneath the clay at the lower end of the well 

transect. The conductance of the general-head boundary was 

calculated using the calibrated vertical hydraulic conductivity 

of the Corcoran Clay from the regional model and a constant 

thickness (18 m) determined from the geologic log for the 

USGS well.

Stresses in the local model included recharge from 

agricultural return flow, infiltration of precipitation, and 

inflow through the boundaries; and discharge from outflow 

to the Merced River and through the boundaries. The lateral 

boundaries have been discussed, and there was no substantial ground-water use in the local study area because a canal 

provides irrigation water. Recharge from agricultural return 

flow was estimated using the crop demand calculated in the 

regional water-budget analysis and a variable consumptive 

use of applied water estimated from the irrigation method 

(California Department of Water Resources, 2001a) used on 

each parcel (fig. 18). Given that most of the local study area is 

cultivated, topographic slopes are shallow, fields generally are 

terraced, and precipitation falls primarily during the 

period when crops are dormant, it was assumed that about 

60 percent of rainfall became recharge. The average estimated 

net recharge flux across the land surface in the local model 

area was 0.45 m/yr, one third of which was from precipitation. 

The average local estimated recharge was 10 percent lower 

than that for the regional model in the same area.

Interaction of ground water with the Merced River 

(discharge) was simulated in the local model using the River 

package in MODFLOW-2000 (Harbaugh and others, 2000). 

The river stage at the study reach was assigned the average 

of continuous on-site measurements from 2003 to 2005. This 

stage at the study reach was extrapolated for upstream and 

downstream river cells on the basis of the topographic gradient 

of the river channel. The conductance of the river bed was calculated using the approximate area of the bed, an assumed bed 

thickness of 1 m, and an assigned riverbed vertical hydraulic 

conductivity of 30 m/d.

Estimation of Aquifer Hydraulic Properties

Regional Model

Hydraulic conductivity was distributed using sediment 

texture, the same method as that used for a previous groundwater flow model of the central western San Joaquin Valley 

(Belitz and Phillips, 1995; Phillips and Belitz, 1991). This 

method uses the estimated sediment texture for each model 

cell and horizontal and vertical hydraulic conductivity estimates for each textural end member.

A hydraulic conductivity value was specified for the 

Corcoran Clay (Kcorc), which was assumed to be isotropic. For 

the remaining aquifer-system materials, horizontal hydraulic conductivities were calculated using the coarse-grained 

(Kcoarse) and fine-grained (Kfine) lithologic end members and the 

distribution of sediment texture. The lithologic end members 

were specified for two lithologic subareas: the older fan deposits along the northeastern edge of the model (the upslope area 

in fig. 15) and everywhere else. Horizontal hydraulic conductivity (Kh

) was calculated for each cell in the model using the 

arithmetic mean:

K K h c = × oarse F K coarse + × fine Ffine (1)

where Fcoarse is the fraction of coarse-grained sediment in a 

cell, estimated from sediment texture data 

as described earlier in this report, and 

 Ffine is the fraction of fine-grained sediment 

in a cell (1–Fcoarse).

Ground-Water Flow Simulations  25
Figure 18. Estimated rates of recharge for the local model, water year 2000, San Joaquin local study 

area, California. 

3,600 7,200 FEET

1,000 2,000 METERS

0

0

120 4930 120 48 120 4630

37

24

37

22

30

Active area of local model

USGS well cluster

EXPLANATION

0.15 to 0.24

0.25 to 0.33

0.34 to 0.43

0.44 to 0.52

0.53 to 0.61

0.62 to 0.71

0.72 to 0.80

0.81 to 0.90

Estimated recharge rate, in meters per year

26  Simulation of Multiscale Ground-Water Flow in Part of the Northeastern San Joaquin Valley, California
Vertical hydraulic conductivity between model layers (Kv

) 

either was set to Kcorc, if the Corcoran Clay was present within 

one of the layers, or was calculated using the harmonic mean:

K F

K

F

K

v

coarse

coarse

fine

fine

=

+

1

(2)

where Fcoarse is the fraction of coarse-grained sediment 

between layer midpoints, and 

 Ffine is the fraction of fine-grained sediment between 

layer midpoints.

The calibrated value of Kcorc was 1.3 × 10–3 m/d and that 

for Kfine was 8 × 10–3 m/d. The calibrated value of Kcoarse varied 

by lithologic subarea: 53 m/d for the older fan deposits and 80 

m/d for the remaining area. The resulting values of Kh and Kv

are summarized in figure 19. The distributions of Kh and Kv are 

the same as those for the sediment texture (fig. 5).

Local Model

Effective hydraulic conductivity in the three principal 

directions of each of 200 texture realizations was estimated 

using 600 simulations. These simplified simulations were used 

to compute flow in each principal direction for each realization. Constant-head boundaries were assigned at the up-gradient and down-gradient faces to produce an arbitrary hydraulic 

gradient of 0.0009, and no stresses were imposed. Isotropic 

hydraulic conductivities were assigned: 0.08 m/d for the clay 

hydrofacies, 2 m/d for silt, 24 m/d for silty sand, 160 m/d for 

sand, and 0.00008 m/d for the Corcoran Clay.

Five of the TProGS-generated realizations of the threedimensional distribution of hydrofacies within the local model 

were chosen for calibration and sensitivity. This subset of 

realizations was selected on the basis of a relative ranking of 

the bulk flow properties in the X, Y, and Z directions. Four 

were chosen to represent the extremes:

The maximum sum of flow in the x, y and z directions (highest effective conductivity);

The minimum sum of flow in the x, y and z directions (lowest effective conductivity);

The maximum of (z flow – (x flow + y flow)) (least 

domain-scale anisotropy); and

The minimum of (z flow – (x flow + y flow)) (greatest domain-scale anisotropy).

A fifth realization was chosen randomly for use in 

developing the local model, and ultimately was used in the 

calibrated model. Of the 200 realizations, this ranked 54th, 48th, 

and 33rd for flow in the X, Y, and Z directions, respectively. 

Figure 20 shows one view of the vertical distribution of 

hydrofacies for this realization.

1.

2.

3.

4.

To simplify model calibration, the three hydrofacies in 

the Holocene deposits associated with the incised river channel were assumed to be hydraulically equivalent to the same 

hydrofacies in the Pleistocene deposits. Therefore, the total 

remained at four hydrofacies: sand, silty sand, silt, and clay. 

The overall proportions of these facies are as shown in the 

Pleistocene section in table 1. The calibrated and specified 

values of horizontal and vertical hydraulic conductivity 

associated with each hydrofacies are shown in table 3.

Model Calibration and Sensitivity

Regional Model

Calibration of the regional model consisted of a systematic application of the parameter estimation method (described 

in the “Aquifer Hydraulic Properties” section in this report) to 

narrow the range of possible solutions. This was followed by 

manual adjustments to best match the highest-quality waterlevel measurements in midslope areas while simultaneously 

honoring the overall conditions in upslope and downslope 

areas. Kcoarse and Kfine were varied systematically for a given 

value of Kcorc, which was adjusted to roughly match vertical 

gradients across the Corcoran Clay (assumed to be isotropic). 

Simulated hydraulic heads were compared to measured water 

levels in 49 wells representing various parts of the aquifer system, including 22 wells installed and monitored by the USGS. 

The resulting error distributions constrained the parameter set 

and constitute a sensitivity analysis of these parameters.

Wells used to calibrate the regional model were divided 

into several categories. The first category included the USGS 

wells and associated measurements, which were considered 

the highest quality because of the short screened intervals (0.6 

to 3 m) and hourly measurements during 2003–2005. Most 

of these wells are in midslope areas in and near Modesto and 

the local study area. These wells are multi-depth completions, 

and thus were used to evaluate simulated vertical gradients as 

well as simulated hydraulic heads. Two other key categories of 

wells were defined geographically. The downslope area where 

the water table is shallow was represented by 17 wells, most 

of which were 4.6 m deep and monitored on a monthly basis. 

Data from these wells were ranked second highest in overall 

quality. The upslope area northeast of Modesto and Turlock 

was represented by 11 wells, including one USGS well in 

Eastside Water District. The final well used to calibrate the 

regional model was a USGS well screened below the Corcoran 

Clay at the lower end of the USGS well transect in the local 

study area.

Ground-Water Flow Simulations  27
Model error was quantified by average error and the rootmean-square error (RMSE):

RMSE h h

n

meas sim i

i

n

= −

=

∑[ ] 2

1 (3)

where hmeas is measured water level, 

 hsim is simulated hydraulic head, 

 i is the summation index, and 

 n is the number of measurements.

The RMSE is a measure of error magnitude, and average 

error indicates whether simulated hydraulic heads were, overall, higher or lower than measured water levels. The RMSE

and average error calculations were used to estimate the range 

of Kcoarse and Kfine values that generated parameter distributions with the lowest error for the conceptual model described 

herein. RMSE and average error values were calculated for 

100 simulations at a time, representing progressively narrower 

ranges of Kcoarse and Kfine. Results from each group of 100 

simulations were plotted as error surfaces describing model fit 

with respect to hydraulic heads for various sets of calibration 

wells (fig. 21). Each plot in figure 21 shows the error surface 

Figure 19. Frequency of estimated horizontal and vertical hydraulic conductivity for the upslope (eastern) and 

downslope (western) alluvial deposits, San Joaquin regional study area, California. 

Horizontal Hydraulic Conductivity Vertical Hydraulic Conductivity

Western area above Corcoran Clay

Western area below Corcoran Clay

Eastern area, entire thickness

RANGE OF HYDRAULIC CONDUCTIVITY, IN METERS PER DAY RANGE OF HYDRAULIC CONDUCTIVITY, IN METERS PER DAY

FREQUENCY OF HYDRAULIC CONDUCTIVITY, IN PERCENT OF TOTAL SPECIFIED PART OF AQUIFER SYSTEM

0

5

10

15

20

25

30

0

10

20

30

40

0

10

20

30

40

0

20

40

60

80

100

0

20

40

60

80

100

0

20

40

60

80

100

10 20 30 40 50 60 70 80 0.008 0.08 0.8 8 80

28  Simulation of Multiscale Ground-Water Flow in Part of the Northeastern San Joaquin Valley, California
Figure 20. Vertical section roughly parallel to the Merced River showing distribution of hydrofacies used in calibrated local 

model, San Joaquin local study area, California. 

Top of Corcoran Clay

Scale is approximate

Vertical exaggeration 30x

Approximate zone above land surface

EXPLANATION

Sand

Silty sand

Silt

Clay

0 1,000 2,000 METERS

0 3,600 7,200 FEET

Table 3. Calibrated and specified hydraulic conductivity 

values for the local model, San Joaquin local study area, 

California. 

[Bold values are calibrated]

Hydrofacies

Horizontal

hydraulic 

conductivity, 

in meters per day

Vertical 

hydraulic 

conductivity, 

in meters per day

Sand 80 40

Silty sand 30 6

Silt 8 1

Clay 0.3 0.15

Ground-Water Flow Simulations  29
for simulated hydraulic heads at the locations of USGS wells 

or wells representing the upslope and downslope parts of the 

aquifer system. The model was numerically stable over a wide 

range of parameter values, but numerical stability decreased as 

values of Kcoarse and Kfine decreased.

The error surfaces constrain Kcoarse and Kfine to the lower 

central region of the plot and indicate that relatively high 

values of Kcoarse and low values of Kfine provide the best solution for the given conceptual model (fig. 21). Simulated values 

compare well to measurements in the USGS wells, and the 

error surface defines a zone of minimum error. However, 

the error surfaces for upslope and downslope areas indicate 

greater error, no minima near that of the USGS wells, and 

slope in opposite directions. This indicates there is some error 

in the conceptual model and (or) the water-level data for the 

upslope and (or) downslope areas. Subsequent manual calibration efforts focused on matching vertical gradients calculated 

from measurements in the USGS wells while minimizing error 

for the downslope wells and key upslope wells and staying 

within the zone of minimum error for the USGS wells. 

Results indicate that Kcoarse and Kfine values of about 80 and 

8 × 10–3 m/d, respectively, generate the best-fit parameter 

distribution. The associated value of Kcorc (1.3 × 10–3 m/d) 

was adjusted to reasonably match vertical hydraulic gradients 

calculated from water levels measured in wells screened above 

and below the Corcoran Clay.

A hydraulic conductivity of 80 m/d is within the typical range of that for clean sand and a hydraulic conductivity 

of 8 × 10–3 m/d is within the range of silty clay (Freeze and 

Cherry, 1979). Both lithologies are common in the study area 

and reasonably represent the lithologic end members. Permeameter tests of cores from the Corcoran Clay indicate vertical 

hydraulic conductivities ranging from 1 × 10–6 to 3 × 10–6 m/d 

(Page, 1977). Previous investigations, however, indicate wells 

screened across the Corcoran Clay have increased the effective vertical hydraulic conductivity by orders of magnitude 

by allowing the clay to be short circuited (Williamson and 

others, 1989; Belitz and Phillips, 1995). The calibrated value 

of Kcorc from this study (1.3 × 10–3 m/d) is consistent with these 

previous findings. The value estimated by Belitz and Phillips (1995) for an area southwest of the regional model is one 

order of magnitude lower than that estimated by this study. 

However, the greater depth of burial of the Corcoran Clay in 

that area (about 100–240 m) and widespread aquifer-system 

compaction may have caused a substantial decrease in its 

vertical hydraulic conductivity.

Regional Simulated Hydraulic Heads

The simulated water table (fig. 22) resembles the contours of measured water levels depicted in figure 8. A simple 

method of assessing overall model fit is to plot the simulated 

head values against the measured water levels. For a perfect 

fit, all points should fall on the 1:1 diagonal line. Figure 23 is 

a plot of the simulated heads versus measured water levels for 

the regional model area and indicates good overall model fit.

Simulated hydraulic heads closely matched measured 

water levels in USGS wells in the midslope areas, as indicated 

by an average residual of 0.3 m and a RMSE of 0.8 m. In the 

downslope area, simulated hydraulic heads in the area underlain by a shallow water table reasonably matched measured 

heads; the average error was 1.5 m and the RMSE was 3.4 m. 

Much of this error, and the primary source of the positive average error, was associated with two wells on the northeastern 

side of this area within Turlock Irrigation District, indicating 

that the simulated ground-water divide was slightly downslope 

of the actual divide. Water levels in the upslope area were also 

simulated well; the average error was 1.2 m and the RMSE

was 2.1 m.

The average error for all wells was 0.9 m; the errors 

ranged from –1.7 to 9.6 m (fig. 22) and the standard deviation 

was 2.1 m. The associated RMSE was 2.3 m, about 7 percent of the range of head observations in the aforementioned 

set of wells (32.9 m). The errors for the USGS wells were 

randomly distributed around zero, and those for the upslope 

and downslope areas were skewed positive by a few measurements in wells near the ground-water divide and within the 

cone of depression in the eastern part of the regional study 

area (fig. 22). Simulated values generally were lower than 

measured values in these areas, although the error for the only 

USGS well in Eastside Water District was very small (–0.4 m).

Local Model

The local model was calibrated using a combination of 

the Sensitivity and Parameter-Estimation Processes in MODFLOW-2000 (Hill and others, 2000) and manual adjustments. 

Hourly water-level measurements in 11 USGS wells along 

a transect north of the Merced River (fig. 11) were averaged 

on a water-year basis for model calibration. The adequacy of 

the head-based calibration was evaluated by using computed 

fluxes to compare simulated and measured concentrations of 

sulfur hexafluoride, an environmental tracer.

Wells used to calibrate the local model included all 4 at 

the upper end of the well transect, the 3 deepest wells at the 

middle site, and 4 wells at the lower end (lower_9, lower_15, 

lower_25, lower_29) (fig. 3). Hourly water-level measurements were recorded in these wells for 1 to 1.6 years, and 

annual averages of these measurements were used for model 

calibration. Data from the shallowest and deepest wells at 

these sites are shown in figure 11. These well clusters were 

used to evaluate simulated vertical gradients as well as simulated hydraulic heads.

A subset of the horizontal and vertical hydraulic conductivity values of the four textural categories defined earlier were 

adjusted during calibration of the local model. Because the 

model was insensitive to the riverbed conductance, it was not 

adjusted during calibration. Recharge estimates, the vertical 

hydraulic conductivity of the Corcoran Clay, and boundary 

fluxes also were not adjusted during calibration.

30 Simulation of Multiscale Ground-Water Flow in Part of the Northeastern San Joaquin Valley, California
The Sensitivity Process in MODFLOW-2000 (Hill and 

others, 2000) identifies the sensitivity of computed values at 

the locations of measurements to changes in model parameters. It was used to identify which hydraulic conductivity 

parameters to include in the Parameter Estimation Process 

(Hill and others, 2000) and to adjust during subsequent manual 

calibration. Results of the Sensitivity Process indicate that 

the local model was most sensitive to the horizontal hydraulic 

conductivities of the sand, silty sand, and silt hydrofacies, 

listed here in declining order of sensitivity (fig. 24). The local 

model was moderately sensitive to the vertical hydraulic conductivity of the clay facies, and essentially insensitive to the 

remaining hydraulic conductivities. Results also showed that 

sensitivity was greatest at the upper end of the well transect 

(fig. 25) because, as in the real system, water levels near the 

Merced River are controlled primarily by the river stage, not 

by irrigation.

The most sensitive hydraulic conductivity parameters 

were estimated initially using the Parameter Estimation 

Process (Hill and others, 2000), followed by manual adjustments. The Parameter Estimation Process minimizes a 

weighted least-squares objective function, thereby finding the 

optimal solution to the problem, assuming it converges numerically. The average water levels used as observations were not 

weighted, because identical equipment and methods were used 

to derive the measurements. The Parameter Estimation Process 

1.2

2.8

2.0

2.0

2.0

1.68

1.74

1.81

1.88

1.94

2.01

 2.08

1.48

1.54

1.61

-2.70 -2.59 -2.48 -2.37 -2.25 -2.14 -2.03 -1.92 -1.81 -1.70

2.0

8.0

6.0

4.0

4.0

1.68

1.74

1.81

1.88

1.94

2.01

 2.08

1.48

1.54

1.61

-2.70 -2.59 -2.48 -2.37 -2.25 -2.14 -2.03 -1.92 -1.81 -1.70

2.0

5.0

4.0

3.0

1.68

1.74

1.81

1.88

1.94

2.01

 2.08

1.48

1.54

1.61

-2.70 -2.59 -2.48 -2.37 -2.25 -2.14 -2.03 -1.92 -1.81 -1.70

5

EXPLANATION

Line of equal root mean square error between

simulated and measured hydraulic heads, in meters

Line of zero average error between simulated and

measured hydraulic heads

Parameter combinations simulated and for which

error was calculated

Parameter combinations for which model numerically

unstable

Calibrated end-member hydraulic conductivities

USGS wells only

LOG HYDRAULIC CONDUCTIVITY FINE-GRAINED END MEMBER, IN METERS PER DAY

LOG HYDRAULIC CONDUCTIVITY FINE-GRAINED END MEMBER, 

IN METERS PER DAY

LOG HYDRAULIC CONDUCTIVITY COARSE-GRAINED END MEMBER, IN METERS PER DAY

Upslope non-USGS wells

Downslope non-USGS wells

Figure 21. Error surfaces used to calibrate, and calibration results for, the regional model, San Joaquin regional study area, 

California. 

USGS, U.S. Geological survey.

Ground-Water Flow Simulations  31
Area not simulated

San Joaquin River

0

0

0

0

3

1

-1

0.4

-0.2

2.2

0.4

0.1

0.2

3.7

0.2

0.4

1.8

2.7

4.7

1.7

8.1

1.8

9.6

3.5

0.9

0.3

0.8

1.3

-0.1

-0.2

-0.4

-0.3

-0.9

-0.4 -0.7

-0.1

-1.1

-1.7

0.3

-0.6

0.6

0.8

5

40

25

25

15

30

40

20

10

15

10

35

35

25

15

15

121 15 121 120 45 120 30

37

45

37

30

EXPLANATION

Urban

Simulated water-table altitude, contour interval 

5 meters. Datum is North American Vertical Datum of 1988.

Simulated hydraulic head in model layer 9, contour 

interval 5 meters. Datum is North American Vertical Datum 

of 1988.

Active area of local model

Regional model extent

Shallowest well

Deepest well

Well at or near the water table

USGS well cluster and model error, in meters

Non-USGS well and model error, in meters

-0.2

-0.6

-0.2

10

15

16 MILES

0 10 20 KILOMETERS

0 8

Modesto

Turlock

Merced

Figure 22. Simulated hydraulic heads at the water table and in layer 9, and errors between measured water levels and simulated 

hydraulic heads at wells used to calibrate the regional model, San Joaquin regional study area, California.

USGS, U.S. Geological Survey. 

32  Simulation of Multiscale Ground-Water Flow in Part of the Northeastern San Joaquin Valley, California
did not converge for this model, but did approach the optimal 

solution prior to diverging. Parameter estimation fit the water 

levels well, but not the vertical gradients. Hydraulic properties were adjusted manually to better match vertical gradients, 

which were not explicitly included in the objective function.

The calibrated hydraulic conductivity values for the local 

model (table 3) can be compared to values for a wide range 

of sedimentary materials and to the results from slug tests of 

local materials. A hydraulic conductivity of 80 m/d is within 

the range typical for clean sand, and 30 m/d is within the range 

for silty sand (Freeze and Cherry, 1979). Slug tests were done 

in 18 wells in the bed and on the banks of the Merced River 

down-gradient of the well transect (Zamora, 2006). The sediments tested ranged from silty sand to well-sorted coarse sand, 

and computed hydraulic conductivity values ranged from 

15 to 250 m/d; the mean value was 85 m/d. These values are 

consistent with those derived by calibrating the local model.

Both hydraulic conductivity estimates for the coarsest 

fraction above the Corcoran Clay in the local and regional 

models were 80 m/d. The local calibrated value for the vertical hydraulic conductivity of clay (0.15 m/d), however, was 

about an order of magnitude greater than the vertical hydraulic 

conductivity above the Corcoran Clay in the regional model 

(median of 0.012 m/d). Simulated vertical hydraulic gradients 

in the regional model within the local study area (fig. 22) were 

greater than those measured, suggesting that spatial variability 

exists in the vertical hydraulic conductivity of fine-grained 

materials. Lower values for the vertical hydraulic conductivity 

of clay in the local model increased vertical gradients above 

those calculated from average measured water levels, which 

were very small (absolute value of about 0–0.02).

Local Simulated Hydraulic Heads

Figure 26 is a plot of the simulated hydraulic heads 

versus measured water levels for the local model and indicates 

excellent model fit. Average water-level measurements from 

11 USGS transect wells were very closely simulated; the average error was 0.0 m and the RMSE was 0.08 m. Errors ranged 

from –0.3 to 0.16 m; the standard deviation was 0.17 m. The 

RMSE was less than 2 percent of the range of head observations in the 11 wells (4.4 m). The largest errors were at the 

middle site of the transect, ranging from 0.3 m near the water 

table (well middle_13) to 0.23 m at the deepest well (middle_25). All simulated heads at the middle site were greater 

than measured water levels. Errors at all other transect wells 

were less than 0.16 m. The simulated water table is shown in 

figure 27.

Figure 23. Relation between simulated hydraulic head and measured water levels for regional 

model, San Joaquin regional study area, California. 

USGS, U.S. Geological Survey. 

10

0

5

15

20

25

30

35

40

45

0 5 10 15 20 25 30 35 40 45

SIMULATED HEAD, IN METERS

ALTITUDE OF MEASURED WATER-LEVEL, IN METERS ABOVE NAVD88

EXPLANATION

Downslope

Upslope

USGS only

Ground-Water Flow Simulations  33
Evaluation of Fluxes in Local Model

Calibration of a model to hydraulic heads alone generally 

results in a non-unique set of parameters. Other parameter sets 

may generate roughly the same head distribution, but simulated fluxes would vary; therefore, it is useful to evaluate headbased calibrations using some measure of system flux. An 

environmental tracer, sulfur hexafluoride, was used to evaluate 

the fluxes in the calibrated local model. Areal recharge and 

boundary fluxes were specified in the local model, and consequently the internal fluxes were highly constrained. Thus, 

the following analysis was more effective in this case as a 

check on the specified fluxes than as a means for evaluating 

hydraulic parameters.

Samples collected from most of the USGS wells along 

the transect in the local study area were analyzed for sulfur 

hexafluoride (SF6), generally a non-reactive, conservative 

environmental tracer in ground water (Busenberg and Plummer, 2000). Atmospheric concentrations of SF6

 were very 

low prior to 1965 and have increased since then, making it a 

good means of dating young ground water. Particle-tracking 

software, MODPATH (Pollock, 1994), was used in conjunction with flux output from the local flow model to calculate 

backward flow paths and associated travel times for water 

particles traveling back in time from the screened intervals of 

sampled wells to the water table. The travel time for each particle (64 per well screen, represented by one model cell) represented only the advective component of flow, but included 

the effects of macro-scale mechanical dispersion caused by the 

three-dimensional distribution of hydrofacies.

Effective porosity was the only hydraulic parameter 

specified in the MODPATH input files. Effective porosity 

values were assigned on the basis of the hydrofacies represented by each model cell. Sand, silty sand, silt, and clay 

were assigned effective porosities of 0.3, 0.35, 0.38, and 0.4, 

respectively. These porosity values were based on literature 

values for different geologic/textural materials (Domenico and 

Schwartz, 1990), previous studies of similar geologic formations in the eastern San Joaquin Valley (Burow and others, 

1999), and measurements made using sediment cores collected 

during the installation of the transect wells. Four cores that 

averaged 89 percent sand had moisture contents ranging from 

0.2

0

0.4

0.6

0.8

1

1.2

Kh-sand Kh-silty

sand

Kh-silt Kv-clay Kh-clay Kv-silty

sand

Kv-silt Kv-sand

COMPOSITE SCALED SENSITIVITY, DIMENSIONLESS

HYDRAULIC CONDUCTIVITY (K) OF HYDROFACIES; h IS HORIZONTAL, v IS VERTICAL

Figure 24. Relative composite sensitivity of computed hydraulic head at calibration points to 

changes in the horizontal and vertical hydraulic conductivities of the defined hydrofacies, local 

model, San Joaquin local study area, California. 

Composite scaled sensitivity values are used here to show relative sensitivity; the definition and 

derivation are described in Hill and others (2000). 

34  Simulation of Multiscale Ground-Water Flow in Part of the Northeastern San Joaquin Valley, California
32 to 37 percent, and a single core consisting of 83 percent silt 

had a moisture content of 48 percent. Effective porosity is a 

lower value than moisture content, and the difference between 

them increases with increasing content of fine-grained materials; thus, the estimated effective porosities are consistent with 

those measured in the local study area.

The travel time for each particle was used to determine 

the atmospheric concentration of SF6 when the particle was at 

the water table. Assuming conservative transport and steadystate conditions, the average atmospheric concentration of 

SF6 associated with all particles for a given well screen can 

be compared with the measured concentration in the well 

(table 4). Simulated concentrations at or near the water table 

are higher (younger age) than those measured at all sites, but 

concentrations at depth generally compare well. The cause 

of the disparity in shallow concentrations is unknown, but the 

good agreement between simulated and measured SF6 concentrations deeper in the system suggests that fluxes, which 

are largely controlled by specified recharge and boundary 

conditions, are reasonably simulated.

Sensitivity of Local Model Parameter Estimates to 

Hydrofacies Distribution and Recharge

The calibrated hydraulic conductivities for the local 

model (table 3) were based on one of 200 realizations of the 

three-dimensional distribution of hydrofacies. The sensitivity 

of parameters to their distribution was determined using four 

end-member realizations. These end members represented the 

minimum and maximum effective three-dimensional hydraulic conductivity and domain-scale vertical anisotropy. Each 

realization was upscaled into the regional model, which was 

then used to generate a new set of specified fluxes for the 

lateral boundaries of the local model. The local model, with 

each realization incorporated, was then re-calibrated until the 

total error approached that of the calibrated model, if feasible. 

Generally, this was accomplished through changes in only the 

most sensitive horizontal (sand) and vertical (clay) hydraulic 

conductivities.

Kh-clay

Kh-silt

Kh-silty sand

Kh-sand

Kv-clay

Kv-silt

Kv-silty sand

-1.6

-1.4

-1.2

-1.0

-0.8

-0.6

-0.4

-0.2

0.0

6.9 14.0 20.1 26.8 13.1 18.9 25.0 8.8 15.2 25.0 29.0

WELL LOCATION AND DEPTH TO MIDPOINT OF SCREEN, IN METERS

DIMENSIONLESS SCALED SENSITIVITY

Upper end of transect Middle of transect Lower end of transect

Figure 25. Relative sensitivity of computed hydraulic head at calibration points to changes in hydraulic parameters, 

local model, San Joaquin local study area, California. 

Dimensionless scaled sensitivity values are used here to show relative sensitivity; the definition and derivation are 

described in Hill and others (2000). 

Ground-Water Flow Simulations  35
The sensitivity of key hydraulic conductivity parameter 

estimates to the three-dimensional distribution of hydraulic conductivity is shown in table 5. All but one realization 

required adjustment of only the horizontal hydraulic conductivity of sand to achieve nearly the same error as the calibrated 

model. These adjustments ranged from a reduction of 25 

percent to an increase of 12.5 percent. The realization representing minimum domain-scale vertical anisotropy required 

a threefold decrease in the vertical hydraulic conductivity of 

clay and was associated with relatively high error. Adjustments of other hydraulic conductivity values failed to reduce 

the error for this realization, suggesting that model performance decreases below a minimum threshold for vertical 

anisotropy. This analysis indicates that if this threshold is met, 

the overall sensitivity of hydraulic conductivity parameter 

estimates to the distribution of hydrofacies is fairly low.

The sensitivity of parameter estimates for the local model 

to areal recharge was determined by increasing and reducing recharge by 20 percent, a quantity that would represent 

substantial error in the water budget. The local model was 

re-calibrated by adjusting the horizontal hydraulic conductivity of sand and vertical hydraulic conductivity of clay, achieving a total error within 13 percent of that of the calibrated 

model. Reducing recharge by 20 percent required a 50-percent 

reduction in the conductivity of sand. A 20-percent increase 

in recharge required increasing the hydraulic conductivity of 

sand by 38 percent and doubling the hydraulic conductivity 

of clay. This analysis shows that the sensitivity of hydraulic 

parameter estimates to large changes in areal recharge, which 

represents 76 percent of the total recharge, is moderate.

The effects of changes in the hydrofacies distribution 

and areal recharge rates on the simulated water budget were 

straightforward. Small changes in net boundary fluxes related 

to hydrofacies distribution, and large changes in areal recharge 

rates, were balanced by like changes in discharge to the 

Merced River.

two data points

22

23

24

25

26

27

22 23 24 25 26 27

SIMULATED HEAD, IN METERS

two data points

two data points

ALTITUDE OF MEASURED WATER LEVEL, IN METERS ABOVE NAVD 88

Figure 26. Relation between simulated hydraulic head and measured water levels for the local 

model, San Joaquin local study area, California. 

36  Simulation of Multiscale Ground-Water Flow in Part of the Northeastern San Joaquin Valley, California
26.9 28.4 30.4

27.1

0 3,600 7,200 FEET

0 1,000 2,000 METERS

22.5

22.5

24.4

26.8

25.7

25.7

120 4930 120 48 120 4630

37

24

37

22

30

21 to 22

22 to 23

23 to 24

24 to 25

25 to 26

26 to 27

27 to 28

28 to 29

29 to 30

30 to 31

31 to 32

EXPLANATION

Simulated water-table altitude, in meters

USGS well cluster along transect and average measured 

water table altitude, 2004-2005, in meters. Datum is North

American Vertical Datum of 1988.

Active area of local model

Water-table well measured monthly by the Turlock 

Irrigation District, and average monthly water-table 

altitude for water year 2000, in meters. Datum is North

American Vertical Datum of 1988.

Merced River

Figure 27. Simulated water-table altitudes for the local model, San Joaquin local study area, California. 

Ground-Water Flow Simulations  37
Table 4. Measured concentrations of sulfur hexafluoride (SF6

) along the U.S. Geological Survey well transect and concentrations 

estimated using simulated travel time and historical atmospheric concentrations of SF6, San Joaquin local study area, California. 

[m, meter; yr, year; pptv, parts per trillion by volume]

Location of well on 

transect

Midpoint of 

screen below 

land surface (m)

Simulated travel time (yr) Concentrations of SF6 (pptv)

Median Maximum Minimum Estimated Measured

Average Maximum Minimum

Upper end 7 0.4 0.5 0.2 5.7 4.2 4.6 3.7

Upper end 20 12.7 16.4 10.0 2.6 2.6 3.4 1.7

Upper end 27 12.9 18.5 11.6 2.6 2.1 2.5 1.7

Middle 13 4.3 6.5 3.6 4.7 3.5 3.5 3.5

Middle 19 8.9 12.3 5.8 3.7 2.5 2.6 2.3

Middle 25 24.1 76.3 14.6 0.9 1.4 1.4 1.3

Lower end 9 9.1 19.2 6.2 3.4 1.1 1.2 1.0

Lower end 15 20.5 49.3 11.4 1.5 1.4 1.7 1.0

Lower end 25 23.6 104.0 17.6 0.9 0.4 0.4 0.3

Lower end 29 39.9 135.5 1.0 1.1 0.6 0.7 0.4

Table 5. Changes in key hydraulic conductivity parameters with alternate three-dimensional distributions of 

hydrofacies in the local model, San Joaquin local study area, California. 

[m/d, meter per day; m, meter] 

Hydrofacies and direction of 

hydraulic conductivity

Hydraulic conductivity for realizations of hydrofacies distribution

Calibrated

model

Effective hydraulic 

conductivity

 Domain-scale vertical 

anisotropy

Maximum Minimum Maximum Minimum

Sand, horizontal (m/d) 80 60 90 70 80

Clay, vertical (m/d) 0.15 0.15 0.15 0.15 0.05

Sum of squared residuals (m) 0.27 0.37 0.1 0.31 1.1

Model Results

The simulated water budget for the regional-scale model 

is presented in table 6. Note that many of the water-budget 

components of the regional model were specified values. Areal 

recharge was mostly agricultural irrigation and precipitation, 

accounting for 80 percent of the total recharge; urban recharge 

added another 1 percent to the total. Areal recharge estimates 

were reduced from those of Burow and others (2004) by 

10 percent during calibration, but remain the dominant component of recharge. Leakage from reservoirs contributed about 

4 percent of the recharge, and the rivers less than 1 percent 

(net). Pumpage from wells, primarily for agriculture, was 

about 70 percent of the total discharge. About 6 percent of the 

discharge was bare-soil evaporation from the shallow water 

table. The remainder of the simulated water budget was flow 

through the lateral head-dependent boundaries, which was 

about a net 8-percent export.

Flow through the lateral boundaries is different at 

each boundary. The northern boundary is dominated by northward flow above and below the Corcoran Clay, exiting the 

regional study area. This is consistent with the limited available water-level data for the area north of the Stanislaus 

River (fig. 8). This northward flow is 13 percent of the simulated budget, more than twice the flow at any other lateral 

boundary. The southern boundary is characterized by flow 

entering the regional model and moving toward the Merced 

River above the Corcoran Clay, and exiting below the clay and 

at depth east of the clay. Flow is in the opposite sense along 

the western boundary, exiting the model area above the Corcoran Clay, and entering from below. The southern boundary and 

the western boundary each have a simulated net flux into the 

regional model domain that comprises only 1–2 percent of the 

total water budget.

The simulated water budget for the local-scale model is 

given in table 7. Note that most of the water-budget components of the local model were specified values. Areal recharge, 

which was dominated by agricultural irrigation and precipitation, accounted for 76 percent of the total recharge. Discharge 

was dominated by flow to the Merced River (65 percent), and 

included downward flow through the Corcoran Clay (16 percent). The remainder of the simulated water budget was flow 

through the lateral specified-flux boundaries, which was a net 

5-percentage gain.

38  Simulation of Multiscale Ground-Water Flow in Part of the Northeastern San Joaquin Valley, California
Recharge from Specified Computed Percent1

Irrigation return 1,997,000 46.9

Precipitation 1,409,000 33.1

Urban, all sources 41,000 1.0

Reservoir leakage 155,000 3.7

Rivers 105,000 10,000 2.7

Flow through lateral boundaries

 Northern 44,000 1.0

 Southern 243,000 5.7

 Western 253,000 6.0

Discharge to

Wells

 Agricultural 2,655,000 63.3

 Urban 294,000 7.0

Evaporation from shallow water table 267,000 6.4

Rivers 88,000 2.1

Flow through lateral boundaries

 Northern 547,000 13.0

 Southern 162,000 3.9

 Western 182,000 4.3

Table 6. Simulated water budget for the regional model, San Joaquin 

regional study area, California. 

[Values are cubic meters per day]

1

Totals do not add to 100 because of rounding.

Table 7. Simulated water budget for the local model, San Joaquin 

local study area, California. 

[Values are cubic meters per day] 

Recharge from Specified Computed Percent1

Irrigation return 14,300 51.3

Precipitation 7,000 25.0

Rivers 0 0.0

Flow through lateral boundaries

 Northwest 700 2.5

 Southeast 3,500 12.7

 Southwest 2,400 8.5

Flow through Corcoran Clay 0 0.0

Discharge to

Rivers 17,700 64.6

Flow through lateral boundaries

 Northwest 3,000 11.1

 Southeast 40 0.2

 Southwest 2,100 7.7

Flow through Corcoran Clay 4,500 16.5 1

Totals do not add to 100 because of rounding.

Ground-Water Flow Simulations  39
The dominance of areal recharge and discharge to the 

Merced River results in downward flow in most of the local 

study area and upward flow along the Merced River, which 

is consistent with measured water levels along the well 

transect. This flow configuration, coupled with downward 

flow through the Corcoran Clay, results in primarily locallyrecharged ground water discharging to the Merced River. The 

combination of measured sulfur hexafluoride concentrations 

and travel times of simulated particles (table 4) suggests that 

most of the ground water discharging to the Merced River was 

recharged less than 25 years ago.

Limitations and Appropriate Use of the Models

The regional and local ground-water flow models were 

developed to generate a better understanding of the flow 

system at both scales. The local model will be used to help 

understand the transport and fate of agricultural chemicals in 

the local study area. Limitations of the modeling software, 

assumptions made during model development, and results of 

model calibration and sensitivity analysis all are factors that 

constrain the appropriate use of these models and highlight 

potential future improvements.

A ground-water flow model is a means for testing a conceptual understanding of a system. Because ground-water flow 

systems are inherently complex, simplifying assumptions were 

made in developing and applying model codes (Anderson and 

Woessner, 1992). Models solve for average conditions within 

each cell, the parameters for which are interpolated or extrapolated from measurements, and (or) estimated during calibration. In light of this, the intent in developing the regional and 

local ground-water flow models was not to reproduce every 

detail of the natural system, but to portray its general 

characteristics. Results from these models should be interpreted generally and are best suited for comparative analysis 

rather than for prediction.

A steady-state model portrays a system that is in equilibrium. Although water-level hydrographs suggest this generally was the case in the regional study area for the year 2000 

(fig. 9), the data were not conclusive. Long-term hydrographs 

are not available for some areas, including the southeastern 

part of the model area, where hydraulic heads may have 

been changing with time. There are no long-term water-level 

records available in the local model area, but the closest wells 

show little change in about 40 years of record. Errors related 

to the assumption of a steady-state condition may be significant in places, and care must be taken in interpreting model 

results and analyses that depend on model output, including 

particle tracking.

A problem related to the steady-state assumption for both 

models was that stresses were based on data from water year 

2000, but the water levels for USGS wells were measured 

during 2003–2005. Although this may be a source of model 

error, none of these years represented climatic aberrations. It 

is likely that deliveries of surface water for agricultural and 

urban use, and associated ground-water pumpage, varied little 

during these years.

Regional Model

Some of the boundary conditions of the regional model 

were poorly constrained, which may be a source of model 

error. The western and northern lateral boundaries were based 

on sparse data; the spatial distribution of hydraulic head below 

the river was poorly understood, and there were no available 

data in the western part of the northern area. Similarly, there 

was little regional information on river-aquifer interaction and 

the hydraulic conductivity of riverbed sediments. Simulation 

results indicated that flows across these poorly constrained 

boundaries (table 6) generally made up a small part of the 

water budget; however, this may not be true in the real system.

The accuracy of model results is related strongly to the 

quality and spatial distribution of input data and of measurements of system state (for example, measured water levels) 

used to constrain the calibration. The local study area and the 

Modesto area were the only locations in the regional model 

that had high-quality input data, including pumpage by well 

and sediment texture, coupled with a good distribution of 

high-quality water-level measurements. The stresses in other 

areas of the model were a combination of measured values and 

values estimated from the water-budget analysis. Accordingly, 

the user should have more confidence in simulation results in 

the local study area and the Modesto area than in other parts of 

the model.

The regional estimate of the vertical hydraulic conductivity of fine-grained materials was about one order of magnitude 

lower than that estimated at the local scale. Simulated vertical 

hydraulic gradients are more accurate (smaller) in the local 

model than in the regional model within the local study area 

(figs. 27, 22). This suggests that there may be substantial 

spatial variability in the vertical hydraulic conductivity of 

fine-grained materials that is not accounted for in the regional 

model.

Local Model

The specified areal recharge and lateral boundary conditions in the local model, which account for all of the simulated 

recharge, highly constrain the internal fluxes. This, in turn, 

constrains the range of estimated hydraulic conductivities. 

Key hydraulic conductivity values are sensitive to substantial changes in areal recharge; rates of chemical transport are 

expected to be equally sensitive. In contrast, these key hydraulic conductivity values, and associated fluxes, are less sensitive to the three-dimensional distribution of the four defined 

hydrofacies.

All of the water-level data used to calibrate the local 

model were collected from USGS transect wells, which are 

concentrated in the central part of the model domain. Accordingly, the user should have higher confidence in simulation 

results for the area near the well transect than for other areas 

represented in the model.

40 Simulation of Multiscale Ground-Water Flow in Part of the Northeastern San Joaquin Valley, California
Summary

 Regional and local models of ground-water flow in the 

northeastern San Joaquin Valley were developed as part of a 

study of the transport and fate of agricultural chemicals by 

the U.S. Geological Survey’s (USGS) National Water-Quality 

Assessment Program. The northeastern San Joaquin Valley, 

near the city of Modesto, is a semi-arid region dominated by 

irrigated agriculture. The aquifer system is predominantly 

alluvial. An unconfined to semiconfined aquifer overlies a 

confined aquifer in the southwestern part of the study area; 

these aquifers are separated by the lacustrine Corcoran Clay. 

Ground water is a key source of water for irrigation and public 

supply, and exploitation of this resource has altered the natural 

flow system. Primarily lateral flow from the mountain front to 

the San Joaquin River has been overprinted with downward flow driven by enhanced recharge from irrigation and 

discharge from irrigation pumpage.

 A regional-scale, 16-layer steady-state model of groundwater flow in the unconfined to confined aquifer system underlying the Modesto area was developed to provide boundary 

conditions for an embedded 110-layer steady-state local-scale 

model of part of the aquifer system overlying the Corcoran 

Clay along the Merced River. The purpose of the local-scale 

model was to develop a better understanding of the aquifer 

system and to provide a basis for simulating reactive transport 

of agricultural chemicals.

Lateral boundary conditions for the regional model were 

no-flow along the Sierra Nevada foothills and general-head 

elsewhere. The water table was a free surface, and the lower 

boundary, far below the depth of wells, was no-flow. Recharge 

and agricultural pumpage were estimated using a water-budget 

approach, and bare-soil evaporation was simulated where the 

water table was shallow. Agricultural pumpage and recharge 

from irrigation return flow were the dominant components of 

the simulated water budget for the regional model.

Lateral boundary conditions for the local model, embedded within the regional, were specified fluxes from the 

regional model. The upper boundary was a free surface, and 

the lower boundary was general-head, allowing flow through 

the Corcoran Clay. Recharge from irrigation return flow was 

estimated on the basis of crop type and irrigation method for 

each field. Ground water generally was not used in the local 

model area. The dominant components of the simulated local 

budget were recharge from irrigation return flow and discharge 

to the Merced River.

The heterogeneity of aquifer materials was explicitly 

incorporated into the regional and local models using information from geologic and drillers’ logs of boreholes. Aquifer 

materials were differentiated in the regional model by the 

percentage of coarse-grained sediments in a cell. This percentage was estimated for most cells in the model by three-dimensional kriging and by downward extrapolation where kriging 

did not generate a value owing to data scarcity. Aquifer materials were differentiated in the local model by four hydrofacies 

(sand, silty sand, silt, and clay). Multiple realizations of the 

distribution of these hydrofacies were estimated using a transition-probability geostatistical technique that honored highquality geologic logs and was conditionally influenced by data 

from drillers’ logs.

Different calibration methods were used for the regional 

and the local models. The regional model was calibrated by 

exploring a range of end-member coarse- and fine-grained 

hydraulic conductivities used to generate horizontal and vertical conductivities for each cell using texture-weighted arithmetic and harmonic means, respectively. The local model 

was calibrated primarily using the parameter estimation 

capabilities within MODFLOW-2000.

The calibrated horizontal hydraulic conductivities of 

the coarse-grained materials in the zone above the Corcoran 

Clay in the regional model and of the sand hydrofacies of the 

local model were about equal (30–80 m/d [meter per day]). 

The vertical hydraulic conductivity of the same zone in the 

regional model (median of 0.012 m/d), which is dominated by 

the finer-grained materials, was about an order of magnitude 

less than that for the clay hydrofacies in the local model.

Data used for calibration of both models included longterm hourly water-level measurements in 20 short-screened 

wells installed by the USGS in the Modesto and the Merced 

River areas. Additional data used for calibrating the regional 

model included water-level measurements in 11 wells upslope 

and 17 wells downslope from these areas. The root mean 

square error was 2.3 m (meter) for all wells in the regional 

model and 0.8 m for the USGS wells; the associated average errors were 0.9 m and 0.3 m, respectively. The root mean 

square error for the 12 USGS wells in the local model area 

was 0.08 m; the average error was 0 m. Particle tracking was 

used for the local model to estimate the concentration of an 

environmental tracer, sulfur hexafluoride, in 10 USGS wells 

near the Merced River that were sampled for this constituent. Measured and estimated concentrations in the mid-depth 

and deepest wells, those most sensitive to errors in hydraulic 

conductivity estimates, were consistent. The combined results 

of particle tracking and sulfur hexafluoride analysis suggest 

that most water sampled from the transect wells was recharged 

less that 25 years ago.

Acknowledgments

Many individuals and organizations aided this study 

through contributions of data and technical expertise. The 

authors gratefully acknowledge the helpful contributions from 

Walter Ward, Joseph Lima, and others from the Modesto Irrigation District; Debbie Liebersbach from the Turlock Irrigation District; and many others from various water purveyors 

in the study area. Special thanks go to the landowners who 

allowed us to drill wells and install other monitoring equipment on their land. Leon Kauffman, USGS, generously offered 

his technical expertise, and for that we are very grateful.

Acknowledgments  41
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Phillips and others—Simulation of Multiscale Ground-Water Flow in Part of the Northeastern San Joaquin Valley, California—SIR 2007–5009

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