Cover. Location and design of model grid and water budget zones at Naval Air Station Patuxent River, Maryland.
Simulation of Ground-Water Flow and 

Optimization of Withdrawals from Aquifers 

at the Naval Air Station Patuxent River, 

St. Mary’s County, Maryland

By Cheryl A. Dieter and William B. Fleck

Prepared in cooperation with Naval Air Station Patuxent River

Scientific Investigations Report 2008–5144

U.S. Department of the Interior

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

DIRK KEMPTHORNE, Secretary

U.S. Geological Survey

Mark D. Myers, Director

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

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reproduce any copyrighted materials contained within this report.

Suggested citation:

Dieter, C.A., and Fleck, W.B., 2008, Simulation of ground-water flow and optimization of withdrawals from aquifers 

at the Naval Air Station Patuxent River, St. Mary’s County, Maryland: U.S. Geological Survey Scientific Investigations 

Report 2008–5144, 36 p.
iii

Contents

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

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

Background............................................................................................................................................1

Purpose and Scope ..............................................................................................................................5

Description of Study Area ...................................................................................................................5

Previous Investigations........................................................................................................................5

Hydrogeologic Framework and Hydraulic Properties of Units ..............................................................6

Surficial Aquifer....................................................................................................................................6

Upper Confining Unit ............................................................................................................................6

Piney Point-Nanjemoy Aquifer...........................................................................................................6

Middle Confining Unit...........................................................................................................................8

Aquia Aquifer.........................................................................................................................................8

Lower Confining Unit............................................................................................................................8

Upper Patapsco Aquifer......................................................................................................................9

Ground-Water-Flow Model ..........................................................................................................................9

Conceptual Model.................................................................................................................................9

Design ..................................................................................................................................................10

Model Grid...................................................................................................................................10

Boundary Conditions.................................................................................................................12

Model Hydraulic Properties.....................................................................................................13

Model Calibration................................................................................................................................17

Model Sensitivity.................................................................................................................................17

Model Limitations................................................................................................................................19

Water Budget ......................................................................................................................................21

Optimization Model......................................................................................................................................23

Response Function .............................................................................................................................23

Application...........................................................................................................................................23

Scenario 1: Minimize Drawdown of Local Heads ...............................................................23

Scenario 2: Locate a Second Well for the Northeast Area in the Aquia Aquifer...........24

Suggestions for Future Water-Supply Assessment...............................................................................29

Summary and Conclusions.........................................................................................................................29

Acknowledgments.......................................................................................................................................29

Selected References...................................................................................................................................30

Glossary.........................................................................................................................................................35

Appendix 1. Specific Capacity Analysis...................................................................................................36
iv

Figures

1. Map showing location of Naval Air Station Patuxent River, Maryland...............................2

2. Hydrographs for wells screened in the Piney Point-Nanjemoy, Aquia, and Upper 

Patapsco aquifers.........................................................................................................................3

3. Maps showing potentiometric surfaces of the (A) Aquia and (B) Upper Patapsco 

aquifers in part of southern Maryland, September 2002........................................................4

4. Diagram of the model layering scheme and boundary conditions for the Naval Air 

Station Patuxent River ground-water-flow model.................................................................10

5. Map showing location and design of model grid and water budget zones......................11

6. Diagram of model layering, vertical discretization, and boundary conditions along 

row 60 ...........................................................................................................................................12

7. Map showing location of observation wells and withdrawal wells simulated in the 

transient ground-water-flow model at Naval Air Station Patuxent River, Maryland ......14

8. Observed and model-simulated hydrographs for well SM Dg 21 screened in the 

Piney Point-Nanjemoy aquifer from the transient simulation.............................................17

9. Observed and model-simulated hydrographs for six wells screened in the Aquia 

aquifer from the transient simulation ......................................................................................18

10. Observed and model-simulated hydrographs for two wells screened in the Upper 

Patapsco aquifer from the transient simulation....................................................................19

11. Graph showing results of the steady-state ground-water-flow model sensitivity 

analysis showing root-mean-squared-error (RMSE) values for the sensitivityanalysis simulations ...................................................................................................................20

12. Diagram showing simulated net inflows and outflows, in cubic feet per day, for the 

parts of the Piney Point-Nanjemoy, Aquia, and Upper Patapsco aquifers that 

underlie the Naval Air Station Patuxent River.......................................................................22

13–15. Maps showing—

13. Groupings of wells (A, B, and C) screened in the Aquia aquifer and control 

node for hypothetical optimization scenario 1 at the Naval Air Station 

Patuxent River, Maryland .................................................................................................25

14. Optimal solution for hypothetical optimization scenario 1 at Naval Air Station 

Patuxent River, Maryland .................................................................................................27

15. Location of ten potential well sites, including the optimal well site, for 

hypothetical optimization scenario 2 at Naval Air Station Patuxent River, 

Maryland .............................................................................................................................28
v

Tables

1. Geologic units, corresponding hydrogeologic units, and model layers at Naval Air 

Station Patuxent River, Maryland ..............................................................................................7

2. Ground-water-flow model input values ..................................................................................13

3. Values used to calculate general-head boundary conductance values, and 

resulting general-head boundary conductance values.......................................................13

4. Transient model stress periods with respective time periods and simulated 

withdrawal rates for the Piney Point-Nanjemoy aquifer, Aquia aquifer, and 

the stress period total, 1900–2002............................................................................................15

5. Root-mean-squared-error (RMSE) values for the transient ground-water-flow 

model simulation.........................................................................................................................17

6. Water budget for the entire model domain from stress period 106 (December 2002) 

of the transient model ................................................................................................................21

7. Hypothetical scenario 1: optimization model managed wells, steady-state groundwater-flow model withdrawal rates, and optimal withdrawal rates from the 

optimization model......................................................................................................................26

8. Hypothetical scenario 1: optimization model unmanaged wells, steady-state 

ground-water-flow model withdrawal rates, and withdrawal rates for the 

optimization model......................................................................................................................26
vi

Conversion Factors and Datums

Multiply By To obtain

Length

inch (in.) 2.54 centimeter (cm)

inch (in.) 25.4 millimeter (mm)

foot (ft) 0.3048 meter (m)

mile (mi) 1.609 kilometer (km)

Area

acre 4,047 square meter (m2)

acre 0.4047 hectare (ha)

acre 0.4047 square hectometer (hm2) 

acre 0.004047 square kilometer (km2)

square mile (mi2) 259.0 hectare (ha)

square mile (mi2) 2.590 square kilometer (km2) 

Flow rate

cubic foot per day (ft3/d) 0.02832 cubic meter per day (m3/d)

gallon per day (gal/d) 0.003785 cubic meter per day (m3/d)

Radioactivity

picocurie per liter (pCi/L) 0.037 becquerel per liter (Bq/L) 

Specific capacity

gallon per minute per foot 

[(gal/min)/ft)]

 0.2070 liter per second per meter [(L/s)/m]

Hydraulic conductivity

foot per day (ft/d) 0.3048 meter per day (m/d)

Hydraulic gradient

foot per mile (ft/mi) 0.1894 meter per kilometer (m/km)

Transmissivity*

foot squared per day (ft2/d) 0.09290 meter squared per day (m2/d) 

Leakance

foot per day per foot [(ft/d)/ft] 1 meter per day per meter [(m/d)/m]

inch per year per foot [(in/yr)/ft] 83.33 millimeter per year per meter

[(mm/yr)/m]

Temperature in degrees Celsius (°C) may be converted to degrees Fahrenheit (°F) as follows:

°F=(1.8×°C)+32

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).

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

*Transmissivity: The standard unit for transmissivity is cubic foot per day per square foot times 

foot of aquifer thickness [(ft3/d)/ft2]ft. In this report, the mathematically reduced form, foot 

squared per day (ft2/d), is used for convenience.

Specific conductance is given in microsiemens per centimeter at 25 degrees Celsius (μS/cm at 

25 °C).

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

or micrograms per liter (μg/L).
Simulation of Ground-Water Flow and Optimization of 

Withdrawals from Aquifers at the Naval Air Station 

Patuxent River, St. Mary’s County, Maryland

By Cheryl A. Dieter and William B. Fleck

Abstract 

Potentiometric surfaces in the Piney Point-Nanjemoy, 

Aquia, and Upper Patapsco aquifers have declined from 1950 

through 2000 throughout southern Maryland. In the vicinity 

of Lexington Park, Maryland, the potentiometric surface in 

the Aquia aquifer in 2000 was as much as 170 feet below sea 

level, approximately 150 feet lower than estimated pre-pumping levels before 1940. At the present rate, the water levels 

will have declined to the regulatory allowable maximum of 80 

percent of available drawdown in the Aquia aquifer by about 

2050. The effect of the withdrawals from these aquifers by the 

Naval Air Station Patuxent River and surrounding users on the 

declining potentiometric surface has raised concern for future 

availability of ground water. Growth at Naval Air Station 

Patuxent River may increase withdrawals, resulting in further 

drawdown. A ground-water-flow model, combined with optimization modeling, was used to develop withdrawal scenarios 

that minimize the effects (drawdown) of hypothetical future 

withdrawals. 

A three-dimensional finite-difference ground-waterflow model was developed to simulate the ground-waterflow system in the Piney Point-Nanjemoy, Aquia, and Upper 

Patapsco aquifers beneath the Naval Air Station Patuxent 

River. Transient and steady-state conditions were simulated to 

give water-resource managers additional tools to manage the 

ground-water resources. The transient simulation, representing 

1900 through 2002, showed that the magnitude of withdrawal 

has increased over that time, causing ground-water flow to 

change direction in some areas.

The steady-state simulation was linked to an optimization 

model to determine optimal solutions to hypothetical watermanagement scenarios. Two optimization scenarios were 

evaluated. The first scenario was designed to determine the 

optimal pumping rates for wells screened in the Aquia aquifer 

within three supply groups to meet a 25-percent increase in 

withdrawal demands, while minimizing the drawdown at a 

control location. The resulting optimal solution showed that 

pumping six wells above the rate required for maintenance 

produced the least amount of drawdown in the local potentiometric surface.

The second hypothetical scenario was designed to determine the optimal location for an additional well in the Aquia 

aquifer in the northeastern part of the main air station. The 

additional well was needed to meet an increase in withdrawal 

of 43,000 cubic feet per day. The optimization model determined the optimal location for the new well, out of a possible 

10 locations, while minimizing drawdown at control nodes 

located outside the western boundary of the main air station. 

The optimal location is about 1,500 feet to the east-northeast 

of the existing well.

Introduction

Beginning in 1998, the U.S. Geological Survey (USGS), 

in cooperation with Naval Air Station (NAS) Patuxent River, 

has been investigating the water resources of the Piney 

Point-Nanjemoy, Aquia, and Upper Patapsco aquifers, which 

are three principal aquifers extensively used in southern 

Maryland. The rapid expansion of the NAS Patuxent River in 

combination with development of the expanding Washington, 

D.C. suburbs (fig. 1) into Calvert and St. Mary’s Counties, 

has resulted in a population increase in the two counties from 

24,000 in 1940 (Forstall, 1995) to 161,000 in 2000 (U.S. 

Census Bureau, 2003). Water-resource managers, including 

State, County, and NAS Patuxent River personnel, as well as 

private citizens, have become deeply concerned with watersupply issues because ground water is the primary source of 

potable water for most of the two-county region. 

Background

NAS Patuxent River started operations in 1942 during 

World War II as an effort to geographically consolidate Navy 

and Marine Corps aircraft testing facilities (United States 

Navy, 2003). NAS Patuxent River has continued to expand 

since World War II, especially during the early 1950s and the 
2 Simulation of Ground-Water Flow at the Naval Air Station Patuxent River, St. Mary’s County, Maryland

Figure 1. Location of Naval Air Station Patuxent River, Maryland. (From Klohe and Kay, 2007)
Introduction 3

1960s. Major reorganizational changes in 1975 resulted in substantial growth both in terms of personnel and in new building construction. On January 1, 1992, the Naval Air Warfare 

Center Aircraft Division was established and located at NAS 

Patuxent River. Since the late 1980s, NAS Patuxent River was 

a receiver base according to the U.S. Department of Defense 

Base Realignment and Closure (BRAC) Commission, which 

resulted in a 3.5-percent-per-year increase in the number of 

employees from 1981 to 1998 (Klohe and Feehley, 2001, p. 2) 

and a 2.7-percent-per-year increase in the number of employees from 1998 to 2006 (Klohe and Kay, 2007, p. 3).

For the lower part of the southern Maryland region, comprised of Calvert and St. Mary’s Counties, a similar population 

increase of 2.7 percent per year occurred during the 1980s and 

1990s. This increase was largely due to the burgeoning of new 

suburbs outward from the established suburbs of the Annapolis, Maryland, and Washington, D.C. metropolitan centers into 

the more available and less expensive urban areas of Calvert 

and St. Mary’s Counties. This was also partly a function of 

the NAS Patuxent River receiver activities, however. The 

Maryland Department of Planning (2007) projects an increase 

in population for Calvert and St. Mary’s Counties from about 

161,000 to 258,000 from 2000 to 2030. With these population 

projections, there will continue to be ever-increasing pressure 

on environmental resources, including the ground-water 

resource. The historical population change and the resulting 

increase in water use have resulted in well-defined cones of 

depression in the Aquia and Upper Patapsco aquifers. Water 

levels in well SM Df 1, which is screened in the Aquia aquifer, 

were more than 70 ft (feet) below sea level (NAVD 88) by 

1984, and continued to drop at about 5 ft/yr (feet per year) 

through 2002 (fig. 2). The water level in well SM Df 84, 

which is screened in the Upper Patapsco aquifer, declined 

from 8 ft below sea level in 1983 to about 48 ft below sea 

level in 2006, a rate of 1.7 ft/yr (fig. 2). From 1998 through 

2006, the water levels in well SM Dg 20, which is screened 

in the Piney Point-Nanjemoy aquifer, were level at approximately 21 to 25 ft below sea level. The cones of depression in 

the potentiometric surfaces in the Aquia and Upper Patapsco 

aquifers as of September 2002 are shown in figure 3.

Ground-water allocations in Maryland are limited by 

permit to the lowering of potentiometric levels to a maximum 

of 80 percent of available drawdown. Available drawdown 

is defined as the total depth from pre-stressed potentiometric 

levels to the top of the aquifer. The top of the Piney PointNanjemoy aquifer is about 200 to 260 ft below sea level, and 

the top of the Aquia aquifer is about 400 to 500 ft below sea 

level. Water levels in the Piney Point-Nanjemoy aquifer have 

recently begun to stabilize in the vicinity of NAS Patuxent 

River at about 20 to 40 ft below sea level. It is likely that if 

present (2007) conditions persist, the 80-percent limit is not 

a concern for the Piney Point-Nanjemoy aquifer. Water levels 

in the Aquia are much deeper, however, and are presently as 

much as 170 ft below sea level and falling at rates of about 

4 to 5 ft/yr. If the rate of decline of 4 to 5 ft/yr continues, the 

80-percent limit would be reached in about 40 to 50 years. 

Due to the declines in water levels of the Aquia aquifer, there 

has been an increase in usage of the Upper Patapsco aquifer, 

Figure 2. Hydrographs for wells screened in the Piney Point-Nanjemoy, Aquia, and 

Upper Patapsco aquifers. (Well locations shown in figure 7.)
4 Simulation of Ground-Water Flow at the Naval Air Station Patuxent River, St. Mary’s County, Maryland

Figure 3. Potentiometric surfaces of the (A) Aquia and (B) Upper Patapsco aquifers in part of southern Maryland, 

September 2002. [Modified from Curtin and others (2003a,b)]
Introduction 5

where water levels are about 40 to 50 ft below sea level and 

declining at about 2 to 4 ft/yr. The top of the Upper Patapsco 

aquifer is more than 600 ft below sea level in this area, however. At the present rate, it would take at least 150 years before 

the 80-percent limit was reached.

Purpose and Scope

This report describes the development, calibration, and 

sensitivity analysis of a steady-state and transient groundwater-flow model of the NAS Patuxent River. Applications 

of an optimization model are presented to demonstrate the 

potential utility of these models, and the effects of current 

and future ground-water withdrawals are discussed. Data 

from published reports, USGS historical well files, the USGS 

National Water Information System (NWIS), recent waterlevel measurements, data provided by NAS Patuxent River, 

and withdrawal data from the USGS State Water-Use Data 

System (SWUDS) and the Maryland Department of the Environment (MDE) Regulatory Analysis Management System 

(RAMS) databases were used to create model input files and 

to calibrate the models.

Description of Study Area

NAS Patuxent River is located in southern Maryland near 

Lexington Park in St. Mary’s County (fig. 1). NAS Patuxent 

River encompasses 13,812 acres, including the main air station 

and Webster Outlying Field (United States Navy, 2003). With 

a workforce of approximately 20,000 personnel in 2006, NAS 

Patuxent River was the largest employer in St. Mary’s County. 

The study area includes the main air station, which is in St. 

Mary’s County immediately east of Lexington Park and along 

the right bank of the Patuxent River and the west shore of the 

Chesapeake Bay (fig. 1). 

Previous Investigations

The geology and the hydrogeology of southern Maryland, 

which includes St. Mary’s and Calvert Counties, have been 

thoroughly discussed in a number of reports published by both 

the Maryland Geological Survey (MGS) and the USGS. These 

reports provide the basic knowledge and data necessary to analyze the interrelation between the geohydrologic framework 

and natural and manmade transient stresses. An early report by 

Clark and others (1918, p. 398–411) described both the geology and the water resources of Calvert and St. Mary’s Counties. The water resources of Calvert and St. Mary’s Counties 

are further described in three MGS Bulletins (Overbeck, 

1951; Ferguson, 1953; Otton, 1955). More recently, several 

publications in the 1970s dealt with either the geology or 

the water resources of southern Maryland. Brown and others 

(1972) discussed a large-scale framework of the Coastal Plain 

sediments. Hansen (1974) discussed various facies trends 

in the Aquia aquifer within southern Maryland. Weigle and 

Webb (1970) presented a series of maps describing the water 

resources of southern Maryland. Hansen and Wilson (1984) 

reported the results of a deep test well in Lexington Park that 

was drilled to investigate the potential of aquifers underlying 

the Aquia aquifer. Klohe and Feehley (2001) published a study 

of the hydrogeology of the Aquia and Piney Point-Nanjemoy 

aquifer system that underlies NAS Patuxent River. Klohe and 

Kay (2007) described the hydrogeology of the Upper Patapsco 

aquifer that underlies the NAS Patuxent River, and provided 

ground-water withdrawals and water levels for the Piney 

Point-Nanjemoy, Aquia, and Upper Patapsco aquifers from the 

1940s through April 2006.

Several important publications present information on the 

location and characteristics of wells and water levels measured 

in these wells. Drummond (1984) published a compilation 

of well data for Calvert and St. Mary’s Counties. The USGS 

compiled water-level-data hydrographs for over 450 wells 

in southern Maryland for 1946–94 (Curtin and Dine, 1995). 

Achmad and Hansen (2001a) published a similar report for 

data from 1970 through 1996.

A series of potentiometric-surface and potentiometricsurface difference maps for the Piney Point-Nanjemoy, 

Aquia, and Upper Patapsco aquifers have been published. 

The potentiometric surface is the elevation to which water 

will rise in tightly cased wells (Fetter, 1994). The difference 

maps represent changes in the potentiometric surface over 

some period of years. Achmad and Hansen (2001a, p. 92–93) 

presented several potentiometric-surface maps for the Piney 

Point-Nanjemoy aquifer in southern Maryland. A potentiometric-surface map for the Aquia aquifer for spring 1980 

(Chapelle and others, 1981) has been followed by a series of 

potentiometric-surface maps of the Aquia aquifer for almost 

every year since 1982 and up to the present (Mack and others, 

1983a, 1985a, 1987, 1987a, 1989, 1991, 1992b; Curtin and 

others, 1993a, 1994a, 1995a, 1996a, 1997a, 1999a, 2000a, 

2001a, 2002a, 2002c, 2003a, 2005a). Potentiometric-surfacedifference maps published for the Aquia aquifer (Mack and 

others, 1983b, 1985b, 1987b, 1990b, 1992a; Curtin and others, 

1994b, 1996b, 1999c, 2001b, 2002e, 2005b) show changes 

in the potentiometric surface for periods as short as 1 year 

to as long as 19 years. Part of the potentiometric surface 

of the Aquia aquifer for 2002 is shown in figure 3a (Curtin 

and others, 2003a). Mack and others (1992c) published a 

potentiometric-surface map for the Upper Patapsco aquifer for 

1990. Curtin and others (1993b, 1994c, 1995b, 1996c, 1997b, 

1999b, 2000b, 2001c, 2002b, 2002d, 2003b, 2005c) continued 

to publish potentiometric-surface maps for the Upper Patapsco 

aquifer for essentially every year from 1991 to 2005. Achmad 

and Hansen (2001a, p. 94) presented a potentiometric-surfacedifference map for 1980–1996 for the Upper Patapsco aquifer. 

Curtin and others (1999d, 2001d, 2002f, 2005d) published 

potentiometric-surface-difference maps for the Upper Patapsco 

aquifer that compare 1990 to 1997, 1999, 2001, and 2003. Part 

of the potentiometric surface of the Upper Patapsco aquifer for 

2002 is shown in figure 3b (Curtin and others, 2003b).
6 Simulation of Ground-Water Flow at the Naval Air Station Patuxent River, St. Mary’s County, Maryland

A number of reports that describe the results of digital 

ground-water-flow models that include NAS Patuxent River 

are available. Kapple and Hansen (1976) reported on the 

results of a ground-water-flow model of the Aquia aquifer 

in southern Maryland that was centered at NAS Patuxent 

River. The results of two large-scale models that included the 

complete wedge of Coastal Plain sediments of Maryland and 

Delaware (Fleck, 1983; Fleck and Vroblesky, 1996) describe 

the generalized flow system for the complete set of aquifers at 

NAS Patuxent River. A more refined model of the Aquia and 

Piney Point-Nanjemoy aquifers underlying southern Maryland 

was completed by Chapelle and Drummond (1983). More 

recently, reports on the results and application of a groundwater model that simulates flow conditions within the Aquia 

and Piney Point-Nanjemoy aquifers underlying Calvert and St. 

Mary’s Counties have been published (Achmad and Hansen, 

1997, 2001a, 2001b, and Achmad and Fewster, 2003). In addition, Drummond (2005) developed a ground-water-flow model 

to simulate the water-supply potential of the Coastal Plain 

aquifers including the Piney Point-Nanjemoy, Aquia, Upper 

Patapsco, and Lower Patapsco aquifers in Calvert, Charles, 

and St. Mary’s Counties, Maryland. All of these models provided important results for the purposes for which they were 

designed; however, additional modeling was needed to refine 

the grid, to more accurately define the individual wells at the 

main air station, and to allow for optimization of withdrawals 

from wells.

Hydrogeologic Framework and 

Hydraulic Properties of Units

The geologic formations underlying NAS Patuxent 

River are part of the Coastal Plain Physiographic Province. 

These unconsolidated sediments are composed of beds of 

clays, silts, sands, and gravels. The thickness of the Coastal 

Plain sediments is approximately 2,600 ft in the vicinity of 

NAS Patuxent River (Hansen and Wilson, 1984), and they 

range in age from Early Cretaceous to Quaternary (Achmad 

and Hansen, 1997, p. 6) (table 1). The bedding strike of the 

Coastal Plain sediments in the vicinity of NAS Patuxent River 

is north-northeast, and the dip is to the east-southeast at an 

angle of approximately 0.1 to 0.3 degrees (Vroblesky and 

Fleck, 1991, p. 12, 15, 29, 31). Underlying the unconsolidated 

Coastal Plain sediments are mostly indurated metamorphic 

rocks of Paleozoic age (Achmad and Hansen, 1997, p. 6). The 

hydrogeologic units discussed in this report from youngest to 

oldest are: the surficial aquifer, the upper confining unit, the 

Piney Point-Nanjemoy aquifer, the middle confining unit, the 

Aquia aquifer, the lower confining unit, and the Upper Patapsco aquifer (table 1; fig. 4). Although there are Cretaceous 

units between the Patapsco aquifer and the Paleozoic rocks, 

they are not discussed in this report because they are below the 

section of interest. 

Surficial Aquifer

The surficial aquifer in the vicinity of the NAS Patuxent 

River is composed of mostly undifferentiated sediments ranging in grain size from clay to gravel. These sediments underlie most of the main air station and range in age from early 

Pleistocene to Holocene and consist of sand, gravel, silt, and 

clay of the early Pleistocene Chicamuxen Church Formation; 

the late Pleistocene Omar, Maryland Point, and Kent Island 

Formations; and undifferentiated Holocene deposits. The oldest sediments of the surficial aquifer are the upland deposits 

on the west side of the main air station. These consist of sands 

and gravels of the late Pliocene age Park Hall Formation and 

Upland gravel (McCartan, 1989). The hydraulic properties of 

the surficial aquifer have not been tested within the study area.

Upper Confining Unit

The upper confining unit consists of three Miocene 

formations deposited under marine conditions, which in 

decreasing age are the Calvert, Choptank, and St. Mary’s 

Formations (Achmad and Hansen, 1997, p. 8). These three 

formations form the Chesapeake Group in southern Maryland. 

The Calvert Formation, which is about 150 ft thick, consists 

principally of olive gray to olive brown silt and clay, and some 

fine sand. The 10- to 20-ft basal part, which consists of sand 

and some gravel, is effectively a part of the underlying Piney 

Point-Nanjemoy aquifer. The Choptank Formation, which 

overlies the Calvert Formation, is principally composed of 

grayish-green silty clays interbedded with some highly fossiliferous fine sand, and ranges from 30 to 100 ft thick. The thinner St. Mary’s Formation, which is generally less than 50 ft in 

thickness, overlies the Choptank Formation. This formation is 

more blue in color than the underlying Choptank Formation, 

but is otherwise a very similar deposit of interbedded silty clay 

and fine sand.

Chapelle and Drummond (1983, table 2) reported six 

vertical hydraulic conductivity values for the clayey part of the 

Chesapeake Group. These values were calculated by laboratory methods and range from 6 x 10-5 to 2 x 10-2 ft/d. This 

range of values is consistent with values for marine clays as 

reported in standard texts (Domenico and Schwartz, 1990, 

table 3.2; Freeze and Cherry, 1979, table 2.2; Fetter, 1994, 

table 4.6).

Piney Point-Nanjemoy Aquifer

Underlying the Chesapeake Group marine clays are a 

sequence of sandy deposits that structurally form the Piney 

Point-Nanjemoy aquifer (table 1). The geologic formations 

include the upper part of the lower Eocene Nanjemoy Formation, the middle Eocene Piney Point Formation, an unnamed 

Oligocene(?) bed that may correlate with the Old Church 

Formation (Achmad and Hansen, 1997, p. 12), and the lower 
Hydrogeologic Framework and Hydraulic Properties of Units 7

part of the Miocene Calvert Formation, which is the lower part 

of the Chesapeake Group (table 1). The total thickness of this 

aquifer in the vicinity of the NAS Patuxent River is about 45 

to 75 ft.

 The Nanjemoy Formation is a coarsening-upward 

sequence from dark greenish-gray sandy clays to olive or 

olive-brown clayey sands. Glauconite is common to abundant 

throughout this section. The lower part of this sequence, which 

is predominantly clay, is the uppermost sequence of the middle 

confining unit. The formation crops out in a small band principally in eastern Prince George’s and southern Anne Arundel 

Counties. The overlying Piney Point Formation is predominantly composed of glauconitic sand that is gray to grayishgreen, medium- to coarse-grained, and well sorted. The Piney 

Point Formation does not crop out, but rather pinches out 

across central Calvert and northern St. Mary’s Counties. The 

Oligocene(?) deposit that overlies the Piney Point is thin and 

discontinuous and is composed of clayey quartz sand (Achmad 

and Hansen, 1997, p. 12). The thickness of this bed is about 

1 to 1.5 ft. As a consequence, it is not possible to distinguish 

this bed in the subsurface from the overlying Calvert Formation, which is the oldest unit of the Chesapeake Group in the 

model area, and is about 150 ft thick. The basal 10 to 20 ft of 

the Calvert Formation consists of fine to medium sand with 

some gravel that crops out in a narrow belt adjacent to and 

downdip from the Nanjemoy Formation in Anne Arundel, 

Prince George’s, and Charles Counties (Cooke and Cloos, 

1951; Glaser, 1976; Mathews, 1933; Hansen, 1972, p. 79, 115; 

Hack, 1977; Achmad and Hansen, 1997, p. 10).

The horizontal hydraulic conductivity of both the Nanjemoy and Piney Point Formations is generally in the range 

of 5 to 20 ft/d. Hansen (1972) reported a value of 16 ft/d for 

the Piney Point Formation from a test at Lexington Park. In 

the vicinity of the NAS Patuxent River, the transmissivity is 

approximately 400 ft2/d (feet squared per day) and the thickness is about 50 ft (Williams, 1979, plate 5, fig. 5); thus, the 

horizontal hydraulic conductivity would be about 8 ft/d. The 

specific capacity of wells in the vicinity of the main air station 

(Drummond, 1984, table 3) was used to calculate horizontal 

hydraulic conductivities. The procedure used is described 

in Appendix 1. For 11 wells screened in the Piney PointNanjemoy aquifer, the median value was 15 ft/d (Appendix 1). 

The mean value of 10 ft/d for horizontal hydraulic conductivity is consistent with a fine- to medium-sorted sand as reported 

in standard texts (Domenico and Schwartz, 1990, table 3.2; 

Freeze and Cherry, 1979, table 2.2; Fetter, 1994, table 4.6). 

Storage coefficient values of 0.0003 to 0.0004 were reported 

by Hansen (1972), 0.00009 to 0.0004 by Williams (1979), 

and 0.0004 by Chapelle and Drummond (1983). Williams 

(1979) used a storage coefficient of 0.0003 for the Piney 

Point-Nanjemoy aquifer in a ground-water-flow model, and 

Chapelle and Drummond (1983) used a storage coefficient 

of 0.0004 for the Piney Point-Nanjemoy aquifer in a groundwater-flow model.

Table 1. Geologic units, corresponding hydrogeologic units, and model layers at Naval Air Station Patuxent River, 

Maryland. [Modified from Klohe and Kay, 2007]
8 Simulation of Ground-Water Flow at the Naval Air Station Patuxent River, St. Mary’s County, Maryland

Middle Confining Unit

The middle confining unit directly underlies the Piney 

Point-Nanjemoy aquifer in the model area. The sediments of 

this unit are composed of the lower part of the lower Eocene 

Nanjemoy Formation, and the underlying lower Eocene and 

upper Paleocene Marlboro Clay (Achmad and Hansen, 1997, 

p. 17). The total thickness of this unit in the vicinity of the 

NAS Patuxent River as described by Achmad and Hansen 

(1997, fig. 6) is about 90 ft; however, Chapelle and Drummond (1983, fig. 6) and Klohe and Feehley (2001, p. 13 and 

fig. 6) calculated a thickness of about 140 ft. The thickness of 

the part of the middle confining unit that underlies the NAS 

Patuxent River for the model described in this report ranges 

from 123 to 170 ft.

The lower part of the Nanjemoy Formation, which 

directly underlies the Piney Point-Nanjemoy aquifer, is 

composed of greenish to black olive-black silts and clays. The 

bottom section of the middle confining unit, the Marlboro 

Clay, is composed of pale red or gray plastic clay (Achmad 

and Hansen, 1997; Klohe and Feehley, 2001). The difference 

in the composition of the sediments between the upper and 

lower part of the middle confining unit is reflected in the 

hydraulic conductivity values at various depths within the unit. 

Values of hydraulic conductivity from the confining part of the 

Nanjemoy Formation in Kent Island, Queen Anne’s County 

ranged from 6.6 x 10-3 to 6.9 x 10-2 ft/d (Kapple and Hansen, 

1976, table 2). Two values for vertical hydraulic conductivity 

for the Marlboro Clay from locations within 10 mi (miles) 

of the NAS Patuxent River were 5.8 x 10-5 and 9.5 x 10-5 ft/d 

(Chapelle and Drummond, 1983, table 2). These two vertical hydraulic conductivity values for the Marlboro Clay fall 

within the expected range for marine clay of about 5 x 10-6

to 3 x 10-3 ft/d (Fetter, 1994, p. 98; Freeze and Cherry, 1979, 

p. 29; Domenico and Schwartz, 1990, p. 65). Due to stratification, it is necessary to use a weighted harmonic mean to 

calculate an average vertical hydraulic conductivity value for 

the full thickness of the confining unit (Lee and Fetter, 1994, 

p. 22). Assuming a thickness of 120 ft and a vertical hydraulic 

conductivity of 4 x 10-2 ft/d for the Nanjemoy part of the unit 

and for the Marlboro Clay, values of 30 ft and 8 x 10-5 ft/d, 

respectively, the weighted harmonic mean for vertical hydraulic conductivity is about 4 x 10-4 ft/d for the full thickness. 

This value is consistent with a value of 5 x 10-4 ft/d used in the 

model developed by Achmad for southern Maryland (Achmad 

and Hansen, 1997, p. 19).

Aquia Aquifer

The Aquia aquifer correlates with the upper Paleocene 

Aquia Formation (Achmad and Hansen, 1997, p. 19), which 

underlies the upper Paleocene Marlboro Clay and overlies 

the lower Paleocene Brightseat Formation. The recharge area 

for the Aquia aquifer, which is the outcrop belt that extends 

across central Anne Arundel County and into east-central 

Prince George’s County, is located about 40 to 50 mi to the 

northwest of the NAS Patuxent River (fig. 1). This recharge 

area is sub-parallel to and just to the northwest of the recharge 

area for the Piney Point-Nanjemoy aquifer. A sandy to clayey 

facies change occurs about 5 mi downdip from NAS Patuxent River (Hansen, 1972, p. 64). The top of the aquifer is at 

an elevation of about 450 ft below sea level (NAVD 88) and 

the thickness is about 100 ft (Achmad and Hansen, 1997, 

p. 22). The sediments of the Aquia aquifer were deposited on 

a shoaling marine shelf that resulted in a coarsening-upward 

sequence. The lower quarter of the Aquia aquifer is generally 

a poorly sorted clayey to fine-grained sand with thin, calcareously cemented sandstone and shell layers. The upper part is 

a coarser-grained, well-sorted sand, also with thin shelly beds 

throughout. Green to black, well-sorted, medium to coarse 

glauconite is abundant throughout the upper three quarters of 

the Aquia aquifer. This gives it a “salt and pepper” appearance.

Hansen (1972, p. 66) lists three “transmissibility” values 

ranging from 5 x 103 to 7.5 x 103 gallons per day per foot 

(670 to 1,000 ft2/d) for locations within about 10 mi of NAS 

Patuxent River. Horizontal hydraulic conductivity is calculated 

by dividing the transmissibility of the aquifer by the thickness 

of the aquifer. The thickness at these locations ranges from 

110 to 150 ft and thus, the horizontal hydraulic conductivity 

for Hansen’s values averaged about 5 ft/d. A median value 

of 20 ft/d was calculated from 30 specific capacity values as 

described in Appendix 1. A storage coefficient value determined from a pumping test at Lexington Park, St. Mary’s 

County, was 0.0002 (Hansen, 1972, p. 66). Eight other values 

from the Aquia aquifer throughout Maryland ranged from 

0.0001 to 0.0004, with a median value of 0.0002 (Hansen, 

1972, p. 66). Storage coefficient values for the Aquia aquifer 

used in three previous models were 0.0001 (Achmad and 

Hansen, 1997, p. 20), 0.0003 (Kapple and Hansen, 1976, 

p. 20), and 0.0001 (Chapelle and Drummond, 1983, p. 44).

Lower Confining Unit

The lower confining unit consists of sediments of the 

Paleocene Brightseat Formation and the uppermost sediments 

of the Patapsco Formation of Early Cretaceous age. The Late 

Cretaceous formations throughout much of Maryland, which 

include the Monmouth, Matawan, and Magothy Formations, 

are missing in the lithologic section in the vicinity of the NAS 

Patuxent River. The Brightseat Formation is typically gray to 

grayish black, micaceous clay and silt with some fine sand 

lenses (Achmad and Hansen, 1997, p. 7). The fine sand layers 

provide minimal water to a few domestic wells. The Brightseat 

Formation in the area of the NAS Patuxent River is about 50 ft 

thick. The lower half of the lower confining unit is composed 

of the uppermost 50 to 90 ft of the Patapsco Formation. This 

section of the Patapsco Formation principally consists of a 

red plastic clay (Vroblesky and Fleck, 1991, p. 16). The total 

thickness of the lower confining unit is about 110 to 140 ft 

(Klohe and Kay, 2007). 
Ground-Water-Flow Model 9

The hydrologic properties of the lower confining unit 

have not been extensively measured. An analysis of a Brightseat core from Prince George’s County indicated values for 

hydraulic conductivity and specific storage of 9.5 x 10-4 ft/d 

and 7.4 x 10-5 ft-1, respectively (Hansen, 1977, p. 12). Assuming a thickness of about 125 ft in the NAS Patuxent River 

area, the storage coefficient would be about 0.009. Laboratory 

analyses of a core from the Patapsco Formation that was 64 

percent clay indicated hydraulic conductivity values of 1 x 10-5

and 7 x 10-6 ft/d (Mack, 1974, p. 16).

Upper Patapsco Aquifer

The Upper Patapsco aquifer, which is Early Cretaceous 

in age, immediately underlies the lower confining unit in the 

vicinity of the NAS Patuxent River. The sediments are composed of about 200 ft of medium- to fine-grained sand, some 

gravel, and interbeds of gray clay (Klohe and Kay, 2007). 

The top of the aquifer is located at an elevation of about 

680 ft below sea level. Recharge to the Upper Patapsco aquifer 

occurs in the subcrop area, which extends as a narrow band to 

the east and sub-parallel to the Fall Line, which is the approximate boundary between the Coastal Plain and Piedmont 

Physiographic Provinces (fig. 1). The upper and lower parts of 

the Patapsco aquifer are not differentiated in various areas of 

Maryland, as well as in various reports such as Hansen (1972); 

therefore, in instances where upper and lower are not specified, the aquifer is referred to as the Patapsco aquifer. 

Transmissibility values for the Patapsco aquifer determined from aquifer tests that were reported by Hansen (1972, 

p. 34) for Charles County ranged from 1,000 to 5,000 gallons per day per foot (135 to 670 ft2

/d). The thickness of the 

Patapsco ranged from 75 to 105 ft, resulting in a horizontal 

hydraulic conductivity of 8 to 58 ft/d, with a median value of 

13 ft/d. The results of an aquifer pump test at NAS Patuxent 

River production well SM Df 100 indicated a transmissivity 

value of about 3,900 ft2/d (Klohe and Kay, 2007). The well 

has 60 ft of screen over a thickness of 200 ft (Klohe and Kay, 

2007). Thus, the horizontal hydraulic conductivity at this location is about 65 ft/d, which is higher than the value of 45 ft/d 

obtained from the specific capacity calculations in Appendix 1 

for the same well. Analysis of another aquifer test at the NAS 

Patuxent River Webster Outlying Field for the Upper Patapsco 

well SM Ff 65 indicated a transmissivity value of 2,100 ft2/d 

(Klohe and Kay, 2007). Well SM Ff 65 has 50 ft of screen over 

a thickness of 239 ft (Klohe and Kay, 2007). Thus, the hydraulic conductivity is on the order of 10 ft/d. Hansen (1972, p. 34) 

reported values for storage coefficients for the Patapsco aquifer; values in Charles and Prince George’s Counties ranged 

from 0.0001 to 0.0004. 

A confining unit, composed of beds of clay with low vertical hydraulic conductivity, lies beneath the Upper Patapsco 

aquifer. Achmad and Hansen (2001a) referred to the unit as 

the Patapsco Confining Bed and determined that it is approximately 300 ft thick at Lexington Park. 

Ground-Water-Flow Model

The following sections describe the ground-water-flow 

model designed to simulate the aquifers underlying NAS 

Patuxent River, including the conceptual model, and the 

design, input parameters, calibration, and sensitivity of the 

numerical flow model. Two simulations of the ground-waterflow model are presented in this report: a three-dimensional 

transient simulation, and a three-dimensional steady-state 

simulation. The transient and steady-state simulations use the 

same model grid and input parameters. The purpose of the 

transient simulation was to calibrate the model to observed 

(measured) water levels recorded over the past 50 years and to 

simulate the changes in ground-water head gradients (fluxes 

and directions) from pre-stressed conditions in the early 1900s 

to stressed conditions beginning in the 1940s, and continuing 

through 2002. The steady-state model was constructed in order 

to link the ground-water-flow model simulating flow conditions at the end of 2002 with an optimization model code.

The USGS MODFLOW-96 code (McDonald and 

Harbaugh, 1984), updated in 1996 by Harbaugh and 

McDonald (1996), was used to mathematically simulate 

ground-water flow and calculate ground-water budgets. The 

MODFLOW code uses finite-difference techniques to solve 

the partial differential equations that describe ground-water 

flow. Processing MODFLOW graphical-user interface 

(PMWIN) (Chiang and Kinzelbach, 1998) was used as the preand post-processing software program, enhancing the capabilities of MODFLOW. PMWIN tools were used to interpret 

MODFLOW output by extracting, plotting, and calculating 

water budgets for subsets of the modeled area.

Conceptual Model

The conceptual model is a representation of the current 

understanding of the components of the ground-water-flow 

system that underlie NAS Patuxent River. The conceptual 

model attempts to describe how water enters the system, 

how it moves through the system, how much is stored in the 

system, and finally, how it exits the system. Essentially, it is 

a synthesis of the geologic framework, recharge conditions, 

hydraulic parameters, and discharge conditions (including 

withdrawal rates).

The conceptual model, shown in figure 4, encompasses a 

layered system of aquifers and confining units. These layers, 

described in the previous section, include (from top to bottom) the surficial aquifer, upper confining unit, Piney PointNanjemoy aquifer, middle confining unit, Aquia aquifer, lower 

confining unit, and the Upper Patapsco aquifer. The topmost 

layer represents the surficial aquifer. The heads in this layer 

remain relatively constant and there is minimal interaction 

with the next lower aquifer. The confining layers restrict flow 

between aquifers. In the model region, inflows are primarily 

lateral fluxes from outside the model region. Vertical fluxes 

occur between layers as a result of hydraulic gradients. Some 
10 Simulation of Ground-Water Flow at the Naval Air Station Patuxent River, St. Mary’s County, Maryland

water is stored in the aquifers and confining units. Outflow 

from the ground-water-flow system underlying the NAS 

Patuxent River under pre-stressed conditions was mostly 

lateral discharge. During stressed conditions, the substantial 

pumping withdrawals from the aquifers account for much of 

the discharge out of the system.

Design

The design of the transient and steady-state groundwater-flow simulations includes horizontal and vertical 

discretization of space representing the aquifer and confining 

unit layers, boundary conditions, and input parameters such as 

hydraulic conductivity and pumping withdrawals. The design 

is the same for both the steady-state and transient simulations 

with the following exceptions: the transient model simulation includes time discretization, storage coefficients, variable 

withdrawals, and time-specified boundary heads.

Model Grid

The model encompasses an area of 5.6 by 4.8 mi, 

approximately 27 mi2 (square miles). The horizontal extent of 

the model, in relation to the main air station boundary, and cell 

discretization are shown in figure 5. The grid is composed of 

118 columns and 102 rows. There are a total of 84,252 cells, 

each 250 ft wide by 250 ft long, with each cell representing 

an area of 62,500 ft2 (square feet), or approximately 1.4 acres. 

The cell size is small to adequately represent variations in 

hydraulic properties, and to simulate pumping effects. In 

comparison, the cell sizes for the southern Maryland model by 

Achmad and Hansen (1997) and the Drummond (2005) model 

are both approximately 110 times larger than the cell size for 

the NAS Patuxent River model.

The vertical discretization of the model was designed 

to encompass the three aquifers from which NAS Patuxent 

River withdraws water, as well as the intervening confining 

units, and the shallow surficial aquifer as an upper boundary 

condition. Thus, the model encompasses seven layers, which 

are shown in table 1, and are numbered from top to bottom 

(figs. 4 and 6). Layer thickness and hydraulic properties are 

presented in table 2. Model layer 1 represents the surficial 

unconfined aquifer underlying NAS Patuxent River; this 

aquifer is not tapped for potable water by the main air station, 

but is included in the model as a model boundary condition. 

Layer 1, as represented by the model, ranges in thickness from 

10 to 101 ft. Achmad and Hansen (1997, fig. 2, p. 9) indicate 

a possible paleochannel underlying NAS Patuxent River with 

thicknesses of the surficial aquifer up to 130 ft. For the NAS 

Patuxent River model, however, the simulated thickness is 

not critical because layer 1 is (1) simulated as a constant head 

Figure 4. Diagram of the model layering scheme and boundary conditions for the Naval Air Station Patuxent River groundwater-flow model.
Ground-Water-Flow Model 11

Figure 5. Location and design of model grid and water budget zones.
12 Simulation of Ground-Water Flow at the Naval Air Station Patuxent River, St. Mary’s County, Maryland

boundary condition, and (2) underlain by a thick layer of silt 

and clay (figs. 4 and 6). Layer 2, which represents the upper 

confining unit, ranges in thickness from 190 to 265 ft. Layer 3 

represents the Piney Point-Nanjemoy aquifer. The thickness of 

the Piney Point-Nanjemoy aquifer underlying NAS Patuxent 

River ranges from 45 to 75 ft. Layer 4 represents the middle 

confining unit, and ranges in thickness from 123 to 185 ft. 

Layer 5 represents the Aquia aquifer, one of the principal 

aquifers in southern Maryland, and ranges in thickness from 

70 to 144 ft. Layer 6 represents the lower confining unit, and 

ranges in thickness from 45 to 120 ft. The bottom model layer 

(layer 7) represents the Upper Patapsco aquifer, and is 200 ft 

in thickness (Klohe and Kay, 2007).

Boundary Conditions

There are three different types of boundary conditions in 

the model (figs. 4 and 6). The uppermost layer (layer 1) represents the surficial aquifer, and is a constant-head boundary. 

The constant-head values in this layer ranged from 0.5 to 91 ft 

above sea level. These values, which are a rough reflection 

of the topography, were calculated by digitizing the topography and then adjusting for an approximated thickness of the 

unsaturated zone (or depth to the saturated zone). The constant 

heads of layer 1 represent an average water level in each 

model cell. Recharge is not input into the model because layer 

1 is represented as a constant-head boundary. The thickness 

of the upper confining unit, which is represented as model 

layer 2, ranges from 190 to 265 ft thick, resulting in minimal 

interaction between layer 1 and the rest of the model. Thus, 

the representation of the water levels in layer 1 is not critical 

to the model results and representing this layer as a constant 

head is justified. 

The bottom of layer 7 is represented in the model as 

a no-flow boundary. The laterally discontinuous nature of 

the clays, silts, and sands within the Upper Patapsco aquifer 

makes it difficult to delineate the lower boundary. However, 

Achmad and Hansen (2001a) describe the Patapsco Confining 

Bed as approximately 300 ft thick at Lexington Park. Borehole geophysical logs from wells near the air station indicate 

local layers of low-permeability silts and clays that are able to 

retard vertical flow. Therefore, the use of a no-flow boundary 

is justified.

The third boundary condition, a general-head boundary, 

encompasses the perimeters of layers 2–7. A general-head 

boundary specifies both a head at some distance from the 

general-head boundary cell and a conductance of the material 

between the distant head and the physical model boundary 

(McDonald and Harbaugh, 1984, p. 347). The general-head 

boundary was used because no close natural hydrologic 

boundaries exist. Extending the model domain to the natural 

boundaries would have likely resulted in larger model grid 

cells reducing accuracy within the study area, and an expansion of model development beyond the scope of the study.

The specified heads along the boundaries of model layers 

3,5, and 7, which represent the Piney Point-Nanjemoy, Aquia, 

and Upper Patapsco aquifers, respectively, were derived from 

published potentiometric maps for these aquifers (Achmad 

and Hansen, 2001a, figs. 14, 15, 85, 86, 92, 93, map nos. S-13 

to 18, S-25 to 34; Fleck and Vroblesky, 1996, pl. 2; Achmad 

and Hansen, 1997, figs. 20-23). The specified heads along 

the boundaries of model layers 2, 4, and 6, which represent 

the confining units, were estimated by calculating the mean 

value between the aquifer heads from the aquifer layers above 

and below. A linear hydraulic gradient was assumed between 

aquifers. For the transient model, general-head boundary 

conditions are specified for each stress period. For some stress 

periods, published head maps were not available; therefore, 

heads were interpolated from head maps from the nearest time 

periods. For the steady-state model, the general-head boundary conditions specified for the December 2002 stress period 

were used. 

Figure 6. Diagram of model layering, vertical discretization, and boundary conditions along row 60 (see figure 5).
Ground-Water-Flow Model 13

The general head-boundary conductance (C) for each 

layer is the product of the horizontal hydraulic conductivity of 

the material (Kh) and the cross-sectional area (A) of the cell 

perpendicular to flow, divided by the distance between the 

specified head and the general-head boundary cell (L). The 

values used to calculate C and the resulting C values used in 

the transient and steady-state models are shown in table 3. The 

cross-sectional area (A) is calculated by multiplying the width 

of the cell (250 ft for all cells and all layers) by an average 

thickness for each layer. The L for each general-head boundary 

cell is 125 ft. The resulting C value remains constant through 

all stress periods (table 3).

Model Hydraulic Properties

Hydraulic properties input into the model include initial 

heads, vertical and horizontal hydraulic conductivities, and 

withdrawal data. The input values and the heads that are 

calculated for the model are average values for each 1.4-acre 

cell. Recharge is not explicitly modeled because layer 1 has a 

constant-head boundary condition.

The initial heads for the transient model represent prestressed conditions. The initial head values for the Upper Patapsco, Aquia, and Piney Point-Nanjemoy aquifers were based 

on pre-pumping conditions simulated by Fleck and Vroblesky 

(1996, pls. 1, 5, and 6). The initial heads for the surficial aquifer ranged from 0.5 to 91 ft and were determined by adjusting 

the topography by an approximate thickness of the unsaturated 

zone. Limited data exist for head values in the confining units, 

therefore the initial heads for the confining unit model layers 

were calculated as a mean value of the heads in the aquifer 

layers adjacent to the confining unit layers. Constant values 

of 7, 8, 10, 12, 18, and 25 ft were used for the initial heads for 

layers 2 through 7, respectively. 

Initial Kh values were estimated from previously published specific capacity, transmissivity, or hydraulic conductivity values. Calibrated Kh

 values for the aquifer model 

layers range from 10 to 20 ft/d; Kh for the confining units is 

0.0002 ft/d (table 2).

Few vertical hydraulic conductivity (Kv) values have 

been reported in the literature. When available, these values 

were used for initial Kv input values. Calibrated Kv values in 

the model range from 1 to 2 ft/d for aquifer layers and a value 

of 0.00002 ft/d was used for all confining units (table 2); 

these values are one order of magnitude less than the Kh of the 

respective layer.

The transient ground-water-flow model simulates the 

period from 1900 (unstressed) through 2002. The time is 

discretized into 106 stress periods and subdivided into 161 

Table 2. Ground-water-flow model input values.

[ft, feet; ft/d, feet per day]

Hydrogeologic Unit Layer 

number

Model layer 

thickness, in ft

Horizontal hydraulic 

conductivity, 

in ft/d

Vertical hydraulic 

conductivity, 

in ft/d

Surficial aquifer 1 10–101 10 1

Upper confining unit 2 190–265 0.0002 .00002

Piney Point-Nanjemoy aquifer 3 45–75 10 1

Middle confining unit 4 123–185 .0002 .00002

Aquia aquifer 5 70–144 15 1.5

Lower confining unit 6 45–120 .0002 .00002

Upper Patapsco aquifer 7 200 20 2

Table 3. Values used to calculate general-head boundary conductance values, and resulting general-head 

boundary conductance values. 

[ft, feet; ft/d, feet per day; ft2/d, feet squared per day]

Layer

Horizontal hydraulic 

conductivity (Kh), 

in ft/d

Cell width (W), 

in ft

Average cell 

thickness (b), 

in ft

Distance (L), 

in ft

Calculated conductance 

value (C), 

in ft2/d

2 0.0002 250 230 125 0.092

3 10 250 65 125 1260

4 0.0002 250 150 125 0.060

5 15 250 110 125 3360

6 0.0002 250 90 125 0.036

7 20 250 200 125 7980
14 Simulation of Ground-Water Flow at the Naval Air Station Patuxent River, St. Mary’s County, Maryland

time steps varying in length from multiple years to 7 days. 

Withdrawal data were obtained from several sources (Klohe 

and Feehley, 2001, table 3; Achmad and Hansen, 1997, 

Appendices D, E; C. I. Frederick, Jr., Jahn Corporation, NAS 

Patuxent River, written commun., 2003) and input to the 

model for each of the 106 stress periods. The locations of the 

Piney Point-Nanjemoy and Aquia withdrawal wells used in the 

model are shown in figure 7. Ground-water withdrawal rates 

vary from stress period to stress period, but remain constant 

within each stress period of the transient model (table 4). The 

time span of each of the stress periods and the total daily withdrawal rate for the Piney Point-Nanjemoy and Aquia aquifers 

for each period are shown in table 4. Major withdrawals from 

these aquifers did not begin until the 1940s; therefore, there is 

no simulated withdrawal from any of the three aquifers until 

stress period three, which represents 1940 to 1950. Withdrawal 

from the Upper Patapsco production well at NAS Patuxent 

River began in November 2003, but the transient model simulation ended in December 2002, so withdrawal from the Upper 

Patapsco aquifer is not simulated.

Figure 7. Location of observation wells and withdrawal wells simulated in the transient ground-water-flow model at Naval 

Air Station Patuxent River, Maryland.
Ground-Water-Flow Model 15

Table 4. Transient model stress periods with respective time periods and simulated withdrawal rates for the 

Piney Point-Nanjemoy aquifer, Aquia aquifer, and the stress period total, 1900–2002.—Continued

Stress

period 

number

Time period

Withdrawal rate, in cubic feet per day

Piney PointNanjemoy aquifer Aquia aquifer Total

1 1900–1919 0 0 0

2 1920–1939 0 0 0

3 1940–1949 13,500 235,000 248,500

4 1950–1959 13,200 212,000 225,200

5 1960–1969 20,300 192,000 212,300

6 1970–1979 13,600 239,400 253,000

7 1980 11,200 222,000 233,200

8 1981 11,200 227,200 238,400

9 1982 11,200 236,200 247,400

10 1983 11,200 342,200 353,400

11 1984 11,200 242,400 253,600

12 1985 11,200 273,000 284,200

13 1986 11,200 273,000 284,200

14 1987 11,200 282,600 293,800

15 1988 11,200 301,200 312,400

16 1989 12 276,700 276,712

17 1990 12 239,600 239,612

18 1991 12 293,000 293,012

19 1992 12 257,670 257,682

20 1993 7,600 266,730 274,330

21 1994 23,600 259,200 282,800

22 1995 5,495 286,615 292,110

23 Jan. 1996 5,490 239,116 244,606

24 Feb. 7,130 241,691 248,821

25 Mar. 4,998 252,670 257,668

26 Apr. 6,174 256,834 263,008

27 May 496 250,689 251,185

28 June 7,359 252,687 260,046

29 July 9,830 244,464 254,294

30 Aug. 5,940 250,053 255,993

31 Sept. 7,487 244,967 252,454

32 Oct. 6,819 241,155 247,974

33 Nov. 6,199 237,112 243,311

34 Dec. 5,613 236,386 241,999

35 Jan. 1997 8,649 203,535 212,184

36 Feb. 11,185 217,262 228,447

37 Mar. 6,558 198,906 205,464

38 Apr. 16,629 232,877 249,506

39 May 4,202 207,608 211,810

40 June 19,451 222,240 241,691

41 July 8,484 235,055 243,539

42 Aug. 11,020 218,981 230,001

43 Sept. 8,421 212,656 221,077

44 Oct. 406 216,069 216,475

45 Nov. 171 219,256 219,427

46 Dec. 167 215,372 215,539

47 Jan. 1998 202 233,761 233,963

48 Feb. 157 233,129 233,286

49 Mar. 164 245,243 245,407

50 Apr. 363 240,123 240,486

51 May 186 249,375 249,561

52 June 347 245,005 245,352

53 July 321 256,745 257,066

54 Aug. 228 283,640 283,868

55 Sept. 159 283,736 283,895

56 Oct. 148 241,851 241,999
16 Simulation of Ground-Water Flow at the Naval Air Station Patuxent River, St. Mary’s County, Maryland

Table 4. Transient model stress periods with respective time periods and simulated withdrawal rates for the 

Piney Point-Nanjemoy aquifer, Aquia aquifer, and the stress period total, 1900–2002.—Continued

Stress

period 

number

Time period

Withdrawal rate, in cubic feet per day

Piney PointNanjemoy aquifer Aquia aquifer Total

57 Nov. 131 232,465 232,596

58 Dec. 150 228,304 228,454

59 Jan. 1999 1,430 230,679 232,109

60 Feb. 686 236,863 237,549

61 Mar. 178 243,334 243,512

62 Apr. 1,318 245,742 247,060

63 May 3,669 245,258 248,927

64 June 7,018 251,004 258,022

65 July 10,676 252,428 263,104

66 Aug. 8,160 237,657 245,817

67 Sept. 4,961 222,988 227,949

68 Oct. 132 234,817 234,949

69 Nov. 58 215,970 216,028

70 Dec. 67 218,133 218,200

71 Jan. 2000 43 254,555 254,598

72 Feb. 38 251,575 251,613

73 Mar. 34 256,583 256,617

74 Apr. 56 246,418 246,474

75 May 71 246,776 246,847

76 June 87 253,090 253,177

77 July 84 243,123 243,207

78 Aug. 111 245,865 245,976

79 Sept. 122 244,200 244,322

80 Oct. 104 240,992 241,096

81 Nov. 94 235,725 235,819

82 Dec. 80 236,495 236,575

83 Jan. 2001 75 262,383 262,458

84 Feb. 153 249,678 249,831

85 Mar. 124 250,724 250,848

86 Apr. 134 257,012 257,146

87 May 134 279,652 279,786

88 June 147 271,475 271,622

89 July 323 275,575 275,898

90 Aug. 270 280,764 281,034

91 Sept. 345 273,468 273,813

92 Oct. 147 260,588 260,735

93 Nov. 253 255,065 255,318

94 Dec. 109 244,196 244,305

95 Jan. 2002 94 250,904 250,998

96 Feb. 96 254,164 254,260

97 Mar. 121 257,998 258,119

98 Apr. 135 261,096 261,231

99 May 244 277,129 277,373

100 June 252 301,923 302,175

101 July 194 303,796 303,990

102 Aug. 195 301,854 302,049

103 Sept. 201 277,495 277,696

104 Oct. 174 269,657 269,831

105 Nov. 166 260,376 260,542

106 Dec. 239 260,800 261,039
Ground-Water-Flow Model 17

Model Calibration

Initial heads, and horizontal and vertical hydraulic 

conductivity of the aquifers and confining beds were adjusted 

using trial-and-error methods to calibrate the transient groundwater-flow model. The model was considered calibrated when 

the simulated water-level trends matched the observed waterlevel trends, the error between the observed (or measured) 

water levels and the simulated water levels was minimized, 

and the input parameters, water budgets, and simulated flow 

directions were reasonable. The well locations for which 

water-level observations were available for model calibration 

are shown in figure 7. A total of 27 wells were used in model 

calibration (10 screened in the Piney Point-Nanjemoy aquifer, 

15 screened in the Aquia aquifer, and 2 screened in the Upper 

Patapsco aquifer). The root-mean-squared error (RMSE) was 

used to calculate the error between the observed and simulated 

water levels. The RMSE is equal to the average of the squared 

differences in measured and simulated water levels (Anderson 

and Woessner, 1992). Simulated water levels from the transient model were generally consistent with observed water levels. A hydrograph of observed and simulated water levels for 

well SM Dg 21 screened in the Piney Point-Nanjemoy aquifer 

is shown in figure 8. The RMSE for Piney Point-Nanjemoy 

well SM Dg 21 was 1.19 ft (table 5).

Hydrographs of observed and simulated water levels for 

wells (SM Df 1, SM Df 61, SM Df 80, SM Df 95, SM Dg 10, 

and SM Dg 14) screened in the Aquia aquifer are shown in 

figure 9. The simulated water levels generally agree with the 

observed values and closely match the downward trend of 

water levels in the observation wells. RMSE values for wells 

screened in the Aquia aquifer range from 5.9 to 11 ft, with a 

mean of 7.7 ft (table 5). The RMSE for SM Df 61 (10.98 ft) is 

skewed by two observations that likely reflect short-term withdrawals not accounted for in the transient model. If those two 

observations are not used in the RMSE calculation, the RMSE 

is approximately 7 ft, rather than 11 ft.

Two wells screened in the Upper Patapsco aquifer (SM 

Df 84 and SM Df 100) were used to calibrate model layer 7. 

Hydrographs of observed and simulated water levels for 

wells SM Df 84 and SM Df 100 are shown in figure 10. The 

simulated water levels agree with the observed water levels 

and closely match the downward trend of water levels in the 

observation wells. The RMSEs for wells SM Df 84 and SM Df 

100 are 2.42 and 1.69 ft, respectively.

Model Sensitivity

In addition to checking model calibration, it is also 

important to test the sensitivity of the model to changes in 

model input parameters. The sensitivity analysis helps quantify the uncertainty of the calibrated model due to uncertainty 

in model input parameters, stresses, and boundary conditions 

(Anderson and Woessner, 1992). By systematically changing 

one input parameter at a time, the effects of the input parameter on the model-simulated heads and flow can be evaluated. 

The sensitivity analysis indicates which input parameters 

impact the ability of the model to match observed values 

(Reilly and Harbaugh, 2004).

A sensitivity analysis was performed on the calibrated 

model under steady-state conditions (December 2002 simulation) by systematically changing the Kh

 of selected layers 

(while keeping Kv constant and therefore changing the Kh to 

Kv ratio), the Kh and Kv of selected layers (keeping the Kh to 

Kv ratio constant), the general-head boundary conductance 

values, and the withdrawal rates. In each simulation, one 

parameter was changed by increasing the parameter by one 

and two orders of magnitude and then decreasing the parameter by one and two orders of magnitude. The steady-state 

simulated water levels were compared to the observed water 

levels for each sensitivity analysis simulation. The RMSE was 

calculated for 18 wells (1 Piney Point-Nanjemoy aquifer well, 

6 Aquia aquifer wells, and 2 Upper Patapsco aquifer wells) for 

Table 5. Root-mean-squared-error (RMSE) values for the 

transient ground-water-flow model simulation. 

[USGS, U.S. Geological Survey]

USGS well 

number Aquifer (model layer)

RMSE, 

in feet

SM Dg 21 Piney Point-Nanjemoy aquifer (3) 1.19

SM Df 1 Aquia aquifer (5) 7.45

SM Df 61 Aquia aquifer (5) 10.98

SM Df 80 Aquia aquifer (5) 5.90

SM Df 95 Aquia aquifer (5) 6.08

SM Dg 10 Aquia aquifer (5) 7.30

SM Dg 14 Aquia aquifer (5) 8.27

SM Df 84 Upper Patapsco aquifer (7) 2.42

SM Df 100 Upper Patapsco aquifer (7) 1.69

Figure 8. Observed and model-simulated hydrographs for well 

SM Dg 21 screened in the Piney Point-Nanjemoy aquifer from the 

transient simulation. (Well locations shown in figure 7.)
18 Simulation of Ground-Water Flow at the Naval Air Station Patuxent River, St. Mary’s County, Maryland

Figure 9. Observed and model-simulated hydrographs for six wells screened in the Aquia aquifer from the transient simulation. 

(Well locations shown in figure 7.)
Ground-Water-Flow Model 19

Figure 10. Observed and model-simulated hydrographs for two wells screened in the Upper Patapsco aquifer from the transient 

simulation. (Well locations shown in figure 7.)

each sensitivity analysis simulation to compare the observed 

water levels to the simulated water levels.

The sensitivity analysis indicates that the model-simulated water levels are most sensitive to decreases in the Kh,

and large decreases (two orders of magnitude) in general-head 

boundary conductance (fig. 11). The model-simulated water 

levels are also sensitive to increases in withdrawal rates, and 

the two orders-of-magnitude increase in the Kh and Kv of the 

confining units (layers 2, 4, and 6).

Model-simulated water levels were least sensitive to 

increases or decreases in the Kh of the upper and middle 

confining units, decreases in Kh and Kv of all confining units, 

decreases in withdrawal rates, increases or decreases in Kh of 

layer 3, increases in general-head boundary conductance, or 

increases in the Kh of layer 5 (fig. 11). The sensitivity analysis 

is limited because it was conducted on the steady-state simulation. Thus, the sensitivity of the model to changes in the 

storage coefficient could not be tested.

The sensitivity analysis also demonstrates the appropriateness of using the general-head boundary for the model 

boundary conditions. When using a general-head boundary, it 

is important to use an appropriate head value and conductance 

value. If the general-head boundary conductance is too high, 

the general-head boundary will act like a constant-head boundary, causing water levels in the boundary cells to remain constant even when stresses, such as withdrawal rates, increase. 

In contrast, if the general-head boundary conductance is 

too low, the general-head boundary will act like a no-flow 

boundary, causing greater drawdowns than would realistically be expected when stresses increase. For this model, an 

appropriate general-head boundary conductance is necessary 

so that the boundary does not act like either a constant head 

boundary or a no-flow boundary; that is, both water levels and 

fluxes should change when model stresses change, since the 

stresses are near the boundary. As the general-head boundary 

conductance increases, the RMSE does not change (fig. 11), 

and as the general-head boundary conductance decreases by 

two orders of magnitude, the RMSE increases dramatically, 

indicating that the general-head boundary begins to act like 

a no-flow boundary (fig. 11). The sensitivity analysis of the 

general-head boundary conductance indicates that within 

the range of values used, the general-head boundary was 

appropriate.

Model Limitations

The model is limited by the validity of the conceptual 

model, the design of the ground-water-flow model, and the 

accuracy of the input parameters. Specific issues and assumptions that may limit the model include: (1) the model was 

designed to simulate ground-water levels and fluxes in the 

aquifers beneath the NAS Patuxent River. The model was calibrated to water levels measured at the NAS Patuxent River, 

and nearby monitoring wells. If the model area is increased, 

re-calibration would be necessary; (2) the model assumes that 

the no-flow boundary between the Upper Patapsco aquifer and 

the confining unit below is a reasonable representation; however, given the complex nature of the fluvial sediments of the 

Patapsco Formation, if leakage to or from the deeper aquifers 

does occur, it is not accounted for in the model; (3) the model 

assumes that the surficial aquifer water levels are constant 

over time and mimic land-surface elevations; (4) the model 

assumes that using an average Kh is appropriate. In reality, 

there are likely heterogeneities in hydraulic conductivities; and 

(5) the model assumes that withdrawal rates outside the main 

air station are accounted for in the heads of the general-head 

boundaries, or they are far enough outside the model boundary 

so that they do not affect the modeled area. 
20 Simulation of Ground-Water Flow at the Naval Air Station Patuxent River, St. Mary’s County, Maryland

Figure 11. Results of the steady-state ground-water-flow model sensitivity analysis showing root-meansquared-error (RMSE) values for the sensitivity-analysis simulations.
Ground-Water-Flow Model 21

Water Budget

The water budget of the ground-water-flow model 

describes the sources and sinks of ground water in the flow 

system. The overall water budget for stress period 106, time 

step 4 of the transient simulation, which represents December 

2002 conditions, is shown in table 6. The results of the simulation indicate that there are three inflows of water into the modeled system: general head boundaries, storage, and constant 

head cells. Ninety-seven percent of the inflow is through the 

general-head boundaries, 2 percent is from storage, and 1 

percent is through the constant-head cells. Flows out of the 

modeled system are through pumping wells and general-head 

boundaries. The pumping wells account for 64 percent of the 

outflow, and the general-head boundaries account for the other 

36 percent.

A more detailed budget analysis of the part of the Piney 

Point-Nanjemoy, Aquia, and Upper Patapsco aquifers that 

underlie the main air station is summarized in figure 12. The 

schematic shows net flows in and between the model layers 

for model stress periods 2, 22, and 106 from the transient 

model, which represent simulations of the periods 1920–1940, 

1995, and December 2002, respectively. For this analysis, the 

net inflows and outflows, or net water budgets, are subdivided 

into 3 zones within each model layer: the area on the land side 

of the main air station, the area directly underlying the main 

air station, and the shore side of the main air station (figure 5). 

Net flows directly from the land side of the main air station 

to the shore side of the main air station are not shown in 

figure 12.

The simulated net inflows and outflows for the period 

1920 to 1940 represent pre-pumping conditions in the aquifer 

system. There are no simulated withdrawals from any of the 

aquifers. There is minimal flow vertically between the aquifers 

and confining units. For the Piney Point-Nanjemoy and Aquia 

aquifers, the net flow is from the land side of the main air station to the shore side of the main air station. In the Patapsco 

aquifer, the net flow is from the shore side of the main air station to the land side (fig. 12).

Between 1940 and 1995, there were many changes in 

the simulated net inflows and outflows as withdrawals of the 

Piney Point-Nanjemoy and Aquia aquifers began and continued to increase. In 1995, the rate of withdrawal from the 

Piney Point-Nanjemoy aquifer was 5.5 x 103 ft3/d (cubic feet 

per day) and the withdrawal rate from the Aquia aquifer was 

98 x 103 ft3/d. This caused the hydraulic gradients to change 

the net flow directions in both aquifers to be towards the area 

underlying the base from both the land side and the shore side 

of the main air station. All of the net vertical flows increased 

to accommodate the large increase in withdrawal from the 

Aquia aquifer. The magnitude of the net horizontal flow also 

increased by as much as 35 times the amount simulated in 

1940 (fig. 12).

Between 1995 and 2002, the rate of withdrawal from the 

Piney Point-Nanjemoy aquifer decreased from 5.5 x 103 ft3/d 

to 0.2 x 103 ft3/d, and the rate of withdrawal from the Aquia 

aquifer decreased from 98 x 103 ft3/d to 90 x 103 ft3/d (fig. 12). 

The decrease in withdrawal rates decreases the net flow from 

the shore side to the area underlying the main air station from 

all three aquifers. The net vertical flows to the Aquia aquifer 

from the lower and middle confining units were slightly higher 

in 2002 than in 1995 (fig. 12).

The Upper Patapsco aquifer was not pumped within the 

model area through the end of 2002. The net flux into and 

out of the Upper Patapsco is controlled either by withdrawal 

upgradient from the model area, or flows vertically up through 

the lower confining unit to the Aquia aquifer. The upgradient 

withdrawals are represented in the model by the changing 

potentiometric surfaces used to calculate the specified heads 

for the general-head boundaries for the transient simulation. 

Large regional increases in ground-water withdrawal, likely 

from both the Upper Patapsco and Aquia aquifers, from 1940 

to 1995 and 2002 have increased the net rate of flow through 

the Upper Patapsco aquifer that underlies the NAS Patuxent 

River, as shown in figure 12.

Table 6. Water budget for the entire model domain for stress period 106 (December 2002) of the transient model.

[ft3/d, cubic feet per day]

Inflows Outflows

Component ft3

/d percent Component ft3/d percent

Storage 9,843 2 Storage 0

Constant-head boundaries 2,746 1 Constant-head boundaries 0

Wells 0 Wells 261,039 64

General-head boundaries 393,041 97 General-head boundaries 144,591 36

Total 405,631 100 Total 405,630 100

Total inflows - outflows 1
22 Simulation of Ground-Water Flow at the Naval Air Station Patuxent River, St. Mary’s County, Maryland

Figure 12. Simulated net inflows and outflows, in cubic feet per day, for the parts of the Piney PointNanjemoy, Aquia, and Upper Patapsco aquifers that underlie the Naval Air Station Patuxent River. 

(Negative values indicate flow out of the model.)
Optimization Model 23

Optimization Model

Optimization modeling of aquifer systems links groundwater-flow models with optimization methods. This approach 

allows the development of optimization strategies that 

optimize ground-water utilization while minimizing aquifer 

stress to be tested (Barlow, 2005). Deninger (1970) was the 

first to use the combination of a ground-water-flow model and 

optimization methods for the management of water resources. 

He developed an optimization model to maximize water 

withdrawals from a well field subject to certain limitations 

on drawdown. Since Deninger’s approach was developed, 

there have been over 100 studies in which ground-waterflow and optimization models were combined to manage the 

ground-water resource (Gorelick, 1983; Wagner, 1995; Banks 

and Dillow, 2001; Czarnecki and others, 2003; Granato and 

Barlow, 2005; Andreasen, 2007).

There are four main components of an optimization 

model. The first component is defining the objective function. 

Typical objective functions for optimization models include 

minimizing well construction or pumping costs, maximizing 

water withdrawals, or minimizing hydrologic impacts. The 

second component is defining the constraints of the optimization model. Several types of constraints may be specified, 

including hydrogeologic, withdrawal (balance), integer, and 

withdrawal-rate bounds. A combination of constraints may 

need to be used in order to achieve the goal of the objective 

function, and to avoid non-uniqueness of an optimization 

model. The third component is defining the decision variables. 

The decision variables describe the parameters that control the 

solution to the optimization model. The fourth component is 

to develop the formulation statement. The formulation statement combines all of the other three components by relating 

the objectives of the design, the constraints of the design, and 

the goals of the design to each other (Ahlfeld and Mulligan, 

2000).

Linear optimization software translates the formulation 

statement into mathematical equations that are solved to determine the optimal solution. A response matrix method is used 

to transform the optimization problem into a linear or mixed 

integer formulation that is written into an ASCII file in MPS 

(Mathematical Programming System) format. The MPS file is 

read into the linear optimization software that generates a file 

that contains the optimal solution. The solution is translated 

back to a form that can be read by the ground-water modeling software. For the optimization models developed for the 

NAS Patuxent River and discussed later in this report, LINDO 

(Schrage, 1997; HyperLINDO/PC, 1998; Lindo Systems, Inc., 

2001) is used to solve the objective function formulation, and 

then MODMAN (MODFLOW MANagement) (Greenwald, 

1998a, 1998b) interfaces between LINDO and MODFLOW.

Response Function

The concept and use of the response function is critical to 

the implementation of the linear or mixed integer optimization 

programming methodology. Linear response theory in confined ground-water-flow systems, such as the one that underlies NAS Patuxent River, is based on the principle of linear 

superposition. This theory specifies first, that an increase in 

the withdrawal rate by a factor increases drawdown at any 

given cell by the same factor and second, that drawdown 

induced by withdrawal from more than one well is equal to 

the sums of drawdown induced by the withdrawal from each 

individual well (Greenwald, 1998a). Linear superposition is 

applicable to both the transient and the steady-state versions of 

the NAS Patuxent River ground-water-flow model. 

Coefficients are calculated at each well by applying a 

withdrawal rate and then determining the drawdown at each 

control location. This withdrawal rate is referred to as the unit 

stress or unit rate. The drawdown response at each control 

location is equal to the unmanaged head minus the head resulting from the unit rate. The unit response is equal to the drawdown response divided by the unit rate. This is the drawdown 

resulting from a rate of one unit. Thus, the drawdown due 

to the actual withdrawal, which is referred to as the induced 

drawdown, is equal to the unit response times the well rate.

Application

Two hypothetical optimization scenarios were designed 

and evaluated for NAS Patuxent River. The optimization 

model was based on a steady-state simulation of December 

2002 conditions (withdrawals and general-head boundary 

heads) using the calibrated model. The overall goals of the 

optimization model were to (1) demonstrate the potential 

utility of optimization models, and (2) optimize ground-water 

withdrawals for two scenarios at NAS Patuxent River given 

specific constraints while minimizing drawdown in the Aquia 

aquifer at Lexington Park. The objective of the first scenario 

was to optimize the withdrawal from wells, while minimizing 

the drawdown in the local potentiometric surface of the Aquia 

aquifer. The objective of the second scenario was to determine 

the optimal location for a hypothetical new well for increased 

withdrawals in the eastern-northeastern part of the main air 

station while minimizing the drawdown at control nodes along 

the western boundary of the main air station.

Scenario 1: Minimize Drawdown of Local Heads

The objective of this scenario was to optimize the 

withdrawal from three groups of main air station wells, while 

minimizing the drawdown in the local potentiometric surface 
24 Simulation of Ground-Water Flow at the Naval Air Station Patuxent River, St. Mary’s County, Maryland

of the Aquia aquifer. The objective was achieved by minimizing drawdown at a control node (row 67, column 22) (figs. 5 

and 13) in layer 5 (Aquia aquifer) located at the western edge 

of the base and adjacent to St. Mary’s Metropolitan Commission production wells at Lexington Park.

The constraints specified included three types—

hydrogeologic, balance, and withdrawal-rates bounds. At the 

control node location, a hydrogeologic constraint of 10 ft of 

drawdown was set as the maximum limit. The other two types 

of constraints are discussed below.

There are two types of production wells at the NAS 

Patuxent River. The bulk of the production is from 15 wells 

that are separated into three groupings, which operate as 

individual units. These groupings are referred to as the “A,” 

”B,” and “C” groups (fig. 13, table 7) and their rates will be 

managed by the optimization model. Another eight production wells are sole-source, site-specific wells and are required 

to pump a specific amount of water. Withdrawals from these 

eight wells, and nine wells located off the main air station in 

Lexington Park, were not optimized by the model. Withdrawals from these unmanaged wells totaled 178,379 ft3

/d (table 8). 

Balance constraints were applied to the three production 

well groupings. The air station continues to be a receiver base 

as a result of BRAC, with workforce population potentially 

increasing by 9,000 above the 2002 population of 19,000. 

This workforce population increase results in an increased 

demand for water. For this scenario, it was assumed that this 

is a 25-percent increase above the 2002 production levels for 

each of the three production well groups. Thus, this would be 

a balance constraint of 34,000; 59,000; and 26,000 ft3/d for the 

A, B, and C groups, respectively (fig. 13). Total withdrawals 

from the three groups at the main air station are 119,000 ft3/d 

(table 7).

Two types of withdrawal-rate-bounds constraints were 

applied to all 15 managed wells. It was assumed, for this 

scenario, that for maintenance purposes, each of the 15 wells 

needed to be pumped at an average minimum rate of 

1,000 ft3/d. A maximum withdrawal constraint was also set for 

each managed well. This rate was determined by increasing 

the maximum average monthly rate for the period 1995–2002 

by 10 percent. The maximum withdrawal constraint for each 

well is shown in table 7. 

The optimization algorithm of the LINDO program 

calculated that pumping the managed wells at the rates shown 

in table 7 and figure 14 attains a minimum drawdown for the 

control node of 5.7 ft. Four of the managed wells are pumped 

at maximum capacity, another two are pumped at lower rates, 

and the other nine are pumped at the minimum rate necessary 

for pump maintenance. The unmanaged wells were pumped at 

the December 2002 rate (table 8). The optimization program 

calculated that the minimum drawdown caused by a 25-percent increase in withdrawals over the December 2002 rates 

from the managed wells was 5.7 ft at the control location.

Scenario 2: Locate a Second Well for the 

Northeast Area in the Aquia Aquifer

In this scenario, an optimal location resulting in the least 

amount of drawdown at eight control node locations for a second Aquia aquifer well in the northeast part of NAS Patuxent 

River near production well SM Dg 19 was selected. The 

optimized location resulted in the least amount of drawdown 

at the eight control nodes.

In scenario 1, three well groupings were optimized to 

accommodate a possible increase in base withdrawals at the 

NAS Patuxent River (fig. 13). The well groupings are in the 

central and western parts of the main air station. Well withdrawals in the northeast part of the main air station were not 

optimized. In this scenario, there is a hypothetical need for an 

increased total withdrawal of 66,800 ft3/d in the northeast part 

of the main air station. For this scenario, well SM Dg 19 is 

pumped at 33,400 ft3/d, half of the hypothetical withdrawal of 

66,800 ft3/d. For the period 1995 through 2002, the maximum 

average monthly pumping rate for SM Dg 19 was 23,797 ft3/d. 

The optimization program was used to determine the best location of a second well also pumping at 33,400 ft3

/d and located 

near well SM Dg 19 so that the wells could be tied to the same 

distribution system. Ten candidate locations near well SM 

Dg 19 were distributed in an approximate circle around well 

SM Dg 19, as shown in figure 15. The management model 

was used to determine which of these sites produced the least 

amount of drawdown at the eight control nodes located along 

the western boundary of the main air station (fig. 15). 

 The well-rate-bound and drawdown constraints from 

scenario 1 were used in this scenario. Additionally, seven more 

drawdown constraint nodes were added to the problem. These 

control nodes are located outside the perimeter of the main air 

station (fig. 15). The candidate well locations were specified 

with head limits, where the heads in the cells cannot fall below 

the top of the aquifer (approximately 375 ft below sea level).

The optimal location for the additional well is also 

shown in figure 15. The effect of the additional well and well 

SM Dg 19 (pumping at a combined rate of 66,800 ft3/d), an 

increase of 43,000 ft3/d above the rate well SM Dg 19 alone 

withdrew, resulted in an additional drawdown of about 0.2 ft 

at the control node location that was used in both scenarios. 

Predicted drawdown at well SM Dg 19 due to the combined 

withdrawal at well SM Dg 19 and the additional well was 

about 49 ft.
Optimization Model 25

Figure 13. Groupings of wells (A, B, and C) screened in the Aquia aquifer and control node for hypothetical optimization 

scenario 1 at the Naval Air Station Patuxent River, Maryland.
26 Simulation of Ground-Water Flow at the Naval Air Station Patuxent River, St. Mary’s County, Maryland

Table 7. Hypothetical scenario 1: optimization model managed wells, steady-state ground-water-flow model withdrawal rates, and 

optimal withdrawal rates from the optimization model.

[USGS, U.S. Geological Survey; ft3/d, cubic feet per day] 

USGS well 

number Row Column Layer Group

Steady-state model 

withdrawal rate, 

in ft3/d

Maximum withdrawal 

constraint rate, 

in ft3/d

Optimal optimization 

model withdrawal rate, 

in ft3/d

SM Df 98 52 22 5 A 10,369 29,400 29,400

SM Df 95 59 33 5 A 9,117 23,500 1,600

SM Df 1 69 26 5 A 1,055 13,000 1,000

SM Df 61 64 19 5 A 5,916 10,700 1,000

SM Df 94 60 24 5 A 397 17,900 1,000

Total 26,854 94,500 34,000

SM Df 96 32 50 5 B 13,847 38,500 38,000

SM Df 10 36 37 5 B 2,378 14,900 14,900

SM Df 99 39 44 5 B 9,050 12,700 3,100

SM Df 43 47 51 5 B 2,227 9,700 1,000

SM Df 93 51 41 5 B 13,562 38,700 1,000

SM Df 97 43 42 5 B 5,444 13,400 1,000

Total 46,508 127,900 59,000

SM Dg 16 57 83 5 C 12,499 27,900 23,000

SM Dg 17 60 67 5 C 2,833 10,600 1,000

SM Dg 15 60 71 5 C 2,792 16,000 1,000

SM Dg 18 63 77 5 C 2,998 22,000 1,000

Total 21,122 76,500 26,000

Table 8. Hypothetical scenario 1: optimization model unmanaged 

wells, steady-state ground-water-flow model withdrawal rates, 

and withdrawal rates for the optimization model.

[USGS, U.S. Geological Survey; ft3/d, cubic feet per day]

USGS well 

number Row Column Layer

Optimization model and 

steady-state model 

withdrawal rate, 

in ft3/d

SM Df 39 60 59 3 57

SM Df 42 76 15 5 17,887

SM Df 62 53 3 5 69,545

SM Df 64 51 9 3 15

SM Df 76 72 9 5 19,866

SM Df 78 74 18 5 13,903

SM Df 80 78 61 5 6,254

SM Df 86 71 17 5 33,783

SM Dg 9 15 90 5 6,122

SM Dg 13 78 65 5 7,660

SM Dg 14 13 93 5 1,222

SM Dg 19 24 108 5 457

SM Dg 20 35 87 3 13

SM Dg 21 14 68 3 91

SM Dg 22 30 74 5 128

SM Ef 82 97 54 5 1,243

SM1989G029 97 5 5 133

Total 178,379
Optimization Model 27

Figure 14. Optimal solution for hypothetical optimization scenario 1 at Naval Air Station Patuxent River, Maryland. [The 

number next to wells is the optimized withdrawal rate in ft3/d (cubic feet per day). The optimized withdrawal rate at all other 

managed wells is 1,000 ft3/d.]
28 Simulation of Ground-Water Flow at the Naval Air Station Patuxent River, St. Mary’s County, Maryland

Figure 15. Location of ten potential well sites, including the optimal well site, for hypothetical optimization scenario 2 at 

Naval Air Station Patuxent River, Maryland.
Acknowledgments 29

Suggestions for Future Water-Supply 

Assessment

Water use continues to increase in southern Maryland and 

appropriations for new withdrawals have transitioned from the 

Aquia to the Upper Patapsco aquifer. For continued maximum 

benefit to the NAS Patuxent River, these changes would need 

to be incorporated into future ground-water-flow and optimization models. Since the modeling for this study was done, 

upgrades to the calibration process (Hill and others, 2000), 

and optimization modeling (Ahlfeld and others, 2005) have 

been made and could be incorporated into future modeling. 

Withdrawals from the Upper Patapsco aquifer at both the main 

air station and in surrounding communities have increased 

since 2002. The effects of these increased withdrawals could 

be assessed by use of the ground-water-flow and optimization 

models to properly manage the resource. Additionally, other 

non-hypothetical management scenarios with more complex 

constraints could be evaluated as wells at the main air station are installed or de-commissioned, or as withdrawal rates 

change. Additional constraints related to well efficiency, or 

saltwater intrusion, for example, could be applied. The models 

are also useful tools for understanding the regional groundwater-flow system in southern Maryland, and the effects of the 

NAS Patuxent River withdrawals on that flow system.

Summary and Conclusions

In southern Maryland, the Piney Point-Nanjemoy, Aquia, 

and Upper Patapsco aquifers are three of the six principal 

aquifers tapped for potable water in this area. These are also 

the three aquifers upon which the Naval Air Station (NAS) 

Patuxent River relies for their water supply. Water levels in 

these aquifers are below sea level (NAVD 88), and in the 

case of the Aquia aquifer, are as much as 170 feet below sea 

level, in the vicinity of Lexington Park, Maryland. The planners and engineers within the NAS Patuxent River Public 

Works Department are attempting to limit withdrawals by 

NAS Patuxent River so that they have minimal impact on the 

regional water levels within these three aquifers. To evaluate the effect of NAS Patuxent River withdrawals on the 

local flow system, the U.S. Geological Survey developed a 

ground-water-flow model. In order to minimize the effect of 

the NAS Patuxent River withdrawals on the local potentiometric surface of the Aquia aquifer, while still meeting the 

withdrawal needs of the main air station, the ground-waterflow model was coupled with an optimization model.

The ground-water-flow model for NAS Patuxent River 

includes the main air station and the immediate surroundings, including Lexington Park. The model is discretized into 

102 rows by 118 columns. The intersection of adjacent rows 

and adjacent columns forms cells that are 250 by 250 feet on 

a side. The model in the vertical dimension is discretized into 

seven layers. Thus, there are a total of 84,252 cells, each with 

an area of about 1.4 acres. The model layering includes the 

three aquifers that are the source for the main air station water 

supply, the Piney Point-Nanjemoy, Aquia, and Upper Patapsco 

aquifers. A transient simulation representing 1900 through 

2002 was calibrated to match simulated heads to observed 

heads over that period. 

A steady-state ground-water-flow simulation was used 

to test the sensitivity of the model to various input parameters. The results of the model sensitivity analysis indicate 

that model-simulated heads are not sensitive to: increases or 

decreases in the horizontal hydraulic conductivity of the upper 

and middle confining units, decreases in the horizontal and 

vertical hydraulic conductivity of all confining units, decreases 

in withdrawal rates, increases or decreases in the horizontal 

hydraulic conductivity of layer 3, increases in general-head 

boundary conductance, or increases in the horizontal hydraulic 

conductivity of layer 5. In contrast, model-simulated heads 

are sensitive to: decreases in the horizontal hydraulic conductivity and large decreases (two orders of magnitude) in 

general-head boundary conductance. The model-simulated 

water levels also are sensitive to increases in withdrawal rates, 

and a two-orders-of-magnitude increase in the horizontal and 

vertical hydraulic conductivity of the confining units (layers 2, 

4, and 6).

The steady-state ground-water-flow simulation was 

linked to the optimization model using MODMAN software. 

Two hypothetical optimization scenarios were evaluated. The 

first scenario was designed to determine the optimal pumping rates for wells screened in the Aquia aquifer within three 

supply groups (15 total wells) to meet a 25-percent increase 

in withdrawal demands, while minimizing the drawdown at a 

control location just outside the main air station boundary. The 

resulting optimal solution determined that pumping six wells 

above the rate required for maintenance produced the least 

amount of drawdown at the control location.

The second hypothetical scenario was designed to determine the optimal location for an additional well in the Aquia 

aquifer in the northeastern part of the main air station. The 

additional well was needed to meet an increase in withdrawal 

of 43,000 cubic feet per day. The optimization model was 

used to determine the optimal location for the new well, out 

of a possible 10 locations, while minimizing drawdown in the 

control nodes outside the western boundary of the main air 

station. The optimal location is about 1,500 feet to the eastnortheast of the existing well.

Acknowledgments

The authors would like to thank the many personnel at 

Naval Air Station Patuxent River in the Public Works Department and the Environmental Support Group who assisted the 

project over the past 10 years. In addition, the authors thank 

the many reviewers of this report for their helpful comments, 
30 Simulation of Ground-Water Flow at the Naval Air Station Patuxent River, St. Mary’s County, Maryland

especially David Andreasen of the Maryland Geological 

Survey, and Charles Dunning of the U.S. Geological Survey 

Wisconsin Water Science Center.

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Professional Paper 1404–E, 45 p.

Wagner, B.J., 1995, Recent advances in simulation-optimization groundwater management modeling: U.S. National 

Report to IUGG, 1991–1994, Rev Geophysics. v. 33 suppl., 

American Geophysical Union, p. 1021–1028.

Walton, W.C., 1970, Groundwater resource evaluation: New 

York, McGraw-Hill Book Co., 664 p.

Weigle, J.M., and Webb, W.E., 1970, Southern Maryland 

records of selected wells, water levels and chemical analyses of water: Maryland Geological Survey Basic Data 

Report No. 4, 48 p. 

Williams, J.F., III, 1979, Simulated changes in water level in 

the Piney Point aquifer in Maryland: Maryland Geological 

Survey Report of Investigations No. 31, 49 p.
Glossary 35

Glossary

aquifer A saturated unit that is part of one or 

more formations and yields water in sufficient 

quantity to be a viable source of potable water 

(Walton, 1970, p. 29).

conductance (on general-head boundary) A 

combination of several parameters in Darcy’s 

law so that Darcy’s law can be expressed as:

Q = C(h2 - h1)

where

Q	 is the flow (L3 T-1);

h1 - h2 is the head difference across 

the length of the boundary 

(L); and

C is conductance (L2 T-1) and is 

defined as:

C = KA / L

where 

K is the hydraulic conductivity 

of the material in the 

direction of flow (L T-1);

A is the cross-sectional area 

perpendicular to flow (L2); 

and

L	 is the length of the flow

path (L) (McDonald and 

Harbaugh, 1984, p. 130).

confining unit Arbitrarily defined as a 

geologic layer in which the hydraulic conductivity is less than about 3 x 10-2 ft/d (Fetter, 

1994, p. 110). Generally, ground water moves 

through confining layers very slowly.

hydraulic conductivity The volume of water 

that moves in a unit of time through a unit 

cross section under a unit hydraulic gradient 

(L3 T-1/L2).

porosity The part of the rock or sediment 

that is void space and is expressed as a percentage of the total volume (Domenico and 

Schwartz, 1990).

specific capacity The productivity of a 

well, given as the pumping rate of the well per 

unit of drawdown (from Freeze and Cherry, 

1979, p. 313–314).

specific yield Aquifer tests are not normally 

performed on new wells. Newly installed 

wells are typically pumped at a set rate for 

a few hours and the maximum drawdown is 

recorded, however. The pumping rate divided 

by the drawdown is the specific yield (Fetter, 

1994, p. 256).

transmissivity The volume of water that 

passes through a vertical section of unit width 

through the full thickness of the aquifer 

under a unit head (egg unit hydraulic gradient 

of 45 degrees) per day and is expressed in 

units of cubic feet per foot of thickness per 

day (L3 T-1L±), or in its reduced form as feet 

squared per day (ft2/d).
36 Simulation of Ground-Water Flow at the Naval Air Station Patuxent River, St. Mary’s County, Maryland

Appendix 1. Specific Capacity Analysis

There were 186, 83, and 7 specific capacity analyses 

for the Piney Point-Nanjemoy, Aquia, and Upper Patapsco 

aquifers, respectively, for an area extending about 10 miles 

outward from the NAS Patuxent River. The median, first 

quartile, and third quartile values of the calculated hydraulic 

conductivity values are shown in table A1. 

Within the confines of the model area, there were 11 

specific capacity analyses for the Piney Point-Nanjemoy 

aquifer. From these 11 analyses, hydraulic conductivity values 

were calculated using equations 1 and 2. The median hydraulic conductivity value for the Piney Point-Nanjemoy aquifer 

in the model area is 15 feet per day as indicated in table A1. 

Similarly, the median value for the Aquia aquifer in the model 

area is 20 feet per day. There is only one value for the Upper 

Patapsco aquifer in the model area, 45 feet per day.

References

Johnson, E.E., Inc., 1966, Ground water and wells (1st ed.): 

Saint Paul, Minnesota, Edward E. Johnson, Inc., 440 p.

Kozeny, Josef, 1933, Theorie und berechnung der brunnen: 

Wasserkraft und Wasserwirtschaft, v. 28, no. 9, p. 101–105.

Theis, C.V., 1963, Estimating the transmissivity of a watertable aquifer from the specific capacity of a well: U.S. 

Geological Survey Water Supply Paper 1536–I, p. 332–336.

Hydraulic conductivities for the three principal aquifers 

that are used in the area of NAS Patuxent River were determined from specific capacity analysis. Theis (1963) developed 

an equation to calculate transmissivity from specific capacity:

T = 2.3Y

4 log 2.25Ttr2

S

(1)

where

T is transmissivity (L2 T-1);

Y	 is specific capacity for fully penetrating well

(L2 T-1);

t is time (T);

r is pumping well radius (L); and

S is aquifer storativity (dimensionless).

This equation assumes that the well is screened across 

the full thickness of the aquifer. To account for wells screened 

across only a part of the aquifer, a correction was made using 

the Kozeny equation (Johnson, 1966, p. 134; Kozeny, 1933, p. 

104):

Y = Yp

p 1+ 7 r

2bp

0.5

cos

b

2

(2)

where

Yp	 is specific capacity for a well partially

screened across full thickness (L2 T-1);

b is aquifer thickness (L); and 

p is the ratio of the screen to the aquifer 

thickness (dimensionless).

Table A1. Statistical estimates of horizontal hydraulic conductivity calculated from specific capacity values.

Aquifer and area

Horizontal hydraulic conductivity (feet per day)

Number of values Median First quartile Third quartile

Piney Point-Nanjemoy Aquifer

Local area 186 20 12 42

Model area 11 15 10 17

Aquia Aquifer

Local area 83 28 20 50

Model area 30 20 20 50

Upper Patapsco Aquifer

Local area 7 24 18 39

Model area 1 45 Not calculated Not calculated


Prepared by West Trenton, NJ Publishing Service Center.

Edited by Valerie M. Gaine.

Graphics by Timothy W. Auer.

Layout by Denis K. Sun.

For additional information, contact:

Director, MD-DE-DC Water Science Center

U.S. Geological Survey

5522 Research Park Drive

Baltimore, MD 21228

or visit our Web site at:

http://md.water.usgs.gov