U.S. Department of the Interior

U.S. Geological Survey

Fact Sheet 2005–3095

August 2005

Use of Simulation-Optimization Modeling to Assess Regional 

Ground-Water Systems

By Paul M. Barlow

Increasing—and often competing—demands on the Nation’s 

ground-water resources are creating a need for improved 

scientific information and analysis techniques to better understand and manage ground-water systems. Since the 1960s, 

numerical simulation models have been important tools for the 

assessment of ground-water flow systems and ground-water 

development strategies. Commonly, these models are used to 

test specific water-resource management plans, or, in a trialand-error approach, to select a single plan from a few alternative plans that best meets management goals and constraints. 

Because of the complex nature of ground-water systems, 

however, and the large number of engineering, legal, and economic factors that often affect ground-water development and 

management, the process of selecting a best operating procedure 

or policy can be extremely difficult. To address this difficulty, 

ground-water simulation models have been linked with 

optimization-modeling techniques to determine best (or optimal) management strategies from among many possible strategies. Optimization models explicitly account for water-resource 

management objectives and constraints, and have been referred 

to as management models (Ahlfeld and Mulligan, 2000).

The use of combined simulation-optimization models greatly 

enhances the utility of simulation models alone by directly 

incorporating management goals and constraints into the modeling process (fig. 1). In the simulation-optimization approach, 

the modeler specifies the desired attributes of the hydrologic 

and water-resource management systems (such as minimum 

streamflow requirements or maximum allowed ground-waterlevel declines) and the model determines, from a set of several 

possible strategies, a single management strategy that 

best meets the desired attributes. In some cases, 

however, the model may determine that 

none of the possible strategies are able 

to meet the specific set of management goals and constraints. Such 

outcomes, while often not desirable, can be useful for identifying 

the hydrologic, hydrogeologic, 

and management variables that 

limit water-resource development 

and management options.

Because of their usefulness for 

evaluating complex hydrogeologic 

and water-resource management systems, simulation-optimization models 

have been developed to assess various 

types of regional ground-water management 

problems, such as

• Ground-water-level declines and aquifer-storage depletions 

• Conjunctive use of ground-water and surface-water 

resources

• Saltwater intrusion

• Ground-water contamination

• High ground-water levels

Combined simulation-optimization models also can be used to 

determine tradeoffs between various hydrologic constraints and 

future uses of the Nation’s ground-water resources.

The U.S. Geological Survey (USGS) has been an important 

contributor to the development and application of both simulation and simulation-optimization models for assessment of 

ground-water flow systems. These models advance our understanding of hydrologic systems and hydrologic processes, and 

provide a scientific basis for determining how water-resource 

development affects hydrologic systems. Recently, simulationoptimization models have been applied to the important issue 

of ground-water sustainability—a broad topic that includes 

the interaction between hydrologic systems, water-resource 

management decisions, environmental impacts, and emerging 

technologies (National Research Council, 2000). Two case 

studies from Rhode Island and Arkansas are described in 

the following sections to demonstrate the use of simulationoptimization modeling in USGS investigations. Additional 

applications to ground-water management issues in Wisconsin 

and California are given in Walker and others (1998) and Reichard and others (2003), respectively. The final section of this Fact 

Sheet describes a new computer program to facilitate 

simulation-optimization modeling.

EFFECTS OF MINIMUM 

STREAMFLOW CRITERIA ON 

GROUND-WATER PUMPING, 

BIG RIVER BASIN, 

RHODE ISLAND

Shallow, high-yielding 

sand and gravel aquifers are 

an important source of water 

for many communities of the 

northeastern United States. 

Typically, ground-water wells that 

pump water from these aquifers are 

located close to streams and rivers that 

are in direct hydraulic connection with the 

Figure 1. Principal steps in the development and 

application of a ground-water simulation-optimization model.

Page 1

Sheet describes a new computer program to facilitate 

Identify water-resource 

management problem

Collect and analyze hydrologic 

and hydrogeologic data

Collect water-resource

management information

Develop and calibrate a 

ground-water 

simulation model 

Define objectives and constraints 

of the water-resource management

 (optimization) model

Link simulation and optimization models

Apply simulation-optimization 

model
in figure 2). The values of the minimum streamflow rates were 

varied in a series of model runs to test several criteria that are 

being considered by the State.

Ground-water pumping rates were calculated for several 

model runs (fig. 3). Each streamflow criterion is plotted on 

figure 3 as the minimum amount of streamflow required at each 

of the four streamflow-constraint sites per square mile of drainage area to each site. For the criteria shown in figure 3, modelcalculated average annual pumping rates from the basin ranged 

from a minimum of about 5 Mgal/d (million gallons per day) for 

the most restrictive criteria to a maximum of about 15 Mgal/d 

for the least restrictive. The graph indicates that relatively small 

changes in the streamflow criteria can result in large changes 

in model-calculated pumping rates. For example, a decrease in 

total pumping of almost 4 Mgal/d was calculated for an increase 

in the streamflow requirement from 0.65 cubic feet per second 

of streamflow per square mile of drainage area (ft3

/s/mi2) to 

0.72 ft3/s/mi2. The nonlinear shape of the graph results from the 

unique hydrologic and hydrogeologic characteristics of the Big 

River Basin and the specific set of well sites and streamflow 

locations used in the simulation-optimization model. The results 

shown on the figure would have been difficult to determine by 

use of a simulation model alone.

ESTIMATION OF SUSTAINABLE YIELD FROM THE 

MISSISSIPPI RIVER VALLEY ALLUVIAL AQUIFER, 

SOUTHEASTERN ARKANSAS

The Mississippi River Valley alluvial aquifer underlies an area 

of about 32,000 square miles in eastern Arkansas and several 

adjacent States. Historically, the aquifer has provided large 

volumes of water for agriculture in Arkansas. Because of heavy 

demands placed on the aquifer, water levels have declined in 

several areas. In some places, these declines have resulted in 

decreasing water availability, lower well yields, and degraded 

water quality. In response to these water-level declines, several 

counties in southeastern Arkansas that lie within the extent of 

underlying ground-water system. Pumping from these wells 

reduces streamflow by capturing ground water that would 

otherwise discharge to the streams and, in some cases, by 

drawing water out of the streams and into the adjoining aquifer.

Streamflow reductions caused by ground-water pumping can 

be an environmental problem when such reductions decrease 

the amount of water that is available to aquatic and riparian 

communities below minimum levels required to sustain healthy 

ecosystems. In response to such reductions, many States and 

communities are attempting to define minimum streamflow 

criteria that are protective of aquatic and riparian habitats. For 

example, the State of Rhode Island recently developed minimum streamflow standards that protect the biological, chemical, and physical integrity of the State’s waters, but also allow 

for maximum sustainable use of these waters. One area of the 

State to which these standards may be applied is the Big River 

Basin (fig. 2), which is a largely untapped and potential future 

source of water for the State. The USGS, in collaboration with 

the Rhode Island Water Resources Board, recently developed 

a simulation-optimization model for the basin to determine the 

relation between minimum streamflow criteria and groundwater withdrawals (Granato and Barlow, 2005). 

The simulation-optimization model was developed to 

determine the maximum amount of ground water that could 

be pumped from 13 wells distributed across the basin while 

simultaneously maintaining minimum streamflow rates at four 

locations in the basin (referred to as streamflow-constraint sites 

Page 2

0 10 MILES

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RHODE

ISLAND

42O00'

71O45'

71O15'

41O30'

STUDY AREA

Boundary of active area of simulation model

 Flat River 

Reservoir

Lake Mishnock

Carr River

Mishnock River

Big River

41O

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0

0

1 MILE

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SIMULATED STREAM, POND, OR LAKE

INACTIVE CELL

STREAMFLOW-CONSTRAINT SITE

SIMULATED PRODUCTION WELL

EXPLANATION

Figure 2. Well sites and streamflow locations, Big River Basin, Rhode 

Island. Figure modified from Granato and Barlow (2005).

Figure 3. Relation between minimum streamflow criteria and total 

ground-water withdrawals calculated by the optimization model of the 

Big River Basin, Rhode Island. Each open circle on the figure represents a model run. Figure modified from Granato and Barlow (2005).

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MINIMUM STREAMFLOW CRITERION, 

IN CUBIC FEET PER SECOND PER SQUARE MILE OF 

DRAINAGE AREA

AVERAGE ANNUAL GROUND-WATER 

WITHDRAWALS, IN MILLION GALLONS PER DAY
areas of the aquifer to dewater, as shown by the dry areas of the 

model in figure 5A. In contrast, simulated water levels resulting 

from withdrawal rates determined by the simulation-optimization model yielded no dewatered areas (fig. 5B). These results 

illustrate how the model can assist water managers in determining pumping rates that prevent dewatering of the aquifer. 

GWM—A NEW GROUND-WATER MANAGEMENT 

PROCESS FOR MODFLOW

Several computer codes have been developed during the past 

two decades to facilitate ground-water simulation-optimization 

modeling (Lefkoff and Gorelick, 1987; Greenwald, 1998; Zheng 

and Wang, 2002; Ahlfeld and Riefler, 2003; Peralta, 2004). 

These codes differ in the numerical model used to represent the 

ground-water flow system and the types of ground-water management problems that can be solved.

Recently, the USGS worked collaboratively with researchers 

at the University of Massachusetts and Woods Hole Oceanographic Institution to develop a new optimization-modeling 

process for the widely used MODFLOW ground-water simulation model developed by the USGS (Harbaugh and others, 

2000). The new process, which is called the Ground-Water 

Management (GWM) process (Ahlfeld and others, 2005), 

can be applied to a broad range of ground-water management problems, such as limiting ground-water-level declines 

or streamflow depletions, managing ground-water withdrawals, and conjunctively using ground water and surface water. 

Management variables that can be specified in GWM include 

withdrawal and injection wells, artificial-recharge basins, and 

imports and exports of water. The types of constraints that 

the alluvial aquifer have been designated Critical Ground-Water 

Areas by the Arkansas Soil and Water Conservation Commission (ASWCC) (Czarnecki and others, 2003). This designation is made in areas where ground-water-level declines have 

reduced the original (predevelopment) saturated thickness of the 

aquifer by more than 50 percent.

The effects of ground-water withdrawals on continued water 

availability from the alluvial aquifer are major concerns of 

water managers, water users, and the general public. These 

concerns have resulted in a continued cooperative effort by the 

ASWCC, the U.S. Army Corps of Engineers, and the USGS to 

develop, maintain, and utilize models to analyze the groundwater system and to provide information to assist water managers and policy makers to manage the ground-water resources. 

An important component of this cooperative effort has been 

the estimation of the sustainable yield of the aquifer, which is 

defined as the rate at which water can be withdrawn from the 

aquifer indefinitely without lowering water levels to less than 

half the predevelopment saturated thickness of the aquifer or 

reducing streamflow in hydraulically connected streams below 

minimum specified flow rates. 

A simulation-optimization model was developed as the basis 

for estimating the sustained yield of the aquifer. The model covers a 3,800-square-mile area lying south of the Arkansas River 

(fig. 4). The objective of the management model was to maximize water withdrawals from wells pumping from the alluvial 

aquifer and from two streamflow-withdrawal sites, one on the 

Arkansas River and the second on Bayou Bartholomew. Modelcalculated withdrawals were limited, however, by several management constraints. First, for consistency with the ASWCC 

designation, water levels in the aquifer were required to remain 

higher than half the predevelopment saturated thickness of the 

aquifer. Second, simulated streamflows along the Arkansas 

River and Bayou Bartholomew were required to remain above 

minimum levels regulated by the ASWCC for purposes of maintaining water quality, navigation, and species habitat. Finally, 

maximum allowed withdrawal rates were specified at 1,841 

model cells where wells were simulated. Total withdrawals from 

the aquifer within the modeled area were 73.5 million cubic feet 

per day (Mft3/d) in 1997, which was the baseline simulation 

period selected for the study.

The combined simulation-optimization model determined 

withdrawal rates at each of the 1,841 simulated well locations 

for three scenarios. In each of these scenarios, the maximum 

withdrawal rate allowed at each withdrawal location was equal 

to 100, 150, and 200 percent of the total 1997 withdrawal rate, 

respectively. Model results indicated that the sustainable yield 

of the aquifer is dependent on the maximum withdrawal rate 

allowed at the well sites; the yield increased from 70.3 Mft3

/d 

for maximum withdrawal rates equal to 100 percent of the 1997 

withdrawal rates to 110.2 Mft3

/d for maximum withdrawal rates 

equal to 200 percent of the 1997 withdrawal rates. The model 

also indicated that the unmet demand of 3.2 Mft3/d for the first 

scenario, which is equal to the 1997 total withdrawal rate 

(73.5 Mft3/d) minus the optimal withdrawal rate calculated by 

the model (70.3 Mft3/d), could be satisfied by stream withdrawals, but these would require the construction of withdrawal and 

distribution facilities.

Simulated water levels calculated for the 1997 withdrawal 

rates differed in several respects from those calculated on the 

basis of withdrawal rates determined for the first management 

scenario. For example, the 1997 withdrawal rates caused some 

Page 3

Figure 4. Location of Mississippi River Valley alluvial aquifer in southeastern Arkansas. Figure modified from Czarnecki and others (2003).

Drew

Ashley

Desha

Chicot

Lincoln

Bradley

Jefferson

Arkansas

Union

Union

Morehouse

BolivarWashington Phillips

West CarrollEast Carroll

Issaquena

Active Model

Area Boundary

ARKANSAS

LOUISIANA

MISSISSIPPI

LOUISIANA

ARKANSAS

MISSISSIPPI

Base from U.S. Geological Survey digital data, 1:100,000

Study

Area

Arkansas

River

Saline River

Bayou Bartholomew

M ississippi

River

0 1 5 0 20 MILES

0 1 5 0 20 KILOMETERS

92o91o

33o

34o
can be specified include upper and lower bounds on pumping and injection rates, water-supply demands, hydraulic-head 

constraints such as drawdowns and hydraulic gradients, and 

streamflow and streamflow-depletion constraints. GWM uses a 

widely applied technique called the response-matrix approach to 

solve ground-water management problems.

The GWM code and supporting documentation can be 

accessed on the internet at http://water.usgs.gov/nrp/gwsoftware/mf2k-gwm/MF2K-GWM.html. Additional ground-water 

software developed by the USGS is provided at http://water.

usgs.gov/software/ground_water.html. 

REFERENCES CITED

Ahlfeld, D.P., Barlow, P.M., and Mulligan, A.E., 2005, GWM—A ground-water 

management process for the U.S. Geological Survey modular ground-water 

model (MODFLOW-2000): U.S. Geological Survey Open-File Report 2005-

1072, 124 p.

Ahlfeld, D.P., and Mulligan, A.E., 2000, Optimal management of flow in 

groundwater systems: San Diego, CA, Academic Press, 185 p.

Ahlfeld, D.P., and Riefler, Guy, 2003, Documentation for MODOFC—A 

program for solving optimal flow control problems based on MODFLOW 

simulation, version 2.3: Amherst, MA, University of Massachusetts Department of Civil and Environmental Engineering, 48 p.

Czarnecki, J.B., Clark, B.R., and Stanton, G.P., 2003, Conjunctive-use optimization model of the Mississippi River Valley alluvial aquifer of southeastern 

Arkansas: U.S. Geological Survey Water-Resources Investigations Report 

03-4233, 26 p.

Granato, G.E., and Barlow, P.M., 2005, Effects of alternative instream-flow criteria and water-supply demands on ground-water development options in the 

Big River area, Rhode Island: U.S. Geological Survey Scientific Investigations Report 2004-5301, 110 p.

Greenwald, R.M., 1998, Documentation and user’s guide–MODMAN, an optimization module for MODFLOW, version 4.0: Freehold, NJ, HSI GeoTrans, 

112 p.

Harbaugh, A.W., Banta, E.R., Hill, M.C., and McDonald, M.G., 2000, MODFLOW-2000, the U.S. Geological Survey modular ground-water model 

— User guide to modularization concepts and the ground-water flow process: U.S. Geological Survey Open-File Report 00-92, 121 p.

Lefkoff, L.J., and Gorelick, S.M., 1987, AQMAN-Linear and quadratic 

programming matrix generator using two-dimensional ground-water flow 

simulation for aquifer management modeling: U.S. Geological Survey 

Water-Resources Investigations Report 87-4061, 164 p.

National Research Council, 2000, Investigating groundwater systems on 

regional and national scales: Washington, DC, National Academy Press, 

143 p.

Peralta, R.C., 2004, Simulation/Optimization Modeling System (SOMOS): 

Logan, UT, Utah State University Department of Biological and Irrigation 

Engineering, accessed July 28, 2004, at URL http://www.engineering.usu.

edu/bie/

Reichard, E.G., Land, Michael, Crawford, S.M., Johnson, Tyler, Everett, R.R., 

Kulshan, T.V., Ponti, D.J., Halford, K.J., Johnson, T.A., Paybins, K.S., and 

Nishikawa, Tracy, 2003, Geohydrology, geochemistry, and ground-water 

simulation-optimization of the Central and West Coast Basins, Los Angeles 

County, California: U. S. Geological Survey Water-Resources Investigations 

Report 03-4065, 184 p.

Walker, J.F., Saad, D.A., and Krohelski, J.T., 1998, Optimization of groundwater withdrawal in the Lower Fox River communities, Wisconsin: U.S. 

Geological Survey Water-Resources Investigations Report 97-4218, 24 p.

Zheng, Chunmiao, and Wang, P.P., 2002, MGO—A Modular Groundwater 

Optimizer incorporating MODFLOW and MT3DMS, Documentation and 

user’s guide: Tuscaloosa, AL, The University of Alabama and Groundwater 

Systems Research Ltd., 118 p.

Page 4

A. B.

92o 91o

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34o

92o 91o

0 1 5 0 20 MILES

0 1 5 0 20 KILOMETERS

ARKANSAS

LOUISIANA

MISSISSIPPI

MISSISSIPPI

ARKANSAS

LOUISIANA

181 to 200

161 to 180

141 to 160

121 to 140

101 to 120

81 to 100

61 to 80

51 to 60

Dry area

HYDRAULIC HEAD

ALTITUDE, IN FEET Arkansas River

Saline River

Bayou Bartholomew

Bayou Bartholomew

Arkansas River

Saline River

River

River

M ississippi

M ississippi

Hydraulic head altitude relative to National Geodetic Vertical Datum 1929

EXPLANATION

Figure 5. Simulated water levels in 

the Mississippi River Valley alluvial 

aquifer using (A) 1997 withdrawal 

rates and (B) sustainable-yield withdrawal rates calculated with the 

optimization model. Figure modified 

from Czarnecki and others (2003).

Additional information on USGS ground-water programs 

and activities can be found at http://water.usgs.gov/ogw/, 

or by contacting

Office of Ground Water 

U.S. Geological Survey

411 National Center

12201 Sunrise Valley Drive

Reston, VA 20192

(703) 648-5001