0 5 10 KILOMETERS

0 5 10 MILES

Biscayne Bay

ATLANTIC OCEAN

EVERGLADES

NATIONAL

PARK

N

Model boundary

Biscayne aquifer

NOT TO SCALE

Rainfall

Lateral

boundary

flow

Evapotranspiration

Canal

Canal

Municipal

well fields

Recharge Submarine

groundwater

discharge

Freshwater

Brackish water

Seawater

Water table

Biscayne Bay

Surface water in Everglades

FLORIDA

Model

boundary

U.S. Department of the Interior

U.S. Geological Survey

Fact Sheet 2009–3105

November 2009 Printed on recycled paper

U.S. Geological Survey Groundwater Modeling Software:

Making Sense of a Complex Natural Resource

Computer models of groundwater systems simulate the flow of groundwater, including water levels, and the transport of 

chemical constituents and thermal energy. Groundwater models afford hydrologists a framework on which to organize their 

knowledge and understanding of groundwater systems, and they provide insights water-resources managers need to plan 

effectively for future water demands (fig. 1). Building on decades of experience, the U.S. Geological Survey (USGS) 

continues to lead in the development and application of computer software that allows groundwater models to address 

scientific and management questions of increasing complexity. 

Figure 1.  A conceptual model (above) of groundwater discharge to Biscayne

Bay, Florida, forms the basis for a computer model (right) that simulates groundwater salinity in the coastal aquifer. Colors on map denote the transition from

freshwater (tan) to seawater (red). (Figure modified from Langevin, 2001.)

Groundwater Flow and Transport Modeling: 

Moving From Paper to Silicon

C.V. Theis (1935) of the USGS recognized that the flow of 

groundwater through porous materials is analogous to the flow 

of heat through conductive solids and deduced the equation 

that describes the hydraulic response of an idealized aquifer to 

a pumping well. Early groundwater models based on variations 

of Theis’ formula represented highly simplified hydrogeologic 

conditions (Bredehoeft, 1976).

In the 1950s and 1960s, USGS hydrologists and others 

took further advantage of physical and mathematical analogies 

to create more realistic models of complex groundwater systems.

These analog models cleverly exploited the properties of rubber 

sheets, resistance paper, electrolyte solutions, viscous fluids, 

and networks of resistors and capacitors to mimic the effects 

of hydrologic processes such as seawater intrusion, thermal 

convection, evapotranspiration, and flow through multilayered 

aquifers (Prickett, 1976).

As computers became increasingly powerful, affordable, 

and widely available in the 1960s and 1970s, many hydrologists 

turned to digital, or numerical, groundwater modeling. Most of 

the early numerical models were based on the finite-difference 

method, which is easy to understand and is founded on the same 

mathematical principles as the relatively expensive resistorcapacitor network models the method eventually supplanted 

(Prickett, 1976). The first groundwater modeling program 

developed at the USGS simulated flow in two dimensions 

(Pinder, 1969). Five years later, Trescott (1975) published a 

program that simulated three-dimensional flow. This program

1970s First USGS groundwaterflow modeling software

First USGS geochemical

analysis software, WATEQ

First publicly available USGS

solute-transport modeling software
Figure 2.  A model based on

MODFLOW and MODPATH

simulates groundwater

flow in the Middle Rio

Grande Basin. Twelve

“hydrogeochemical zones”

(colored) denote waters

of different origins and

compositions. The zones

were identified using

a combination of

geochemical

sampling and

groundwater

modeling. (Figure

modified from

Sanford and

others, 2004.)

0 10 20 KILOMETERS

0 10 20 MILES

Albuquerque NEW MEXICO

Model

area

N

was widely used and underwent numerous modifications as USGS 

investigators adapted it to the needs of their groundwater studies.

The early 1970s also saw the arrival of software for 

simulating movement of chemical constituents, or solute 

transport, in groundwater (Bredehoeft and Pinder, 1973; 

Rubin and James, 1973). A program developed by Konikow 

and Bredehoeft (1978) was the first publicly available USGS 

solute-transport simulator.

By the early 1980s, numerical groundwater modeling was 

commonplace, and a number of programs were available to 

model typical conditions in a variety of aquifer systems. Differences in computer architecture and programming languages, 

inconsistent documentation, and variations in input-data 

requirements and output-data formats, however, complicated 

attempts to share programs and adapt them to new applications.

Researchers at the USGS undertook to resolve this 

difficulty, and in the winter of 1983 the USGS released to the 

public a modular three-dimensional finite-difference groundwater flow model, or MODFLOW (McDonald and Harbaugh, 

1984). The program was written in the popular FORTRAN 

programming language to ensure its portability across a variety 

of computing platforms, and it was designed with a modular 

structure to facilitate the addition of new capabilities. In time, 

these attributes enabled MODFLOW to evolve into the most 

widely used groundwater modeling program in the world.

Geochemical Modeling: Focusing a Powerful Lens 

on Water Quality

As numerical modeling of groundwater flow gained 

momentum in the 1960s, so did the use of fundamental 

principles of aqueous geochemistry in the study of natural 

groundwater (Back and Cherry, 1976). Mathematical models 

of aqueous geochemistry, along with numerical solute-transport 

models, significantly expanded the array of tools available to 

hydrologists investigating water quality.

The chemical makeup of groundwater is the result of interactions between water and the various materials it encounters as 

it moves through the hydrologic cycle, such as gases, minerals, 

natural and manmade contaminants, and biological agents. 

The advent of computer programs that can solve the nonlinear 

equations of aqueous chemical equilibrium led to widespread 

use of a class of models called speciation models. Given 

concentrations of basic chemical components determined by 

laboratory analysis of a groundwater sample, along with temperature and other relevant environmental conditions, programs 

such as WATEQ (Truesdell and Jones, 1974) can estimate the 

equilibrium concentrations of dissolved chemical species and 

the tendency of solid minerals to precipitate or dissolve. Despite 

their limitations, speciation models provide important clues to

the chemical processes that affect the composition of groundwater (Truesdell and Jones, 1974; Back and Cherry, 1976). 

The next advance in geochemical modeling was to go 

beyond purely aqueous calculations and simulate the reaction 

of water with minerals and gases. Given an analyzed water 

composition, programs such as PHREEQE (Parkhurst and 

others, 1980) can estimate what the composition of water would 

be if it were to equilibrate with a specified set of minerals and 

gases. Geochemists use the results of such “forward” modeling, 

which proceeds from specified initial concentrations to computed final concentrations, to infer the origins, mobility, and 

toxicity of chemicals in groundwater under various conditions.

The chemistry of groundwater depends in large part on how 

it flows through the subsurface (fig. 2). Thus, geochemistry can 

provide valuable insight into the origins of groundwater and the 

paths along which it flows. The computer program NETPATH 

(Plummer and others, 1991) facilitates understanding of the 

relations between groundwater flow and chemistry by allowing 

“inverse” modeling of waters encountered along a hydrologic 

flow path. Given an initial water composition, or a set of waters 

that can be mixed together, and information regarding the minerals 

and gases that can enter or leave the water, NETPATH computes 

all possible mixing proportions and net geochemical mass-balance

reactions that can account for an observed final water composition.

WATEQ, PHREEQE, NETPATH and their derivatives 

have been used widely both inside and outside of the USGS. 

These programs have been modified since their initial releases 

to include an ever-widening array of processes, including ion 

exchange, sorption, solid solutions, environmental isotopes, 

and reaction kinetics.

1980s PHREEQE geochemical

analysis software

SUTRA and HST3D variable-density

flow and transport modeling software

First version

of MODFLOW

MODFLOW packages: PCG solver,

subsidence, and stream

“Perhaps the most significant development 

in the field of water-quality hydrology 

during the 1970’s was the increasing use 

of mathematical modeling techniques.”

—J.D. Hem (1985)
Today’s Modeling Software

In formulating a groundwater model of a specific hydrologic system, the hydrologist must choose which features and 

processes to include and the spatial and temporal scales at 

which to represent them based on the purpose of the study. A 

model that omits important characteristics of the groundwater 

system will not accurately simulate the behavior of interest, 

whereas one that includes unnecessary detail will be unwieldy 

and inefficient.

The variety of software developed by the USGS reflects 

the broad spectrum of applications that groundwater models 

are called upon to address. Some programs are designed to be 

adaptable to a wide range of complex problems. MODFLOW, 

the USGS’s flagship groundwater-flow simulator, includes more 

than 20 “packages” and “processes” that have been added by 

individuals and groups both inside and outside of the USGS 

to take into account hydrologic processes such as land subsidence caused by groundwater withdrawals, interaction of 

aquifers with streams and lakes, and agricultural water use. 

General-purpose programs that simulate both flow and transport 

include SEAWAT, SUTRA, and HST3D, which account for 

the effects of variable density; PHAST, which includes multicomponent geochemical reactions; BIOMOC, which computes 

biodegradation of contaminants; HYDROTHERM, which 

simulates heat transport and flow of both liquid water and water 

vapor; VS2DT, which allows detailed representation of the 

unsaturated zone; and MODFLOW-GWT, which adds solutetransport capabilities to MODFLOW. The program MODPATH 

complements MODFLOW by computing particle tracks from 

simulated flow fields. Other programs, such as PHREEQC, are 

designed to efficiently carry out calculations in more restricted 

geometries or under specific hydrologic conditions.

Relevant, Dependable, and Freely Available

The distributed, application-driven approach to USGS 

groundwater modeling software development encourages 

innovation and results in programs that are versatile and 

relevant to today’s water-resources problems. Every program 

is fully documented and peer reviewed to ensure quality before 

it is released to the public. Upon release, the program and its 

documentation and source code are available free-of-charge 

at http://water.usgs.gov/software/lists/groundwater/.

A Rich Variety of Applications

Groundwater modeling software plays an integral 

role in the USGS’s research projects and cooperative waterresources studies with various Federal, State, and local 

agencies. Applications range from the highly practical to the 

theoretical (table 1). The resulting models not only provide 

tools for addressing specific water-management problems, 

but also shed light on broader issues related to the availability 

and sustainability of the Nation’s groundwater resources. These 

issues include quantity and quality of groundwater and surface 

water, environmental preservation, land use, and water rights 

(Alley and others, 1999; Reilly and others, 2008).

Among the many scientific investigations that have relied 

on USGS modeling capabilities, one of the largest and most 

fruitful was the Regional Aquifer-System Analysis (RASA) 

Program. Between 1978 and 1995, USGS investigators created 

groundwater-flow and geochemical models to define the 

regional hydrogeology and establish a framework of geologic, 

hydrologic, and geochemical information for 25 of the Nation’s 

major aquifer systems (Sun and Johnston, 1994). These models 

1990s MODFLOW packages, including new solvers, generalized

finite-difference, rewetting, and reservoir

NETPATH geochemical

inverse modeling software

MODPATH particle

tracking software

All USGS groundwater modeling software is fully 

documented and available free-of-charge at

http://water.usgs.gov/software/lists/groundwater/.

Table 1.  Applications of USGS groundwater modeling software range from support of management decisions to cutting-edge research.

Evaluation of water-management alternatives1 Demonstration of general hydrologic principles3

Effects of groundwater withdrawals on 

water levels and native vegetation

Effects of groundwater withdrawals on discharge 

to streams and springs

Conjunctive management of groundwater 

and surface-water resources

Importance of transient groundwater response 

times in long-term planning

Management responses to saltwater intrusion Importance of post-auditing and updating 

groundwater models

Hydrogeologic and geochemical characterization2 Basic research4

Evaluation of changes to the water budget of an 

aquifer resulting from changes in land use, 

withdrawals, and climate

Development and testing of new 

modeling techniques

Use of environmental tracers to estimate groundwater age and identify sources of rechargeStudy of the role of groundwater flow and 

chemistry in geologic processes

For more information, please see 1 Galloway and others (2003), 2 Reilly and others (2008), 3 Alley and others (1999), and 4 U.S. Geological Survey (2005).

Photo and image credits, clockwise from upper left: Loren Metzger, USGS; Mark Uhrich, USGS; Christian Langevin, USGS; USGS Office of Human Resources.
compose a solid platform for the critical and never-ending task 

of assessing changes in water availability and are updated as 

modeling techniques improve and environmental conditions and 

societal needs evolve (Reilly and others, 2008). Regional-scale 

RASA models also serve as the basis for more refined models 

designed to address groundwater-resources issues in smaller 

geographic areas.

The Drive to Innovate

The way in which USGS water-resources studies inspire 

and drive new development is exemplified by the advances in 

modeling made in RASA-related projects, in which regional 

scales and broad scientific scope posed a variety of new 

technical challenges. Investigators responded with a series of 

improvements and innovations that included a multiaquifer 

well-simulation technique, an improved method of simulating 

movement of variable-density groundwater, mass-transfer 

and reaction models, and basin geochemical models (Sun and 

Johnston, 1994). These efforts also spawned precursors to 

the widely used “Streamflow-Routing” and “Subsidence and 

Aquifer-System Compaction” packages for MODFLOW.

As the demand for our Nation’s limited water resources 

continues to increase, the expectations placed on groundwater 

models show no sign of abating. In response, the USGS is 

continually developing software that enhances the power and 

utility of groundwater models. Supporting software includes 

graphical user interfaces, more efficient equation solvers, and 

parameter-estimation software that assists in model formulation 

and quantifies the uncertainties inherent in modeling real-life 

groundwater systems. Such advances and innovations help 

hydrologists apply their full understanding to today’s complex 

water-resources problems.

Solving Tomorrow’s Challenges

Scientists’ increasing understanding and society’s growing 

awareness of the interrelatedness of our natural resources 

requires ever-closer integration of the USGS’s multidisciplinary 

approach to fulfilling its scientific mission (U.S. Geological 

Survey, 2008). The need to view water resources in a broader 

context, together with continual advances in computing power, 

is leading to the development of groundwater modeling software that increasingly brings together various fields of earth 

science and applied mathematics. Examples include PHAST, 

which combines three-dimensional groundwater flow with 

transport of reactive contaminants; GSFLOW, which simulates 

coupled groundwater and surface-water flow; the MODFLOW 

GWM process, which solves simulation-optimization problems; 

and the MODFLOW HUF package, which facilitates the integration of geologic information into groundwater models by 

allowing hydrologic properties to be input in terms of hydrogeologic units rather than model layers. As hydrologists design 

tomorrow’s groundwater models to account for interactions 

between hydrologic, chemical, biological, geological, climatic, 

and human influences on ecosystems, USGS software will 

continue to provide the tools they need.

References

Alley, W.M., Reilly, T.E., and Franke, O.L., 1999, Sustainability of ground-water 

resources: U.S. Geological Survey Circular 1186, 79 p.; accessible online in 

November 2009 at http://pubs.usgs.gov/circ/circ1186/ .

Back, William, and Cherry, J.A., 1976, Chemical aspects of present and future hydrogeologic problems, in Saleem, Z.A., ed., Advances in groundwater hydrology, Symposium proceedings: Chicago, American Water Resources Association., p. 153–172.

Bredehoeft, J.D., 1976, Status of quantitative groundwater hydrology, in Saleem, 

Z.A., ed., Advances in groundwater hydrology, Symposium proceedings: 

Chicago, American Water Resources Association, p. 8–14.

Bredehoeft, J.D., and Pinder, G.F., 1973, Mass transport in flowing groundwater: 

Water Resources Research, v. 9, no. 1, p. 194–210.

Galloway, D.L., Alley, W.M., Barlow, P.M., Reilly, T.E., and Tucci, P., 2003, 

Evolving issues and practices in managing ground-water resources—Case 

studies on the role of science: U.S. Geological Survey Circular 1247, 83 p.; 

accessible online in November 2009 at http://pubs.usgs.gov/circ/2003/circ1247/ .

Hem, J.D., 1985, Study and interpretation of the chemical characteristics of natural 

water (3d ed.): U.S. Geological Survey Water-Supply Paper 2254, 264 p.

Konikow, L.F., and Bredehoeft, J.D., l978, Computer model of two-dimensional 

solute transport and dispersion in ground water: Techniques of Water-Resources 

Investigations of the U.S. Geological Survey, book 7, chap. C2, 90 p.

Langevin, C.D., 2001, Simulation of ground-water discharge to Biscayne Bay, 

southeastern Florida: U.S. Geological Survey Water-Resources Investigations 

Report 00–4251, 127 p.; accessible online in November 2009 at http://pubs.

er.usgs.gov/usgspubs/wri/wri004251 .

McDonald, M.G., and Harbaugh, A.W., 1984, A modular three-dimensional 

finite-difference ground-water flow model: U.S. Geological Survey Open-File 

Report 83– 875, 528 p.

Parkhurst, D.L., Thorstenson, D.C., and Plummer, L.N., 1980, PHREEQE—A 

computer program for geochemical calculations: U.S. Geological Survey WaterResources Investigations Report 80–96, 195 p. (revised and reprinted August 1990).

Pinder, G.F., 1969, An iterative digital model for aquifer evaluation: U.S. Geological 

Survey Open-File Report 69–207, 35 p.

Plummer, L.N., Prestemon, E.C., and Parkhurst, D.L., 1991, An interactive code 

(NETPATH) for modeling NET geochemical reactions along a flow PATH: 

U.S. Geological Survey Water-Resources Investigations Report 91– 4078, 227 p.

Prickett, T.A., 1976, Advances in groundwater modeling, in Saleem, Z.A., ed., 

Advances in groundwater hydrology, Symposium proceedings: Chicago, 

American Water Resources Association, p. 102–112.

Reilly, T.E., Dennehy, K.F., Alley, W.M., and Cunningham, W.L., 2008, Groundwater availability in the United States: U.S. Geological Survey Circular 1323, 

70 p.; accessible online in November 2009 at http://pubs.usgs.gov/circ/1323/ .

Rubin, J., and James, R.V., 1973, Dispersion-affected transport of reacting solutes 

in saturated porous media—Galerkin method applied to equilibrium controlled 

exchange in unidirectional steady water flow: Water Resources Research, v. 9, 

no. 5, p. 1332–1356.

Sanford, W.E., Plummer, L.N., McAda, D.P., Bexfield, L.M., and Anderholm, S.K., 

2004, Use of environmental tracers to estimate parameters for a predevelopment 

ground-water-flow model of the Middle Rio Grande Basin, New Mexico: 

U.S. Geological Survey Water-Resources Investigations Report 03– 4286, 102 p.

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the U.S. Geological Survey, 1978 –1992: U.S. Geological Survey Circular 1099, 

126 p.

Theis, C.V., 1935, The relation between the lowering of the piezometric surface 

and the rate and duration of discharge of a well using groundwater storage: 

Transactions of the American Geophysical Union, v. 16, p. 519–524.

Trescott, P.C., l975, Documentation of finite-difference model for simulation 

of three-dimensional ground-water flow: U.S. Geological Survey Open-File 

Report 75– 438, 32 p.

Truesdell, A.H., and Jones, B.F., 1974, WATEQ, a computer program for calculating 

chemical equilibrium of natural waters: Journal of Research of the U.S. Geological Survey, v. 2, no. 2, p. 233–248.

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November 2009 at http://pubs.usgs.gov/fs/2008/3008/ . 

By Alden M. Provost, Thomas E. Reilly, Arlen W. Harbaugh, and 

David W. Pollock

2000s MODFLOW-2000 with

parameter estimation

MODFLOW-2005 with

local grid refinement

Coupling of three-dimensional groundwater flow with variabledensity transport (SEAWAT, SUTRA), reactive transport (PHAST), 

optimization (GWM), and surface-water flow (GSFLOW)