U.S. Department of the Interior

U.S. Geological Survey

Figure 1. Features of an aquifer system that can be simulated by MODFLOW.

Simulation Capabilities of 

MODFLOW 

MODFLOW is designed to simulate 

aquifer systems in which (1) saturatedflow conditions exist, (2) Darcy's Law 

applies, (3) the density of ground water 

is constant, and (4) the principal 

directions of horizontal hydraulic 

conductivity or transmissivity do not 

vary within the system. These conditions 

are met for many aquifer systems for 

which there is an interest in analysis of 

ground-water flow and contaminant 

movement. For these systems, 

MODFLOW can simulate a wide 

variety of hydrologic 

Unconfined and confined aquifers— 

Ground-water flow and storage changes

Faults and other barriers—Resistance to 

horizontal ground-water flow

Fine-grained confining units and interbeds

Confining units—Ground-water flow and 

storage changes

Rivers—Exchange of water with aquifers

Drains and springs—Discharge of water 

from aquifers

Ephemeral streams—Exchange of water 

with aquifers

Reservoirs—Exchange of water with 

aquifers

Recharge from precipitation and irrigation

Evapotranspiration

Wells—Withdrawal or recharge at specified rates

The modular finite-difference groundwater flow model (MODFLOW) developed 

by the U.S. Geological Survey (USGS) is 

a computer program for simulating common 

features in ground-water systems 

(McDonald and Harbaugh, 1988; 

Harbaugh and McDonald, 1996). The 

program was constructed in the early 

1980’s and has continually evolved since 

then with development of many new 

packages and related programs for groundwater studies. Currently, MODFLOW is the 

most widely used program in the world for 

simulating ground-water flow. The 

popularity of the program is attributed 

to the following factors:

The finite-difference method used by 

MODFLOW is relatively easy to understand and apply to a wide variety of realworld conditions. 

MODFLOW works on many different 

computer systems ranging from per-sonal 

computers to super computers.

MODFLOW can be applied as a onedimensional, two-dimensional, or quasior full three-dimensional model.

Each simulation feature of 

MODFLOW has been extensively tested.

Data input instructions and theory are 

well documented.

The modular program design of 

MODFLOW allows for new simulation 

features to be added with relative ease.

A wide variety of computer programs 

written by the USGS, other federal 

agencies, and private companies are 

available to analyze field data and construct input data sets for MODFLOW.

A wide variety of programs are available to read output from MODFLOW and 

graphically present model results in ways 

that are easily understood. 

MODFLOW has been accepted in 

many court cases in the United States as 

a legitimate approach to analysis of 

ground-water systems.

This publication outlines the major features 

of MODFLOW and several related 

programs and gives information on 

obtaining programs and documentation.

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Modeling Ground-Water Flow with Modeling Ground-Water Flow with

MODFLOW and Related Programs MODFLOW and Related Programs

features and processes (fig. 1). Steadystate and transient flow can be 

simulated in unconfined aquifers, 

confined aquifers, and confining units. 

A variety of features and processes such 

as rivers, streams, drains, springs, 

reservoirs, wells, evapotranspiration, 

and recharge from precipitation and 

irrigation also can be simulated. At 

least four different solution methods 

have been implemented for solving the 

finite-difference equations that 

MODFLOW constructs. The 

availability of different solution 

approaches allows model users to select 

the most efficient method 

for their problem.
Application of MODFLOW

MODFLOW simulates ground-water 

flow in aquifer systems using the finitedifference method. In this method, an 

aquifer system is divided into rectangular blocks by a grid (fig. 2). The grid of 

blocks is organized by rows, columns, 

and layers, and each block is commonly 

called a “cell.”

Model Input

For each cell within the volume of the 

aquifer system, the user must specify 

aquifer properties. Also, the user specifies 

information relating to wells, rivers, and 

other inflow and outflow features for cells 

corresponding to the location of the 

features. For example, if the interaction 

between a river and an aquifer system is 

simulated, then for each cell traversed by 

the river, input information includes layer, 

row, and column indices; river stage; and 

hydraulic properties of the river bed.

Model Output

MODFLOW uses the input to 

construct and solve equations of groundwater flow in the aquifer system. The 

solution consists of head (ground-water 

level) at every cell in the aquifer system 

(except for cells where head was specified 

as known in the input data sets) at 

intervals called “time steps.” The head 

can be printed and (or) saved on a 

computer storage device for any time 

step. Hydrologists commonly use water 

levels from a model layer to construct 

contour maps for comparison with similar 

maps drawn from field data. They also 

compare computed water levels at 

parameters. Typically, input parameters are 

adjusted during model calibration using a 

trial-and-error process. This calibration 

process can yield acceptable agreement 

between computed model results and field 

data but is time consuming, may not 

produce parameter values that result in the 

best fit of field data, and does not result in 

quantitative estimates of uncertainty in 

model results and estimated parameter 

values.

Inverse modeling is a more formal 

approach to model calibration that includes 

automatic parameter adjustment in order to 

match field data. Program MODFLOWP 

(pronounced MOD•FLOW•P) is the USGS 

version of MODFLOW that includes 

automatic parameter estimation (Hill, 

1992). MODFLOWP uses a weighted 

least-squares objective function as a 

measure of how well model results agree 

with field measurements. Weights are used 

to reflect reliability of individual 

measurements. Parameters that can be 

estimated by MODFLOWP include 

transmissivity; hydraulic conductivity; 

storage coefficient; vertical leakance; 

vertical and horizontal anisotropy; 

hydraulic conductance between aquifer 

systems and rivers, drains and other 

features; areal recharge; maximum evapotranspiration; pumping; and water levels at 

constant-head boundaries. Measured or 

externally estimated information on 

parameters also can be included. Parameter 

values that minimize the objective function 

(fig. 5) are calculated by MODFLOWP 

using the modified Gauss-Newton method 

or the conjugate-direction method. The 

resulting parameter values are “best-fit” in 

that they provide the closest match between 

measured and simulated heads and flows, 

as measured by the objective function. The 

task of the modeler is to evaluate how well 

these calculated values represent the 

physical system being simulated.

Model output includes estimates of 

parameters and statistics relating to the 

parameter estimates. The statistics can be 

used to quantify the reliability of the 

resulting model, suggest changes in model 

construction, and compare results of 

models constructed in different ways. Postprocessors can be used to calculate 

confidence intervals on predicted heads and 

flows to depict prediction uncertainty.

To effectively use MODFLOWP, an 

understanding of principles of groundwater flow and basic statistics is needed.

individual cells with measured water 

levels from wells at corresponding 

locations to determine model error (fig. 3). 

The process of adjusting the model input 

values to reduce the model error is 

referred to as model calibration.

In addition to water levels, 

MODFLOW prints a water budget for the 

entire aquifer system. The budget lists 

inflow to and outflow from the aquifer 

system for all hydrologic features that 

add or remove water.

Other program output consists of flow 

rates for each model cell. MODFLOW 

can write the flow rates onto a computer 

storage device for any hydrologic feature 

in a simulation. These cell-by-cell flow 

rates commonly are read by postprocessing programs for detailed analysis 

of the simulated ground-water system.

Inverse Modeling with 

MODFLOWP

In conventional or “forward modeling,” 

model parameters (such as aquifer 

properties) are specified and water levels 

and flow quantities are computed (fig. 4). 

For most aquifer systems, however, more 

information is available from field data on 

water levels, flows, and advective transport or ground-water age than on input 

1 2 3 4 5 6 7

Columns 8 9 10 1 2 3 4 5 6 7 8 9

Rows

Layer 3

Layer 2

Layer 1

Cells outside of

aquifer system

Cells inside of

aquifer system

Figure 2. Example of model grid for 

simulating three-dimensional groundwater flow.

Figure 3. Example comparison of computed and measured water levels.

Figure 4. Forward and inverse 

approaches to modeling.

Simulated

water level

Measured

water level

MODEL

PARAMETERS

WATER

LEVEL

AND FLOW

SIMULATION TIME

WATER LEVEL

FORWARD

INVERSE
Particle Tracking with 

MODPATH

Many studies require information such 

as the average rate of movement of 

ground water and contaminants. Also, 

information often is needed on the 

recharge or capture areas for water 

discharging to wells, springs, stream 

reaches, and other features. Although 

MODFLOW does not compute this 

information directly, simulation with 

MODFLOW provides basic information 

needed for such analyses. The particletracking program, MODPATH, is a postprocessing program for MODFLOW to 

estimate flow paths (fig. 6) and times of 

travel in ground-water systems. An 

accompanying program, MODPATHPLOT, displays particle paths, contours, 

and model features.

MODPATH can be used for studies of 

steady-state and transient flows. Common 

applications include studies of paths and 

time of travel of contaminant movement 

(fig. 7); and source (recharge) areas of 

wells, springs, rivers, and other features.

MODPATH can place particles at 

specified locations or generate starting 

locations of arrays of particles in selected 

regions. Particles can be tracked forward 

from starting locations to calculate where 

water is going or backwards to map 

where it came from. Multiple particlerelease times can be used to simulate 

“plumes” of contamination.

Figure 5. Example of an objective 

function and "best-fit" parameter values 

for a linear problem with two parameters.

Figure 7. Application of particle 

tracking to estimate ground-water 

travel time.

VALUE OF PARAMETER 2

VALUE OF PARAMETER 1

VALUE OF OBJECTIVE FUNCTION

Contours of

objective function

Objective-function

surface

“Best-fit” values of parameters 1 and

2 at objective-function minimum

<1 10 100 1,000 10,000 >100,000

SIMULATED GROUND-WATER

TRAVEL TIME, IN YEARS

GRAN

R

I

O

DE

ALBUQUERQUE

Figure 6. Flow paths of particles discharging at two wells. Pathlines were computed 

by MODPATH and are denoted by red and green lines. Blue squares are river cells 

and light blue lines are contours of water levels, in feet above sea level, computed 

by MODFLOW.

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Wells
Solute Transport with 

MOC3D

To evaluate or remediate contaminated aquifers, it is important to be 

able to compute the concentration of 

dissolved chemicals. Hydrologists and 

water managers need to know how 

contaminants will spread in the future, 

or how the concentration distributions 

will respond to changes in the flow 

field that might arise from new watersupply stresses, remediation efforts, or 

other management activities.

MOC3D is a solute-transport program 

that is integrated with MODFLOW and 

has the capability to calculate changes 

in concentration (fig. 8) of a single solute 

as affected by processes of advection, 

dispersion, diffusion, fluid sources, decay, 

and retardation. In addition to input data 

requirements for MODFLOW, the user 

must also define porosity, thickness, 

dispersivity, initial concentrations, and 

source-fluid concentrations. Model output 

includes the calculated concentration 

distribution in space and time.

MOC3D is based on a particletracking method coupled with an 

explicit finite-difference procedure. This 

numerical technique is optimal for 

advection-dominated problems. 

August 1997

References

Appel, C.A., and Reilly, T.E., 1994, Summary 

of selected computer programs produced 

by the U.S. Geological Survey for 

simulation of ground-water flow and 

quality, 1994: U.S. Geological Survey 

Circular 1104, 98 p.

Harbaugh, A.W., and McDonald, M.G., 1996, 

User’s documentation for MODFLOW-96, 

an update to the U.S. Geological Survey 

modular finite-difference ground-water 

flow model: U.S. Geological Survey 

Open-File Report 96–485, 56 p.

Hill, M.C., 1992, A computer program 

(MODFLOWP) for estimating parameters 

of a transient, three-dimensional, groundwater flow model using nonlinear 

regression: U.S. Geological Survey OpenFile Report 91–484, 358 p.

Konikow, L.F., Goode, D.J., and Hornberger, 

G.Z., 1996, A three-dimensional methodof- characteristics solute-transport model 

(MOC3D): U.S. Geological Survey 

Water-Resources Investigations 

Report 96 – 4267, 87 p.

McDonald, M.C., and Harbaugh, A.W., 

1988, A modular three-dimensional finitedifference ground-water flow model: U.S. 

Geological Survey Techniques of WaterResources Investigations, book 6, chap. 

A1, 586 p.

Pollock, D.W., 1994, User’s guide for 

MODPATH/MODPATH-PLOT, version 

3: a particle tracking post-processing 

package for MODFLOW, the U.S. 

Geological Survey finite-difference 

ground-water flow model: U.S. 

Geological Survey Open-File Report 

94–464, 234 p.

Reports documenting USGS model 

programs can be purchased from

U.S. Geological Survey

Branch of Information Services

Box 25286

Denver, CO 80225-0286

For information on local USGS studies 

and research applications of the 

MODFLOW family of computer 

programs, contact the USGS state 

representative for the area of interest. A 

list of state representatives is available 

from the World Wide Web site 

http://water.usgs.gov/public/wrd011.html/.

—S.A. Leake

USGS Fact Sheet

FS-121-97

Alternative numerical methods are 

planned to broaden the range of types of 

field problems for accurate and efficient 

application of the model.

How to Obtain Ground-Water 

Model Programs, Documentation, and Additional Information

Additional references for USGS 

computer programs for ground-water 

simulation are given by Appel and Reilly 

(1994). Many of the programs including MODFLOW, MODFLOWP, 

MODPATH, and MOC3D are available 

from the USGS at no cost at World Wide 

Web site http://water.usgs.gov/software/.

The site includes links to download 

program source code and compiled 

versions for some computers. Also, some 

of the programs are available by 

anonymous ftp from Internet site 

water.usgs.gov in the directory 

pub/software/ground_water/.

The MODFLOW program obtained 

from the USGS includes most simulation 

capabilities currently documented by the 

USGS. Added features for MODFLOW 

have been documented in separate 

reports. A bibliography of the 

documentation reports is included with 

copies of MODFLOW distributed 

by the USGS.

Contaminant source

Direction of

ground-water flow

Figure 8. Ground-water contaminant concentrations 

computed by MOC3D. Colors represent different 

concentration ranges, with highest contaminant concentrations in red and lowest 

concentrations in blue.