METHOD AND COMPUTER PROGRAMS TO IMPROVE 

PATHLINE RESOLUTION NEAR WEAK SINKS 

REPRESENTING WELLS IN MODFLOW AND MODPATH 

GROUND-WATER-FLOW SIMULATIONS

By Frederick J. Spitz

U.S. GEOLOGICAL SURVEY 

Open-File Report 00-392

West Trenton, New Jersey 

2001
DEPARTMENT OF THE INTERIOR

GALE A. NORTON, Secretory

U.S. GEOLOGICAL SURVEY

Charles G. Groat, Director

For additional information Copies of this report can be 

write to: purchased from:

District Chief U.S. Geological Survey

U.S. Geological Survey Branch of Information Services

Mountain View Office Park Box 25286, Building 810

810 Bear Tavern Road Denver, CO 80225-0286

Suite 206

West Trenton, NJ 08628
PREFACE

This report documents computer programs to improve pathline resolution near weak sinks 

representing wells when using MODPATH, a particle-tracking simulation package for 

MODFLOW, the modular finite-difference ground-water-flow model. Information on obtaining 

and installing the computer programs can be found in appendix 1 of this report.

The computer programs have been tested successfully on models of hypothetical and 

actual ground-water systems; however, future applications of the programs could reveal problems 

that were not detected or anticipated in the test simulations. Users are requested to notify the U.S. 

Geological Survey (USGS) if problems are found. Correspondence should be sent to

U.S. Geological Survey 

810 Bear Tavern Road, Suite 206 

West Trenton, NJ 08628 

Telephone: (609) 771-3900 

Internet: http://nj.usgs.gov

Although these programs have been used by the USGS, no warranty, expressed or implied, 

is made by the USGS or the United States Government as to the accuracy and functioning of the 

programs and related program material. Nor shall the fact of distribution constitute any such 

warranty, and no responsibility is assumed by the USGS in connection therewith.
CONTENTS

Page

Abstract............................................................................................................................................!

Introduction......................................................................................................................................!

Method development.......................................................................................................................3

Technical considerations and limitations.........................................................................................5

Computer programs .........................................................................................................................6

Organization and structure...................................................................................................6

Fortran code.............................................................................................................8

Input and output files ...............................................................................................9

Program compatibility .............................................................................................9

Operation .............................................................................................................................9

Setup instructions................................................................................................... 11

Procedure............................................................................................................... 12

Error checking........................................................................................................14

Sample problem.............................................................................................................................14

Description......................................................................................................................... 14

Analysis of capture areas and pathlines............................................................................. 15

Summary and conclusions .............................................................................................................21

References cited.............................................................................................................................23

Appendix 1. Obtaining and installing the computer programs......................................................24

Appendix 2. Interactive menu responses for sample problem.......................................................25

Appendix 3. Input files for sample problem..................................................................................28

Appendix 4. Output files for sample problem ...............................................................................35

ILLUSTRATIONS

Figure 1. Diagram showing model cells representing a weak sink and a strong sink.............2

2. Plan view of model grid around cell representing pumped well in the original

model and the submodel ....................................................................................4

3. Plan view of particle locations and pathlines in the submodel and the original

model .................................................................................................................5

4. Flowchart showing nested rediscretization method for determining capture areas of 

wells...................................................................................................................7

5. Diagram of simulated hypothetical flow system................................................... 14

6. Map view of capture area of the weak sink well in the original model determined 

with MODPATH..............................................................................................16

7. Map view of capture area of the strong sink well in the original model determined 

with the nested rediscretization method...........................................................16

8. Map view of pathlines inside the weak sink cell in the original model determined 

with MODPATH..............................................................................................18

9. Profile view of pathlines inside the weak sink cell in the original model determined 

with MODPATH..............................................................................................18
CONVERSION FACTORS

Multiply

foot (ft)

foot per day (ft/d)

square foot (ft2)

square foot per day (ft2/d)

cubic foot (ft3 )

cubic foot per second (ft3/s)

cubic foot per day (ft3/d) 

million gallons per day (Mgal/d)

By To obtain

0.3048 meter

0.3048 meter per day

0.0929 square meter

0.0929 square meter per day

0.0283 cubic meter

0.0283 cubic meter per second

0.0283 cubic meter per day

3785.2 cubic meter per day

VI
ILLUSTRATIONS-Continued

Page

10. Map view of pathlines inside the submodel determined with the nested

rediscretization method.................................................................................... 19

11. Profile view of pathlines inside the submodel determined with the nested

rediscretization method.................................................................................... 19

12. Profile view of pathlines inside the submodel showing endpoint locations used in 

particle transfer to the original model..............................................................20

13. Profile view of pathlines inside layer 1 of the original model showing starting

locations generated by particle transfer from the submodel ............................20

TABLES

Table 1. Computer program input and output files.............................................................. 10

2. Maximum travel times to a weak sink well with and without using the nested

rediscretization method.................................................................................... 15
METHOD AND COMPUTER PROGRAMS TO IMPROVE PATHLINE

RESOLUTION NEAR WEAK SINKS REPRESENTING WELLS IN 

MODFLOW AND MODPATH GROUND-WATER-FLOW SIMULATIONS

By Frederick J. Spitz

ABSTRACT

This report documents a method for 

converting weak sinks representing wells to 

strong sinks when using the particle-tracking 

postprocessor MODPATH for the ground-waterflow model MODFLOW. A weak sink is a 

model cell (representing a well, for example) 

that does not discharge at a sufficiently large rate 

to capture all of the flow entering the cell; thus, 

some of the flow leaves the cell across one or 

more of the cell faces. Because of this limitation 

of model discretization, flow paths to weak sink 

cells cannot be uniquely defined, as it is impossible to know whether a specific water particle 

discharges to the sink or passes through the cell. 

Creating a finer discretization of the cell by 

using the nested rediscretization method can 

eliminate this ambiguity by converting the cell 

representing the well into a strong sink. The 

method is presently limited to applications 

involving well sinks, backtracking particle 

endpoint analysis, and steady-state conditions. 

Software for applying the method consists of 

five Fortran programs that are operated 

manually. Program input is a combination of 

data files and interactive keyboard entry. 

Program output consists of a composite endpoint 

file. Application of the method to a sample 

problem demonstrates that the particle-tracking 

results obtained can be more accurate than those 

obtained by using a coarsely discretized model 

alone. This method is a relatively simple alternative to more involved telescopic mesh 

refinement approaches and does not require 

additional information. For certain types of 

problems involving identification of recharge 

source areas, this method can provide improved

pathline resolution with modest effort. This 

method could be adapted for use in simulating 

other types of weak sinks, such as stream cells, 

but each type of sink boundary has unique 

considerations that may have to be treated differently than those described in this report.

INTRODUCTION

The nested rediscretization method is a 

set of computer programs designed to help eliminate weak sinks representing wells when using 

MODPATH (Pollock, 1994), a particle-tracking 

package designed for use with the U.S. 

Geological Survey's modular finite-difference 

ground-water-flow model, MODFLOW 

(Harbaugh and McDonald, 1996a, 1996b). 

Particle-tracking programs are postprocessors to 

ground-water-flow models because they use the 

cell-by-cell flow distribution calculated with the 

model to calculate the ground-water velocity 

distribution throughout the ground-water 

system, which then is used to determine flow 

paths (pathlines) of infinitely small particles. 

Three-dimensional water-particle flow paths are 

calculated in MODPATH by using the flow-field 

results from MODFLOW to track particles from 

user-defined starting locations in the model grid, 

cell by cell, until the particles reach a boundary, 

reach an internal sink/source, or satisfy some 

other termination criterion.

The effects of spatial grid discretization 

limit the level of detail and accuracy of model 

and particle-tracking results. For example, 

spatial discretization effects in MODFLOW 

cause the local flow field around a well to be 

represented insufficiently. This discrepancy is 

the result of a linear velocity interpolation
scheme that cannot reflect that the closer flow is 

to a well in the center of a cell, the greater the 

flow velocity. Also, the well is not precisely 

located within the cell. Similarly, MODPATH 

has limitations resulting from discretization, 

such as those relating to weak internal sinks. A 

weak sink is a cell (representing a well, for 

example) that does not discharge at a sufficiently 

large rate to capture all of the flow entering the 

cell; thus, some of the flow leaves the cell across 

one or more of the cell faces (fig. 1). As a result 

of these conditions, particle flow paths calculated within weak sink cells cannot be uniquely 

defined because it is impossible to know 

whether a specific water particle discharges to 

the weak sink or passes through the cell.

(b)

Flow rate is proportional 

to length of arrow

Figure 1. Model cells representing (a) a weak sink 

and (b) a strong sink.

In MODPATH, the problem of weak 

sinks is resolved by asking the user to arbitrarily 

decide how particles will be treated whenever 

they enter cells with internal sinks: either pass 

through a weak sink, stop at a weak sink, or stop 

at a weak sink where discharge to the sink is 

larger than a specified fraction of the total inflow 

to the cell. If these options are not satisfactory, 

the user could resolve the problem by modifying 

the model so that no weak sinks occur. For 

example, weak sinks can be converted to strong 

sinks by reducing the grid cell size in the vicinity 

of the well. This approach would require additional work and, possibly, recalibration of the 

model because of the effects of a finer discretization on boundary conditions. For manually 

prepared models, modifying the model in this 

manner can be a difficult process. Models 

prepared with graphical-user interfaces (for 

example, Shapiro and others, 1997) can be 

modified with less difficulty if the data used to 

generate the model are stored in a grid-independent fashion. Limitations in the amount of 

overall cell reduction are still possible with this 

approach, however.

I

Various approaches have been used by 

previous investigators to resolve the weak sink 

problem to improve the accuracy of pathlines in 

particle-tracking simulations (Spitz and others, 

in press). For example, the flow velocity distribution in the vicinity of the well can be refined 

mathematically so that all particles that should 

be captured by the well converge toward the 

well. A submodel around the weak sink could 

be designed by using telescopic mesh 

refinement, but this option may not be practical 

because of the amount of additional work 

required, especially if the weak sinks are scattered. Other complications with this approach 

include submodel boundaries that cut across 

original model boundaries, the need for recalibration in the submodel when using headdependent sources and sinks in the original 

model, and the need to rerun the original model 

(and generate new boundary conditions for the 

submodel) if additional detail is incorporated 

into the submodel. Recently developed procedures and software involving telescopic mesh 

refinement with MODFLOW could assist with 

model rediscretizing (Leake and Claar, 1999). 

In this report the terms "original model" and 

"submodel" are used to refer to the larger, 

encompassing model and the smaller, embedded 

model, respectively. In previous studies, other 

terms such as "regional model" and "local 

model" have been used to represent the 

respective models.
The purpose of this study, conducted in 

cooperation with the New Jersey Department of 

Environmental Protection and begun in 1996, is 

to develop an approach to resolve some of the 

weak sink limitations of MODPATH for cells 

representing wells. The approach was to achieve 

this purpose without requiring rediscretion of the 

original model or modification of the original 

model concept by incorporating new data. The 

result, called the nested rediscretization method, 

can be useful when MODFLOW models with 

coarse discretization, such as regional-scale 

models, are used to determine capture areas of 

wells. Advantages of the method presented here 

are that it does not require additional information beyond that specified in the original 

MODFLOW and MODPATH input files, it is 

easy to use, and it provides an unambiguous 

determination of how particles are treated. 

Disadvantages of the method described in this 

report are that it is applicable only to weak sinks 

representing wells in steady-state models. If it is 

important to know which particle enters a sink, 

then more detail must be given than is provided 

in the model. This information could be 

obtained by refining the model.

This report documents the development 

of the nested rediscretization method, describes 

the computer programs and their operation, and 

presents an application of the method to a hypothetical sample problem. The computer 

programs have been tested successfully on 

available models of real-world flow systems that 

consist of surficial aquifer systems with stream 

boundaries and large (500-2,000 ft) grid spacing. 

These real-world systems include glacial valleyfill aquifers (Nicholson and others, 1996) and 

Coastal Plain aquifers in New Jersey (Nicholson 

and Watt, 1997; L.J. Kauffman, U.S. Geological 

Survey, written commun., 2000) and Louisiana 

(R.B. Winston, U.S. Geological Survey, written 

commun., 2000).

Special thanks are given to the following 

USGS colleagues for their insightful technical

comments related to this work: Robert 

Nicholson, Daryll Pope, Anthony Navoy, and 

Herbert Buxton; Leon Kauffman and Richard 

Winston, who reviewed this report; and David 

Pollock, Paul Barlow, Dennis Risser, and Arthur 

Baehr, who reviewed related articles.

METHOD DEVELOPMENT

The nested rediscretization method 

involves refining the discretization of the 

original model at the weak sink to make it a 

strong sink by creating a submodel of the cell 

representing the well, coupling the submodel 

with the original model, and performing a linked 

MODPATH analysis with both models. A 

separate MODFLOW simulation is run with the 

submodel. Flow across the cell faces calculated 

in the original model are used as constant-flux 

boundary conditions in the submodel (fig. 2). 

The well in the original model is replaced by one 

or more constant-head cells in the submodel to 

allow for at least one constant head in the 

submodel. The actual horizontal location of the 

well can be specified and more than one 

constant-head cell is allowed in the vertical 

direction (only one per submodel layer) to 

represent the well. A constant-head cell is 

required to remove the constant flux of water 

entering through the boundaries of the 

submodel. Tests conducted during development 

of the method have shown the center cell of the 

submodel to be the most numerically stable 

position for a constant-head cell. In order to 

maintain a center cell at each rediscretization, 

only odd-numbered submodel dimensions are 

used. For example, the initial rediscretization is 

from 1 layer, 1 row, and 1 column (the original 

model cell) to 3 layers, 3 rows, and 3 columns 

(27-cell submodel); the next finer rediscretization, if necessary, is 5 layers, 5 rows, and 5 

columns (125-cell submodel). The level of 

rediscretization also can be user-defined. Rediscretization can be continued to a total of 99 

layers, 99 rows, and 99 columns (970,299-cell 

submodel).
(a)

L

(b)

-h-

-».

 *.

 \ t t t f

-fr 

-*

A

Constant head

Pumped 

well

Flow across 

cell face

Flow distributed 

across corresponding 

cell faces

Figure 2. Plan view of model grid around cell representing pumped well 

in (a) the original model and (b) the submodel.

The value of hydraulic head assigned to 

the constant-head cell(s) also affects the stability 

of the submodel solution. Although assigning a 

value based on heads in neighboring cells of the 

original model would be advantageous, this 

value might be too low and could cause dry cells 

to result in the submodel. In the absence of dry 

cells, however, the value assigned does not 

affect particle flow patterns in the submodel. 

Accordingly, the value assigned is set equal to 

the simulated head in the cell in the original 

model.

The dimensions of the cells in the 

submodel are calculated from the dimensions of 

the cell in the original model divided by the level 

of rediscretization. A Well Package file (WEL) 

that contains the flow across boundary cell faces 

is created for the submodel. The flow across any 

particular submodel cell face is calculated from 

the flow across the corresponding face in the 

original model divided by the level of rediscretization. If the cell in the original model represents ground water under unconfined conditions, 

the elevation of the top of the submodel is set 

equal to the water-table elevation in the original 

model cell. If the cell in the original model is 

confined, the elevation of the top of the 

submodel is set equal to the elevation of the top

of the cell in the original model cell. Hydraulic 

properties of cells in the submodel are derived 

from the properties of the original model cell. In 

addition, vertical anisotropy can be set for the 

cells in the submodel.

In applying the method for capture-area 

analysis, particles are started from the faces of 

the constant-head cell(s) of the submodel and 

tracked backward to the boundaries of the 

submodel. Backward particle tracking from the 

well is used instead of forward tracking from the 

water table to minimize the number of particles 

needed. The method could be modified for 

forward tracking, but this option is currently not 

available. Particles are not tracked from inside 

the constant-head cell(s) for the same reason, as 

well as to minimize pathline redundancy. Upon 

termination in the submodel, particles are transferred to equivalent locations in the original 

model and particle tracking is continued to 

completion (fig. 3). Particles that terminate at 

the top boundary of the submodel, which also is 

the top boundary of the original model, are not 

transferred. Similarly, particles that terminate at 

the bottom boundary of the submodel, which 

also is the bottom boundary of the original 

model, are not transferred.
(a) (b)

Particle 

pathline

Constant head

Capture area Pumped well

Figure 3. Plan view of particle locations and pathlines in (a) 

the submodel and (b) the original model.

Particle coordinate transfer in the horizontal direction is straightforward and is done by 

adding an offset distance (from the original 

model origin to the submodel origin) to the 

global x- and y-coordinates in the submodel. 

Particle coordinate transfer in the vertical 

direction is more complicated because of the 

MODPATH grid geometry code (IGRID). 

Vertical coordinates are handled either by using 

consistent global coordinates between the 

models (IGRID=1; true rectangular three-dimensional grid) or by converting local z-coordinates 

in the submodel to local z-coordinates in the 

original model (IGRID=0; grid with variable 

thickness and (or) nonhorizontal layers).

TECHNICAL CONSIDERATIONS AND 

LIMITATIONS

Certain aspects of the nested rediscretization method must be understood in order to 

correctly interpret the results obtained by using 

the method. These aspects are related to the (1) 

design of the original model, (2) discretization of 

the original model, and (3) application of the 

method.

For the first case, the effect of constanthead cells in the original model on particle pathlines should be examined to ensure that these 

cells are not exerting an unrealistic artificial 

constraint on flow volume, direction, or travel

time. These effects may overshadow results 

obtained by using the method. Certain boundary 

conditions in the original model also need to be 

evaluated. For example, a gaining stream in the 

same cell as the well may falsely prevent the 

well in the submodel from containing any part of 

the capture area.

For the second case, wells commonly 

may be represented in the original model as if 

they are screened over the entire thickness of the 

layer, which generally is greater than the actual 

length of the screened interval. Rediscretization 

can be done or continued beyond the point at 

which the well is converted to a strong sink in 

the submodel if the thickness of the constanthead cell(s) is greater than the length of the 

screened interval. In the opposite case, the well 

may need to be screened over more than one 

submodel layer. (The choice of well placement 

in the submodel will affect the delineation of 

capture area and calculation of travel time.) 

Also, a single model cell can represent more 

than one well in the original model, precluding a 

discrete determination of the capture area of 

individual wells. In these instances, the total 

withdrawal from the group of wells is represented by an equivalent composite withdrawal 

extracted at the center of the cell, and provides a 

composite capture area. Finally, because the 

model location of the well and the associated
capture area are always affected by the scale of 

the original model discretization (even in the 

submodel), they may not be accurate. Resolving 

all the limitations related to the original model 

discretization would require the redevelopment, 

and possibly recalibration, of a large part of the 

model with a finer horizontal and vertical 

discretization.

For the third case, the method is designed 

to be run manually for each well in the original 

model to verify that each submodel runs and 

converges to an accurate solution without error 

messages. The method could be modified for 

rediscretizing the well and adjacent cells, both 

horizontally and vertically, but this would 

require extensive computer programming. A 

limitation of the current method design is that 

boundary effects occur at the edges of capture 

areas determined from submodels representing a 

well screened over multiple layers in the original 

model. The method also is designed for steadystate conditions. Design for transient conditions 

would require substantial additional 

programming. Steady-state conditions provide 

the stable extent of the capture area and durations of particle travel time under a given set of 

pumping conditions. If a constant head is placed 

in any cell other than the center cell of the 

submodel, numerical problems may occur. For 

example, a submodel boundary cell could 

contain a constant head and a constant flux. The 

user can avoid this situation by further rediscretizing the submodel so that the constant head 

can be located away from the boundary. Even if 

no problems occur for this case, submodel 

results should be evaluated to determine whether 

results are reasonable. When the method is 

applied to very weak sinks, the iterative effort 

required to achieve the necessary rediscretization can be substantial, whereas the capture 

area that is defined can be very small. A practical solution may be to establish a minimum 

withdrawal for applying the method to a specific 

model or simply to backtrack particles from the

exact location of the well screen in the original 

model.

Also for the third case, the potential for 

well interference must be evaluated. For 

example, consider two weak sink wells, one 

upgradient from the other. If it is specified that 

particles stop at weak sinks in the model domain, 

the size of capture area of the downgradient 

weak sink will be underestimated. If particles 

are allowed to pass through other weak sinks (as 

is specified for the nested rediscretization 

method), overlapping capture areas are possible. 

To resolve the overlap case, the overlapping 

capture area of the upgradient well can be 

subtracted from the capture area of the downgradient well, so long as the capture area of the 

upgradient well does not lie outside the capture 

area of the downgradient well.

COMPUTER PROGRAMS

The software consists of five Fortran 

programs that are operated manually. The 

programs have been compiled and tested on a 

UNIX mainframe computer and compiled only 

on a Windows NT personal computer. Not all 

possible MODFLOW and MODPATH applications have been tested with the computer 

programs. Future applications of the programs 

may lead to problems requiring modification and 

recompilation of the source codes. Instructions 

on obtaining and installing the computer 

programs and associated files are given in 

appendix 1. The associated files include two 

generic MODPATH response files (a special 

output file that records interactive input from the 

keyboard). The names of the programs and 

associated files are shown in italics throughout 

this report.

Organization and Structure

The determination of capture areas of 

wells by using particle tracking and the nested 

rediscretization method is shown schematically 

in figure 4. The first step is to identify weak and
Rerun programs 

for finer rediscretization

Create submodel

I

Run submodel

* ^^^~~^-^

Begin particle tracking from 

constant-head cell(s) to 

boundaries of submodel

Transfer particle coordinatas 

and continue particle 

tracking in original model

Combine particle-coordinate 

and travel-time data from 

both models

Figure 4. Nested rediscretization method for determining 

capture areas of wells.
strong sinks in the particular model domain. If 

particle tracking is desired at this point for either 

type of well, MODPATH then can be run. If use 

of the nested rediscretization method is chosen, 

it can be run as described below.

The default rediscretization of the cell 

containing the weak sink well is 3 layers, 3 rows, 

and 3 columns (27-cell submodel). (For each 

rediscretization, the flow to the constant-head 

cell(s) representing the well in the submodel is 

equal to the discharge rate of the well in the 

original model.) Input files and particle-tracking 

files are created for the submodel. The number 

of particles tracked is set by the user infine.rsp. 

The submodel then is run and the model solution 

is checked for potential problems and errors. If 

these discrepancies occur, adjustments (for 

example, changes to model solver parameters) 

may be necessary to the submodel and (or) 

original model. If adjustments can be made or if 

no problems occur, the well in the submodel then 

is checked for sink strength. If the well is still a 

weak sink, modifications are made for a finer 

submodel rediscretization and the previous steps 

are repeated until the well becomes a strong 

sink. When this condition is met, particles are 

started from the well in the submodel. Then, 

depending on whether particles are transferred 

back to the original model (by converting 

particle ending locations in the submodel to 

corresponding particle starting locations in the 

original model), particle tracking is continued to 

completion. If particles are separated into two 

endpoint files, one for each model, a composite 

endpoint file is created that includes cumulative 

travel times from recharge locations to discharge 

at the well. See the MODPATH documention 

(Pollock, 1994) for more information about the 

input starting locations file and output particlecoordinate endpoint file.

Fortran Code

The program identify.f identifies strong 

and weak sink wells in the original model by (1)

finding the packages that are used in the model, 

(2) reading the model binary (unformatted) cellby-cell flow file, (3) separating the weak from 

the strong sinks, and (4) creating files listing the 

weak and strong sinks. The program is dimensioned for a model with 300 rows, 300 columns, 

and 100 layers simulating 1,000 wells.

The program rediscretize.f makes use of 

an original, coarsely discretized MODFLOW 

model to create input files for a finely 

discretized submodel of a weak sink cell by (1) 

finding the packages that are used in the model, 

(2) reading the model cell-by-cell flow and head 

files, and (3) creating a MODFLOW name file 

and Basic, Block-Centered Flow, Well, Output 

Control Option, and Solver Packages for the 

submodel. The program then (4) reformats the 

original model MODPATH name and main files 

for the submodel. The program is dimensioned 

for a model with 300 rows, 300 columns, and 

100 layers, and a level of rediscretization of 99 

layers, 99 rows, and 99 columns.

The program transfer.f converts 

MODPATH endpoint locations resulting from 

particle tracking in the submodel to starting 

locations for particle tracking in the original 

model. This is accomplished by (1) finding the 

packages that are used in the model, (2) determining the global coordinates of the submodel 

origin, (3) converting coordinates of particles in 

the submodel to coordinates in the original 

model, and (4) creating files listing particles that 

terminate in the submodel and (or) particles to 

be continued in the original model. The program 

is dimensioned for a model with 300 rows, 300 

columns, and 100 layers, a level of rediscretization of 99 layers, 99 rows, and 99 columns, 

and 50,000 tracked particles.

The program combine.f combines 

MODPATH endpoint locations from the 

submodel with endpoint locations from the 

original model to create a composite endpoint 

file. Tracking time for particles transferred from
the submodel to the original model is accumulated to provide a total tracking time for these 

particles. The program is dimensioned for 

50,000 tracked particles.

The utility program utility./performs 

various tasks, including checking the submodel 

solution and particle-tracking results as well as 

evaluating the strength of the sink in the 

submodel. The strength of the sink is determined by checking the cell-by-cell flow file for 

the constant-head cell(s) for outflow across cell 

faces. Once the weak sink has been converted to 

a strong sink, the program interactively prorates 

the number of particles to be tracked from each 

inflow face of the cell on the basis of the cell 

water budget. When the program is executed, 

the user is queried for which task to perform. 

Output from the program is to the computer 

monitor only. The program is dimensioned for a 

model simulating 1,000 wells and a level of 

rediscretization of 99 layers, 99 rows, and 99 

columns.

Input and Output Files

The names of input and output files for 

the Fortran programs are shown in table 1. The 

prefix enclosed in brackets is unique to the 

user's original model. The original model files 

used as input files to the programs must exist in 

order for the programs to operate.

Program Compatibility

The computer programs developed for 

the nested rediscretization method were 

designed for the versions of MODFLOW and 

MODPATH that were available at the time of 

method development. The programs are neither 

backward compatible with earlier versions of 

these codes nor forward compatible with updates 

to these codes, such as MODFLOW-2000 

(Harbaugh and others, 2000). Therefore, model 

and particle-tracking files may need to be 

modified to be compatible with these versions of 

the codes. The programs do not accommodate

working with cross-sectional models. Such 

applications may lead to program termination or 

errors that require modification of the programs. 

Additionally, MODFLOW and MODPATH were 

not executed in batch mode; batch files for these 

codes will interfere with the procedure for the 

method.

The computer programs can accommodate free- or fixed-format model input. The 

programs are designed for working with 

standard and not compact MODFLOW binary 

budget and head files. Not all MODFLOW 

packages have been tested with the programs. 

The Drain (DRN), River (RIV), Recharge 

(RCH), and Strongly Implicit Procedure (SIP) 

Packages were tested. The Block-Centered 

Flow (BCF) and General-Head Boundary (GHB) 

Packages were tested partially in terms of 

parameters. The Evapotranspiration (EVT), 

Stream (STR), Reservoir (RES), Slice 

Successive Overrelaxation (SOR), and Preconditioned Conjugate Gradient (PCG) Packages are 

accounted for in the computer programs, but 

were not tested. The programs are designed for 

working with standard (not compact or binary) 

MODPATH endpoint files; they are not designed 

for working with pathline or time-series files. 

The MODFLOW name file must be compatible 

with the MODPATH name file as well as with 

the MODPATH main data file.

Operation

For detailed instructions on using 

MODFLOW refer to Harbaugh and McDonald 

(1996a, 1996b). For detailed instructions on 

using MODPATH, refer to Pollock (1994). User 

input for the computer programs is a combination of data files and interactive keyboard 

entries in response to menu queries. Data output 

(MODPATH particle endpoint file) can be used, 

for example, to delineate capture areas as part of 

a wellhead-protection program in the model 

domain by using MODPATH-PLOT (Pollock, 

1994) or a geographic-information-systems-
Table 1. Computer program input and output files

Computer program

identify./

rediscretize.f

transfer./

combine./

utility./

Input file

[modelj.pnm

[model]. bud

[modelj.fnm

[model]. has

[model]. be/

[model J.slv

[model], ghb

[model]. data

[model]. bud

[modelj.bhd

[modelj.pnm

[modelj.mdf

[modelj.bhd

[modelj.pnm

[modelj.mdf

fine.ept

coarse, stl

separ.ept

coarse, ept

fine.lst

summary.pth

fine, bud

Output file

strongwells

weakwells

fine.fnm

fine, has

fine.oc

fine.bc/

fine.slv

fine.wel

fine.pnm

fine.mdf

fine.ept

coarse, ept

separ.ept

coarse, stl

outpoint

File description

Name file 1

rt

Binary cell-by-cell flow file

Strong sink wells

Weak sink wells

Name file3

Basic Package

Block-Centered Flow Package3

Solver Package3

General-Head Boundary Package3

1 ^

Ancillary data file '

rt

Binary cell-by-cell flow file

Binary head file2

Name file 1

Main data file 1

o

Name file

Basic Package3

Output Control Option Package3

Block-Centered Flow Package3

Solver Package3

Well Package3

Name file 1

Main data file 1

Dummy endpoint file4

Dummy endpoint file4

Binary head file2

Name file 1

Main data file

Endpoint file4

Endpoint file

Starting locations file 1

Starting locations file 1

Endpoint file4

Endpoint file4

Composite endpoint file

Summary output file

Summary output file4

o

Binary cell-by-cell flow file

1 MODPATH input file

2 MODFLOW output file

3 MODFLOW input file ([modelj.ghb used only if included)

4 MODPATH output file

10
based plotting program such as MODTOOLS 

(Orzol, 1997). Interactive menu responses, input 

files, and output files for the sample problem 

presented farther on in this report are listed in 

appendixes 2, 3, and 4, respectively.

Five Fortran programs and two 

MODPATH response files must be used to 

follow the procedure shown in figure 4. The 

response files, fine.rsp and coarse.rsp (references the name file coarse.pnni), are for the 

submodel and original model, respectively. To 

create coarse.pnm, make a copy of the original 

model MODPATH name file and edit the line 

containing the keyword "ENDPOINT" in the 

copied file so that the associated file name is 

coarse.ept.

Setup Instructions

This section provides the necessary setup information for using the computer programs. 

Certain requirements must be met for the proper 

operation of the programs and apply mainly to 

the associated MODFLOW and MODPATH 

files. For example, the MODFLOW output 

binary cell-by-cell flow data must be written to a 

file. MODFLOW output binary head data also 

must be written to a file for a well screened in 

any layer containing the water table.

Special input files called name files are 

used in MODFLOW and MODPATH. Name 

files specify the data files being used in a model 

or particle-tracking simulation and provide the 

information needed to manage these files. Each 

line in the name file must contain three items for 

each file used in the simulation: a character 

string keyword signifying the type of data file, a 

unique integer Fortran unit number to be used 

when reading from or writing to the file, and a 

file name. Lines in the MODPATH name file 

containing keywords not accounted for by the 

computer programs need to be converted into 

comment lines by adding the "#" character to 

column 1 of the file (for example, "PATHLINE,"

"TIME-SERIES," "TIME," "LOCATIONS," 

and so on). Full pathnames are necessary to 

access files located in other computer directories 

or folders. Because binary files are opened in 

the programs by using the MODPATH name file, 

any ancillary MODFLOW binary files must be 

specified in this name file. (The DATA 

(BINARY) keyword entry will be ignored by 

MODPATH.) If drawdown output is desired, the 

user must interactively add entries for drawdown 

files to the appropriate submodel name files. 

The STR and RES Packages are currently not 

accounted for in MODPATH, but entries are still 

required in the MODPATH name file if these 

packages are used in the model.

Although MODFLOW and MODPATH 

are designed to work independently, operation of 

the computer programs described in this report 

requires the Fortran unit numbers in the 

respective name files to be consistent; therefore, 

editing of the model name files may be 

necessary. Associated data-file internal unit 

numbers also may need to be adjusted. Fortran 

unit numbers from 79 to 99 are reserved for use 

by the computer programs. Fortran unit 77 

should be connected to the MODFLOW GHB 

Package, if used, and unit 78 should be 

connected to the MODPATH main data file.

When the computer programs are used 

with MODFLOW, solution problems may occur 

in the submodel when the SIP Package is used. 

The program rediscretize.f includes parameter 

adjustments to enhance solution stability, 

including adjustments to the maximum number 

of iterations (MXITER=150), head-change 

convergence criterion (HCLOSE=HCLOSEinput 

/10), and iteration parameter seed flag 

(IPCALC=1). If problems still occur with the 

package, however, the parameter HCLOSE in 

the submodel or the iteration parameter seed 

(WSEED) in the original model could be 

adjusted manually and the model could be rerun. 

Alternatively, the PCG or SOR Package could be

11
used instead of the SIP Package for the 

submodel.

In MODPATH, individual flow terms for 

model stress packages can be assigned as 

distributed internal sources and sinks or assigned 

to specific faces of the cell by using the variables 

IFACE/ITOP (Pollock, 1994, p. 3-8). When the 

computer programs are used with MODPATH, 

stress-package data files should be edited so that 

only wells are assigned as internal sinks. Other 

model stresses representing sinks should be 

assigned to specific faces of the cell. This modification is particularly important when the WEL 

Package also is used to simulate other model 

flows, such as boundary flows. If the GHB 

Package is used, the IFACE value is used to 

determine which cell face transmits the cell-bycell flow.

The total number of particles tracked and 

their starting array locations at the constant-head 

cell(s) representing the well in the submodel 

should be set by the user mfine.rsp. This file is 

designed for one submodel layer to represent the 

screened interval; if multiple layers are needed, 

this file will need to be modified. Starting locations for particles can be generated from an 

existing data file by MODPATH or, as in the 

case of the sample problem, prorated internally 

from inflow cell faces by using utility./. 

Prorating means that the particles are distributed 

on the cell faces according to the percentage of 

total inflow contributed by each face. Prorating 

is the preferred choice because using an equal 

distribution of particles on all cell faces may 

result in a bias toward longer travel times. 

Prorating is done interactively in utility./(met 

the weak sink has been converted to a strong 

sink (there is no outflow across cell faces). The 

user is queried for an approximate total number 

of particles to be tracked and the program determines the distribution of the particles on the cell 

faces. No particles should be used on a face with 

zero flow or a face adjacent to another constanthead cell. (Because the particles are distributed

in square arrays on the cell faces, the actual total 

number of particles tracked may differ from the 

number entered by the user.)

Procedure

This section provides the steps that must 

be followed to run the computer programs. The 

setup instructions given in the last section must 

be completed before proceeding with these 

instructions. Additional details on the procedure 

can be found in other sections of this report. For 

example, all of the output files from the 

programs can be found in table 1.

Identify weak sink wells and strong sink wells 

in the original model:

Run identify./. This program will query 

the user for the dimensions of the original 

model and the name of the MODPATH 

input name file. This program creates 

weakwells and strongwells, which list 

these wells.

Repeat the following steps for each selected 

weak sink listed in weakwells:

 Create and run submodel for one weak sink

(1) Run rediscretize./. This program will 

query the user for the dimensions of the 

original model, the level of rediscretization (for example, parameter NRZ=3 is 

for a submodel with 3 layer, 3 rows, and 3 

columns (27 total cells), NRZ=5 is for a 

submodel with 5 layers, 5 rows, and 5 

columns (125 total cells), and so on), and 

vertical anisotropy. The program also 

queries the user for the name of the 

MODFLOW input name file for the 

original model; the name of the 

MODPATH input name file for the 

original model; layer, row, and column 

indices for the cell containing the weak 

sink well in the original model; and the 

top layer, bottom layer, row, and column

12
indices of the constant head(s) in the 

submodel (for example, for NRZ=3, the 

center cell would be 2,2,2,2).

(2) Run MODFLOW for the submodel. 

MODFLOW will query the user for the 

name of the input name file for the 

submodel. (Reply v/ithfine.fnm.)

(3) Does the submodel solution converge? 

Does the volumetric budget for the 

submodel indicate that outflow to the 

constant-head cell(s) representing the well 

approximately equals the withdrawal in 

the original model? (If not, then 

submodel solver parameters could be 

made more stringent.) Run utility./ 

(option 1) to identify other common 

problems. If problems occur, evaluate 

and correct them; then repeat steps 2 and 

3.

(4) Run utility./(option 2) to evaluate whether 

the weak sink has been converted to a 

strong sink. This option will query the 

user for the level of rediscretization. If 

the well is still a weak sink, then repeat 

steps 1 through 4 using a finer level of 

rediscretization until the well becomes a 

strong sink. (At the point at which the 

well becomes a strong sink, utility/will 

also query the user for the approximate 

total number of particles to be tracked.)

 Begin particle tracking in the submodel

(1) Edit the submodel layer, row, and column 

indices of the constant head(s) infine.rsp. 

Also, edit the distribution of particles per 

cell face in this file on the basis of 

prorating output from utility./. Run 

MODPATH to begin particle tracking in 

the submodel. MODPATH will query the 

user for the name of the submodel input 

response file. (Reply wiihfine.rsp.)

(2) Run utility./ (option 3) to identify 

common particle-tracking problems. If 

problems occur, evaluate and correct 

them; then repeat steps 1 and 2.

 Transfer particles and continue tracking in the 

original model

(1) Run transfer./\a convert appropriate 

particle endpoint locations in the 

submodel into corresponding particle 

starting locations in the original model. 

This program will query the user for the 

dimensions of the original model, the 

number of particles tracked, the level of 

rediscretization, and the layer, row, and 

column indices of the model cell 

containing the weak sink. This program 

creates coarse, stl, which is the file of 

particle starting locations.

(2) Skip the remaining steps if all of the 

particles terminate in the submodel 

domain that is, coarse.stl is empty or 

the final step if no particles terminate in 

the submodel domain that is, separ.ept is 

empty. For the former case, rename 

fme.ept to outpoint; for the latter case, 

rename coarse.ept to outpoint after step 4.

(3) Run MODPATH to continue the particle 

tracking, which is now done in the 

original model. MODPATH will query 

the user for the name of the original model 

input response file. (Reply with 

coarse.rsp.) As a result of simulation in 

the submodel, a few particles in coarse.stl 

may not have valid starting locations in 

the original model; these particles will be 

discarded.

(4) Run utility./ (option 3) to identify 

common particle-tracking problems. If 

problems occur, evaluate and correct 

them, then repeat steps 3 and 4.

13
 Combine endpoint files

Run combine./to merge the endpoint file 

from the submodel with the endpoint file 

from the original model. This program 

will query the user for the dimensions of 

the original model and the number of 

particles tracked. The program creates 

outpoint, which is a composite endpoint 

file of particle data listed in original 

model coordinates. (Rename outpoint to a 

new file for each well in weakwells to 

avoid overwriting during repeat 

processing.)

Error Checking

The user should review computer 

program output any time a composite endpoint 

file is not created properly. The utility program 

utility./ (options 1 and 3) checks MODFLOW 

and MODPATH results for common problems 

during processing. The program does this by 

searching for key phrases in the files fine.1st or 

summary.pth. As examples, the submodel 

should not have variable-head cells that are 

converted to dry cells, solution convergence 

problems (or other run-time errors), or waterbudget errors. If these problems occur, adjustments in the original model and (or) submodel 

may be necessary. Not all the key phrases 

indicate problems; some merely bring information to the attention of the user.

The Fortran programs were designed to 

include other error and warning checks. Error 

checks are included for inappropriate responses 

to program queries, the existence of input files, 

problems opening files, and the necessary sizing 

of arrays. Warning messages are included when 

the well is located near certain types of boundary 

cells. Descriptive information also is output to 

the computer monitor during execution of each 

program for debugging purposes. As discussed 

above, the programs were designed for working 

with certain MODFLOW packages and files. 

Packages not accounted for or incomplete cellby-cell flow files will cause errors when the

programs are used. User comment statements 

added to data files also may cause errors when 

the programs are run.

SAMPLE PROBLEM

A simple hypothetical problem is 

presented below to illustrate the use of the 

computer programs. The problem is identical to 

the hypothetical steady-state flow problem 

designed by Pollock (1994, p. 6-2), except for 

the pumping rate and location. Variations of the 

problem were used during the development and 

testing of the computer programs.

Description

The flow system consists of two aquifers 

separated by a confining layer (fig. 5). The 

lower aquifer is 200 ft thick, the confining layer 

is 20 ft thick, and the thickness of the upper 

aquifer varies according to the water-table 

elevation. Recharge to the system is uniformly 

distributed over the water table at a rate of 

0.0045 ft/d. Discharge from the system is to a 

partially penetrating river along the right side of 

the flow system in the upper aquifer and to a 

well screened in the upper aquifer.

Well River recharge 

discharge or discharge

Subregion shown 

in figures 6 and 7

\

220 feet _ 

200 feet ~

0 feet -LUpper aquifer Well

Confining layer

Lower aquifer

-8,060 feetFigure 5. Diagram of simulated hypothetical flow 

system. (Modified from Pollock, 1994, p. 6-2)

14
27 columns, and 5 layers. Horizontal grid 

spacing varies from 40-ft by 40-ft cells to 400-ft 

by 400-ft cells. The upper aquifer is represented 

with one model layer. A quasi-three-dimensional representation is used for the confining 

layer; that is, only vertical flow is simulated in 

the layer. The lower aquifer is represented by 

four 50-ft-thick layers. The well is located in 

layer 1, row 20, column 20, and is discharging at

3,000 ft3/d (0.023 Mgal/d). The input data files 

for the original model and response files for 

particle tracking for this problem are provided in 

appendix 3. By using program identify/, it can 

be determined that the well captures only 35 

percent of the flow into the cell, and thus is a 

weak sink.

Analysis of Capture Areas and Pathlines

The capture area of the well is the part of 

the flow system that contributes water to the 

well. The capture area of the flow system 

described above is at the water table and was 

determined for the well as a weak sink and after 

the well was converted to a strong sink by using 

the nested rediscretization method. These areas 

are shown in figures 6 and 7, respectively. These 

figures were created by using backward tracking 

in MODPATH-PLOT. The rediscretization 

required to make the well a strong sink is 7 

layers, 7 rows, and 7 columns (343-cell

submodel). The number of particles tracked was 

prorated from cell faces (7,983 total particles). 

The input data files for the submodel and 

particle tracking (excluding particle endpoint 

files) are provided in appendix 3.

Because the well is represented in the 

original model as a weak sink, some of the 

endpoints shown in figure 6 correspond to 

particles that discharge downgradient from the 

well rather than to the well itself; thus, the extent 

of the capture area is overestimated. The net 

amount of recharge entering the flow system

over this area is approximately 8,600 ft3/d 

(0.065 Mgal/d), which exceeds the pumping rate 

by 185 percent. When the well is converted to a 

strong sink, the capture area is smaller. This 

capture area, shown in figure 7, is 35 percent of 

the area defined when the well was a weak sink 

as determined from output in weakwells. The 

net amount of recharge entering the flow system 

over this area now equals the pumping rate of

3,000 ft3/d (0.023 Mgal/d).

The distribution of particle travel times 

also changes when the well is converted from a 

weak sink to a strong sink, as shown in table 2. 

The table shows the maximum travel time for 

the selected subgroups of particles. After the 

conversion, particles follow longer flow paths as 

a result of additional travel time in the submodel.

Table 2. Maximum travel times to a weak sink well with and without using the nested 

rediscretization method 

[Travel times are in years]

Percentage of particles

Rediscretization level

20 40 60 80 100

1,1,1 (original model) 

7,7,7 (submodel)

1.98 

4.20

6.25 

8.09

11.7 

12.7

18.8 

18.7

28.9 

28.8

15
COLUMN

23

0 200 400 600 800 1,000 FEET

100 200 300 METERS

EXPLANATION

HI Original model grid Particle that discharges to well 

fj Original model well cell

Figure 6. Map view of capture area of the weak sink well in the original model determined with 

MODPATH. (Location of subregion shown in figure 5.)

COLUMN

23

13

O

CC

23

0 200 400 600 800 1,000 FEET

J

100

\

200 300 METERS

EXPLANATION

Original model grid D Submodel well cell 

Submodel grid Particle that discharges to well

Figure 7. Map view of capture area of the strong sink well in the original model determined with 

the nested rediscretization method. (Location of subregion shown in figure 5.)

16
This difference between the original model and 

submodel decreases to zero as travel time 

increases.

Some of the changes to the flow system 

within the cell when the well is converted from a 

weak sink to a strong sink are shown in figures 

8-11. Particle pathlines and time points in the 

original model are shown in figures 8 and 9; 

similar information for the submodel is shown in 

figures 10 and 11. These figures were produced 

by using forward tracking in MODPATH-PLOT. 

Flow direction in figures 8-11 (as well as in 

figures 12 and 13 farther on) is from left to right. 

Pathlines shown in the figures are the result of 

judicious selection of particle starting locations 

at the edge of the cell and do not represent 

streamlines, which are curves tangent to the 

flow-velocity vector at every node in the 

discretized flow field. Time points are discrete 

points along a pathline that delineate equal 

intervals of time. The difference in vertical scale 

between figures 9 and 11 is the result of the 

choice of starting head in the submodel (that is, 

the head in the submodel does not correspond to 

the head in the original model).

When the well is a weak sink (figs. 8 and 

9), most of the flow enters the cell at the left and 

exits at the right. The 35 percent of the flow that 

is captured by the well is evident in the deceleration of flow in the original model, as shown by 

the slight decrease in distance between the time 

points on the pathlines (that is, particles travel a 

shorter distance in a given time). When the well 

is converted to a strong sink (figs. 10 and 11), 

some of the flow that enters the submodel is 

diverted to the well and accelerates, as shown by 

the curve in the pathlines and the increase in 

distance between the time points on the pathlines 

near the center of the submodel. Simulated 

heads and flow-velocity vectors in the submodel 

layers and profiles (not shown) display a horizontal and vertical gradient toward the center 

cell representing the well in the submodel.

The vertical transfer of particles from the 

submodel to the original model also can be 

demonstrated with the sample problem. To best 

show this transfer, the submodel rediscretization 

is increased to 15 layers, 15 rows, and 15 

columns (3,375-cell submodel); the well

discharge is reduced to 800 ft3/d (0.006 Mgal/d); 

and the number of particles is reduced to 400. 

Pathlines for particles started at the center cell of 

the submodel and backtracked to the submodelboundary are shown in figure 12; pathlines for 

particles started at the boundary of the cell representing the well in the original model and backtracked to the water table are shown in figure 13. 

The particle starting locations in the original 

model match the transferred particle endpoint 

locations in the submodel.

The results presented show that capture 

areas determined by using particle tracking and 

the nested rediscretization method are smaller 

than those determined by using particle tracking 

alone because the method refines the groundwater flow field near the well. Some of the 

particle pathlines now converge in the cell representing the well, rather than diverging out of the 

cell. Particle travel times are greater when the 

method is used because of additional travel time 

within the submodel. When the method is 

applied to a well that is already a strong sink 

(Spitz and others, in press), the capture area 

remains approximately the same, particle travel 

times are slightly greater because flow paths are 

extended in the submodel, and the cone of 

depression is smoothed. The cone of depression 

will be exaggerated if the submodel is not 

created in the water-table layer in the original 

model because of the assumption that inflow is 

evenly distributed along the top and bottom 

faces of the submodel.

17
0 20 40 60 80 100 FEET

10 20 30 METERS

EXPLANATION

- Pathline and time points; 

interval is 0.25 years

Figure 8. Map view of pathlines inside the weak sink cell in the original 

model determined with MODPATH.

20 40 60 80

I i I

100 FEET

0 10 20 30 METERS 

VERTICAL EXAGGERATION x 2.5

EXPLANATION

Pathline and time points; 

interval is 0.25 years

Figure 9. Profile view of pathlines inside the weak sink cell in the original 

model determined with MODPATH.

18
COLUMN

0 20 40 60 80 100 FEET EXPLANATION

| i I i, I i I , LJ_| ^

0 10 20 30 METERS S± Submodel grid

D Submodel well cell

- - Pathline and time points; 

interval is 0.25 years

Figure 10. Map view of pathlines inside the submodel determined with the nested 

rediscretization method. (The view is of layer 4.)

COLUMN

cc

HI

40

I

60 80 100 FEET

0 10 20 30 METERS 

VERTICAL EXAGGERATION x 2.5

EXPLANATION 

i3 Submodel grid

O Submodel well cell

 - Pathline and time points; 

interval is 0.25 years

Figure 11. Profile view of pathlines inside the submodel determined with the nested 

rediscretization method. (The view is along row 4.)

19
COLUMN

0 20 40 60 80 100 FEET

I i i i i i i i i :

0 10 20 30 METERS 

VERTICAL EXAGGERATION x 2.5

EXPLANATION 

gj Submodel grid 

3 Submodel well cell 

 Pathline

Figure 12. Profile view of pathlines inside the submodel showing endpoint locations used in 

particle transfer to the original model. (The view is along row 8.)

COLUMN

27

rr LU

0 1,000 FEET

I I I I I I

0 100 200 300 METERS 

VERTICAL EXAGGERATION x 50.0

EXPLANATION 

i Original model grid 

J Original model well cell 

 Pathline

Figure 13. Profile view of pathlines inside layer 1 of the original model showing starting locations 

generated by particle transfer from the submodel. (The view is along row 20.)

20
SUMMARY AND CONCLUSIONS

The effects of spatial grid discretization 

limit the level of detail and accuracy of groundwater model and particle-tracking results. The 

purpose of this study is to develop an approach 

to resolve some of the discretization limitations 

of MODPATH, a particle-tracking package 

designed for use with the U.S. Geological 

Survey's modular finite-difference groundwater-flow model, MODFLOW. As a result of 

insufficient discretization, particle flow paths 

calculated within weak sink cells cannot be 

uniquely defined because it is impossible to 

know whether a specific water particle 

discharges to the weak sink or passes through the 

cell. A weak sink is a cell (representing a well, 

for example) that does not discharge at a sufficiently large rate to capture all of the flow 

entering the cell; thus, some of the flow leaves 

the cell across one or more of the cell faces.

The nested rediscretization method documented here is a set of computer programs 

designed to help eliminate this limitation. The 

method involves refining the discretization of 

the original model at the weak sink to make it a 

strong sink by creating a submodel of the cell 

representing the well, coupling the submodel 

with the original model, and performing a linked 

MODPATH analysis with both models. A 

separate MODFLOW simulation is run with the 

submodel. Successive rediscretizations of the 

cell are applied until the well becomes a strong 

sink.

Advantages of the method are that it does 

not require additional information beyond that 

specified in the original MODFLOW and 

MODPATH input files, it is easy to use, and it 

provides an unambiguous determination of how 

particles are treated. Disadvantages of the 

method are that it is applicable only to weak 

sinks representing wells in steady-state models 

and to backtracking particle endpoint analysis.

If it is important to know which particle enters a 

weak sink, then more detail must be given than 

is provided in the model. This information could 

be obtained by refining the model or by specifying the actual location of the well in the cell. 

Specifying the actual location in the submodel is 

possible when using this method.

The software consists of five Fortran 

programs and two MODPATH response files 

that are operated manually in series. The 

programs perform different tasks, including 

identifying strong and weak sink wells in the 

original model; making use of an original, 

coarsely discretized MODFLOW model to 

create input files for a finely discretized 

submodel of a weak sink cell; converting 

MODPATH endpoint locations resulting from 

particle tracking in the submodel to starting 

locations for particle tracking in the original 

model; combining MODPATH endpoint locations from the submodel with endpoint locations 

from the original model to create a composite 

endpoint file; and error checking the submodel 

solution and particle-tracking results as well as 

evaluating the strength of the sink in the 

submodel. User input for the computer 

programs is a combination of data files and 

interactive keyboard responses to menu queries. 

Data output (MODPATH particle endpoint file) 

can be used, for example, to delineate capture 

areas of wells in the model domain.

Technical considerations and limitations 

of the method that relate to the design of the 

original model, discretization of the original 

model, and application of the method are 

presented. Set-up requirements necessary for 

the successful operation of the computer 

programs are described. Because not all 

possible MODFLOW and MODPATH applications have been tested with the programs, future 

applications of the programs may lead to 

problems requiring modification and recompilation of the source codes.

21
A simple hypothetical problem is 

presented to illustrate the use of the computer 

programs. The results show that capture areas 

determined by using particle tracking and the 

nested rediscretization method are smaller than 

those determined by using particle tracking 

alone because the method refines the groundwater flow field near the well. Some of the 

particle pathlines now converge in the cell representing the well, rather than diverging out of the 

cell. Particle travel times are greater when the 

method is used because of additional travel time 

within the submodel, which increases the length 

of the flow path. The difference in travel time 

created by using the method decreases to zero as 

travel time increases.

The computer programs have been tested 

successfully on available models of real-world 

flow systems, including glacial valley-fill 

aquifers and Coastal Plain aquifers in New 

Jersey and Louisiana. The method can be 

expected to provide the greatest improvement in 

pathline resolution when used in such existing 

regional models with coarse discretization; 

however, it also can be useful in analyzing local 

flow systems with low-volume pumped wells.

REFERENCES CITED

Harbaugh, A.W., Banta, E.R., Hill, M.C., and 

McDonald, M.G., 2000, MODFLOW2000, 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.

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

User's documentation for MODFLOW96, an update to the U.S. Geological 

Survey modular finite-difference groundwater flow model: U.S. Geological 

Survey Open-File Report 96-485, 56 p.

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

Programmer's documentation for 

MODFLOW-96, an update to the U.S. 

Geological Survey modular finitedifference ground-water flow model: 

U.S. Geological Survey Open-File 

Report 96-486, 220 p.

Leake, S.A., and Claar, D.V., 1999, Procedures 

and computer programs for telescopic 

mesh refinement using MODFLOW: 

U.S. Geological Survey Open-File 

Report 99-238, 53 p.

Nicholson, R.S., McAuley, S.D., Barrihger, J.L., 

and Gordon, A.D., 1996, Hydrogeology 

of, and ground-water flow in, a valleyfill and carbonate-rock aquifer system 

near Long Valley in the New Jersey 

Highlands: U.S. Geological Survey 

Water-Resources Investigations Report

93-4157, 159 p.

Nicholson, R.S., and Watt, M.K., 1997,

Simulation of ground-water flow in the 

unconfined aquifer system of the Toms 

River, Metedeconk River, and Kettle 

Creek Basins, New Jersey: U.S. 

Geological Survey Water-Resources 

Investigations Report 97-4066, 100 p.

Orzol, L.L., 1997, User's guide for

MODTOOLS: Computer programs for 

translating data of MODFLOW and 

MODPATH into geographic information 

system files: U.S. Geological Survey 

Open-File Report 97-240, 86 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.

22
REFERENCES CITED-Continued

Shapiro, A.M., Margolin, J., Dolev S., and BenIsrael, Y., 1997, A graphical-user 

interface for the U.S. Geological Survey 

modular three-dimensional finitedifference ground-water flow model 

(MODFLOW-96) using Argus 

Numerical Environments: U.S. 

Geological Survey Open-File Report 

97-121, 50 p.

Spitz, F.J., Nicholson, R.S., and Pope, D.A., in 

press, Description and application of a 

nested rediscretization method to 

improve pathline resolution by 

eliminating weak sinks representing 

wells: Ground Water.

23
APPENDIX 1. OBTAINING AND INSTALLING THE COMPUTER PROGRAMS

The source code for the Fortran programs and associated MODPATH response files is 

available for downloading over the Internet from the USGS, New Jersey District, web site at URL 

http://nj.usgs.gov/pub/OFR/00-392/. The zip file contains the five programs, two response files, a 

"readme" file, and the sample problem input files from appendix 3 of this report. Updates might 

occasionally be made to the computer programs. MODFLOW and MODPATH are available for 

downloading over the Internet from the main USGS web site at URL http://water.usgs.gov/software 

or by anonymous ftp from water.usgs.gov in the pub/software/ground_water directory.

The programs are installed by copying the executable or Fortran program source code and 

associated files onto your computer system. The programs have been compiled in Fortran 77 on a

Data General UNIX platform and in Lahey Fortran 95 on a personal computer Windows NT 

platform. No links to special Fortran library subroutines are required. Because these programs were 

tested on a UNIX platform, personal computer users may encounter run-time errors (as a result of 

stricter error handling, for example) that were not encountered before. Programs should be compiled 

as Windows-Console Programs on a Windows NT platform in order to observe error and warning 

messages. The programs and MODFLOW and MODPATH should be compiled with the same 

compiler to avoid problems with reading binary files. The two response files should not require 

computer system modification; however, these files should be obtained in ASCII format to ensure 

they will work properly on a personal computer.

'Use of trade names in this report is for identification purposes only and does not constitute endorsement by the 

U.S. Geological Survey.

24
APPENDIX 2. INTERACTIVE MENU RESPONSES FOR SAMPLE PROBLEM

An example of an interactive input session with the computer follows. The procedure is a 

subset of the complete procedure described on pages 12-14. (Program output is not shown.) This 

example is for the case in which the well in the submodel has been converted to a strong sink. 

Program names below are shown in bold italics, program prompts and messages are shown in regular 

text, and user responses are shown in bold text. A program can be run by typing the program name at 

the command prompt and pressing the enter key. Following that command, each program writes 

output to the computer monitor asking the user for specific information. Responses should be entered 

in lowercase, using commas as field separators, with single quotation marks around full pathnames (if 

necessary), and decimal values where appropriate. Users may want to embed program names and 

responses in UNIX shell files or personal computer batch files to automate this procedure.

identify

Enter number of model layers, rows, and columns: 

5,27,27

Enter name of modpath name file: 

demo.pnm

rediscretize

Enter number of model layers, rows, columns, level of rediscretization, and vertical anisotropy: 

5,27,27,7,1.0

Enter name of modflow name file: 

demo.fnm

Enter name of modpath name file: 

demo.pnm

Enter model layer, row, and column of well: 

1,20,20

Enter submodel top layer, bottom layer, row, and column for constant head(s): 

4,4,4,4

modflow

Enter the name of the NAME FILE: 

fine.fnm

utility

Enter option: 

1-Check submodel solution, 2-Check sink strength, 3-Check particle-tracking results

25
utility

Enter option: 

1-Check submodel solution, 2-Check sink strength, 3-Check particle-tracking results

2

Enter level of rediscretization: 

7

This cell is now a strong sink, so prorating will be done; 

Enter approximate total number of particles to be tracked:

8140

Try a different number of particles (y,n=quit)? 

n

Edit fine, rsp according to output from utility.

modpath

MODPATH Version 3.00 (V3, Release 1, 9-94)

TO READ INPUT FROM AN EXISTING RESPONSE FILE, ENTER FILE NAME: 

( <CR> = ENTER DATA INTERACTIVELY ) 

[? = Help] 

fine.rsp

utility

Enter option:

1-Check submodel solution, 2-Check sink strength, 3-Check particle-tracking results 

3

transfer

Enter number of model layers, rows, columns, level of rediscretization, and particles tracked: 

5,27,27,7,7983

Enter model layer, row, and column of weak sink well: 

1,20,20

26
modpath

MODPATH Version 3.00 (V3, Release 1, 9-94)

TO READ INPUT FROM AN EXISTING RESPONSE FILE, ENTER FILE NAME: 

( <CR> = ENTER DATA INTERACTIVELY ) 

[? = Help]

coarse.rsp

utility

Enter option: 

1-Check submodel solution, 2-Check sink strength, 3-Check particle-tracking results

3

combine

Enter number of model layers, rows, columns, and particles tracked: 

5,27,27,7983

27
APPENDIX 3. INPUT FILES FOR SAMPLE PROBLEM

MODFLOW Data Files

Name File [file: demo.fnm]

list

bas

bcf

wel

riv

rch

oc

sip

data (binary)

data (binary)

9

10

11

12

14

18

22

19

50

60

demo. 1st

demo . bas

demo. bcf

demo . wel

demo. riv

demo . rch

demo . oc

demo. sip

demo . bud

demo . bhd

Basic Package [file: demo.bas]

MODPATH SAMPLE PROBLEM

27 27

999

1

0

0

0

0

0

0

.9

0

0

0

0

0

.0

0

1

1

1

1

1

280.

280.

280.

280.

280.

1 1.0

Block-Centered Flow Package [file: demo, bcf]

50 l.OE+30

10000

0

11

400. 400. 400.

1.0

1.0 (16F5.0) 

400. 400. 400. 400. 400. 300. 200. 150. 100.

400. 400.

60.

150. 200. 300. 400. 400. 400. 400. 400. 400.

11 1.0 (16F5.0)

400. 400. 400. 400. 400. 400. 400. 400. 300. 200. 150. 100. 60.

150. 200. 300. 400. 400. 400. 400. 400. 400. 400. 400.

40. 60. 100.

40. 60. 100.

0

0

0

0

0

0

0

0

0

0

50.

220.

0.0005

1250.

0.01

1250.

0.01

1250.

0.01

1250.

28
River Package [file: demo.riv]

27

27

1

1

1

1

1

1

1

1

1

1

1

1

1

1

1

1

1

1

1

1

1

1

1

1

1

1

1

50

1

2

3

4

5

6

7

8

9

10

11

12

13

14

15

16

17

18

19

20

21

22

23

24

25

26

27

27

27

27

27

27

27

27

27

27

27

27

27

27

27

27

27

27

27

27

27

27

27

27

27

27

27

27

280.

280.

280.

280.

280.

280.

280.

280.

280.

280.

280.

280.

280.

280.

280.

280.

280.

280.

280.

280.

280.

280.

280.

280.

280.

280.

280.

3200.

3200.

3200.

3200.

3200.

3200.

3200.

3200.

2400.

1600.

1200.

800.

480.

320.

480.

800.

1200.

1600.

2400.

3200.

3200.

3200.

3200.

3200.

3200.

3200.

3200.

275.

275.

275.

275.

275.

275.

275.

275.

275.

275.

275.

275.

275.

275.

275.

275.

275.

275.

275.

275.

275.

275.

275.

275.

275.

275.

275.

6

6

6

6

6

6

6

6

6

6

6

6

6

6

6

6

6

6

6

6

6

6

6

6

6

6

6

: reach 1

: reach 2

: reach 3

: reach 4

: reach 5

: reach 6

: reach 7

: reach 8

: reach 9

: reach 10

: reach 11

: reach 12

: reach 13

: reach 14

: reach 15

: reach 16

: reach 17

: reach 18

: reach 19

: reach 20

: reach 21

: reach 22

: reach 23

: reach 24

: reach 25

: reach 2 6

: reach 27

Recharge Package [file: demo.rch]

50

0

0.0045

Well Package [file: demo.wel]

50

20 20 -3000.

Output Control Option [file: demo.oc]

4

0

1

60

1

1

Strongly Implicit Procedure Package [file: demo.sip]

400

1.

5

.0001 0.0005

29
MODPATH Data Files

Name File [file: demo.pnm]

main

wel

riv

rch

budget

head(binary) 60 demo.bhd

endpoint 75 demo.ept

78 demo.mdf

12 demo.wel

14 demo.riv

18 demo.rch

50 demo.bud

Main Data File [file: demo.mdf]

27 27 5 0 999.9 l.OE+30 0

100. 150. 200. 300. 400.

10000 

10000 

internal 1.0 (free) 0

400. 400. 400. 400. 400. 400. 400. 400. 300. 200.

150. 100. 60. 40. 60. 100. 150. 200. 300. 400.

400. 400. 400. 400. 400. 400. 400. 

internal 1.0 (free) 0

400. 400. 400. 400. 400. 400. 400. 400. 300. 200.

150. 100. 60. 40. 60.

400. 400. 400. 400. 400. 400. 400. 

internal 1.0 (free) 0

100. 50. 50. 50. 50. 

internal 1.0 (free) 0

20. 0. 0. 0. 0. 

220.

open/close ibound.l 1 

constant 1 

constant 1 

constant 1 

constant 1 

constant 0.3 

constant 0.3 

constant 0.3 

constant 0.3 

constant 0.3 

constant 0.3

(free)

Name File [file: coarse.pnm]

main

wel

riv

rch

budget

78 demo.mdf

12 demo.wel

14 demo.riv

18 demo.rch

50 demo.bud

head(binary) 60 demo.bhd

endpoint 75 coarse.ept

30
IBOUND Array for Layer 1 [file: ibound. 1]

1

1

1

1

1

1

1

1

1

1

1

1

1

1

1

1

1

1

1

1

1

1

1

1

1

1

1

1

1

1

1

1

1

1

1

1

1

1

1

1

1

1

1

1

1

1

1

1

1

1

1

1

1

1

1

1

1

1

1

1

1

1

1

1

1

1

1 

1

1

1

1

1

1

1

1

1

1

1

1

1

1

1

1

1

1

1

1

1

1

1

1

1

1

1

1

1

1

1

1

1

1

1

1

1

1

1

1

1

1

1

1

1

1

1

1

1

1

1

1 

1

1

1

1

1

1

1

1

1

1

1

1

1

1

1

1

1

1

1

1

1

1

1

1

1

1

1

1

1

1

1

1

1

1

1

1

1

1

1

1

1

1

1

1

1

1

1

1

1

1

1

1

1

1

1

1

1

1

1

1

1

1

1

1

1

1

1

1

1

1

1

1

1

1

1

1

1

1

1

1

1

1

1

1

1

1

1

1

1

1

1

1

1

1

1

1

1

1

1

1

1

1

1

1

1

1

1

1

1

1

1

1

1

1

1

1

1

1

1

1

1

1

1

1

1

1

1

1

1

1

1

1

1

1

1

1

1

1

1

1

1

1

1

1

1

1

1

1

1

1

1

1

1

1

1

1

1

1

1

1

1

1

1

1 

1

1

1

1

1

3

1

1

1

1

1

1

1

1

1

1 

1

1

1

1

1 

1

1

1

1

1

1

1

1

1

1

1 

1

1

1

1

1

1 

1

1

1

1

1

1

1

1

1

1

1

1 

1

1

1

1

1

1 

1

1

1

1

1

1

1

1

1

1

1

1 

1

1

1

1

1

1 

1

1

1

1

1

1

1

1

1

1

1

1 

1

1

1

1

1

1 

1

1

1

1

1

1

1

1

1

1 

1

1

1 

1

1 

1

1

1

1

1

1 

1

1

1

1

1

1

1

1

1

1

1 

1

1

1

1 

1

1 

1

1

1

1

1

1 

1

1

1

1

1

1

1

111111111111111111111111111

31
MODPATH Response Files 

Submodel [file: fine.rsp]

@[MODPATH Version 3.00 (V3, Release 1, 9-94)]

* ENTER THE NAME FILE: 

0RESPONSE: HELP LABEL = 4.2.1 

fine.pnm

* DO YOU WANT TO STOP COMPUTING PATHS AFTER A SPECIFIED LENGTH OF TIME ?

0RESPONSE: HELP LABEL = 2.1.41

n

* SELECT THE OUTPUT MODE:

* 1 = ENDPOINTS

* 2 = PATHLINE

* 3 = TIME SERIES 

0RESPONSE: HELP LABEL =2.1.6

1

* HOW ARE STARTING LOCATIONS TO BE ENTERED?

* 1 = FROM AN EXISTING DATA FILE

* 2 = ARRAYS OF PARTICLES WILL BE GENERATED INTERNALLY 

@RESPONSE: HELP LABEL = 2.1.9

2

* DO YOU WANT TO STORE INTERNALLY-GENERATED STARTING LOCATIONS ON DISK ?

0RESPONSE: HELP LABEL = 2.1.44

n

* IN WHICH DIRECTION SHOULD PARTICLES BE TRACKED?

* 1 = FORWARD IN THE DIRECTION OF FLOW

* 2 = BACKWARDS TOWARD RECHARGE LOCATIONS

0RESPONSE: HELP LABEL = 2.1.10

2

* HOW SHOULD PARTICLES BE TREATED WHEN THEY ENTER CELLS WITH INTERNAL SINKS 7

* 1 = PASS THROUGH WEAK SINK CELLS

* 2 = STOP AT WEAK SINK CELLS

* 3 = STOP AT WEAK SINK CELLS THAT EXCEED A SPECIFIED STRENGTH

@RESPONSE: HELP LABEL = 2.1.11

1

* DO YOU WANT TO STOP PARTICLES WHENEVER THEY ENTER ONE SPECIFIC ZONE ?

0RESPONSE: HELP LABEL = 2.1.45

n

* STARTING LOCATIONS WILL BE GENERATED FOR 3-D SUBREGIONS.

*

* SHOULD PARTICLES BE PLACED IN CONSTANT HEAD CELLS ? 

0RESPONSE: HELP LABEL = 2.1.46

y

* ENTER DATA FOR SUBREGION 1 :

*

* DEFINE THE SUBREGION BY ENTERING THE MINIMUM AND MAXIMUM J,I,K COORDINATES.

* ENTER: MINIMUM J, MAXIMUM J, MINIMUM I, MAXIMUM I, MINIMUM K, MAXIMUM K

@RESPONSE: HELP LABEL = 2.1.14

4,4,4,4,4,4

* WHERE SHOULD THE PARTICLES BE LOCATED ?

* 1 = WITHIN A CELL

* 2 = ON ONE OR MORE OF THE CELL FACES

0RESPONSE: HELP LABEL = 2.1.15

2

* WHAT CELL FACES DO YOU WANT TO PLACE PARTICLES ON ?

* (ENTER ALL THE FACE NUMBERS ON A SINGLE LINE) 

@RESPONSE: HELP LABEL = 2.1.47

32
123456

* ENTER A 2-D ARRAY OF PARTICLES FOR FACE 1: NY NZ 

SRESPONSE: HELP LABEL = 2.1.17 

27 27

* ENTER A 2-D ARRAY OF PARTICLES FOR FACE 2: NY NZ 

0RESPONSE: HELP LABEL = 2.1.18 

10 10

* ENTER A 2-D ARRAY OF PARTICLES FOR FACE 3: NX NZ 

0RESPONSE: HELP LABEL = 2.1.19 

21 21

* ENTER A 2-D ARRAY OF PARTICLES FOR FACE 4: NX NZ 

0RESPONSE: HELP LABEL = 2.1.20 

21 21

* ENTER A 2-D ARRAY OF PARTICLES FOR FACE 5: NX NY 

0RESPONSE: HELP LABEL = 2.1.21 

56 56

* ENTER A 2-D ARRAY OF PARTICLES FOR FACE 6: NX NY 

0RESPONSE: HELP LABEL = 2.1.22 

56 56

* 7983 PARTICLES USED OUT OF 500000 MAXIMUM

* DO YOU WANT TO SPECIFY ANOTHER SUBREGION ?

0RESPONSE: HELP LABEL = 2.1.53

n

* DO YOU WANT TO COMPUTE VOLUMETRIC BUDGETS FOR ALL CELLS ?

0RESPONSE: HELP LABEL = 3.1.4

n

* DO YOU WANT TO CHECK DATA CELL BY CELL ?

0RESPONSE: HELP LABEL = 3.1.2

n

* SUMMARIZE FINAL STATUS OF PARTICLES IN SUMMARY.PTH FILE ?

0RESPONSE: HELP LABEL = 3.1.3

n

Original Model [file: coarse.rsp]

@[MODPATH Version 3.00 (V3, Release 1, 9-94)]

* ENTER THE NAME FILE: 

0RESPONSE: HELP LABEL = 4.2.1 

coarse.pnm

* DO YOU WANT TO STOP COMPUTING PATHS AFTER A SPECIFIED LENGTH OF TIME ?

0RESPONSE: HELP LABEL = 2.1.41

n

* SELECT THE OUTPUT MODE:

* 1 = ENDPOINTS

* 2 = PATHLINE

* 3 = TIME SERIES 

0RESPONSE: HELP LABEL = 2.1.6 

1

* HOW ARE STARTING LOCATIONS TO BE ENTERED?

* 1 = FROM AN EXISTING DATA FILE

* 2 = ARRAYS OF PARTICLES WILL BE GENERATED INTERNALLY

0RESPONSE: HELP LABEL = 2.1.9

1

* ENTER NAME OF DATA FILE CONTAINING STARTING LOCATIONS: 

0RESPONSE: HELP LABEL = 2.1.39 

coarse.stl

* IN WHICH DIRECTION SHOULD PARTICLES BE TRACKED?

* 1 = FORWARD IN THE DIRECTION OF FLOW

* 2 = BACKWARDS TOWARD RECHARGE LOCATIONS

33
SRESPONSE: HELP LABEL = 2.1.10 

2

* HOW SHOULD PARTICLES BE TREATED WHEN THEY ENTER CELLS WITH INTERNAL SINKS ?

* 1 = PASS THROUGH WEAK SINK CELLS

* 2 = STOP AT WEAK SINK CELLS

* 3 = STOP AT WEAK SINK CELLS THAT EXCEED A SPECIFIED STRENGTH

SRESPONSE: HELP LABEL = 2.1.11

1

* DO YOU WANT TO STOP PARTICLES WHENEVER THEY ENTER ONE SPECIFIC ZONE ?

0RESPONSE: HELP LABEL = 2.1.45

n

* DO YOU WANT TO COMPUTE VOLUMETRIC BUDGETS FOR ALL CELLS ?

0RESPONSE: HELP LABEL = 3.1.4

n

* DO YOU WANT TO CHECK DATA CELL BY CELL ?

SRESPONSE: HELP LABEL = 3.1.2

n

* SUMMARIZE FINAL STATUS OF PARTICLES IN SUMMARY.PTH FILE ?

SRESPONSE: HELP LABEL = 3.1.3

n

34
APPENDIX 4. OUTPUT FILES FOR SAMPLE PROBLEM 

MODFLOW Data Files

Name File [file: fine.fnm]

LIST 70 fine.1st

BAS 10 fine.bas

BCF 11 fine.bcf

WEL 72 fine.wel

OC 22 fine.oc

SIP 19 fine.slv

DATA(BINARY) 73 fine.bhd

DATA(BINARY) 74 fine.bud

Basic Package [file: fine.bas]

SUBMODEL OF WEAK SINK CELL IN ORIGINAL MODEL

FREE

1

1

1

1

1

1

1

1

1

1

1

1

1

1

1

1

1

1

1

1

1

1

1

1

1

1

1

1

1

1

1

1

1

1

1

1

1

1

1

1

1

1

1

1

1

1

1

1

1

1

7

0

10

1

1

1

10

1

1

1

1

1

10

1

1

1

1

1

1

1

10

1

1

1

1

1

1

1

10

1

1

1

1

1

1

1

1

1

1

1

1

1

1

1

1

1

1

1

1

1

-1

1

1

1

1

1

1

1

1

1

1

1

1

1

1

1

1

1

1

1

1

1

1

1

1

1

1

1

1

1

1

1

1

1

1

1

1

1

1

1

1

1

1

1

1

1

1

1

1

1

1

1

1

1

1

1

1

1

1

1

7

0

1

1

1

1

1

1

1

1

1

1

1

1

1

1

1

1

1

1

1

1

1

1

1

1

1

1

1

1

1

1

1

1

1

7 1

(713)

(713)

(713)

(713)

(713)

35
1

1

1

1

1

10

11111

11111

11111

11111

11111

10

999.9

0 301.5

0 301.5

0 301.5

0 301.5

0 301.5

0 301.5

0 301.5

i

1

1

1

1

I

I

I

1

1

1

1. 1.

Block-Centered Flow Package [file: fine.bcf]

74 0.10E+31 1.

1333333

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

1.000

57.14

57.14

50.00

289.9

4.293

50.00

278.2

4.293

289.9

50.00

266.6

4.293

278.2

50.00

254.9

4.293

266.6

50.00

243.3

4.293

254.9

50.00

231.6

4.293

HYCON

EOT

VCONT

HYCON

EOT

VCONT

TOP

HYCON

EOT

VCONT

TOP

HYCON

EOT

VCONT

TOP

HYCON

EOT

VCONT

TOP

HYCON 6

EOT 6

VCONT 6

1

1

1

2

2

2

2

3

3

3

3

4

4

4

4

5

5

5

5

36
0 243.3 TOP 6

0 50.00 HYCON 7

0 220.0 EOT 7

0 231.6 TOP 7

Solver Package [file: fine.slv]

150 5 

1.00 0.100E-04 101

Well Package [file: fine.wel]

294

294

1

2

3

4

5

6

7

1

2

3

4

5

6

7

1

74

1

1

1

1

1

1

1

2

2

2

2

2

2

2

3

7

7

7

7

7

7

7

7

7

7

7

7

7

7

7

-114

-114

-114

-114

-114

-114

-114

-114

-114

-114

-114

-114

-114

-114

-114

.01

.01

.01

.01

.01

.01

.01

.01

.01

.01

.01

.01

.01

.01

.01

2

2

2

2

2

2

2

2

2

2

2

2

2

2

2

7

1

2

3

4

5

6

7

1

2

3

4

5

6

7

1

7

1

1

1

1

1

1

1

2

2

2

2

2

2

2

3

7

1

1

1

1

1

1

1

1

1

1

1

1

1

1

1

-114.01

130.66

130.66

130.66

130.66

130.66

130.66

130.66

130.66

130.66

130.66

130.66

130.66

130.66

130.66

130.66

2

1

1

1

1

1

1

1

1

1

1

1

1

1

1

1

7

1

2

3

4

5

6

7

7

7

7

7

7

7

7

7

1

1

1

1

1

1

1

1

130.66

14.667

14.667

14.667

14.667

14.667

14.667

14.667

1

3

3

3

3

3

3

3

37
Ill 14.667 3

111 15.585 4

211 15.585 4

311 15.585 4

411 15.585 4

511 15.585 4

611 15.585 4

711 15.585 4

112 15.585 4

212 15.585 4

312 15.585 4

4 1 2 15.585 4

512 15.585 4

612 15.585 4

712 15.585 4

113 15.585 4

2

2

2

2

2

2

2

3

7

1

1

1

1

1

1

1

2

2

2

2

2

2

2

3

7

1

1

1

1

1

1

1

2

2

2

2

2

2

2

3

7

1

2

3

4

5

6

7

1

2

14.667

14.667

14.667

14.667

14.667

14.667

14.667

14.667

14.667

15.585

15.585

15.585

15.585

15.585

15.585

15.585

15.585

15.585

15.585

15.585

15.585

15.585

15.585

15.585

15.585

-0.36834

-0.36834

-0.36834

-0.36834

-0.36834

-0.36834

-0.36834

-0.36834

-0.36834

-0.36834

-0.36834

-0.36834

-0.36834

-0.36834

-0.36834

-0.36834

14.694

14.694

14.694

14.694

14.694

14.694

14.694

14.694

14.694

717 15.585 4

711 -0.36834 5

721 -0.36834 5

731 -0.36834 5

741 -0.36834 5

751 -0.36834 5

761 -0.36834 5

771 -0.36834 5

712 -0.36834 5

722 -0.36834 5

732 -0.36834 5

742 -0.36834 5

752 -0.36834 5

762 -0.36834 5

772 -0.36834 5

713 -0.36834 5

111 -0.36834 5

111 14.694 6

112 14.694 6

113 14.694 6

114 14.694 6

115 14.694 6

116 14.694 6

1 1 7 14.694 6

121 14.694 6

122 14.694 6

38
1 2 3 14.694 6

1 2 4 14.694 6

1 2 5 14.694 6

126 14.694 6

127 14.694 6

1 3 1 14.694 6

1 7 7 14.7 6

Output Control Option [file: fine.oc]

15 

0111

0 73 0

1010

39
MODPATH Data Files

Name File [file: fine.pnm]

MAIN 

WEL 

HEAD (BINARY) 

BUDGET 

ENDPOINT

71 fine.mdf 

72 fine.wel 

73 fine.bhd 

74 fine. bud 

75 fine.ept

Main Data File [file: fine.mdf]

7 7

1 3

1 1

constant

constant

internal

7

3

1

6

3

1

57

57

1.0

3

1

.

.

1

3

1

14

14

0 0 999.9 0.10E+31 0

3

0

(free)

11.65

internal 1.0

11 .65 11.65 11.65 11.65 11.65 11.65

(free)

O.OOOOE+00

289.9

internal

1 1

1 1

1 1

1 1

1 1

1 1

internal

1 1

1 1

1 1

1 1

1 1

1 1

1 1

internal

1 1

1 1

1 1

1 1 

1 1

1 1

internal

1 1

1 1

1 1

1 1

1 1

1 1

1 1

internal

1 1

1 1

1 1

1

1

1

1

1

1

1

1

1

1

1

1

1

1

1

1

1

1

1

1

1

1

1

1

1

1

1

1

1

1

1

1

1

1

1

1

1

1

1

1

1

1

1

1

1

1

1

1

1

1

1

1

1

-1

1

1

1

1

1

1

1

1

1

1

1

1

1

1

1

1

1

1

1

1

1

1

1

1

1

1

1

1

1

1

1

1

1

1

1

O.OOOOE+00 O.OOOOE+00 O.OOOOE+00 O.OOOOE+00 O.OOOOE+00 O.OOOOE+00

1

1 

1

1

1

1

1

1

1

1

1

1

1

1

1

1

1

1

1

1

1

1

1

1

1

1

1

1

1

(713)

1

1 

1

1

1

1

1

(713)

1

1

1

1

1

1

1

(713)

1

1

1

1

1

(713)

1

1

1

1

1

1

1

(713)

1

1

1

40
1 1

1 1

internal

1 1

1 1 

1 1

1 1

1 1

1 1

internal

1 1

1 1

1 1

1 1

1 1

1 1

1 1

constant

constant

constant

constant

constant

constant

constant

constant

constant

constant

constant

constant

constant

1

1

1

1

1

1

1

1

1

1

1

1

1

1

1

1

1

1

1

1

1

1

1

1

1

1

1

1

1

1

0.

0.

0.

0.

0.

0.

0.

0.

0.

0.

0.

0.

0.

1

1

1

1

1

1

1

1

1

1

1

1

1

1

3000

3000

3000

3000

3000

3000

3000

3000

3000

3000

3000

3000

3000

1

1

1

1

1 

1

1

1

1

1

1

1

1

1

1

1

1

1

1

1 

1

1

1

1

1

1

1

1

1

1

(713)

(713)

1

1

2

2

3

3

PORAQ 

PORCB 

PORAQ 

PORCB 

PORAQ 

PORCB 

PORAQ 4 

PORCB 4 

PORAQ 5 

PORCB 5 

PORAQ 6 

PORCB 6 

PORAQ 7

41