U.S. Department of the Interior

U.S. Geological Survey

Scientific Investigation Report 2004-5087

Regional Ground-Water-Flow Models of Surficial Sand and 

Gravel Aquifers Along the Mississippi River Between Brainerd and St. Cloud, Central Minnesota
Regional Ground-Water-Flow Models of 

Surficial Sand and Gravel Aquifers Along 

the Mississippi River Between Brainerd 

and St. Cloud, Central Minnesota

By J.F. Ruhl, and T.K. Cowdery

Prepared in cooperation with the Minnesota Department of Health

Scientific Investigations Report 2004-5087

U.S. Department of the Interior

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

Gale A. Norton, Secretary

U.S. Geological Survey

Charles G. Groat, Director

U.S. Geological Survey, Reston, Virginia: 2004

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Although this report is in the public domain, permission must be secured from the individual copyright owners to 

reproduce any copyrighted materials contained within this report.

Suggested citation:

Ruhl, J.F., and Cowdery, T.K., 2004, Regional ground-water-flow models of surficial sand and gravel aquifers along the 

Mississsippi River between Brainerd and St. Cloud, central Minnesota: U.S. Geological Survey Scientific Investigations Report 2004-5087, 21 p.
iii

Contents

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

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

Purpose and Scope ............................................................................................................................. 3

Hydrogeologic Setting ........................................................................................................................ 3

Ground-Water Flow Models ........................................................................................................................ 3

Numerical Model Description and Assumptions ........................................................................... 4

Model Input .......................................................................................................................................... 4

Model Calibration, Sensitivity, and Results ................................................................................... 10

Northern Study Area ................................................................................................................ 10

Southern Study Area ................................................................................................................ 11

Model limitations ........................................................................................................................................ 14

Summary ...................................................................................................................................................... 20

Acknowledgments ...................................................................................................................................... 20

References ................................................................................................................................................... 20

Figures

Figure 1. Locations of northern and southern study areas and extent of surficial sand and 

gravel aquifers along the Mississippi River between Brainerd and St. Cloud in 

central Minnesota ....................................................................................................................... 2

Figure 2. Boundary conditions for the northern model along the Mississippi River between 

Brainerd and Little Falls in central Minnesota ........................................................................ 5

Figure 3. Boundary conditions for the southern model along the Mississippi River betweeen 

Little Falls and St. Cloud in central Minnesota ....................................................................... 6

Figure 4. Measured versus simulated water levels in wells for the northern and southern 

models along the Mississippi River between Brainerd and St. Cloud in central 

Minnesota .................................................................................................................................. 12

Figure 5. Modeled ground water elevations of the northern model along the Mississsippi 

River between Brainerd and Little Falls in central Minnesota. .......................................... 13

Figure 6. Modeled ground water elevations of the southern model along the Mississippi 

River between Little Falls and St. Cloud, in central Minnesota ......................................... 16

Figure 7. Simulated water levels above land surface and dry cells in the northern model 

along the Mississippi River between Brainerd and Little Falls in central Minnesota .... 18

Figure 8. Simulated water levels above land surface and dry cells in the southern model 

along the Mississippi River between Little Falls and St. Cloud in central Minnesota. .. 19

Tables

Table 1. Data sets used to construct the northern and southern ground-water-flow models 

between Brainerd and St. Cloud in central Minnesota. ........................................................ 7

Table 2. Inital values used to define boundary conditions in the ground-water-flow models 

along the Mississippi River between Brainerd and St. Cloud in central Minnesota ........ 9

Table 3. Sensitivity analysis of the northern ground-water-flow model between Brainerd 

and Little Falls in central Minnesota. ..................................................................................... 11
iv

Tables--Continued

Table 4. Simulated volumetric water budget for the northern ground-water-flow model 

between Brainerd and Little Falls in central Minneosta ..................................................... 14

Table 5. Sensitivity analysis of the southern ground-water-flow model between Little Falls 

and St. Cloud in central Minnesota. ...................................................................................... 15

Table 6. Simulated volumetric water budget for the southern ground-water-flow model 

between Little Falls and St. Cloud in central Minnesota. ................................................... 17

Multiply By To obtain

Length

centimeter (cm) 0.3937 inch (in.)

meter (m) 3.281 foot (ft) 

kilometer (km) 0.6214 mile (mi)

Area

square meter (m2) 0.0002471 acre 

square kilometer (km2) 0.3861 square mile (mi2)

Flow rate

cubic meter per day (m3/d) 35.31 cubic foot per day (ft3/d) 

Hydraulic conductivity

meter per day (m/d) 3.281 foot per day (ft/d) 

Transmissivity*

meter squared per day (m2/d) 10.76 foot squared per day (ft2/d) 

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

 °F=(1.8×°C)+32

Vertical coordinate information is referenced to the insert datum name (and abbreviation) here, 

for instance, “North American Vertical Datum of 1988 (NAVD 88)”

Horizontal coordinate information is referenced to the insert datum name (and abbreviation) 

here, for instance, “North American Datum of 1983 (NAD 83)”

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

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

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

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

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

25°C).
Abstract

This report documents regional ground-waterflow models constructed by the U.S. Geological 

Survey in cooperation with the Minnesota Department 

of Health (MDH) to satisfy the requirements of their 

Source Water Protection Plan (SWPP). Steady-state 

single-layer ground-water-flow models were constructed with the computer program MODFLOW to 

simulate flow in surficial sand and gravel aquifers 

along the Mississippi River between Brainerd and St. 

Cloud in central Minnesota. The hydrogeologic data 

that were used to construct the models were compiled 

from available sources.

Calibrated values of horizontal hydraulic conductivity and areal recharge for the aquifer in a northern 

model area were 70 m/d and 3.0x10-4 m/d, respectively. This model was sensitive to net areal recharge, 

vertical hydraulic conductivity of perennial streambed 

sediments, and horizontal hydraulic conductivity. The 

major source of net inflow to the model was from 

edge boundary cells. The major source of net outflow 

was ground-water discharge to perennial and ephemeral streams.

Calibrated values of horizontal hydraulic conductivity and areal recharge for the aquifer in a southern 

model area were 70 m/d and 6.0x10-4 m/d, respectively. This model was sensitive mostly to horizontal hydraulic conductivity. Net areal recharge and 

ground-water discharge to perennial streams were the 

major sources of net inflow and outflow, respectively. 

Introduction

The Minnesota Department of Health (MDH) is 

responsible for implementation of the U.S. Environmental Protection Agency’s (USEPA) Source-Water 

Protection Program (SWPP) in Minnesota. One 

component of this program is to designate contributing recharge areas that surround public water-supply 

wells. The USEPA (1987) designed the SWPP to 

assist state and local agencies and municipalities in 

the protection of recharge areas that contribute water 

to public water-supply wells against infiltration, percolation, and transport of contaminants.

The SWPP considers the capture zone of a public 

water-supply well to be a particularly sensitive area 

that requires special protection. The capture zone is 

the area around a supply well bounded by lines of 

equal ground-water travel time. In this study the capture zone is considered to be the area that contributes 

recharge to the well for a specific ground-water travel 

time.

The methods used to delineate capture zones 

around supply wells range from simple techniques, 

such as specification of an area of constant radius 

around the well of interest, to construction of groundwater-flow models combined with particle-tracking 

programs (U.S. Environmental Protection Agency, 

1987). The MDH has adopted the latter, more complex, technique to delineate capture zones around 

supply wells (Bruce Olsen, Minnesota Department of 

Health, written commun., 2002). The MDH will use 

nested, local ground-water-flow models developed 

within the framework of regional flow models to 

delineate capture zones around supply wells of interest.

The MDH, in cooperation with the U.S. Geological Survey (USGS), developed regional ground-waterflow models for aquifers in two areas to be used in 

their SWPP. These models incorporated existing data 

from the USGS and various state agencies; much of 

these data were compiled by the MDH. The modeled 

aquifers consist of surficial sand and gravel deposited 

by glacial meltwater along the present course of the 

Mississippi River (fig. 1).

Regional Ground-Water-Flow Models of Surficial Sand 

and Gravel Aquifers Along the Mississippi River Between 

Brainerd and St. Cloud, Central Minnesota

By James F. Ruhl, and Timothy K. Cowdery
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Figure 1. Locations of northern and southern study areas and extent of surficial sand and gravel aquifers along the Mississippi River 

between Brainerd and St. Cloud in central Minnesota

2 Ground-Water Flow Models of Surficial Sand and Gravel Aquifers along the Mississippi River 
Purpose and Scope

The purpose of this report is to document regional 

ground-water-flow models constructed for the MDH 

to satisfy the requirements of their SWPP. The models 

were constructed during 2001-02 for surficial sand 

and gravel aquifers in two areas along the Mississippi River between Brainerd and St. Cloud in central 

Minnesota. This area was divided into overlapping 

northern and southern portions, each about 2,000-km2, 

for construction of the two models (fig. 1). The two 

models (hereinafter referred to as the northern and 

southern models) simulate ground-water flow in the 

aquifers within these areas as single layer systems 

under water-table, steady-state conditions. Available 

hydrologic data were used as model inputs and for 

model calibration. Ground-water levels measured in 

wells drilled during the last 50 years and baseflow 

measurements of the Mississippi River made in 1988 

(Payne, 1995) were used for model calibration. 

Hydrogeologic Setting

Average monthly temperatures during 1961-90 

for St. Cloud, Minnesota, located at the southern end 

of the study area, ranged from -23.9oC in January to 

32.4oC in July (Minnesota State Climatologist, 2002). 

Average annual precipitation during 1961-90 for St. 

Cloud was 69.6 cm (Minnesota State Climatologist, 

2002). About 80 percent of the annual precipitation 

occurs during May through October. Estimated mean 

annual evaporation in the study area is 56 cm (Helgesen and others, 1975).

Unconsolidated glacial deposits from several 

lobes of the Laurentian Ice Sheet (100,000-10,000 

years ago) overlie crystalline bedrock throughout the 

study area (Wright, 1972). These deposits, which 

are either stratified (sands and gravels) or unstratified (tills), range from 0 to about 90 m in thickness 

(Helgesen and others, 1975). The stratified deposits 

consist of outwash, ice contact, alluvial, and terrace 

sediments. The alluvial and terrace sediments are 

glacial deposits reworked by post-glacial streams. 

The stratified deposits include both extensive surficial 

sediments and buried sediments of unknown extent 

lying within unstratified deposits. The locations of 

most stratified buried sediments and the nature of the 

hydraulic connections of these deposits to surficial 

sediments and surface-water bodies are unknown. 

Based on sediment texture, the hydraulic conductivity 

of the stratified deposits is 1–6 orders of magnitude 

greater than the unstratified deposits (Fetter, 1988)

The surficial sand and gravel aquifers in the 

two study areas consist of stratified glacial deposits adjacent to the Mississippi River. These aquifers 

are surrounded by unstratified glacial deposits (till). 

Areal recharge to the aquifers ranges from 1.5x10- 4

to 8.5x10-4 m/d (Helgesen and Lindholm, 1977; 

Lindholm, 1980; and Ruhl, 2002). The aquifers are 

recharged from precipitation, including snow melt, 

and, to a lesser extent, from bank overflow along the 

Mississippi River during high water and from infiltration along the aquifer edges where the surficial sand 

and gravel abuts surrounding till. Sources of edge 

recharge could include overland flow from adjacent 

till uplands or seepage from ephemeral streams near 

the aquifer-upland boundary during high-flow periods, and ground-water flow from aquifers buried 

within surrounding till. The aquifers may also derive 

recharge from portions of some lakes and wetlands. 

The aquifers mostly discharge to both perennial 

(the Mississippi, Sauk, and Crow Wing Rivers) and 

ephemeral streams and to portions of some lakes and 

wetlands. 

 The aquifers are as much as 62 m thick with as 

much as 44 m of saturation (Lindholm, 1980). The 

horizontal hydraulic conductivity of these aquifers 

ranges from 10 to 200 m/d. The transmissivity can 

be locally as much as 3,700 m2/d (Lindholm, 1980). 

Yields from wells completed in the aquifers range 

from several hundred square meters per day where 

the saturated thickness is less than 5 m to greater than 

5,000 m3/d (Lindholm, 1980). 

Ground-Water Flow Models

Separate models simulated ground-water flow 

in surficial sand and gravel aquifers for the northern 

and southern portions of the study area (fig. 1). The 

conceptual model of the aquifers is based on information in the Hydrogeologic Setting section. Aquifer 

properties, recharge and discharge characteristics, 

and aquifer extent and thickness were incorporated 

into USGS MODFLOW numerical models (McDonald and Harbaugh, 1988) using the U.S. Department 

of Defense Groundwater Modeling System (GMS) 

(Environmental Modeling Systems, Incorporated, 

2002). MODFLOW is a three-dimensional, finite-difference computer program used to solve the groundwater-flow equation over a modeled area. GMS is a 

commercial computer program used to prepare input 

data sets for MODFLOW and to graphically illustrate 

model input and output. No attempt was made to 

simulate ground-water flow from or to the unmapped 

Introduction 3
4 Ground-Water Flow Models of Surficial Sand and Gravel Aquifers along the Mississippi River 

buried sand and gravel aquifers within surrounding 

till. 

Numerical Model Description and Assumptions

Both numerical ground-water models (hereinafter, models) were single-layer, unconfined, twodimensional (horizontal), and steady-state. The northern model area extends along the Mississippi River 

from Brainerd to Little Falls (fig. 1). The southern 

model area extends along the Mississippi River from 

Little Falls to the confluence of the Mississippi and 

Sauk Rivers near St. Cloud (fig. 1). The most detailed 

aquifer geometry data are sand and gravel thickness 

on a 100-m square gridded array produced by the 

Minnesota Geological Survey (MGS) (written commun., 1999; 2000). This grid was used as the model 

grid and is adequate to represent aquifer geometry, 

hydraulic properties, and boundary conditions in sufficient detail for construction of subsequent nested 

local models.

Flow of ground water within the surficial sand 

and gravel aquifers was assumed to be under watertable (unconfined) conditions. Underlying and surrounding tills originally were assumed to represent 

no-flow boundaries. This assumption proved inaccurate in the first model (southern study area) that was 

constructed because the edges of the aquifer abutting 

till were always dry, contrary to actual conditions 

measured in the aquifers. Consequently, a general 

head-dependent flux boundary condition was added to 

the horizontal edges of the northern-study-area model 

to account for possible runoff infiltration recharge, 

ephemeral-stream recharge, and recharge from lateral 

till or buried aquifers.

A general head-dependent flux boundary allows 

water flow into or out of a cell at a rate proportional 

to the head gradient between the cell and an external 

source, and to a proportionality constant that represents the hydraulic conductivity and area of the intervening material. Single values for hydraulic conductivity and area were used for all of the head-dependent 

flux boundary cells in the model. The original value 

of hydraulic conductivity was adjusted during the 

calibration process to produce realistic model output 

of hydraulic heads and fluxes.

Based on regional water-table maps of the northern and southern ends of each model, ground-water 

flow was assumed to be perpendicular to the Mississippi, Sauk, and Crow Wing Rivers, the main hydrologic sinks. Therefore, these boundaries were assumed 

to be no-flow. The southern model terminated at a 

string of lakes and streams in the northeast part of 

the model, which also were assumed to be no-flow 

boundaries.

 Net areal recharge, which represents net infiltration of precipitation at land surface (total infiltration 

minus evapotranspiration), was applied uniformly to 

each model. Explicit simulation of seasonal evapotranspiration was not attempted in either model 

because it was beyond the scope of the study.

Surface-water features in each model were 

simulated as MODFLOW river, general-head, and 

drain boundaries in the models (figs. 2 and 3). The 

Mississippi River and smaller perennial streams were 

modeled as river boundaries; lakes and wetlands were 

modeled as general-head boundaries; and ephemeral streams (northern study area only) were modeled as drain boundaries. River cells allow leakage 

through the stream bottom based on the difference in 

water levels and streambed conductance. A river cell 

will provide or receive as much water as the model 

requires to reach a mathematical solution. Drain 

cells allow leakage only from the aquifer to the drain 

(ephemeral stream). 

Ground-water withdrawals from the aquifer were 

simulated for 19 and 63 production wells (irrigation 

and public-supply wells) in the northern and southern 

models, respectively. Domestic-supply well withdrawals were not simulated because these withdrawals were very small compared to withdrawals from 

production wells.

Model Input 

Input data for both models were prepared as 

ARC/INFO coverages and shapefiles (Environmental Science Research Institute, 2004), imported into 

GMS, and edited and converted into MODFLOW 

input files. Information regarding the original data 

sets are shown in table 1. The MGS produced a 100-

m grid of sand and gravel thickness from existing 

well stratigraphic logs. These data were modified to 

produce an aquifer extent and bottom elevation array 

by subtracting the thickness array from a land-surface digital elevation model (DEM). Model cells with 

aquifer thickness less than 1m were removed as active 

cells, resulting in the creation of arrays of aquifer bottom elevation.

The DEM of the land-surface, which is coincident with the MGS sand-and-gravel-thickness array, 

is interpolated from the USGS 30-m DEM based on 

the hypsography of 1:24,000-scale USGS quadrangle 

maps. This DEM, which was assumed to represent 

the land surface, was used to calculate all elevations 
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Figure 2. Boundary conditions for the northern model along the Mississippi River between Brainerd and Little Falls in central Minnesota

Ground-Water Flow Models 5
6 Ground-Water Flow Models of Surficial Sand and Gravel Aquifers along the Mississippi River 

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Figure 3. Boundary conditions for the southern model along the Mississippi River betweeen Little Falls and St. Cloud in central Minnesota
Table 1. Data sets used to construct the northern and southern ground-water-flow models between Brainerd and St. Cloud in central Minnesota—Continued.

[—, not applicable; MGS, Minnesota Geological Survey; CWI, county well index; m, meter; NM, northern model; SM, southern model; USGS, U.S. Geological Survey; DEM, digital elevation model; DLG, digital line graph; PIC, Primary Information Code; GH, general head; RIV, river; DRN, drain; MDH, Minnesota Department of Health; MNDNR, Minnesota Department of Natural Resources; <, less than; >, greater than; m, meter; m/d, meter per day; RCH, recharge; WEL, well]

Model input Data agency Data source Original data 

set

Scale Northern model 

input data set

Southern model 

input data set

Data modification MODFLOWstress Reference

Aquifer 

Active cells MGS CWI well log 

compilation

sandthk_rev.txt 

(NM) sandthck.txt (SM)

100-m cells N-act_aq.shp modelarea.shp polygons created from 

sandthk_rev.txt (NM) or sandthck.txt (SM), including areas >1-m thick

Cell-top 

elevation

USGS 1:24,000 quadrangle hypsography 30-m DEM grid 100-m cells N-dem100m landsurf interpolated to 100-m grid USGS, 1999

Cell-bottom elevation

USGS 1:24,000 quadrangle hypsography 30-m DEM grid 100-m cells N-aqbottom sandbott interpolated to 100-m grid USGS, 1999MGS CWI well log 

compilation

sandthk_rev.txt 

(NM) sandthck.txt (SM)

100-m cells excluded cell bottom within 

1 m of DEM

Hydraulic 

Conductivity

Calibrated

Hydrography

Lakes USGS quadrangle 

hydrography

USGS DLG 1:100,000 N-lakes.shp Lakes.shp PIC code = 421, removed 

lakes covering less than 1/4 

cell

GH USGS, 1983

Wetlands USGS quadrangle 

hydrography

USGS DLG 1:100,000 N-wetland_

1m.shp

Wetland.shp PIC code = 109, 111, split 

polygons into 1-m elevation intervals

GH USGS, 1983

River areas USGS quadrangle 

hydrography

USGS DLG 1:100,000 N-river_poly.

shp

River.shp split polygons into 1-m 

elevation intervals (2-m intervals in the northern model)

RIV USGS, 1983

River lines USGS quadrangle 

hydrography

USGS DLG 1:100,000 N-peren_

stream.shp

Streams.shp PIC code =421, width assumed to be 10 m (SM) RIV USGS, 1983

Intermittent river lines

USGS quadrangle 

hydrography

USGS DLG 1:100,000 N-inter_stream.

shp

— DRN USGS, 1983

Hydrographic elevations

USGS 1:24,000 quadrangle hypsography 30-m DEM grid 100-m cells hydrography shapefiles, N- peren_pts.shp, 

N-inter_pts.shp

hydrography shapefiles, 

strnodes.shp

interpolated to 100-m grid, then to hydrographic centroid or endpoint

USGS, 1999

Ground-Water Flow Models 7
8 Ground-Water Flow Models of Surficial Sand and Gravel Aquifers along the Mississippi River Table 1. Data sets used to construct the northern and southern ground-water-flow models between Brainerd and St. Cloud in central Minnesota—Continued. [—, not applicable; MGS, Minnesota Geological Survey; CWI, county well index; m, meter; NM, northern model; SM, southern model; USGS, U.S. Geological Survey; DEM, digital elevation model; DLG, digital line graph; PIC, Primary Information Code; GH, general head; RIV, river; DRN, drain; MDH, Minnesota Department of Health; MNDNR, Minnesota Department of Natural Resources; <, less than; >, greater than; m, meter; m/d, meter per day; RCH, recharge; WEL, well] Model input Data agency Data source Original data set Scale Northern model input data set Southern model input data set Data modification MOD- FLOW- stress Reference Initial ground- water heads MDH CWI well log compilation 100-m cells N-w_table wtelev excluded heads in buried aquifers, above land surface, below aquifer bottom, assumed no stickup of mea- suring point USGS quadrangle hydrography USGS DLG 100-m cells USGS, 1983 Lake and wetland bed conductance calibrated N-lakes.shp, N- wetland_1m.shp lakes.shp, wet- land.shp initial: 2 m/d (SM)

—

River bed conductance calibrated river hydrogra- phy shapefiles river hydrogra- phy shapefiles initial: 20 m/d (SM)

—

Hydrographic bed thickness

assumed hydrography 

shapefiles

hydrography shapefiles

2 m for streams, 5 m for wetlands (SM)

—

Inputs and outputs

Net areal recharge area MGS CWI well log compilation sandthk_rev.txt (NM) sandthck.

txt (SM)

100-m cells N-act_aq.shp modelarea.shp polygons created from 

sandthk_rev.txt (NM) or sandthck.txt (SM), excluding areas <1-m thick

RCH

—

Net edge recharge area USGS constructed constructed

— N-edge-points.

shp

— edge cell of model not 

containing a hydrographic stress

GH

—

Well Withdrawal MNDNR Well Water Use mrcpum.shp (SM)

— wells.shp excluded wells screened 

in buried aquifers, above land surface, below aquifer bottom

WEL

—

Initial net areal recharge rate

calibrated

—

Initial net edge conductivity

calibrated

— initial value: 0.1 m/d (NM)

—

Calibration data

Heads MDH CWI retrieval wells.shp (NM), 

wells (SM)

— calibration 

wells.shp

obwell1.shp excluded heads in buried 

aquifers, above land surface, below aquifer bottom, assumed no stickup

—

Flux USGS 1988 Seepage 

run

—

—

—

— compiled from report

— Payne, 1995
used in the models. The area of hydrologic features 

(streams, lakes and wetlands, hereinafter referred to as 

hydrography) originated from the USGS 1:100,000-

scale digital line graphs (DLG). 

To ease importing the model input data into 

GMS, the original DLG coverages of the perennial 

and ephemeral streams, lakes, and wetlands were converted into polygon and arc shapefiles. Polygons less 

than one-quarter cell in area (2,500 m2) were excluded 

from all shapefiles for simplicity. Wetland and river 

polygons (southern model only) were divided into 

100-m-grid sized polygons and assigned a surface 

elevation from the DEM. These polygons were aggregated into polygons of equal elevation class based on 

1-m elevation intervals. River polygons in the northern model were divided into 2-m elevation interval 

polygons based on DEM elevations along a line 

tracing the middle of the river. Two-meter intervals 

were selected to keep the number of river polygons 

manageable. This choice produces 2-m high waterfalls 

in the model periodically on the Mississippi River, 

which do not exist in reality. Modeled ground-water 

flow near these artificial waterfalls is inaccurate. 

The water-table surfaces used to define initial 

heads in the models are based on the DEM landsurface data for the streams, lakes, wetlands, and on 

water-table depth data from well logs. The MDH 

compiled the water-table depth data from the MGS 

County Well Index data base. These water-level data 

generally are of poor and variable quality. Most water 

levels were collected by the well driller, just after well 

construction. These water levels were affected by 

drilling and may not be adjusted for the height of the 

casing above land surface. The water levels were measured during the last 50 years, but most were obtained 

during the last 30 years. These wells exist throughout 

the study area, but are spaced more closely near areas 

of greater population. Average water levels were used 

at a few sites with multiple measurements. 

A water-table surface was needed for initial heads 

in the model. This surface was generated by interpolating all water-level data using the Inverse-Weighted 

Distance Method and adjusting the value to 1-m above 

the aquifer bottom, or to the land surface where the 

interpolated value was outside those ranges. The measured water-depth data also were used as a water-level 

calibration data set. 

Values of horizontal hydraulic conductivity (table 

2) and net areal recharge were applied uniformly 

throughout the two modeled areas. Net areal recharge 

was 3 x 10-4 and 6 x 10-4 m/d for the northern and 

southern models, respectively. Differences in geology 

and topography probably cause variation from the 

uniform values of model input parameters within the 

study areas. Construction of the models based on the 

spatial variations of these model input parameters was 

beyond the scope of the study.

Withdrawals from the aquifer were simulated 

based on pumping for production wells used for irrigation and municipal water supply reported in Minnesota Department of Natural Resources (DNR) wateruse data base. These data were supplied by the MDH 

in 1999 and reported data for 1998. Pumping amounts 

have increased over the period during which water 

levels were measured. However, most water levels 

used in calibration were measured more recently when 

the greater pumping was occurring. Pumping during 

baseflow measurement in 1988 (Payne, 1995) probably was greater than usual because of the drought at 

Model Surface-water feature Modeled in 

MODFLOW as

Feature geometry 

in model

Bed sediment 

thickness (m)

River width

(m)

Initial hydraulic 

conductivity (m/d)

Northern lakes and wetlands GHB polygon 2 — 2

perennial streams RIV polygon 2 — 0.2

perennial streams RIV line 2 8 0.2

ephemeral streams DRN line 2 6 20

edge recharge GHB point — — 1

10,000

Southern lakes GHB polygon 2 — 2

wetland GHB polygon 5 — 2

perennial streams RIB polygon 2 — 20

perennial streams RIV line 2 10 20

Table 2. Inital values used to define boundary conditions in the ground-water-flow models along the Mississippi River between Brainerd 

and St. Cloud in central Minnesota

[—, not applicable; GHB, general head boundary package; RIV, river boundary package; DRN, drain boundary package; m, meter; m/d, meter per day]

1

 MODFLOW conductance for the entire 100-m x 100-m cell.

Ground-Water Flow Models 9
10 Ground-Water Flow Models of Surficial Sand and Gravel Aquifers along the Mississippi River 

that time. Pumping during 1988 may be comparable 

to the presumably greater pumping rates of the late 

1990’s. While the climatological and pumping data 

for this comparison exist, this analysis was not done 

for this study. Pumping in the northern and southern 

model areas ranged from about 9 to 1,000 and from 

about 2 to 2,000 m3/d per well, respectively.

Perennial streams were simulated with the 

MODFLOW river package (RIV), ephemeral streams 

with the MODFLOW drain package (DRN), and lakes 

and wetlands with the MODFLOW general-head 

boundary package (GHB). The packages require user 

specified values for conductance (a parameter incorporating length, width, and thickness of the connection with the aquifer, and its hydraulic conductivity) 

and a driving head. Constant values of thickness (and 

width for line features) and hydraulic conductivity 

were specified for each connection (table 2). The area 

(or length for line features) of each connection was 

derived from the hydrography of USGS 1:100,000 

scale digital maps. The dimensions used to define the 

thicknesses of the bed sediments of streams, lakes, 

and wetlands are considered to be reasonable estimates of their true values.

The specified conductances are based on estimates of the vertical hydraulic conductivities of the 

bed sediments. These estimates are considered to be 

reasonable approximations of their true values based 

on previously published values of silty, low-permeability unconsolidated materials (Heath, 1983). The 

conductance specified for the edge recharge cells in 

the northern model was not chosen on the basis of 

physical characteristics of the aquifer materials, but 

rather was adjusted to simulate reasonable groundwater head and flux in the aquifer. 

Model Calibration, Sensitivity, and Results

The models were calibrated by varying horizontal 

hydraulic conductivity, net areal recharge, and conductance for the GHB and RIV packages. Values for 

these model inputs were selected based on: (1) comparison of the simulated and measured baseflow to the 

Mississippi River and its tributaries (Payne, 1995); 

and (2) minimization of the mean errors computed 

from the differences between measured and simulated hydraulic heads at well locations. In calibration, 

matching baseflow was given a higher priority than 

matching heads because of the inaccuracies contained 

in the head data set. 

The baseflows used to calibrate the models were 

based on a study of baseflow to the reaches of the 

Mississippi River and tributaries upstream from the 

Minneapolis-St. Paul area during July 1988 (Payne, 

1995). Results of this study were used to estimate 

tributary and mainstem channel baseflow, which was 

assumed to be net (ground-water discharge minus possible ground-water recharge) ground-water discharge 

to the Mississippi River and tributaries in the modeled 

areas. These measured baseflows were 414,282 and 

358,685 m3/d for the northern and southern models, respectively. These measurements are based on 

the fractions of the reaches of the Mississippi River 

within each modeled area relative to the total reach of 

the Mississippi River analyzed in the study by Payne 

(1995). The measurements of baseflow to tributaries 

of the Mississippi River within each modeled area are 

based on the same approach. 

 Output from the calibrated models included 

steady-state hydraulic head values and volumetric 

inflow and outflow components for the modeled areas. 

Convergence criteria used to determine solutions for 

the models were a maximum change in hydraulic head 

of 0.1 m for any grid cell with a maximum of 250 

iterations.

Northern Study Area

Calibrated model inputs for the northern model 

and the sensitivity of the model to adjustments of 

these inputs are shown in table 3. The calibrated values of horizontal hydraulic conductivity (70 m/d) and 

net areal recharge (3.0x10-4 m/d) are consistent with 

previously reported values. 

Figure 4 shows the correspondence of measured 

to simulated hydraulic heads at 236 well locations for 

the calibrated northern model. The least-squares fit of 

the measured to simulated hydraulic heads has as an 

R2 value of 0.9540. The position of the least-squares 

line above and to the left of the line of correspondence (fig. 4) indicates a positive bias in the modeled 

heads. The spatial distribution of these values indicates that the residuals generally are greatest near the 

periphery of the aquifers distant from the Mississippi 

River (fig. 5). Steady-state hydraulic heads computed 

by the model range from about 340 to 370 m above 

NGVD88. 

The mean absolute error for ground-water levels 

in the sensitivity analysis indicates that the model 

is most sensitive to net areal recharge and vertical 

hydraulic conductivity of perennial streambed sediments, and, to a lesser extent, horizontal hydraulic 

conductivity (table 3). The sensitivity analysis, based 

on a comparison of the computed as a percent of measured baseflow, produced similar results. This comparison indicates that the model is most sensitive to, 

in decreasing order, vertical hydraulic conductivity of 
Table 3. Sensitivity analysis of the northern ground-water-flow model between Brainerd and Little Falls in central Minnesota.

[The percent discrepancy between total inflow and total outflow for all model runs was within 1.35 percent; m, meter; m/d, meter per day; m3/d, cubic meter per 

day]

Calibration variable Calibrated values 

(m/d)

Multiplication 

factor

Computed baseflow as 

percent of measured 

baseflow 

(m3/d)

Mean absolute error for 

ground-water levels 

(m)

Horizontal hydraulic conductivity 70 0.1 31 2.35

0.2 42 1.97

0.5 69 1.82

1.0 100 1.84

2.0 139 1.94

5.0 194 2.11

10.0 232 2.24

Net areal recharge 3.0x10-4 0.1 94 1.70

0.2 94 1.71

0.5 97 1.76

1.0 100 1.84

2.0 108 1.99

5.0 131 2.37

10.0 167 3.04

Vertical hydraulic 

conductivity of 

perennial streambed sediments

0.02 0.1 23 2.46

0.2 39 2.31

0.5 71 2.03

1.0 100 1.84

2.0 133 1.68

5.0 188 1.58

10.0 251 1.56

Vertical hydraulic 

conductivity of

 lakebed and wetland sediments

2 0.1 107 1.74

0.2 105 1.76

0.5 103 1.81

1.0 100 1.84

2.0 98 1.86

5.0 96 1.88

10.0 95 1.89

Hydraulic conductivity of edge recharge 

cells

10,000 0.1 98 1.81

0.2 99 1.82

0.5 99 1.83

1.0 100 1.84

2.0 100 1.84

5.0 101 1.85

10.0 101 1.85

perennial streambed sediments, horizontal hydraulic 

conductivity, and net areal recharge (table 3).

The volumetric flow budget of the model indicates that net inflow consists of recharge from edge 

cells (75 percent) (table 4). The volumetric flow budget also indicates that discharge to perennial streams, 

lakes, and wetlands accounts for 88 percent of the net 

outflow, and that discharge to ephemeral streams (11 

percent) and to well withdrawals (1 percent) account 

for the remainder.

Southern Study Area

The southern model was more unstable (less 

likely to converge to a solution) than the northern 

model. Thus, calibration and sensitivity analysis of 

the southern model are based on smaller ranges of 

model input adjustments. The calibrated model inputs 

for the southern model and the sensitivity of the 

model to adjustments of these inputs are tabulated in 

table 5. The calibrated values of horizontal hydraulic 

conductivity (70 m/d) and net areal recharge (6.0x10-4

m/d) are consistent with previously reported values 

Ground-Water Flow Models 11
12 Ground-Water Flow Models of Surficial Sand and Gravel Aquifers along the Mississippi River 

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Figure 4. Measured versus simulated water levels in wells for the northern and southern models along the Mississippi River between 

Brainerd and St. Cloud in central Minnesota [RSME, Root Mean Square Error] 
Figure 5. Modeled ground water elevations of the northern model along the Mississsippi River between Brainerd and Little Falls in 

central Minnesota.

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Ground-Water Flow Models 13
14 Ground-Water Flow Models of Surficial Sand and Gravel Aquifers along the Mississippi River 

(Helgesen and Lindholm, 1977; Lindholm, 1980; and 

Ruhl, 2002).

Figure 4 shows the correspondence of measured 

to simulated hydraulic heads at 216 well locations for 

the calibrated southern model. The least-squares fit 

of the simulated to measured hydraulic heads has an 

R2 value of 0.9539. As was the case for the northern 

model, the position of the least-squares line above 

and to the left of the line of correspondence (fig. 4) 

indicates a positive bias in modeled heads. Unlike 

the northern model, the spatial distribution of these 

values indicates that the residual water levels generally are greatest within the interior portions of the 

aquifers distant from the active cell boundary and near 

to the Mississippi River (fig. 6) However, much of the 

periphery of the southern model are dry cells, which 

do not yield residuals. Also, areas with the greatest 

residuals are near interior areas that have gone dry, 

demonstrating the inadequacy of the model in these 

areas. The range of the residuals is less in the southern model than in the northern model. Steady-state 

hydraulic head computed by the model range from 

about 305 to 340 m above NGVD88. 

The mean absolute error for the ground-water 

levels in the sensitivity analysis indicates that the 

model is sensitive to increased horizontal hydraulic 

conductivity and decreased net areal recharge (table 

5). The model was unstable to decreased horizontal 

hydraulic conductivity and increased areal recharge. 

The sensitivity of the model to vertical hydraulic 

conductivity of lakebed sediments was not evaluated 

because of the instability of the model to changes in 

this input (table 5). The sensitivity analysis, based on 

a comparison of the computed as a percent of measured baseflow, indicates that the model was most 

sensitive to decreased horizontal hydraulic conductivity, and to a lesser extent, increased recharge.

The volumetric-flow budget of the model indicates that net inflow consists of predominantly net 

areal recharge (88 percent) and to a lesser extent 

discharge from lakes and wetlands (12 percent) (table 

6). The volumetric-flow budget also indicates that 

discharge to perennial streams accounts for the 96 

percent of the net outflow and that well withdrawals 

account for the remainder.

Model limitations

The ground-water-flow models are numerical 

simplifications of real aquifer flow systems. Model 

results are affected by numerical approximations used 

to solve the ground-water-flow equation, discretization of the modeled area, and the availability and 

accuracy of hydrogeologic data used to define boundary conditions and model stresses. Another important 

limitation of calibrated ground-water-flow models is 

the non-uniqueness of their solutions. Multiple combinations of model input values may result in equally 

good fits of simulated model outputs to measured 

data. Limitations of the northern and southern models 

were evaluated based on the availability and reliability of hydraulic-head and baseflow data used in their 

calibration.

Hydraulic-head data were available for 236 wells 

in the northern model and for 216 wells in the southern model. These data are considered accurate to 

within 2 meters. Comparison of the simulated hydraulic head data to the measured data indicated a positive 

bias for both the northern and southern models (fig. 

4). 

Construction of the two models did not address 

spatial variation of horizontal hydraulic conductivSources/Sinks Inflow Outflow Net flow (inflow - outflow)

Rate Percent Rate Percent Rate Percent net 

inflow

Percent net 

outflow

Perennial streams 3,846 0 420,298 4 -416,452 — 47

Ephemeral streams 0 0 98,006 1 -98,006 — 11

Lakes and wetlands

9,655,657 82 10,023,679 85 -368,022 — 41

Well withdrawals 0 0 7,126 0 -7,126 — 1

Edge recharge 1,852,970 16 1,238,395 11 614,575 75 —

Net areal recharge 202,539 2 0 0 202,539 25 —

Total 11,715,012 100 11,787,504 101 -72,492 100 100

Table 4. Simulated volumetric water budget for the northern ground-water-flow model between Brainerd and Little Falls in central Minnesota

[flow rates in cubic meters per day; —, not applicable; total percentages greater than 100 are due to rounding]
Introduction 15

Table 5. Sensitivity analysis of the southern ground-water-flow model between Little Falls and St. Cloud in central Minnesota. 

[The percent discrepancy between total inflow and total outflow for all model runs was within 1.14 percent; *, indicates model did not converge to solution; m, 

meter; m/d, meter per day; m3/d, cubic meter per day]

Calibration variable Calibrated values 

(m/d)

Multiplication 

factor

Computed baseflow as percent of measured baseflow 

(m3/d)

Mean absolute error for 

water levels (m)

Horizontal hydraulic conductivity 70 0.10 * *

0.20 * *

0.50 * *

1.00 101 1.41

2.00 142 1.10

5.00 266 0.96

10.00 446 0.87

Net areal recharge 6.0x10-4 0.10 * *

0.20 50 0.96

0.50 72 1.07

1.00 101 1.41

2.00 * *

5.00 * *

10.00 * *

Vertical hydraulic conductivity of 

perennial streambed sediments

20 for polygons and 

100 for line features

0.10 * *

0.20 91 1.37

0.50 89 1.39

1.00 101 1.41

2.00 * *

5.00 * *

10.00 * *

Vertical hydraulic conductivity of 

lakebed sediments

2 0.10 * *

0.20 * *

0.50 * *

1.00 101 1.41

2.00 * *

5.00 * *

10.00 * *
16 Ground-Water Flow Models of Surficial Sand and Gravel Aquifers along the Mississippi River 

Figure 6. Modeled ground water elevations of the southern model along the Mississippi River between Little Falls and St. Cloud, in 

central Minnesota

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Model limitations 16
ity and recharge. Construction of the models in 

this manner, which would have required detailed 

hydrogeologic information from aquifer tests and 

site-specific studies, was beyond the scope of the 

study. Therefore, single, uniform values of horizontal 

hydraulic conductivity and recharge were specified for 

each model.

Recharge was simulated differently in the two 

models. These models were developed sequentially. 

Improvements in model recharge learned while constructing the first model (the southern model area) 

were incorporated into the second model (the northern model area). Recharge in both models included 

leakage from rivers, lakes and wetlands, and areal 

infiltration. The northern model also included lateral recharge from edge grid cells (as a general-head 

boundary). As a result, the areal recharge rate for the 

southern model is twice that for the northern model 

to make up for the lack of edge recharge. Lateral 

recharge is probably also important in the southern 

model. Lack of this recharge in the southern model 

probably explains why so many peripheral cells were 

dry at steady state. Streambed conductance in the 

southern model is 5,000 times greater than for the 

northern model. In the southern model, streambed 

conductance is greater than aquifer hydraulic conductivity, meaning that the rivers sit within the aquifer 

material with the river bed material providing no 

resistance to ground-water flow. This is probably an 

unrealistic condition and may be related to the lack of 

edge recharge in the southern model. Future simulations of the southern model area should incorporate 

edge recharge to address the deficiencies of this 

model. In the northern model, river bed conductance 

was decreased to help prevent cells near the river from 

drying out.

Payne (1995) estimated baseflow to the Mississippi River for subreaches, which were incorporated 

in the calibration of the two modeled areas. Gunard 

and others (1988), which indicates that the reported 

estimated baseflow measurement to be accurate to 

within 10 percent. The simulated net discharge to 

the Mississippi River and its tributaries (perennial 

streams) were calibrated to within 1 percent for both 

the northern and southern models. Therefore, measurement errors greatly outweigh calibration errors in 

terms of model flux. Payne’s (1995) baseflow measurement was conducted during a period of extreme 

low flow, and represents a minimum value. Therefore, 

the flux through, and the recharge to, these models 

also are minimum values.

Both calibrated models include flooded (simulated water level above land surface) and dry cells. 

Figures 7 and 8 show cells where the simulated water 

levels are above land surface by the following two 

ranges—0.5 to less than 5 m and greater than or equal 

to 5 m. The elevation of the land surface contains 

several sources of error. However, one error source 

is that inherent in the 30-m DEM elevation source, 

which itself is derived from USGS 1:24,000 scale 

hypsography. This accuracy is ± 5 ft (1.5 m). The 

accuracy of the 30-DEM is ± 3 ft (1 m). The land-surface elevation in these models is an interpolation of 

the 30-DEM to 100 m, which has an unknown accuracy worse than that of the 30-m DEM. Therefore, the 

true land-surface elevation could vary as much as ±2 

m from the surface elevation used in the models. Grid 

cells with simulated water levels 2 m above the model 

land surface (flooded cells) may still be hydrologically valid. Grid cells with water levels higher than 2 

m above model land surface probably are invalid and 

model results in or near these areas are not reliable.

The areal extent of dry cells generally was within 

the interior portion of the northern model and along 

the periphery of the southern model. The relatively 

small occurrence of dry cells along the periphery of 

the northern model compared to the southern model 

resulted from simulating recharge from till areas using 

a general head-dependent boundary condition and a 

large hydraulic conductivity (1,000 m/d).

Sources/Sinks Inflow Outflow Net flow (inflow - outflow)

Rate Percent Rate Percent Rate Percent net 

inflow

Percent net 

outflow

Perennial streams 2,529,557 59 2,892,604 67 -363,047 — 96

Lakes and wetlands

1,438,393 34 1,397,947 32 40,446 12 —

Net areal recharge 298,614 7 0 0 298,614 88 —

Well withdrawals 0 0 15,342 1 -15,342 — 4

Total 4,266,564 100 4,305,893 100 -39,329 100 100

Table 6. Simulated volumetric water budget for the southern ground-water-flow model between Little Falls and St. Cloud in central Minnesota. 

[flow rates in cubic meters per day; —, not applicable]

Model limitations 17
18 Ground-Water Flow Models of Surficial Sand and Gravel Aquifers along the Mississippi River 

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Figure 7. Simulated water levels above land surface and dry cells in the northern model along the Mississippi River between Brainerd 

and Little Falls in central Minnesota
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Figure 8. Simulated water levels above land surface and dry cells in the southern model along the Mississippi River between Little Falls 

and St. Cloud in central Minnesota.

Model limitations 19
20 Ground-Water Flow Models of Surficial Sand and Gravel Aquifers along the Mississippi River 

Summary

This report documents regional ground-waterflow models constructed by the U.S. Geological 

Survey in cooperation with the Minnesota Department 

of Health (MDH) to satisfy the requirements of their 

Source Water Protection Plan (SWPP). One component of the SWPP is designation of contributing 

recharge areas (capture zones) that surround public 

water-supply wells. The SWPP considers the capture 

zone of a public water-supply well to be a particularly 

sensitive area that requires special protection. The 

MDH will use nested, local ground-water-flow models developed within the framework of these regional 

flow models for delineation of capture zones around 

supply wells of interest. 

The models were constructed for the surficial 

sand and gravel aquifers along the Mississippi River 

between Brainerd and St. Cloud in central Minnesota. 

A model was constructed in each of the two areas 

(northern and southern) of about 2,000 km2. Steadystate, single layer, ground-water-flow models constructed with the computer program MODFLOW simulated flow in the surficial aquifer. The hydrogeologic 

data used to construct the models were compiled from 

available sources.

Calibrated values of horizontal hydraulic conductivity and net areal recharge for the northern model 

were 70 m/d and 3.0x10-4 m/d, respectively. This 

model was sensitive to net areal recharge, vertical 

hydraulic conductivity of perennial streambed sediments, and horizontal hydraulic conductivity. The 

major source of net inflow to the model was from 

edge boundary cells. The major source of net outflow 

was ground-water discharge to perennial and ephemeral streams.

Calibrated values of horizontal hydraulic conductivity and net areal recharge for the southern model 

were 70 m/d and 6.0x10-4 m/d, respectively. This 

model was sensitive mostly to horizontal hydraulic 

conductivity. Net areal recharge and ground-water 

discharge to perennial streams were the major sources 

of net inflow and outflow, respectively.

Acknowledgments

The authors thank the people who compiled and 

mapped hydrogeologic data that were essential to 

construction of the ground-water-flow model. Bob 

Tipping and Gary Meyer, geologists, Minnesota 

Geological Survey, provided surficial sand and gravel 

thickness data. Steve Robertson, hydrologist, Minnesota Department of Health, provided information 

about water depth in the surficial aquifer and water 

use.

References

Environmental Modeling Systems, Incorporated, 2002, The 

Department of Defense groundwater modeling system 

online reference manual, accessed December 11, 2002, at 

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