Simulation of the Shallow Groundwater-Flow System near 

the Hayward Airport, Sawyer County, Wisconsin

Scientific Investigations Report 2010–5049

Prepared in cooperation with the Wisconsin Department of Transportation 

U.S. Department of the Interior

U.S. Geological Survey
Cover: Photograph showing northern tributary stream to the Namekagon River, Wisconsin.
Simulation of the Shallow Groundwater‐Flow 

System near the Hayward Airport, Sawyer 

County, Wisconsin

By Randall J. Hunt, Paul F. Juckem, and Charles P. Dunning

Prepared in cooperation with the Wisconsin Department of Transportation

Scientific Investigations Report 2010–5049

U.S. Department of the Interior

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

KEN SALAZAR, Secretary

U.S. Geological Survey

Marcia K. McNutt, Director

U.S. Geological Survey, Reston, Virginia: 2010

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Suggested citation:

Hunt, R.J., Juckem, P.F., and Dunning, C.P., 2010, Simulation of the shallow groundwater-flow system near the 

Hayward Airport, Sawyer County, Wisconsin: U.S. Geological Survey Scientific Investigations Report 2010–5049, 14 p.
iii

Contents

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

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

Purpose and Scope ..............................................................................................................................1

Physical Setting.....................................................................................................................................3

Assumptions and Limitations..............................................................................................................3

Methods ..........................................................................................................................................................3

Field Methods........................................................................................................................................3

Modeling.................................................................................................................................................6

Conceptual Model..........................................................................................................................................6

Refinement of the Regional Model near the Hayward Airport...............................................................6

Groundwater-Flow System Results ............................................................................................................7

Field-Data Collection............................................................................................................................7

Model Calibration .................................................................................................................................8

Simulation of Contributing Area for the Northern Tributary ..........................................................8

Summary........................................................................................................................................................12

References Cited..........................................................................................................................................12

Figures

Figure 1. Map showing location of the Hayward Airport, Northern Tributary, 

surface water level measurements, and aquifer zones and linesinks 

used to simulate groundwater in the refined groundwater-flow model in 

Sawyer County, Wisconsin ............................................................... 2

Figure 2A. Map showing results of surface-water measurements in the Northern

Tributary, Sawyer County, February 21–23, 2007 ....................................... 4

Figure 2B. Map showing results of groundwater levels and flow measurements in the

Northern Tributary, Sawyer County, February 21–23, 2007.............................. 5

Figure 3. Graphs showing observed and simulated flows and groundwater levels for the

refined groundwater-flow model ......................................................... 10

Figure 4. Map showing simulated contributing area delineated using particle tracking in

the refined groundwater-flow model...................................................... 11
iv

Tables

Table 1. Surface-water and groundwater levels measured February 21–23, 2007, 

during the real-time kinematic (RTK) global positioning system (GPS) 

survey near the Hayward Airport, Sawyer County, Wisconsin ........................ 7

Table 2. Observed and simulated values, residuals (observed minus simulated 

values), and parameter-estimation weight ............................................. 9

Table 3. Parameter values and composite scaled sensitivity resulting from 

parameter estimation ..................................................................... 9

Conversion Factors, Datums, and Abbreviations

Conversion Factors

Multiply By To obtain

Length

inch (in.) 2.54 centimeter (cm)

foot (ft) 0.3048 meter (m)

Flow rate

cubic foot per second (ft3/s) 0.02832 cubic meter per second (m3/s)

cubic foot per day (ft3/d) 0.02832 cubic meter per day (m3/d)

inch per year (in/yr) 25.4 millimeter per year (mm/yr)

Hydraulic conductivity*

foot per day (ft/d) 0.3048 meter per day (m/d)

Datums

Vertical coordinate information is referenced to the North American Vertical Datum of 1988 

(NAVD 88).

Horizontal coordinate information is referenced to the North American Datum of 1983 as 

adjusted for Wisconsin in 1997 (NAD 83 (97)).

*Hydraulic conductivity: The standard unit for hydraulic conductivity is cubic foot per day per 

square foot of aquifer cross-sectional area (ft3/d/ft2). In this report, the mathematically reduced 

form, foot per day (ft/d), is used for convenience.

Abbreviations

GPS global positioning system

PEST parameter-estimation code (Doherty, 2010)

RTK real-time kinematic

USGS U.S. Geological Survey

UTM Universal Transverse Mercator
Simulation of the Shallow Groundwater-Flow System near 

the Hayward Airport, Sawyer County, Wisconsin

By Randall J. Hunt, Paul F. Juckem, and Charles P. Dunning

Abstract

There are concerns that removal and trimming of 

vegetation during expansion of the Hayward Airport in Sawyer 

County, Wisconsin, could appreciably change the character 

of a nearby cold-water stream and its adjacent environs. In 

cooperation with the Wisconsin Department of Transportation, 

a two-dimensional, steady-state groundwater-flow model 

of the shallow groundwater-flow system near the Hayward 

Airport was refined from a regional model of the area. The 

parameter-estimation code PEST was used to obtain a best 

fit of the model to additional field data collected in February 

2007 as part of this study. The additional data were collected 

during an extended period of low runoff and consisted of 

water levels and streamflows near the Hayward Airport. 

Refinements to the regional model included one additional 

hydraulic-conductivity zone for the airport area, and three 

additional parameters for streambed resistance in a northern 

tributary to the Namekagon River and in the main stem of 

the Namekagon River. In the refined Hayward Airport area 

model, the calibrated hydraulic conductivity was 11.2 feet 

per day, which is within the 58.2 to 7.9 feet per day range 

reported for the regional glacial and sandstone aquifer, and is 

consistent with a silty soil texture for the area. The calibrated 

refined model had a best fit of 8.6 days for the streambed 

resistance of the Namekagon River and between 0.6 and 

1.6 days for the northern tributary stream. The previously 

reported regional groundwater-recharge rate of 10.1 inches 

per year was adjusted during calibration of the refined model 

in order to match streamflows measured during the period of 

extended low runoff; this resulted in an optimal groundwaterrecharge rate of 7.1 inches per year during this period. The 

refined model was then used to simulate the capture zone of 

the northern tributary to the Namekagon River. 

Introduction

There are concerns that removal and trimming of 

vegetation as part of an expansion of the Hayward Airport in 

Sawyer County, Wisconsin (fig. 1) could appreciably change 

the character of a small stream and its adjacent environs. 

This stream is a tributary to the Namekagon River and is 

referred to herein as “Northern Tributary” (an unofficial name 

that is only used for the purposes of this report). During site 

visits by the U.S. Geological Survey (USGS) in January 

and February 2007, the Northern Tributary appeared to be 

ephemeral in its upper reaches and perennial in its lower 

reaches owing to the distribution of groundwater discharge. 

Knowledge of the sources of streamflow is needed to better 

estimate potential effects caused by nearby vegetation change. 

Delineation of the area that contributes groundwater flow to 

the Northern Tributary was a primary concern because it is 

considered a cold-water/trout habitat. This report describes a 

screening-level study done by the USGS, in cooperation with 

the Wisconsin Department of Transportation, to estimate the 

areas that contribute groundwater to the Northern Tributary so 

that state and federal regulators could assess the potential for 

adverse impacts to the cold-water resource. Study objectives 

included collection of field data near the airport area so that 

a regional model of the area could be refined and used to 

simulate the contributing area to the Northern Tributary. 

Purpose and Scope

This report describes the refinement and recalibration 

of a two-dimensional, steady-state groundwater-flow model, 

which is described in detail in Juckem and Hunt (2007). 
2 Simulation of the Shallow Groundwater-Flow System near the Hayward Airport, Sawyer County, Wisconsin

!!!

!!!!

!

!!

!!!!

!

!

!

!

!

%%%

%

%

EXPLANATION

% Water level estimated from ice surface

! Surface-water levels

GFLOW linesinks

Rivers and lakes

Roads

General extent of the Hayward Airport

Local hydraulic-conductivity zone

Glacial thrust-mass zone of Juckem and Hunt (2007)

0 0.25 0.5 1 MILES

Northern Tributary

Hatchery Creek

Namekagon River

Mosquito Brook

Hayward 

Airport

46°01'W

46°03'W

91°28'N 91°23'N

W I S C O N S I N

Location of

study area in

Sawyer County

Base map compiled and modified from digital data sources: 

U.S. Geological Survey, 1:24,000. 

Horizontal datum is NAD 83 (97).

Figure 1. Location of the Hayward Airport, Northern Tributary, surface water level measurements, and aquifer zones and 

linesinks used to simulate groundwater in the refined groundwater-flow model in Sawyer County, Wisconsin.
Methods 3

Additional groundwater-level and streamflow data collected 

near the Hayward Airport formed the basis for refinement 

and recalibration of the regional model. The refined, 

recalibrated model of the shallow hydrologic system near 

the Hayward Airport was used as a tool to delineate the 

groundwater‐contributing area of the Northern Tributary. The 

refinement and recalibration of the model is discussed, and the 

results of the contributing-area simulation are described.

Physical Setting

The regional setting is described by Juckem and Hunt 

(2007). Important features of the local setting near the 

Hayward Airport are briefly described here. The airport is 

in northwestern Sawyer County along the southern shores 

of the Namekagon River. The sand and gravel aquifer has 

relatively high horizontal hydraulic conductivity (Juckem 

and Hunt, 2007) and no laterally extensive confining beds. 

On the northern boundary of the airport is the Northern 

Tributary, a first-order stream (no tributaries) reported to 

have cold‐water‐habitat characteristics (Sather and Threinen, 

1969; Pratt, 1982). The local groundwater-flow system is 

characterized by terrestrial recharge, with discharge primarily 

to the Namekagon River and secondarily to other rivers 

and streams. 

Assumptions and Limitations

The groundwater and surface-water systems were 

assumed to be in close hydraulic connection in the modeled 

area given the coarse nature of the unconsolidated sediments, 

high net-annual precipitation, presence of springs and 

perennial headwater streams, and previous modeling. It 

follows then that elevations of surface-water features can 

be assumed to be representative of the groundwater system. 

Areal two-dimensional assumptions were appropriate for 

the model because the groundwater-flow system is thin and 

areally extensive; however, because areal two-dimensional 

assumptions may not be representative within two to three 

aquifer thicknesses of a surface-water feature (Haitjema, 1995, 

2006; Hunt and others, 2003), simulated groundwater levels 

near surface-water features can be considered approximate 

only. Moreover, the streambed-resistance parameter values 

used to match measured streamflows also can be considered 

only approximate because simulated streamflow depends 

on simulated heads near the stream in addition to streambed 

resistance. Therefore, calibrated values of streambed resistance 

will include artifacts that result from the effects of the areal 

two-dimensional assumption on heads near surface-water 

features. Steady-state simulations were assumed appropriate 

for this study and can be expected to result in an estimate 

of the high range of system response to a hydrologic stress, 

because steady-state simulations ignore groundwater release 

from storage. Although the model was refined by adding some 

additional parameterization in the Hayward Airport area, 

small-scale properties of the groundwater system (for example, 

local variations in hydraulic conductivity and recharge) were 

not investigated during this study and are approximated in 

the refined model. Finally, the field measurements were made 

during a time of below-normal precipitation, as evidenced by 

the low streamflow measurement of record occurred during 

this year at a long-term streamgage in the study area (USGS 

05331833 Namekagon River at Leonards, Wisconsin). Model 

parameters calibrated to these measurements reflect these 

drier conditions and may not correspond to more normal 

precipitation conditions. 

Methods 

This study included refining the regional 

groundwater‐flow model of Juckem and Hunt (2007). 

Additional field data were collected in the Hayward Airport 

area for use in calibration of the refined local model. 

Field Methods

Field data were collected in the Hayward Airport area 

(fig. 1) as part of this study. A real-time kinematic (RTK) 

global positioning system (GPS) was used to survey horizontal 

and vertical locations of interest around the Northern Tributary 

near the Hayward Airport during February 21–23, 2007. 

This RTK-GPS system is capable of providing sub-inch level 

accuracy by differentially correcting GPS signals recorded 

at two separate GPS receivers (Wolf and Ghilani, 2002). 

The field survey was referenced to the Universal Transverse 

Mercator (UTM) coordinate system and the NAD83 (97) 

horizontal and NAVD88 vertical datums. Streamflow was 

measured at three locations on the Northern Tributary 

within 200 ft of the culvert at Airport Road (fig. 2A) during 

February 21–23, 2007. Streamflow was measured using a 3-in. 

modified Parshall flume (Rantz and others, 1982). The flume 

was installed slightly above the streambed, with an attached 

rubber apron secured to the streambed sediment upstream 

of the flume. This design allowed water to pool upstream of 

the flume and maintain free-fall conditions at the exit of the 

flume. The flume was leveled and water levels in an attached 

stilling well were recorded until the water level in the stilling 

well, and thus streamflow, had stabilized. Streamflow was 

determined from the water level (gage height) based on Rantz 

and others (1982, table 14).

Piezometers were installed in and around the bed of the 

Northern Tributary and in the area of the headwater wetland 

to investigate local groundwater/surface-water interaction. For 

each piezometer, a 0.5-ft long screen was set approximately 1 

to 2 ft below land surface. The depth to water (or height above 

the stream stage) was measured until the water level stabilized 

in each piezometer. A reference point at each piezometer 

was established during the RTK-GPS survey to associate the 

measured water level in each piezometer with an elevation.
4 Simulation of the Shallow Groundwater-Flow System near the Hayward Airport, Sawyer County, Wisconsin

!

!

!

Namekagon-4 Namekagon-4 

pz1-stream

surface 

1,206.3

pz2-stream

surface 

1,207.2

Flume-middle

1,205.5

 (0.017)

Culvert-upstream 

1,205.1

Flume-downstream

1,199.8

 (0.025)

Flume-upstream

1,207.1

(0.007)

Flume-upstream

1,207.1

(0.007)

Approximate

downstream

extent of ice

Airport Road

Airport Road

Namekagon River

EXPLANATION

! Location and name of streamflow measurement—Number is surface-water 

 elevation in feet above NAVD 88 (see table 1). Number in parentheses is flow 

 where measured, in cubic feet per second

Rivers and streams

Airport Road (approximate)

0 30 60 120 FEET

46°02'14"W

91°26'32"N

46°02'15"W

91°26'28"N

! !

! !

1,198.0

A.

Base map compiled and modified from digital 

data sources: U.S. Geological Survey, 1:24,000. 

Horizontal datum is NAD 83 (97).

Note: Geometry of the Northern Tributary 

channel is approximate.

Northern Tributary

Figure 2A. Results of surface-water measurements in the Northern Tributary, Sawyer County, February 21–23, 

2007.
Methods 5

! !

! !

!

!

pz9

pz6 pz5

pz1 pz2 pz3 pz4

pz10

1,206.5

1,207.3

1,209.4

Airport Road Airport Road

1,210.1 1,210.9

1,213.3

1,213.1

1,214.4

Namekagon River

46°02'14"W Northern Tributary

46°02'08"W

91°26'30"N 91°26'14"N

EXPLANATION

! Piezometer and name—Number is measured groundwater-level 

 elevation, in feet above NAVD 88 (see table 1)

Roads

Rivers and streams

0 95 190 380 FEET

! !

pz5

1,214.4

Base map compiled and modified from digital 

data sources: U.S. Geological Survey, 1:24,000. 

Horizontal datum is NAD 83 (97).

Vertical datum is NAVD 88.

Note: Geometry of the Northern Tributary 

channel is approximate.

B.

Figure 2B. Results of groundwater levels and flow measurements in the Northern Tributary, Sawyer County, 

February 21–23, 2007.
6 Simulation of the Shallow Groundwater-Flow System near the Hayward Airport, Sawyer County, Wisconsin

Modeling

An analytic-element groundwater-flow model, using 

the computer program GFLOW (Haitjema, 1995), was 

used to simulate the groundwater system and its interaction 

with surface-water features. Hunt (2006) gives a review of 

applications of the analytic element method and Haitjema 

(1995) discusses the underlying concepts and mathematics of 

the method in detail. A brief description of analytic element 

methods is as follows.

An infinite aquifer is assumed in analytic-element 

modeling. To construct an analytic-element model, features 

important for controlling groundwater flow (for example, 

wells and surface-water features) are entered as mathematical 

elements or strings of elements. The amount of detail specified 

for the features depends on distance from the area of interest. 

Each element is represented by an analytic solution. The 

effects of these individual solutions are added together to form 

a solution for any location in the simulated groundwater-flow 

system. In the model code used here, the analytic elements 

are two dimensional and are used only to simulate steadystate conditions (water levels that do not vary with time). The 

analytic-element method and comparisons of analytic-element 

to finite-difference numerical-model techniques have been 

discussed by others (Haitjema, 1995; Hunt and Krohelski, 

1996; Hunt and others 1998, 2003).

The GFLOW model was calibrated by means of 

parameter-estimation techniques. The advantages of 

parameter-estimation models are discussed by Poeter and 

Hill (1997) and Hill (1998). Briefly, the primary benefit of a 

properly prepared parameter-estimation model over typical 

trial-and-error calibration is the ability to calculate parameter 

values (for example, hydraulic conductivity and streambed 

resistance) that are a quantified best fit between simulated 

model output and observed data (groundwater levels and 

streamflows). In addition, parameter correlation and parameter 

sensitivity can be quantified and assessed. In this study, the 

GFLOW model was coupled with the parameter-estimation 

code PEST (Doherty, 2010). 

Conceptual Model

A conceptual model is a simplification of the 

hydrologic system that is necessary because inclusion of 

all hydrogeologic complexities into a model is not feasible. 

Steps in the development of the conceptual model include: 

(1) characterization of the aquifer(s), (2) identification 

of sources and sinks of water, and (3) identification and 

delineation of hydrologic boundaries in the area of interest. 

The conceptual model of the hydrologic system is described in 

this section.

Although the regional groundwater system comprises 

shallow and deep aquifers (Juckem and Hunt, 2007), 

groundwater flow is dominated by flow through the shallow 

aquifer, which consists of glacial deposits that are composed 

primarily of sandy till and stream deposits that are about 100‐ft 

thick near the Hayward Airport. The deep aquifer consists of 

Cambrian sandstones (roughly 100-ft thick near Grindstone 

Lake) that pinch out east of the Hayward Airport. Where the 

sandstone is absent, glacial sediments are deposited directly 

onto crystalline bedrock. The sandstone and glacial deposits 

were simulated as a single aquifer in the groundwater‐flow 

model because the ability of the sandstone to transmit water 

is less than that of the overlying glacial aquifer, meaning 

that the groundwater-flow system is dominated by the glacial 

deposits. Moreover, Juckem and others (2003) demonstrated 

that simulated base-flow reductions in nearby Grindstone 

Creek owing to pumping agreed to within 1 percent when 

results from a one-layer model were compared to results from 

a four-layer model that explicitly included the sandstone and 

glacial aquifers. 

The distant boundaries for the system are directly derived 

from the regional model of Juckem and Hunt (2007); however, 

the local boundaries are important for the modeling objective 

because the problem is one of distribution of flow between 

two competing discharge points or “sinks” to the groundwater 

system. The first possible sink is the regionally important 

Namekagon River. The second possible sink for the local 

groundwater-flow system is the small tributary of interest, the 

Northern Tributary. Thus, the conceptual model includes local 

infiltration of precipitation that recharges the groundwater 

system, which is in turn discharged to either the Northern 

Tributary or the Namekagon River.

Refinement of the Regional Model 

near the Hayward Airport

The regional groundwater-flow model of Juckem and 

Hunt (2007) was refined to improve simulation of local scale 

groundwater flow near the Hayward Airport. For the refined 

model simulations, properties of the regional model remained 

unchanged except near the Hayward Airport. Modifications 

to geologic properties in the model included the addition of 

one zone in which the hydraulic conductivity was allowed to 

vary from the regional value (fig. 1). The Namekagon River 

shoreline location also was refined for local simulations 

near the Hayward Airport by adding detail based on USGS 

topographic maps. Small tributaries not included in the 

regional model, such as the Northern Tributary, were added 

using the site hydrography. Streambed resistance of the 

Namekagon River was changed from 0.5 to 5 days owing 

to results of initial sensitivity runs that showed the regional 

model value was not representative of heads and flows in the 

Hayward Airport area. Streambed resistance is defined as the 
Groundwater-Flow System Results 7

streambed‐sediment thickness divided 

by the vertical hydraulic conductivity. 

For example, the model value of 5 days 

corresponds to a 1-ft sediment thickness 

and a vertical hydraulic conductivity of 

0.2 ft/d. Initial resistance of the Northern 

Tributary was specified as 5 days in the 

location where the stream appeared to be 

ephemeral and 3 days where perennial. 

The stages of the Namekagon River, 

adjacent streams, and the Northern 

Tributary were specified using the field 

data collected in February 2007 so that 

all stage data were contemporaneous and 

therefore representative of the conditions 

present when groundwater levels 

were measured. 

Groundwater-Flow System 

Results

This section describes field data 

used for calibration, the calibration of 

the model, and use of particle tracking 

to simulate the contributing area to the 

Northern Tributary. 

Field-Data Collection

Although conducted in winter, 

results of a 3-day field survey were used 

to characterize hydrologic conditions 

near the Northern Tributary (fig. 2 and 

summarized in table 1). Measured 

streamflows and water levels of the 

Northern Tributary are shown in 

figure 2A. Measured water levels in 

piezometers are shown in figure 2B. 

Streamflow in the Northern Tributary was 

evident approximately 200 ft upstream of 

Airport Road (fig. 2A). Farther upstream 

of this location, the streambed was 

covered by as much as 3 ft of ice. Augured 

holes through the ice along the stream 

channel showed no signs of flowing water 

along the streambed. Ponded water in 

the wetland also was frozen completely. 

Water levels in piezometers PZ1 and 

PZ2 (fig. 2B and table 1) showed upward 

Table 1. Surface-water and groundwater levels measured February 21–23, 2007, 

during the real-time kinematic (RTK) global positioning system (GPS) survey near the 

Hayward Airport, Sawyer County, Wisconsin.

[Wl, water-level elevation was measured directly with the RTK-GPS; ice, the measured elevation is 

that of frozen water and was inferred to correspond with the stream stage at that location; easting and 

northing coordinates are referenced to the Universal Transverse Mercator coordinate system, North 

American Datum of 1983 as adjusted for Wisconsin in 1997; elevation is relative to North American 

Vertical Datum of 1988]

Location name Easting 

(meters)

Northing 

(meters)

Water-level 

elevation 

(feet)

Description

Surface-water measurement locations

Flume-upstream 620,622.25 5,099,353.94 1,207.10 Wl

Flume-middle 620,593.88 5,099,354.92 1,205.50 Wl

Flume-downstream 620,562.15 5,099,358.75 1,199.82 Wl

PZ1-stream surface 620,611.35 5,099,352.21 1,206.30 Wl

PZ2-stream surface 620,627.60 5,099,351.30 1,207.21 Wl

Culvert-upstream 620,588.39 5,099,353.81 1,205.07 Wl

Namekagon-1 623,210.71 5,102,913.60 1,221.46 Wl

Namekagon-2 621,330.60 5,100,955.89 1,210.82 Ice

Namekagon-3 620,573.17 5,099,524.57 1,198.34 Wl

Namekagon-4 620,553.08 5,099,374.68 1,198.02 Wl

Namekagon-5 620,336.84 5,098,619.27 1,193.75 Wl

Namekagon-6 620,088.40 5,098,158.69 1,191.24 Wl

Namekagon-7 619,841.03 5,097,341.48 1,187.80 Wl

Hatchery1 619,839.95 5,096,403.02 1,189.77 Ice

Hatchery2 621,398.96 5,097,637.36 1,219.34 Wl

Hatchery3 621,449.58 5,097,637.49 1,221.11 Wl

Hatchery4 621,473.50 5,097,641.61 1,222.77 Wl

Hatchery5 621,361.17 5,097,673.99 1,217.47 Wl

Hatchery6 621,363.04 5,097,788.94 1,214.88 Wl

Hatchery7 619,914.89 5,096,371.24 1,191.24 Ice

Hatchery8 619,984.19 5,096,412.39 1,193.95 Ice

Mosquito_Brook-1 624,271.33 5,100,413.48 1,278.72 Wl

Mosquito_Brook-2 624,176.13 5,100,396.20 1,274.74 Wl

Mosquito_Brook-3 621,739.90 5,100,675.97 1,216.73 Ice

Location name Easting 

(meters)

Northing 

(meters)

Water-level 

elevation 

(feet)

Piezometer 

bottom 

elevation 

(feet)

Groundwater measurement locations

PZ1 620,611.35 5,099,352.21 1,206.54 1,203.76

PZ2 620,627.60 5,099,351.30 1,207.34 1,204.77

PZ3 620,671.99 5,099,352.69 1,209.42 1,208.51

PZ4 620,926.05 5,099,352.68 1,210.88 1,209.51

PZ5 620,991.72 5,099,284.65 1,214.42 1,213.30

PZ6 620,899.74 5,099,293.15 1,213.25 1,213.05

PZ9 620,743.05 5,099,356.43 1,210.13 1,209.50

PZ10 621,004.05 5,099,320.49 1,213.07 1,211.42

gradients relative to the stream stage (fig. 2A and table 1), as 

expected, given the measurements of increasing base flow in 

the downstream direction. Water levels in piezometers PZ3 

and PZ4 (fig. 2B) were below the streambed, indicating that 

groundwater was not discharging into the tributary stream 

during February 21–23, 2007. Water levels in the wetland 

piezometers (PZ5, PZ6, and PZ10) were 1.5 to 2.5 ft below 

land surface. Piezometer PZ9 was installed adjacent to the 

Northern Tributary (fig. 2B).
8 Simulation of the Shallow Groundwater-Flow System near the Hayward Airport, Sawyer County, Wisconsin

Model Calibration 

Groundwater levels from eight piezometers (fig. 2B) 

measured during the February 2007 survey were used to 

calibrate the refined model of the Hayward Airport area. These 

measured values were contemporaneous and had a datum 

consistent with measurements of stage on the Namekagon 

River, adjoining tributaries, and the Northern Tributary. 

Streamflows measured during February 2007 also were used to 

calibrate the refined model. Flows measured in February 2007 

were considered to be entirely base flow (the component 

of streamflow derived solely from groundwater discharge), 

because winter in Wisconsin is a period of low or negligible 

stormflow. Thus, the measured streamflows were used directly 

as target values at the three flume stations. In addition, an 

observed base-flow value of 0.0 was entered for the area where 

the stream transitioned from ephemeral to perennial (extent 

of ice in fig. 2A), and one low-weight target was entered to 

evaluate how the conditions simulated in the February 2007 

calibrated run compared to the previous base-flow value for 

Hatchery Creek reported by Juckem and Hunt (2007). 

The regional hydraulic-conductivity values were not 

varied from the values of Juckem and Hunt (2007). The 

regional recharge value, the local hydraulic-conductivity zone 

near the Hayward Airport, and the local streambed resistance 

of the Namekagon River and the Northern Tributary were 

estimated during calibration. The calibration was performed 

by coupling the groundwater-flow model GFLOW to the 

parameter-estimation program PEST (Doherty, 2010). The 

parameter estimation varied the GFLOW-parameter values 

to achieve a best fit between simulated and observed base 

flows and groundwater levels. Weights were assigned to 

the observed values that reflect their relative importance to 

the overall modeling objective, and thus directly affect the 

fit between simulated and measured values. In PEST, the 

higher weights represent higher importance in the parameter 

estimation. In this study, the most downstream flume target 

was the most important target (highest weight) because 

the objective of this modeling was to identify the entire 

groundwater-contributing area for the Northern Tributary. 

Although other targets are included in the calibration, the 

emphasis of the calibration was not on simulating the local 

groundwater levels or the distribution of groundwater flow 

within the Northern Tributary. Rather, the primary objective 

of the modeling was to simulate the distribution of flow 

between the entire Northern Tributary (as represented by 

the most downstream base-flow measurement) and the other 

potential sink for water recharged in the Hayward Airport 

area—the adjacent Namekagon River. The weights assigned to 

each calibration target, along with residuals derived from the 

calibrated-model solution, are listed in table 2. 

The resulting calibrated-model hydraulic conductivity 

value (table 3) is within the 58.2 to 7.9 ft/d range reported 

for the regional glacial and sandstone aquifer by Juckem 

and Hunt (2007), and are consistent with silty soil reported 

by Clayton (1984). Regional recharge and local hydraulic 

conductivity were the most sensitive parameters (had the 

largest effect on the calibration) of the calibrated parameters 

(table 3). The calibrated-recharge value (7.1 in/yr) was 

about 70 percent of the value (10.1 in/yr) used by Juckem 

and Hunt (2007) and reflects persistent low-precipitation 

conditions that characterized the area during this study. 

Results from the calibrated model agreed well with the 

observed downstream‐flume measurement (table 2, 

fig. 3). Other head and flow measurements were less well 

simulated (fig. 3) because they were given lesser weight in 

the parameter‐estimation process, but are still considered 

acceptable given the stated modeling objective. 

Simulation of Contributing Area for the 

Northern Tributary

The calibrated model was used to estimate the 

configuration of the land-surface area that contributes 

groundwater recharge for the Northern Tributary. The 

contributing area of the stream is the land area with the same 

horizontal extent as that part of the aquifer that contributes 

groundwater flow to the stream. The contributing area of the 

Northern Tributary was delineated by forward particle tracking 

using particles placed near the Northern Tributary. Simulated 

particles of water were placed at the water table and tracked 

forward in time using the calibrated model. The contributing 

area simulated by the calibrated model is shown in figure 4; it 

is about 300 ft wide and about 15,000 ft long.
Groundwater-Flow System Results 9

Table 2. Observed and simulated values, residuals (observed minus simulated values), and parameter-estimation weight.

[ft3/d, cubic foot per day]

Location name Observed Simulated Residual Units Weight

pz6 1,213.25 1,215.40 -2.15 feet 1

pz5 1,214.42 1,218.58 -4.16 feet 1

pz10 1,213.07 1,218.69 -5.62 feet 1

pz4 1,210.88 1,215.40 -4.52 feet 1

pz9 1,210.13 1,210.06 .07 feet 1

pz3 1,209.42 1,207.88 1.54 feet 1

pz2 1,207.34 1,206.16 1.18 feet 1

pz1 1,206.54 1,205.37 1.17 feet 1

Flume-upstream 605 2,266 -1,661 ft3/d 1.0E-03

Flume-middle 1,469 2,096 -627 ft3/d 1.0E-02

Flume-downstream 2,160 2,240 -80 ft3/d 1.0E-01

Hatchery Creek 144,288 135,408 8,880 ft3/d 1.0E-06

Approximate downstream extent of ice 0 2,429 -2,429 ft3/d 1.0E-04

Namekagon at Leonards 6.39E+06 6.39E+06 -997 ft3/d 1.0E-03

Table 3. Parameter values and composite scaled sensitivity resulting from parameter 

estimation.

[in/yr, inch per year; ft/d, foot per day]

Parameter name Initial

value

Calibrated

value

Composite 

scaled 

sensitivity

Recharge (in/yr) 10.1 7.1 208

Local hydraulic conductivity (ft/d) 58.2 11.2 170

Namekagon streambed resistance (days) 5.0 8.6 4.4

East Northern Tributary resistance (days) 5.0 .6 8.7

West Northern Tributary resistance (days) 3.0 1.6 .5
10 Simulation of the Shallow Groundwater-Flow System near the Hayward Airport, Sawyer County, Wisconsin

1,195

1,200

1,205

1,210

1,215

1,220

pz6 pz5 pz10 pz4 pz9 pz3 pz2 pz1

PIEZOMETER NAME

FLUME-UPSTREAM

FLUME-MIDDLE

FLUME-DOWNSTREAM

GROUNDWATER LEVEL (FEET ABOVE DATUM)

Observed

Simulated

1

10

100

1,000

10,000

100,000

1,000,000

10,000,000

HATCHERY CREEK

APPROXIMATE DOWN 

STREAM EXTENT OF ICE

NAMEKAGON AT LEONARDS

BASE FLOW (CUBIC FEET PER DAY)

Observed

Simulated

Most highly weighted

 

Figure 3. Observed and simulated flows and groundwater levels for the refined groundwater-flow

model. Datum is North American Vertical Datum of 1988.

Figure 3. Observed and simulated flows and groundwater levels for the refined groundwater-flow model. Datum 

is North American Vertical Datum of 1988.
Groundwater-Flow System Results 11

0 0.25 0.5 1 MILES

1205

1250

1300

91°23'N

46°03'W

46°01'W

91°23'N

0 1,000 2,000 500 FEET

1205

1225

1250

46°02'W

91°26' 30"N

46°02' 45"W

91°25'N

EXPLANATION

Simulated groundwater level

 contour—contour interval, 5 feet. 

 Datum is NAVD 88

GFLOW linesinks

Rivers and lakes

Roads

Simulated contributing area

to the Northern Tributary

General extent of the Hayward Airport

Local hydraulic-conductivity zone

Glacial thrust-mass zone of Juckem and Hunt (2007)

Direction of groundwater flow

Figure 4. Simulated contributing area delineated using particle tracking in the refined groundwater-flow model.
12 Simulation of the Shallow Groundwater-Flow System near the Hayward Airport, Sawyer County, Wisconsin

Summary

A hydrologic investigation near the Hayward Airport 

in Sawyer County, Wisconsin, focused on a small tributary 

stream (“Northern Tributary”) and its adjacent environs. 

During site visits by the U.S. Geological Survey (USGS) 

in January and February 2007 (a time of drought in the 

region), the Northern Tributary was dry in its upper reaches 

and flowing in its lower reaches owing to the distribution of 

groundwater discharge. The source of groundwater to the 

tributary stream was a primary focus of investigation because 

the stream is considered a cold-water habitat that is maintained 

by groundwater flow. To estimate the areas that contribute 

groundwater to the Northern Tributary, a modeling study 

was done by the USGS, in cooperation with the Wisconsin 

Department of Transportation. Field data collected from the 

site were used to refine a regional groundwater-flow model, 

which was then used to simulate the contributing area to the 

Northern Tributary. 

Water levels along streams in the area of interest were 

surveyed with a real-time kinematic (RTK) global positioning 

system (GPS) to refine the geometry and stage of streams in 

the model. Streamflow was measured with a flume at three 

locations on the Northern Tributary and ranged from 0.007 

to 0.025 cubic feet per second. Piezometers were installed 

in and around the streambed of the Northern Tributary and 

in the area of the headwater wetland to investigate local 

groundwater/surface-water interaction. The streamflows and 

groundwater levels in piezometers were used to calibrate 

model-parameter values.

For the refined model, modifications from the regional 

model included: (1) refinement of local stream geometry and 

elevation, (2) addition of one zone in which the hydraulic 

conductivity was allowed to vary from the regional value, 

(3) additional refinement of streambed resistance for 

the Namekagon River and along the Northern Tributary, 

and (4) adjustment of the regional groundwater-recharge 

rate to account for drought conditions in the region. The 

calibrated‐model values are within the range of parameters 

reported by Juckem and Hunt (2007) and agreed with an area 

of silty soil reported by Clayton (1984). 

The calibrated model was used to estimate the location 

of the land surface that contributes groundwater recharge for 

the Northern Tributary. The contributing area simulated by 

the calibrated model extends west and southwest of the 

Northern Tributary and is about 300 feet wide by about 

15,000 feet long.

References Cited

Clayton, L., 1984, Pleistocene geology of the Superior Region, 

Wisconsin: Wisconsin Geological and Natural History 

Survey Information Circular 46, 40 p., 1 pl.

Doherty, J., 2010, PEST—Model-independent parameter 

estimation: Brisbane, Australia, Watermark Numerical 

Computing. http://www.pesthomepage.org/files/pestman.pdf

Haitjema, H.M., 1995, Analytic element modeling of 

groundwater flow: San Diego, Calif., Academic Press, 

394 p.

Haitjema, H.M., 2006, The role of hand calculations in 

ground water flow modeling: Ground Water, v. 44, no. 6, 

p.786–791.

Hill, M.C., 1998, Methods and guidelines for effective model 

calibration; with application to UCODE, a computer 

code for universal inverse modeling, and MODFLOWP, 

a computer code for inverse modeling with MODFLOW: 

U.S. Geological Survey Water-Resources Investigations 

Report 98–4005, 90 p.

Hunt, R.J., 2006, Ground water modeling applications using 

the analytic element method: Ground Water, v. 44, no. 1, 

p. 5–14.

Hunt, R.J., Anderson, M.P., and Kelson, V.A., 1998, 

Improving a complex finite-difference ground water flow 

model through the use of an analytic element screening 

model: Ground Water, v. 36, no. 6, p. 1011–1017.

Hunt, R.J., Haitjema, H.M., Krohelski, J.T., and Feinstein, 

D.T., 2003, Simulating ground water-lake interactions—

Approaches and insights: Ground Water, v. 41, no. 2, 

p. 227–237.

Hunt, R.J., and Krohelski, J.T., 1996, The application of an 

analytic element model to investigate groundwater-lake 

interactions at Pretty Lake, Wisconsin: Journal of Lake and 

Reservoir Management, v. 12, no. 4, p. 487–495.

Juckem, P.F., and Hunt, R.J., 2007, Simulation of the 

shallow ground-water-flow system near Grindstone 

Creek and the Community of New Post, Sawyer County, 

Wisconsin: U.S. Geological Survey Scientific Investigations 

Report 2007–5014, 29 p.
References Cited 13

Juckem, P.F., Hunt, R.J., and Tyrolt, D.D., 2003, Using 

characteristic leakage length as a guide to model design—

Application to the Grindstone Springs Area, Lac Courte 

Oreilles, Wisconsin, in American Water Resources 

Association, Wisconsin state section, proceedings: p. 51.

Poeter, E.P., and Hill, M.C., 1997, Inverse models—A 

necessary next step in ground-water modeling: Ground 

Water, v. 35, no. 2, p. 250–260.

Pratt, F.B., 1982, Comprehensive Trout Survey Report, 

Namekagon River, 1981-1982: unpublished Wisconsin 

Department of Natural Resources report, 68 p.

Rantz, S.E., and others, 1982, Measurement and computation 

of streamflow—Volume 1, Measurement of stage 

and discharge: U.S. Geological Survey Water Supply 

Paper 2175, 284 p.

Sather, L.M., and Threinen, C.W., 1969, Surface water 

resources of Sawyer County: Wisconsin Department of 

Natural Resources, 214 p.

Wolf, P.R., and Ghilani, C.D., 2002, Elementary surveying—

An introduction to geomatics (10th ed.): Englewood Cliffs, 

N.J., Prentice-Hall, 900 p.
14 Simulation of the Shallow Groundwater-Flow System near the Hayward Airport, Sawyer County, Wisconsin

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Hunt and others— Simulation of Groundwater-Flow System near Hayward Airport, Sawyer County, Wisconsin—Scientific Investigations Report 2010–5049