Prepared in cooperation with the Lac du Flambeau Band of Lake Superior Chippewa 

and Indian Health Service

Simulation of the Probabilistic Plume Extent for 

a Potential Replacement Wastewater-Infiltration Lagoon, 

and Probabilistic Contributing Areas for Supply Wells 

for the Town of Lac du Flambeau, Vilas County, Wisconsin

"" " "" """" "" """""" "" """"""""" "" """""""""""""" "" """"""""" """ " """"""""""""" " """" " """""""""""""""" """ """ " """""""""""" """ """"""""""""" """" """""""""""" """ """ """""""""""" """" """"""" """"""""""" """ """""""""" """""""" """ """ """""""""""""" """"""""""" """" """"""""""""""""" """""""" "" """ """""""""""""""""""" """"""""""""" " """ """"""""""""""""""""""" """"" """"""""""""""""""""""""""""""""" """""""" """"""""""""""""""""""""""""""""""" " """"""" """"""""""""""""""""""""""""""""""""""" """""" """"""""""""""""""""""""""""""""""""""""" """""" """"""""""""""""""""""""""""""""""""""""""" """"""" """""""""""""""""""""""""""""""""""""""""""""" """"" """"""""""""""""""""""""""""""""""""""""""""""""" " """"" """""""""""""""""""""""""""""""""""""""""""""""""" """""" """"""""""""""""""""""""""""""""""""""""""""""""""" """"" """"""""""""""""""""""""""""""""""""""""""""""""""""" "" " " """ " """"""""" """" """"""""""""""""""""""""""""""""""""""" """""""""""""""""""""""""" """"""""""""""""""""" """"""""""""""" """"""" """"""""""""""""""""""""""""""""""""""""""""""""""""""" """""" """"""""""""""""""""""""""""""""""""""""""""""""""""""""""" """ """""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""" """""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""" "" """"""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""" " """ """"""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""" " """"""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""" """"" """"""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""" """" " " """"""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""" """ """""""""""""""""""""""""""""" """"""" """"" """"""""""""""""""""""""""" """"""""""""""""""""""""""""""""""""""""""""""""""""" """"""""""""""""""""""""""""""""" """"""""""""""" """"""""""" """"""""""""""""" """" """"""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""" """""""""""""""""""""""""" """"""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""" """"""""""""""""""""""""""""" """"""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""" """"""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""" """"""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""" """""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""" """"""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""" """"""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""" """"""""""""""" """""""""" """"""""""""" """""""""""""""""""""""""""""""" """"""""""""""""""""""""""""""""" """"""""" """"""""" """"""""""""""""""""""""""""""" """"""""""""" """"""""""""""""""""""""""""""""""""""""""""""""" """"""""""""""""""""""""""" """"""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""" """""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""" """"""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""" """"""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""" """""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""" """""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""" """""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""" """"""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""" """""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""" """""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""" """"""""""""""""""""""" """""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""" """"""""""""""""""""""""""""""""""""""""""""""""""""""" """"""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""" """""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""" """"""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""" """"""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""" """""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""" """""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""" """"""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""" """"""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""" """""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""" """""" """""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""" """"""""""""""""""" """"""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""" """"""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""" """"""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""" """"""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""" " """"""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""" """ """""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""" """""" """""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""" """""""" """""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""" """"""""""""""""""""" """" """""""" """"""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""" """""""""""" """""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""" """""""""""""""""" """"""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""" """"""""""""""""""" """""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""" """"""""""""""""""" """"""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""" """""""""""""""""""" """""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""" """""""""""""""""""" """"""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""" """""""""""""""""""" """"""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""" """"""""""""""""""""" """"""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""" """"""""""""""""""""" """"""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""" """""""""""""""""""""""""""""""""""""""""" """" """""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""" """""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""" """""""""""""""""""""""""""""""""""""""""""" """"""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""" """""""""" """"""""""""""""""""" """"""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""" """""""""""""""""""" """"""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""" """""""""""""""""""" """""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""" """""""""""""""""""" """"""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""" """""""""""""""""""" """""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""" """"""""""""""""""" """""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""" """""""""""""""""""" """"""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""" """"""""""""""""""" """"""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""" """"""""""""""""""" """""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""" """"""""""""""""""""""""""""""""""""" """"""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""" """"""""" """""""""""""""""" """"""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""" """""""""""""""""" """"""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""" """""""""""""""""" """"""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""" """""""""""""""""" """""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""" """""""""""""""""" """"""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""" """""""""""""""""" """"""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""" """""""""""""""""" """""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""" """"""""""""""""""" """""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""" """""""""""""""""""""""""""""""""""" """"""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""" """""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""" """"""""""""""""" """"""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""" """"""""""""""""" """"""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""" """"""""""""""""" """""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""" """"""""""""""""" """"""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""" """""""""""""""" """"""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""" """""""""""""" """"""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""" """"""""""""" """""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""" """"""""""""" """"""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""" """""""""""""" """""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""" """""""""""""""""""""""""""""" " "" """"""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""" """""""""""""""""" """""""""""""""""""""""" """"""""""""""" """"""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""" """""""""""""""" """"""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""" """"""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""" """"""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""" """""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""" """"""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""" """""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""" """""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""" """""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""" """""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""" """"""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""" """""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""" """"""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""" """"""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""" """""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""" """"""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""" """""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""" """""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""" """"""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""" """"""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""" """""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""" """""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""" """"""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""" """"""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""" """"""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""" """""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""" """"""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""" """""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""" """""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""" """"""""""""""""""""""""""""""""""""""""""""""""""""""""""""" """"""""""""""""""""""""""""""""""""""""""""""""""" """"""""""""""""" """""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""" """"""""""""""""""""""""""""""""" """"""""""""""""""""""""""""""" """""""""""""""""""""""""""""" """""""""""""""""""""""""" """""""""""""""""""""" """"""""""""""""""" """"""

Moss Lake

Fence Lake

#*#*

89°53' 89°52'

45°58'

Lake simulated with lake-water 

budget linesinks

Wetland simulated with lake-water 

budget linesinks

Proposed infiltration lagoon

General direction of groundwater flow

Simulated water-table contour using 

calibrated parameters. Contour 

f

Base map from National Agriculture Imagery Program, 2010

North American Datum of 1927

"

"

"

"

"

"

"

"

"

"

"

"

"

"High

Probability of plume extent

1,584

EXPLANATION

1,598

1,598

1,584

1,596

1,594

1,592

1,590

1,588

1,586

1,584

1,600

1,602

0 1,000 1,500 2,000 500 FEET

0 250 500 METERS

Open-File Report 2020–1032

U.S. Department of the Interior

U.S. Geological Survey
Cover. Simulated probability of the plume extent for a scenario with wastewater discharged

from proposed infiltration lagoons north of the lined treatment lagoons, Town of Lac du Flambeau, 

Vilas County, Wisconsin (figure 2 of this report).
Simulation of the Probabilistic Plume 

Extent for a Potential Replacement 

Wastewater-Infiltration Lagoon, and 

Probabilistic Contributing Areas for Supply 

Wells for the Town of Lac du Flambeau, 

Vilas County, Wisconsin

By Paul F. Juckem and Michael N. Fienen

Prepared in cooperation with the Lac du Flambeau Band of Lake Superior 

Chippewa and Indian Health Service

Open-File Report 2020–1032

U.S. Department of the Interior

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

DAVID BERNHARDT, Secretary

U.S. Geological Survey

James F. Reilly II, Director

U.S. Geological Survey, Reston, Virginia: 2020

For more information on the USGS—the Federal source for science about the Earth, its natural and living resources, 

natural hazards, and the environment—visit https://www.usgs.gov or call 1–888–ASK–USGS.

For an overview of USGS information products, including maps, imagery, and publications, visit 

https://store.usgs.gov/.

Any use of trade, firm, or product names is for descriptive purposes only and does not imply endorsement 

by the U.S. Government.

Although this information product, for the most part, is in the public domain, it also may contain copyrighted materials 

as noted in the text. Permission to reproduce copyrighted items must be secured from the copyright owner.

Suggested citation:

Juckem, P.F., and Fienen, M.N., 2020, Simulation of the probabilistic plume extent for a potential replacement 

wastewater-infiltration lagoon, and probabilistic contributing areas for supply wells for the Town of Lac du Flambeau, 

Vilas County, Wisconsin: U.S. Geological Survey Open-File Report 2020–1032, 10 p., https://doi.org/10.3133/

ofr20201032.

Associated data for this publication:

Juckem, P.F., 2020, GFLOW model files used to generate probabilistic waste-water plume extents and contributing 

areas to supply wells for a proposed waste-water infil-tration lagoon scenario, Lac du Flambeau, Wisconsin: 

U.S. Geological Survey data release, https://doi.org/10.5066/P9Z2YUW5.

ISSN 2331-1258 (online)
iii

Acknowledgments

Thank you to Mathew Zoch, Deputy District Engineer, Indian Health Service, for providing guidance on the location and character of the proposed wastewater treatment lagoons, as well as 

project guidance.

v

Contents

Acknowledgments........................................................................................................................................iii

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

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

Purpose and Scope ..............................................................................................................................2

Physical Setting.....................................................................................................................................2

Data Sources .........................................................................................................................................2

Methods...........................................................................................................................................................4

Simulation of the Wastewater Plume Extent from Proposed Infiltration Lagoons .............................4

Simulation of Areas Contributing Recharge to the Main Pumphouse Wells .......................................5

Assumptions and Limitations .......................................................................................................................9

Summary..........................................................................................................................................................9

References Cited..........................................................................................................................................10

Figures

1. Map showing the location of the Town of Lac du Flambeau, the existing 

wastewater treatment and infiltration lagoons, and the proposed location for 

replacement infiltration lagoons, Vilas County, Wisconsin ...................................................3

2. Map showing the simulated probability of the plume extent for a scenario with 

wastewater discharged from proposed infiltration lagoons north of the lined 

treatment lagoons, Town of Lac du Flambeau, Vilas County, Wisconsin ............................6

3. Map showing the simulated probabilistic areas contributing recharge to the 

Main Pumphouse wells, pumping at the 2010 estimated rate, with wastewater 

discharged from proposed infiltration lagoons north of the lined treatment 

lagoons, Town of Lac du Flambeau, Vilas County, Wisconsin ..............................................7

4. Map showing the simulated probabilistic areas contributing recharge to the 

Main Pumphouse wells, pumping at the 2035 estimated rate, with wastewater 

discharged from proposed infiltration lagoons north of the lined treatment 

lagoons, Town of Lac du Flambeau, Vilas County, Wisconsin ..............................................8

Conversion Factors

U.S. customary units to International System of Units

Multiply By To obtain

Length

foot (ft) 0.3048 meter (m)

Flow rate

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

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)
vi

Datum

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

(NAVD 88).

Horizontal coordinate information is referenced to North American Datum of 1927 (NAD 27).

Abbreviations

GFLOW groundwater flow computer model

USGS U.S. Geological Survey
Simulation of the Probabilistic Plume Extent for a 

Potential Replacement Wastewater-Infiltration Lagoon, 

and Probabilistic Contributing Areas for Supply Wells for 

the Town of Lac du Flambeau, Vilas County, Wisconsin

By Paul F. Juckem and Michael N. Fienen

Abstract

An existing two-dimensional, steady-state groundwaterflow model of the shallow groundwater-flow system of the 

Lac du Flambeau Reservation in Vilas County, Wisconsin, 

originally developed by the U.S. Geological Survey, was 

used to simulate the potential for wastewater from a proposed relocation of a wastewater lagoon to contaminate 

the Lac du Flambeau Band of Lake Superior Chippewa’s 

drinking-water-supply wells. This simulation was completed 

by the U.S. Geological Survey in cooperation with the Lac 

du Flambeau Band of Lake Superior Chippewa and Indian 

Health Service. The simulated scenarios consisted of removing 

wastewater infiltration from existing lagoons and re-applying 

that infiltration at the proposed location. Two analyses were 

performed for the scenarios. First, the probable extent of the 

plume discharging from the proposed infiltration lagoons was 

mapped with a Monte Carlo algorithm that used uncertainty 

identified during the calibration process to simulate thousands 

of possible outcomes. Second, the Monte Carlo method was 

again used to simulate a probabilistic contributing area for the 

Tribe’s nearby “Main Pumphouse” supply wells. The purpose 

of the simulations was to evaluate the potential for infiltrated 

wastewater to be captured by the public-supply wells.

Most features of the previously developed model 

remained unchanged, including calibrated parameters such as 

hydraulic conductivity and recharge. Thus, the same covariance distributions that were generated during calibration 

of the regional model (Juckem and others, 2014) remained 

unchanged and were used to inform the Monte Carlo simulations for the scenario simulations described in this report. The 

reader is encouraged to read the full report by Juckem and 

others (available at https://doi.org/10.3133/sir20145020) for 

a detailed description of the model design and calibration, as 

well as a description of the Monte Carlo method, its limitations, and the original results.

Results for these new scenarios indicate that the probabilistic plume extent for the proposed infiltration lagoons does 

not reach the Main Pumphouse wells using pumping rates and 

wastewater volumes estimated for 2010. Similarly, the contributing area for the Main Pumphouse wells does not capture 

water from within the proposed infiltration lagoon footprint. 

However, at higher pumping rates and wastewater volumes, as 

projected by the Tribe for about 2035, the contributing area for 

the Main Pumphouse wells do include particles that originated 

within the proposed lagoon footprint, albeit at low probabilities. That is, for a few of the thousands of simulations that 

represented a range of calibration-informed parameter covariances, some amount of infiltrated wastewater was captured by 

the Main Pumphouse wells under projected 2035 conditions.

Introduction

The Lac du Flambeau Band of Lake Superior Chippewa 

(referred to hereafter as “the Tribe”) and the Indian Health 

Service have been working to identify a new location for 

wastewater infiltration lagoons for the Town of Lac du 

Flambeau on the Lac du Flambeau Reservation in Wisconsin. 

Previous work involving the construction and calibration of a 

regional groundwater flow (GFLOW; Haitjema, 1995) model 

(Juckem and others, 2014) illustrated that the probable wastewater plume extent from the existing lagoons overlapped with 

the contributing area for drinking-water supply wells (pumped 

wells; fig. 1) at the “Main Pumphouse” site and elevated the 

water table near Moss Lake, thereby limiting the thickness of 

the unsaturated zone below the infiltration lagoons. New simulated scenarios were needed to evaluate the likelihood that the 

wastewater plume from a proposed set of infiltration lagoons 

would reach the Main Pumphouse wells. A second method, the 

area contributing recharge method, also was used to evaluate 

the potential that the wells would capture water that originated 

within the footprint of the proposed infiltration lagoons.
2 Simulation of the Probabilistic Plume Extent and Contributing Areas for Supply Wells, Town of Lac du Flambeau

Purpose and Scope

This report describes the modifications to the original 

GFLOW model (Juckem and others, 2014) and results from 

the simulation of new model scenarios of two-dimensional, 

steady-state, groundwater flow through the shallow hydrologic 

system near the Town of Lac du Flambeau, Wisconsin. The 

purpose of these scenarios was to evaluate the probability that 

the Main Pumphouse wells would capture infiltrated wastewater from the proposed relocation of the infiltration lagoons. 

This evaluation was accomplished by simulating the probabilistic contributing area to the Main Pumphouse wells under 

2010 and projected 2035 pumping rates, and the probabilistic 

wastewater plume extent for the proposed set of infiltration 

lagoons using parameter covariance matrices developed during calibration of the original GFLOW model. The probabilistic contributing area and plume extent scenarios combine 

thousands of plausible model simulations, or realizations, into 

individual maps that when combined convey the uncertainty 

associated with the model, and are preferable for informing risk management decisions in that they highlight rather 

than hide the range of possible outcomes. The model theory, 

construction, calibration of the underlying regional model, 

and methods for simulating probabilistic contributing areas 

and plume extents were fully described by Juckem and others 

(2014). The scope of the evaluations described in this report 

are limited to uncertainty ranges informed during the original 

model calibration (Juckem and others, 2014) because no additional groundwater data were collected in the area of interest, 

and the underlying model was not recalibrated. Computer 

model files for the scenarios described in this report have been 

archived and made available by Juckem (2020).

Physical Setting

The regional and local settings were described by Juckem 

and others (2014); important features of the local setting are 

shown in figure 1 and briefly described here. The Town of Lac 

du Flambeau (hereafter, Town) is in western Vilas County, 

Wisconsin, and surrounded by several lakes that form the 

headwaters of the Bear River, a tributary to the Flambeau 

River (not shown in figures). The groundwater-flow system 

near the Town is bounded by Pokegama and Long Interlaken 

Lakes to the west, Moss Lake to the south, and Fence Lake 

to the east. Locally, groundwater generally flows in a southwesterly direction from an upland area northeast of the Town 

toward Long Interlaken Lake (fig. 2). The area is underlain by 

a permeable sand and gravel aquifer, which is underlain by a 

relatively continuous layer of clay-rich till (Attig, 1985; Batten 

and Lidwin, 1996), and relatively impermeable crystalline 

bedrock (Attig, 1985) that forms the base of the groundwaterflow system. The sand and gravel aquifer has a high horizontal 

hydraulic conductivity (Juckem and others, 2014).

Data Sources

No new data were collected or incorporated into this 

effort; the location of the proposed infiltration lagoons was 

provided by the Indian Health Service (Matthew Zoch, written 

commun., December 7, 2018).
Introduction 3

STATE HIGHWAY 47

THOROFARE ROAD

MOSS LAKE DRIVE

89°52'0"W 89°54'00"

45°58'30"

45°58'00"

45°57'30"

89°53'30" 89°53'00" 89°52'30"

Long 

Interlaken 

Lake

Pokegama 

Lake

Moss Lake

Fence Lake

Town of 

Lac du Flambeau

Base map from U.S. Census Bureau, 2013 and 

Wisconsin Department of Natural Resources, 2009

Lake or pond

Wetland

Pumped well location

Municipal and county roads

State highway

Proposed infiltration lagoon

Existing infiltration lagoon

EXPLANATION

Wastewater treatment lagoon

0 0.25 0.5 MILE

0 0.5 1 KILOMETER

LAC DU FLAMBEAU 

RESERVATION

WISCONSIN

VILAS COUNTY

IRON COUNTY

Figure 1. Location of the Town of Lac du Flambeau, the existing wastewater treatment and infiltration lagoons, and the proposed 

location for replacement infiltration lagoons, Vilas County, Wisconsin.
4 Simulation of the Probabilistic Plume Extent and Contributing Areas for Supply Wells, Town of Lac du Flambeau

Methods

An analytic-element groundwater-flow model, developed 

with the computer program GFLOW (Haitjema, 1995), was 

used to simulate the groundwater system and its interaction 

with surface-water features. A complete description of analytic 

elements is beyond the scope of this report, but additional 

information on analytic element modeling can be found in a 

review of applications of the method by Hunt (2006) and a 

detailed discussion of the underlying concepts and mathematics by Haitjema (1995). Juckem and others (2014) described 

development and application of a GFLOW model for the Lac 

du Flambeau Reservation, and a brief overview of important 

features of the model are highlighted here.

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 singular mathematical 

elements (wells) or strings of elements (linesinks). The amount 

of detail specified for the features depends on distance from 

the area of interest and the purpose of the model. 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 

GFLOW code used here, the analytic elements are two dimensional and are used only to simulate steady-state conditions 

(water levels that do not vary with time).

Hydraulic conductivity and recharge values calibrated by 

Juckem and others (2014) were not changed for the simulations described in this report. Similarly, the distribution 

of parameters used to evaluate uncertainty and probability 

through the Monte Carlo method were identical to those 

used by Juckem and others (2014). The scenario simulations 

described in this report differ from previous scenarios in that 

the wastewater infiltration lagoons were moved to a new 

proposed location north of the lined treatment lagoons (fig. 1). 

Pumping rates from the Main Pumphouse wells also matched 

the values used by Juckem and others (2014) to simulate 2010 

(“current”) and 2035 (“future”) conditions, as estimated by the 

Tribe. Similarly, following the methods of Juckem and others 

(2014), the volume of simulated wastewater applied to the proposed infiltration lagoons was provided by the Tribe, and then 

adjusted for precipitation onto and evaporation off the surface 

area of the lagoons.

Simulation of the Wastewater Plume 

Extent from Proposed Infiltration 

Lagoons

The horizontal extent of the wastewater plume downgradient from the proposed infiltration lagoons was simulated 

using particle tracking, with particles starting at the water 

table within the infiltration lagoons and traced to a terminal 

surface-water body or well. The method considered only 

advective flow from the sources; no attempt was made to evaluate the transport of contaminant mass or concentration. That 

is, source concentrations, dispersion, sorption, and geochemical reactions were all ignored. Instead, results were posed in 

terms of the probability that one or more particles would flow 

through a synthetic grid cell in the area downgradient from 

the lagoons. A synthetic grid was introduced for mapping 

purposes because analytic element methods do not rely upon 

grid-based solutions, yet a uniform mesh was needed to evaluate the density of particle path lines over small areas, or pixels, 

for each of the thousands of realizations. Monte Carlo techniques were used to estimate the probable horizontal extent 

of the wastewater plume given a range of parameter values 

that were informed by covariance matrices developed during 

the calibration process and variance estimates for parameters 

that were fixed during calibration (Juckem and others, 2014). 

The range of model parameter values were sampled using a 

Latin Hypercube approach (Starn and Bagtzoglou, 2012) to 

construct thousands of possible parameter realizations for the 

Monte Carlo simulations.

The horizontal extent of the probable wastewater plume 

was evaluated according to whether one or more particles 

passed through individual cells, or pixels, of the synthetic grid 

that covered the aquifer in the area of interest (see Juckem and 

others, 2014 for additional details). The method is susceptible 

to the level of detail used to represent the synthetic grid and 

the number of particles released from the wastewater source 

(Juckem and Fienen, 2013), as both influence the density 

of particle path lines that cross individual cells of the grid. 

For this plume extent scenario, particles were placed 33 feet 

(10 meters) apart within the infiltration lagoon area, and the 

synthetic grid used a 33-foot cell spacing. Because of the 

method’s sensitivity to particle and grid resolution, results for 

source tracking of the wastewater plume are considered to 

be qualitative only. Nonetheless, areas with extreme probabilities (grid cells at the ends of the color spectrum for the 

“Probability of plume extent”) are expected to be less sensitive 

to the number of particles and level of discretization than areas 

with less definitive outcomes (grid cells near the middle of the 

color spectrum).

Wastewater infiltrated from the proposed wastewater 

infiltration lagoons flows radially away from the lagoons, 

and then flows predominantly west toward a wetland located 

between the proposed lagoons and the Main Pumphouse 

wells, south toward a wetland adjacent to Moss Lake, and east 

toward Fence Lake as it integrates with the regional groundwater flow system (fig. 2). Most of the infiltrated wastewater 

discharges to the wetlands west and south of the lagoons. 

However, some of the infiltrated wastewater is simulated as 

having a moderate probability of flowing beneath the wetland 

between the lagoons and the Main Pumphouse wells before 

discharging to Moss Lake. Groundwater flow is simulated and 

shown below the wetlands because of their relatively higher 

simulated sediment resistance compared with the adjacent 

drainage lakes. That is, the calibrated resistance was 24 days 
Simulation of Areas Contributing Recharge to the Main Pumphouse Wells 5

for wetlands and 1 day for drainage lakes, with both values 

being varied around their calibrated values for the Monte 

Carlo analysis based on the covariances computed for each 

parameter during the calibration process (Juckem and others, 

2014). This flow pattern indicates that there may be a low to 

moderate probability that some wastewater could flow beneath 

the wetland toward the Main Pumphouse wells (fig. 2). While 

wastewater does not appear to intersect the Main Pumphouse 

wells, it is important to recognize some limitations of the 

model. Specifically, tracking of wastewater through the 

groundwater system is halted when the water discharges into 

a wetland or lake. That is, the possibility remains that some 

wastewater that discharges to the wetland west of the proposed 

lagoon could, in reality, move within the wetland as surface 

water and then re-infiltrate into the aquifer and possibly reach 

the wells. This pathway, along with other sources of uncertainty, such as seasonal variability, were not simulated, and 

therefore impart an additional degree of uncertainty that could 

not be quantified with the simulations described in this report.

Simulation of Areas Contributing 

Recharge to the Main Pumphouse 

Wells

Areas contributing recharge to the Main Pumphouse 

wells were delineated by forward tracking of particles from the 

water table to the wells; this, in combination with Monte Carlo 

techniques, enabled maps to be produced showing the probability of capture for the well nest. That is, a range of model 

parameter values were sampled using a Latin Hypercube 

approach (Starn and Bagtzoglou, 2012) to construct thousands of parameter realizations. For every realization, or 

combination of parameter values, the model was re-solved 

and simulated particle tracks were evaluated as to whether 

each particle was or was not captured by a pumped well. After 

completing all realizations, the percentage of realizations for 

which a particle was captured by a well was computed for 

each particle. The starting location for each particle was then 

plotted on a map, with the color code indicating the percentage of realizations, or probability, that the particle would be 

captured by a nearby well (figs. 3 and 4). Particles were started 

on a 82-foot (25-meter) resolution grid upgradient from the 

Main Pumphouse wells, except within areas simulated as lakes 

and wetlands because surface-water flow within these features 

cannot be tracked in GFLOW, and groundwater/surface-water 

interaction between the aquifer and these features occurs along 

the perimeter analytic elements that define them in the model. 

Steady-state (no change over time) pumping conditions were 

used to simulate two scenarios—a scenario with pumping rates 

that reflect 2010 conditions, and a high-pumping scenario in 

which the rate was set at the expected water demand for 2035, 

as estimated by the Tribe. Per the methods of Juckem and others (2014), pumping rates for individual wells were estimated 

as a percentage of the total water demand for the Town based 

on the maximum pumping capacity of each well.

The results of the Monte Carlo simulations show a relatively sharp spatial contrast from areas of high probability of 

capture to low probability of capture for the Main Pumphouse 

wells under 2010 and 2035 pumping scenarios (figs. 3 and 4). 

This sharp gradation in probability is a result of the simulated steady-state conditions, as well as the well-constrained 

groundwater-flow patterns that result from the presence of 

regionally important boundary conditions (for example, Fence, 

Long Interlaken, and Pokegama Lakes; fig. 1). That is, the 

large lakes that occupy much of the Reservation have strong 

control over groundwater-flow directions, and reasonable 

changes to modeling parameters (for example, hydraulic conductivity and lake bed resistance) have only moderate capacity 

to modify the flow patterns near these large lakes. Most of 

the area contributing recharge to the Main Pumphouse wells 

is downgradient from a large wetland that extends between 

the wells and the proposed wastewater infiltration lagoons. 

In the model, surface water infiltrates from the wetland along 

its western border, enters the aquifer, and flows toward the 

wells. Probability of capture was not shown inside the wetland 

because the wetland was simulated as a boundary condition (a 

lake element), and therefore no particles were started within 

the wetland area. That is, water in the simulated wetlands and 

lakes was assumed to be fully mixed, so the origin of water 

discharging from the wetland into the aquifer is indiscernible 

for particle-tracking purposes. In other words, surface-water 

movement is not simulated within lakes or wetlands represented by lake elements in GFLOW, although groundwater 

movement is simulated below them. Given these features of 

the model, figures 3 and 4 show that groundwater recharged 

in areas east of the wetland has a low to moderate probability 

of being captured by the Main Pumphouse wells. Indeed, a 

few particles originate at the mounded water table beneath 

the proposed infiltration lagoons for the 2035 scenario, which 

illustrates a small potential for the Main Pumphouse wells 

to capture infiltrated wastewater if pumping and associated 

wastewater volumes increase to meet projected future demand.
6 Simulation of the Probabilistic Plume Extent and Contributing Areas for Supply Wells, Town of Lac du Flambeau

"" " "" """" "" """""" "" """"""""" "" """""""""""""" "" """"""""" """ " """"""""""""" " """" " """""""""""""""" """ """ " """""""""""" """ """"""""""""" """" """""""""""" """ """ """""""""""" """" """"""" """"""""""" """ """""""""" """""""" """ """ """""""""""""" """"""""""" """" """"""""""""""""" """""""" "" """ """""""""""""""""""" """"""""""""" " """ """"""""""""""""""""""" """"" """"""""""""""""""""""""""""""""" """""""" """"""""""""""""""""""""""""""""""" " """"""" """"""""""""""""""""""""""""""""""""""" """""" """"""""""""""""""""""""""""""""""""""""" """""" """"""""""""""""""""""""""""""""""""""""""" """"""" """""""""""""""""""""""""""""""""""""""""""""" """"" """"""""""""""""""""""""""""""""""""""""""""""""" " """"" """""""""""""""""""""""""""""""""""""""""""""""""" """""" """"""""""""""""""""""""""""""""""""""""""""""""""" """"" """"""""""""""""""""""""""""""""""""""""""""""""""""" "" " " """ " """"""""" """" """"""""""""""""""""""""""""""""""""""" """""""""""""""""""""""""" """"""""""""""""""""" """"""""""""""" """"""" """"""""""""""""""""""""""""""""""""""""""""""""""""""" """""" """"""""""""""""""""""""""""""""""""""""""""""""""""""""""" """ """""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""" """""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""" "" """"""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""" " """ """"""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""" " """"""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""" """"" """"""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""" """" " " """"""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""" """ """""""""""""""""""""""""""""" """"""" """"" """"""""""""""""""""""""""" """"""""""""""""""""""""""""""""""""""""""""""""""""" """"""""""""""""""""""""""""""""" """"""""""""""" """"""""""" """"""""""""""""" """" """"""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""" """""""""""""""""""""""""" """"""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""" """"""""""""""""""""""""""""" """"""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""" """"""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""" """"""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""" """""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""" """"""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""" """"""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""" """"""""""""""" """""""""" """"""""""""" """""""""""""""""""""""""""""""" """"""""""""""""""""""""""""""""" """"""""" """"""""" """"""""""""""""""""""""""""""" """"""""""""" """"""""""""""""""""""""""""""""""""""""""""""""" """"""""""""""""""""""""""" """"""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""" """""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""" """"""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""" """"""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""" """""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""" """""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""" """""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""" """"""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""" """""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""" """""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""" """"""""""""""""""""""" """""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""" """"""""""""""""""""""""""""""""""""""""""""""""""""""" """"""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""" """""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""" """"""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""" """"""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""" """""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""" """""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""" """"""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""" """"""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""" """""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""" """""" """""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""" """"""""""""""""""" """"""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""" """"""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""" """"""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""" """"""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""" " """"""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""" """ """""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""" """""" """""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""" """""""" """""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""" """"""""""""""""""""" """" """""""" """"""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""" """""""""""" """""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""" """""""""""""""""" """"""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""" """"""""""""""""""" """""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""" """"""""""""""""""" """"""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""" """""""""""""""""""" """""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""" """""""""""""""""""" """"""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""" """""""""""""""""""" """"""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""" """"""""""""""""""""" """"""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""" """"""""""""""""""""" """"""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""" """""""""""""""""""""""""""""""""""""""""" """" """""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""" """""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""" """""""""""""""""""""""""""""""""""""""""""" """"""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""" """""""""" """"""""""""""""""""" """"""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""" """""""""""""""""""" """"""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""" """""""""""""""""""" """""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""" """""""""""""""""""" """"""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""" """""""""""""""""""" """""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""" """"""""""""""""""" """""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""" """""""""""""""""""" """"""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""" """"""""""""""""""" """"""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""" """"""""""""""""""" """""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""" """"""""""""""""""""""""""""""""""""" """"""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""" """""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""" """"""""" """""""""""""""""" """"""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""" """""""""""""""""" """"""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""" """""""""""""""""" """"""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""" """""""""""""""""" """""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""" """""""""""""""""" """"""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""" """""""""""""""""" """"""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""" """""""""""""""""" """""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""" """"""""""""""""""" """""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""" """""""""""""""""""""""""""""""""""" """"""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""" """""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""" """"""""""""""""" """"""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""" """"""""""""""""" """"""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""" """"""""""""""""" """""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""" """"""""""""""""" """"""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""" """""""""""""""" """"""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""" """""""""""""" """"""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""" """"""""""""" """""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""" """"""""""""" """"""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""" """""""""""""" """""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""" """""""""""""""""""""""""""""" " "" """""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""" """"""""""""""""""""""""""""""""" """"""""""""""" """"""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""" """""""""""""""" """"""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""" """"""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""" """"""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""" """""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""" """"""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""" """""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""" """""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""" """""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""" """""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""" """"""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""" """""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""" """"""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""" """"""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""" """""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""" """"""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""" """""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""" """""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""" """"""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""" """"""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""" """""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""" """""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""" """"""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""" """"""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""" """"""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""" """""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""" """"""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""" """""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""" """""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""" """"""""""""""""""""""""""""""""""""""""""""""""""""""""""""" """"""""""""""""""""""""""""""""""""""""""""""""""" """"""""""""""""" """""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""" """"""""""""""""""""""""""""""""" """"""""""""""""""""""""""""""" """""""""""""""""""""""""""""" """""""""""""""""""""""""" """""""""""""""""""""" """"""""""""""""""" """"""

Moss Lake

Fence Lake

#*#*

89°53' 89°52'

45°58'

Lake simulated with lake-water 

budget linesinks

Wetland simulated with lake-water 

budget linesinks

Proposed infiltration lagoon

General direction of groundwater flow

Simulated water-table contour using 

calibrated parameters. Contour 

interval 2 feet. Datum is North American

Vertical Datum of 1988

Pumped well location

Base map from National Agriculture Imagery Program, 2010

North American Datum of 1927

"

"

"

"

"

"

"

"

"

"

"

"

"

"

"

"

"

"

"

"High

Low

Probability of plume extent

*#

1,584

EXPLANATION

1,598

1,598

1,584

1,596

1,594

1,592

1,590

1,588

1,586

1,584

1,600

1,602

0 1,000 1,500 2,000 500 FEET

0 250 500 METERS

Figure 2. Simulated probability of the plume extent for a scenario with wastewater discharged from proposed infiltration lagoons north 

of the lined treatment lagoons, Town of Lac du Flambeau, Vilas County, Wisconsin.
Simulation of Areas Contributing Recharge to the Main Pumphouse Wells 7

""""""" """"""""" """"""""""" """""""""""" """"""""""""" """""""""""""" """""""""""""""" """""""""""""""" """"""""""""""""" """"""""""""""""""" """""""""""""""""""" """""""""""""""""" """"""""""""""" """"""""""""" """"""""""""" """""""""""" """"""""" """""

" """"" """"" """"" """"" """""" """"""" """"""" """"""" " """""""" """"""""" """""""""" """""""" """ """""""""" """"" """"""""""""" " """"""""""" " " """""""""" """ "" """""""""""" " "" """"""""""""" """"""""""" """ """""" "" "" " " " " "

#*#*

Lake simulated with lake-water 

budget linesinks

Wetland simulated with lake-water 

budget linesinks

Proposed infiltration lagoon

General direction of groundwater flow

Simulated water-table contours using 

calibrated parameters. Contour 

interval 2 feet. Datum is North American

Vertical Datum of 1988

"

"

"

Pumped well location

"

"

"

"

"

"

"

"

"

"

"

"

"

"

"

"

"100 percent

0 percent

Probability of capture

*#

1,584

EXPLANATION

Base map from National Agriculture Imagery Program, 2010

North American Datum of 1927

1,584

1,584

1,586

1,588

1,592

1,594

1,596

1,598

1,598

1,600

1,590

Moss Lake

0 500 1,000 1,500 2,000 FEET

0 250 500 METERS

89°53'30" 89°53'00" 89°52'30" 89°52'00"

45°58'30"

45°58'00"

Figure 3. Simulated probabilistic areas contributing recharge to the Main Pumphouse wells, pumping at the 2010 estimated rate, with 

wastewater discharged from proposed infiltration lagoons north of the lined treatment lagoons, Town of Lac du Flambeau, Vilas County, 

Wisconsin.
8 Simulation of the Probabilistic Plume Extent and Contributing Areas for Supply Wells, Town of Lac du Flambeau

"""""" """""""""" """"""""""""" """"""""""""""" """""""""""""""" """""""""""""""""" """"""""""""""""""" """"""""""""""""""" """"""""""""""""""""" """""""""""""""""""""" """"""""""""""""""""""" """"""""""""""""""""""""" """""""""""""""""""""""" """"""""""""""""""""""" """""""""""""""""""""" """"""""""""""""""" """""""""""""""""" """"""""""""""""" """"""""""""""""" """""""""""""" " """""""""" """"" " """ """""" """"""" "" """""" " """"""" " """"""""" "" """"""""" "" " """"""""""" " " """"""""""""""""""" " """ """""""""""""""" "" """" """""""""""""""""" """""""" """"""""""""""""""""""" " """"""""""""""""""""""""" """"""""""""""""""""""""" """"""""""""""""""""""" """"""""""""""""""""""" """"""""""""""""""""" """""""""""""""""""" """ "" """"""""" "" """""" """" " """"""""

""

"

"

#*#*

0 500 1,000 1,500 2,000 FEET

0 250 500 METERS

Base map from National Agriculture Imagery Program, 2010

North American Datum of 1927

Moss Lake

89°53'30" 89°53'00" 89°52'30" 89°52'00"

45°58'30"

45°58'00"

Lake simulated with lake-water 

budget linesinks

Wetland simulated with lake-water 

budget linesinks

Proposed infiltration lagoon

General direction of groundwater flow

Simulated water-table contours using 

calibrated parameters. Contour 

interval 2 feet. Datum is North American

Vertical Datum of 1988

"

"

"

Pumped well location

"

"

"

"

"

"

"

"

"

"

"

"

"

"

"

"

"100 percent

0 percent

Probability of capture

*#

1,584

EXPLANATION

1,592

1,594

1,596

1,586

1,584

1,582

1,588

1,590

1,598

1,600

1,600

1,602

Figure 4. Simulated probabilistic areas contributing recharge to the Main Pumphouse wells, pumping at the 2035 estimated rate, with 

wastewater discharged from proposed infiltration lagoons north of the lined treatment lagoons, Town of Lac du Flambeau, Vilas County, 

Wisconsin.
Summary 9

Assumptions and Limitations

Given the relatively coarse nature of the unconsolidated sediments, relatively high net annual precipitation, and 

groundwater-flow patterns being controlled by the surrounding lakes, the groundwater and surface-water systems were 

assumed to have a close hydrologic connection in the modeled 

area. Therefore, elevations of surface-water features were 

assumed to be representative of the groundwater system. A 

two-dimensional model was assumed to be appropriate for the 

larger model domain because the groundwater-flow system 

is thin and areally extensive. Finally, steady-state simulations 

were also assumed appropriate for this study because hydraulic conductivity is high and distances between surface-water 

features are relatively small; these characteristics help dampen 

the effects of periodic transient stresses applied to the system 

(Haitjema, 1995). Steady-state simulations can be expected to 

result in an estimate of the higher range of system response to 

a hydrologic stress because they are not mitigated by groundwater release from storage.

Limitations of the model arise from these assumptions; 

specifically, local three-dimensional flow and transient system 

response expected near wells, infiltration lagoons, and shorelines of surface-water features are not represented. In addition, 

local features of the groundwater system (for example, local 

variations in hydraulic conductivity and recharge) are only 

approximated by using large zones. These limitations add to 

the uncertainty associated with estimating areas contributing recharge to wells and mapping wastewater plume extents 

(Franke and others, 1999). However, the Monte Carlo methods 

that were used for this study take uncertainty associated with 

parameter values partially into account. Other uncertainties 

resulting from the model structure were not evaluated (for 

example, alternative distributions of parameters or alternative 

conceptual models); therefore, some additional uncertainty 

in simulated results is expected beyond that presented in 

this report. In particular, results of Monte Carlo simulations 

for tracking of wastewater from the infiltration lagoons are 

sensitive to user-specified settings. These settings include the 

number of simulated particles (138) and the resolution of the 

synthetic grid (33 feet). Consequently, the wastewater infiltration tracking simulation (fig. 2) is considered qualitative and 

should be used with caution for informing management decisions; the methods used to assess areas contributing recharge 

to wells (figs. 3 and 4) are less sensitive to user-specified settings and are therefore considered more quantitative.

Summary

The Lac du Flambeau Band of Lake Superior Chippewa 

and Indian Health Service have been working to identify a 

new location for wastewater infiltration lagoons for the Town 

of Lac du Flambeau on the Lac du Flambeau Reservation 

in Wisconsin. Previous work by the U.S. Geological 

Survey involving the construction and calibration of a 

regional groundwater flow (GFLOW) model (available at 

https://doi.org/10.3133/sir20145020) illustrated that the probable wastewater plume extent from the existing infiltration 

lagoons overlapped with the contributing area for drinkingwater supply wells at the “Main Pumphouse” site. New 

simulation scenarios were needed to evaluate the probability 

that the wastewater plume from a proposed set of infiltration 

lagoons would reach the Main Pumphouse wells. This report 

describes scenario simulations for the proposed wastewater 

infiltration lagoons that are based on the original field work 

and model development. The model was used for scenario 

simulations to estimate the probable extent of infiltrated wastewater from the proposed lagoons and probable areas contributing recharge to the Main Pumphouse wells for pumping rates 

estimated for 2010 and 2035.

Major conclusions from this study include the following:

A qualitative Monte Carlo assessment of the wastewater plume extent was simulated by evaluating the probability 

that each forward-tracked particle from within the proposed 

infiltration lagoons would intersect an individual cell of a 

synthetic grid applied across the downgradient aquifer. Results 

show that wastewater infiltrated from the proposed lagoons 

flows west and south before discharging to local wetlands, and 

east as it integrates with the regional groundwater-flow system 

upgradient from Fence Lake. No mathematical particles of 

infiltrated wastewater reached the Main Pumphouse wells 

during the simulation; instead, most of the infiltrated wastewater discharged to the nearby wetlands where tracking of the 

wastewater is halted in the model.

Simulated results of the wastewater-plume-extent 

scenario are sensitive to the number of mathematical water 

particles used to represent infiltrating wastewater and the level 

of detail in the synthetic grid used for the probability analysis. Therefore, simulated probabilities of wastewater plume 

extents are qualitative only. Moreover, the Monte Carlo methods used in this study to evaluate uncertainty associated with 

parameter values do not allow for evaluation of alternative 

distributions of parameters or alternative conceptual models, 

and therefore, some level of additional uncertainty beyond the 

simulated results is unavoidable. Nonetheless, the uncertainty 

analyses were developed from the basis of a physically based 

groundwater-flow model and covariances developed through 

calibration to extensive target datasets.

Areas contributing recharge to the Main Pumphouse 

wells were delineated by tracking simulated particles from the 

water table to wells in combination with Monte Carlo techniques, which produced maps of the probability of capture 

for the wells. Simulations were performed with estimates 

of 2010 and 2035 pumping rates. The simulations show a 

relatively sharp spatial contrast from areas of high probability 

of capture to areas of low probability of capture for the Main 

Pumphouse wells under both pumping scenarios. Most of 

the area contributing recharge to the Main Pumphouse wells 

is downgradient from a large wetland between the wells and 

the proposed wastewater infiltration lagoons. Results show 
10 Simulation of the Probabilistic Plume Extent and Contributing Areas for Supply Wells, Town of Lac du Flambeau

show no infiltrated wastewater from the proposed lagoons 

being captured by the Main Pumphouse wells under 2010 

pumping conditions. However, a few particles of water originating from near or within the proposed infiltration lagoons 

were captured by the wells for the 2035 scenario when higher 

pumping rates and increased wastewater volume, as estimated 

by the Lac du Flambeau Band of Lake Superior Chippewa, 

were simulated.

References Cited

Attig, J.W., 1985, Pleistocene geology of Vilas County, 

Wisconsin: Wisconsin Geological and Natural History 

Survey, Information Circular 50, 32 p. [Also available at 

https://wgnhs.uwex.edu/pubs/ic50/.]

Batten, W.G., and Lidwin, R.A., 1996, Water resources of the 

Lac du Flambeau Indian Reservation, Wisconsin, 1981–86: 

U.S. Geological Survey Water-Resources Investigations 

Report 94–4025, 42 p. [Also available at https://doi.org/

10.3133/wri944025.]

Franke, O.L., Reilly, T.E., Pollock, D.W., and LaBaugh, J.W., 

1999, Estimating areas contributing recharge to wells—

Lessons from previous studies: U.S. Geological Survey 

Circular 1174, 14 p. [Also available at https://doi.org/

10.3133/cir1174.]

Haitjema, H.M., 1995, Analytic element modeling of groundwater: San Diego, Academic Press, 394 p. [Also available at 

https://doi.org/10.1016/B978-0-12-316550-3.X5000-4.].

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

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

p. 5–15. [Also available at https://doi.org/10.1111/j.1745-

6584.2005.00143.x.]

Juckem, P.F., 2020, GFLOW model files used to generate 

probabilistic waste-water plume extents and contributing 

areas to supply wells for a proposed waste-water infiltration 

lagoon scenario, Lac du Flambeau, Wisconsin: 

U.S. Geological Survey data release, https://doi.

org/10.5066/P9Z2YUW5.

Juckem, P.F., and Fienen, M.N., 2013, Estimating prediction uncertainty with Monte Carlo techniques and analytic 

elements: Proceedings of the MODFLOW and More 2013 

Conference, Colorado School of Mines, Golden, Colo., 

June 3–5, 2013.

Juckem, P.F., Fienen, M.N., and Hunt, R.J., 2014, Simulation 

of groundwater flow and interaction of groundwater 

and surface water on the Lac du Flambeau Reservation, 

Wisconsin: U.S. Geological Survey Scientific Investigations 

Report 2014–5020, 34 p. [Also available at https://doi.org/

10.3133/sir20145020.].

Starn, J.J., and Bagtzoglou, A.C., 2012, Programs for 

calibration-based Monte Carlo simulation of recharge areas: 

Ground Water, v. 50, no. 3, p. 472–476. [Also available at 

https://doi.org/10.1111/j.1745-6584.2011.00868.x.]
For more information about this publication, contact:

Director, USGS Upper Midwest Water Science Center

8505 Research Way

Middleton, WI 55562

United States

608-828-4901

Publishing support provided by the Madison and Rolla 

Publishing Service Centers
Juckem and Fienen—Simulation of the Probabilistic Plume Extent and Contributing Areas for Supply Wells, Town of Lac du Flambeau—OFR 2020–1032

ISSN 2331-1258 (online)

https://doi.org/10.3133/ofr20201032