U.S. Department of the Interior

U.S. Geological Survey

Prepared as part of the Glacial Aquifer System Groundwater Availability Study, 

a cooperative effort between the U.S. Department of the Interior’s WaterSMART Initiative 

and the U.S. Geological Survey’s Water Availability and Use Science Program

Simulation of Potential Groundwater Recharge for the 

Glacial Aquifer System East of the Rocky Mountains, 

1980–2011, using the Soil-Water-Balance Model

Scientific Investigations Report 2018–5080

Driftless area

MT

CO

KS

UT

SD

IL

CANADA

WY

NE

IA

ND MN

WI

MO

PA

IN

MI

NY

NY

VA

OH

KY

ME

WV

MI VT

NH

MD

MA

CT

DE

NJ

RI

Lake Superior Lake Michigan

Lake

Huron

Lake Erie

Lake Ontario

110° 100° 90° 80° 70°

45°

40°

Base map image is the intellectual property of Esri and is

used herein under license. Copyright © 2017 Esri and

its licensors. All rights reserved. Base modified from Esri

digital data, 1:70,000 (Esri, 2009)

Base map of states from U.S. Geological Survey 1:2,000,000 digital data

Albers Equal-Area Conic projection, standard parallels 29°30' N., and 45°30' N.

Central meridian 96°00' W., latitude of origin 23°00’ N.

EXPLANATION

0 125 250 MILES

0 125 250 KILOMETERS

Area of

enlargement Glacial Soil-Water-Balance model mean annual 

potential recharge rate, in inches per year

0 to 3.00

3.01 to 6.00

6.01 to 9.00

9.01 to 12.00

12.01 to 15.00

15.01 to 18.00

18.01 to 21.00

21.01 to 24.00

24.01 to 27.00

27.01 to 43.00
Cover. Map showing mean annual potential recharge rates from 1980 to 2011 simulated

with the glacial Soil-Water-Balance model modified from figure 14 of the report.
Simulation of Potential Groundwater 

Recharge for the Glacial Aquifer System 

East of the Rocky Mountains, 1980–2011, 

using the Soil-Water-Balance Model

By Jared J. Trost, Jason L. Roth, Stephen M. Westenbroek, and 

Howard W. Reeves

Prepared as part of the Glacial Aquifer System Groundwater Availability Study, 

a cooperative effort between the U.S. Department of the Interior’s WaterSMART 

Initiative and the U.S. Geological Survey’s Water Availability and Use Science 

Program

Scientific Investigations Report 2018–5080

U.S. Department of the Interior

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

RYAN K. ZINKE, Secretary

U.S. Geological Survey

James F. Reilly II, Director

U.S. Geological Survey, Reston, Virginia: 2018

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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:

Trost, J.J., Roth, J.L., Westenbroek, S.M., and Reeves, H.W., 2018, Simulation of potential groundwater recharge for 

the glacial aquifer system east of the Rocky Mountains, 1980–2011, using the Soil-Water-Balance model: U.S. Geological Survey Scientific Investigations Report 2018–5080, 51 p., https://doi.org/10.3133/sir20185080.

ISSN 3828-0328 (online)
iii

Contents

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

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

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

Description of the Study Area ............................................................................................................3

Definition of Potential Groundwater Recharge for this Report.....................................................3

Previous Studies ...................................................................................................................................3

Methods...........................................................................................................................................................6

Model Theory and Description...........................................................................................................6

Model Limitations and Assumptions .................................................................................................6

Model Input Data ..................................................................................................................................8

Meteorological Data ...................................................................................................................8

Land Cover....................................................................................................................................9

Soil Hydrologic Data....................................................................................................................9

Hydrologic Soil Group ........................................................................................................9

Available Water Capacity................................................................................................12

Maximum Recharge Rate................................................................................................15

Lookup Tables and Control File................................................................................................15

Initial Conditions ........................................................................................................................16

Model Calibration and Evaluation Methods...................................................................................16

Calibration Targets.....................................................................................................................17

Basin Selection .................................................................................................................17

Base-Flow (Recharge) Observations and Weights.....................................................17

Parameter Estimation................................................................................................................19

Statistical Methods for Evaluating Model Fit and Model Error..........................................21

Model Verification .....................................................................................................................22

Simulation of Potential Groundwater Recharge.....................................................................................22

Model Fit and Model Error.................................................................................................................22

1980–2011 Potential Recharge to the Glacial Aquifer System ....................................................27

Comparison to Previous Recharge Estimates................................................................................32

Sensitivity Analysis......................................................................................................................................41

Glacial Soil-Water-Balance Model..................................................................................................41

Comparison of Parameter Sensitivities...........................................................................................41

Summary........................................................................................................................................................44

Acknowledgments.......................................................................................................................................45

References Cited..........................................................................................................................................45

Appendix. Model Archive........................................................................................................................51
iv

Figures

1. Map showing extent of the glacial aquifer system included in the domain of the

glacial Soil-Water-Balance model and the basins used for model calibration .................2

2. Conceptual diagram of the Soil-Water-Balance model.........................................................4

3. Map showing mean annual gross precipitation within the extent of the glacial

aquifer system at a 1-kilometer resolution for 1980–2011, summarized from the

Daymet dataset.............................................................................................................................8

4. Map showing land-cover classes according to the 2006 National Land Cover

Database within the extent of the glacial aquifer system at a 1-kilometer resolution ...11

5. Map showing hydrologic soil groups within the extent of the glacial aquifer

system at a 1-kilometer resolution, based on the Digital General Soil Map of the

United States ...............................................................................................................................12

6. Map showing available soil-water capacity within the extent of the glacial

aquifer system at a 1-kilometer resolution, based on the Digital General Soil Map

of the United States....................................................................................................................15

7. Graph showing example stream hydrograph and base flow from three

hydrograph separation techniques, HYSEP local minimum, PART, and base-flow

index for U.S. Geological Survey streamgage 01552000, Loyalsock Creek at

Loyalsockville, Pennsylvania ....................................................................................................19

8. Map showing the 38 basins used to verify the glacial Soil-Water-Balance model.........23

9. Graphs showing relations between HYSEP local minimum base flow and 

potential recharge simulated with the glacial Soil-Water-Balance model for 

39 calibration basins during 1980–2011...................................................................................24

10. Histogram of residuals during 1980–2011...............................................................................24

11. Map showing residuals in mean annual potential recharge between the glacial 

Soil-Water-Balance model and base flow determined with the HYSEP

local minimum method for the 39 calibration basins during 1980–2011 ............................25

12. Graph showing mean annual potential recharge from the glacial Soil-WaterBalance model, mean annual HYSEP local minimum base flow, and range of 

mean annual base flow from five hydrograph separation techniques, PART, 

HYSEP local minimum, HYSEP fixed-interval, HYSEP sliding, and base-flow 

index during 1980–2011..............................................................................................................26

13. Graphs showing mean annual HYSEP local minimum base flow and mean annual 

potential recharge simulated with the glacial Soil-Water-Balance model for 

38 verification basins .................................................................................................................27

14. Map showing mean annual potential recharge from 1980 to 2011 simulated

with the glacial Soil-Water-Balance model ...........................................................................28

15. Histogram of mean annual potential recharge from the glacial

Soil-Water-Balance model during 1980 to 2011 for the glacial aquifer system ...............29

16. Maps showing results from the glacial Soil-Water-Balance model..................................30

17. Graphs showing percent of 1980–2011 potential recharge to the glacial

aquifer system.............................................................................................................................31

18. Map showing mean annual potential recharge as a percent of mean annual

gross precipitation based on results from the glacial Soil-Water-Balance model .........32

19. Graph showing annual potential recharge from 1980 to 2011 simulated with

the glacial Soil-Water-Balance model within three regions of the glacial aquifer

system extent ..............................................................................................................................33

20. Map showing boundaries of the glacial Soil-Water-Balance model and

boundaries of previously published recharge models .........................................................34
v

21. Boxplot showing cell-by-cell differences between mean annual potential

recharge from the glacial Soil-Water-Balance model and four previously

published recharge estimates .................................................................................................35

22. Maps showing the glacial aquifer system..............................................................................36

23. Map showing the difference between the 1951–80 mean annual recharge

determined by Wolock and the 1980–2011 mean annual potential recharge

simulated with the glacial Soil-Water-Balance model.........................................................37

24. Maps showing 1981–2011 mean annual potential recharge in the coincident

model domains ............................................................................................................................38

25. Maps showing 1996–2010 mean annual potential recharge in the coincident

model domains ............................................................................................................................39

26. Maps showing 1980–2011 mean annual potential recharge in the coincident

model domains ............................................................................................................................40

Tables

1. Percentage of the glacial aquifer system by 2001 land-cover class from the

National Land Cover Database dataset and the Digital General Soil Map of the

United States hydrologic soil group ..........................................................................................9

2. Percentage of the glacial aquifer system by 2006 land-cover class from the

National Land Cover Database dataset and the Digital General Soil Map of the

United States hydrologic soil group ........................................................................................10

3. Percentage of the glacial aquifer system by 2011 land-cover class from the

National Land Cover Database dataset and the Digital General Soil Map of the

United States hydrologic soil group ........................................................................................10

4. Lookup table for the calibrated Soil-Water-Balance model, corresponding land

cover to runoff curve number, maximum recharge rate, interception storage, and

root-zone depth...........................................................................................................................13

5. Selected characteristics, simulated potential recharge from the glacial

Soil-Water-Balance (SWB) model, recharge determined using five hydrograph

separation techniques, residual statistics, and calibration weights for 77 basins

used for the glacial SWB model calibration and verification available at

https://doi.org/10.3133/sir20185080

6. Distribution of land cover in the calibration basins and for the glacial

Soil-Water-Balance model domain, based on the 2006 National Land Cover

Database ......................................................................................................................................18

7. Distribution of hydrologic soil groups in the calibration basins and for the glacial

Soil-Water-Balance model domain, based on the STATSGO2 soil database...................18

8. Calibration parameter descriptions, values, and bounds for the glacial

Soil-Water-Balance model available at https://doi.org/10.3133/sir20185080

9. Model evaluation statistics between recharge determined with the HYSEP local

minimum technique and corresponding potential recharge estimates from the

glacial Soil-Water-Balance model for the 39 calibration basins and 38

verification basins ......................................................................................................................23

10. Mean annual potential recharge rates simulated by the glacial

Soil-Water-Balance model, by land-cover class and hydrologic soil group, for

the period 1980–2011..................................................................................................................29

11. Sensitivity of model error to changes in parameters of the calibrated glacial

Soil-Water-Balance model........................................................................................................42
vi

Conversion Factors

U.S. customary units to International System of Units

Multiply By To obtain

Length

inch (in.) 2.54 centimeter (cm)

inch (in.) 25.4 millimeter (mm)

foot (ft) 0.3048 meter (m)

mile (mi) 1.609 kilometer (km)

yard (yd) 0.9144 meter (m)

Area

square mile (mi2) 2.590 square kilometer (km2) 

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)

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

°F = (1.8 × °C) + 32.

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

°C = (°F – 32) / 1.8.

Datum

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 (NAD 83).

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

Abbreviations

> greater than

AME absolute mean error

ASCII American Standard Code for Information Interchange

AWC available water capacity

BFI base-flow index

CFGI continuous frozen ground index

ET evapotranspiration

GAGES II Geospatial Attributes of Gages for Evaluating Streamflow, version II

HSG hydrologic soil group

HUC hydrologic unit code

NLCD National Land Cover Database

NSE Nash-Sutcliffe model efficiency coefficient

PPCC probability plot correlation coefficient

RMSE root mean squared error

RSR root mean squared error to standard deviation of the observations ratio

SC snow cover

SSURGO Soil Survey Geographic [database]

STATSGO2 State Soil Geographic [database]

SWB Soil-Water-Balance

SWC soil-water content

USGS U.S. Geological Survey

Simulation of Potential Groundwater Recharge for the 

Glacial Aquifer System East of the Rocky Mountains, 

1980–2011, using the Soil-Water-Balance Model

By Jared J. Trost, Jason L. Roth, Stephen M. Westenbroek, and Howard W. Reeves

Abstract

An understanding of the spatial and temporal extent of 

groundwater recharge is critical for many types of hydrologic 

assessments involving water quality, contaminant transport, 

ecosystem health, and sustainable use of groundwater. Annual 

potential groundwater recharge was simulated at a 1-kilometer resolution with the Soil-Water-Balance (SWB) model for 

the glacial aquifer system east of the Rocky Mountains, from 

central Montana east to Maine, for calendar years 1980–2011. 

The SWB model used high resolution meteorological, land 

cover, and soil hydrology datasets that are nationally consistent and publicly available. The SWB model computed daily 

potential groundwater recharge as precipitation in excess of 

interception, runoff, evapotranspiration, and soil-water storage 

capacity. Daily potential recharge values within each year 

of the simulation were summed to produce annual potential 

recharge rates. Potential recharge as described in this report 

is water that infiltrates vertically below the plant rooting zone 

and is assumed to reach the water table.

The calibrated SWB model in this report is called the 

glacial SWB model. Model calibration assumed that the area 

contributing to groundwater discharge equaled the surface 

watershed. The model was calibrated to stream base flows 

from 39 watersheds throughout the model domain that had 

hydrologic conditions appropriate for hydrograph separation. 

Base flows were calculated from daily streamflow records with 

the HYSEP local minimum hydrograph separation method 

The glacial SWB model reproduced the mean annual baseflow calibration targets well; the Nash-Sutcliffe efficiency 

coefficient was 0.94, and the root mean squared error was 

1.28 inches per year.

The glacial SWB model provides insight into the spatial 

and temporal variability in potential annual recharge across the 

glacial aquifer system. About 20 percent of the active model 

area had an average potential recharge rate of less than 1 inch 

per year. Total precipitation, total recharge, and recharge as a 

percentage of precipitation increased from west to east. A substantial amount of the recharge water (39 percent) entering the 

glacial aquifer system travels through developed (urbanized) 

and agricultural landscapes, which are known to cause waterquality impairments. Regional climatic events, such as the 

1988 to 1989 drought, are apparent in the potential recharge 

time series. Potential recharge generally increased across the 

glacial aquifer system between 2001 and 2011.

A comparison of the potential recharge from the glacial SWB model to previous broad-scale recharge estimates 

reveals several important considerations for future SWB 

modeling applications. Shifts in the overall distribution of 

potential recharge between separate models can be explained 

by methods used to generate base-flow calibration target datasets. Spatial patterns in potential recharge simulated by SWB 

models are strongly dependent on the data and assumptions 

used to assign model cells to hydrologic soil groups. A review 

of several SWB models used to estimate groundwater recharge 

(and not surface runoff) revealed that model results are most 

sensitive to input climatic data, followed by surface runoff 

(curve number) and root-zone depth parameters.

Introduction

The glacial aquifer system is an important source of 

water for millions of people and supports numerous natural 

ecosystems across 26 States in the northern United States 

(Warner and Arnold, 2006). The glacial aquifer system 

includes all unconsolidated aquifers above bedrock within the 

glaciated area of the United States (fig. 1). It is the “principal 

aquifer” for most of the northern United States. A principal 

aquifer is a regionally extensive aquifer system from which 

potable water supplies are being or could be extracted (Warner 

and Arnold, 2006). Approximately 41 million people relied on 

the glacial aquifer system for public and private water supply 

in 2000 (Warner and Arnold, 2006). The glacial aquifer system 

is subject to a range of climatic conditions: humid to semiarid, 

maritime to continental to arctic (Reeves and others, 2017). 

Groundwater availability in the system may be controlled 

by climatic conditions that affect water inputs and losses in 

addition to hydrogeological constraints of storage capacity and 

low hydraulic conductivity. Other considerations related to 
2 Simulation of Potential Groundwater Recharge for the Glacial Aquifer System East of the Rocky Mountains, 1980–2011

fig 01

Driftless area

MT

CO

KS

UT

SD

IL

WY

NE

IA

ND MN

WI

MO

PA

IN

MI

NY

NY

VA

OH

KY

ME

WV

MI VT

NH

MD

MA

CT

DE

NJ

RI

Lake Superior Lake Michigan

Lake

Huron

Lake Erie

Lake Ontario

38

37

35

34

32

27

23

21

13

12 14 19

24

22

25

28

26

29

30

31

33

36

2

1

5

7

15

17 9

11

8 10 20

18

4

3

6

39

16

110° 100° 90° 80° 70°

45°

40°

Area of

enlargement

Base map image is the intellectual property of Esri and is

used herein under license. Copyright © 2017 Esri and

its licensors. All rights reserved. Base modified from Esri

digital data, 1:70,000 (Esri, 2009)

Base map of states from U.S. Geological Survey 1:2,000,000 digital data

Albers Equal-Area Conic projection, standard parallels 29°30' N., and 45°30' N.

Central meridian 96°00' W., latitude of origin 23°00’ N.

EXPLANATION

Extent of glacial Soil-Water-Balance model domain

Basins used for model calibration, labeled by map number

Glacial region

0 125 250 MILES

0 125 250 KILOMETERS

CANADA

Central 

East

West central

Figure 1. Extent of the glacial aquifer system included in the domain of the glacial Soil-Water-Balance model and the 

basins used for model calibration.

changes in groundwater availability include the introduction of 

poor water quality from natural or anthropogenic constituents, 

concerns of conflicts with current groundwater users, or the 

desire to maintain or restore environmental streamflows.

Quantifying sustainable water withdrawal rates for 

human use requires careful consideration of inputs (recharge) 

to and losses from groundwater systems at a variety of spatial 

and temporal scales. Sustainable withdrawals ensure that terrestrial and aquatic ecosystems and future water resources for 

human needs are not adversely affected by overuse. Groundwater recharge replenishes water lost from aquifers by processes such as evapotranspiration (ET), discharge to surface 

water, seepage to other aquifers, and pumping withdrawals. 

Groundwater recharge is challenging to quantify because of 

variability in time and space caused by many factors, such as 

multiyear climate trends, seasonal weather patterns, hydrogeologic properties, land use, and land cover. An understanding 

of the spatial and temporal extent of groundwater recharge is 

critical for many types of hydrologic assessments involving 

water quality, contaminant transport, ecosystem health, and 

groundwater availability; for example, recharge to groundwater in semiarid or arid regions may be so low that withdrawals 

from the system lead to groundwater mining and depletion of 

the resource.

The combined effect of lower recharge and higher 

demand may be transient but can result in undesired consequences, such as land subsidence, temporary streamflow 

depletion, water levels dropping below the level of existing 

pumps or wells, and migration of poor-quality water into the 

aquifer. Seasonal, annual, or decadal variations in climate can 

lead to changes in the recharge to the groundwater system and 

the demands on the system for public, domestic, irrigation, 

and industrial supply; therefore, modeling recharge using only 

average conditions fails to incorporate extremes in climatic 

variations and water use. Failure to incorporate these extremes 

may result in undesired consequences that affect aquatic ecosystem health, human water supply, and public safety (Reeves 

and others, 2017).

Purpose and Scope

The purpose of this report is to document the calibration 

and use of the Soil-Water-Balance (SWB) model (Westenbroek and others, 2010) to simulate potential recharge for 

the glacial aquifer system east of the Rocky Mountains in 

the conterminous United States at a 1-kilometer (km) resolution for 1980–2011. This report is prepared as part of the 
Introduction 3

U.S. Geological Survey’s (USGS) Glacial Aquifer System 

Groundwater Availability Study, which assesses groundwater 

availability for the glacial aquifer system of the United States. 

The SWB model was calibrated to base-flow estimates calculated from daily streamflow data by the HYSEP local minimum method (Sloto and Crouse, 1996) for 39 basins across 

the glacial aquifer system. A total of five base-flow separation 

techniques were compared as calibration targets. The HYSEP 

local minimum method was chosen because it produced estimates in the midrange of the five methods. Calibration targets 

for each basin included the mean annual base flow, annual 

total base flow, and annual total base-flow deciles.

The model was calibrated initially with parameter values 

from previously published SWB recharge models (Aurand, 

2013; Masterson and others, 2013; Metropolitan Council 

Environmental Services, 2013; Smith and Westenbroek, 2015; 

Westenbroek and others, 2010). A sensitivity analysis was 

completed to understand how the SWB model responds to 

changes in some important parameters and inputs. Although 

potential recharge estimates and most model inputs are in U.S. 

customary units, spatial data such as model grid spacing and 

some model inputs use the International System of Units.

Description of the Study Area

The subset of the glacial aquifer system in the United 

States included in this study extends from central Montana 

east to Maine (fig. 1). The system is made of material deposited by the Laurentide ice sheet that extended into North 

America in a series of advances and retreats of continental 

glaciers between 2.5 million and 12,000 years ago (Booth and 

others, 2003; Dorr and Eschman, 1970; Marshall and others, 

2003; Mickelson and Colgan, 2003). In some areas, more 

recent glaciation removed old material, and glacially deposited 

material is only from the last advance. In other areas, glacial 

deposits are from sequential ice sheet advances and retreats. 

Glacial landforms have material that affects groundwater 

yield, aquifer hydraulic properties, and, ultimately, groundwater availability at local and regional scales (Anderson, 

1989; Eyles, 1983; Eyles and others, 1985). For this report, 

all unconsolidated materials within the glaciated parts of the 

conterminous United States are considered to be of the glacial 

aquifer system even if the material has been deposited more 

recently by mechanisms other than glaciation (Reeves and others, 2017). One unique unglaciated feature in the Midwest is 

the Driftless Area (fig. 1), which is a highly eroded landscape 

with shallow soils overlying Paleozoic bedrock (Albert, 1994).

The extent of the model presented in this report is a 

subset of the glacial aquifer system study area established for 

the USGS National Water-Quality Assessment (Warner and 

Arnold, 2006). This report only discusses the east, central, and 

west-central regions of the glacial aquifer system (fig. 1). The 

west region of the glacial aquifer system, which corresponds 

to the extent of the Cordilleran ice sheet advance in western 

Montana, Idaho, Washington, and Alaska, was excluded from 

this model application (see fig. 1 in Warner and Arnold, 2006); 

however, the extent of the model includes the glaciated extent, 

not just the extent of the glacial sand and gravel principal 

aquifer (Miller, 1999). Water supplying wells for domestic 

water supply, irrigation, and industrial use may be produced 

from glacial deposits with low hydraulic conductivity or local 

units of isolated sand or gravel that typically are not mapped 

as sand and gravel aquifers. Deposits with lower hydraulic 

conductivity also contribute important storage to the system 

and can be important to water availability and water-quality 

characteristics anywhere in the system (Reeves and others, 

2017).

Definition of Potential Groundwater Recharge 

for this Report

A variety of mechanisms, only a subset of which are 

represented by the SWB model in this report, can lead to 

groundwater recharge. Recharge is defined conceptually as the 

downward flow of water reaching the water table, forming an 

addition to the groundwater reservoir (de Vries and Simmers, 

2002).

Lerner and others (1990) define three principal recharge 

mechanisms to a groundwater system: (1) direct recharge is 

water added to the groundwater reservoir in excess of soilmoisture deficits and ET by direct vertical percolation through 

the vadose zone; (2) indirect recharge is percolation to the 

water table through the beds of surface-water courses; and 

(3) localized recharge is an intermediate form of groundwater 

recharge resulting from the horizontal (near-) surface concentration of water in the absence of well-defined channels. The 

glacial SWB model is conceptualized as only representing 

the direct recharge mechanism (fig. 2) and does not explicitly 

consider indirect or localized recharge mechanisms.

Recharge estimation techniques like SWB that are 

based on surface-water and unsaturated-zone data provide 

estimates of potential recharge in contrast to methods based 

on groundwater data, which generally provide estimates of 

actual recharge (Healy and Scanlon, 2010). Therefore, the 

SWB model estimates potential direct recharge, defined as 

precipitation water in excess of interception, runoff, ET, and 

soil-water storage capacity that infiltrates vertically below the 

plant rooting zone that is assumed to reach the water table. In 

this report, the term “recharge” in the context of any estimate 

determined using the SWB model is synonymous with potential direct recharge.

Previous Studies

Numerous methods have been used to estimate groundwater recharge at various temporal and spatial scales (Scanlon 

and others, 2002). Important considerations for the selection of an appropriate recharge estimation method include: 

(1) the time scale of interest, (2) the need for static or transient estimates, (3) spatial scale of the recharge estimates, 
4 Simulation of Potential Groundwater Recharge for the Glacial Aquifer System East of the Rocky Mountains, 1980–2011

(4) availability of the necessary data, and (5) the ease of use of 

the recharge estimation method or model (Scanlon and others, 

2002). In this report, only two methods of recharge estimation, 

hydrograph separation and SWB model applications, will be 

discussed in detail. Both methods have been applied previously at broad spatial and temporal scales (as discussed below) 

and are well suited to estimate time-varying recharge across 

the glacial aquifer system.

Many regional studies have used some form of hydrograph separation to estimate the spatial distribution of groundwater recharge (for example, Arnold and Allen, 1999; Neff and 

others, 2006; Wolock, 2003a; Wolock, 2003b). The base flow 

of a stream or river is the amount of groundwater discharged 

from an aquifer to surface water. Over the course of a year, 

assuming there is no trend in the quantity of water stored in 

the aquifer, the total base flow is assumed to equal the total 

groundwater recharge for a basin (watershed). This base flow 

is supplemented by direct runoff during and immediately after 

precipitation or snowmelt, resulting in peaks on hydrographs. 

The process of dividing these peaks into base flow and runoff 

(overland flow) is called hydrograph separation (Neff and others, 2005).

Various mathematical approaches are used for hydrograph separation, including (1) digital filtering (Arnold and 

others, 1995; Eckhardt, 2005; Nathan and McMahon, 1990), 

(2) recession-curve methods (Chapman, 1999; Rorabaugh, 

1964), and (3) linear interpolation methods (Gustard and 

others, 1992; Rutledge, 1998; Sloto and Crouse, 1996). The 

minimum time scale for these methods is a few months, but a 

time scale of a year or longer typically is used. Recharge over 

longer times can be estimated by summation of estimates over 

shorter times (Scanlon and others, 2002). Generally, average 

annual estimates are more reliable than monthly or daily estimates of base flow or surface runoff (Sloto and Crouse, 1996). 

The following paragraphs describe a few example applications 

of hydrograph separation. 

fig02

Evapotranspiration 

Temperature Precipitation

Snowfall

Snowmelt

Rain

Rejected

recharge 

Snow

storage 

Interception

Root-zone depth

Maximum soilwater capacity

Potential recharge = Base flow

Direct runoff

Figure 2. Conceptual diagram of the Soil-Water-Balance model.
Introduction 5

Wolock (2003b) estimated the mean annual natural 

groundwater recharge in the conterminous United States for 

a 1-km resolution (grid) dataset for 1951–80. This 1-km grid 

was created by multiplying a grid of base-flow index values 

(the ratio of base flow to total streamflow) by a grid of mean 

annual runoff values derived from a mean annual runoff 

contour map for 1951‒80. Mean annual runoff is the 1951‒80 

mean annual streamflow expressed on a per-unit-area basis. 

The base-flow index point values were computed according to 

the base-flow index (BFI) method, described in Gustard and 

others (1992). The base-flow index point values estimated for 

USGS streamgages were interpolated to a raster dataset using 

an inverse distance weighting interpolation method (Wolock, 

2003a).

In another example regional study, Neff and others (2006) 

calculated the long-term average groundwater recharge to 

shallow aquifers (generally less than 100 feet [ft] deep) in the 

United States and Canada for the eight-digit hydrologic unit 

code (HUC) watersheds within the Great Lakes Basin in gaged 

and ungaged watersheds. The base-flow index was estimated 

from the PART hydrograph separation method (Rutledge, 

1998). In gaged areas, the base-flow index values were related 

to surficial geologic materials and surface-water features in 

a regression model. In ungaged watersheds, the regression 

model that was developed in gaged watersheds was used to 

predict base-flow index values based on their surficial geology 

and surface-water features. The predicted base-flow index then 

was multiplied by the long-term average total streamflow at 

the eight-digit HUC level to get a long-term average recharge 

per year (Neff and others, 2006).

The previous two example studies produced long-term 

average rates of groundwater recharge for large spatial extents, 

but the estimates did not vary through time. A series of studies 

done in Wisconsin demonstrated that temporal trends in annual 

base flow or low flow varied by land use and geology (Gebert 

and others, 2011a, 2011b; Gebert and others, 2007; Gebert 

and Krug, 1996). For example, a significant increasing trend 

in base flow was observed in agricultural watersheds and the 

driftless area (fig. 1), whereas most forested watersheds had 

no significant trend in base flow. Similar to these studies in 

Wisconsin, the SWB model produces time-varying estimates 

of groundwater recharge.

The SWB model commonly is compared to recharge 

estimates derived from hydrograph separation and takes 

advantage of nationally consistent meteorological, land-cover, 

and soil hydrology datasets to simulate recharge across the 

landscape at user-defined resolutions (Fry and others, 2011; 

Homer and others, 2007, 2015; Natural Resources Conservation Service, 2015; Thornton and others, 2014). The SWB 

model code has been used to estimate spatially and temporally 

variable potential recharge for several diverse regional systems 

across the United States, some of which overlap the model 

domain in this report. A few previous SWB model applications include the State of Minnesota (Smith and Westenbroek, 

2015), the Lake Michigan Basin (Feinstein and others, 2010; 

Westenbroek and others, 2010), the High Plains aquifer (Stanton and others, 2011), the Williston and Powder River Basins 

(Aurand, 2013), the North Atlantic Coastal Plain (Masterson 

and others, 2013), and the Appalachian Plateaus (McCoy and 

others, 2015).

The Lake Michigan Basin, Minnesota, and Appalachian 

Plateaus SWB models were calibrated to recharge estimates 

derived from the base-flow component of hydrographs 

(Feinstein and others, 2010; McCoy and others, 2015; Smith 

and Westenbroek, 2015; Westenbroek and others, 2010). An 

SWB model that has been calibrated to base flow distributes 

that volume of water at the time step of interest throughout a 

watershed based on land-cover and soil hydrology characteristics. The Lake Michigan Basin SWB model was calibrated 

by iteratively modifying model parameters such as the runoff 

curve number, soil available water capacity, and rooting 

depth to increase the correspondence between 10-year mean 

potential recharge values calculated by the SWB model and 

the recharge calculated for 100 basins associated with USGS 

streamgages (Westenbroek and others, 2010). The Minnesota 

SWB model was calibrated using a combination of automated 

and manual parameter adjustment processes. The calibration 

targets were annual base flows during 1996–2010 and the 

15-year mean base flow in 35 watersheds estimated with 3 

different techniques, including PART (Rutledge, 1998) and 

HYSEP fixed interval and sliding methods (Sloto and Crouse, 

1996). The Appalachian Plateaus SWB model was calibrated 

by adjusting three parameter groups: root-zone depth, runoff 

curve number, and plant-canopy interception values. The calibration targets were annual base flows estimated with PART in 

20 gaged watersheds with at least 24 years of record (McCoy 

and others, 2015).

Several SWB models were not calibrated directly to base 

flow but were compared to other types of recharge estimates or 

were calibrated as part of the calibration exercise for groundwater modeling (Anderson and others, 2015). The Williston 

and Powder River Basin SWB model output covered parts of 

Montana, Wyoming, North Dakota, and South Dakota. Model 

outputs were compared to point estimates of recharge at 

specific wells calculated by the water-table fluctuation method 

and the chloride mass balance method (Aurand, 2013). The 

High Plains aquifer SWB model output was compared to the 

SOil WATer (SOWAT) model (Kahle and others, 2011) and 

43 local and regional studies published for various locations 

across the High Plains aquifer. The sensitivities of a subset of 

model parameters were reported, but the SWB model was not 

calibrated to any hydrologic measurements of water levels or 

streamflow (Stanton and others, 2011). For the North Atlantic 

Coastal Plain SWB model, the model parameters of available 

water capacity, runoff curve number, and rooting depths were 

derived from previously published studies, and model calibration processes were not specified. The average annual potential recharge rate from the SWB model output was compared 

to 17 previously published recharge estimates within the study 

area (Masterson and others, 2013).
6 Simulation of Potential Groundwater Recharge for the Glacial Aquifer System East of the Rocky Mountains, 1980–2011

Methods

This section contains a brief discussion of the SWB 

model theory and how the input datasets for the glacial SWB 

model were prepared. Also included are discussions of the 

model calibration process and methods used for evaluating 

model fit and error.

Model Theory and Description

The SWB model uses a modified Thornthwaite-Mather 

soil-water-balance approach (Thornthwaite and Mather, 1955, 

1957) to estimate daily potential recharge. Recharge estimates 

can be imported into regional groundwater-flow models or other 

hydrologic assessments where spatially distributed recharge 

estimates are necessary. Also, the gridded approach of the SWB 

model allows for potential recharge estimates to be rescaled to 

match the resolution of grid-based groundwater-flow model.

The SWB model uses a soil-water accounting method 

to calculate potential recharge separately for each grid cell in 

the model domain (Westenbroek and others, 2010). Potential 

recharge is calculated daily within each grid cell of the model 

domain as the difference between sources (liquid precipitation, snowmelt, upslope inflow), sinks (interception, outflow 

[runoff], ET), and change in soil moisture (eq. 1):

recharge = (precipitation + snowmelt + inflow) – (1)

(interception + outflow + evapotranspiration)

– Δsoil moisture

Each of the water-budget components in equation 1 is 

handled by one or more modules within the SWB model. The 

SWB model has the capability for routing runoff through the 

model domain; however, runoff routing was not used in this 

modeling application because the grid scale (1 km) was sufficiently large so that overland flow was expected to infiltrate 

within a grid cell before entering an adjacent cell. Computation of water-budget components relies on relations between 

surface runoff, land cover, and hydrologic soil group (HSG) 

(Cronshey and others, 1986) and estimated values of ET. 

Water storage in the soil column was estimated daily using a 

modified Thornthwaite-Mather accounting method (Westenbroek and others, 2010). A brief summary of model processes 

is shown in figure 2. Additional theoretical and background 

details about the SWB model processes are detailed in Westenbroek and others (2010). For the glacial SWB model in this 

report, algorithms as described in Westenbroek and others 

(2010) were used for determining precipitation type (liquid 

or snow), snowmelt timing and rates, periods of frozen soil, 

runoff volumes according to the curve number method, and 

daily changes in soil moisture with the necessary intermediary 

values. Interception and the start and end of the growing season were determined with separate algorithms not described 

in Westenbroek and others (2010) and are described in the 

“Lookup Tables and Control File” section.

Model Limitations and Assumptions

The original concept behind the SWB model code was 

to allow for the spatial distribution of potential groundwater 

recharge to be quickly and easily calculated from readily available data and standardized parameters (Dripps and Bradbury, 

2007; Westenbroek and others, 2010); however, SWB results 

are typically not directly constrained by measured field data 

and thus should be corroborated with recharge estimates generated from other methods. The SWB model described in this 

report is intended to provide information about the distribution of potential recharge in time and space at a 1-km scale for 

annual to multiyear timescales. Although SWB approaches 

are a preferred approach for groundwater modeling (Anderson 

and others, 2015), comparing the SWB-calculated potential recharge estimates from the current model to recharge 

estimated from groundwater-level fluctuations, hydrograph 

separation, or other methods in a particular area of interest is 

highly recommended. Multiple methods of indirect measurement and associated errors frequently are compared because 

potential recharge rates cannot be measured easily across large 

areas (Healy and Scanlon, 2010).

The SWB model was calibrated to stream base flows 

determined using hydrograph separation. Hydrograph separation methods require several simplifying assumptions (adapted 

from McCoy and others, 2015):

1. Streamflow hydrographs only reflect contributions 

from two sources: surface runoff from precipitation 

and base flow resulting from groundwater discharge 

to streams.

2. Direct, diffuse groundwater recharge happens throughout a basin, as opposed to indirect recharge through 

streambeds.

3. Groundwater discharge to streams is a continuous process (Healy and Scanlon, 2010).

4. All groundwater recharge within the basin discharges 

to the receiving stream network.

5. Groundwater contributing areas are perfectly coincident with surface-watershed boundaries.

6. Groundwater storage within the basin does not change 

over the period of interest.

7. The base-flow component of streamflow is all groundwater discharge and does not result from other factors 

that create a stable flow signal such as slow snowmelt, streamflow regulation, or wastewater return 

flows.

The hydrograph separation techniques used in this report 

are appropriate only when used over a period of 1 year or 

more (Rutledge, 1998; Sloto and Crouse, 1996). Assuming that base flow from hydrograph separation is equal to 

groundwater recharge requires a period of analysis that is long 
Methods 7

enough so that the effect on the water balance of changes in 

storage can be considered negligible (Rutledge, 1998). This 

critical assumption likely is met most consistently across the 

model domain for the 1980–2011 period, making the 32-year 

mean annual potential recharge the most reliable estimate from 

this SWB model application. The annual potential recharge 

estimates (that is, the potential recharge total for each of the 

32 years of the simulation) were useful in that they demonstrated the temporal variability in potential recharge under 

changing climatic and land-use conditions. Groundwater contributing areas do not always coincide with surface-watershed 

boundaries (Kanivetsky, 1979), but surface-watershed boundaries are assumed to be an adequate approximation of groundwater contributing areas for the purposes SWB model calibration and is consistent with previous SWB model applications 

(McCoy and others, 2015; Smith and Westenbroek, 2015; 

Westenbroek and others, 2010).

Base flow used to calibrate the SWB model is an estimate 

of groundwater recharge that has an absolute minimum error 

of 5 percent (from streamflow measurement error), though the 

actual error likely is greater than this minimum. Hydrograph 

separation methods are applied to streamflow measurements, 

which themselves have variable error rates. Streamflow measurements made by the USGS typically are rated as “good,” 

“fair,” or “poor,” which correspond to approximate error rates 

of 5, 8, or 10 percent, respectively (Turnipseed and Sauer, 

2010). Differing amounts of error also are introduced from the 

hydrograph separation method and the characteristics of the 

watershed where the method is applied.

The five hydrograph separation methods used in this 

report produced variable estimates of base flow, as discussed 

in the “Model Fit and Model Error” section. Certain flow conditions in watersheds, such as flow regulation structures, slow 

snowmelt, tile drainage, or wastewater discharge contribute 

to a streamflow signal that mimics groundwater discharge and 

may result in overestimates of base flow, and thus overestimates of groundwater recharge (Schilling and Helmers, 2008; 

Sloto and Crouse, 1996). For the SWB model calibration, 

criteria were used to select calibration basins such that these 

types of error were minimized (refer to “Calibration Targets” 

section); nevertheless, these errors were inevitable in varying 

amounts in the calibration basins.

Subsurface drainage tiles are used extensively throughout 

the Midwest to lower the water table and drain soils that are 

seasonally or perennially wet so that those areas can be used 

for agricultural production (Madramootoo and others, 2007; 

Zucker and Brown, 1998). Tile drainage can increase the 

base-flow component determined with hydrograph separation but may not represent the timing of natural groundwater 

seepage into streams (for example, Schilling and Helmers, 

2008). Nationally consistent tile drainage records are not 

available, and assessing the density of tile drainage in each 

of the calibration basins was beyond the scope of this study; 

however, a map of drained land density in the United States 

(Madramootoo and others, 2007) indicates that calibration basins in southern Minnesota, Iowa, Illinois, southern 

Michigan, Indiana, and Ohio (fig. 1) have a high likelihood of 

being affected by tile drain flow. Therefore, it is possible that 

results from glacial SWB model calibration might have tiledrain artifacts from hydrograph separation done for heavily 

tile-drained watersheds in the Midwest.

Model results should not be used for periods of less than 

1 year because the SWB model does not account for lag times 

resulting from transport in the unsaturated zone, which affects 

timing between precipitation events and related groundwater 

recharge (Hunt and others, 2008). Even yearly estimates of 

potential recharge only should be used as an approximate 

range of potential recharge rates. Potential recharge in the 

SWB model is assumed to happen instantaneously within the 

daily time step, whereas actual recharge can take months or 

even years. An annual time step requires the assumption that 

all potential recharge happening on the landscape within a 

basin is measured at the streamgage during that same year. 

This assumption does not hold where there are flow paths with 

long travel times to the stream of interest. Aggregating SWB 

recharge annually also assumes no change in basin storage 

over a year. It should be noted, however, that when SWB 

results are linked to groundwater modeling, it is possible to 

account for unsaturated zone recharge lags (Hunt and others, 

2008).

Precipitation is aggregated to the daily time step to limit 

the model run time, and the daily time step generally is the 

smallest time step available in large meteorological datasets; 

however, for an equal amount of precipitation, surface runoff 

will differ between a 30-minute storm and steady rainfall 

lasting several hours., The SWB model cannot distinguish 

between these two events based on the daily time step (Smith 

and Westenbroek, 2015).

The glacial SWB model domain covers an immense 

study area and does not simulate all combinations of land 

cover, soil types, and climate equally well. Within the SWB 

model code, potential recharge is calculated as the difference 

between sources and sinks (eq. 1), so any errors in the various 

hydrologic components will be superimposed on the potential 

recharge error. The errors associated with different hydrologic 

components are not distributed equally throughout the model; 

a few specific cases of expected greater error are described 

below.

The SWB code is best suited for conditions in which the 

water table is below the root-zone depth (fig. 2). The SWB 

model does not record the depth to the water table. The SWB 

model cannot directly account for ET taken directly from 

the groundwater system, nor can it reject recharge based on 

reduced subsurface storage resulting from high water tables 

(Westenbroek and others, 2010); therefore, some of the major 

hydrologic processes in areas with abundant wetlands, springs, 

lakes, or other landscape features where the water table regularly intersects the land surface are not represented in the SWB 

code, which could result in simulations that differ substantially 

from observed conditions. All open-water features, such as 

lakes, ponds, and large rivers, were assumed to have no direct 

potential recharge; exchanges between surface-water and 
8 Simulation of Potential Groundwater Recharge for the Glacial Aquifer System East of the Rocky Mountains, 1980–2011

groundwater features are not simulated explicitly in the SWB 

code. Parts of the model domain receive substantial amounts 

of precipitation as snowfall. The SWB code uses a continuous frozen ground index (CFGI), based on air temperature, 

to assign the runoff curve number of model cells between 

antecedent moisture conditions II (unfrozen) and III (frozen). 

As the percentage of precipitation that falls as snow increases, 

errors associated with snowmelt infiltration likely become 

larger. For additional discussion on the limitations of the SWB 

model code, refer to Westenbroek and others (2010).

Model Input Data

The glacial SWB model consists of a 1-km grid spacing of 1,374 rows and 3,548 columns. The rectangular model 

domain extent was defined by the extent of the glacial aquifer 

system as outlined in figure 1. Of the nearly 4.9 million model 

cells within that area, only approximately 1.8 million are 

within the boundaries of the glacial aquifer system and active 

for the SWB model simulations.

The SWB model requires input for parameters that 

govern the simulation of hydrologic processes for each land 

use-soil type combination within a model domain. The following gridded datasets were required to use the SWB model to 

calculate potential recharge on a cell-by-cell basis, as detailed 

in Westenbroek and others (2010): (1) meteorological data 

(daily precipitation in inches, daily maximum air temperature, daily minimum air temperature), (2) land-cover class, 

(3) HSG, and (4) available soil-water capacity.

An optional grid for surface-water flow direction, which 

routes overland flow between cells, was not included as part of 

the glacial SWB model. The lookup tables for (1) soil and land 

cover and (2) soil-water retention are necessary for the SWB 

code to run. Details of these two lookup tables are given in the 

“Lookup Tables and Control File” section.

Meteorological Data

All the potential recharge estimates in this report were 

based on meteorological data from the Daymet dataset 

(Thornton and others, 2014). Daymet data are daily continuous surfaces of meteorological data, including precipitation 

and daily minimum/maximum air temperature, which have 

been applied broadly in hydrological and terrestrial vegetation 

growth models (Thornton and others, 1997). Mean annual 

gross precipitation in inches per year (in/yr) for 1980–2011 

at a 1-km resolution from the Daymet dataset is shown in 

figure 3.

Driftless area

MT

CO

KS

UT

SD

IL

CANADA

WY

NE

IA

ND MN

WI

MO

PA

IN

MI

NY

NY

VA

OH

KY

ME

WV

MI VT

NH

MD

MA

CT

DE

NJ

RI

Lake Superior Lake Michigan

Lake

Huron

Lake Erie

Lake Ontario

110° 100° 90° 80° 70°

45°

40°

Base map image is the intellectual property of Esri and is

used herein under license. Copyright © 2017 Esri and

its licensors. All rights reserved. Base modified from Esri

digital data, 1:70,000 (Esri, 2009)

Base map of states from U.S. Geological Survey 1:2,000,000 digital data

Albers Equal-Area Conic projection, standard parallels 29°30' N., and 45°30' N.

Central meridian 96°00' W., latitude of origin 23°00’ N.

0 125 250 MILES

0 125 250 KILOMETERS

Area of

enlargement 87

80

60

40

20

0

Mean annual gross precipitation during 

1980–2011, in inches per year

EXPLANATION

Figure 3. Mean annual gross precipitation within the extent of the glacial aquifer system at a 1-kilometer resolution for 

1980–2011, summarized from the Daymet dataset (Thornton and others, 2014).
Methods 9

Land Cover

Input land-cover data for the SWB model were derived 

from the National Land Cover Database (NLCD) dataset 

for the reference years of 2001 (Homer and others, 2007), 

2006 (Fry and others, 2011), and 2011 (Homer and others, 

2015). The use of NLCD products incorporates a consistent 

classification scheme that captures the spatial and temporal 

variability in land use over the model domain through time. 

The 2001 NLCD dataset was used for 1980 to 2003, the 2006 

NLCD was used for 2004 to 2008, and the 2011 NLCD was 

used for 2009 to 2011. The NLCD characterizes land cover 

into 16 categories at a 30-meter (m) resolution. Input datasets 

were resampled from the native 30-m resolution of the NLCD 

to 1-km resolution using a majority resampling protocol in 

Esri ArcMap 10.1 (Esri, 2012) and exported to an American 

Standard Code for Information Interchange (ASCII) data grid 

for use in the SWB model.

Of the 16 land-cover classes, 15 are in the active SWB 

model domain (tables 1, 2, 3, fig. 4). At 1-km resolution, no 

land-cover class changed by more than 0.2 percent among 

the 2001, 2006, and 2011 datasets. Cultivated crops (landcover class 82) covered the largest area (38 percent) of the 

model domain. The second largest land-cover class was forest, 

covering about 25 percent of the model domain. Within the 

forest classification, deciduous forest covered 18 percent, and 

evergreen and mixed forests covered less than 4 percent each 

(tables 1, 2, 3, fig. 4).

Soil Hydrologic Data

The glacial SWB model required two input grids of soil 

hydrologic characteristics: HSG and available water capacity (AWC). Each cell within the model domain was assigned 

to an HSG and assigned an AWC value. Both grids were 

derived from the Digital General Soil Map of the United 

States (STATSGO2) dataset (Natural Resources Conservation 

Service, 2015). STATSGO2 is described as “a broad-based 

inventory of soils and non-soil areas that occur in a repeatable pattern on the landscape and that can be cartographically 

shown at the scale mapped of 1:250,000 in the continental 

U.S.” (Natural Resources Conservation Service, 2015).

The 1-km HSG and AWC grids were derived from areaand depth-weighted averages of hydrologic variables in the 

STATSGO2 dataset. The area- and depth-weighted averages were computed on a 100-m grid scale using methods 

originally applied to the Soil Survey Geographic (SSURGO) 

dataset as described in Wieczorek (2014). The area- and depthweighted STATSGO2 data are preliminary and are subject to 

revision. The processed STATSGO2 data have not received 

final approval by the U.S. Geological Survey (USGS).

Hydrologic Soil Group

The 100-m HSG grid (Michael Wieczorek, written commun., January 16, 2015) was resampled to 1-km resolution 

using a majority resampling protocol in Esri ArcMap 10.1 

Table 1. Percentage of the glacial aquifer system by 2001 land-cover class from the National Land Cover Database dataset (Homer and 

others, 2007) and the Digital General Soil Map of the United States (STATSGO2) hydrologic soil group (Natural Resources Conservation 

Service, 2015).

[The total number of active square kilometer cells in the model domain is 1,736,651; NA, not applicable; --, no data]

Landcover 

class

Description

Percentage of domain

Hydrologic 

soil group 

A

Hydrologic 

soil group 

B

Hydrologic 

soil group 

C

Hydrologic 

soil group 

D

Organic soil 

group

Open 

water

Glacial 

domain total 

land cover

11 Open water 0.259 0.947 0.478 0.135 0.063 1.259 3.1

21 Developed, open space 0.351 1.437 0.958 0.164 0.035 0.005 3.0

22 Developed, low intensity 0.262 0.943 0.599 0.113 0.018 0.003 1.9

23 Developed, medium intensity 0.116 0.332 0.247 0.035 0.006 0.001 0.7

24 Developed, high intensity 0.048 0.126 0.084 0.013 0.003 0.001 0.3

31 Barren land (rock/sand/clay) 0.03 0.05 0.05 0.024 0.005 0.009 0.2

41 Deciduous forest 2.205 5.988 8.405 0.728 0.325 0.024 17.7

42 Evergreen forest 0.784 0.472 1.925 0.303 0.108 0.015 3.6

43 Mixed forest 0.397 0.448 2.569 0.214 0.067 0.008 3.7

52 Shrubland 0.183 0.21 0.651 0.208 0.027 0.003 1.3

71 Grasslands 0.477 4.287 2.053 1.947 0.022 0.026 8.8

81 Pasture/hay 0.501 5.131 3.911 0.736 0.076 0.004 10.4

82 Cultivated crops 1.145 24.532 9.728 2.306 0.21 0.007 37.9

90 Woody wetlands 0.996 1.783 1.483 0.306 1.165 0.024 5.8

95 Herbaceous wetlands 0.226 0.715 0.284 0.079 0.339 0.029 1.7

NA Glacial domain total in soil group 8.0 47.4 33.4 7.3 2.5 1.4 --
10 Simulation of Potential Groundwater Recharge for the Glacial Aquifer System East of the Rocky Mountains, 1980–2011

Table 2. Percentage of the glacial aquifer system by 2006 land-cover class from the National Land Cover Database dataset (Fry and 

others, 2011) and the Digital General Soil Map of the United States (STATSGO2) hydrologic soil group (Natural Resources Conservation 

Service, 2015).

[The total number of active square kilometer cells in the model domain is 1,736,651; NA, not applicable; --, no data]

Landcover 

class

Description

Percentage of domain

Hydrologic 

soil group 

A

Hydrologic 

soil group 

B

Hydrologic 

soil group 

C

Hydrologic 

soil group 

D

Organic soil 

group

Open 

water

Glacial 

domain total 

land cover

11 Open water 0.255 0.911 0.473 0.132 0.063 1.229 3.1

21 Developed, open space 0.346 1.472 0.974 0.171 0.032 0.005 3.0

22 Developed, low intensity 0.282 0.979 0.619 0.115 0.021 0.003 2.0

23 Developed, medium intensity 0.117 0.344 0.25 0.037 0.006 0.001 0.8

24 Developed, high intensity 0.05 0.132 0.088 0.013 0.004 0.001 0.3

31 Barren land (rock/sand/clay) 0.029 0.052 0.05 0.024 0.005 0.009 0.2

41 Deciduous forest 2.211 5.998 8.392 0.724 0.33 0.024 17.7

42 Evergreen forest 0.768 0.468 1.952 0.306 0.109 0.016 3.6

43 Mixed forest 0.402 0.454 2.595 0.22 0.067 0.008 3.7

52 Shrubland 0.156 0.2 0.656 0.22 0.021 0.002 1.3

71 Grasslands 0.51 4.316 2.092 1.953 0.024 0.033 8.9

81 Pasture/hay 0.506 5.117 3.922 0.735 0.076 0.004 10.4

82 Cultivated crops 1.142 24.462 9.712 2.299 0.209 0.007 37.8

90 Woody wetlands 0.986 1.763 1.366 0.282 1.162 0.028 5.6

95 Herbaceous wetlands 0.222 0.735 0.28 0.08 0.339 0.048 1.7

NA Glacial domain total in soil group 8.0 47.4 33.4 7.3 2.5 1.4 --

Table 3. Percentage of the glacial aquifer system by 2011 land-cover class from the National Land Cover Database dataset (Homer and 

others, 2015) and the Digital General Soil Map of the United States (STATSGO2) hydrologic soil group (Natural Resources Conservation 

Service, 2015).

[The total number of active square kilometer cells in the model domain is 1,736,651; NA, not applicable; --, no data]

Landcover 

class

Description

Percentage of domain

Hydrologic 

soil group 

A

Hydrologic 

soil group 

B

Hydrologic 

soil group 

C

Hydrologic 

soil group 

D

Organic soil 

group

Open 

water

Glacial 

domain total 

land cover

11 Open water 0.262 1.008 0.492 0.15 0.064 1.274 3.3

21 Developed, open space 0.358 1.468 0.976 0.164 0.035 0.005 3.0

22 Developed, low intensity 0.268 0.977 0.622 0.117 0.018 0.003 2.0

23 Developed, medium intensity 0.132 0.397 0.286 0.043 0.007 0.001 0.9

24 Developed, high intensity 0.052 0.142 0.095 0.015 0.003 0.001 0.3

31 Barren land (rock/sand/clay) 0.032 0.056 0.056 0.022 0.006 0.006 0.2

41 Deciduous forest 2.179 5.934 8.328 0.715 0.322 0.023 17.5

42 Evergreen forest 0.742 0.461 1.939 0.308 0.104 0.015 3.6

43 Mixed forest 0.385 0.435 2.513 0.207 0.063 0.008 3.6

52 Shrubland 0.226 0.226 0.687 0.208 0.03 0.002 1.4

71 Grasslands 0.492 4.24 2.068 1.941 0.027 0.022 8.8

81 Pasture/hay 0.492 5.059 3.88 0.728 0.075 0.004 10.2

82 Cultivated crops 1.139 24.509 9.709 2.303 0.208 0.006 37.9

90 Woody wetlands 0.989 1.77 1.477 0.306 1.158 0.024 5.7

95 Herbaceous wetlands 0.231 0.722 0.294 0.083 0.347 0.023 1.7

NA Glacial domain total in soil group 8.0 47.4 33.4 7.3 2.5 1.4 --
Methods 11

(Esri, 2012). Then, the grid was exported to an ASCII data 

grid for use in the SWB model. The following paragraphs 

describe the HSG classification systems used for this report as 

shown in figure 5.

The Natural Resources Conservation Service (2007) provides numeric definitions and detailed descriptions of the HSG 

classes; only general descriptions are included here. Soils in 

group A are typically sandy with a high infiltration capacity 

and low runoff potential when thoroughly wet. In contrast, 

soils in group D are typically clayey with a very low infiltration capacity and high runoff potential. Group B and C soils 

fall between these extremes. The slope of the soil surface is 

not considered when assigning HSGs.

Certain wet soils are placed in group D based solely on 

the presence of a water table within 24 in. of the surface even 

though the saturated hydraulic conductivity may be favorable 

for water transmission. These soils are assigned to dual HSGs 

(A/D, B/D, and C/D) because infiltration is limited only by 

a shallow water table. The first letter applies to the drained 

condition and the second to the undrained condition (Natural 

Resources Conservation Service, 2007). For the glacial SWB 

model, all A/D, B/D, and C/D soils were classified according 

to their drained condition; for example, soils of type A/D were 

classified as soil type A. The Minnesota SWB model used 

soils classified to their drained condition because the soils 

commonly were in parts of the State with extensive artificial 

drainage (Smith and Westenbroek, 2015). Soils with the dual 

designations comprise about 9 percent of the active glacial 

SWB model domain. Most (79 percent) of these dual-group 

soils are in States west of Pennsylvania, and the distribution 

of these soils generally coincides with areas of tile drainage 

(Madramootoo and others, 2007); therefore, classification of 

these soils in their drained condition was the most representative classification for the glacial SWB model.

fig 04

Driftless area

MT

CO

KS

UT

SD

IL

CANADA

WY

NE

IA

ND MN

WI

MO

PA

IN

MI

NY

NY

VA

OH

KY

ME

WV

MI VT

NH

MD

MA

CT

DE

NJ

RI

Lake Superior Lake Michigan

Lake

Huron

Lake Erie

Lake Ontario

110° 100° 90° 80° 70°

45°

40°

Base map image is the intellectual property of Esri and is

used herein under license. Copyright © 2017 Esri and

its licensors. All rights reserved. Base modified from Esri

digital data, 1:70,000 (Esri, 2009)

Base map of states from U.S. Geological Survey 1:2,000,000 digital data

Albers Equal-Area Conic projection, standard parallels 29°30' N., and 45°30' N.

Central meridian 96°00' W., latitude of origin 23°00’ N.

EXPLANATION

0 125 250 MILES

0 125 250 KILOMETERS

Area of

enlargement Extent of glacial Soil-Water-Balance model domain

Open water

Developed, open space

Developed, low intensity

Developed, medium intensity

Developed, high intensity

Barren land (rock/sand/clay)

Deciduous forest

Evergreen forest

Land cover (modified from Fry and others, 2011)

Mixed forest

Shrubland

Grasslands/herbaceous

Pasture/hay

Row crops

Woody wetlands

Emergent herbaceous wetlands

Figure 4. Land-cover classes according to the 2006 National Land Cover Database within the extent of the glacial 

aquifer system at a 1-kilometer resolution (Fry and others, 2011).
12 Simulation of Potential Groundwater Recharge for the Glacial Aquifer System East of the Rocky Mountains, 1980–2011

Soils with greater than 20 percent organic matter and 

less than 50 percent clay in the averaged STATSGO2 dataset 

(Michael Wieczorek, written commun., January 16, 2015) 

were assigned to an “organic” HSG. This classification is 

based on the definition from Donahue and others (1983) 

and methods used in the Minnesota SWB model (Smith and 

Westenbroek, 2015). This unique class was created because 

organic soils can hold more water than the same volume of 

a nonorganic, mineral soil (Natural Resources Conservation 

Service, 2007) that potentially would be underpredicted by the 

STATSGO2 available soil-water capacity.

An “open-water” HSG was assigned to cells that were 

classified as such in the STATSGO2 data. Model cells in this 

category produced no potential recharge because the curve 

numbers were set to 100 (table 4).

Available Water Capacity

The 100-m AWC grid from STATSGO2 (Michael Wieczorek, written commun., January 16, 2015) was resampled to 

1-km resolution using a bilinear interpolation protocol in Esri 

ArcMap 10.1 (Esri, 2012) and exported to an ASCII data grid 

for use in the SWB model as shown in figure 6.

The AWC input data reflect the amount of water the soil 

profile can hold, typically given as inches of water holding 

capacity per foot of soil thickness, or inches per foot. For 

each model cell, the AWC value is multiplied by the root-zone 

depth to calculate the maximum soil-water capacity, which 

represents the maximum amount of soil-water storage that 

can take place in a grid cell (fig. 2). Because root-zone depths 

are assigned according to land cover and HSG (table 4), the fig 05

Driftless area

MT

CO

KS

UT

SD

IL

CANADA

WY

NE

IA

ND MN

WI

MO

PA

IN

MI

NY

NY

VA

OH

KY

ME

WV

MI VT

NH

MD

MA

CT

DE

NJ

RI

Lake Superior Lake Michigan

Lake

Huron

Lake Erie

Lake Ontario

16

110° 100° 90° 80° 70°

45°

40°

Base map image is the intellectual property of Esri and is

used herein under license. Copyright © 2017 Esri and

its licensors. All rights reserved. Base modified from Esri

digital data, 1:70,000 (Esri, 2009)

Base map of states from U.S. Geological Survey 1:2,000,000 digital data

Albers Equal-Area Conic projection, standard parallels 29°30' N., and 45°30' N.

Central meridian 96°00' W., latitude of origin 23°00’ N.

0 125 250 MILES

0 125 250 KILOMETERS

Area of

enlargement

Group A

Group B

Group C

Group D

Organic

Water

Hydrologic soil group

EXPLANATION

Extent of glacial Soil-Water-Balance model domain

Figure 5. Hydrologic soil groups within the extent of the glacial aquifer system at a 1-kilometer resolution, based on the 

Digital General Soil Map of the United States (STATSGO2) (Natural Resources Conservation Service, 2015; Wieczorek, 

2014).
Table 4. Lookup table for the calibrated Soil-Water-Balance model, corresponding land cover to runoff curve number (by hydrologic soil group), maxhydrologic soil group), interception storage (growing season/dormant season), and root-zone depth (by hydrologic soil group).[a is the intercept in equation 2; b is the slope in equation 2; n=0 for open water and n=1 for all other land-cover types in equation 2; NA, not applicable]

Landcover 

class 

Description

Assumed 

imperviousness

Runoff curve number Maximum recharge rate (

Hydrologic 

soil group 

A

Hydrologic 

soil group 

B

Hydrologic 

soil group 

C

Hydrologic 

soil group 

D

Organic 

soil 

group

Open 

water

Hydrologic 

soil group 

A

Hydrologic 

soil group 

B

Hydrologic 

soil group 

C

Hy

s

11 Open water NA 100.0 100.0 100.0 100.0 100.0 100.0 0.0 0.0 0.0 

21 Developed, open 

space

NA 48.9 60.9 71.3 79.5 60.9 100.0 4.5 0.8 0.3 

22 Developed, low 

intensity

30 percent 61.2 73.9 82.9 88.6 73.9 100.0 4.4 0.8 0.3 

23 Developed, medium 

intensity

60 percent 76.3 86.0 91.2 93.8 86.0 100.0 4.0 0.9 0.5 

24 Developed, high 

intensity

90 percent 88.7 93.2 95.0 95.6 93.2 100.0 3.3 0.9 0.4 

31 Barren land (rock/

sand/clay)

NA 61.2 73.9 82.9 88.6 73.9 100.0 5.2 1.0 0.5 

41 Deciduous forest NA 42.0 57.8 67.1 71.3 57.8 100.0 4.9 1.4 0.5 42 Evergreen forest NA 54.0 70.3 79.0 82.8 70.3 100.0 5.7 2.4 0.8 43 Mixed forest NA 47.8 64.0 73.0 77.1 64.0 100.0 5.3 2.3 0.7 52 Shrubland NA 53.9 68.9 76.7 80.1 68.9 100.0 5.4 1.5 0.5 71 Grasslands NA 48.3 64.7 74.0 78.1 64.7 100.0 4.0 0.4 0.1 81 Pasture/hay NA 65.5 83.6 93.1 97.2 83.6 100.0 3.7 0.6 0.2 82 Cultivated crops NA 21.8 40.6 59.4 71.5 40.6 100.0 4.0 0.4 0.1 90 Woody wetlands NA 61.7 65.2 66.6 67.1 65.2 100.0 5.1 1.7 0.6 95 Herbaceous wetlands NA 61.7 65.2 66.6 67.1 65.2 100.0 4.7 0.9 0.4 
Table 4. Lookup table for the calibrated Soil-Water-Balance model, corresponding land cover to runoff curve number (by hydrologic soil group), maxhydrologic soil group), interception storage (growing season/dormant season), and root-zone depth (by hydrologic soil group).—Continued [a is the intercept in equation 2; b is the slope in equation 2; n=0 for open water and n=1 for all other land-cover types in equation 2; NA, not applicable] Land- cover class Description Assumed impervious- ness Growing season interception Dormant season interception Root-zone dept

(feet) a b n a b n Hydrologic soil group A Hydrologic soil group B Hydrologic soil group C Hydr

soil 

11 Open water NA 0.0000 0.0000 0 0.0000 0.0000 0 0.00 0.00 0.00 0

21 Developed, open space NA 0.0013 0.0030 1 0.0013 0.0020 1 2.11 2.33 1.93 122 Developed, low intensity 30 percent 0.0012 0.0030 1 0.0012 0.0020 1 1.60 1.82 1.42 123 Developed, medium intensity 60 percent 0.0010 0.0020 1 0.0010 0.0020 1 1.16 1.38 0.98 024 Developed, high intensity 90 percent 0.0009 0.0020 1 0.0009 0.0020 1 0.78 1.00 0.60 031 Barren land (rock/sand/ clay) NA 0.0010 0.0030 1 0.0010 0.0020 1 1.60 1.82 1.42 141 Deciduous forest NA 0.0014 0.0290 1 0.0014 0.0130 1 4.35 4.15 4.06 442 Evergreen forest NA 0.0017 0.0970 1 0.0017 0.0590 1 5.20 4.69 4.44 443 Mixed forest NA 0.0016 0.0630 1 0.0016 0.0630 1 4.77 4.42 4.25 452 Shrubland NA 0.0013 0.0080 1 0.0013 0.0050 1 3.25 2.53 3.25 371 Grasslands NA 0.0008 0.0070 1 0.0008 0.0050 1 2.68 2.35 2.68 281 Pasture/hay NA 0.0013 0.0080 1 0.0013 0.0050 1 4.01 3.29 4.01 482 Cultivated crops NA 0.0010 0.0100 1 0.0010 0.0020 1 2.39 2.36 2.28 290 Woody wetlands NA 0.0014 0.0230 1 0.0014 0.0160 1 2.39 2.39 2.39 295 Herbaceous wetlands NA 0.0014 0.0230 1 0.0014 0.0160 1 1.48 1.48 1.48 1
Methods 15

maximum soil-water capacity incorporates land-cover and 

soils information. Water added to the soil column in excess 

of the maximum soil-water capacity value becomes recharge 

(fig. 2).

Maximum Recharge Rate

The maximum daily recharge rate is specified for each 

combination of land cover and HSG in the lookup table. For 

the glacial aquifer SWB model, maximum daily recharge rates 

for each land-cover HSG combination were estimated by zonal 

statistics of hydraulic conductivities from the STATSGO2 

dataset (Michael Wieczorek, written commun., January 16, 

2015). The method assumes that saturated hydraulic conductivity can be used as a surrogate of maximum recharge rates 

amongst the HSG and land-cover class combinations. Pedotransfer functions from Saxton and Rawls (2006) were used 

to estimate hydraulic conductivities from the percentage of 

clay, sand, and organic matter given in the 100-m resolution 

STATSGO2 dataset. Hydraulic conductivities were calculated 

for each map unit polygon in the active glacial SWB model 

domain. These hydraulic conductivities then were resampled 

to a 1-km grid resolution using bilinear interpolation. The 

mean hydraulic conductivity of each land-cover HSG combination represented the maximum recharge rate for each 

combination.

Lookup Tables and Control File

The SWB model uses two lookup tables to assign 

model cell properties related to soils and land cover: (1) the 

soil and land-cover parameter lookup table (table 4), and 

(2) the extended Thornthwaite-Mather soil-water retention 

table (Thornthwaite and Mather, 1957). The soil and landcover parameter lookup table (table 4) assigns parameters 

fig 06

Driftless area

MT

CO

KS

UT

SD

IL

CANADA

WY

NE

IA

ND MN

WI

MO

PA

IN

MI

NY

NY

VA

OH

KY

ME

WV

MI VT

NH

MD

MA

CT

DE

NJ

RI

Lake Superior Lake Michigan

Lake

Huron

Lake Erie

Lake Ontario

110° 100° 90° 80° 70°

45°

40°

Base map image is the intellectual property of Esri and is

used herein under license. Copyright © 2017 Esri and

its licensors. All rights reserved. Base modified from Esri

digital data, 1:70,000 (Esri, 2009)

Base map of states from U.S. Geological Survey 1:2,000,000 digital data

Albers Equal-Area Conic projection, standard parallels 29°30' N., and 45°30' N.

Central meridian 96°00' W., latitude of origin 23°00’ N.

EXPLANATION

0 125 250 MILES

0 125 250 KILOMETERS

Area of

enlargement

Less than 1

1.01 to 2.00

2.01 to 3.00

3.01 to 4.00

4.01 to 5.00

5.01 to 6.00

6.01 to 7.00

Available soil-water capacity, in 

inches of water per foot of soil

Extent of glacial Soil-Water-Balance model domain

Figure 6. Available soil-water capacity within the extent of the glacial aquifer system at a 1-kilometer resolution, 

based on the Digital General Soil Map of the United States (STATSGO2) (Natural Resources Conservation Service, 2015; 

Wieczorek, 2014).
16 Simulation of Potential Groundwater Recharge for the Glacial Aquifer System East of the Rocky Mountains, 1980–2011

describing the processes of interception, runoff, ET, infiltration, and recharge to each of the 90 unique combinations 

of 15 land-cover classes and 6 soil classes (4 HSG classes, 

organic soil class, and open-water class) in the glacial aquifer 

system model domain. Specifically, table 4 contains calibrated values of dimensionless curve numbers (Cronshey and 

others, 1986), maximum recharge rates (in inches per day), 

root-zone depths (in feet), and plant-canopy interception 

parameters for growing and dormant seasons. The extended 

Thornthwaite-Mather soil-water retention table describes 

the ability of different soils to hold water (Thornthwaite 

and Mather, 1957). This table assists in the calculation of 

soil-moisture adjustments during periods of unsatisfied 

potential ET. Adjustments were not made to the extended 

Thornthwaite-Mather soil-water retention table during model 

calibration.

The control file used to run the glacial SWB model is in 

the model archive (Trost, 2018); a few specifications in the 

glacial SWB model control file are noted here. The control file 

handles all the user-defined options for an individual SWB 

simulation, such as the growing season length, model domain 

grid definition, the routing method, location of input files, and 

control over the SWB output. Overland-flow routing (also 

known as runoff routing) was turned off.

The Hargreaves-Samani method (1985) was used to estimate potential ET and required the daily maximum and minimum temperatures from the Daymet dataset (Thornton and 

others, 2014). In the SWB model, initial values for abstraction 

can be set by multiplying the maximum soil-moisture holding 

capacity by either 0.2 or 0.05. For the glacial SWB model, the 

smaller initial abstraction was used and resulted in more runoff for smaller precipitation events, which has been recognized 

as more appropriate for multiyear simulations (Woodward and 

others, 2003).

The SWB model code version used to simulate potential recharge for the glacial aquifer system used an interception algorithm based on Horton (1919) that is different 

from the “bucket” interception method used in previously 

published SWB models (for example, Feinstein and others, 

2010; Westenbroek and others, 2010; Masterson and others, 

2013; Smith and Westenbroek, 2015). The “bucket” interception method only allows for a single interception value 

regardless of the total storm volume, whereas the Horton 

interception algorithm produces a series of “working formulas” that relate the daily or storm total rainfall to the amount 

of interception by vegetation. These working formulas are 

typically simple linear models with intercepts and slope 

terms. Parameters for the Horton interception algorithm 

required inputs in the lookup table that varied by land-cover 

type as in previous SWB models; however, the parameters 

in the lookup table (table 4) now were used by SWB in the 

following equation: 

ILs=aL+bLs×Pn (2)

where 

I is the daily interception for land cover L

during season s (growing or dormant), in 

inches;

aL is the intercept for land cover L, in inches; 

bLs is the slope for land cover L during season s

(growing or dormant), unitless; 

P is the daily precipitation total, in inches; and

n is 0 for open-water land-cover types and 1 for 

all nonopen-water land-cover types.

Growing season start and end dates differ greatly across 

the glacial SWB model domain. The SWB model code 

version used to simulate potential recharge for the glacial 

aquifer system had two options for switching between the 

growing season and dormant season: fixed Julian start and 

end dates, or a dynamic start and end for each model cell 

based on growing degree-day calculations and a killing frost 

temperature from meteorological data. The dynamic option 

was used in the glacial SWB model, which means that for 

each year in each model cell, the growing season began 

when growing degree days accumulated above the threshold 

specified in the control file (GROWING_SEASON_STARTING_GDD). Growing degree days represent an accumulation of heat units above a base temperature below which the 

process of interest does not progress (McMaster and Wilhelm, 

1997). The growing season was terminated in each model 

cell when daily meteorological data for that cell fell below 

the killing frost temperature specified in the control file 

(GROWING_SEASON_KILLING_FROST).

Initial Conditions

For individual model calibration basins, spatially distributed initial conditions for soil-water content (SWC), CFGI, 

and snow cover (SC) were generated by completing a 1-year 

simulation using initial, uncalibrated parameter values. For 

basins with records that began in 1980, initial SWC, CFGI, 

and SC conditions were determined from a simulation of 

the year 1980 because gridded meteorological data were not 

available for years before 1980. For basins with streamflow 

records starting after 1980, initial SWC, CFGI, and SC were 

determined from a simulation beginning 1 year before the 

streamflow record. For the 1980–2011 model domain run, 

SWC, CFGI, and SC outputs from a “warm up” simulation of 

the year 1980 were used as initial conditions.

Model Calibration and Evaluation Methods

Model calibration is an iterative process that investigates the effects that model parameters have on the ability 

of a model to reproduce a set of measured observations. The 

SWB model was calibrated to base-flow observations from 

39 basins across the glacial aquifer system study area. A total 
Methods 17

of 62 model parameters were calibrated. Calibrated parameter 

values were compared to values from previously published 

SWB models that overlapped parts of the glacial SWB model 

domain (Aurand, 2013; Feinstein and others, 2010; McCoy 

and others, 2015; Smith and Westenbroek, 2015; Westenbroek 

and others, 2010). The fit of the SWB-simulated potential 

recharge to observed recharge (derived from base flow for 

39 calibration basins) was evaluated using graphical analysis 

and error evaluation statistics. Observed recharge rates from 

a second set of 38 “verification” basins not used for model 

calibration were used as an independent verification of the 

ability of the SWB model to simulate potential recharge across 

the model domain.

Calibration Targets

The glacial SWB model was calibrated to base flow calculated with the HYSEP local minimum method in 39 basins 

(Sloto and Crouse, 1996). Recharge was determined by 

summing the quantity of base flow for each year and dividing that total by the area of each respective basin. The resulting summary dataset is given in inches of recharge per year 

(table 5, available for download at https://doi.org/10.3133/

sir20185080).

Basin Selection

Basins selected for calibration met three general criteria: 

(1) the basins exhibited hydrologic conditions appropriate 

for hydrograph separation (for example, were not regulated); 

(2) the basins represented the model domain spatially (fig. 1); 

and (3) the basins represented the model domain temporally in 

that they had at least 15 years of continuous streamflow data 

between 1980 and 2011 (table 5). The following paragraphs 

describe each of these characteristics (hydrologic, spatial, 

temporal) in more detail.

Calibration basins were selected using criteria listed in 

the Geospatial Attributes of Gages for Evaluating Streamflow, version II (GAGES II) database (Falcone, 2011). The 

GAGES II dataset consists of gages that have had either at 

least 20 complete years of streamflow record since 1950 or are 

currently active as of water year 2009 and whose watersheds 

lie within the United States (Falcone, 2011). A water year is 

the period from October 1 to September 30 and is designated 

by the year in which it ends; for example, water year 2009 was 

from October 1, 2008, to September 30, 2009. All 39 calibration basins were identified as “reference” sites in GAGES II, 

and 34 basins were part of the higher quality 2009 Hydroclimatic Data Network.

Reference gages in the GAGES II dataset met the following three primary criteria (Lins, 2012): (1) hydrologic disturbance of the watershed was less than at least 75 percent of all 

other gaged watersheds in its region; (2) the USGS Annual 

Water Data Reports did not identify the presence of “regulated” streamflows, although some sites considered to have 

minor modifications were retained; and, (3) the watershed 

passed a visual screen using satellite imagery (typically 

Google Earth) of the watershed for the presence of human 

activities that indicated flow diversions, groundwater withdrawal, and other factors known to affect natural streamflows.

Several additional criteria listed in GAGES II were 

used to identify candidate calibration basins: (1) major dams 

were not in the watershed; (2) watershed sizes were between 

39 square miles (mi2; 100 square kilometers [km2]) and 

734 mi2 (1,900 km2); (3) BFI averages, as determined by 

Wolock (2003b), were between 10 percent and 90 percent of 

total streamflow; (4) less than 40 percent of precipitation fell 

as snow; (5) there were fewer than 100 days of 0 cubic feet 

per second (ft3/s) streamflow between 1980 and 2011, except 

for two basins in North Dakota; (6) less than 25 percent of 

the basin area was classified as woody wetlands or emergent 

wetlands; (7) the nearest major National Pollutant Discharge 

Elimination System discharge point was at least 2 mi away 

(33 basins had no National Pollutant Discharge Elimination 

System discharge point); and (8) freshwater withdrawals were 

less than 48 million gallons per mi2 (70 megaliters per year per 

km2) according to 1995 to 2000 county-level estimates. Within 

the glacial domain, 77 basins met all the above criteria.

The 77 basins were mapped, and a spatially distributed 

subset of 39 basins was selected for model calibration. Computation times limited the number of calibration basins; the 

other 38 basins were used to verify that the model simulated 

reasonable results for areas not used for calibration. Some 

basins were clustered and adjacent to one another; in these 

cases, only one basin per cluster was included for calibration. The 39 basins were selected from the 77 basins through 

an iterative process used to minimize the differences in the 

relative frequency of the 2006 NLCD land-cover classes 

and STATSGO2 HSGs between the calibration basins and 

overall active model domain. The resulting 39 basins compared reasonably well with the overall domain distributions 

(tables 6, 7). The cumulative area of the calibration basins was 

24,465 km2, about 1.4 percent of the total active model domain 

area. The distributions of land-cover classes in the calibration 

basins were all within 5 percent of the domain distribution 

(table 6). The HSG C soils were overrepresented in the calibration dataset by 8.9 percent; otherwise, all other soil types 

were within 5 percent of the domain distribution (table 7).

Streamflow records from the calibration basins represented the temporal variability during 1980–2011. Of the 

39 calibration basins, 3 had 15 to 20 years of daily streamflow data, 2 had 21 to 30 years of daily streamflow data, and 

34 basins had more than 30 years of daily streamflow data 

(table 5).

Base-Flow (Recharge) Observations and Weights

Five methods of hydrograph separation were investigated 

for use as calibration targets: PART (Rutledge, 1998), HYSEP 

fixed interval, HYSEP sliding interval, HYSEP local minimum 

(Sloto and Crouse, 1996), and BFI (Gustard and others, 1992). 

Of these five methods, the HYSEP local minimum method 
18 Simulation of Potential Groundwater Recharge for the Glacial Aquifer System East of the Rocky Mountains, 1980–2011

was selected because it consistently produced results between 

the higher predictions of PART and HYSEP fixed and sliding 

interval and the lower estimates yielded by the BFI method 

(table 5). A streamflow hydrograph and the separation of 

runoff from base flow, as determined by three different methods, PART, HYSEP local minimum, and BFI, are shown in 

figure 7. The PART method (green line) typically was higher 

than the HYSEP local minimum method (red line) and the BFI 

method (blue dashed line), thus a higher proportion of the total 

streamflow was classified as base flow with the PART method 

as compared to the other two methods (fig. 7).

The five hydrograph separation methods were applied 

to daily streamflow values using the package DVstats in R 

version 3.1.2 (R Development Core Team, 2014). Recharge 

was determined by summing the quantity of base flow for 

each year and dividing that total by the area of each respective basin. The resulting summary dataset is given in inches of 

recharge per year (table 5). The following paragraphs use the 

term “base flow,” which, in this report, is considered equivalent to “recharge over the basin area” for the calibration of the 

SWB model.

Three base-flow temporal data aggregations were used 

for model calibration: annual total base flow for each year of 

complete flow data, annual total base-flow duration deciles 

(10 deciles per basin, 10 percent through 100 percent), and 

the mean of all annual total base flows (mean annual) during 1980–2011. The calibration observation dataset consisted 

of 1,191 annual total base-flow observations, 340 base-flow 

decile observations, and 39 mean annual base-flow observations. Base-flow deciles only were computed for the 34 basins 

with a complete 32-year record. The three data aggregations 

provided information during calibration about mean annual 

recharge, variability in annual recharge rates, and the cumulative frequency distribution of annual recharge rates; therefore, 

the glacial SWB model is appropriate for examining mean 

annual potential recharge and temporal variability in potential 

recharge.

Recharge observations used for model calibration were 

computed as follows. Daily streamflow data were downloaded from the USGS National Water Information System 

(U.S. Geological Survey, 2015) for each calibration station 

Table 6. Distribution of land cover in the calibration basins and for the glacial Soil-Water-Balance model domain, based on the 

2006 National Land Cover Database (Fry and others, 2011).

Land-cover class Description

Land-cover distribution, in percent Difference, in percent 

between calibration 

watersheds and glacial 

model domain

39 calibration watersheds 

(table 5)

Entire glacial 

model domain

11 Open water 1.11 3.06 −1.95

21 Developed, open space 1.75 3.00 −1.26

22 Developed, low intensity 0.59 2.02 −1.43

23 Developed, medium intensity 0.11 0.75 −0.65

24 Developed, high intensity 0.02 0.29 −0.27

31 Barren land (rock/sand/clay) 0.02 0.17 −0.15

41 Deciduous forest 21.16 17.68 3.49

42 Evergreen forest 3.53 3.62 −0.09

43 Mixed forest 5.13 3.75 1.39

52 Shrubland 1.21 1.26 −0.04

71 Grasslands 4.44 8.93 −4.49

81 Pasture/hay 12.02 10.36 1.66

82 Cultivated crops 42.15 37.83 4.31

90 Woody wetlands 5.11 5.59 −0.48

95 Herbaceous wetlands 1.66 1.70 −0.04

Table 7. Distribution of hydrologic soil groups in the calibration 

basins and for the glacial Soil-Water-Balance model domain, 

based on the STATSGO2 soil database (Natural Resources 

Conservation Service, 2015).

Hydrologic 

soil group

Hydrologic soil group distribution, 

in percent

Difference, 

in percent 

between 

calibration 

watersheds and 

glacial model 

domain

39 calibration 

watersheds 

(table 5)

Entire glacial 

model domain

A 7.5 8.0 −0.4

B 44.2 47.4 −3.2

C 42.3 33.4 8.9

D 4.8 7.3 −2.5

Organic 1.1 2.5 −1.4

Open water 0.0 1.4 −1.4
Methods 19

listed in table 5. The Time-Series Processor, TSPROC (Westenbroek and others, 2012), was used on the daily streamflow 

data to screen out periods with no streamflow data, run the 

HYSEP local minimum hydrograph separation technique, 

aggregate daily base flow to annual base-flow totals, compute 

the annual base-flow duration deciles, and determine the longterm mean base flow. The final processing step implemented 

by TSPROC was dividing the volumetric outputs by basin area 

to produce recharge in inches per year.

Weights were assigned to each of the base-flow observations used for evaluating model fit; observations from 

different “observation groups” (basins, in this case) can be 

weighted such that each group contributes nearly equally to 

the objective function at the start of the calibration exercise. 

The objective function is the sum of the weighted squared differences between simulated potential recharge and measured 

recharge (base-flow) values in inches per year over the basin. 

The weights were assigned so that the initial combined total 

sum of squares from annual, decile, and mean annual observations were nearly equal among basins. Within each basin, the 

mean annual observations were weighted highest, followed 

by the base-flow decile observations, followed by the annual 

base-flow total observations. For the five basins for which 

deciles were not computed, the weights assigned to the annual 

observations were increased relative to the weight assigned to 

the mean annual value so that temporal variability in the base 

flow of these basins still was represented adequately during 

the calibration process.

Parameter Estimation

A total of 62 parameters were adjusted during calibration. An additional 16 fixed parameters were not adjusted 

during calibration but were necessary for computing final 

parameter values listed in the lookup table (table 4) also are 

included in table 8 (available for download at https://doi.

org/10.3133/sir20185080). Of the 62 adjustable parameters, 5 

were “global” parameters that affected recharge computations 

in every active model cell and 57 were parameters applied to 

specific combinations of HSG and land cover according to the 

lookup table (table 4).

Parameters were adjusted to improve the match between 

the estimated potential recharge simulated by the SWB 

model and the recharge determined from hydrograph separation. Previously published SWB recharge models (Feinstein 

and others, 2010; Westenbroek and others, 2010; Aurand, 

2013; McCoy and others, 2015; Smith and Westenbroek, 

2015) were the basis for the initial values of parameters 

and the ranges of possible parameter values tested during 

calibration.

The five “global” parameters that were adjusted during the calibration affected potential recharge computations 

in every active model cell. Two parameters, CFGI_LO and 

CFGI_MULT, set the minimum and maximum thresholds for 

the CFGI. The CFGI is used to vary curve numbers between 

frozen and thawed soil conditions (Molnau and Bissell, 

1983; Westenbroek and others, 2010). The growing season 

length was controlled by two parameters. The first parameter 

(GDD_STR) specified the minimum accumulation of growing degree days to trigger the start of the growing season. The 

second parameter (GDD_TMN) specified the killing frost 

temperature that ended the growing season, in degrees Celsius. The final global parameter (AMAXINF) represented the 

maximum recharge rate, in inches per day, for HSG A with 

deciduous forest land cover (table 4). This parameter was 

included in the global parameter group because the maximum 

recharge rates for all other soil and land-cover combinations 

were derived from this value (table 4). The 57 nonglobal 

parameters that were calibrated included 14 parameters for 

deriving runoff curve numbers, 16 parameters for deriving 

root-zone depths, 23 parameters for deriving values to use in 

the Horton interception algorithm, and 4 parameters to calculate the maximum recharge rate in HSG soils B, C, D, and 

organic soils (table 8).

Similar to Smith and Westenbroek (2015), predefined 

relations were used to calculate parameters from parameters 

adjusted during calibration; for example, within deciduous 

forest land cover, runoff curve numbers for HSGs A, B, C, 

and organic soils were calculated from the calibrated value 

of HSG D. By using a preprocessor (par2par; Doherty 2010), 

fig 7

10

100

1,000

10,000

100,000

Daily mean discharge, in cubic feet per second

Jan. Feb. Mar. Apr. May June July Aug. Sept. Oct. Nov. Dec.

2011

EXPLANATION

Daily mean discharge

HYSEP local minimum base flow

PART base flow

Base-flow index base flow

Figure 7. Example stream hydrograph and base flow from 

three hydrograph separation techniques, HYSEP local minimum

(Sloto and Crouse, 1996), PART (Rutledge, 1998), and base-flow 

index (Gustard and others, 1992) for U.S. Geological Survey 

streamgage 01552000, Loyalsock Creek at Loyalsockville, 

Pennsylvania (map number 12 on fig. 1).
20 Simulation of Potential Groundwater Recharge for the Glacial Aquifer System East of the Rocky Mountains, 1980–2011

only 57 nonglobal parameters were varied directly, but all the 

384 parameters in table 4 potentially could vary in successive 

model iterations according to the relations specified in the 

preprocessor. The following paragraphs describe the relations 

between parameters defined in the preprocessor.

Groups of runoff curve numbers for different land covers were optimized in the calibration process to improve the 

accuracy of the simulated potential recharge compared to 

measured values throughout the study area. Similar to Smith 

and Westenbroek (2015), relations between curve numbers 

within land-cover classes were established to ensure an 

appropriate progression of curve numbers from A through 

D. Curve number values from previously published SWB 

models (Aurand, 2013; Metropolitan Council Environmental 

Services, 2013; Smith and Westenbroek, 2015; Westenbroek 

and others, 2010) were used to develop the logistic relation (eq. 3) between curve numbers within each land-cover 

class. Additionally, tables 2.2A–D from Cronshey and others 

(1986) were referenced for guidance on appropriate curve 

number values for different land-cover types. The logistic 

equation is an exponential function that can be used to model 

relations approaching an asymptotic theoretical maximum 

value.

Runoff curve numbers are derived from an empirical 

relation, where values of curve numbers for a specific landuse type approach a maximum value as soils transition the 

spectrum from sand (HSG A) to clay (HSG D). Generally, 

curve numbers increase across this spectrum of soils and the 

incremental change in successive curve numbers diminishes as soils transition from sand to clay. The exponential 

logistic function was selected for modelling and constraining curve number groups for the SWB model because of 

the ability to generate a variety of different curves with the 

modification of only three variables. Base values for each 

of the three logistic equation parameters for each land use 

were determined by fitting the mean of previously published 

SWB models for that land use. Ranges of these parameters 

were determined such that their adjustment could accommodate most of the range observed in previously published 

SWB models. Runoff curve numbers for HSG A, B, C, and 

organic soils were derived from the HSG D runoff curve 

number for each land cover according to the following 

logistic equation:

CN

CN

e

L

L

i a b c

D

g i g

=

+ ( ) − − ( ) 1 * (3)

where

CNL i is the runoff curve number for a soil type 

(HSG A, B, C, D, or organic) for each land 

cover L;

CNLD is the runoff curve number for HSG D soil for 

land cover L;

e is the natural logarithm base;

ag is the decay coefficient for land-cover group 

g;

bi is the offset for soil type as follows: 1 for 

HSG A soil, 2 for HSG B soil and organic 

soils, 3 for HSG C soil, and 4 for HSG D 

soil; and 

cg is the x-axis offset for land-cover group g.

A subset of root-zone depths in table 4 was also calibrated. Relations specified in the preprocessor were used to 

calculate additional root-zone depths within each land cover 

that ensured a logical progression of root-zone depths over different soil types. Root-zone depths are used to determine the 

maximum soil-water capacity (fig. 2). Root-zone depths for 

land covers from previous SWB models (for example, Smith 

and Westenbroek, 2015) indicate a general decline in rootzone depth from more permeable soils (HSG A and B soils) 

to less permeable soils (HSG C and D soil). In developed, 

shrubland, grassland, pasture/hay, and wetland land cover, 

root-zone depths for HSG A, C, and D soils were derived from 

the HSG B root-zone depth. In forest and cultivated crop land 

cover, root-zone depths for HSG A, B, and D were derived 

from the HSG C root-zone depth. An example of an inverse 

quadratic equation used to calculate root-zone depth is shown 

in equation 4:

RZL g i C = + RSLP b i b RZL* B

2 (4)

where

RZLi is the root-zone depth for a soil type (HSG A, 

B, C, or D) for each land cover L, in feet;

RSLPgb is a slope coefficient for land-cover group 

g (urban, forest, grass/cropland, and 

wetland); 

RZL BC

is the root-zone depth for HSG B or C soil for 

land cover L, in feet; and

bi is the offset for soil type.

The mean hydraulic conductivities for each land-cover 

HSG combination that were calculated from the STATSGO2 

dataset were incorporated into the model calibration as follows. Within each HSG, the ratio of the mean hydraulic 

conductivity of each land-cover class to land-cover class 41 

(deciduous forest) was determined. Hydraulic conductivity 

data were normalized to deciduous forest because deciduous 

forest covered a substantial proportion of the model domain 

in all HSG types. Additionally, the ratios of the mean hydraulic conductivity of deciduous forest on HSG A soil to mean 

hydraulic conductivities of deciduous forests on HSGs B, 

C, D and organic soils were calculated. During parameter 

estimation, the global parameter, AMAXINF, represented the 

hydraulic conductivity (maximum recharge rate) of deciduous 

forest on HSG A soils. The ratios between deciduous forest 

on A soils and deciduous forest on B, C, D, and organic soils 

were represented in the calibration as BMAXINF, CMAXINF, 

DMAXINF, and EMAXINF, respectively. All these parameters 

(AMAXINF through EMAXINF) were allowed to vary during 

model calibration, but the hydraulic conductivity ratios among 

land-cover classes within each HSG were fixed.
Methods 21

Statistical Methods for Evaluating Model Fit and 

Model Error

Several techniques are available to evaluate the ability of a 

model to accurately and precisely simulate observed conditions. 

Three general techniques were applied to evaluate the SWB 

model in this report: graphical analysis, dimensionless model 

evaluation statistics, and error index model evaluation statistics. 

Graphical analyses provide a visual comparison of simulated 

and measured constituent data and a first overview of model 

performance (American Society of Civil Engineers, 1993).

Dimensionless model evaluation statistics provide a relative model evaluation assessment (Moriasi and others, 2007). 

Three dimensionless statistics are given: the Nash-Sutcliffe 

efficiency (NSE) (Nash and Sutcliffe, 1970), the probability 

plot correlation coefficient (PPCC) of the model residuals (Helsel and Hirsch, 2002), and the root mean squared error (RMSE) 

to standard deviation ratio of the observed data (RSR).

Error index model evaluation statistics quantify the 

deviation in the units of the data of interest (Moriasi and others, 2007). Four error index statistics are given: (1) the absolute mean error (AME); (2) the RMSE; (3) the mean residual, 

and (4) the mean relative error. The model evaluation statistics 

for individual basins are included in table 5. The NSE, AME, 

RMSE, RSR, and mean relative error were calculated using 

the R package HydroGOF, version 0.3–8 (Zambrano-Bigiarini, 

2014). The PPCC test was completed using the R package 

smwrStats, version 0.7.2 (Lorenz, 2015). The predicted (simulated) and observed variables in equations 5, 6, 7, and 8 have 

units of inches per year. 

The NSE is a normalized statistic that determines the 

relative magnitude of the residual variance (“noise”) compared 

to the measured data variance (“information”) (Nash and Sutcliffe, 1970). The NSE indicates how well the plot of observed 

versus simulated data fits the 1:1 line (Moriasi and others, 

2007). For the NSE, a value of 1 is considered a perfect match 

between the model simulations and observations, a value of 0 

denotes that the observed mean is as good a predictor as the 

model simulations, and negative values for NSE indicate that 

the observed mean is a better predictor than the model. The 

NSE was computed by the following equation:

NSE

O P

O O

i i

i m

= − ∑ − ( )

∑ − ( )

1

2

2 (5)

where

NSE is the Nash-Sutcliffe model efficiency 

coefficient;

n is the number of years of streamflow data at 

each streamgage;

Pi is the predicted (simulated) potential recharge 

value; 

Oi is the observed recharge value from 

hydrograph separation; and

Om is the overall mean of the observed 

hydrograph separation data.

Differences between simulated and observed values of 

recharge are termed residuals. If the model accurately represents the system, the residuals are expected to be random, 

independent, and normally distributed (Hill, 1998). The PPCC 

test evaluates whether or not the model residuals are distributed normally by computing the linear correlation coefficient 

between data and their normal quantiles. Samples from a 

normal distribution will have a correlation coefficient very 

close to 1.0. The null hypothesis in this test is the data are distributed normally, and the alternative hypothesis that the data 

are not distributed normally. The correlation coefficient (r) 

between the data and their normal quantiles is tested to see if 

the correlation coefficient is significantly less than 1.0 (Helsel 

and Hirsch, 2002). The alpha level of significance was set to 

0.05 for this test.

Residuals were calculated as the simulated potential recharge value from the glacial SWB model minus the 

observed recharge value from base flow, in inches per year. 

A negative residual indicates the simulated value is lower 

than the observed value, and a positive residual indicates the 

simulated value is higher than the observed value. The mean 

residual is simply the mean of all residuals for a given data 

aggregation, in inches per year. The mean relative error is 

the mean residual divided by the mean of the observed data 

multiplied by 100. 

The AME is a measure of the mean absolute value of 

the residuals and is calculated according to equation 6; for 

example, an AME of 1.0 in/yr for the glacial SWB potential 

recharge value means that this predicted value is on average 

1.0 in/yr different from the observed hydrograph separation 

value.

AME

n

= × ∑ − P O i i

1 (6)

where

AME is the absolute mean error;

n is the number of years of streamflow data at 

each streamgage;

Pi is the predicted (simulated) potential recharge 

value; and

Oi is the observed recharge value from 

hydrograph separation.

The RMSE indicates the amount of deviation between 

the simulated value and the measured value. The RMSE yields 

the deviation between the simulated (potential recharge value) 

and measured (hydrograph separation base-flow value) values 

approximately 67 percent of the time according to the following equation:

RMSE

n

= × ∑ − P O i i ( ) 1 2 (7)

where

RMSE is the root mean squared error;

n is the number of years of streamflow data at 

each streamgage;
22 Simulation of Potential Groundwater Recharge for the Glacial Aquifer System East of the Rocky Mountains, 1980–2011

Pi is the predicted (simulated) potential recharge 

value; and

Oi is the observed recharge value from 

hydrograph separation.

Generally, lower RMSE values indicate better model 

performance; however, for the glacial SWB model, data from 

a variety of spatial and temporal scales were compared. The 

RSR incorporates the benefits of error index statistics and 

includes a scaling/normalization factor so that the resulting 

statistic and reported values can be compared across different 

groups of data (Moriasi and others, 2007). The RSR standardizes RMSE using the standard deviation of the observed data, 

and the RSR combines an error index and additional information recommended by Legates and McCabe (1999). The RSR 

was computed according to the following equation:

RSR

O P

O O

i i

i m

= ∑ − (( ) )

∑ − (( ) )

2

2 (8)

where

RSR is the RMSE to standard deviation ratio;

Oi is the observed recharge value from 

hydrograph separation;

Pi is the predicted (simulated) potential recharge 

value; and

Om is the overall mean of the observed 

hydrograph separation data.

The AME, RMSE, and RSR were evaluated at different scales. These statistics were calculated for the composite 

model calibration and composite model verification datasets, 

including all years and all basins of each respective type. 

These statistics also were calculated for all years for each of 

the 39 individual calibration basins and each of the 38 individual verification basins.

Moriasi and others (2007) provide general performance 

ratings for several model evaluation statistics typically used 

to simulate continuous, long-term streamflow at a monthly 

time step. Ratings can be relaxed for observations with higher 

error and tightened for longer time steps. Despite the longer 

calibration time steps used for the SWB model, these ratings 

were considered appropriate for this SWB application because 

of the error inherent to the hydrograph separation method. The 

thresholds for a model performance rating of “very good” are 

as follows: RSR (less than 0.50), NSE (greater than 0.75), and 

statistics that convey bias (such as relative error, within plus or 

minus 10 percent) (Moriasi and others, 2007).

Model Verification

Verification basins (fig. 8) had characteristics appropriate 

for hydrograph separation and were used as an independent 

evaluation of the SWB model. These basins were not included 

in model calibration because computation times would have 

been too long if they were included. For the glacial SWB 

model, the same acceptance criteria were applied to the verification basins as were applied to the calibration basins.

Simulation of Potential Groundwater 

Recharge

This section contains a discussion of the performance of 

the calibrated model compared to measured base-flow data, a 

summary of the simulated potential recharge for 1980–2011 

in the glacial aquifer system, and a comparison of the glacial 

SWB model simulation to previously published recharge estimates within the glacial SWB model domain.

Model Fit and Model Error

The ability of the calibrated glacial SWB model to 

simulate observed base-flow data is described in this section. Simulated potential recharge values are compared to 

observed data from 39 calibration basins and 38 verification 

basins using a variety of techniques. The model fit and error 

are discussed first in the context of 3 pooled datasets in which 

values from all 39 basins are combined for each data type: 

mean annual recharge, deciles of annual recharge, and annual 

recharge. Model fit and error then are evaluated at the individual basin scale for the calibration basins. Finally, model fit 

and error are evaluated for mean annual recharge, deciles of 

annual recharge, and annual recharge pooled datasets of the 

38 verification basins. 

Potential recharge rates simulated by the glacial SWB 

model closely matched pooled observed base-flow data for 

the calibration basins for mean annual recharge, deciles of 

annual recharge, and annual recharge (table 9). The SWB 

model produced results that exceeded “very good” ratings 

(Moriasi and others, 2007) for the statistics NSE, RSR, and 

mean relative error (table 9). Generally, model results were 

most accurate for the mean annual recharge dataset which 

had an NSE of 0.94 and an RMSE of 1.28 in/yr (table 9). 

The NSE values indicate that each of the combined calibration datasets approximate a 1:1 relation with the observed 

data (table 9, fig. 9). The RSR statistic demonstrates that the 

error of each of the pooled calibration datasets, measured as 

RMSE, is less than 50 percent of the standard deviation of the 

observed values. The mean of the residuals for each dataset 

was small compared to the observed mean recharge rate for all 

aggregated datasets; the mean relative errors all were less than 

10 percent (table 9). Simulated potential recharge values for 

the aggregated calibration datasets were, on average, between 

0.5 and 0.7 in/yr lower than observed values (mean residuals, 

table 9). This slight negative bias also is evident in the residual 

distribution histograms in figure 10.
Simulation of Potential Groundwater Recharge 23

fig 08

Driftless area

MT

CO

KS

UT

SD

IL

CANADA

WY

NE

IA

ND MN

WI

MO

PA

IN

MI

NY

NY

VA

OH

KY

ME

WV

MI

VT

NH

MD

MA

CT

DE

NJ

RI

Lake Superior Lake Michigan

Lake

Huron

Lake Erie

Lake Ontario 75

76

74

73 72

71

62

61

5960 55 58

54 49

53

50 51

56

57

63 65 64

66 69

68

42

44

45 48

46

47

40

41

43

77

52

70 67

110° 100° 90° 80° 70°

45°

40°

Base map image is the intellectual property of Esri and is

used herein under license. Copyright © 2017 Esri and

its licensors. All rights reserved. Base modified from Esri

digital data, 1:70,000 (Esri, 2009)

Base map of states from U.S. Geological Survey 1:2,000,000 digital data

Albers Equal-Area Conic projection, standard parallels 29°30' N., and 45°30' N.

Central meridian 96°00' W., latitude of origin 23°00’ N.

EXPLANATION

0 125 250 MILES

0 125 250 KILOMETERS

Area of

enlargement Extent of glacial Soil-Water-Balance model domain

Basin used for model verification, labeled by

map number

Figure 8. The 38 basins used to verify the glacial Soil-Water-Balance model.

Table 9. Model evaluation statistics between recharge determined with the HYSEP local minimum technique and corresponding 

potential recharge estimates from the glacial Soil-Water-Balance model for the 39 calibration basins and 38 verification basins.

[NSE, Nash-Sutcliffe model efficiency coefficient; PPCC, probability plot correlation coefficient; RSR, root mean squared error to standard deviation of observations ratio; AME, absolute mean error; RMSE, root mean squared error]

Basin type Data Number of 

observations

NSE PPCC 

p-value RSR AME RMSE Mean residual

Mean 

relative 

error

Dimensionless Inches per year Percent

Model 

calibration

Mean annual recharge 39 0.94 0.08 0.25 0.96 1.28 −0.55 −7.10

Deciles of annual 

recharge, all basins 

combined1

340 0.92 <0.0005 0.29 1.14 1.61 −0.62 −8.20

Annual recharge, all basins 

combined

1,191 0.83 <0.0005 0.41 1.68 2.27 −0.54 −6.90

Model 

verification

Mean annual recharge 38 0.87 0.53 0.35 1.59 2.14 −0.34 −3.40

Deciles of annual 

recharge, all basins 

combined1

170 0.86 <0.0005 0.37 1.80 2.43 −0.74 −6.00

Annual recharge, all basins 

combined

985 0.78 <0.0005 0.46 2.24 3.03 −0.41 −4.10

1

Only includes gages with complete 32 years of record.
24 Simulation of Potential Groundwater Recharge for the Glacial Aquifer System East of the Rocky Mountains, 1980–2011

fig 9

 0

 5

10

15

20

25

 0 5 10 15 20 25

1:1 line

 0

 5

10

15

20

25

30

35

 0 5 10 15 20 25 30 35

1:1 line

 0

 5

10

15

20

25

30

35

 0 5 10 15 20 25 30 35

1:1 line

A. Mean annual potential recharge

B. Deciles of annual potential recharge

C. Annual potential recharge

Base-flow estimate from HYSEP local minimum,

in inches per year

Potential recharge estimate from glacial Soil-Water-Balance model, in inches per year

Figure 9. Relations between HYSEP local minimum base 

flow and potential recharge simulated with the glacial 

Soil-Water-Balance (SWB) model for 39 calibration basins 

during 1980–2011. A, for mean annual potential recharge; B, 

for deciles of annual potential recharge; and C, for annual 

potential recharge.

fig 10

 0

 2

 4

 6

 8

10

12

14

−3 −2 −1 0 1 2 3

 0

 20

 40

 60

 80

100

120

Number of residuals

−7 −6 −5 −4 −3 −2 −1 0 1 2 3 4 5 6

 0

100

200

300

400

500

−8 −6 −4 −2 0 2 4 6 8 10 12

Residual (simulated minus observed), in inches

A. Mean annual potential recharge

B. Deciles of annual potential recharge

C. Annual potential recharge

−

Figure 10. Histogram of residuals (simulated potential 

recharge from glacial Soil-Water-Balance model minus 

observed base flow) during 1980–2011. A, for mean 

annual potential recharge; B, for deciles of annual 

potential recharge; and C, for annual potential recharge.
Simulation of Potential Groundwater Recharge 25

The residuals between glacial SWB potential recharge 

and base flow for each of the three pooled datasets were not 

all normally distributed. Only the residuals from the mean 

annual calibration dataset were classified as normally distributed according to the PPCC test (p-value>0.05, table 9). 

The nonnormality of the residuals from the deciles of annual 

recharge resulted from a few extreme outliers; for example, if 

11 residual outliers (3 high, 8 low) from 5 basins are removed 

from the decile dataset, which contains 340 data points from 

34 basins, the PPCC test indicates the data are normally distributed. The tails of the residual distribution from the pooled 

annual data were wider than expected for a normal distribution (fig. 10C); therefore, within the pooled annual dataset, 

large-magnitude residuals were more common than would be 

expected if the distribution were normal.

Despite good model performance for the pooled data in 

which all 39 basins were considered together, the SWB model 

performance was much more variable at the individual basin 

scale. Mean relative error, AME, and RMSE provide additional information on the uncertainty of the simulated results 

for the individual calibration basins. The mean relative error 

for annual recharge comparisons varied from −62.2 percent 

to 81.4 percent (table 5). The mean relative error for deciles 

of annual recharge comparisons varied from −63.2 percent to 

110.9 percent (table 5). A total of 21 of 39 basins had a mean 

relative error of more than 10 percent for annual recharge, 

and 18 of 34 basins had a mean relative error of more than 

10 percent for deciles of annual recharge (table 5). The mean 

relative error and the AME generally varied according the 

magnitude of the observed recharge rate. The mean relative error tended to increase as the observed recharge rate 

decreased, and the AME tended to increase as the observed 

recharge rate increased (table 5). For the annual recharge 

comparisons, the AME ranged from 0.44 to 3.50 in/yr. For 

the deciles of annual recharge comparisons, the AME ranged 

from 0.12 to 3.18 in/yr. In both cases, the poorest model fit 

was in Michigan (fig. 11).

Spatially, the SWB model tended to underpredict 

recharge relative to hydrograph separation for mean annual 

recharge in the Midwest in the States of Minnesota, Iowa, 

Nebraska, Wisconsin, Illinois, Indiana, and Michigan (fig. 11). 

The residuals were not correlated strongly to the percentage 

Driftless area

MT

CO

KS

UT

SD

IL

CANADA

WY

NE

IA

ND MN

WI

MO

PA

IN

MI

NY

NY

VA

OH

KY

ME

WV

MI VT

NH

MD

MA

CT

DE

NJ

RI

Lake Superior Lake Michigan

Lake

Huron

Lake Erie

Lake Ontario

38

37

32

14

28 31

2

1

18

3

39

35

34

27

23

21

13

12

19

24

22

25

26 29

30

33

36

5

7 15

17 9

11

8 10 20

4

6

16

110° 100° 90° 80° 70°

45°

40°

Base map image is the intellectual property of Esri and is

used herein under license. Copyright © 2017 Esri and

its licensors. All rights reserved. Base modified from Esri

digital data, 1:70,000 (Esri, 2009)

Base map of states from U.S. Geological Survey 1:2,000,000 digital data

Albers Equal-Area Conic projection, standard parallels 29°30' N., and 45°30' N.

Central meridian 96°00' W., latitude of origin 23°00’ N.

EXPLANATION

0 125 250 MILES

0 125 250 KILOMETERS

Area of

enlargement Extent of glacial Soil-Water-Balance (SWB) model domain

Mean annual potential recharge residual during 1980–2011, 

in inches

−3.00 to −2.01

−2.00 to −1.01

−1.00 to 0

SWB underpredicts SWB overpredicts

0 to 1.00

1.01 to 2.00

2.01 to 3.00

Figure 11. Residuals in mean annual potential recharge between the glacial Soil-Water-Balance model and base flow 

determined with the HYSEP local minimum method for the 39 calibration basins during 1980–2011.
26 Simulation of Potential Groundwater Recharge for the Glacial Aquifer System East of the Rocky Mountains, 1980–2011

of any of the land-cover classes or HSG classes within the 

calibration basins (data not shown), indicating a variety of 

explanations for the low values of recharge simulated by the 

glacial SWB model for the Midwestern calibration basins; for 

example, two Michigan basins (map numbers 22 and 25) had 

large negative recharge residuals of −2.12 in. and −2.86 in., 

respectively (fig. 11). The basins had the highest proportion 

of HSG A soils, the highest percentage of sand in the soils 

(Falcone, 2011), and the highest proportion of streamflow as 

base flow of all the calibration basins (table 5). The glacial 

SWB model underpredicted recharge compared to base flow 

in these basins with such sandy conditions. Thought not a 

strong correlation, residuals tended to be more negative as 

the percentage of HSG A soils increased in calibration basins 

(data not shown), indicating that the glacial SWB model may 

underpredict recharge in sandy areas.

In another example, a basin in Indiana (map number 23, 

fig. 11) was 95 percent row crop land cover on HSG C 

soils, which means recharge simulations in this basin were 

extremely sensitive to adjustments in parameters representing 

row crops on HSG C soils (table 4). This basin represents an 

extreme case in which one land-cover class and HSG combination dominated the basin. The glacial SWB model underpredicted recharge in this basin.

The SWB model underpredicted recharge for another 

basin in the Upper Peninsula of Michigan (map number 19, 

fig. 11). This basin had the highest percent area (27 percent) 

of wetland land cover of all the calibration basins. Calibration 

basins were specified to have less than 25 percent wetland 

cover according to GAGES II; however, when the NLCD 

land-cover data were rescaled to 1 km, the model input data 

contained 27 percent wetland cover. As described in the 

“Model Limitations and Assumptions” section, tthe SWB 

model does not fully represent processes occurring in areas 

where the water table regularly intersects land surface.

Variability in recharge derived from hydrograph separation methods differs among the calibration basins. The 

range of mean annual recharge rates determined with the five 

hydrograph separation methods and the mean annual potential recharge rates simulated with the glacial SWB model are 

shown in figure 12. Map numbers in this figure correspond to 

figures 1 and 11 and generally increase from west to east. For 

the mean annual dataset, simulated potential recharge rates 

were within the range of base-flow recharge rates in 23 of 

39 calibration basins (fig. 12). Generally, as the mean annual 

base flow (“observed” data for model calibration) increased, 

the range in base-flow values from the five methods of hydrograph separation also increased (fig. 12). The coefficient of 

 0

 2

 4

 6

 8

10

12

14

16

18

20

22

SWB potential recharge or base flow,

 in inches per year 

 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40

Map number

EXPLANATION

Mean annual base flow determined with HYSEP local minimum method

Mean annual base flow, maximum of 5 hydrograph separation methods

Mean annual base flow, minimum of 5 hydrograph separation methods

Mean annual potential recharge determined with glacial Soil-Water-Balance (SWB) model

Figure 12. Mean annual potential recharge from the glacial Soil-Water-Balance model, mean annual HYSEP local minimum 

base flow, and range of mean annual base flow from five hydrograph separation techniques, PART, HYSEP local minimum, 

HYSEP fixed-interval, HYSEP sliding, and base-flow index during 1980–2011.
Simulation of Potential Groundwater Recharge 27

variation (standard deviation divided by the mean) of the five 

hydrograph separation methods (table 5) was fairly consistent 

in the calibration basins, averaging about 15 percent, indicating that there is a consistent relative amount of variability in 

hydrograph separation methodology. 

After the model was calibrated, simulated recharge rates 

were compared to base flow from 38 verification basins. Potential recharge rates simulated by the glacial SWB model closely 

matched pooled base-flow data from the verification basins for 

mean annual recharge, deciles of annual recharge, and annual 

recharge. The SWB model produced results that exceeded “very 

good” ratings (Moriasi and others, 2007) for NSE, RSR, and 

mean relative error statistics (table 9). As with the calibration 

dataset, the model produced the most accurate results for the 

mean annual recharge dataset which had an NSE of 0.87 and an 

RMSE of 2.14 in/yr (table 9). The NSE indicates that each of 

the combined calibration datasets approximates a 1:1 relation 

with the observed data (table 9, fig. 13). The RSR demonstrates 

that the error of each of the combined calibrated datasets, measured as RMSE, is less than 50 percent of the standard deviation 

of the observed values. The mean of the residuals for each dataset was small compared to observed mean recharge rates for all 

aggregated datasets; the mean relative errors all were less than 

10 percent (table 9). Simulated potential recharge values for 

the aggregated calibration datasets were, on average, between 

0.3 and 0.8 in/yr lower than observed values (mean residuals, 

table 9). The residuals of the mean annual recharge dataset were 

distributed normally (PPCC test p-value=0.53, table 9). A full 

discussion of the model fit and error for the verification basins is 

not included here, but summary statistics are provided in table 5 

for all the verification basins.

In conclusion, the calibrated glacial SWB model adequately reproduced the observed recharge for the calibration 

and verification basins. Most statistical measures applied for 

model evaluation indicated acceptable results. Some parts of 

the model domain had lower error rates than others. Generally, 

deviations between simulated and observed recharge were largest in the upper Midwest. Model evaluation statistics indicated 

that the model most accurately simulated the mean annual 

recharge. Variability in recharge derived from hydrograph separation methods differed among the calibration basins.

1980–2011 Potential Recharge to the Glacial 

Aquifer System

The calibrated glacial SWB model was used to simulate 

potential groundwater recharge rates for the glacial aquifer 

system for 1980–2011. The year 1980 was run first to establish 

initial conditions, and then the model was started again at 1980 

and run for the period. The glacial SWB model encompasses a 

broad range of climatic conditions, from semiarid in the west 

to humid in the east. The broad range of climatic conditions 

is reflected in the potential recharge rates. Most cells in the 

western part of the model had an average potential recharge 

rate of less than 3 in/yr, whereas most cells in the eastern part 

of the model had potential recharge rates of more than 20 in/

yr (fig. 14). The glacial SWB model simulated a mean annual 

potential recharge rate of 0.6 in/yr for the westernmost calibration basin (map number 1, fig. 1) and a mean annual potential 

recharge rate of 19.3 in/yr for one of the easternmost basins 

 0

 5

10

15

20

25

Potential recharge estimate from Soil-Water-Balance model, 

in inches per year

 0 5 10 15 20 25

Base-flow estimate from HYSEP local minimum,

 in inches per year 

1:1 line

A

 0

 2

 4

 6

 8

10

12

Number of residuals

−5 0 5

Potential recharge residual (simulated minus observed), 

in inches

B

Figure 13. Mean annual HYSEP local minimum base flow and mean annual potential recharge simulated with the 

glacial Soil-Water-Balance model for 38 verification basins. A, showing relation between them; and B, showing 

residuals. 
28 Simulation of Potential Groundwater Recharge for the Glacial Aquifer System East of the Rocky Mountains, 1980–2011

(map number 38, fig. 1). Nearly 20 percent of model cells had 

an average potential recharge rate of less than 1 in/yr (fig. 15).

The calibrated glacial SWB model provides insight into 

variability of annual potential recharge rates. Annual potential 

recharge grids for the domain for 1980–2011 are available 

with the model archive (Trost, 2018). As an alternate method 

of visualizing variability, a cumulative distribution function 

was calculated for each model cell for 1980–2011. Maps of 

the 10 percent potential recharge quantile and 90 percent 

potential recharge quantile for each model cell are shown in 

figure 16 (note: this figure shows model output and should 

not be confused with the decile base-flow calibration targets). 

The 10 percent potential recharge quantile represents dry, low 

potential recharge conditions, specifically the probability that 

annual potential recharge at that location will be that value 

or lower 10 percent of the time. Conversely, the 90 percent 

potential recharge quantile represents wet, high potential 

recharge conditions, specifically the probability that annual 

potential recharge at that location will be that value or higher 

10 percent of the time. At the 10 percent potential recharge 

quantile, the mean potential recharge rate of the model domain 

is 3.0 in/yr, and the median potential recharge rate is 1.5 in/yr. 

A total of 43 percent of model cells (or nearly half of the active 

model area) have less than 1.0 in/yr of potential recharge, and 

77 percent of model cells have less than 5.0 in/yr of potential 

recharge (fig. 16A). In contrast, in the 90 percent potential 

recharge quantile, the mean potential recharge rate is 9.0 in/yr, 

and the median potential recharge rate is 8.0 in/yr. Only 11 percent of model cells have less than 1.0 in/yr of potential recharge, 

and only 37 percent of model cells have less than 5.0 in/yr of 

potential recharge (fig. 16B).

The calibrated SWB model outputs demonstrate the interacting effects of land use, soil type, and precipitation on potential 

recharge (table 10, figs. 17, 18). Forest (25 percent of area) and 

agriculture (48 percent of area) are the two dominant land-cover 

types within the model area (fig. 4; tables 1,2,3). Approximately 

46 percent of the potential recharge in the active model domain 

was in forested areas (fig. 17A, deciduous, evergreen, and mixed 

forest), and about 30 percent of the potential recharge was in 

agricultural areas (fig. 17A, pasture/hay and cultivated crops). 

Approximately 39 percent of all the potential recharge in the glacial aquifer system travels through highly disturbed land-cover 

types, including developed and agricultural areas (figs. 4, 17A), 

which are known to cause water-quality impairments.

fig 14

Driftless area

MT

CO

KS

UT

SD

IL

CANADA

WY

NE

IA

ND MN

WI

MO

PA

IN

MI

NY

NY

VA

OH

KY

ME

WV

MI VT

NH

MD

MA

CT

DE

NJ

RI

Lake Superior Lake Michigan

Lake

Huron

Lake Erie

Lake Ontario

110° 100° 90° 80° 70°

45°

40°

Base map image is the intellectual property of Esri and is

used herein under license. Copyright © 2017 Esri and

its licensors. All rights reserved. Base modified from Esri

digital data, 1:70,000 (Esri, 2009)

Base map of states from U.S. Geological Survey 1:2,000,000 digital data

Albers Equal-Area Conic projection, standard parallels 29°30' N., and 45°30' N.

Central meridian 96°00' W., latitude of origin 23°00’ N.

EXPLANATION

0 125 250 MILES

0 125 250 KILOMETERS

Area of

enlargement Glacial Soil-Water-Balance model mean annual 

potential recharge, in inches per year

0 to 3.00

3.01 to 6.00

6.01 to 9.00

9.01 to 12.00

12.01 to 15.00

15.01 to 18.00

18.01 to 21.00

21.01 to 24.00

24.01 to 27.00

27.01 to 43.00

Figure 14. Mean annual potential recharge from 1980 to 2011 simulated with the glacial Soil-Water-Balance model.
Simulation of Potential Groundwater Recharge 29

Most of the land area west of Indiana and Michigan consists of HSG B, and most of the land area from Indiana to the 

east consists of HSG C (fig. 5). The HSG C soils have higher 

curve numbers than HSG B soils (table 4), which means, 

under identical hydrologic conditions, HSG C soils will generate more runoff and less potential recharge than HSG B soils. 

However, because HSG C soils are more common in areas of 

higher precipitation (figs. 3 and 5), the mean potential recharge 

through HSG C soils was greater than the mean potential 

recharge through HSG B soils (table 10). The HSG B soils 

covered much more of the model domain (42.4 percent) than 

HSG C soils (29.6 percent); therefore, potential recharge was 

slightly higher in HSG B soils than HSG C soils (tables 1,2,3; 

figs. 5, 17B). Sandy areas belonging to HSG A were a small 

proportion of the model area (7.4 percent, tables 1,2,3) but 

contributed about 15 percent of the total potential recharge 

(fig. 17B).

Total precipitation and the relative amount of precipitation that becomes recharge vary from west to east (fig. 18). In 

North Dakota, mean precipitation generally is less than 20 in/yr 

(fig. 3), and potential recharge generally is less than 4 percent of precipitation (fig. 18). Conversely, in Maine, mean 

precipitation generally is above 40 in/yr (fig. 3), and potential 

recharge generally is at least 18 percent of precipitation.

fig 15

 0

 5

10

15

20

Percent of active domain cells at 1-kilometer resolution

 0 5 10 15 20 25 30 35 40 45

Mean annual potential recharge, in inches per year

Figure 15. Histogram (by percent) of mean annual potential 

recharge from the glacial Soil-Water-Balance model during 1980 

to 2011 for the glacial aquifer system.

Table 10. Mean annual potential recharge rates simulated by the glacial Soil-Water-Balance model, by land-cover class and 

hydrologic soil group, for the period 1980–2011.

[The glacial domain area-weighted mean by land-cover class and hydrologic soil group is an area-weighted mean potential recharge estimate for the entire 

glacial model domain for active cells; NA, not applicable]

Land-cover 

class Description

Mean annual potential recharge (inches per year)

Hydrologic 

soil group 

A

Hydrologic 

soil group 

B

Hydrologic 

soil group 

C

Hydrologic 

soil group 

D

Organic 

soil group

Glacial domain 

area-weighted 

mean, by landcover class

21 Developed, open space 14.46 7.66 8.45 4.58 7.67 8.55

22 Developed, low intensity 16.89 9.12 8.14 5.64 8.76 9.67

23 Developed, medium intensity 18.48 9.65 11.01 6.94 9.51 11.36

24 Developed, high intensity 16.10 7.35 8.13 8.10 5.62 9.14

31 Barren land (rock/sand/clay) 14.87 8.94 10.82 3.60 8.63 9.84

41 Deciduous forest 10.45 8.28 11.04 4.80 6.35 9.69

42 Evergreen forest 10.79 8.32 12.87 8.17 7.00 11.25

43 Mixed forest 12.66 9.18 13.17 10.77 6.52 12.38

52 Shrubland 11.89 8.49 9.05 2.81 6.42 8.29

71 Grasslands 6.34 1.52 0.44 0.28 7.38 1.27

81 Pasture/hay 8.51 3.88 2.59 0.26 4.41 3.36

82 Cultivated crops 8.72 3.96 1.73 1.90 6.25 3.42

90 Woody wetlands 10.42 8.05 10.43 7.65 5.31 8.49

95 Herbaceous wetlands 8.33 4.31 5.82 5.34 5.00 5.31

NA Glacial domain area-weighted mean, 

by hydrologic soil group

10.49 4.83 6.64 2.58 5.67 NA
30 Simulation of Potential Groundwater Recharge for the Glacial Aquifer System East of the Rocky Mountains, 1980–2011

fig 16

Driftless area

Driftless area

MT

CO

KS

UT

SD

IL

CANADA

WY

NE

IA

ND MN

WI

MO

PA

IN

MI

NY

NY

VA

OH

KY

ME

WV

MI VT

NH

MD

MA

CT

DE

NJ

RI

Lake Superior Lake Michigan

Lake

Huron

Lake Erie

Lake Ontario

MT

CO

KS

UT

SD

IL

CANADA

WY

NE

IA

ND MN

WI

MO

PA

IN

MI

NY

NY

VA

OH

KY

ME

WV

MI VT

NH

MD

MA

CT

DE

NJ

RI

Lake Superior Lake Michigan

Lake

Huron

Lake Erie

Lake Ontario

110° 100° 90° 80° 70°

45°

40°

110° 100° 90° 80° 70°

45°

40°

Base map image is the intellectual property of Esri and is

used herein under license. Copyright © 2017 Esri and

its licensors. All rights reserved. Base modified from Esri

digital data, 1:70,000 (Esri, 2009)

Base map of states from U.S. Geological Survey 1:2,000,000 digital data

Albers Equal-Area Conic projection, standard parallels 29°30' N., and 45°30' N.

Central meridian 96°00' W., latitude of origin 23°00’ N.

0 125 250 MILES

0 125 250 KILOMETERS

Area of

enlargement

A. 10th percentile annual potential recharge

Base map image is the intellectual property of Esri and is

used herein under license. Copyright © 2017 Esri and

its licensors. All rights reserved. Base modified from Esri

digital data, 1:70,000 (Esri, 2009)

Base map of states from U.S. Geological Survey 1:2,000,000 digital data

Albers Equal-Area Conic projection, standard parallels 29°30' N., and 45°30' N.

Central meridian 96°00' W., latitude of origin 23°00’ N.

0 125 250 MILES

0 125 250 KILOMETERS

B. 90th percentile annual potential recharge

EXPLANATION

Glacial Soil-Water-Balance model annual 

potential recharge, in inches per year

0 to 3.00

3.01 to 6.00

6.01 to 9.00

9.01 to 12.00

12.01 to 15.00

15.01 to 18.00

18.01 to 21.00

21.01 to 24.00

24.01 to 27.00

27.01 to 43.00

Figure 16. Results from the glacial Soil-Water-Balance model. A, 10th percentile annual potential recharge for each grid 

cell from 1980 to 2011; and B, 90th percentile annual potential recharge for each grid cell from 1980 to 2011.
Simulation of Potential Groundwater Recharge 31

fig 17

 0

 2

 4

 6

 8

10

12

14

16

18

20

22

24

26

28

30

32

34

36

38

40

Percent of potential recharge in glacial Soil-Water-Balance model

Developed, open space

Developed, low intensity

Developed, medium intensity

Developed, high intensity

Barren land (rock/sand/clay)

Deciduous forest

Evergreen forest

Mixed forest

Shrubland

Grasslands

Pasture/hay

Cultivated crops

Woody wetlands

Herbaceous wetlands

Land-cover class

 0

 5

10

15

20

25

30

35

40

45

Percent of potential recharge in 

glacial Soil-Water-Balance model

A B C D Organic

Hydrologic soil group

A

B

Figure 17. Percent of 1980–2011 potential 

recharge to the glacial aquifer system. A, by 

land-cover class from 2006 National Land Cover 

Database; and B, by hydrologic soil group (Fry 

and others, 2011; Natural Resources Conservation 

Service, 2015).
32 Simulation of Potential Groundwater Recharge for the Glacial Aquifer System East of the Rocky Mountains, 1980–2011

The calibrated glacial SWB model also demonstrated 

changes in annual potential recharge through time in the 

eastern, central, and west-central regions of the glacial aquifer 

system (figs. 1 and 19), as delineated for the National WaterQuality Assessment. Regional climatic events are apparent 

in the simulated potential recharge data. Annual potential 

recharge rates in all three regions generally have been increasing since 2000 (fig. 19). During the years 1987–89, much of 

the United States was under a severe drought (Trenberth and 

Branstator, 1992), which is apparent as a series of very low 

potential recharge years in the west-central and central regions 

(fig. 19). The lowest potential recharge for the eastern region 

happened in 2001, a year in which many of the eastern States 

had well below average precipitation (National Oceanic and 

Atmospheric Administration, 2002).

Comparison to Previous Recharge Estimates

The glacial SWB model was compared to several previously published recharge estimates within the glacial SWB 

model domain: a 1951–80 mean annual recharge rate for the 

glacial model domain (Wolock, 2003b), the Williston Basin 

SWB model (Aurand, 2013), the Minnesota SWB model 

(Smith and Westenbroek, 2015), and the Appalachian Plateaus 

SWB model (McCoy and others, 2015). The coincident model 

boundaries are shown in figure 20, and the distribution of cellby-cell differences is shown in figure 21. The glacial SWB 

model simulated mean annual recharge rates generally higher 

than the 1951–80 mean annual BFI study (Wolock, 2003b), 

the Williston Basin SWB model (Aurand, 2013), and the 

Appalachian Plateaus SWB model (McCoy and others, 2015). 

The glacial SWB model simulated mean annual recharge rates 

generally lower than the Minnesota SWB model (Smith and 

Westenbroek, 2015). Possible explanations for these differences are discussed in the following paragraphs.

Wolock (2003b) estimated the mean annual natural 

groundwater recharge in the conterminous United States using 

a 1-km resolution (grid) dataset for 1951–80 (figs. 20, 22A). 

This method provides a single long-term average recharge 

smoothed over large areas and does not take explicitly into 

account local variations in soil hydrologic characteristics and 

land cover (fig. 22A). In contrast, the SWB model accounts for 

local variability and provides recharge estimates with greater 

spatial and temporal resolution (figs. 16, 22B).

fig 18

Driftless area

MT

CO

KS

UT

SD

IL

CANADA

WY

NE

IA

ND MN

WI

MO

PA

IN

MI

NY

NY

VA

OH

KY

ME

WV

MI VT

NH

MD

MA

CT

DE

NJ

RI

Lake Superior Lake Michigan

Lake

Huron

Lake Erie

Lake Ontario

110° 100° 90° 80° 70°

45°

40°

Base map image is the intellectual property of Esri and is

used herein under license. Copyright © 2017 Esri and

its licensors. All rights reserved. Base modified from Esri

digital data, 1:70,000 (Esri, 2009)

Base map of states from U.S. Geological Survey 1:2,000,000 digital data

Albers Equal-Area Conic projection, standard parallels 29°30' N., and 45°30' N.

Central meridian 96°00' W., latitude of origin 23°00’ N.

0 125 250 MILES

0 125 250 KILOMETERS

Area of

enlargement

EXPLANATION

Mean annual potential recharge as a percent of 

mean annual gross precipitation during 1980–2011

0 to 4.00

4.01 to 11.00

11.01 to 18.00

18.01 to 24.00

24.01 to 29.00

29.01 to 34.00

34.01 to 39.00

39.01 to 44.00

44.01 to 50.00

50.01 to 74.00

Figure 18. Mean annual potential recharge as a percent of mean annual gross precipitation (Thornton and others, 2014) 

based on results from the glacial Soil-Water-Balance model.
Simulation of Potential Groundwater Recharge 33

The 1951–80 mean annual recharge for the model domain 

according to the method developed by Wolock (2003b) 

is 4.6 in/yr, whereas the 1980–2011 mean annual potential 

recharge for the glacial SWB model is 25 percent higher at 

5.8 in/yr. The differences between the two models are shown 

in figures 21 and 23. Because these two datasets cover different periods, the differences between the models could represent 

differences in the methodology, differences in climate, or some 

combination thereof. The overall positive shift between the 

glacial SWB model and the Wolock (2003b) method likely 

results from differing hydrograph separation techniques. The 

BFI hydrograph separation method was used for the Wolock 

recharge dataset, whereas the HYSEP local minimum method 

was used for the glacial SWB model. For all the verification and 

calibration basins in table 5, the HYSEP local minimum method 

was, on average, 27 percent higher than the BFI method.

The glacial SWB model predicted lower potential 

recharge than the Wolock (2003b) study in some areas 

(figs. 22, 23); for example, the glacial SWB model predicted 

lower recharge than the BFI method for 1980–2011 in calibration basins in northern Wisconsin and Michigan. This finding 

indicates that differences in potential recharge between the 

glacial SWB model and the Wolock (2003b) study in this 

area are not attributable solely to the differences in hydrograph separation methods (figs. 11, 12). Climatic differences 

between the two periods, 1951–80 and 1980–2011, were 

not evaluated in this report. Further evaluation of climatic 

differences could help to determine factors that contribute to 

observed differences.

The glacial SWB model simulated mean annual potential recharge rates that were, on average, about 21 percent 

higher than the Williston Basin SWB model (figs. 20, 21, 24) 

(Aurand, 2013; Long and others, 2014). The 1981–2011 mean 

annual potential recharge for the Williston Basin SWB model 

was 0.42 in/yr, whereas the 1981–2011 mean annual potential 

recharge for the glacial SWB model was 0.51 in/yr for the 

same model extent. The differences in mean annual potential 

recharge between the Williston Basin SWB model and the 

glacial SWB model are shown in figure 21. More specifically, 

84 percent of the coincident model cells had mean annual 

potential recharge values within 0.5 in. of each other, and 

97 percent of model cells had a difference of less than 1 in. At 

the basin scale, the mean annual potential recharge for USGS 

streamgage 05120500 (map number 1 on fig. 1) was 0.5 in/yr 

using the Williston Basin model and 0.6 in/yr using the glacial 

SWB model (note: the glacial SWB potential recharge rate 

number differs from table 5 because the spatial and temporal extents were constrained to those of the Williston SWB 

model). Recharge determined with the HYSEP local minimum 

base-flow method over this same period was 0.4 in/yr.

The differences between the Williston Basin SWB and 

glacial SWB model outputs reflect differences in model input 

data and calibration methods. Both models used the Daymet 

dataset (Thornton and others, 2014) and the NLCD (Fry and 

others, 2011), but the models used different HSG data. Model 

cells with the largest differences generally were in the eastern part of the coincident model domains in North and South 

Dakota (fig. 24). The Williston Basin model used geologic 

datasets (for example, Fullerton and others, 2003) to assign 

HSGs to model cells, whereas STATSGO2 was used for the 

glacial SWB model. The geologic dataset classified sediments 

using a much deeper sediment profile based on depositional 

processes than the STATSGO2 dataset, which only describes 

materials in the upper 2 m of the sediment profile.

fig 19

 0

 5

10

15

20

Annual potential recharge simulated by 

glacial Soil-Water-Balance model, in inches 

1980 1985 1990 1995 2000 2005 2010 2015

Year

Eastern region

Central region

West-central region

 

EXPLANATION

[Region extents are in figure 1]

Figure 19. Annual potential recharge from 1980 to 2011 simulated with the glacial Soil-Water-Balance model within three 

regions of the glacial aquifer system extent.
34 Simulation of Potential Groundwater Recharge for the Glacial Aquifer System East of the Rocky Mountains, 1980–2011

The highest rates of recharge in the Willison Basin SWB 

model were in narrow bands of glaciofluvial deposits in the 

eastern part of the coincident model domain (fig. 24B, fig. 10 

in Aurand, 2013). The highest rates of recharge in the glacial 

SWB model are more widely distributed in the eastern part of 

the coincident model domain (fig. 24A). The Williston Basin 

SWB model was calibrated manually by comparing model 

output to point estimates of recharge at specific wells calculated by the water-table fluctuation method and the chloride 

mass balance method (Aurand, 2013). In contrast, the glacial 

SWB model was calibrated to base flow using an automated 

process.

The glacial SWB model simulated mean annual potential recharge rates that were, on average, about 34 percent 

lower than the Minnesota SWB model (figs. 20, 21, 25) 

(Smith and Westenbroek, 2015). The 1996–2010 mean 

annual potential recharge for the Minnesota SWB model 

was 4.9 in/yr, whereas the 1996–2010 mean annual potential recharge for the glacial SWB model was 3.3 in/yr for 

the same model extent. At the basin scale, the mean annual 

potential recharge for USGS streamgage 5317200 (map number 7 on fig. 1) was 4.1 in/yr using the Minnesota SWB 

model and 3.0 in/yr using the glacial SWB model (note: the 

glacial SWB potential recharge rate number differs from 

TX

MT

AZ

ID

NM

CO

KS

UT

SD

IL

WY

NE

IA

MN

ND

OK

WI

MO

AL GA

AR

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NC

IN

MI

MS

NY

TN

VA

OH

KY

SC

ME

WV

MI VT

NH

MD

MA

CT

DE

NY

NJ

RI

Lake Superior Lake Michigan

Lake

Huron

Lake Erie

Lake Ontario

Driftless area

50°

45°

40°

35°

110° 100° 90° 80° 70°

0 150 300 MILES

0 150 300 KILOMETERS

Base map image is the intellectual property of Esri and is

used herein under license. Copyright © 2017 Esri and

its licensors. All rights reserved. Base modified from Esri

digital data, 1:70,000 (Esri, 2009)

Base map of states from U.S. Geological Survey 1:2,000,000 digital data

Albers Equal-Area Conic projection, standard parallels 29°30' N., and 45°30' N.

Central meridian 96°00' W., latitude of origin 23°00’ N.

Area of

enlargement

EXPLANATION

Williston Basin Soil-Water-Balance (SWB) model 

active domain boundary (Long and others, 2014; 

Aurand, 2013)

Minnesota SWB model active domain boundary 

(Smith and Westenbroek, 2015)

Appalachian Plateaus SWB model active domain boundary 

(McCoy and others, 2015)

Extent of this report's glacial SWB model domain comparison 

with Wolock (2003b)

CANADA

g 20

Figure 20. Boundaries of the glacial Soil-Water-Balance (SWB) model and boundaries of previously published recharge 

models (Wolock, 2003b; Long and others, 2014; Aurand, 2013; McCoy and others, 2015; Smith and Westenbroek, 2015).
Simulation of Potential Groundwater Recharge 35

table 5 because the spatial and temporal extents were constrained to those of the Minnesota SWB model). Recharge 

determined with the HYSEP local minimum base-flow 

method over this same period was 4.3 in/yr.

The overall spatial pattern in recharge is similar between 

the Minnesota SWB model and the glacial SWB model 

(fig. 25). Recharge generally increased from west to east, 

and the highest potential recharge was in the east-central and 

northeastern parts of the State. The Minnesota SWB model 

and the glacial SWB model used Daymet data and the NLCD. 

The Minnesota SWB model was calibrated by adjusting 

parameter values to minimize error between SWB potential 

recharge and estimates of base flow. The Minnesota SWB 

model used SSURGO data (rather than STATSGO2) to assign 

available water capacities and HSGs to model cells. Both 

models assumed that cells with dual HSGs were drained; for 

example, A/D soils were classified as A soils.

The combination of different hydrograph separation 

methods and differences in basin selection criteria likely 

led to the generally lower potential recharge estimates from 

the glacial SWB model compared to the Minnesota SWB 

model. The Minnesota SWB model was calibrated using an 

average of three hydrograph separation techniques: PART, 

HYSEP fixed-interval, and HYSEP sliding methods, whereas 

the glacial SWB model was calibrated to base flow from the 

HYSEP local minimum method. The HYSEP local minimum 

method produced base-flow estimates that were, on average, 

16 percent lower than the average of the 3 methods used in the 

Minnesota SWB model for the 39 calibration basins (table 5); 

furthermore, the basins used for the Minnesota SWB model 

calibration were not selected based on the same strict criteria 

for minimizing base-flow error as was used for the glacial 

SWB model. Only 6 of the 35 calibration basins were classified as GAGES II reference basins in the Minnesota SWB 

model, and several streams had regulated flows or were heavily tile drained (Falcone, 2011). Regulated flows and heavy tile 

drainage are known to cause overestimation of base flow from 

hydrograph separation (Schilling and Helmers, 2008; Sloto 

and Crouse, 1996).

Potential recharge to the Appalachian Plateaus during 

1980–2011 was simulated using an SWB model by McCoy 

and others (2015) (fig. 20). The glacial SWB model simulated 

mean annual potential recharge rates that were, on average, 

about 17 percent higher (1.2 in/yr) than the Appalachian 

Plateaus SWB model within overlapping model extents. A 

side by side comparison of the mean annual potential recharge 

simulated with the glacial SWB model in this report and the 

mean annual potential recharge simulated with the Appalachian Plateaus SWB model is shown in figure 26. The Appalachian Plateaus model used SSURGO data to assign HSGs and 

available water capacity to model cells, whereas the glacial 

SWB model used STATSGO2 data for this task; furthermore, 

the Appalachian Plateaus SWB model assigned dual HSG 

soils (A/D, B/D, and C/D) to HSG D, whereas the glacial 

SWB model classified these soils to their drained condition, A, 

B, or C.

fig 21

1951−80 base-flow index 

 (Wolock, 2003b)

Williston Basin SWB model 

 (Aurand, 2013)

Minnesota SWB model 

 (Smith and 

Westenbroek, 2015)

Appalachian Plateaus SWB model 

 (McCoy and others, 2015)

Source of previous recharge estimate

−12

−10

 −8

 −6

 −4

 −2

 0

 2

 4

 6

 8

 10

 12

Difference between glacial Soil-Water-Balance (SWB) model

and previous recharge estimate, in inches per year

1,676,287 189,179 201,273 86,265

32 Number of active, overlapping

model cells

Interquartile

range

95th percentile

75th percentile

50th percentile

 (median)

25th percentile

5th percentile

EXPLANATION

Glacial SWB greater than previous model

Glacial SWB less than previous model

Figure 21. Cell-by-cell differences between mean annual potential recharge from the glacial Soil-Water-Balance (SWB) model and four 

previously published recharge estimates.
36 Simulation of Potential Groundwater Recharge for the Glacial Aquifer System East of the Rocky Mountains, 1980–2011

fig 22

Driftless area

Driftless area

MT

CO

KS

UT

SD

IL

CANADA

WY

NE

IA

ND MN

WI

MO

PA

IN

MI

NY

NY

VA

OH

KY

ME

WV

MI VT

NH

MD

MA

CT

DE

NJ

RI

Lake Superior Lake Michigan

Lake

Huron

Lake Erie

Lake Ontario

MT

CO

KS

UT

SD

IL

CANADA

WY

NE

IA

ND MN

WI

MO

PA

IN

MI

NY

NY

VA

OH

KY

ME

WV

MI VT

NH

MD

MA

CT

DE

NJ

RI

Lake Superior Lake Michigan

Lake

Huron

Lake Erie

Lake Ontario

110° 100° 90° 80° 70°

45°

40°

110° 100° 90° 80° 70°

45°

40°

Base map image is the intellectual property of Esri and is

used herein under license. Copyright © 2017 Esri and

its licensors. All rights reserved. Base modified from Esri

digital data, 1:70,000 (Esri, 2009)

Base map of states from U.S. Geological Survey 1:2,000,000 digital data

Albers Equal-Area Conic projection, standard parallels 29°30' N., and 45°30' N.

Central meridian 96°00' W., latitude of origin 23°00’ N.

0 125 250 MILES

0 125 250 KILOMETERS

Area of

enlargement

A. Mean annual recharge for 1951–80 (Wolock, 2003b) 

Base map image is the intellectual property of Esri and is

used herein under license. Copyright © 2017 Esri and

its licensors. All rights reserved. Base modified from Esri

digital data, 1:70,000 (Esri, 2009)

Base map of states from U.S. Geological Survey 1:2,000,000 digital data

Albers Equal-Area Conic projection, standard parallels 29°30' N., and 45°30' N.

Central meridian 96°00' W., latitude of origin 23°00’ N.

0 125 250 MILES

0 125 250 KILOMETERS

B. Mean annual potential recharge for 1980–2011 from the glacial Soil-Water-Balance model (fig. 14) 

EXPLANATION

Mean annual potential recharge, 

in inches per year

0 to 3.00

3.01 to 6.00

6.01 to 9.00

9.01 to 12.00

12.01 to 15.00

15.01 to 18.00

18.01 to 21.00

21.01 to 24.00

24.01 to 27.00

27.01 to 43.00

Wolock, 2003b 

Figure 22. The glacial aquifer system. A, mean annual recharge for 1951–80 according to Wolock (2003b); and B, the 

mean annual potential recharge for 1980–2011 simulated with the glacial Soil-Water-Balance (SWB) model.
Simulation of Potential Groundwater Recharge 37

Regional patterns in figure 26 indicate that the glacial 

SWB model tends to simulate higher potential recharge in forested land cover and simulate lower potential recharge on agricultural crop and pasture lands compared to the Appalachian 

Plateaus SWB model (figs. 4, 26). The combination of HSG 

classification and parameterization for forest soils may explain 

why the glacial SWB model produced potential recharge estimates that are so much larger than potential recharge estimates 

produced by the Appalachian Plateaus SWB model in the 

forested areas of northwestern Pennsylvania and southwestern 

New York (fig. 26). In the glacial SWB model, this area was 

classified primarily as HSG C, whereas in the Appalachian 

Plateaus model, this region was classified primarily as HSG D 

(fig. 13 in McCoy and others, 2015).

The Appalachian Plateaus SWB model potential recharge 

estimates were at least 5 in below recharge estimated with 

the PART hydrograph separation technique for northwestern Pennsylvania and southwestern New York (McCoy and 

other, 2015), indicating that the Appalachian Plateaus SWB 

model underpredicted recharge there. At the basin scale 

in this area, the mean annual potential recharge for USGS 

streamgage 04213000 (map number 30, fig. 1) was 

6.0 in/yr using the Appalachian Plateaus SWB model and 

8.8 in/yr using the glacial SWB model. Recharge was determined to be 8.7 in/yr using the HYSEP local minimum baseflow method and 9.1 in/yr using the PART method (table 5).

In summary, model comparisons demonstrate that shifts 

in the overall distribution of potential recharge between models can be explained by methods used to generate base-flow 

calibration target datasets. The glacial SWB model potential 

recharge generally was lower than the Minnesota SWB model, 

likely because of differing basin selection criteria and hydrograph separation techniques. The glacial SWB model generally was higher than the Wolock (2003b) recharge estimates, 

again likely driven by the different hydrograph separation 

methods used for each model. Spatial patterns in potential 

recharge simulated by SWB models are strongly dependent on 

the data and assumptions used to assign model cells to HSGs. 

fig 23

Driftless area

MT

CO

KS

UT

SD

IL

CANADA

WY

NE

IA

ND MN

WI

MO

PA

IN

MI

NY

NY

VA

OH

KY

ME

WV

MI VT

NH

MD

MA

CT

DE

NJ

RI

Lake Superior Lake Michigan

Lake

Huron

Lake Erie

Lake Ontario

110° 100° 90° 80° 70°

45°

40°

Base map image is the intellectual property of Esri and is

used herein under license. Copyright © 2017 Esri and

its licensors. All rights reserved. Base modified from Esri

digital data, 1:70,000 (Esri, 2009)

Base map of states from U.S. Geological Survey 1:2,000,000 digital data

Albers Equal-Area Conic projection, standard parallels 29°30' N., and 45°30' N.

Central meridian 96°00' W., latitude of origin 23°00’ N.

0 125 250 MILES

0 125 250 KILOMETERS

Area of

enlargement

EXPLANATION

Difference in mean annual potential recharge between 1951–80 (Wolock, 2003b) and 

1980–2011 glacial Soil-Water-Balance model, in inches per year

<−10.00

−9.99 to −8.00

−7.99 to −6.00

−5.99 to −4.00

−3.99 to −2.00

−1.99 to 0

0.01 to 2.00

2.01 to 4.00

4.01 to 6.00

6.01 to 8.00

8.01 to 10.00

>10.00

Recharge from glacial Soil-Water-Balance

 model less than recharge from 

Wolock (2003b)

Recharge from glacial Soil-Water-Balance 

model greater than recharge from 

Wolock (2003b)

Figure 23. The difference between the 1951–80 mean annual recharge determined by Wolock (2003b) and the 1980–

2011 mean annual potential recharge simulated with the glacial Soil-Water-Balance model.
38 Simulation of Potential Groundwater Recharge for the Glacial Aquifer System East of the Rocky Mountains, 1980–2011

fig 24

MT ND

SD

WY

110° 100°

45°

CANADA

0 40 80 MILES

0 40 80 KILOMETERS

MT ND

SD

WY

110° 100°

45°

A. Glacial Soil-Water-Balance model

B. Williston Basin Soil-Water-Balance model (Aurand, 2013)

CANADA

Base map image is the intellectual property of Esri and is

used herein under license. Copyright © 2017 Esri and

its licensors. All rights reserved. Base modified from Esri

digital data, 1:70,000 (Esri, 2009)

Base map of states from U.S. Geological Survey 1:2,000,000 digital data

Albers Equal-Area Conic projection, standard parallels 29°30' N., and 45°30' N.

Central meridian 96°00' W., latitude of origin 23°00’ N.

Area of

enlargement

EXPLANATION

Mean annual potential recharge

during 1981–2011, in inches 

per year

0 to 0.50

0.51 to 1.00

1.01 to 1.50

1.51 to 2.00

2.01 to 2.50

2.51 to 3.00

3.01 to a maximum of 10.14

Figure 24. 1981–2011 mean annual potential recharge in the coincident model domains. A, of the glacial Soil-Water-Balance (SWB) 

model; and B, of the Williston Basin SWB model (Aurand, 2013).
Simulation of Potential Groundwater Recharge 39

fig 25

MN

WI

SD

IA

ND

MI

Lake

Superior

Lake

Superior

90°

45°

MN

WI

SD

ND

MI

IA

CANADA

CANADA

90°

45°

A. Glacial Soil-Water-Balance model

B. Minnesota Soil-Water-Balance model 

(Smith and Westenbroek, 2015)

Area of

enlargement

0 60 120 MILES

0 60 120 KILOMETERS

Base map image is the intellectual property of Esri and is

used herein under license. Copyright © 2017 Esri and

its licensors. All rights reserved. Base modified from Esri

digital data, 1:70,000 (Esri, 2009)

Base map of states from U.S. Geological Survey 1:2,000,000 digital data

Albers Equal-Area Conic projection, standard parallels 29°30' N., and 45°30' N.

Central meridian 96°00' W., latitude of origin 23°00’ N.

Mean annual potential recharge during 

1996–2010, in inches per year

0 to 2.00

2.01 to 4.00

4.01 to 6.00

6.01 to 8.00

8.01 to 10.00

10.01 to 12.00

12.01 to 14.00

14.01 to 16.00

16.01 to a maximum of 18.14

EXPLANATION

Figure 25. 1996–2010 mean annual potential recharge in the coincident model domains. A, of the glacial Soil-Water-Balance 

(SWB) model; and B, of the Minnesota SWB model (Smith and Westenbroek, 2015).
40 Simulation of Potential Groundwater Recharge for the Glacial Aquifer System East of the Rocky Mountains, 1980–2011

fig 26

PA

OH

MI

VA

WV

NY

IN

KY

DE

NJ

NJ

DC MD

Lake

Erie

CANADA

80°

40°

Base map image is the intellectual property of Esri and is

used herein under license. Copyright © 2017 Esri and

its licensors. All rights reserved. Base modified from Esri

digital data, 1:70,000 (Esri, 2009)

PA

OH

MI

VA

WV

NY

IN

KY

DE

NJ

NJ

DC MD

Lake

Erie

CANADA

80°

40°

B. Appalachian Plateaus Soil-Water-Balance model 

(McCoy and others, 2015)

Area of

enlargement

Base map of states from U.S. Geological Survey 1:2,000,000 digital data

Albers Equal-Area Conic projection, standard parallels 29°30' N., and 45°30' N.

Central meridian 96°00' W., latitude of origin 23°00’ N.

0 100 200 MILES

0 100 200 KILOMETERS

Mean annual potential recharge during 

1980–2011, in inches per year

0 to 3.00

3.01 to 6.00

6.01 to 9.00

9.01 to 12.00

12.01 to 15.00

15.01 to 18.00

18.01 to 21.00

21.01 to 24.00

24.01 to 27.00

27.01 to 30.00

30.01 to a maximum of 93.41

EXPLANATION

A. Glacial Soil-Water-Balance model

Figure 26. 1980–2011 mean annual potential recharge in the coincident model domains. A, of the glacial Soil-Water-Balance (SWB) 

model; and B, of the Appalachian Plateaus SWB model (McCoy and others, 2015).
Sensitivity Analysis 41

Sensitivity Analysis

Results of a sensitivity analysis of parameters used for 

the glacial SWB model are provided. Also included is a discussion of parameter sensitivities from previous SWB model 

applications.

Glacial Soil-Water-Balance Model

Model parameter sensitivities were evaluated by running the calibrated SWB model for all 39 calibration basins in 

the sensan utility of the PEST parameter-estimation software 

(Doherty, 2010). Of the 62 parameters that were adjusted during calibration, 55 were examined in the sensitivity analysis. 

The seven parameters that were excluded (cnmu_lu52, xstp_

mu2x, rzmu_lu2x, rzmu_lu52, rzmu_lu95, inmg_lu2x, and 

inma_lu52; table 8) were all multipliers that dealt with small 

areas of the model. Some of the 55 examined parameters were 

evaluated independently and others were grouped, resulting 

in 16 parameter groups that were increased by 10 percent and 

decreased by 10 percent. In rare cases, a 10 percent change 

would put a parameter out of bounds (for example, a curve 

number greater than 100). In these cases, the parameter was 

adjusted only to the maximum allowable value. The resulting 

change in the objective function (model error) for each parameter group perturbation was recorded. The percent change 

from the calibrated objective function is shown in table 11.

Negative values in table 11 indicate lower error compared to the calibrated model. In most cases, the reductions 

in error are minor; however, there is a large reduction in error 

(−3.47%) when the root-zone depth parameters (RZB/RZC) 

are reduced by 10 percent (table 11). This observed reduction 

in error indicates that future automated calibration approaches 

tuned for mathematically underdetermined problems (such as 

SWB models) could improve on the current calibration; for 

example, singular value decomposition would address issues 

of parameter insensitivity and correlation (Doherty and Hunt, 

2010).

The most sensitive parameters were those that dealt 

with the size of the soil-water reservoir (RZB/RZC) and the 

maximum rate at which water in the soil reservoir can become 

potential recharge on a daily basis (AMAXINF, BMAXINM, 

CMAXINM, and DMAXINM). The parameter AMAXINF 

affected every model cell (except for open water) because 

AMAXINF defined the maximum recharge rates for HSG A 

soils and was used for calculating the maximum recharge rates 

in all other HSGs. The parameter groups BMAXINM through 

EMAXINM (organic soils) only affected model cells within 

their respective HSG. In most cases, increases or decreases in 

maximum recharge rates resulted in substantial increases in 

model error, the notable exception being DMAXINM, where 

the model error was reduced when the maximum recharge 

rates on D soils were increased by 10 percent.

Potential recharge simulations also were sensitive to 

changes in the CND group of parameters. These parameters 

were used in calculations to define the runoff curve numbers 

for all model cells. The curve numbers partition water between 

runoff and infiltration; higher curve numbers increase runoff 

and decrease infiltration. The 10 percent decrease in curve 

numbers resulted in a substantial increase in model error, 

whereas a 10 percent increase in curve numbers caused a 

slight decrease in model error (table 11).

Comparison of Parameter Sensitivities

The recharge estimates from each of four SWB models 

(Lake Michigan Basin SWB model [Feinstein and others, 

2010; Westenbroek and others, 2010], Minnesota SWB model 

[Smith and Westenbroek, 2015], High Plains aquifer SWB 

model [Stanton and others, 2011], and Appalachian Plateaus 

SWB model [McCoy and others, 2015]) had somewhat different parameter sensitivities. Sensitive parameters are those 

that, when changed, cause a large change in potential recharge 

estimates relative to the change in parameter value. One likely 

reason for recharge estimates having different parameter sensitivities is that the optimal parameter values for each model 

were in different parts of the parameter sensitivity spectrum. 

Though the calibration procedures for each of these three 

models were different and slightly different versions of the 

SWB model codes were used, parameter sensitivity results 

provide insight about the dependence of SWB model applications on certain types of information. 

A parameter sensitivity analysis was completed for the 

Lake Michigan Basin SWB model in which curve number, 

root-zone depth, interception, and maximum recharge rate 

parameters from the lookup table and global parameters from 

the model control file were evaluated. The five most sensitive 

parameters were curve number controlling runoff volumes 

from the most abundant land-cover and HSG combinations. 

Of the 34 most sensitive parameters listed in the report, 15 

were curve numbers, 8 were “global” parameters that affected 

recharge calculations in every single model cell, 5 were rootzone depths, 3 were maximum recharge rates, and 3 were 

plant-canopy interceptions. The sensitive global parameters 

controlled ET rates, growing season length, the CFGI, and 

rainfall (Westenbroek and others, 2010).

Smith and Westenbroek (2015) evaluated the sensitivity of curve numbers and root-zone depth parameters in the 

lookup table and climate data inputs including daily precipitation and daily maximum and minimum air temperatures. The 

Minnesota SWB model results were extremely sensitive to 

adjustments in precipitation and temperature input data. Of 

the curve number and root-zone depth parameters, the curve 

number for the dominant land-cover class (cultivated crops) 

was the single most sensitive parameter (Smith and Westenbroek, 2015).

In the Appalachian Plateaus SWB model, a sensitivity 

analysis was completed for curve number, root-zone depth, 

and canopy interception parameters on soils in HSGs B and 

C. In this SWB model application, simulated recharge was 
42 Simulation of Potential Groundwater Recharge for the Glacial Aquifer System East of the Rocky Mountains, 1980–2011

Table 11. Sensitivity of model error (objective function) to changes in parameters of the calibrated glacial Soil-Water-Balance model.

Parameter 

or parameter 

prefix

Parameter description Extent of model affected 

by parameter

Parameter 

general 

description

−10 percent 

change in 

parameter 

value

+10 percent 

change in 

parameter 

value

Percent change,

 in objective function

AMAXINF Maximum recharge rate in inches per day for 

hydrologic soil group A with deciduous forest 

land cover (41).

All model cells except 

open water.

Maximum 

recharge 

rate.

3.25 1.26

BMAXINM Multiplier to calculate the maximum recharge rate 

in inches per day for hydrologic soil group B.

Only cells with hydrologic soil group B.3.23 1.26

CMAXINM Multiplier to calculate the maximum recharge rate 

in inches per day for hydrologic soil group C.

Only cells with hydrologic soil group C.1.24 1.68

DMAXINM Multiplier to calculate the maximum recharge rate 

in inches per day for hydrologic soil group D.

Only cells with hydrologic soil group D.0.46 −0.35

EMAXINM Multiplier to calculate the maximum recharge rate 

in inches per day for organic soils.

Only cells with organic 

soils.

0.00 0.00

CND All 7 CND1 parameters (table 8) were varied 

up or down 10 percent simulaneously. CND_ 

parameters represent the curve number for soils 

of hydrologic soil group D. 

All model cells except 

open water.

Curve 

number.

1.44 −0.36

XSTP All 6 XSTP1 parameters (table 8) were varied 

up or down 10 percent simultaneously. XSTP 

parameters represent the x-axis offset for computing curve numbers with a logistic equation 

for hydrologic soil groups A, B, C, and organic 

soils. 

All model cells except 

open water.

−0.06 0.08

CFGI_LO Lower limit of the continuous frozen ground index 

(CFGI).

All model cells except 

open water.

Continuous 

frozen 

ground 

index.

0.07 −0.04

CFGI_MULT Multiplier used to calculate the upper limit of the 

continuous frozen ground index from the lower 

limit.

All model cells except 

open water.

0.03 −0.02

GDD_STR Minimum accumulation of growing degree days to 

trigger the start of the growing season.

All model cells except 

open water.

Start and end 

of growing 

season.

0.00 0.00

GDD_TMN Growing season killing frost in degrees Fahrenheit.All model cells except 

open water.

0.15 −0.07

INT_Ga All 7 INT_Ga1 parameters (table 8) were varied 

up or down 10 percent simulaneously. INT_Ga 

parameters represent the intercept in equation 2 

for computing daily interception by vegetation 

during the growing season.

All model cells except 

open water.

Daily 

interception of 

precipitation by 

vegetation.

−0.09 0.09

INT_Gb All 7 INT_Gb1 parameters (table 8) were varied 

up or down 10 percent simulaneously. INT_Gb 

parameters represent the slope in equation 2 for 

computing daily interception by vegetation during the growing season.

All model cells except 

open water.

0.21 −0.06

INT_MDb All 7 INT_MDb1 parameters (table 8) were varied 

up or down 10 percent simulaneously. INT_

MDb parameters represent the slope in equation 

2 for computing daily interception by vegetation 

during the dormant season.

All model cells except 

open water.

−0.08 0.09
Sensitivity Analysis 43

insensitive to changes in curve number parameters and more 

sensitive to changes in root-zone depth and plant-canopy 

interception parameters. Global parameters and maximum 

daily recharge values were not evaluated in this SWB model 

application (McCoy and others, 2015).

Stanton and others (2011) used an SWB model linked to 

a groundwater-flow model to estimate recharge to the High 

Plains aquifer; a sensitivity analysis for curve number parameters, root-zone depth parameters, and precipitation input 

was not completed. In this case, simulated recharge was most 

sensitive to changes in precipitation input, somewhat less sensitive to changes in root-zone depth, and insensitive to changes 

in curve number (Stanton and others, 2011).

Simulated recharge rates from three previous SWB 

models were evaluated for sensitivity to climatological input 

data or parameters that modified the input data (Westenbroek 

and others, 2010; Stanton and others, 2011; Smith and Westenbroek, 2015). Simulated recharge rates in all three cases 

were very sensitive to changes in input data, illustrating the 

importance of using reliable climatological data for any SWB 

model. The Daymet data (Thornton and others, 2014) used for 

the glacial SWB model is just one interpolation of climatic 

data that is easy to use with the SWB model. Local precipitation records may differ substantially from the Daymet data, 

especially if the area of interest is not near a precipitation gage 

used in the Daymet algorithms.

Simulated recharge rates from four previous SWB models 

were evaluated for sensitivity to curve number parameters and 

root-zone depth parameters (Westenbroek and others, 2010; 

Stanton and others, 2011; McCoy and others, 2015; Smith 

and Westenbroek, 2015). The relative sensitivity of simulated 

recharge to curve number parameters and root-zone depth 

parameters is mixed among the four SWB models, which 

means that separate model applications depend differentially 

on different types of parameters. In the Lake Michigan SWB 

model, potential recharge was more sensitive to curve number 

parameters than to root-zone depth parameters (Westenbroek 

and others, 2010). In the High Plains aquifer SWB model 

and the Appalachian Plateaus SWB model, potential recharge 

was more sensitive to root-zone depths than curve numbers 

(Stanton and others, 2011; McCoy and others, 2015). In the 

Minnesota SWB model, potential recharge was nearly equally 

sensitive to curve number and root-zone depth parameters 

(Smith and Westenbroek, 2015), though the single most sensitive parameter was a curve number.

The increased sensitivity of potential recharge to 

changes in root-zone depth compared to changes in curve 

number observed for the glacial SWB model was more similar to observed responses for the Appalachian Plateaus and 

High Plains aquifer SWB models. Most previous sensitivity 

analyses did not consider maximum recharge rates; results 

from the glacial SWB model indicate that this parameter set 

also is important to evaluate. The comprehensive evaluation of parameters in the glacial SWB model also indicates 

that model results were not particularly sensitive to changes 

in global parameters that affect the length of the growing season nor to parameters controlling interception by 

vegetation.

Table 11. Sensitivity of model error (objective function) to changes in parameters of the calibrated glacial Soil-Water-Balance 

model.—Continued

Parameter 

or parameter 

prefix

Parameter description Extent of model affected 

by parameter

Parameter 

general 

description

−10 percent 

change in 

parameter 

value

+10 percent 

change in 

parameter 

value

Percent change,

 in objective function

RSLP All 6 RSLP1

 parameters (table 8) were varied up 

or down 10 percent simultaneously. RSLP parameters represent the slope in slope coefficient 

for computing root-zone depths in hydrologic 

soil groups A, B, C, D, and organic soils.

All model cells except 

open water, hydrologic 

soil group B soils in 

land-cover classes 21, 

22, 23, 24, 31, 52, 71, 

81, 90, and 95, and hydrologic group C soils 

in land-cover classes 

41, 42, 43, 81, and 821

. 

Root-zone 

depths.

−0.11 0.10

RZB/RZC All 7 RZB1

 and RZC1 parameters (table 8) were 

varied up or down 10 percent simultaneously. 

RZB and RZC parameters represent the rootzone depth on hydrologic soil group B or C 

soils. 

All model cells except 

open water.

−3.47 4.85

1

Land-cover classes defined in tables 1, 2, and 3.
44 Simulation of Potential Groundwater Recharge for the Glacial Aquifer System East of the Rocky Mountains, 1980–2011

Summary

An understanding of the spatial and temporal extent of 

groundwater recharge is critical for many types of hydrologic 

assessments involving water quality, contaminant transport, 

ecosystem health, and sustainable use of groundwater. This 

report documents a Soil-Water-Balance (SWB) model used to 

simulate potential groundwater recharge to the glacial aquifer 

system. The glacial SWB model uses high resolution meteorological, land-cover, and soil hydrology datasets that are 

nationally consistent and publicly available, including Daymet 

meteorological data, the 2001, 2006, and 2011 National Land 

Cover Databases and STATSGO2 soils data as primary data 

inputs.

The SWB model was calibrated and used to simulate 

annual potential groundwater recharge rates for calendar years 

1980–2011 using at a 1-kilometer resolution for the glacial 

aquifer system east of the Rocky Mountains. The SWB model 

computed daily potential groundwater recharge as precipitation in excess of interception, runoff, evapotranspiration, and 

soil-water storage capacity. Daily potential recharge values 

within each year of the simulation were summed to produce 

annual potential recharge rates. Potential recharge as described 

in this report is water that infiltrates vertically below the plant 

rooting zone and is assumed to reach the water table.

The glacial SWB model used parameters grouped by 

land-cover class, hydrologic soil group, or both in a lookup 

table for calculating the various water balance components. 

Parameter values for interception, runoff curve numbers, maximum recharge rates, and root-zone depths in the lookup table 

were adjusted during calibration. The SWB model calibration 

assumed that the area contributing to groundwater discharge 

equaled the surface watershed and was calibrated to stream 

base flows from 39 watersheds throughout the model domain 

that had hydrologic conditions appropriate for hydrograph 

separation. The calibration basins were minimally disturbed 

“reference” watersheds with high-quality, continuous streamflow records that spanned most or all of 1980–2011. Base 

flows were calculated from daily streamflow records with the 

HYSEP local minimum hydrograph separation method. Three 

base-flow data aggregations were used for model calibration: 

annual total base flow for each year of complete flow data, 

annual total base-flow duration deciles (10 deciles per basin, 

10 percent through 100 percent), and the mean of all annual 

total base flows (mean annual) during 1980–2011. The glacial 

SWB model was verified with 38 basins that met the criteria 

for being a calibration basin.

The calibrated glacial SWB model adequately reproduced the observed recharge for the calibration and verification basins. The glacial SWB model reproduced the mean 

annual base-flow calibration targets well; the Nash-Sutcliffe 

efficiency (NSE) was 0.94 and the root mean squared error 

(RMSE) was 1.28 inches per year (in/yr). The calibrated 

model also simulated mean annual potential recharge rates 

that agreed well with mean annual base-flow in 38 verification 

basins; the NSE was 0.87 and the RMSE was 2.14 in/yr. Most 

statistical measures applied for model evaluation indicated 

acceptable results. Some parts of the model domain had lower 

error rates than others. Generally, deviations between simulated and observed recharge were largest in the upper Midwest. Model evaluation statistics indicate that the model most 

accurately simulated the mean annual recharge. Variability in 

recharge derived from hydrograph separation methods differs 

among the calibration basins.

The glacial SWB model provides insight into the spatial 

and temporal variability in potential recharge across the glacial 

aquifer system. About 20 percent of the active model area 

had an average potential recharge rate of less than 1 in/yr. A 

substantial part of the recharge water (39 percent) entering the 

glacial aquifer system travels through developed (urbanized) 

and agricultural landscapes, which are known to cause waterquality impairments. Approximately 46 percent of the potential recharge in the active model domain was in forested areas, 

and about 30 percent of the potential recharge was in agricultural areas. In North Dakota, mean precipitation generally 

is less than 20 in/yr (fig. 3), and potential recharge generally 

is less than 4 percent of precipitation. Conversely, in Maine, 

mean precipitation generally is above 40 in/yr, and potential recharge generally is at least 18 percent of precipitation. 

Regional climatic events such as the 1988 to 1989 drought are 

apparent in the potential recharge time series. Annual potential 

recharge rates in all three regions of the glacial aquifer system 

generally increased between 2001 and 2011. 

A comparison of the potential recharge from the glacial SWB model to previous broad-scale recharge estimates 

reveals several important considerations for future SWB 

modeling applications. Shifts in the overall distribution of 

potential recharge between separate models can be explained 

by methods used to generate base-flow calibration target datasets. Spatial patterns in potential recharge simulated by SWB 

models are strongly dependent on the data and assumptions 

used to assign model cells to hydrologic soil groups.

A sensitivity analysis indicated that the most sensitive 

parameters for the glacial SWB model dealt with the size 

of the soil-water reservoir and the maximum rate at which 

water in the soil reservoir can become potential recharge on a 

daily basis. Curve number parameters, which partition water 

between runoff and infiltration, also were sensitive. The comprehensive evaluation of parameters in the glacial SWB model 

indicated that model results were not particularly sensitive 

to changes in global parameters that affect the length of the 

growing season or to parameters controlling interception by 

vegetation. A review of several SWB models used to estimate 

groundwater recharge (and not surface runoff) revealed that 

model results have been most sensitive to input climatic data, 

followed by curve number and root-zone depth parameters.
References Cited 45

Acknowledgments

The authors thank the Groundwater Resources Program 

of the U.S. Geological Survey (USGS) for supporting this 

modeling effort. The authors also thank Erik Smith and Kurt 

McCoy of the USGS for their technical reviews of the manuscript, which greatly improved the quality of this report.

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Appendix. Model Archive

The model archive is available at Trost (2018). The archive contains all files necessary to run 

the glacial Soil-Water-Balance (SWB) model described in this report. The model archive also 

contains model outputs, including the 1980–2011 annual recharge grids and the mean annual 

recharge grid. The binary output files also are available so users can extract recharge data at 

daily or monthly intervals with the SWBstats utility. 
For more information about this publication, contact

Director, USGS Upper Midwest Water Science Center 

2280 Woodale Drive

Mounds View, MN 55112

(763) 783–3100

For additional information visit https://mn.water.usgs.gov

Publishing support provided by the 

Rolla Publishing Service Center

Trost and others—Simulation of Potential Groundwater Recharge for the Glacial Aquifer System East of the Rocky Mountains, 1980–2011—SIR 2018–5080

ISSN 2328-0328 (online)

https://doi.org/10.3133/sir20185080