U.S. Department of the Interior

U.S. Geological Survey

Scientific Investigations Report 2010–5100

National Water-Quality Assessment Program

Relations That Affect the Probability and Prediction 

of Nitrate Concentration in Private Wells in the 

Glacial Aquifer System in the United States
Front Cover. Most private wells are located in rural areas with surrounding agricultural 

land use. The photograph was taken by Kelly Warner and Troy Daugherty on 

June 28, 2010, near Eureka, IL.
Relations That Affect the Probability and 

Prediction of Nitrate Concentration in 

Private Wells in the Glacial Aquifer System 

in the United States

By Kelly L. Warner and Terri L. Arnold

National Water-Quality Assessment Program

Scientific Investigations Report 2010–5100

U.S. Department of the Interior

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

KEN SALAZAR, Secretary

U.S. Geological Survey

Marcia K. McNutt, Director

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

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Suggested citation:

Warner, K.L., and Arnold, T.L., 2010, Relations that affect the probability and prediction of nitrate concentration in 

private wells in the glacial aquifer system in the United States: U.S. Geological Survey Scientific Investigations Report 

2010–5100, 55 p. plus appendixes.

ISBN 978–1–4113–2951–5
iii

Foreword

The U.S. Geological Survey (USGS) is committed to providing the Nation with reliable scientific 

information that helps to enhance and protect the overall quality of life and that facilitates 

effective management of water, biological, energy, and mineral resources (http://www.usgs.

gov/). Information on the Nation’s water resources is critical to ensuring long-term availability 

of water that is safe for drinking and recreation and is suitable for industry, irrigation, and fish 

and wildlife. Population growth and increasing demands for water make the availability of that 

water, measured in terms of quantity and quality, even more essential to the long-term sustainability of our communities and ecosystems.

The USGS implemented the National Water-Quality Assessment (NAWQA) Program in 1991 

to support national, regional, State, and local information needs and decisions related to 

water-quality management and policy (http://water.usgs.gov/nawqa). The NAWQA Program 

is designed to answer: What is the quality of our Nation’s streams and groundwater? How are 

conditions changing over time? How do natural features and human activities affect the quality 

of streams and groundwater, and where are those effects most pronounced? By combining 

information on water chemistry, physical characteristics, stream habitat, and aquatic life, the 

NAWQA Program aims to provide science-based insights for current and emerging water issues 

and priorities. From 1991 to 2001, the NAWQA Program completed interdisciplinary assessments and established a baseline understanding of water-quality conditions in 51 of the Nation’s 

river basins and aquifers, referred to as Study Units (http://water.usgs.gov/nawqa/studies/

study_units.html). 

In the second decade of the Program (2001–2012), a major focus is on regional assessments 

of water-quality conditions and trends. These regional assessments are based on major river 

basins and principal aquifers, which encompass larger regions of the country than the Study 

Units. Regional assessments extend the findings in the Study Units by filling critical gaps in 

characterizing the quality of surface water and groundwater, and by determining water-quality 

status and trends at sites that have been consistently monitored for more than a decade. In 

addition, the regional assessments continue to build an understanding of how natural features 

and human activities affect water quality. Many of the regional assessments employ modeling 

and other scientific tools, developed on the basis of data collected at individual sites, to help 

extend knowledge of water quality to unmonitored, yet comparable areas within the regions. 

The models thereby enhance the value of our existing data and our understanding of the hydrologic system. In addition, the models are useful in evaluating various resource-management 

scenarios and in predicting how our actions, such as reducing or managing nonpoint and point 

sources of contamination, land conversion, and altering flow and (or) pumping regimes, are likely 

to affect water conditions within a region.

Other activities planned during the second decade include continuing national syntheses of 

information on pesticides, volatile organic compounds (VOCs), nutrients, trace elements, and 

aquatic ecology; and continuing national topical studies on the fate of agricultural chemicals, 

effects of urbanization on stream ecosystems, bioaccumulation of mercury in stream ecosystems, effects of nutrient enrichment on stream ecosystems, and transport of contaminants to 

public-supply wells.
iv

The USGS aims to disseminate credible, timely, and relevant science information to address 

practical and effective water-resource management and strategies that protect and restore 

water quality. We hope this NAWQA publication will provide you with insights and information 

to meet your needs, and will foster increased citizen awareness and involvement in the protection and restoration of our Nation’s waters. 

The USGS recognizes that a national assessment by a single program cannot address all waterresource issues of interest. External coordination at all levels is critical for cost-effective management, regulation, and conservation of our Nation’s water resources. The NAWQA Program, 

therefore, depends on advice and information from other agencies—Federal, State, regional, 

interstate, Tribal, and local—as well as nongovernmental organizations, industry, academia, and 

other stakeholder groups. Your assistance and suggestions are greatly appreciated.

Matthew C. Larsen

Associate Director for Water
v

Contents

Foreword ........................................................................................................................................................iii

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

1.0 Introduction and Hydrostratigraphy of the Glacial Aquifer System ............................................2

2.0 Methods ..............................................................................................................................................10

3.0 Background Nitrate Concentration.................................................................................................14

4.0 Comparison of Nitrate Concentration in the Glacial Aquifer System and 

Other Principal Aquifers................................................................................................................16

5.0 Nitrate Sources ..................................................................................................................................20

6.0 Nitrate Transport ...............................................................................................................................22

6.1 Nitrate and Groundwater Age.................................................................................................22

6.2 Nitrate Concentrations and Depth .........................................................................................26

7.0 Nitrate Concentrations in Private, Public, and Monitoring Wells ................................................28

7.1 Nitrate Concentrations in Water from Private Supplies .......................................................28

7.2 Comparison of Nitrate Concentrations in Water from Private, Public, 

and Monitoring Wells ...........................................................................................................32

8.0 Statistical Models of Nitrate Concentration..................................................................................36

9.0 Probability of Nitrate Occurrence Above Threshold Concentrations ......................................40

10.0 Prediction of Mean Nitrate Concentrations in Networks of Wells ..........................................44

11.0 Conclusions.......................................................................................................................................48

References Cited..........................................................................................................................................51

Glossary.........................................................................................................................................................55

Appendixes

1. Variable names, descriptions, units, and sources used in the models described 

in this report............................................................................................................................57

2. Results of a comparison of nitrate measured in private and monitoring wells 

in the glacial aquifer system to the nationwide model of probability of nitrate 

concentration greater than 4 milligrams per liter as nitrogen based on all 

monitoring wells (Nolan and others, 2002). (Data are from a spatial overlay of 

wells in the glacial aquifer system with a model of probability of nitrate 

contamination of groundwater (Nolan and others, 2002)................................................58

3. Results of using a logistic regression model with six categories to calculate 

the probability of nitrate concentration greater than 4 milligrams per liter 

as nitrogen...............................................................................................................................59

4. Results of recalibrating a logistic regression model (Nolan and others, 2002): 

(A) Coefficients resulting from recalibrating the regression equation from Nolan 

and others (2002) and results of test to determine whether estimated coefficients 

of new variables are significant predictors; and (B) observed and predicted 

probabilities using the 6 categories of predicted probabilities in Nolan and 

others (2002) and the standard 10 categories ............................................................ 60–61

5. Logistic regression parameter estimates and odds ratio estimates for each 

of 10 logistic regression models ................................................................................... 62–65
vi

6. Scatterplots showing predicted and observed probabilities of nitrate 

concentration greater than the specified concentration in private wells in 

the glacial aquifer system for all 10 logistic regression models developed 

for this study............................................................................................................................66

7. Spearman rank correlations of nitrate concentration with selected variables, 

probability significance (p), and number of samples ................................................ 67–70

8. Variables selected in each of three iterations of the development of the 

10 logistic regression models developed for this study ........................................... 71–72

9. Linear regression to predict network mean nitrate concentration using the 

same variables used in the logistic regression models. The variables were 

used because they were used in the logistic regression models. 

The significance level of variables was not a consideration for this model................73

Figures

1–1. Agriculture is the major land use overlying the glacial aquifer system..........................2

1–2. The highest rate (1992–2001) of nitrogen fertilizer application is over the 

Midwestern states which are part of the glacial aquifer system....................................3

1–3. Despite the gaps in the spatial distribution of wells across the glacial 

aquifer system in the United States, all four glacial framework areas are 

represented in the wells sampled as part of the U.S. Geological Survey 

National Water-Quality Assessment program. Framework areas are based 

on similarity of physiography and source of aquifer material. The wells in 

Nebraska are included in this study because they are located in areas of 

reworked glacial deposits. .....................................................................................................5

1–4. Wells in buried bedrock valleys are less susceptible to nitrate contamination 

because of the thick overlying layer of till which is mostly fine-grained 

material, whereas wells in valley-fill deposits and in sheets, layers, and 

lenses of sand are more likely to have a connection to the land surface......................6

1–5. Fine-grained sediment is present at land surface across most of the glacial 

aquifer system, but the texture of sediment at land surface is not indicative 

of the presence or absence of an underlying aquifer........................................................8

1–6. There are numerous soil types overlying the glacial aquifer system. 

Alfisols are soils that overlie approximately 25 percent of the glacial aquifer 

system, mostly in the Midwest. Alfisols are typically formed in humid areas 

under deciduous forests and mixed vegetation..................................................................9

3–1. The graph shows the deviation of the mean and median nitrate concentrations 

from background in groundwater samples from reference wells selected to 

represent areas minimally affected by human activities. Mean and median 

nitrate concentrations in water from reference wells in Nebraska were 

greater than the background nitrate concentration used in this report 

(1 milligram per liter as nitrogen); however, mean and median nitrate 

concentrations in water from reference wells in other parts of the glacial 

aquifer system generally were less than the background concentration....................15

4–1. Locations of U.S. Geological Survey National Water-Quality Assessment 

(NAWQA) program regional assessments in principal aquifers in the 

United States. The glacial aquifer system covers about 953,000 square miles and 

parts of 26 States. The two highest concentrations of nitrate in private 

wells measured during the NAWQA program (1995–2005) were in water from the 

glacial aquifer system ...........................................................................................................16
vii

4–2. Although the glacial aquifer system had a larger range of nitrate plus 

nitrate concentration compared to other principal aquifers, the median 

concentration of nitrate was relatively low. Concentration of nitrate plus 

nitrite as nitrogen measured in water from private and public-supply wells 

in selected principal aquifers and other aquifers of different lithologies 

sampled as part of the U.S. Geological Survey National Water-Quality 

Assessment (NAWQA) Program (1995–2005) are shown................................................17

4–3. The glacial aquifer system receives a higher nitrogen load than most 

other aquifers, but the capacity for nitrogen attenuation also is greater ....................19

5–1. Median nitrate concentration was lowest in water from wells in areas 

where agriculture is the predominant land use within a 1,640 foot (500 meter) 

radius of the well, but nitrate concentrations in these areas also were the 

most variable. Median nitrate concentration was highest in areas where 

urban land use is predominant within a 1,640 foot radius of the well ...........................21

6.1–1. Groundwater flow to large- and small-diameter wells may represent 

recharge that was a mixture of groundwater of different ages 

(Sandra Eberts, U.S. Geological Survey, written commun., 2007). The largediameter wells generally are shallow and contain “young” (recharged 

after 1955) water.....................................................................................................................22

6.1–2. All samples in which nitrate concentrations were greater than 4 milligrams 

per liter as nitrogen were from private wells containing only groundwater 

that was recharged after 1955 (“young”)...........................................................................24

6.1–3. Groundwater recharged after 1955 (“young”) consisted of a higher 

percentage of oxic water than groundwater recharged before 1955 (“old”). 

Nitrate is mobile under oxic conditions..............................................................................25

6.1–4. (A) The glacial aquifer system in the United States has been divided into 

four framework areas on the basis of physiography and source of aquifer 

material. (B) Private wells in these areas contained a mixture of old and 

young groundwater. The wells in the West area contained mostly “young” 

(recently recharged) groundwater......................................................................................25

6.2–1. The difference in mean and median well depth shows the large variability 

of well depths associated with nitrate concentrations less than 6 milligrams 

per liter. The samples with concentrations greater than 6 milligrams per liter 

were from relatively shallow wells .....................................................................................27

6.2–2. Mean and median nitrate concentrations were highest in water from 

private wells less than 20 feet deep, but most private wells were more 

than 60 feet deep....................................................................................................................27

7.1–1. Agriculture was the predominant land use within 1,640 feet of the private 

wells sampled .........................................................................................................................28

7.1–2. Nitrate concentrations in most of the private wells sampled in this study 

were less than the background nitrate concentration of 1 milligram per liter 

as nitrogen (<1 mg/L as N). The background nitrate concentration of <1 mg/L 

as N is less than one-tenth of the U.S Environmental Protection Agency 

Maximum Contaminant Level (MCL) of 10 mg/L as N; such concentrations 

are not likely a human-health concern. In this study, samples with nitrate 

concentrations between 1 and 10 mg/L as N are considered to approach 

concentrations of potential human-health concern, and nitrate concentrations 

greater than the MCL of 10 mg/L as N are of potential human-health concern..........29

7.1–3. The Central framework area of the glacial aquifer system had a high nitrate 

application rate but a low median concentration of nitrate in groundwater 

from private wells. The Central and West-central areas had a large variability 

in nitrate concentrations.......................................................................................................29
viii

7.1–4. Most private wells sampled in this study were constructed during 1990–99 

and the water from these wells sampled by NAWQA had the highest mean 

nitrate concentration compared to water from other private wells..............................30

7.2–1. Most private and monitoring wells sampled were located in agricultural 

settings, whereas most public-supply wells sampled were in forested or 

mixed-land-use areas. The public-supply wells sampled by NAWQA were 

mostly in the northeastern United States, where forest and mixed land use 

are common ............................................................................................................................32

7.2–2. Private and monitoring wells in the glacial aquifer system sampled as part 

of the U.S. Geological Survey National Water-Quality Assessment program 

had similar geographic distribution. More public-supply wells were sampled 

in the East framework area than in other framework areas...........................................34

7.2–3. Survival curves were plotted to examine the difference in measured nitrate 

concentrations among private, public-supply, and monitoring wells in the 

glacial aquifer system. Nitrate concentrations exceeded 4 milligrams per liter 

as nitrogen in about 12 percent of private wells, 0 percent of public-supply 

wells, and 36 percent of monitoring wells .........................................................................35

8–1. Scatterplots showing the accuracy of the nationwide nitrate model (Nolan 

and others, 2002) for predicting the probability of nitrate concentration 

greater than 4 milligrams per liter as nitrogen in private wells in the glacial 

aquifer system ........................................................................................................................38

9–1. The interaction between open-interval diameter and depth to top of open 

interval indicates that the relation between nitrate concentration and openinterval diameter in private wells in the glacial aquifer system changes at 

depths of about 71 feet below land surface ......................................................................41

9–2. Fewer variables are needed to predict higher nitrate concentrations 

(7–10 milligrams per liter as nitrogen) than lower nitrate concentrations 

(1–6 milligrams per liter as nitrogen); at lower concentrations, most variables 

represent natural conditions and well-construction characteristics ...........................42

9–3. Probability of occurrence of nitrate concentrations greater than 1 milligram 

per liter in private wells in the glacial aquifer system. This map was developed 

by setting the depth to top of open interval and open-interval length to the 

mean of the values for these variables in all private wells in the glacial 

aquifer system (91 and 8 feet, respectively)......................................................................43

10–1. The relation between mean observed nitrate concentrations and mean 

nitrate concentrations predicted with the linear regression model indicates 

that the model is a good fit (R2=0.82)...................................................................................45

10–2. Mean observed and predicted nitrate concentrations show the goodness 

of fit for the linear regression model, which is based on data from these 

17 well networks. The networks for which the residuals are closer to zero 

have the best fit to the model. Data needed for the model were unavailable 

for Alaska.................................................................................................................................46

10–3. The area of highest predicted mean nitrate concentration in water from 

private wells in the glacial aquifer system is in the glacial deposits in westcentral Illinois. ........................................................................................................................47

11–1. There was no distinct geographic pattern in nitrate concentration in water 

from private wells in the glacial aquifer system, although most high 

concentrations (greater than 10 milligrams per liter as nitrogen) were in 

the central part of the glaciated United States.................................................................49

11– 2. Changes in nitrate concentrations in water from private wells in the highly 

heterogeneous glacial aquifer system were most variable with depth........................50
ix

Tables

1–1. The glacial aquifer system has many local and regional names, as shown 

by the nomenclature for Quaternary aquifers of glacial origin used in the 

U.S. Geological Survey’s Regional Aquifer System Assessment (RASA) 

program. In this report, the term “glacial aquifer system” is used to |

represent all of these aquifers as one system....................................................................6

4–1. Mean nitrate concentrations are higher in sand and gravel aquifers than 

most other lithologies ............................................................................................................18

5–1. Comparison of nitrate concentration in groundwater from private wells to 

nitrogen sources indicates that atmospheric deposition of nitrogen, septicsystem density, and sewer density are significantly related to nitrate 

concentration with 95 percent confidence, but the relations are weak.......................20

6.1–1. Most detections of nitrate in private wells were in “young” (recently 

recharged) groundwater that is oxic. In this study, only samples of young, 

oxic groundwater contained nitrate at concentrations greater than 10 milligrams 

per liter as nitrogen................................................................................................................23

6.2–1. Shallow wells (75 feet deep or less) generally were associated with higher 

nitrate concentration, younger groundwater, and more oxic conditions than 

wells deeper than 75 feet......................................................................................................26

7.2–1. Private, public-supply, and monitoring wells in the glacial aquifer system 

differ with respect to groundwater nitrate concentration and wellconstruction characteristics................................................................................................33

7.2–2. Samples from all well types in the glacial aquifer system represent a mixture 

of groundwater of different ages.........................................................................................35

8–1. Variables used in selected models to predict probability of nitrate 

concentration exceeding a given level are compared. The logistic regression 

models included some or all of the variables in the linear regression model 

highlighted in this report, plus an interaction term for models with nitrate 

thresholds of 5 mg/L or greater............................................................................................37

9–1. Variables used in logistic regression models for 10 thresholds of nitrate 

concentrations include source, transport, and attenuation variables. 

The intercept is a statistical variable that was important in all models for 

thresholds of 1 to 10 mg/L. ....................................................................................................40

10–1. Coefficient values, standard error and p-values of variables used in the linear 

regression model used to predict mean nitrate concentration in private-well networks in the glacial aquifer system ....................................................................................45
x

Conversion Factors

SI to Inch/Pound

Multiply By To obtain

Length

centimeter (cm) 0.3937 inch (in.)

meter (m) 3.281 foot (ft) 

kilometer (km) 0.6214 mile (mi)

Area

square kilometer (km2) 0.3861 square mile (mi2)

Volume

liter (L) 0.2642 gallon (gal)

Mass

kilogram (kg) 2.205 pound avoirdupois (lb)

cubic meter per second 22.82 million gallons per day (mgd)

megaliters per day 0.2642 million gallons per day (mgd)

Application rate

kilograms per hectare per year 

[(kg/ha)/yr]

0.8921 pounds per acre per year 

[(lb/acre)/yr]

Abbreviated water-quality units: 

μg/L micrograms per liter 

mg/L milligrams per liter 
xi

Abbreviations

CFC Chlorofluorocarbon

DO Dissolved oxygen

MCL Maximum Contaminant Level

NAWQA National Water-Quality Assessment Program

RASA Regional Aquifer System Assessment

Redox Oxidation and reduction potential

ROC Receiver Operating Characteristic

STATSGO U.S. Department of Agriculture State Soil Geographic database

TU Tritium Units

USEPA U.S. Environmental Protection Agency

USGS U.S. Geological Survey.

> Greater than

< Less than

% Percent

Terms in text that are shown in boldface are defined in the glossary at the back of the report.

Relations That Affect the Probability and Prediction of 

Nitrate Concentration in Private Wells in the Glacial 

Aquifer System in the United States

By Kelly L. Warner and Terri L. Arnold 

A series of 10 logistic regression models was developed 

to estimate the probability of nitrate concentration above various thresholds. The threshold concentration (1 to 10 mg/L) 

affected the number of variables in the model. Fewer explanatory variables are needed to predict nitrate at higher threshold 

concentrations. The variables that were identified as significant predictors for nitrate concentration above 4 mg/L as N 

included well characteristics such as open-interval diameter, 

open-interval length, and depth to top of open interval. Environmental variables in the models were mean percent silt in 

soil, soil type, and mean depth to saturated soil. The 10-year 

mean (1992–2001) application rate of nitrogen fertilizer 

applied to farms was included as the potential source variable. A linear regression model also was developed to predict 

mean nitrate concentrations in well networks. The model is 

based on network averages because nitrate concentrations are 

highly variable over short distances. Using values for each of 

the predictor variables averaged by network (network mean 

value) from the logistic regression models, the linear regression model developed in this study predicted the mean nitrate 

concentration in well networks with a 95 percent confidence 

in predictions. 

Abstract

Nitrate in private wells in the glacial aquifer system is a 

concern for an estimated 17 million people using private wells 

because of the proximity of many private wells to nitrogen 

sources. Yet, less than 5 percent of private wells sampled in 

this study contained nitrate in concentrations that exceeded 

the U.S. Environmental Protection Agency (USEPA) Maximum Contaminant Level (MCL) of 10 mg/L (milligrams per 

liter) as N (nitrogen). However, this small group with nitrate 

concentrations above the USEPA MCL includes some of the 

highest nitrate concentrations detected in groundwater from 

private wells (77 mg/L). Median nitrate concentration measured in groundwater from private wells in the glacial aquifer 

system (0.11 mg/L as N) is lower than that in water from other 

unconsolidated aquifers and is not strongly related to surface 

sources of nitrate. Background concentration of nitrate is less 

than 1 mg/L as N.

Although overall nitrate concentration in private wells 

was low relative to the MCL, concentrations were highly 

variable over short distances and at various depths below land 

surface. Groundwater from wells in the glacial aquifer system 

at all depths was a mixture of old and young water. Oxidation 

and reduction potential changes with depth and groundwater 

age were important influences on nitrate concentrations in 

private wells. 
Urban (4 percent)

Forest and shrub (30 percent)

Grasslands and herbaceous (8 percent)

Agricultural (51 percent)

Wetlands (6 percent)

Other (1 percent)

EXPLANATION

LAND USE/LAND COVER

Figure 1-1.

2 Relations That Affect the Probability and Prediction of Nitrate Concentration in Private Wells, Glacial Aquifer System

1.0 Introduction and Hydrostratigraphy of the Glacial Aquifer System

The glacial aquifer system is characterized by the heterogeneity of the aquifer material. A framework for 

the system groups areas of similar intrinsic susceptibility and natural vulnerability.

The glacial aquifer system is the principal aquifer for 

most of the northern United States and is present in parts of 

26 States. A principal aquifer is a regionally extensive aquifer 

system that is used and has the potential to be used as a source 

of potable water (Lapham and others, 2005). The area overlying the glacial aquifer system receives some of the largest surface applications of nitrate as a fertilizer in the Nation, and the 

population using private water supplies from the glacial aquifer system is large. Approximately 41 million people relied on 

the glacial aquifer system for public supply and private use in 

2000 (Warner and Arnold, 2006). The population served by 

private supply from the glacial aquifer system was estimated 

at 17 million people in 2000. Total private withdrawals were 

estimated at 1,200 million gallons per day, which is about 

40 percent of the 2000 groundwater withdrawals for private 

supply nationwide.

The glacial aquifer system is defined as all unconsolidated aquifers above bedrock north of the line of continental 

glaciation in the United States. This aquifer system is an 

important resource for the highly agricultural part of the 

United States including Illinois, Indiana, Iowa, Nebraska, and 

elsewhere because it is the uppermost aquifer. The aquifer extends from land surface to depths of more than 1,000 ft in 

some areas, so it is easily accessible for private well installation. 

Nitrogen is a concern for private well owners because 

it is often applied as a fertilizer in areas near private wells. 

Nitrogen in groundwater is in the forms of nitrite and nitrate. 

Measurements of nitrite plus nitrate as nitrogen (N) in this 

report are hereafter referred to as “nitrate.” Nitrate is a 

concern for private well owners if the water is consumed 

because nitrate can restrict oxygen transport in the bloodstream, which is especially harmful to infants and the elderly. 

The U.S. Environmental Protection Agency (USEPA) has 

established a drinking-water standard of 10 mg/L as N for 

nitrate, which is the Maximum Contaminant Level (MCL) 

(U.S. Environmental Protection Agency, 2009). Nitrate can 

originate from natural sources or from human activities such 

as fertilizer application and wastewater disposal. The concentration and transformation of nitrate are controlled by oxidation and reduction potential (redox) conditions and mediated by microorganisms. Nitrate is stable and mobile under 

oxidizing conditions. Additionally, it is soluble in water and 

can easily pass through soil to the groundwater table, where 

it can persist for decades. The amount of nitrate may increase 

because of continuing yearly inputs (Nolan and Stoner, 2000).

In a study of nitrate in private wells in the United States, 

it was reported to be the only contaminant derived from 

primarily manmade sources that was found at concentrations 

greater than a human-health benchmark in more than 1 percent 

of the wells (DeSimone and others, 2009). Concentrations 

of nitrate were greater than the MCL in nearly 25 percent 

of the private wells in areas of intense agricultural land use 

(DeSimone and others, 2009). The dominant land use overlying the glacial aquifer system is agriculture (fig. 1–1). Nitrate 

is applied at high rates to land (fig. 1–2) overlying the glacial 

aquifer system and its occurrence is a known human-health 

issue in groundwater (Follett and Hatfield, 2001). Private wells 

are commonly located in rural parts of the country where large 

areas are fertilized. Nitrate is a concern in many of these rural 

areas because the residents rely on private wells in the glacial 

aquifer system for drinking water and these wells are not 

routinely monitored for nitrate. States typically recommend 

that water from new wells or wells on transferred property 

be analyzed for nitrate and bacteria, but this analysis is at the 

discretion of the well owner. 

Figure 1–1. Agriculture is the major land use overlying the glacial aquifer system.
110°00 ́ 90°00 ́ 80°00 ́ 

45°00 ́35°00 ́

120°00 ́ 100°00 ́

40°00 ́

C A N A D A

ALASKA CANADA

WA

OR

ID

MT

WY

CO

ND

SD

NE

KS

IA

MN

WI

IL

MO

IN

MI

KY

WV

VA

PA

N

OH M

Pacific Ocean

Lake Superior

Lake Michigan

LakeHuron

Lake Erie

Lake Ontario

U N I T E D S T A T E S

Ain

Aren

Driftless area

Base from U.S. Geological Survey 1:2,000,000 Digital DataAlbers Equal-Area Conic projection, standard parallels 29° 30’and 45° 30’, central meridian -96°, latitude of origin 23°

0 100 MILES0 100 KILOMETERS N

Mean nitrogen fertilizer

applied to farms (1992-2001),in million kilograms per year

0 to 1.75Greater than 1.75 to 5.02Greater than 5.02 to 8.77Greater than 8.77 to 14.60Greater than 14.60 to 36.00

EXPLANATION

Glacial aquifer system extent

(approximate)

No Data are shown for Alaska

Figure 1–2. The highest rate (1992–2001) of nitrogen fertilizer application is over the Midwestern states which are part of the glacial aquifer system. others, 2006.)
4 Relations That Affect the Probability and Prediction of Nitrate Concentration in Private Wells, Glacial Aquifer System

The purpose of this study was to determine the vulnerability of private supplies in the glacial aquifer system to 

nitrate contamination. A well is susceptible if water can flow 

easily from the land surface to the well, but the well becomes 

vulnerable when there is a known source of nitrate that can be 

transported to the susceptible well. This report determines the 

vulnerability of private wells in three ways: 

1. Determine the relation of nitrate in water from private 

wells to potential sources; 

2. Determine the relation of nitrate in water from private 

wells to environmental variables that may affect the transport of nitrate; and

3. Determine which variables are related to the probability 

and prediction of nitrate contamination in private wells in 

the glacial aquifer system. 

This report is based on the U.S. Geological Survey 

(USGS) National Water-Quality Assessment (NAWQA) 

program’s groundwater sampling of the glacial aquifer system 

from 1991 to 2005. The data set includes data collected and 

analyzed in a consistent manner as defined by the NAWQA 

program (Koterba and others, 1995). The data analyzed in this 

study are combined from 15 geographically separated study 

areas (NAWQA study units). Only the wells originally selected 

to address the overall water quality of the glacial aquifer system—379 private wells–were used in this study (fig. 1–3). 

Extensive quality-assurance data have been collected to 

measure the accuracy of the data (Mueller and Titus, 2005), 

and concentrations of nitrite plus nitrate were determined 

to be essentially unaffected by contamination. Laboratory 

nitrite concentration commonly is less than the reporting 

level of 0.01 mg/L as N in groundwater sampled as part of the 

NAWQA program, resulting in negligible contribution to the 

nitrite plus nitrate concentration (Nolan and Stoner, 2000). 

The nomenclature for the glacial aquifer system is varied. 

Other names for the glacial aquifer system have included 

stratified drift, surficial aquifer, unconsolidated deposits, and 

sand and gravel aquifers, as well as many local aquifer names. 

The term “stratified-drift aquifer” was formerly used in the 

eastern States where proglacial lakes or marine embayments 

developed in major valleys or lowlands during deglaciation 

and were filled with a sequence of stratified sediment (Randall, 

2001; Kontis and others, 2004). The exceptions are Cape Cod 

and Long Island, which are covered in sheet-type sands. The 

term “surficial” or “glacial” aquifer has been used in the midcontinent area for aquifers in sands and tills (Bugliosi, 1999; 

Eberts and George, 2000). In this part of the glacial aquifer 

system, buried bedrock valleys are filled with sediment in 

which the water-producing units are sand lenses within clayey 

deposits or coarse-grained deposits at the bottom of buried 

bedrock valleys. In the western glaciated area, the unconsolidated deposits of glacial origin are part of the Puget Sound 

aquifer system (Jones, 1999). The USGS Regional Aquifer 

System Assessment (RASA) program delineated hydrogeologic units in the glacial aquifer system in different geographic 

areas (table 1–1). Additionally, the USGS Ground Water 

Atlas of the United States refers to all of these aquifers as the 

surficial aquifer system of sand and gravel aquifers (Miller and 

Appel, 1997; Trapp and Horn, 1997; Lloyd and Lyke, 1995) 

or unconsolidated-deposit aquifers (Whitehead, 1996). All 

of these aquifers contain groundwater in the unconsolidated 

material that ranges from land surface to bedrock (including 

materials of glacial and alluvial origin). This aquifer system is 

referred to as the glacial aquifer system in this report. 

The three general environmental settings for private 

wells in the glacial aquifer system are buried bedrock valleys; 

sheets, layers, or discontinuous lenses of sand; and valley-fill 

deposits (fig. 1–4). Buried bedrock valleys are known in some 

areas and the glacial aquifer system in this setting is often 

sought for public and private supplies. Aquifers in buried bedrock valleys commonly provide large water supplies for cities 

and private homeowners. Because wells that withdraw water 

from sand and gravel in a buried bedrock valley typically are 

very deep, it is not likely they will contain water with measurable nitrate concentrations. The valley-fill environmental setting is similar to the buried bedrock valley except there is frequently hydraulic connection to land surface and surface-water 

bodies (fig. 1–4). Groundwater from the glacial aquifer system 

in this setting is more likely to contain measurable nitrate 

because of the hydraulic connection of sand and gravel to the 

land surface. If wells are drilled deep in a valley-fill setting, 

then nitrate reduction is likely. The environmental setting of 

sheets, layers, or lenses of discontinuous sand is the most difficult to assess for vulnerability to nitrate. If wells are drilled 

in shallow sands and gravels, nitrate applied at land surface 

may enter the groundwater. If wells are drilled deeper, below 

some clays or clayey tills, then nitrate is less likely to be in the 

groundwater because water does not travel easily through clay. 

Understanding the geology and environmental setting of a 

private well helps in assessing the vulnerability of the aquifer 

to contamination from nitrate applied at the land surface.
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Puget

Sound

Basin

Red River

of the

North Basin

Eastern

Iowa

Basins

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Illinois

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Basin

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Illinois

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Basin

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Study

Allegheny 

Monongah

River Bas

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Inlet

Basin

0 100 MILES0 100 KILOMETERS N

EXPLANATION

Study-unit boundaryGlacial aquifer system extent

(approximate)

Private well

EastCentralWest-central

Glacial framework area

West

Figure 1–3. Despite the gaps in the spatial distribution of wells across the glacial aquifer system in the United States, all four glacial framework areawells sampled as part of the U.S. Geological Survey National Water-Quality Assessment program. Framework areas are based on similarity of physiogmaterial. The wells in Nebraska are included in this study because they are located in areas of reworked glacial deposits.
Sand and gravel

Clay, silt, and very

fine to fine sand

Till

Bedrock

Water

EXPLANATION

Valley-fill

deposits Fracture

Sheets, layers,

and lenses

Buried

bedrock

valley

Buried

bedrock

valley

Figure 1-4.

6 Relations That Affect the Probability and Prediction of Nitrate Concentration in Private Wells, Glacial Aquifer System

Table 1–1. The glacial aquifer system has many local and regional names, as shown by the nomenclature for Quaternary aquifers 

of glacial origin used in the U.S. Geological Survey’s Regional Aquifer System Assessment (RASA) program. In this report, the term 

“glacial aquifer system” is used to represent all of these aquifers as one system.

Glacial framework area Reference

Regional Aquifer System 

Assessment (RASA) 

study area

Name of Quaternary aquifers of glacial origin

East Randall, 2001 Stratified-drift aquifers Stratified-drift aquifers.

Central Bugliosi, 1999 Midwestern Basins and Arches Glacial deposits and confining unit.

Central and West-Central Young, 1992 Cambrian-Ordovician aquifer Drift aquifer.

West Jones ,1999 Puget Sound Aquifer System Various river aquifers, Fraser aquifer, or Puget aquifer.

Figure 1–4. Wells in buried bedrock valleys are less susceptible to nitrate 

contamination because of the thick overlying layer of till which is mostly fine-grained 

material, whereas wells in valley-fill deposits and in sheets, layers, and lenses 

of sand are more likely to have a connection to the land surface. (Modified from 

Whitehead, 1996.)
1.0 Introduction and Hydrostratigraphy of the Glacial Aquifer System 7

Heterogeneity characterizes the geology of the glacial 

aquifer system. Because of its clay content, especially in the 

Midwest, the glacial aquifer system differs from other unconsolidated aquifer systems, such as the High Plains of Colorado 

and Nebraska. The distribution of the sand and gravel units 

that make up the glacial aquifer system and the clay and silt 

confining units that are interbedded can be extremely complex 

(Miller, 1999). Because the lobes of continental ice associated with these glacial deposits advanced repeatedly and from 

different directions, different materials were eroded, transported, and deposited, depending on the predominant rock 

types underlying the ice. The mixtures of clay and sand are 

widely variable both spatially and vertically, and this variability affects the transport of nitrate through the aquifer system. 

Randall (2001) notes that the susceptibility of a given aquifer 

to contamination, if determined from aquifer material near the 

surface (fig. 1–5), can be misleading because the distribution 

of aquifer material with depth does not match the surficial 

distribution. For example, some of the coarse-grained deposits 

that make up the productive part of the glacial aquifer system 

may be buried beneath fine-grained deposits and generally are 

not depicted on maps of surficial geology. 

Another key difference between the glacial aquifer 

system and other unconsolidated aquifers is the mixture of 

clay and organic material it contains. The clay and organicmatter content is an important aquifer characteristic because 

these materials can slow down the transport of contaminants 

to deeper groundwater. Subsurface drains, which are installed 

in agricultural areas with clayey soils such as alfisols, can 

impede nitrate in recharge water from reaching the water table. 

McMahon and others (2008) found that the extent of nitrate 

attenuation is related to the depositional environment of the 

aquifer materials and generally increases from fluvial sand 

to glacial sand to glacial/marine clay, and, finally, to marine 

shale. Susceptibility of wells in the glacial aquifer system 

to contamination also is affected by organic material, which 

commonly originates as peat and soils buried beneath glacial 

deposits and in forested areas. Organic material can affect the 

redox of the groundwater system by promoting consumption 

of dissolved oxygen and denitrification. Alfisols, naturally productive soils typically formed under deciduous forest or mixed 

vegetative cover in humid areas, overlie 25 percent of the 

glacial aquifer system–mostly in the Midwestern United States 

(fig. 1–6). This soil type results from weathering processes that 

leach clay and minerals from the surface layer into lower soil 

layers. Alfisols are characterized by discolored features that 

indicate particular redox conditions, such as recurring periods 

of soil saturation (U.S. Department of Agriculture, 2006). 

Grouping areas of similar hydrogeology may help to 

assess the regional water quality of the glacial aquifer system. 

The glacial aquifer system was divided into four areas by Warner and Arnold (2006) based on factors affecting the intrinsic 

susceptibility (related to the ease of groundwater flow) and the 

natural vulnerability of wells. These four areas of the glacial 

framework are used in this report to delineate areas of similar 

susceptibility, but local information on geochemical conditions and land use would be needed to refine the determination of vulnerability to nitrate contamination. Bedrock is not 

considered as part of this framework because nitrate is not 

likely to be derived from a bedrock source. The 379 private 

wells sampled as part of this study include 71 wells in the 

East framework area, 174 in the Central framework area, 

83 in the West-central framework area, and 51 in the West 

framework area. 
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EXPLANATION

Texture of near-surface deposits of the glacial aquifer system

Coarse-grained sedimentFine-grained sediment (includes till and patchy Quaternary or organic-rich sediment)Undifferentiated or mixed fine- and coarse-grained sediment

Unclassified

Glacial aquifer system extent (approximate)

No Data are shown for Alaska

Figure 1–5. Fine-grained sediment is present at land surface across most of the glacial aquifer system, but the texture of sediment at land surface is presence or absence of an underlying aquifer. (From Arnold and others, 2008.)
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0 100 MILES0 100 KILOMETERS N

EXPLANATION

Glacial aquifer system extent (approximate)Predominant soil type (greater than 50% of soil)

AlfisolsEntisolsHistosolsInceptisols

Other (andisols, aridisols, ultisols, or vertisols)

MollisolsSpodosolsMixed–none predominant

No Data are available for Alaska

Figure 1–6. There are numerous soil types overlying the glacial aquifer system. Alfisols are soils that overlie approximately 25 percent of the glacial Midwest. Alfisols are typically formed in humid areas under deciduous forests and mixed vegetation. (Modified from Wolock, 1997.)
10 Relations That Affect the Probability and Prediction of Nitrate Concentration in Private Wells, Glacial Aquifer System

2.0 Methods 

0.05 mg/L as N. These treated values were used in the calculations of general descriptive statistics. Spearman correlation 

coefficients were used to examine relations among variables 

related to nitrate concentrations in private wells and in monitoring wells. A confidence level of 90 percent (where the probability of the relation being one of chance is less than or equal 

to 10 percent, or alpha = 0.10) was considered a “significant 

correlation.” Low Spearman correlation coefficients generally 

indicate a weak correlation; however, in the case of the data 

set that was used in this analysis, the sample size was sufficiently large (n > 300) that even small coefficients could be 

significant. Nonparametric statistics, such as the Kruskal-Wallis rank sum test, were used to compare groups of data. The 

Kruskal-Wallis rank sum test is a robust nonparametric test for 

differences among groups; this test is largely unaffected by the 

presence of outliers. Survival curves were plotted to examine 

the difference among nitrate concentrations measured in private, public-supply and monitoring wells in the glacial aquifer 

system. Survival curves resemble upside-down cumulative 

frequency distribution curves that can take into account 

censored data (Helsel, 2005). The nonparametric rank of the 

nitrate concentrations was used to draw the survival curves.

Data used to model probabilities and predictions of 

nitrate concentrations were derived mostly from spatial data; 

however, some data were from well-construction records. 

Well-construction data used in the models include openinterval diameter, open-interval length, and depth to top 

of open interval. The term “open interval,” also called the 

screened interval, describes the length of the well that is open 

to the aquifer materials, where the water can enter the well. 

The open-interval-diameter variable was used to represent 

the diameter of the well. If the open-interval diameter was 

not available, then casing diameter was used. Spatial data 

include depth to saturated soil, mean silt in soil, and percent of 

alfisols, all of which were derived from the U.S. Department 

of Agriculture’s State Soil Geographic (STATSGO) database 

(Wolock, 1997). Ten-year mean (1992–2001) nitrogen fertilizer applied to farmland was derived from Ruddy and others 

(2006). The 10-year mean fertilizer application was calculated for this report by summing the county nitrogen-fertilizer 

applications from 1992 through 2001 (Ruddy and others, 

2006) and dividing by 10. All spatial data were calculated as 

area-weighted averages for the area within a 1,640-ft radius 

(500 m) around the well. Soils data were area-weighted by the 

fraction of a soil unit defined in STATSGO that overlapped the 

area within a 1,640-ft radius around a well. The farm-fertilizer 

data were area-weighted by county and agricultural land-use 

area within a 1,640-ft radius around a well. Descriptions of 

variables, variable names, and data sources used for models 

Standardized sample collection and analysis aids in regional aggregation of data. Nonparametric statistics 

and models are used to interpret the analytical results.

The USGS NAWQA program is the primary source of 

long-term, nationwide water-quality data from groundwater 

and surface water (http://water.usgs.gov/nawqa/). Groundwater data collected as part of the NAWQA program are based 

on networks of 20 to 30 wells. Nitrate data were collected 

at 1,290 groundwater-sampling sites in 15 studies across 

the glacial aquifer system during 1991–2005. Within these 

15 studies, there are 17 well networks that were designed to 

collect data targeted for a specific purpose. Most of the 430 

private wells in the glacial aquifer system that were sampled in 

the 15 studies were selected to assess the overall water quality 

of the major aquifer system, but 51 of the private wells were 

initially selected to address the impact of land use on water 

quality or for other, special studies (Lapham and others, 1995). 

Only the private or public supply wells in networks selected 

to assess the overall water quality of the major aquifer system 

are included in this report. This study analyzed data from 379 

private wells, 41 public-supply wells, and 870 shallow monitoring wells. Public supplies sampled as part of the NAWQA 

assessment of major aquifers were selected if the wells were 

pumped at a low capacity (Lapham and others, 1995). All 

of the private and public wells sampled for this study were 

wells installed by the owners; all of the monitoring wells were 

installed by the USGS specifically to examine the effects of 

land use on shallow, recently recharged groundwater (generally less than 10 years old) (Gilliom and others, 1995). Additionally, 20 reference wells that are a subset of the monitoring 

wells were selected in areas identified as minimally impacted 

by humans. Data have been collected at these wells since 1994 

and include 78 analyses (completed by January 2007). These 

reference-well data were used to determine the background 

nitrate concentration.

Data were collected following NAWQA protocols 

(Lapham and others, 1995; Koterba and others, 1995; Koterba, 

1998; and Squillace and Price, 1996). Analyses for groundwater-age indicators were completed at several laboratories. 

Tritium was measured at the USGS Menlo Park Isotope 

Research Laboratory in Menlo Park, CA, or at the University 

of Miami Tritium Laboratory in Miami, FL. Chlorofluorocarbon (CFC) and tritium-helium were measured at the USGS 

Chlorofluorocarbon Laboratory in Reston, VA, or at the 

Lamont-Doherty Laboratory in Palisades, NY. Nitrogen compounds were measured at the USGS National Water- Quality 

Laboratory using methods documented in Fishman (1993) and 

Patton and Kryskalla (2003).

Some nitrate data used in this analysis were censored (the 

concentration was less than the reporting limit) at 0.05 mg/L 

as N. For most of this analysis, nitrate concentrations that 

were censored were treated as if they had been measured at 
2.0 Methods 11

described in this report are shown in appendix 1. Alaska 

private-well data were not included in the models because 

spatial data were unavailable. 

Nitrate concentrations in private wells in the glacial aquifer system were compared to results of a nationwide logistic 

regression model that predicts the probability of occurrence 

of nitrate concentrations greater than 4 mg/L as N in recently 

recharged (shallow) groundwater in all aquifers across the 

United States (Nolan, 2001; Nolan and others, 2002). The 

nationwide logistic regression model was applied to the glacial 

aquifer system in three ways: spatial overlay of points representing wells over the spatial model, using the exact regression 

equation of the nationwide model, and recalibrating the model 

specifically for the data from the glacial aquifer system. 

Private wells in the glacial aquifer system were first 

overlain with the nationwide spatial model of probability of 

groundwater nitrate contamination (Nolan and others, 2002) to 

identify the probability category for each well. The observed 

and average predicted probabilities were calculated (app. 2) 

and plotted on a scatter plot for the same six categories used in 

Nolan and others (2002).

Nitrate concentrations in private wells in the glacial 

aquifer system also were compared to results of the nationwide logistic regression model by calculating the probability 

of occurrence of a nitrate concentration greater than 4 mg/L as 

N for each private well in the glacial aquifer system using the 

logistic regression equation and coefficients from Nolan and 

others (2002). The following equation was used:

P=eF(x)/(1 + eF(x)) ,

where 

	 P = probability of being in a category and

	 F(x) = (-5.541 + (0.004 * 1992 fertilizer nitrogen, in 

kilograms per hectare) + (0.016 * percent 

agricultural land use) + (0.229 * natural 

log of 1990 population density) + (0.025 

* percent of well-drained soils) + (1.088 

* depth to seasonally high water table, in 

meters) + (0.424 * presence or absence or 

unconsolidated sand and gravel aquifers)).

The sources of variables used in the equation were calculated for a 1,640-ft radius around a well and provided more 

accurate representation of well attributes than information at 

the well point, except for the sand and gravel presence/absence 

indicator variable, which was still available only as a point on 

a polygon overlay. The results were divided into the same six 

categories as in Nolan and others (2002). The observed and 

the mean predicted probabilities were calculated for each of 

the six categories (app. 3) and plotted on a scatter plot. The 

number of wells with a measured nitrate concentration greater 

than 4 mg/L as N was tabulated for each of the six categories and the observed probability was calculated by dividing 

the number of wells with nitrate concentration greater than 

4 mg/L as N by the total number of wells in the category. The 

mean predicted probability was calculated as the mean of all 

probabilities resulting from the logistic regression equation for 

each of the six categories. 

The nationwide logistic regression model was recalibrated for private wells in the glacial aquifer system to obtain 

new coefficients (app. 4). The following recalibrated model 

equation was developed:

P=eF(x)/(1 + eF(x)) ,

where 

	 P = probability of being in a category and

	 F(x) = (-4.274 + (0.0000938 * 1992 fertilizer nitrogen, 

in kilograms per hectare) + (0.0083 * percent 

agricultural land use) + (0.0759 * natural 

log of 1990 population density) + (0.0058 

* percent of well-drained soils) + (0.256 

* depth to seasonally high water table, in 

meters) + (-0.0127 * presence or absence of 

unconsolidated sand and gravel aquifers)).

The model variables were examined for significance of 

predicting probability of nitrate concentration greater than 

4 mg/L as N using partial t-tests and an analysis of deviance 

chi-square test (app. 4). The predicted and observed probabilities of a nitrate concentration greater than 4 mg/L as N 

were calculated and plotted on a scatter plot using the same six 

probability categories as in Nolan and others (2002); however, 

only the three lower probability categories were represented 

by observed data. To better evaluate the recalibrated model 

fit, the predicted and observed probabilities were calculated 

and plotted on a scatter plot using 10 probability categories 

(app. 4).

Ten regional logistic regression models for assessing the 

probability of nitrate occurrence in groundwater in private 

wells were developed for thresholds from 1 to 10 mg/L as N 

(app. 5, app. 6). Logistic regression modeling was used to 

more closely examine relations between significantly correlated variables and nitrate concentrations in private wells. The 

logistic regression models used a binary variable to indicate 

(flag) whether the nitrate concentration in a sample was above 

or below a given threshold concentration and resulted in a predicted probability of encountering a nitrate value greater than 

the various thresholds, based on a set of independent predictor 

variables. The nitrate thresholds that were modeled overlapped 

each successive threshold. For example, using the threshold 

value “nitrate concentration greater than 1 mg/L as N” flagged 

all nitrate concentrations that were greater than 1 mg/L as 

N and overlapped the next threshold, “nitrate concentration greater than 2 mg/L as N.” In other words, every nitrate 

concentration that was flagged as a concentration greater than 

2 mg/L as N was also flagged as a nitrate concentration greater 

than 1 mg/L as N.
12 Relations That Affect the Probability and Prediction of Nitrate Concentration in Private Wells, Glacial Aquifer System

 A series of more than 100 variables in relation to measured nitrate concentration was visually examined on scatter 

plots. Forty-six of these variables appeared visually to be linearly related to nitrate concentration in private wells in the glacial aquifer system. The relations of the 46 variables to nitrate 

concentration were examined with Spearman correlations 

(app. 7). Eighteen variables were correlated at the 95-percent 

confidence level (p<0.05). 

All 10 logistic regression models for thresholds from 1 to 

10 mg/L nitrate as N were developed using a semi-automated 

method in SAS (SAS Institute Inc., 2003) where the program 

selected a subset of independent variables using stepwise 

forward selection to predict the binary dependent variable 

(above or below the threshold). For a variable to be added 

and retained in a model, the addition of the variable to the 

model had to contribute to explaining the variability in the 

nitrate concentrations at a significance level of at least 0.05. In 

general, it was theorized that variables important for a model 

of one threshold would most likely also be important for the 

model of the next lower threshold because the concentrations 

in the samples in each successive threshold overlapped. An 

example of overlapping thresholds is the set of wells with 

nitrate concentrations greater than 2 mg/L as N, which is 

included in the set of wells with nitrate concentrations greater 

than 1 mg/L as N. 

Each of the 10 logistic regression models was run three 

times. The first iteration for each model allowed the potential inclusion of 18 variables that were correlated to nitrate 

concentrations at the 95-percent confidence level (app. 8) plus 

the 10-year mean (1992–2001) nitrate fertilizer applied to 

farms, which was included as an additional potential predictor 

variable. Nitrogen fertilizer is known to be a potential source 

of nitrate in groundwater and has been used successfully as 

a predictor variable in other nitrate models (Nolan and Hitt, 

2003; Nolan and Hitt, 2006). Some variables were used in all 

10 models, whereas others were used in only 1 or 2 models. 

The variables that were used in only a few of the models 

were evaluated as to whether the inclusion was scientifically 

justified and whether there was a similar variable in the model 

for the next higher or lower threshold. If the variable was not 

used in the model for the next higher or lower threshold, it was 

excluded from further iterations of the logistic regression models. For example, in the first iteration, soil bulk density was 

one of the variables selected for the logistic regression model 

in which the threshold level was nitrate concentration greater 

5 mg/L as N; however, soil bulk density was not selected to 

predict the probability of nitrate concentration greater than 

4 mg/L as N or greater than 6 mg/L as N. Therefore, soil bulk 

density was not included as a possible predictor variable for 

subsequent iterations for the final models. The third iteration 

resulted in the final 10 logistic regression models, in which the 

variables were specified for each model (app. 8). 

Several of the models include an interaction term. 

Interaction occurs when the relation between an independent 

variable and a dependent variable depends on the value of a 

different independent variable (Kleinbaum and others, 1988; 

Ahlbom and Alfredsson, 2005). 

The significance of all variables in each model was tested 

using the Wald chi-square test statistic, which is the squared 

ratio of the estimate to the standard error of the respective 

predictor. The variables used in the final logistic regression 

models also were evaluated for tolerances and variance inflation factors to ensure they were not collinear (SAS Institute 

Inc., 2003). Colinearity means that the variables might be representing similar variability in the models; therefore, collinear 

variables should not be used in the same model. The quality of 

the models was evaluated using two goodness-of-fit statistics: 

area under the Receiver Operating Characteristic (ROC) curve, 

and the Hosmer-Lemeshow goodness-of-fit statistic (Hosmer 

and Lemeshow, 2000). Each of these goodness-of-fit statistics evaluates the association of predicted probabilities and 

observed responses and is used to compare the results of the 

initial models to those of the final, modified models in which 

only eight of the possible variables were used.

The ROC curve statistic describes the model’s ability to 

discriminate between the two cases of the binary dependent 

variable–in this case, nitrate concentration above a threshold 

(1 to 10 mg/L as N). The value of the statistic is the area under 

the ROC curve. The value ranges from zero to one and is a 

measure of the model’s ability to discriminate between samples that have a nitrate concentration greater than a threshold 

(Hosmer and Lemeshow, 2000). A value of the ROC statistic 

that is above 0.8 is considered “excellent discrimination.” 

The Hosmer-Lemeshow statistic uses a Pearson chisquare test to evaluate the relation between observed and 

predicted probability. Predicted probabilities are divided into a 

number of percentile groups, usually deciles, and compared to 

the probability that an observed value will be in that percentile 

category (Hosmer and Lemeshow, 2000). Probabilities should 

be greater than an alpha level of 0.05 to indicate a good fit, 

which means that the observed and predicted probabilities 

in the percentile groups are not significantly different. The 

model for nitrate concentration greater than 4 mg/L as N was 

validated using an interactive variable selection method based 

on the Mallows’ Cp statistic (Mallows, 1973).

A linear regression model also was developed to evaluate 

how accurately actual nitrate concentrations could be predicted based on the same variables used in the logistic regressions (regardless of p-value). The linear regression equation 

used the same variables (averaged by network) as the logistic 

regressions, cumulatively; however, the interaction term 

was omitted from the linear regression analysis (app. 9). The 

predictor variables were not selected specifically for this linear 

regression; therefore, some of the p-values are insignificant. 

The linear regression model included network means of the 

following variables: depth to saturated soil, percent silt in soil, 

percent alfisols soil type, 10-year mean nitrogen applied to 

farms, diameter of open interval, depth to top of open interval, 

and length of open interval. Each variable was averaged for 

wells within each network. Data for a network were used in 
2.0 Methods 13

the linear regression model only if the network consisted of 

five or more wells. Residuals resulting from the linear regression model were plotted against quantiles of the standard 

normal distribution to check for a normal distribution. The 

approach of using network averages is based on the methods 

of the Groundwater Vulnerability Assessment for Drinking 

Water (GWAVA-DW) model developed by Nolan and Hitt 

(2006). Unlike the GWAVA-DW model, the prediction model 

in this report was developed with a linear relation. 
14 Relations That Affect the Probability and Prediction of Nitrate Concentration in Private Wells, Glacial Aquifer System

3.0 Background Nitrate Concentration

Data have been collected from these reference wells as part 

of NAWQA since 1994. The mean nitrate concentration in 

these wells was 1.16 mg/L as N (when censored data were 

set to the censored value, which may have slightly overestimated the mean), but the median was only 0.13 mg/L as 

N, indicating substantial variability. Groundwater from the 

glacial aquifer system reference wells in Nebraska had a 

much higher mean concentration of 6.2 mg/L as N that may 

be caused by the limited area unaffected by agricultural land 

use. The nitrate concentration in the Nebraska wells influenced 

the mean nitrate concentration for all reference wells in the 

glacial aquifer system, but the median, which is not affected 

by data extremes, was similar regardless of whether or not 

the estimate of the median included the data from Nebraska 

(0.13 mg/L as N or 0.10 mg/L as N, respectively). Nitrate concentrations in 75 percent of the wells were less than 0.49 mg/L 

as N. Therefore, the background nitrate concentration in the 

glacial aquifer system may vary geographically, but the nitrate 

concentration in more than half of the reference wells was less 

than 0.13 mg/L as N and in 75 percent of the reference wells 

was less than 0.49 mg/L as N. These values are slightly lower 

than the background concentration for all aquifers of 1.0 mg/L 

as N as determined by Nolan and Hitt (2003) based on the 75th

percentile of nitrate concentrations and slightly higher than 

the background concentration of 0.14 mg/L as N used in a 

study of the glacial aquifer system in Connecticut (Garabedian 

and others, 1998). Water in the reference wells was mostly 

(72 percent) oxic (dissolved-oxygen concentration greater than 

or equal to 0.5 mg/L as N), so the concentration of nitrate in 

reference wells was not unusually low for the glacial aquifer 

system. The concentration of 1.0 mg/L as N used by Nolan 

and Hitt (2003) is a conservative estimate of background 

concentration of nitrate that is applicable to the glacial aquifer 

system because nitrate concentrations in water from 97 percent 

of glacial aquifer system reference wells were below this 

value. Therefore, for the purposes of this report, water containing nitrate concentrations greater than 1.0 mg/L as N is 

considered to be impacted by human activities, although local 

differences in background concentration may exist, such as in 

Nebraska (fig. 3–1). 

Background concentration of nitrate in the glacial aquifer system is low (less than 1 mg/L as N).

The background concentration of nitrate in groundwater is used as a threshold value above which influence by 

anthropogenic sources is indicated. This value is important 

because it identifies areas where the nitrate concentration may 

be increasing and provides the lowest threshold for modeling the vulnerability of private wells to nitrate contamination used in this study. Relative background concentration 

can vary depending, in part, on land use, hydrogeology, and 

climate. Several nationwide assessments of nitrate concentration compared to background concentration have been done, 

but without regard to the type of aquifer. In one of the first 

assessments of background concentration of nitrate, Madison 

and Brunett (1985) chose 3 mg/L as N to represent the level 

above which human input is likely. A concentration less than 

0.2 mg/L as N represented natural background concentrations 

and a concentration between 0.21 and 3.0 mg/L as N was 

transitional, meaning the water may or may not be affected by 

human activity. Mueller and Helsel (1996), in their nationwide 

assessment of nitrate concentrations in groundwater from 

more than 10,000 wells, concluded that concentrations less 

than 2 mg/L as N were unaffected by human activity. More 

recently, Nolan and Hitt (2003) assessed background concentrations of nitrate in shallow, recently recharged groundwater 

beneath areas in the United States that are relatively unaffected 

by agricultural and urban land uses. Their assessment was 

based on 81 wells sampled as part of NAWQA in addition to 

320 of the wells used by Mueller and Helsel (1996). Nolan and 

Hitt (2003) concluded that 1 mg/L as N is a reasonable upperbound estimate of background concentration of nitrate. Data 

from 232 spring-water and 200 karst well-water samples in 

the Midwest were examined statistically by Panno and others 

(2006) to identify threshold nitrate concentrations by separating background from anomalous nitrate concentrations using 

cumulative probability plots. The thresholds of 2.5 mg/L as N 

(springs) and 2.1 mg/L as N (karst wells) were interpreted to 

represent the present-day background concentration of nitrate. 

Reference wells in the glacial aquifer system that are 

minimally impacted by human activities, including two to 

three monitoring wells in each of the 15 NAWQA studies, 

were installed to assess background groundwater quality. 
-1.0 -0.5 0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0 4.5 5.0 5.5

Background nitrate

concentration used

in this report

(1 milligram per

liter as nitrogen)

DEVIATION OF NITRATE CONCENTRATION FROM

BACKGROUND, IN MILLIGRAMS

PER LITER AS NITROGEN

Nebraska

Vermont, New

Hampshire, Massachusetts,

and Connecticut

Iowa and

Minnesota

Ohio and

Michigan

Maine, New Hampshire,

and Massachusetts

Washington

Wisconsin, Illinois,

and Indiana

Minnesota

Indiana

and Ohio

Wisconsin

GEOGRAPHIC AREA

Mean

Median

Deviation of nitrate concentration

from background

Figure 3-1.

0 5 10 15 20

10

12

4

2

3

10

4

15

10

6

NUMBER

OF SAMPLES

3.0 Background Nitrate Concentration 15

Figure 3–1. The graph shows the deviation of the mean and median nitrate concentrations from background in groundwater 

samples from reference wells selected to represent areas minimally affected by human activities. Mean and median nitrate 

concentrations in water from reference wells in Nebraska were greater than the background nitrate concentration used in this 

report (1 milligram per liter as nitrogen); however, mean and median nitrate concentrations in water from reference wells in other 

parts of the glacial aquifer system generally were less than the background concentration.
Glacial aquifer system

Mississippi embaymentT

a

exas coastal uplands

quifer system

Northern Atlantic

Coastal Plain

aquifer system

New England

crystalline-rock

aquifers

Hawaiian

volcanicrock

aquifers

Coastal lowlands

aquifer system

California

Coastal Basins

aquifers

Central Valley

aquifer system

Biscayne

aquifer

Cambrian-Ordovician

aquifer system

Basin and Range

basin-fill and

carbonate-rock

aquifers

Edwards-Trinity

aquifer system

Surficial

aquifer

system

(overlying

the Floridan) Floridan

aquifer

system

Glacial aquifer system

Early Mesozoic Basin

aquifers

Piedmont and Blue

Ridge carbonate- and

crystalline-rock aquifers

Valley and

Ridge

aquifers

Snake River Plain

basin-fill and basalticrock aquifers

High Plains

aquifer

Denver

Basin

aquifer

system

Columbia Plateau

basin-fill and basalticrock aquifers

Rio Grande

aquifer

system

Figure 4-1.

76

77

75

EXPLANATION

Private well – Number is nitrate

concentration, in milligrams per liter

as nitrogen

76

16 Relations That Affect the Probability and Prediction of Nitrate Concentration in Private Wells, Glacial Aquifer System

4.0 Comparison of Nitrate Concentration in the Glacial Aquifer System and 

Other Principal Aquifers

The USGS, as part of its NAWQA program, currently 

(2010) is studying the quality of water in principal aquifers of 

the United States (fig. 4–1). Sand and gravel aquifers generally are susceptible to nitrate contamination because of ease of 

transport of contaminants through the permeable aquifer materials. Among the principal aquifers currently being studied, 

the glacial aquifer system had one of the lowest median nitrate 

concentrations measured in private well water and the lowest 

median concentration (0.11 mg/L as N) among sand and gravel 

aquifers (fig. 4–2). 

In contrast, the two highest nitrate concentrations (77 and 

76 mg/L as N) in NAWQA wells in principal aquifers were 

measured in water from private wells in the glacial aquifer 

system (fig. 4–1). These concentrations were measured in 

Median nitrate concentration measured in water from private wells in the glacial aquifer system was 

lower than that in water from other sand and gravel aquifers.

groundwater from older, weathered glacial deposits in Illinois 

and in thick glacial deposits in North Dakota. The next highest 

nitrate concentration measured in water from private wells in 

all the principal aquifers studied was 75 mg/L as N in water 

from the Central Valley aquifer system, a principal aquifer in 

central California that consists of sand and gravel (fig. 4–2). 

Overall, the median nitrate concentration in water from 

private wells in the glacial aquifer system was low—even 

when compared to concentrations in water from other sand 

and gravel aquifers or bedrock aquifers (fig. 4–2, table 4–1). 

The low nitrate concentrations in water from the glacial 

aquifer system may be related to the extreme heterogeneity 

of the deposits comprising the aquifer system and associated 

soil processes (McMahon and Bohlke, 2005). Heterogeneity 

Figure 4–1. Locations of U.S. Geological Survey National Water-Quality Assessment (NAWQA) program regional assessments in 

principal aquifers in the United States. The glacial aquifer system covers about 953,000 square miles and parts of 26 States. The two 

highest concentrations of nitrate in private wells measured during the NAWQA program (1995–2005) were in water from the glacial 

aquifer system
EX

M27LinSinO

Interquartile

range

Mo

M

114 N

New

England

crystalline

Piedmont

carbonate

and

crystalline

California

Coastal

Basins

Central

Valley

Glacial

aquifer

system

High

Plains

Snake

River

Plain

Basin

and

Range

Floridan,

Biscayne,

and

Surficial

CambrianOrdovician Edwards Trinity Coastal lowlands Mississippi embayment/

Texas

coastal

uplands

Northern

Atlantic

Coastal

Plain

0.1

10

100

5

50

0.05

0.5

1

NITRATE , IN MILLIGRAMS PER LITER CONCENTRATION AS NITROGEN

AQUIFER

Columbia

Plateau

Crystalline

Crystalline

and

carbonates

Sand and

gravel

Sand and

gravel and

carbonates

Sandstone

Sandstone

and

carbonate

Semiconsolidated

sand

Sand and

gravel and

basalt

114 212 2 206 379 289 158 74 124 106 103 85 85 15 72

Figure 4–2. Although the glacial aquifer system had a larger range of nitrate plus nitrate concentration compared to other principal aquifers, the menitrate was relatively low. Concentration of nitrate plus nitrite as nitrogen measured in water from private and public-supply wells in selected principaquifers of different lithologies sampled as part of the U.S. Geological Survey National Water-Quality Assessment (NAWQA) Program (1995–2005) are 
18 Relations That Affect the Probability and Prediction of Nitrate Concentration in Private Wells, Glacial Aquifer System

Table 4–1. Mean nitrate concentrations are higher in sand and gravel aquifers than most other lithologies.

Nitrate concentration, in milligrams per liter as nitrogen

Primary 

lithology Aquifer Minimum 25th percentile Mean

50th 

percentile 

(median)

75th 

percentile Maximum Standard deviation

Number of 

samples

Crystalline New England crystallinerock aquifer0.05 0.05 0.96 0.10 0.86 8.96 1.77 114

Crystalline and 

carbonates

Piedmont and Blue 

Ridge carbonateand crystalline-rock 

aquifers

0.05 0.41 4.09 2.38 5.53 25 5.08 212

Sand and 

gravel

California Coastal Basins 

aquifers

3.51 4.62 5.74 5.74 6.86 7.97 3.16 2

Central Valley aquifer 

system

0.05 1.73 8.11 5.42 10.79 74.65 9.52 206

Glacial aquifer system 0.05 0.05 2.00 0.11 1.93 77 6.29 379

High Plains aquifer 0.05 1.38 3.46 2.32 4.44 20.34 3.30 289

Sand and 

gravel and 

basalt

Snake River Plain basinfill and basaltic-rock 

aquifers

0.05 0.67 3.31 1.6 3.88 58 5.88 158

Columbia Plateau basinfill and basaltic rock 

aquifers

0.05 2.05 9.08 5.9 11.75 60 11.19 74

Sand and 

gravel and 

carbonate

Basin and Range basinfill and carbonate-rock 

aquifers

0.05 0.84 4.08 1.87 3.85 32 6.03 124

Floridan 0.05 0.05 0.81 0.10 1.20 6.19 1.23 106

Sandstone Cambrian-Ordovician 0.05 0.05 2.73 0.15 4.05 23 4.80 103

Sandstone 

and 

carbonate

Edwards-Trinity aquifer 

system

0.05 0.12 1.11 0.76 1.57 7 1.34 85

Semi-consolidated sandCoastal lowlands aquifer 

system

0.05 0.05 0.20 0.05 0.11 2.30 0.38 85

Mississippi embayment/

Texas coastal uplands 

aquifer systems

0.05 0.05 1.54 0.66 2.09 6.8 2.19 15

Northern Atlantic 

Coastal Plain aquifer 

system

0.05 0.08 3.92 1.31 5.58 27.21 5.48 72
TOTA

L FERTILIZER AND MANURE

NITROGEN APPLIED TO LAND SURFACE

IN 1997, IN KILOGRAMS PER HECTARE

7

6

5

4

3

2

1

0 5 10 15 20

Increasing nitrogen load

Increasing nitrate attenuation capacity

MEAN APPARENT ELECTRON TRANSFER

FROM MANGANESE (IV) AND IRON (III)

REDUCTION, IN MICROMOLES PER LITER

Sand and gravel

Glacial deposits

Western

volcanics Semiconsolidated

sandstone

Carbonate/Sandstone

Carbonate/crystalline

EXPLANATION

Median nitrate concentration

Highest Lowest

Figure 4-3.

4.0 Comparison of Nitrate Concentration in the Glacial Aquifer System and Other Principal Aquifers 19

Figure 4–3. The glacial aquifer system receives a higher nitrogen load than most other 

aquifers, but the capacity for nitrogen attenuation also is greater. (From McMahon and 

Chapelle, 2008.)

of glacial sediments also is the main reason that redox varies 

more in the glacial aquifer system than in the other principal 

aquifers. The glacial aquifer system and the semi-consolidated 

sandstone aquifer in the southern coastal area of the United 

States had the largest percent of samples with mixed redox 

processes (McMahon and Chapelle, 2008). 

In recent studies, decadal-scale changes in nitrate concentration (Rupert, 2008) and redox characteristics (McMahon 

and Chapelle, 2008) were compared among aquifer lithologies. 

Although nitrogen fertilizer and manure application overlying 

the glacial aquifer system is higher than on most other aquifer 

systems (Ruddy and others, 2006), nitrate concentrations are 

low, possibly as a result of the large attenuation capacity of the 

glacial aquifer system (fig. 4–3). In some places, such as the 

unconsolidated deposits in alluvium that are part of the glacial 

aquifer system in Wisconsin (Saad, 2008), the aquifer system 

is less heterogeneous and contains minimal organic matter. 

In this part of Wisconsin, decadal changes in nitrate concentration in the glacial aquifer system generally were greater 

than those in lithologies of basalt, sandstone, and carbonate 

(Rupert, 2008). Additionally, decadal-scale changes in nitrate 

concentration were significantly smaller in water from wells 

with reduced conditions than in oxidized and mixed waters. 

The glacial aquifer system includes both environments: oxic 

conditions in deposits such as alluvium with gravel where 

decadal-scale changes in nitrate concentration are large and 

reducing conditions in deposits such as clay and silt deposits 

where decadal-scale changes in nitrate concentration are small. 
20 Relations That Affect the Probability and Prediction of Nitrate Concentration in Private Wells, Glacial Aquifer System

5.0 Nitrate Sources 

Correlation of sources to nitrate in water from private 

wells in the glacial aquifer system was weak on a regional 

scale. Nitrogen sources assessed in this study include land use 

(Nakagaki and others, 2007), fertilizer use (Ruddy and others, 

2006), atmospheric deposition (Ruddy and others, 2006), density of septic tanks or cesspools (U.S. Census Bureau, 1992), 

density of public sewers (U.S. Census Bureau, 1992), and 

population density (Hitt, 2003), all of which were compared to 

nitrate concentrations in private water supplies (table 5–1). 

 Land use was evaluated as an indicator for nitrate in 

private wells, but it was not significant (p > 0.05) (table 5–1). 

Examination of the 1,640-ft- radius area around a well can 

provide a broad characterization of local land use affecting 

the well (fig. 5–1), but it may not adequately characterize 

the land use in the entire capture area of the well, which may 

also affect the quality of water in the well (Lorenz and others, 

2003). DeSimone and others (2009) found that nitrate concentrations greater than 10 mg/L as N were most frequently 

detected in agricultural areas. Another potential indicator for 

nitrate is the 10-year mean (1992–2001) of nitrogen applied 

to farms (fig. 1–2), which was a significant relation for nitrate 

concentrations greater than background. The 10-year mean 

(1992-2001) of nitrogen applied to farms was not related 

to nitrate concentrations for all samples. The time period 

Nitrate detections in private wells were not strongly related to surface sources of nitrate. 

Nitrate in the environment has diverse sources and is 

affected by a suite of biological and chemical transformation 

processes (Follett and Hatfield, 2001). Nitrate can be released 

from the soils when organic matter is broken down or mineralized. Previous studies assessing near-surface nitrate concentrations in groundwater have found relations between nitrate 

concentration and point sources such as waste lagoons, septic 

systems, and feedlots, or nonpoint sources such as precipitation, mineralization in soils, and fertilizer application. Atmospheric sources of nitrogen in the northeastern United States 

are associated with vehicle emissions or industry (Elliott and 

others, 2007). A study of private-well water supplies in the 

unconsolidated surficial aquifer on the Delmarva Peninsula 

showed that agriculture was the most important influence on 

groundwater quality on a regional scale (Debrewer and others, 

2007). In England, it is estimated that more than 70 percent of 

the nitrate in natural waters is derived from agricultural land 

use (Lake and others, 2003). In a study of private wells in the 

glacial aquifer system, DeSimone and others (2009) state that 

nitrate concentration greater than 10 mg/L as N was primarily the result of human activities. Increases in agricultural use 

of fertilizer has been identified as a major source of nitrate to 

the glacial aquifer system (Puckett and Cowdery, 2002; Saad, 

2008). Thus, nitrate is a known contaminant in many aquifers.

Table 5–1. Comparison of nitrate concentration in groundwater from private wells to nitrogen sources 

indicates that atmospheric deposition of nitrogen, septic-system density, and sewer density are 

significantly related to nitrate concentration with 95 percent confidence, but the relations are weak.

[p, probability; <, less than; ft, feet; %, percent; values in boldface indicate significance at the 95-percent confidence level]

Variable Spearman 

correlation Significance 

10-year-mean nitrogen deposition -0.25 <0.0001

Septic-system density -0.13 0.01

Public-sewer density 0.13 0.01

Percent forested land use within 1,640 ft of the well 0.10 0.06

Percent agricultural land use within 1,640 ft of the well -0.10 0.06

Percent urban land use within 1,640 ft of the well 0.09 0.09

Forested land use greater than 50% within 1,640 ft of the well (binary) -0.08 0.10

10-year mean nitrogen fertilizer application to farms -0.07 0.16

Urban land use greater than 50% within 1,640 ft of the well (binary) 0.06 0.24

Agricultural land use greater than 50% within 1,640 ft of the well (binary) -0.04 0.43

Population density (for the year 2000) 0.02 0.72
PREDOMINANT LAND USE

WITHIN 1,640 FEET OF THE WELL

NITRATE

AS NITROGEN

CONCENTRATION,

IN MILLIGRAMS PER LITER

0.01

0.1

1

10

100

Urban Agriculture Forest Mixed

25 219 58 77

Reporting limit

EXPLANATION

Median (50th percentile)

25th percentile

75th percentile

Largest value within 1.5 times the

interquartile range

Smallest value within 1.5 times the

interquartile range

Outlier (extreme value)

Interquartile

range Mean (average value)

25 Number of samples

Figure 5-1.

5.0 Nitrate Sources 21

Figure 5–1. Median nitrate concentration was lowest in water from wells in areas where agriculture is the predominant land 

use within a 1,640 foot (500 meter) radius of the well, but nitrate concentrations in these areas also were the most variable. 

Median nitrate concentration was highest in areas where urban land use is predominant within a 1,640 foot radius of the well.

1992–2001 was selected because it coincides with the range of 

sampling dates in this study. 

Other sources may be related to nitrate concentration in private wells, but the variability of the data obscures 

these individual relations. Three sources were weakly but 

significantly (p<0.05) correlated to nitrate concentration in 

private wells—10-year mean nitrogen atmospheric deposition 

(-0.25 rho), septic-system density (-0.13 rho), and publicsewer density (0.13 rho). The relation of nitrate to wastewater 

was represented by the percentage of housing units served 

by sewers or using septic systems (table 5–1). The statistical result based on available data is counterintuitive if the 

nitrate source is sewers. The correlation results indicated that 

when the percentage of housing units served by public sewers 

increased, the nitrate concentration in private wells increased, 

but when the percentage of housing units using septic tanks 

or cesspools increased, the nitrate concentration in private 

wells decreased. The percentage of housing units served by 

sewers or septic systems was interpreted from 1990 census 

data (U.S. Census Bureau, 1992). There are several possible 

reasons for these counterintuitive relations. Public sewers 

generally are associated with areas of high population density 

(p<0.05 significance). Other sources of nitrate, including lawn 

fertilizer applications, could be present in these high population areas. In addition, new sewered or septic-system subdivisions are commonly constructed on land previously used for 

agriculture, and these areas may have subsurface drains that 

impede the transport of nitrate to groundwater. Although septic 

systems may not be a nitrate source on a regional scale, septic 

systems could affect groundwater quality locally. 

Another gauge of sewer and septic-system impact on 

groundwater is the presence of fecal indicators. Analyses for 

fecal indicator bacteria in samples of groundwater from 18 

principal aquifers indicated that counts of coliform bacteria 

were significantly lower in the glacial aquifer system than in 

other aquifer systems sampled as part of NAWQA (Embrey 

and Runkle, 2006). This may be another line of evidence indicating that sewers and septic systems are not major sources of 

nitrate to the glacial aquifer system on a regional scale.
Not to scale DEPTH BELOW LAND SURFACE, IN FEET

0

75

oldest

older

young

High nitrate concentration

Low nitrate concentration

Land surface

Water table

Small-diameter wells

Large-diameter

well

Figure 6.1-1.

water

water

water

Direction of

groundwater flow

22 Relations That Affect the Probability and Prediction of Nitrate Concentration in Private Wells, Glacial Aquifer System

6.0 Nitrate Transport 

6.1 Nitrate and Groundwater Age

The flow of groundwater in a regional, heterogeneous system like the glacial aquifer system is complex. 

Groundwater from wells in the glacial aquifer system commonly is a mixture of old and young water, 

regardless of depth, because “short-circuiting” allows mixing of older and younger groundwater over 

short distances and at various depths. 

Groundwater generally moves slowly from its point 

of recharge to its point of use or discharge. Groundwater 

age, defined as the time elapsed since recharge of water, has 

important implications for understanding the vulnerability and 

sustainability of the aquifer. Aquifers that are more vulnerable to contamination originating at the land surface generally 

contain more recently recharged water than aquifers that are 

less vulnerable (Clark and Fritz, 1997). In the Loess Hills, 

southwestern Iowa, time-of-travel calculations and tritiumconcentration data indicated that groundwater resides in these 

aquifers for decades (Tomer and Burkart, 2003). A study of 

nitrate and groundwater age of the glacial aquifer system in 

Canada showed that nitrate concentrations in groundwater 

recharged after 1960 contained nitrate in concentrations near 

10 mg/L as N, but older groundwater contained nitrate in 

concentrations less than 2.5 mg/L as N (Johnston and others, 

1998). The older groundwater was present under anaerobic 

conditions suitable for denitrification (the conversion of nitrate 

to nitrogen gas (N2)), indicating that the removal of dissolved 

oxygen (DO) may be a slow process taking decades or that the 

older groundwater may simply predate the period of intensive 

fertilizer application. 

Groundwater age can be determined by examining 

constituents that were introduced to the water at the time of 

recharge. For example, tritium is a radioactive tracer whose 

natural presence in groundwater is negligible but was found 

at high levels after nuclear-weapons testing occurred in the 

1950s. Tritium decays with a half-life of 12.32 years, so 

groundwater that does not contain detectable tritium is inferred 

to have recharged prior to 1955 (the beginning of atmospheric 

nuclear-weapons testing). In contrast, groundwater that contains tritium (above 4 tritium units (TU)) is inferred to include 

at least some water that recharged after 1955 (Clark and Fritz, 

1997). Groundwater-age indicators used in this report include 

tritium, tritium-helium, chlorofluorocarbons (CFCs), and 

CFCs with tritium. CFCs, which were introduced to the atmosphere with refrigeration and air conditioning, are useful tracers for groundwater age because these compounds are mostly 

resistant to degradation. Denitrification, a microbial-mediated 

process that transforms nitrate to nitrogen gas in oxygen-deficient environments, can affect groundwater-age estimates by 

degrading CFCs, thereby resulting in decreased concentrations 

of CFCs. A study in Canada found the denitrifying zone to be 

6 to 7 m deep in a glacial aquifer, a zone below which use of 

CFC data resulted in an overestimation of the groundwater 

age (Sebol and others, 2007). It is becoming more difficult to 

accurately date groundwater with tritium because the half-life 

is relatively short and the concentrations are small and diminishing. In this report, estimated dates of recharge in or prior 

to 1955 are grouped together as “old” and estimated dates of 

recharge after 1955 are “young”. Wells for which only tritium 

data are available are considered to contain recently recharged 

water if the tritium concentration was greater than 4 TU.

Most groundwater in private wells is of mixed age. A 

NAWQA study of public-supply wells has shown that mixing 

of groundwater of different ages occurs even in samples from 

wells with short screens (Eberts and others, 2006).Water in 

wells in close proximity to each other may have very different groundwater ages that depend on factors related to nitrate 

Figure 6.1–1. Groundwater flow to large- and small-diameter 

wells may represent recharge that was a mixture of groundwater 

of different ages (Sandra Eberts, U.S. Geological Survey, written 

commun., 2007). The large-diameter wells generally are shallow 

and contain “young” (recharged after 1955) water.
6.0 Nitrate Transport 23

transport, such as depth of the well within the aquifer system 

and changes in geologic material (fig. 6.1–1). Water from 

some private wells in which the groundwater was mostly old 

contained recently applied pesticides, indicating mixing of old 

and young groundwater (Warner and Morrow, 2007). In many 

instances, the older water contained relatively low concentrations of nitrate because of denitrification or recharge of the 

aquifer prior to land application of nitrogen-containing fertilizer. As a result, groundwater that is now used for private supply may contain only a small fraction of water that recharged 

during periods of intensive nitrate application. The contamination of recently recharged groundwater near the water table 

can be an additional concern because this water will eventually recharge the deeper aquifer.

Approximately 210 samples from private wells were 

analyzed for groundwater age and nitrate concentration (table 

6.1–1). Nitrate concentrations in young and old groundwater 

from private wells differed by an order of magnitude. The 

mean nitrate concentration in mostly young groundwater 

was 3.0 mg/L as N (median of 0.41 mg/L as N), whereas 

the mean nitrate concentration in old groundwater was 0.27 

mg/L as N (median of less than 0.05 mg/L as N). All private 

wells in the glacial aquifer system in which nitrate concentrations exceeded 4 mg/L as N contained predominantly young 

groundwater (fig. 6.1–2). Generally, the private-well water 

samples that are old groundwater were collected from deeper 

wells than the samples that are young groundwater, but mixing 

and “short-circuiting” (movement of groundwater along preferential flow paths) can occur. The mean depth of private wells 

in the glacial aquifer system with old water was 145 ft, and the 

mean depth of private wells with young water was 63 ft. Water 

from private wells that was young and oxic (DO greater than 

or equal to 0.5 mg/L) was more likely to have nitrate contamination than older and more reducing water (table 6.1–1). 

The nine samples in which nitrate concentrations were greater 

than or equal to the MCL of 10 mg/L as N were collected from 

recently recharged water (young) under oxic conditions. Old 

groundwater in private wells was mostly anoxic (fig. 6.1–3). 

Approximately 36 percent of the private wells sampled as part 

of this study contained older groundwater. Most of the private 

wells in which nitrate concentrations are greater than 1 mg/L 

as N contained young, oxic groundwater (table 6.1–1). The 

wells that contain young groundwater under anoxic conditions (DO less than 0.5 mg/L) may be subject to denitrification 

that could decrease the nitrate concentration. The necessary 

conditions for denitrification include (1) presence of specific 

bacteria (microbial denitrifiers); (2) availability of electron 

donors such as organic carbon; (3) low DO concentration; 

and (4) availability of nitrate as nitrogen (Follett, 2001). In 

the glacial aquifer system, bacteria are present. The availability of organic carbon is greater in areas with buried soils 

(paleosols), less sand, and more clay or peat or other organic 

Table 6.1–1. Most detections of nitrate in private wells were in “young” (recently recharged) groundwater that is oxic. In this study, 

only samples of young, oxic groundwater contained nitrate at concentrations greater than 10 milligrams per liter as nitrogen.

[<=, less than or equal to; >, greater than; >=, greater than or equal to; mg/L, milligrams per liter; N, nitrogen; <, less than]

Number of samples with specified nitrate concentration

Oxidationreduction state

Number of 

samples in each 

groundwaterage category

Percent of 

samples in each 

groundwaterage category

Nitrate

concentration

<= 1 mg/L

as N

Nitrate

concentration

> 1 mg/L

as N1

Nitrate

concentration

>= 10 mg/L

as N

Nitrate

concentration

<= 1 mg/L

as N

Nitrate

concentration

> 1 mg/L

as N1

Nitrate

concentration

>= 10 mg/L

as N

Median

nitrate 

concentration

 (mg/L as N)

Young Old Young Old Young Old Young Old

Oxic

(dissolved 

oxygen 

concentration 

>= 0.5 mg/L)

82 22 60 30 34 48 9 16 6 0 1.95 0.05

Anoxic

(dissolved 

oxygen 

concentration 

< 0.5 mg/L)

55 51 40 70 46 9 0 51 0 0 0.05 0.05

1

. The set of samples in which nitrate concentrations are greater than 1 mg/L as N contains the set of samples in which nitrate concentrations are greater than 10 

mg/L as N.
0

20

40

60

80

100

Not

detected0 - 1

>1-2

>2-3

>3-4

>4-5

>5-6

>6-7

>7-8

>8-9

>9-10

>10

NITRATE CONCENTRATION, IN

MILLIGRAMS PER LITER AS NITROGEN

PERCENT OF WELLS

Old

Young

> Greater than

Age of recharge water

EXPLANATION

Figure 6.1-2.

9 5 1 1 1 4 10 8 9 15

45

105

NUMBER

OF SAMPLES

120

100

80

60

40

20

0

24 Relations That Affect the Probability and Prediction of Nitrate Concentration in Private Wells, Glacial Aquifer System

matter. Dissolved oxygen concentrations tend to decrease 

with increasing residence time and depth (Puckett and others, 

2002). Additionally, Puckett and others (2002) found that 

riparian-zone groundwater older than 8 years in the glacial 

aquifer system was extremely oxygen deficient (O2 less than 

0.51 mg/L). 

There were differences in groundwater age for wells of 

the same depth in different framework areas that likely result 

from the heterogeneity of the aquifer across the northern 

United States. No samples from private wells in the Eastern area of the glacial aquifer system were analyzed for age 

indicators. Samples from the West-central area of the glacial 

aquifer system were a mixture of nearly equal amounts of 

old and young groundwater (fig. 6.1–4). The groundwater 

from private wells in the West area was mostly young water, 

whereas samples from the West-Central area contained more 

young than old groundwater. Private-well networks in two 

local areas of the glacial aquifer system, central Illinois and 

northeastern Nebraska, contained mostly old water. In Illinois, 

this water is in a deep, buried bedrock valley aquifer; in northeastern Nebraska, it is in poorly permeable glacial till (Stanton 

and others, 2007). Finally, groundwater age indicates the time 

it takes recharge to travel to a well and this varies with location and is related to redox conditions. 

Figure 6.1–2. All samples in which nitrate concentrations were greater 

than 4 milligrams per liter as nitrogen were from private wells containing only 

groundwater that was recharged after 1955 (“young”).
Young (after 1955) Old (before 1955)

AGE OF GROUNDWATER RECHARGE

0

20

40

60

80

100

PERCENT OF WELLS

EXPLANATION

40 percent

(55 wells)

60 percent

(82 wells)

30 percent

(22 wells)

70 percent

(51 wells)

Oxic (dissolved-oxygen greater than

or equal to 0.5 milligrams per liter)

concentration

Anoxic (dissolved-oxygen less than

0.5 milligrams per liter)

concentration

Figure 6.1-3.

0

20

40

60

80

100

FRAMEWORK AREA

PERCENT OF WELLS

Old

Young

West West-central Central EastNo data are available

U n i t e d S t a t e s

C a n a d a

A l a s k a

WestCentral

Central

East

West

A.

B.

Figure 6.1-4.

6.0 Nitrate Transport 25

Figure 6.1–4. (A) The glacial aquifer system in the 

United States has been divided into four framework 

areas on the basis of physiography and source of 

aquifer material. (B) Private wells in these areas 

contained a mixture of old and young groundwater. 

The wells in the West area contained mostly “young” 

(recently recharged) groundwater.

Figure 6.1–3. Groundwater recharged after 1955 (“young”) 

consisted of a higher percentage of oxic water than groundwater 

recharged before 1955 (“old”). Nitrate is mobile under oxic 

conditions.
26 Relations That Affect the Probability and Prediction of Nitrate Concentration in Private Wells, Glacial Aquifer System

6.0 Nitrate Transport—Continued 

6.2 Nitrate Concentrations and Depth

(table 6.2–1). Additionally, the shallower groundwater was 

mostly oxic, whereas the deeper groundwater was commonly 

anoxic and conditions are conducive to denitrification. Therefore, owners of shallow private wells need to be aware of the 

potential for nitrate contamination. 

Regardless of the source of nitrogen, geochemical 

processes such as redox can limit nitrate concentration at 

depth. Redox is a major factor in denitrification, which has 

been shown to decrease the nitrate concentration in the glacial 

aquifer system (McMahon and Chapelle, 2008: Tesoriero and 

others, 2007; Puckett and others, 2002). Therefore, although 

fertilizer application above the glacial aquifer system may be 

large, redox changes with depth in the aquifer can facilitate 

denitrification and consequently, decrease the concentration of nitrate. DO concentration can be easily measured in 

the field to help understand geochemical conditions in the 

aquifer (Lewis, 2006). McMahon and Chapelle (2008) found 

that nitrate concentrations were significantly higher in water 

samples in which DO was greater than or equal to 0.5 mg/L 

than in samples containing DO less than 0.5 mg/L. Deeper 

wells tend to contain older water with less DO; therefore, 

nitrate concentrations also tend to be low. Seventy percent 

of the oxic groundwater samples from private wells in the 

glacial aquifer system were from wells that are 75 ft deep or 

less (table 6.2–1). All concentrations of nitrate greater than the 

MCL of 10 mg/L as N were in samples from private wells that 

are 75 ft deep or less. 

Table 6.2–1. Shallow wells (75 feet deep or less) generally were associated with higher nitrate concentration, younger groundwater, 

and more oxic conditions than wells deeper than 75 feet.

[mg/L, milligrams per liter; N, nitrogen; DO, dissolved-oxygen concentration; >=, greater than or equal to; <, less than; >, greater than]

Depth range 

(feet below 

land surface)

Number of 

wells

Mean nitrate 

concentration

(mg/L as N)

Maximum 

nitrate 

concentration

(mg/L as N)

Percent of 

wells with 

young 

groundwater in 

depth range

Percent of 

wells with old 

groundwater in 

depth range

Percent of 

wells from 

which all 

samples are 

oxic

(DO>=0.5 mg/L)

Percent of 

wells from 

which all 

samples are 

anoxic

(DO <0.5 mg/L)

0–75 194 3.17 77 74 18 70 39

>75 184 0.77 9.11 26 82 30 61

Nitrate concentrations in water from private wells varied vertically more than areally.

The glacial aquifer system is the shallowest aquifer in an 

area where multiple stacked aquifers are used for supply. For 

example, the Cambrian-Ordovician aquifer is a principal aquifer underlying the glacial aquifer system in the Midwest, and 

the New England crystalline-rock aquifers underlie the glacial 

aquifer system in the Northeast. Generally, because privatewell owners have neither the need nor the resources to drill 

deep wells (greater than 500 ft) into the underlying aquifers, 

their wells are screened in the shallow glacial material, except 

in New England, where private wells are commonly drilled 

into bedrock. 

In the glacial aquifer system, nitrate concentrations 

increased as well depth decreased (fig. 6.2–1). Approximately 

half of the private wells in this study are less than 75 ft deep. 

The private wells within 20 ft of the land surface are most susceptible to high nitrate concentrations. The mean nitrate concentration in water from the private wells that are 20 ft deep or 

less (9.6 mg/L) was close to the MCL, but these wells account 

for only 1 percent of the wells in the study (fig. 6.2–2). 

Nitrate concentrations were higher and more variable in 

water from private wells that are 75 ft deep or less (standard 

deviation, 8.5 mg/L; maximum concentration, 77 mg/L as N) 

than in wells that are deeper than 75 ft (standard deviation, 

1.5 mg/L; maximum concentration, 9.1 mg/L as N at 78 ft). 

Several factors contribute to this difference. Most private 

wells less than 75 ft deep draw young groundwater that likely 

was recharged during times of greater fertilizer application 

rather than older water that is typically tapped by deeper wells 
30

40

50

60

70

80

90

Greater than 1

Greater than 2

Greater than 3

Greater than 4

Greater than 5

Greater than 6

Greater than 7

Greater than 8

Greater than 9

Greater than 10

WELL DEPTH, IN FEET

BELOW LAND SURFACE

NITRATE CONCENTRATION, IN

MILLIGRAMS PER LITER AS NITROGEN

Mean well depth

Median well depth

Figure 6.2-1.

0

40

80

120

160

NUMBER

OF WELLS

122

91

68

50

36 26 22 21 19 14

Figure 6.2-2.

0

40

80

NUMBER

OF WELLS

68 76

45

19 21 13 14 14

38

20

60

100

64

6

Mean nitrate concentration

Median nitrate concentration

0-20

21-4041-6061-80

81-100

101-120121-140141-160161-180181-200

Greater

than 200

WELL DEPTH RANGE, IN FEET

BELOW LAND SURFACE

0

2

4

6

8

10

NITRATE CONCENTRATION,

IN MILLIGRAMS PER

LITER AS NITROGEN

6.0 Nitrate Transport 27

Figure 6.2–2. Mean and median nitrate concentrations 

were highest in water from private wells less than 20 

feet deep, but most private wells were more than 60 feet 

deep.

Figure 6.2–1. The difference in mean and median well depth 

shows the large variability of well depths associated with nitrate 

concentrations less than 6 milligrams per liter. The samples with 

concentrations greater than 6 milligrams per liter were from 

relatively shallow wells.

Locally, heterogeneity of the glacial deposits makes it 

difficult to discern patterns of nitrate concentration. McMahon 

and Chapelle (2008) found that private wells in the glacial 

aquifer system, even those with short well-screen lengths, had 

a mixed redox signature resulting from closely spaced zones 

of differing redox conditions. These redox zones are often 

related to the amount of fine or coarse material overlying the 

aquifer. The mixed redox signature may be caused by localized zones of organic carbon and (or) slow groundwater-flow 

velocity. If the redox signature is mixed, then the likelihood 

of nitrate detection is mixed. Although groundwater generally becomes more reducing with depth, depth is not always a 

good indication of groundwater age because the characteristics 

of the aquifer materials affect the velocity of groundwater 

flow. In the Midwest, till is commonly clayey and poorly 

permeable, whereas the coarser-grained outwash and alluvial deposits have a wider range of permeability (Tomer and 

Burkart, 2003). Even within a short well screen or between 

wells in close proximity to each other, there can be large differences in the amount of clay and sand. This heterogeneity 

of glacial deposits is helpful to private well owners concerned 

about nitrate contamination because it implies that redox may 

change quickly over short distances and, consequently, nitrate 

may not persist for long distances along flow paths in the 

glacial aquifer system. Regional patterns of decreasing nitrate 

concentration, increasing groundwater age, and changing 

redox with depth have been observed, but local heterogeneity 

of the aquifer materials makes it difficult to predict the probability of high nitrate concentration at a given well.
0

25

50

75

100

125

150

175

200

225

NUMBER OF WELLS

PREDOMINANT LAND USE WITHIN 1,640 FEET OF THE WELL

Agriculture Urban Forest Mixed

Figure 7.1-1.

28 Relations That Affect the Probability and Prediction of Nitrate Concentration in Private Wells, Glacial Aquifer System

7.0 Nitrate Concentrations in Private, Public, and Monitoring Wells

7.1 Nitrate Concentrations in Water from Private Supplies

The advantage of assessing only private wells is that 

it implicitly recognizes that the type of well will affect the 

water-quality results because well construction and well siting 

tend to differ among well types (Alley, 1993). An additional 

sampling-design consideration is the selection of which private 

wells to include in the regional assessment. The 379 private 

wells included in this study were selected because the wells 

represent local groundwater use. Differences in data-collection 

objectives and analytical methods can bias a regional assessment, but the consistency of the NAWQA sampling design and 

protocols assures similarity in random selection and analysis 

(Bartholomay and others, 2007). The mean and median nitrate 

concentrations (7.8 and 5.5 mg/L as N, respectively) were 

higher in water from private wells in networks designed to 

assess the effects of land use on water quality than in water 

from private wells in networks designed to assess the general 

water quality in the aquifer (2.0 and 0.1 mg/L as N, respectively). Nitrate concentrations in water from private wells of 

networks designed to assess effects of agricultural land use 

were strongly correlated with land-use practices near the well 

(agricultural land as a percentage of land use within 1,640 ft 

of the well). In water from private wells selected to assess 

land-use impacts, high concentrations of nitrate (greater than 

7 mg/L as N) were found at all depths, but not in water from 

private wells selected to assess the overall quality of water in 

the aquifer system. In contrast, nitrate concentration was not 

significantly (p<0.05) correlated with percent agricultural land 

use surrounding private wells selected to assess the quality 

of water in major aquifers, even though more than 50 percent 

of the area surrounding those private wells was agricultural 

(78 percent of the 379 wells in this study) (fig. 7.1–1). Therefore, the land use that affects the concentration of nitrate in 

private wells may be from farther than 1,640 ft from the well, 

or the well may draw older groundwater unaffected by recent 

land use. In regional water-quality analyses, well type and the 

purpose of sampling should be considered before selecting the 

wells. Thus, only data from the 379 private wells sampled for 

the purpose of regional assessment of major aquifers are used 

in this report. Nitrate was not a potential health concern at 

most of the 379 private wells sampled (fig. 7.1–2). The mean 

and median nitrate concentrations in water from these private wells (2.0 mg/L and 0.11 mg/L as N, respectively) were 

below the USEPA MCL for nitrate (10 mg/L as N). Fewer than 

5 percent of the wells contained groundwater with nitrate at 

concentrations above 10 mg/L as N, which is a known human 

health concern (fig. 7.1–2). This is unexpected because the 

nitrogen load at land surface above the glacial aquifer system 

is higher than that above most other regional aquifers (McMahon and Chapelle, 2008).

The distribution of nitrate in private wells of the glacial 

aquifer system differed by framework area (fig. 1–3, 7.1–3). 

The wells in the West-Central area had longer open intervals 

(almost 13 ft on average) than the wells in the other framework areas. The West-central area differs from the other 

framework areas in that the region consists predominantly of 

irrigated agricultural land underlain by clayey till (Arnold and 

others, 2008). The cyclic pumping and recharging of irrigation water in parts of this area may concentrate nitrate in the 

groundwater over time. Mean well depths and casing diameters of the private wells were similar among the framework 

areas. Large-diameter (10- to 45-in.) wells were sampled in 

all framework areas except the West, where the largest casing 

diameter was 6 in.

Nitrate concentrations varied throughout the extent of the 

glacial aquifer system but there was not a distinct areal pattern 

of elevated nitrate in water from private wells (fig. 11–1). 

Figure 7.1–1. Agriculture was the predominant land use within 

1,640 feet of the private wells sampled.

Although overall nitrate concentrations in water from private wells in the glacial aquifer system were low 

relative to the MCL, concentrations were highly variable over short distances and with depth.
Figure 7.1-2.

70%

26%

4%

Not likely a humanhealth concern

Approaching

concentration of

potential humanhealth concern

Potential human-health concern

7.5

6.0

4.5

3.0

1.5

0

MEAN NITROGEN FERTILIZER APPLIED TO FARMS (1992-2001),

IN MILLION KILOGRAMS PER YEAR

NITRATE CONCENTRATION IN GROUNDWATER,

IN MILLIGRAMS PER LITER AS NITROGEN

East Central West- West

central

FRAMEWORK AREA

71 174 83 51

0.01

0.1

10

0.05

0.5

1

5

50

100

Common detection limit

Number of samples

Median (50th percentile)

25th percentile

75th percentile

Largest value within 1.5

times the interquartile range

Smallest value within 1.5

times the interquartile range

Outlier (extreme value)

Interquartile

range

174

EXPLANATION

Mean nitrogen

fertilizer applied to farms

(1992-2001), in million

kilograms per year. Data

are not available for Alaska.

Mean (average value)

7.0 Nitrate Concentrations in Private, Public, and Monitoring Wells 29

Figure 7.1–2. Nitrate concentrations in most 

of the private wells sampled in this study were 

less than the background nitrate concentration 

of 1 milligram per liter as nitrogen (<1 mg/L as N). 

The background nitrate concentration of <1 mg/L 

as N is less than one-tenth of the U.S Environmental 

Protection Agency Maximum Contaminant Level 

(MCL) of 10 mg/L as N; such concentrations are 

not likely a human-health concern. In this study, 

samples with nitrate concentrations between 

1 and 10 mg/L as N are considered to approach 

concentrations of potential human-health concern, 

and nitrate concentrations greater than the MCL 

of 10 mg/L as N are of potential human-health 

concern.

Figure 7.1–3. The Central framework area of the glacial aquifer system had a high nitrate application rate but a low median 

concentration of nitrate in groundwater from private wells. The Central and West-central areas had a large variability in nitrate 

concentrations. (Modified from Ruddy and others, 2006.)
YEAR OF WELL CONSTRUCTION

0

20

40

60

80

100

120

Prior to

1980

1980-1984 1985-1989 1990-1994 1995-1999 2000

and after

NUMBER OF WELLS

Figure 7.1-4.

0

1

2

3

NITRATE CONCENTRATION, IN MILLIGRAMS

PER LITER AS NITROGEN

Mean nitrate

concentration

Median nitrate

concentration

30 Relations That Affect the Probability and Prediction of Nitrate Concentration in Private Wells, Glacial Aquifer System

Figure 7.1–4. Most private wells sampled in this study were constructed 

during 1990-99 and the water from these wells sampled by NAWQA had the 

highest mean nitrate concentration compared to water from other private wells.

In an exploratory data analysis, “hot-spot differentiation” 

(Environmental Systems Research Institute, 2008) was used 

initially to indicate geographic areas where nitrate concentrations were more than one or two standard deviations higher or 

lower than surrounding concentrations. Results of this analysis 

showed that west-central Illinois and east-central North 

Dakota areas are geostatistically different from other areas. 

High nitrate concentrations tend to be clustered in these areas 

compared to other parts of the glacial aquifer system. These 

same areas have relatively high 10-year-mean nitrate fertilizer 

application rates. In other areas of the glacial aquifer system, 

such as in the East area, nitrate concentration in water from 

private wells was lower than in the rest of the glacial aquifer 

system. Although there are areal differences in nitrate concentrations in water from private wells, these differences do not 

occur in a distinct pattern.

The glacial aquifer system is different from other 

unconsolidated aquifers because of the abundance of clay 

and organic layers in the aquifer. The heterogeneity of glacial 

sediments results in highly variable rates of water recharge 

and, consequently, nitrate movement through the aquifer. The 

heterogeneity is one of the most important factors affecting 

variability in flow of water to the wells in the glacial aquifer 

system. The highest mean and median nitrate concentrations 

(3.6 and 0.63 mg/L as N, respectively) were in groundwater in 

the West-central framework area, which includes Iowa, Minnesota, Nebraska, and North Dakota. 

Well construction also is important in determining the 

vulnerability of private wells in the glacial aquifer system to 

contamination with nitrate. Most of the private wells sampled 

for this study were constructed during 1990–2000, and it 

is water from these wells in which the mean concentration 

of nitrate was highest (fig. 7.1–4). Open-interval diameters 

in sampled private wells ranged from 1.25 to 45 in., but 

most were 6 in. Twenty-four wells had very large diameters 

(24–45 in.); most of these wells were constructed between 

1990 and 2000. The larger-diameter wells are built to maximize groundwater storage within the well bore. Networks with 
7.0 Nitrate Concentrations in Private, Public, and Monitoring Wells 31

large-diameter wells (greater than 24 in.) are in Connecticut, 

Illinois, Iowa, Minnesota, and North Dakota.

Even in areas with poorly permeable glacial sediments 

and low transmissivity, the glacial aquifer system is used for 

drinking-water supply, as indicated by the large-diameter 

wells in these areas. In Illinois, the southern half of the State 

is an area of thin glacial sediments, and more than 50 percent of the private wells in this area are large-diameter wells 

(McKenna and Keefer, 1991). Although studies have shown 

that rural, private well construction and placement are factors 

that facilitate nitrate contamination of wells, it is important to 

note that well construction and placement are not sources of 

contamination. 

The depth to water in sampled private wells varied. The 

deepest water level was 202 ft below land surface, but the 

median water level was 27 ft below land surface. Water levels 

were deepest in wells in the West and West-central framework areas (Nebraska, Kansas, Washington, and Alaska) or in 

the deep glacial aquifer system in the Central area (Illinois). 

Although the glacial deposits are unconsolidated, the depth 

to water is not always equivalent to the depth of the water 

table because large amounts of overlying clay (mostly in the 

Midwest) can confine the water and cause differences in the 

hydraulic head or perched groundwater.

The relation of nitrate concentration to potential explanatory variables was complex because of the heterogeneity 

across the aquifer. The variables with the strongest correlations to nitrate concentration in private wells were soils (bulk 

density of soils, -0.29; percent alfisols, -0.21; percent organic 

matter, -0.14; percent silt content, 0.16; mean depth to soil 

saturation, 0.25), land-use infrastructure (percent of houses 

with drilled wells, -0.26; percent of houses with dug wells, 

0.12; percent of houses served by septic systems, -0.13; 

percent of houses served by public sewers, 0.13), depth (well 

depth, -0.24; depth to top of open interval, -0.24), well construction (diameter of open interval, 0.23; open interval length, 

0.13) and 10-year-mean atmospheric nitrate deposition (-0.25). 
Agriculture Urban Forest Mixed

10

20

30

40

50

60

70

PERCENT OF WELLS

0

Private

Public supply

Monitoring

Well type

PREDOMINANT LAND USE WITHIN 1,640 FEET OF THE WELL

32 Relations That Affect the Probability and Prediction of Nitrate Concentration in Private Wells, Glacial Aquifer System

7.2 Comparison of Nitrate Concentrations in Water from Private, Public, and Monitoring Wells

7.0 Nitrate Concentrations in Private, Public, and Monitoring Wells

Nitrate concentration was significantly lower in groundwater from private wells than in groundwater 

from monitoring wells.

Public, private, and monitoring wells sampled as part 

of NAWQA differ with respect to well-construction characteristics (table 7.2–1). The median well-casing diameter and 

screen length were greater for public-supply wells (18 in. 

and 10 ft) than for private wells (6 in. and 5 ft) or monitoring wells (2 in. and 5 ft). Public-supply wells generally are 

open to more of the aquifer than private or monitoring wells 

so there is the potential to draw water from a large zone. The 

large diameter of public-supply wells is typically intended 

to increase production capacity, whereas in private wells the 

large diameter is commonly used in poorly producing areas to 

enhance water storage. The depths of public and private wells 

that were sampled as part of this study were similar (mean 

91 and 96 ft below land surface, respectively; median 62 and 

75 ft below land surface, respectively) (table 7.2–1). However, the private wells were cased at greater depths than the 

public wells, as shown by the median depth to the top of the 

open interval (71 ft and 53 ft, respectively) and generally had 

a shorter open interval than the public wells (5 ft and 10 ft, 

respectively). Because the monitoring wells were shallower 

(mean, 29 ft; median, 25 ft below land surface) than the other 

two well types, the open interval may be near to surface 

sources of nitrate.

More than 50 percent of the sampled private wells were 

surrounded by agricultural land use. The nature of a private 

well implies individual ownership; therefore, these wells are 

typically in isolated areas such as rural areas. Most of the 

sampled public-supply wells were in mixed-land-use areas 

(fig. 7.2–1). A majority of the sampled monitoring wells, like 

the private wells, were in agricultural areas. The sampled 

monitoring and private wells were similar with respect to surrounding land use (within 1,640 ft of the well), but differ with 

respect to depth and well-construction characteristics.

The differences in nitrate concentrations among private, 

public, and monitoring wells reflect the purpose of the well 

installation and well-construction characteristics. The nitrate 

concentration was higher in recently recharged groundwater 

from monitoring wells than in groundwater from private wells 

(table 7.2–1). The lower nitrate concentrations in the water 

from private wells may result from denitrification, dilution, or 

constraints on nitrate transport from land surface to the deeper 

private wells. The mean and median nitrate concentrations 

in water from public supplies were similar, indicating little 

variability; in contrast, the mean and median nitrate concentrations in water from private supplies were different, indicating 

greater variability. 

Groundwater used for private supply contained a larger 

percentage of old water than groundwater from public or 

monitoring wells (table 7.2–2). This means that public and 

monitoring wells are pulling in recharge water that was 

more recently in contact with the land surface and potential 

nitrate sources. Public-supply wells are known to withdraw 

groundwater of multiple ages even over short screen lengths 

(Eberts and others, 2006) because of the large volume of water 

withdrawn. The NAWQA studies on susceptibility of publicwater supplies found that from 20 to nearly 100 percent of 

water produced from these wells was young groundwater, and 

drawdown by short circuiting may be the primary pathway by 

which contaminants enter the wells (Eberts and others, 2006). 

Similar mixing is likely to occur in private wells, but on a 

smaller scale.

Figure 7.2–1 Most private and monitoring wells sampled were 

located in agricultural settings, whereas most public-supply wells 

sampled were in forested or mixed-land-use areas. The publicsupply wells sampled by NAWQA were mostly in the northeastern 

United States, where forest and mixed land use are common. 
7.0 Nitrate Concentrations in Private, Public, and Monitoring Wells 33

Table 7.2–1. Private, public-supply, and monitoring wells in the glacial aquifer system differ with 

respect to groundwater nitrate concentration and well-construction characteristics.

Well type

Statistic Private Public supply Monitoring All well types

Nitrate concentration, in milligrams per liter as nitrogen

Minimum 0.05 0.05 0.05 0.05

Mean 2.00 0.69 4.7 3.8

Median 0.11 0.56 2.0 0.89

Maximum 77 2.5 70 77

Number of wells 379 41 870 1,290

Well depth, in feet below land surface

Minimum 12 27 7 7

Mean 96.23 91.09 28.69 50.48

Median 75 62.4 24.61 32

Maximum 365 420 137 420

Number of wells 378 41 870 1,289

Depth to top of open interval, in feet below land surface

Minimum 3 21 2 2

Mean 91.06 77.61 23.05 43.55

Median 71 53.2 19 25

Maximum 357 348 113 357

Number of wells 347 38 867 1,252

Length of open interval, in feet

Minimum 0 3 2 0

Mean 7.87 14.11 5.12 6.11

Median 8 15 5 5

Maximum 78 72 36.6 78

Number of wells 314 38 867 1,219

Open-interval diameter, in inches

Minimum 1.25 4 0.17 0.17

Mean 7.05 15.56 2.08 3.95

Median 5.63 16 2 2

Maximum 45 24 4 45

Number of wells 371 40 867 1,278
110°00 ́ 90°00 ́ 80°00 ́ 

45°00 ́35°00 ́

120°00 ́ 100°00 ́

40°00 ́

C A N A D A

ALASKA CANADA

WA

OR

ID

MT

WY

CO

ND

SD

NE

KS

IA

MN

WI

IL

MO

IN

MI

KY

WV

VA

PA

N

OH 

Pacific Ocean

Lake Superior

Lake Michigan

LakeHuron

Lake Erie

Lake Ontario

U N I T E D S T A T E S

Ain

Aen

Driftless area

Base from U.S. Geological Survey 1:2,000,000 Digital DataAlbers Equal-Area Conic projection, standard parallels 29° 30’and 45° 30’, central meridian -96°, latitude of origin 23°

0 100 MILES0 100 KILOMETERS N

EXPLANATION

Glacial aquifer system extent

(approximate)

PrivatePublic supply

Monitoring

Well type

Figure 7.2–2. Private and monitoring wells in the glacial aquifer system sampled as part of the U.S. Geological Survey National Water-Quality Assesgeographic distribution. More public-supply wells were sampled in the East framework area than in other framework areas.
12%

36%

0 6 12 18 24 30 36 42 48 54 60 66 72 78

100

80

70

60

90

50

40

30

20

10

0

PERCEN

T OF WELLS

NITRATE CONCENTRATION, IN MILLIGRAMS PER LITER AS NITROGEN

75th percentile

50th percentile

25th percentile

Private

Public supply

Monitoring

7.0 Nitrate Concentrations in Private, Public, and Monitoring Wells 35

Figure 7.2–3 Survival curves were plotted to examine the difference in measured nitrate concentrations among 

private, public-supply, and monitoring wells in the glacial aquifer system. Nitrate concentrations exceeded 4 

milligrams per liter as nitrogen in about 12 percent of private wells, 0 percent of public-supply wells, and 36 percent 

of monitoring wells.

Kruskal-Wallis rank sum tests showed a statistically 

significant (95-percent confidence) difference in median 

nitrate concentrations between monitoring (1.97 mg/L as N) 

and private wells (0.11 mg/L as N). There was no statistical 

difference in median nitrate concentrations between private 

and public-supply wells although most public-supply wells 

sampled by NAWQA are in the east (fig. 7.2–2). Additionally, survival curves were plotted to examine the difference 

between nitrate concentrations measured in water from 

private, public-supply, and monitoring wells in the glacial 

aquifer system. The survival curves indicate that, in the glacial 

aquifer system, nitrate concentrations exceeded 4 mg/L as N in 

about 12 percent of private wells and 36 percent of monitoring 

wells (fig. 7.2–3). Therefore, the results of this study indicate 

some differences in nitrate concentration with well type, especially between shallow monitoring wells and deeper public or 

private wells.

Table 7.2–2. Samples from all well types in the glacial aquifer system represent a mixture of 

groundwater of different ages.

Well type

Number of wells for 

which age data are 

available

Percent of wells 

with old water

Percent of wells 

with young water

Mean depth, 

in feet below

land surface

Private 212 35 65 92

Public 28 18 82 124

Monitoring 632 16 84 29
36 Relations That Affect the Probability and Prediction of Nitrate Concentration in Private Wells, Glacial Aquifer System

Model predictions of nitrate concentration based on nationwide water-quality data are higher than 

nitrate concentrations measured in private wells in the glacial aquifer system

8.0 Statistical Models of Nitrate Concentration

Nitrate concentrations in water from private wells in the 

glacial aquifer system were compared to results of a nationwide logistic regression model that predicts the probability of 

occurrence of nitrate concentrations greater than 4 mg/L as 

N in recently recharged (shallow) groundwater in all aquifers 

across the United States (Nolan, 2001; Nolan and others, 

2002). The nationwide model (Nolan and others, 2002) was 

based on 1992–95 nitrate-concentration data from shallow 

monitoring wells in all principal aquifers of the United States. 

The variables used in the nationwide logistic regression 

models (Nolan and Hitt, 2003; Nolan and Hitt, 2006) represent 

source, transport, and attenuation of nitrate (table 8–1). The 

nationwide models used data from all aquifers and the predictions do not fit data for private wells in the glacial aquifer 

system. 

The fit of the nationwide model was assessed in four 

ways (fig. 8–1). First, the model was assessed by determining 

the probability of nitrate concentration greater than 4 mg/L as 

N for each private well in the glacial aquifer system, which 

was determined by spatially overlaying the private wells on 

the probability map (Nolan and others, 2002) and comparing 

to observed results. The results of this spatial overlay showed 

that the nationwide logistic regression model over-predicted 

the probability of nitrate contamination in the private wells of 

the glacial aquifer system (fig. 8–1A). It is important to note 

that the nationwide model was developed using data from 

monitoring wells that are shallower than the private wells 

assessed in this report (median depth to water in private wells 

in the glacial aquifer system is 39 ft compared to 15 ft for 

monitoring wells used in the nationwide model of all aquifers). Scatter plots of predicted and observed nitrate concentrations greater than 4 mg/L as N show that the nationwide model 

predicts a higher probability of finding nitrate concentrations 

greater than 4 mg/L as N than actually was found for private 

wells in the glacial aquifer system. The nationwide nitrate 

model fit monitoring wells in the glacial aquifer system more 

closely; however, the probability of a nitrate concentration 

greater than 4 mg/L as N was still slightly over-predicted. 

Secondly, the logistic regression equation used to create the 

nationwide probability map (Nolan and others, 2002) was 

applied to the private wells of the glacial aquifer system to 

evaluate whether the fit achieved with the equation was superior to the fit achieved using the map. The equation with the 

coefficients used in the nationwide model did not fit the glacial 

aquifer system data (fig. 8–1B). Next, the nationwide model 

was recalibrated with the private wells in the glacial aquifer 

system to test the fit of the model with new coefficients. The 

recalibrated nationwide model was an excellent fit for the 

private wells when using the same categories of probability, 

but there were only three categories with observed data from 

the glacial aquifer system (fig. 8–1C). Hosmer and Lemeshow 

(2000) found that evaluations of fewer than six categories of 

probability almost always indicated a model fit. Finally, the fit 

of the recalibrated nationwide model was evaluated with the 

commonly used 10 categories of probability. The observed and 

predicted probabilities of nitrate concentration greater than 4 

mg/L as N were moderately correlated (R2 = 0.56) for the 10 

categories (fig. 8–1D). 

The probability predictions of the nationwide model 

generally are higher than the observed probability of nitrate 

occurrence in private wells; therefore, some refinement of 

the model would be needed to accurately predict the probability of nitrate occurrence in private wells. To examine why 

the nationwide nitrate model did not accurately predict the 

probability of nitrate occurrence in private wells in the glacial 

aquifer system, it was hypothesized that private wells are generally deeper than monitoring wells, have different positions 

within the aquifer flow system, and are constructed differently, affecting the ease with which nitrate from the surface 

can reach the groundwater. The deeper private wells are more 

likely to be screened beneath clay layers that partially confine 

the aquifer, increasing the likelihood of reducing redox conditions and decreasing the susceptibility of the aquifer to nitrate 

contamination. 
8.0 Statistical Models of Nitrate Concentration 37

Table 8–1. Variables used in selected models to predict probability of nitrate concentration exceeding a given level are compared. 

The logistic regression models included some or all of the variables in the linear regression model highlighted in this report, plus an 

interaction term for models with nitrate thresholds of 5 mg/L or greater.

[GWAVA-DW, model titled Ground WAter Vulnerability Assessment of Drinking Water; GWAVA-S, model titled Ground WAter Vulnerability Assessment of 

Shallow, recently recharged water; kg/ha, kilograms per hectare; %, percent; km2, square kilometers; km2/cm, square kilometers per centimeter; m, meters; 

ML/d, Megaliters per day]

Method, variable type, 

and variables used in reference

Reference

Nolan and Hitt, 2006

Nolan and others, 2002 GWAVA-DW GWAVA-S 

Regression method Logistic Nonlinear Nonlinear.

Variable values used in 

regression

For each well Average of each well network Average of each well network.

Types of wells used in regression Monitoring wells in all aquifers Private and public- supply wells 

in all aquifers

Monitoring wells and selected 

private wells in all aquifers.

Source variables

1992 nitrogen fertilizer applied 

to farms, in kg/ha

Farm fertilizer, in kg/ha Farm fertilizer, in kg/ha.

Agricultural land, in % Manure from confined animal 

feeding operations, in kg/ha

Manure from confined

animal feeding operations, 

in kg/ha.

1990 population density, in 

people/km2

Orchards/vineyards, in % Orchards/vineyards, in %.

Population density, in people/km2 Population density in people/km2.

Crop/pasture/fallow, in %

Transport variables

Well-drained soils, in % Water input (irrigated land/precipitation), in km2

/cm

Water input (irrigated land/precipitation), in km2

/cm.

Depth to seasonally high water 

table, in m1

Semiconsolidated sand aquifer, 

presence/absence

Carbonate rock, presence/absence.

Unconsolidated sand and gravel 

aquifers, presence/absence 

Sandstone/carbonate

aquifer, presence/absence

Basaltic/volcanic rock

aquifer, presence/absence.

Glacial till, presence/absence Glacial till, presence/absence.

Drainage ditch, in km2 Drainage ditch, in km2.

Hortonian overland flow, 

in % of streamflow

Slope, in %.

Clay sediment, in %.

Attenuation variables

Fresh surface water withdrawals, 

in ML/d

Fresh surface water withdrawals, 

in ML/d.

Irrigation tailwater recovery, 

in km2

Irrigation tailwater recovery, 

in km2.

Dunne overland flow, 

in % of streamflow

Histosol soil type, in %.

Well depth, in m Wetlands, in %.

1

. This variable is equivalent to the depth to saturated soil variable that was used in the logistic and linear regression models for this report 
PREDICTED PROBABILITY OF NITRATE CONCENTRATIONS GREATER THAN 4 MILLIGRAMS PER LITER AS NITROGEN

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1.0

OBSERVED PROBABILITY OF

NITRATE CONCENTRATIONS

GREATER THAN 4 MILLIGRAMS

PER LITER AS NITROGEN

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0

1:1 line

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1.0

1:1 line

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1.0

1:1 line

1:1 line

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1.0

0.79 Scatter plots of predicted and

observed nitrate concentrations

greater than 4 milligrams per liter

as nitrogen showed that the

nationwide model was predicting

a higher probability of finding

nitrate concentrations greater

than 4

than actually were

measured in private wells of the

glacial aquifer system.

milligrams per liter

as nitrogen

Spatial overlay

with national

model shown

with six probability

categories

R-squared

value

Observed probabilities plotted Interpretation

against model predicted probabilities

0.12 National model

equation shown

with six probability

categories

The

with the coefficients used in the

nationwide model did not fit the

glacial aquifer system data.

logistic regression equation

1.00 Recalibrated national

model shown with six

probability categories.

Three categories were

not represented by

data and did not plot

on the graph.

The recalibrated nationwide

model was a excellent fit for

the private wells when using the

same categories of probability, but

there were only three categories with

observed data. Evaluations of fewer

than six categories of probability

almost always indicate a good

model fit (

.

Hosmer and

Lemeshow, 2000)

0.56 Recalibrated national

model shown with 10

standard probability

categories

The fit of the recalibrated nationwide

model was evaluated with the more

commonly used 10 categories of

probability. The observed and

predicted probabilities of nitrate

greater than 4

were moderately

correlated for the 10 categories.

milligrams per liter

as nitrogen

Method

A.

B.

C.

D.

Figure 8-1.

Related

table

Table A2

Table A3

Table A4

Table A4

38 Relations That Affect the Probability and Prediction of Nitrate Concentration in Private Wells, Glacial Aquifer System

Figure 8–1. Scatterplots showing the accuracy of the nationwide nitrate model (Nolan and others, 2002) for predicting the 

probability of nitrate concentration greater than 4 milligrams per liter as nitrogen in private wells in the glacial aquifer system.

40 Relations That Affect the Probability and Prediction of Nitrate Concentration in Private Wells, Glacial Aquifer System

9.0 Probability of Nitrate Occurrence Above Threshold Concentrations 

open interval, and length of open interval), and a source variable (10-year mean nitrogen applied to farms). Several of the 

models include an interaction term between depth to top of 

open interval and casing diameter. Not all variables were used 

to model all thresholds.

The 10-year mean (1992–2001) of farm-applied nitrogen 

fertilizer was included as a potential predictor variable for an 

indication of nitrate source. This variable was significantly 

correlated (0.37 rho and p<0.0001) to nitrate concentrations in 

groundwater above background, although the correlation was 

not significant for all samples. It was included as a potential 

predictor variable because farm-applied nitrogen fertilizer is 

known to be a potential source of nitrate in water and has been 

used successfully as a predictor variable (4-year averages) in 

other nitrate models (Nolan and others, 2002; Nolan and Hitt, 

2006). There are undoubtedly other important source variables 

for which no data are available.

The variables that are important predictors of the probability of nitrate concentration above a selected 

threshold depend on the actual nitrate-concentration threshold chosen.

A series of 10 logistic regression models was developed 

to estimate the probability of nitrate concentration above 

various thresholds in groundwater from private wells in the 

glacial aquifer system across the United States (except Alaska, 

for which no spatial data were available for use in models). 

Thresholds of nitrate concentration ranged from 1 to 10 mg/L 

as N. Forty-six variables were assessed for correlation with 

nitrate concentration. Eighteen variables that were significantly correlated (p<0.05) with nitrate concentrations in water 

from private wells in the glacial aquifer system were used in 

an initial forward-selection process to identify those variables 

that were important for determining the probability that the 

nitrate concentration would be above a given threshold value. 

The variables used in the final 10 models (table 9–1) include 

various combinations of variables describing soil properties (depth to soil saturation, percent silt in soil, and percent 

alfisols soil type), variables describing well-construction 

characteristics (diameter of the open interval, depth to top of 

Table 9–1. Variables used in logistic regression models for 10 thresholds of nitrate concentrations include source, transport, and 

attenuation variables. The intercept is a statistical variable that was important in all models for thresholds of 1 to 10 mg/L.

[mg/L, milligrams per liter; N, nitrogen; >, greater than; kg/yr, kilograms per year; — variable not used in model; S, significant variable for logistic regression 

model at a particular threshold nitrate concentration; logistic regression models used variable values for each private well in the glacial aquifer system]

Variable

 type Variable description

Variable abbreviation

(see appendix A,

 table A1)

Nitrate concentration, in mg/L as N

> 10 > 9 > 8 > 7 > 6 > 5 > 4 > 3 > 2 > 1

Source 

variables

10-year mean (1992–

2001) nitrogen 

applied to farms, 

in kg/yr

NFARM_10YR S S S S S S S — — —

Transport 

variables

Depth to top of open 

interval, in inches

DEPTH_TOI_ S S S S S S S S S S

Open interval Diameter, 

in inches

OI_CASE_DI S S S S S S S — — —

Length of open interval, 

in inches

OILENGTH_I — — — — — — — S S S

Silt in soil, in percent SILTAVE — — — — — S S S S S

Depth to saturated soil, 

in feet

WTDEPAVE — — — — S S S S S S

Attenuation 

variables

Alfisols, in percent ORDA — — — — S S S S S S

Interaction term between 

depth to top and 

diameter of open 

interval

OI_CASW_D*DEPTH_TOI S S S S S S — — — —
NITRAT

E

AS NITROGEN

CONCENTRATION,

IN MILLIGRAMS PER LITER

OPEN-INTERVAL DIAMETER, IN INCHES

100

10

1

0.1

0.01

Depth to top of open interval greater than 71 feet

0 5 10 15 20 25 30 35 40

Downward trend

(least-squares smoothing)

Depth to top of open interval less than or equal to 71 feet

100

10

1

0.1

0.01

Upward trend

(least-squares smoothing)

Figure 9-1.

9.0 Probability of Nitrate Occurrence Above Threshold Concentrations 41

An interaction between open-interval diameter and depth 

to top of open interval was identified as a possible predictor 

variable for nitrate. Nitrate concentration increased as well 

diameter increased to a depth of approximately 71 ft; at greater 

depths, nitrate concentration decreased as well diameter 

increased (fig. 9–1). The relation of nitrate concentration in 

water from private wells to open-interval diameter depends on 

the depth to the top of the open interval in the well. Specifically, trends in nitrate concentration are different in wells shallower than 71 ft than in deeper wells (fig. 9–1). This interaction is reasonable because nitrate concentration was greater 

in large open-interval diameter wells which were not deeper 

than 71 ft. The open-interval diameter and depth to top of open 

interval interact to partly predict nitrate concentrations. 

The final 10 logistic regression models were evaluated 

for goodness of fit using the ROC and the Hosmer-Lemeshow 

statistics (app. 8). All 10 of the final logistic regression models 

developed for this study had ROC statistics between 0.81 and 

0.95, which indicates the models fit the data well. The probabilities corresponding to the Hosmer-Lemeshow statistics for 

all of the final logistic regression models for nitrate in private 

wells developed in this study were above the alpha level of 

0.05, indicating that each of the models fit the independent 

variables adequately. The best fit was for the probability of 

nitrate concentration above 10 mg/L as N. Evaluations of 

colinearity showed that the variables used in the final logistic 

regression models were not collinear and therefore were satisfactory variables to use in the models.

Figure 9–1. The interaction between openinterval diameter and depth to top of open 

interval indicates that the relation between 

nitrate concentration and open-interval 

diameter in private wells in the glacial aquifer 

system changes at depths of about 71 feet 

below land surface.

The 10 models were developed for different nitrate 

thresholds (from 1 to 10 mg/L as N) using the most relevant 

variables for predicting occurrence of nitrate above selected 

concentrations in private wells in the glacial aquifer system. 

The set of significant variables selected for predicting the 

probability of nitrate concentration exceeding a threshold 

depends on the threshold that is modeled, as stated earlier 

(fig. 9–2, table 9–1). At the lower thresholds, more variables 

are needed in the model to describe natural soil-texture characteristics and depth to water. The 1 mg/L as N nitrate model is 

an indicator of background nitrate concentration and requires 

mostly variables that are related to natural characteristics 

of the aquifer and soil. No nitrate-source term is included 

in this model because there should be no specific source of 

“unnaturally high” nitrate under “background conditions.” 

As the thresholds of nitrate concentration increase, generally 

fewer variables are included and, for the larger thresholds, the 

variables mostly represent well-construction characteristics 

and a specific nitrate source. High nitrate concentrations in the 

glacial aquifer system are not natural in most areas; therefore, 

the probability of nitrate concentrations near the MCL can be 

predicted by a few selected variables. No natural variables are 

included in the models with thresholds greater than 7 mg/L 

nitrate as N. 

A map that displays the probability of nitrate concentration greater than a given threshold value requires generalizations because the data displayed have a spatial and continuous 

aspect. However, the glacial aquifer system logistic regression 
0

1

2

3

4

5

6

7

8

10 9 8 7 6 5 4 3 2 1

NITRATE CONCENTRATION, IN MILLIGRAMS PER LITER AS NITROGEN

NUMBER OF

VARIABLES

Interaction between depth to top of

open interval and open-interval

diameter

Length of open interval, in inches

Mean percent silt in soil

within 1,640 feet of the well

Percent alfisols within 1,640 feet

of the well

Depth to saturated soil within

1,640 feet of the well

10-year mean (1992-2001) nitrogen

fertilizer applied to farms within

1,640 feet of the well

Open-interval diameter, in inches

Depth to top of open interval, in inches

Variable used in the models

EXPLANATION

Figure 9-2.

42 Relations That Affect the Probability and Prediction of Nitrate Concentration in Private Wells, Glacial Aquifer System

Figure 9–2. Fewer variables are needed to predict higher nitrate concentrations (7–10 milligrams per liter as 

nitrogen) than lower nitrate concentrations (1–6 milligrams per liter as nitrogen); at lower concentrations, most 

variables represent natural conditions and well-construction characteristics.

models for predicting probability of occurrence of a given 

nitrate concentration depend on well-construction data, which 

are not continuous variables (such as depth to top of open 

interval, open-interval length, and open-interval diameter). A 

generalized map displaying the probability of occurrence of 

nitrate concentrations greater than 1 mg/L as N was developed 

by setting the discrete variables (depth to top of open interval and open-interval length) to the mean of those variables 

in all private wells in the glacial aquifer system (91 ft and 

8 ft, respectively). This map can give a regional indication 

of where nitrate concentrations are more or less likely to 

be above a background level of 1 mg/L as N (fig. 9–3), but 

specific well-construction information is needed to refine the 

map for an individual private well. 

The accuracy of the maps displaying the predicted probability of occurrence of a nitrate concentration above a given 

value in water from private wells decreases rapidly as the 

probability becomes more dependent on the well-construction 

variables because the maps do not include individual wellconstruction variables. The accuracy of the maps for thresholds above 4 mg/L as N was very poor when the appropriate 

well-construction variables were set to a mean for all private 

wells in the glacial aquifer system.
110°00 ́ 90°00 ́ 80°00 ́ 

45°00 ́35°00 ́

120°00 ́ 100°00 ́

40°00 ́

C A N A D A

ALASKA CANADA

WA

OR

ID

MT

WY

CO

ND

SD

NE

KS

IA

MN

WI

IL

MO

IN

MI

KY

WV

VA

PA

N

OH M

Pacific Ocean

Lake Superior

Lake Michigan

LakeHuron

Lake Erie

Lake Ontario

U N I T E D S T A T E S

Ain

Aren

Driftless area

Base from U.S. Geological Survey 1:2,000,000 Digital DataAlbers Equal-Area Conic projection, standard parallels 29° 30’and 45° 30’, central meridian -96°, latitude of origin 23°

0 100 MILES0 100 KILOMETERS N

Measured nitrate concentration,

in milligrams per liter as nitrogen

Less than or equal to 1

(background concentration)

Greater than 1 (some human influence)

Predicted probability that nitrate

concentration is greater than

1 milligram per liter as nitrogen,in percent

High: 92Low: 0

EXPLANATION

Glacial aquifer system extent

(approximate)

No Data are shown for Alaska

Figure 9–3. Probability of occurrence of nitrate concentrations greater than 1 milligram per liter in private wells in the glacial aquifer system. This map the depth to top of open interval and open-interval length to the mean of the values for these variables in all private wells in the glacial aquifer system (9
44 Relations That Affect the Probability and Prediction of Nitrate Concentration in Private Wells, Glacial Aquifer System

10.0 Prediction of Mean Nitrate Concentrations in Networks of Wells

concentration for a network was compared to the observed 

mean concentration. Predicted nitrate concentrations for 

networks with residuals greater than zero are too low, whereas, 

concentrations for networks with residuals less than zero 

are over predicted by the model. In figure 10–2, the network 

results are ordered by the model residual obtained for each 

network. The closer the residual is to zero, the better the fit of 

the model. The networks that fit this model best are those in 

Connecticut, New Hampshire, and Vermont; in Washington; 

and in Illinois (fig. 10–2). The overall fit of the model is good 

(R2=0.82).

The area of highest predicted mean nitrate concentration 

in private wells was in west-central Illinois (fig. 10–3). This 

area is characterized by a relatively high application of nitrate, 

older aquifer materials with fractured till, thinner glacial 

materials than in areas covered by Wisconsin glacial deposits, 

and predominantly large-diameter wells. The mean measured 

nitrate concentration in this west-central Illinois network was 

5.9 mg/L as N. This network also had the largest mean well 

diameter (23.7 in.).

The linear regression model can be used to predict and 

compare regional nitrate concentrations in water from private 

wells in the glacial aquifer system. This model is designed 

for large regional interpretations. The map showing nitrate 

concentrations predicted by using this model (fig. 10–3) can 

be used to indicate where nitrate concentrations in water from 

private wells in the glacial aquifer system are likely to be 

elevated. 

Use of network averages of variables affecting nitrate concentration in linear regression models helps 

minimize the well-to-well differences in nitrate concentration and aids in predicting nitrate concentration 

in water from private wells in the glacial aquifer system at the regional scale. 

A linear regression model also was developed to predict 

nitrate concentrations at the regional scale. In order to remove 

some of the variability, nitrate concentrations were averaged 

by well network. The model is based on network averages 

because nitrate concentrations were highly variable over 

short distances and it was otherwise not possible for a linear 

regression model to fit the individual data points for the glacial 

aquifer system. The nitrate concentrations were averaged by 

network under the assumption that wells in the same network 

would likely be related and be subject to similar influences 

on nitrate concentration. The linear regression was calculated 

using the same predictor variables used in the logistic regressions (cumulatively); however, the interaction term was omitted from the linear regression analysis. The linear regression 

model includes network averages of the following variables: 

depth to saturated soil, percent silt in soil, percent alfisols soil 

type, 10-year mean (1992–2001) nitrogen applied to farms, 

diameter of the open interval, depth to top of open interval, 

and length of open interval (table 10–1). Using values for each 

of the predictor variables averaged by network (network mean 

value) from the logistic regression models, the linear regression model significantly predicted the mean nitrate concentration in networks (R2

 = 0.82 and p-value < 0.0001) (fig. 10–1). 

Residuals resulting from the linear regression model were 

plotted against quantiles of the standard normal distribution 

and were found to be normally distributed.

The nitrate prediction model is a better fit in some 

geographic areas than in others. To determine the goodness 

of fit for the linear prediction model, the predicted mean 
R-squared: 0.82

OBSERVED MEAN NITRATE

CONCENTRATION, IN MILLIGRAMS

PER LITER AS NITROGEN

PREDICTED MEAN NITRATE

CONCENTRATION, IN MILLIGRAMS

PER LITER AS NITROGEN

1:1 line

Private

wells

6

5

4

3

2

1

0 1 2 3 4 5 6

0

lirb2

eiwa2

redn5 pugt1

almn2

delr3

redn2

uirb2 uirb1

lirb1

redn1

leri1

miam1

hpgw4

conn2

wmic2

EXPLANATION

Symbol

almn

conn

eiwa

hpgw

leri

lirb

miam

pugt

redn

uirb

wmic

delr

Study-unit name (see fig. 1-3 for location)

Allegheny and Monongahela River Basins

Connecticut, Housatonic, and Thames River Basins

Eastern Iowa Basins

High Plains regional groundwater study

Lake Erie-Lake St. Clair drainage

Lower Illinois River Basin

White River Basin and Great and Little Miami River Basins

Puget Sound Basin

Red River of the North Basin

Upper Illinois River Basin

Western Lake Michigan drainages

Delaware River Basin

Number (1, 2, 3, 4, or 5) next to symbol indicates the network

number. Some study units have more than one network.

10.0 Prediction of Mean Nitrate Concentrations in Networks of Wells 45

Figure 10–1. The relation between mean observed nitrate concentrations and mean nitrate concentrations predicted 

with the linear regression model indicates that the model is a good fit (R2=0.82).

Table 10–1. Coefficient values, standard error, and p-values of variables used in the linear regression model used to predict mean 

nitrate concentration in private-well networks in the glacial aquifer system.

[ft, feet; kg/yr, kilograms per year]

Coefficient

(see appendix 1, table A1 for a description of coefficient variables)

Coefficient

value

Standard 

error

T-value Probability 

(p-value)

Intercept -2.184 1.420 -1.538 0.163

Open-interval diameter, in inches (mDiamOIin) 0.158 0.081 1.963 0.085

Depth to saturated soil, in ft (mwtdepave) 0.479 0.320 1.495 0.173

Silt in soil, in percent (msiltave) 0.054 0.029 1.878 0.097

10-year-mean (1992-2001) nitrogen applied to farms, in kg/yr (mnfarm.10y) 0.000 0.000 1.448 0.186

Length of open interval, in inches (moilength) -0.003 0.006 -0.483 0.642

Depth to top of open interval, in inches (mdepthtoi) -0.001 0.001 -2.083 0.071

Alfisols, in percent (morda) -0.017 0.011 -1.519 0.167
0

1234568

NITRATE CONCENTRATION, IN

MILLIGRAMS PER LITER AS NITROGEN

RESIDUAL

-2.09 -0.55 -0.52 -0.42 -0.39 -0.24 -0.20 -0.03 -0.03 0.26 0.34 0.40 0.45 0.48 0.61 1.11

0.0 Not

predicted

7

Goodness of fit

NETWORK

Eastern Pennsylvania and New York (delr3)

Western Pennsylvania and New York (almn2)

Ohio and Michigan (leri1)

Minnesota and North Dakota (redn5)

Alaska (cook1a)

Illinois (lirb1)

Illinois and Indiana (uirb2)

Minnesota and North Dakota (redn2)

Indiana and Ohio (miam1)

Connecticut , New Hampshire, and Vermont (conn2)

Iowa (eiwa2)

Illinois (lirb2)

Wisconsin and Michigan (wmic2)

Nebraska (hpgw4)

Washington (pugt1)

Illinois and Wisconsin (uirb1)

Minnesota and North Dakota (redn1)

EXPLA

Symbolalmnconncookeiwahpgwlerilirbmiampugtrednuirbwmicdelr

Study Unit Name (See Allegheny and MonongConnecticut, HousatoniCook InsletEastern Iowa BasinsHigh Plains regional grLake Erie-Lake St. ClaiLower Illinois River BaWhite River Basin and Puget Sound BasinRed River of the North Upper Illinois River BaWestern Lake Michigan Delaware River Basin

Number (1, 2, 3, 4, or 5) next to synumber. Some study units have mo

MeanMeanMedian

Upper confidence levelLower confidence level

PREDICTED CONCENTRA

OBSERVED CONCENTRAT

Figure 10–2. Mean observed and predicted nitrate concentrations show the goodness of fit for the linear regression model, which is based on data networks. The networks for which the residuals are closer to zero have the best fit to the model. Data needed for the model were unavailable for Alas
110°00 ́ 90°00 ́ 80°00 ́ 

45°00 ́35°00 ́

120°00 ́ 100°00 ́

40°00 ́

C A N A D A

ALASKA CANADA

WA

OR

ID

MT

WY

CO

ND

SD

NE

KS

IA

MN

WI

IL

MO

IN

MI

KY

WV

VA

PA

N

OH M

Pacific Ocean

Lake Superior

Lake Michigan

LakeHuron

Lake Erie

Lake Ontario

U N I T E D S T A T E S

Ain

Aren

Driftless area

Base from U.S. Geological Survey 1:2,000,000 Digital DataAlbers Equal-Area Conic projection, standard parallels 29° 30’and 45° 30’, central meridian -96°, latitude of origin 23°

Puget

Sound

Basin

Red River

of the

North Basin

Eastern

Iowa

Basins

Lower

Illinois

River

Basin

Upper

Illinois

River

Basin

Lake ErieLake St. Clair

Drainage

White River Basinand Great and LittleMiami River Basins

Central

Nebraska

Basin

WesternLake MichiganDrainages

De

R

B

Hudson

River

Basin

High Plains 

Regional

Ground Water

Study

Allegheny 

Monongah

River Bas

Cook

Inlet

Basin

0 100 MILES0 100 KILOMETERS N

No Data for Alaska

EXPLANATION

Predicted mean nitrate concentration

for a network of wells, in milligramsper liter as nitrogen

0 to 1Greater than 1 to 2Greater than 2 to 4Greater than 4

Study-unit boundary

Glacial aquifer system extent

(approximate)

Figure 10–3. The area of highest predicted mean nitrate concentration in water from private wells in the glacial aquifer system is in the glacial depo
48 Relations That Affect the Probability and Prediction of Nitrate Concentration in Private Wells, Glacial Aquifer System

11.0 Conclusions

Nitrate concentrations in water from private wells in the 

glacial aquifer system generally decreased with depth. The 

glacial aquifer system may differ from other unconsolidated 

aquifers as a result of its heterogeneity and its content of finegrained material, such as clay and buried soils overlying the 

highly agricultural part of the aquifer system. This heterogeneity with depth obscures a distinct spatial pattern of nitrate 

concentration (fig. 11–1). Fine-grained materials confine the 

deeper aquifer material, causing the geochemical environment 

to be reducing and, therefore, low in nitrate. The deeper the 

well, the more likely the water is to be reducing, and under 

confined or semi-confined conditions. The decrease in nitrate 

concentration with increasing well depth is more distinct than 

any spatial or temporal patterns (fig. 11–2) because depth can 

be an indicator of geochemical conditions. Local differences in 

sediment thickness and texture also can affect nitrate concentrations; the decreased risk of nitrate contamination with depth 

is strongly dependent on the local hydrogeologic conditions.

Because collection and analysis of groundwater samples 

everywhere in the glacial aquifer system is impractical, methods are needed for extrapolating the vulnerability of private 

wells to nitrate contamination from sampled to unsampled 

areas. The methods and data used in the probability and 

prediction models presented in this report may be useful for 

extrapolation of vulnerability for a number of anthropogenic 

constituents with properties similar to nitrate. The models of 

nitrate in private wells indicate that only a small amount of 

information is needed to predict the regional vulnerability to 

nitrate contamination; the same may be true for other surfacederived contaminants as well. Although variables such as 

density of septic systems (as percent of housing units on septic 

systems within 1,640 ft of the well) are correlated with nitrate 

concentration in water from individual wells, they cannot 

be used to predict nitrate concentration in the glacial aquifer 

system on a regional scale, but may be useful to a local well 

owner. Additional information, such as soil type and aquifer 

material, also is important for predicting nitrate concentration. Similarly, well characteristics such as depth to the top of 

the well screen, the length of the screen, and the diameter of 

the open interval can be used to predict nitrate concentration 

because these variables indicate what part of the flow system is utilized. A source variable such as the rate of nitrogen 

applied to farms was useful in predicting regional nitrate 

concentration. 

It is apparent in the various model trials that altering the 

set of variables alters the outcome of the models; however, 

more or less equivalent models can be developed that fit the 

dependent variable using entirely different sets of independent 

predictor variables. If, in future modeling efforts, values of the 

exact variables that were used in these models are not available, alternate variables that describe similar characteristics 

may be substituted to obtain a result that is quantitatively 

similar to the results presented in this report. 

Most people in rural America obtain their drinking water 

from private wells, and the potential for nitrate contamination is one of the most pressing water-quality issues for these 

private-well users. Forty-one million people rely on the glacial 

aquifer system for drinking water. Although only 4 percent of 

private wells contain groundwater with nitrate at concentrations greater than 10 mg/L as N, another 26 percent of private 

wells are approaching a concentration of potential humanhealth concern—that is, they contain nitrate at concentrations 

greater than 1 mg/L as N. A summary of data from reference 

wells indicates that most occurrences of nitrate above 1 mg/L 

as N represent nitrate concentrations above background and 

likely result from anthropogenic sources. If anthropogenic 

nitrate is found in water from a private well, the well owner 

may want to check for other anthropogenic compounds, as 

other compounds may be transported from land surface to 

the well. DeSimone (2009) found that 73 percent of private 

wells had mixtures of two or more contaminants. Nitrate 

alone should not be used as the screening tool for other 

contaminants, however. Squillace and others (2002) showed 

that volatile organic compounds or pesticides were present in 

43 percent of samples even though “anthropogenic” nitrate 

was not present. Testing private well water for nitrate and 

other contaminants would be needed to ensure safe drinkingwater quality.

One reason that nitrate alone may not be a good predictor 

of other anthropogenic constituents is that nitrate is redox sensitive, but not all anthropogenic constituents are redox sensitive. When the dissolved-oxygen concentration in groundwater 

is high, nitrate is relatively stable and may persist. Nitrate is 

less likely to be present in water with low dissolved-oxygen 

content where it may change to nitrogen gas through denitrification. Oxygen content can decrease as well depth increases or 

if recharge is constrained by a confining layer, such as clay or 

clayey till. In areas of high clay content, wells commonly are 

drilled to greater depths to improve the reliability of the supply of groundwater. Understanding the geologic framework, 

including the heterogeneity of the aquifer material with depth, 

is the key to understanding the distribution of nitrate and other 

redox-sensitive constituents. 

The concentrations of nitrate in water from private wells 

in the glacial aquifer system assessed in this study varied with 

time, location, and depth. Comparisons of age of recharge 

water indicates that the mean nitrate concentration was significantly greater in young groundwater than in old groundwater. 

Results of a recent study (Saad, 2008) that assessed trends 

in the shallow glacial aquifer system in Wisconsin indicated 

that nitrate concentration in the shallow, recently recharged 

groundwater increased substantially in near-decadal sampling 

(1994 to 2002) as fertilizer application increased. This study 

was conducted in a highly permeable part of the glacial aquifer 

system; it is not known whether the nitrate concentration also 

increases significantly in private wells in deeper or less permeable parts of the aquifer system. 
C A N A D A

ALASKA CANADA

WA

OR

ID

MT

WY

CO

ND

SD

NE

KS

IA

MN

WI

IL

MO

IN

MI

KY

WV

VA

PA

N

OH 

Pacific Ocean

Lake Superior

Lake Michigan

LakeHuron

Lake Erie

Lake Ontario

U N I T E D S T A T E S

Ai

Aen

Driftless area

Base from U.S. Geological Survey 1:2,000,000 Digital DataAlbers Equal-Area Conic projection, standard parallels 29° 30’and 45° 30’, central meridian -96°, latitude of origin 23°

110°00 ́ 90°00 ́ 80°00 ́ 

45°00 ́35°00 ́

120°00 ́ 100°00 ́

40°00 ́

0 100 MILES0 100 KILOMETERS N

EXPLANATION

Glacial aquifer system extent (approximate)

Less than or equal to 0.05 (not detected)

Greater than 0.05 to 1.0 (background level)Greater than 1 to 4 (some impact from humans)

Nitrate concentration, in milligrams per liter as nitrogen

Greater than 4 to 10 (high concentration)

Greater than 10 (above the U.S. Environmental Protection

Agency Maximum Contaminant Level)

Figure 11–1. There was no distinct geographic pattern in nitrate concentration in water from private wells in the glacial aquifer system, although mo(greater than 10 milligrams per liter as nitrogen) were in the central part of the glaciated United States.
Temporal

Increasing

influence

on nitrate

concentration

in private wells

in the glacial

aquifer system

Vertical

Spatial

Figure 11-2.

50 Relations That Affect the Probability and Prediction of Nitrate Concentration in Private Wells, Glacial Aquifer System

Because the glacial aquifer system covers a large area, 

aggregating network information helps in predicting nitrate 

concentrations. The prediction model based on network means 

indicates that nitrate in water from private wells is less likely 

to be a problem in the two coastal framework areas than in 

parts of the Central and West-central glacial framework areas. 

In these areas, continued monitoring of nitrate concentrations 

and study of the distribution of glacial materials would help 

in understanding the variations in nitrate concentration in the 

glacial aquifer system. 

Some characteristics of the models of nitrate probability 

and prediction must be taken into consideration when applying the model results for making management decisions and 

water-quality assessments. Important among these considerations are that the models (1) focus on spatial rather than 

temporal detail; (2) integrate data over large networks to 

calculate spatial averages for model input; (3) include only the 

water-quality variables that are electronically available and 

statistically correlated with nitrate concentration; and (4) favor 

Figure 11– 2. Changes in nitrate concentrations in 

water from private wells in the highly heterogeneous 

glacial aquifer system were most variable with depth.

water-quality comparisons across broad regions as opposed 

to local systems. Some regional characteristics that may be 

critical in understanding water-quality conditions are not 

well documented for the entire multi-state region. Examples 

include tile-drain location and distribution, land-management 

practices, and septic-system locations. The effects of such 

characteristics were evaluated by extension through available 

variables or explored indirectly by evaluating model fit. Maps 

developed by applying these models may be improved over 

time as new geographic information becomes available or as 

spatial resolution improves. Specifically, the models of nitrate 

concentration in private wells can be used to (1) establish 

links between water quality and constituent sources; (2) assess 

the natural processes that attenuate nitrate; and (3) predict 

where changes in water quality may result from changes in 

environmental management or well construction. Finally, the 

more information available about well construction and nearby 

nitrogen sources, the more likely it is that the vulnerability of a 

given private well to nitrate contamination can be determined.
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also online at http://pubs.usgs.gov/sir/2006/5012/.

Rupert, M.G., 2008, Decadal-scale changes of nitrate in 

ground water of the United States, 1998–2004: Journal of 

Environmental Quality, v. 37, p. S–240 to S–248.
54 Relations That Affect the Probability and Prediction of Nitrate Concentration in Private Wells, Glacial Aquifer System

Saad, D.A., 2008, Agriculture-related trends in groundwater 

quality of the glacial deposits aquifer, central Wisconsin: 

Journal of Environmental Quality, v. 37, p. S–209-S–225.

SAS Institute Inc., 2003, SAS version 9.1.3 for Windows: 

Cary, N.C., SAS Institute Inc., computer software accessed 

May 20, 2008 at http://www.sas.com/.

Sebol, L.A., Roberston, W.D., Busenberg, E., Plummer, L.N., 

Ryan, M.C., and Schiff, S.L., 2007, Evidence of CFC degradation in groundwater under pyrite-oxidizing conditions: 

Journal of Hydrology, v. 347, no. 1–2, p. 1–12.

Squillace, P.J., and Price, C.V., 1996, Urban land-use study 

plan for the National Water-Quality Assessment Program: 

U.S. Geological Survey Open-File Report 96–217, 19 p.

Squillace, Paul J., Scott, Jonathon, Moran, Michael J., Nolan, 

B.T., and Kolpin, Dana W., 2002, VOCs, pesticides, nitrate, 

and their mixtures in groundwater used for drinking water 

in the United States: Environmental Science & Technology, 

v. 36, no. 9, p. 1923–1930.

Stanton, J.S., Steele, G.V., and Vogel, J.R., 2007, Occurrence 

of agricultural chemicals in shallow ground water and the 

unsaturated zone, northeast Nebraska glacial till, 2002–

2004: U.S. Geological Survey Scientific Investigations 

Report 2007–5228, 51 p.

Tesoriero, A.J., Saad, D.A., Burow, K.R., Frick, E.A., Puckett, 

L.J., and Barbash, J.E., 2007, Linking ground-water age and 

chemistry data along flow paths—Implications for trends 

and transformations of nitrate and pesticides: Journal of 

Contaminant Hydrology, v. 94, p. 139–155. 

Tomer, M.D., and Burkart, M.R., 2003, Long-term effects 

of nitrogen fertilizer use on groundwater nitrate in two 

small watersheds: Journal of Environmental Quality, v. 32, 

p. 2158–2171.

Trapp, Henry, Jr., and Horn, M.A., 1997, Ground water atlas 

of the United States—Segment 11, Delaware, Maryland, 

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24 p.

U.S. Census Bureau, 2004, U.S. Census Database, 2000: 

U.S. Geological Survey National Atlas, Reston, Va., digital 

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tenth edition: USDA Natural Resources Conservation Service, chap. 5, p. 35.

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in the United States: U.S. Geological Survey Scientific 

Investigations Report 2005–5223, revised May 2006, 6 p.

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Glossary 55

Glossary

Alfisols — generally light-colored soils 

formed under forest environment (Natural 

Resources Conservation Service, 2008).

Anoxic — water samples, containing less than 

0.5 mg/L of dissolved oxygen.

Bulk density — for soils, mass or weight of 

moist soil per unit volume (in this report, in 

grams per cubic centimeter).

Censored data — results of laboratory analysis of water samples in which the analyte concentration is too low to be reliably detected 

and quantified by the laboratory equipment.

Cumulative frequency distribution curve —

visually shows how many observations in 

a data set are above or below a given value 

(Helsel and Hirsch, 1992).

Framework area — in this report, a preliminary classification scheme that identifies the 

most general and important regional-scale 

characteristics of the glacial aquifer system 

(Warner and Arnold, 2006). Four framework 

areas are defined: East, Central, West-Central, 

and West.

Glacial aquifer system — as defined in this 

report, it is the unconsolidated geologic material above bedrock that lies on or north of the 

line of maximum glacial advance within the 

United States.

Hot-spot differentiation — local clustering 

of high or low values that are significantly 

(statistically) different from the mean for the 

entire study area (Environmental Systems 

Research Institute, Inc., 2008).

Network — group of wells from which water 

samples were collected for a specific purpose.

Organic matter — in this report is the 

non-living component of soils which are a 

heterogeneous mixture composed largely of 

products resulting from microbial and chemical transformations of organic debris. Organic 

matter content of soils used in this report is 

expressed in percent by weight. 

Perched groundwater — a discontinuous 

saturated lense, with unsaturated conditions 

above and below (Freeze and Cherry, 1979).

Residual — the difference between an 

observed value and a predicted value derived 

from a statistical model. A residual of 0 

indicates that the predicted and observed 

values are identical. A negative residual indicates that the observed value is less than the 

predicted value; a positive residual indicates 

that the observed value is greater than the 

predicted value.

Silt content — in this report, the percentage by weight of a sample of unconsolidated 

material that consists of silt. Silt consists 

of small-diameter mineral particles that are 

larger than clay but smaller than sand.

Survival curve — see cumulative frequency 

distribution curve.

Study Unit — one of 51 geographically 

distinct study areas, based on the major river 

basins and aquifers of the United States that is 

an organizational unit of the USGS NAWQA 

program (U.S. Geological Survey, 2010). Data 

from 15 NAWQA study units were analyzed 

for the study described in this report.
56 Relations that Affect the Probability and Prediction of Nitrate Concentration in Private Wells, Glacial Aquifer System

Appendixes 1–9
Appendixes 1–9 57

Appendix 1. Variable names, descriptions, units, and sources used in the models described in this report.

[ft, feet; %, percent; NAWQA, National Water-Quality Assessment Program; STATSGO, State Soil Geographic Database]

Variable name in logistic 

regression models

Variable name 

in linear 

regression 

model

Description of 

variable Units

Values used in 

logistic 

regressions

Values used in 

linear 

regression

Source of data

OI_CASE_DI mDiamOIin Open-interval 

diameter

inches Values for 

each well

Mean for well 

network

NAWQA data warehouse 

(http://infotrek.er.usgs.gov/

traverse/f?p=NAWQA:HO

ME:1931200546639998).

WTDEPAVE mwtdepave Depth to saturated soil 

within 1,640 

ft of well

feet Values for 

each well

Mean for well 

network

STATSGO soil data (Wolock, 

1997). This variable is 

named WTDEPAVE, depth 

to seasonally high water 

table, in Wolock (1997).

SILTAVE msiltave Mean % silt in 

soil within 

1,640 ft of 

the well

area weighted 

percent

Values for 

each well

Mean for well 

network

STATSGO soil data 

(Wolock, 1997).

NFARM_10YR mnfarm.10y 10-year mean 

(1992-2001) 

nitrogen 

applied to 

farms within 

1,640 ft of 

the well

kilograms per 

year

Values for 

each well

Mean for well 

network

10-year mean was calculated 

by summing nitrogen applications for the years 

1992 through 2001 (Ruddy 

and others, 2006) and 

dividing by 10 years.

OILENGTH_I moilength Length of open 

interval

inches Values for 

each well

Mean for well 

network

NAWQA data warehouse 

(http://infotrek.er.usgs.gov/

traverse/f?p=NAWQA:HO

ME:1931200546639998).

DEPTH_TOI_ mdepthtoi Depth to top 

of open 

interval

inches Values for 

each well

Mean for well 

network

NAWQA data warehouse 

(http://infotrek.er.usgs.gov/

traverse/f?p=NAWQA:HO

ME:1931200546639998).

ORDA morda % alfisols 

within

1,640 ft of 

well

area weighted 

percent

Values for 

each well

Mean for well 

network

STATSGO soil data 

(Wolock, 1997).

OI_CASE_D*DEPTH_TOI_ Not used 

in linear 

regression

Interaction 

of casing 

diameter 

and depth to 

top of open 

interval

dimensionless Values for 

each well

Mean for well 

network

Calculated by model.
58 Relations That Affect the Probability and Prediction of Nitrate Concentration in Private Wells, Glacial Aquifer System

Appendix 2. Results of a comparison of nitrate measured in private and monitoring wells in the glacial aquifer system to the 

nationwide model of probability of nitrate concentration greater than 4 milligrams per liter as nitrogen based on all monitoring wells 

(Nolan and others, 2002). Data are from a spatial overlay of wells in the glacial aquifer system with a model of probability of nitrate 

contamination of groundwater (Nolan and others, 2002).

[mg/L, milligrams per liter; N, nitrogen; NA, not applicable; see figure 8–1A for scatter plot of the relation between observed and predicted probabilities]

Category

of predicted 

probabilities

Number of 

wells in which 

measured 

nitrate 

concentration 

is less than 

or equal to 4 

mg/L as N in 

each category

Number of 

wells in which 

measured 

nitrate 

concentration 

is greater than 

4 mg/L as N in 

each category

Total number of 

wells in each 

category

Mean observed 

probability

Mean predicted 

probability

C-test statistic 

(Hosmer and 

Lemeshow, 

2000, p. 148)

Multiple 

R-squared 

regression 

statistic for 

observed and 

predicted 

probabilities

Private wells

0 to 0.17 88 3 91 0.03 0.09 3.56 NA

0.17 to 0.33 78 14 92 0.15 0.27 6.25 NA

0.33 to 0.50 73 13 86 0.15 0.41 23.97 NA

0.50 to 0.67 40 14 54 0.26 0.58 23.09 NA

0.67 to 0.83 23 4 27 0.15 0.73 45.20 NA

0.83 to 1.0 1 1 2 0.50 0.83 1.61 NA

All categories 303 49 352 NA NA 103.68 0.79

Monitoring wells

0 to 0.17 120 35 155 0.23 0.10 28.29 NA

0.17 to 0.33 152 45 197 0.23 0.25 0.66 NA

0.33 to 0.50 153 74 227 0.33 0.42 7.67 NA

0.50 to 0.67 89 78 167 0.47 0.57 7.62 NA

0.67 to 0.83 46 56 102 0.55 0.74 20.56 NA

0.83 to 1.0 3 8 11 0.73 0.85 1.41 NA

All categories 563 296 859 NA NA 66.22 0.96
Appendixes 1–9 59

Appendix 3. Results of using a logistic regression model (Nolan and others, 2002) with six categories to calculate the probability of 

nitrate concentration greater than 4 milligrams per liter as nitrogen.

[mg/L, milligrams per liter; N, nitrogen; NA, not applicable; see figure 8–1A for scatter plot of relation between observed and predicted probabilities]

Category of 

predicted 

probabilities 1

Number of 

wells in which 

measured nitrate 

concentration is 

less than or equal 

to 4 mg/L as N in 

each category

Number of 

wells in which 

measured nitrate 

concentration 

is greater than 

4 mg/L as N in 

each category

Total number of 

wells in each 

category

Mean observed 

probability

Mean predicted 

probability

Multiple 

R-squared 

regression 

statistic for 

observed and 

predicted 

probabilities

0 to 0.17 8 0 8 0 0.12 NA

0.17 to 0.33 4 1 5 0.2 0.25 NA

0.33 to 0.50 4 0 4 0 0.37 NA

0.50 to 0.67 7 0 7 0 0.57 NA

0.67 to 0.83 9 0 9 0 0.77 NA

0.83 to 1.0 276 48 324 0.15 0.99 NA

All categories 308 49 357 NA NA 0.12

1. Six probability Categories as in Nolan and others (2002)
60 Relations That Affect the Probability and Prediction of Nitrate Concentration in Private Wells, Glacial Aquifer System

Appendix 4.A Results of recalibrating a logistic regression model (Nolan and others, 2002): coefficients resulting from recalibrating the 

regression equation from Nolan and others (2002) and results of test to determine whether estimated coefficients of new variables are 

significant predictors (significantly different from 0) at alpha = 0.1.

[NA, not applicable; %, percent; m, meters; km2, square kilometers; kg/ha, kilograms per hectare; mg/L milligrams per liter; N, nitrogen; see figures 8–1C and 

8–1D for scatter plots of relation between observed and predicted probabilities]

Coefficient variable Value Standard 

error

t-value Wald 

statistic Deviance

Residual 

degrees of 

freedom

Residual 

deviance

Probability of 

Chi-square value 

if coefficient 

variable is added 

sequentially, 

first to last

Intercept 

(NULL model)

-4.274 0.947 -4.51 -4.51 NA 356 285.56 NA

1992 nitrogen fertilizer 

applied to farms, 

in kg/ha

0.000 0.000 0.76 0.76 6.20 355 279.36 0.01

Agricultural land, in % 0.008 0.009 0.89 0.89 0.08 354 279.28 0.77

1990 population density, in people/ km2

(natural log)

0.076 0.122 0.62 0.62 0.09 353 279.19 0.77

Well-drained soils, 

in %

0.006 0.008 0.71 0.71 5.51 352 273.68 0.02

Depth to seasonally 

high water table, 

in m1

0.259 0.175 1.48 1.48 2.17 351 271.51 0.14

Unconsolidated sand 

and gravel aquifers, 

presence/absence 

-0.013 0.335 -0.04 -0.04 0.00 350 271.51 0.97

1. This variable is equivalent to the variable called ‘depth to saturated soil’ that was used in the logistic and linear regression models for the glacial aquifer 

system as described in this report.
Appendixes 1–9 61

Appendix 4B. Results of recalibrating a logistic regression model (Nolan and others, 2002): observed and predicted 

probabilities using the 6 categories of predicted probabilities in Nolan and others (2002) and the standard 10 categories.

[NA, not applicable; %, percent; m, meters; km2, square kilometers; kg/ha, kilograms per hectare; mg/L milligrams per liter; N, nitrogen; see figures 

8–1C and 8–1D for scatter plots of relation between observed and predicted probabilities]

Category of 

predicted 

probabilities

Number of 

wells in which 

measured 

nitrate 

concentration 

is less than or 

equal to 4 mg/L 

as N in each 

category

Number of 

wells in which 

measured 

nitrate 

concentration 

is greater than 

4 mg/L as N in 

each category

Total number of 

wells in each 

category

Mean observed 

probability

Mean predicted 

probability

Multiple 

R-squared 

regression 

statistic for 

observed and 

predicted 

probabilities

Observed and predicted probabilities using the 6 categories as in Nolan and others (2002)

0 to 0.17 233 28 261 0.11 0.10 NA

0.17 to 0.33 73 20 93 0.22 0.22 NA

0.33 to 0.50 2 1 3 0.33 0.36 NA

0.50 to 0.67 0 0 0 NA NA NA

0.67 to 0.83 0 0 0 NA NA NA

0.83 to 1.0 0 0 0 NA NA NA

All categories 308 49 357 NA NA 1.00

Observed and predicted probabilities using the standard 10 categories

0.02 to 0.058 35 1 36 0.03 0.04 NA

0.058 to 0.09 71 6 77 0.08 0.08 NA

0.09 to 0.13 61 10 71 0.14 0.11 NA

0.13 to 0.17 65 11 76 0.14 0.15 NA

0.17 to 0.20 26 7 33 0.21 0.19 NA

0.20 to 0.24 24 7 31 0.23 0.22 NA

0.24 to 0.28 15 4 19 0.21 0.25 NA

0.28 to 0.31 8 2 10 0.2 0.29 NA

0.31 to 0.35 2 0 2 0 0.33 NA

0.35 to 0.39 1 1 2 0.5 0.38 NA

All categories 308 49 357 NA NA 0.56
Appendix 5. Logistic regression parameter estimates and odds ratio estimates for each of 10 logistic regression models.—[<, less than; >, greater than; mg/L, milligrams per liter; N, nitrogen; —, not applicable; see Appendix 6 for scatter plots of the relation between prabilities for each logistic regression model] Coefficient2 Value Standard error Chi-square value Probability the coefficient is significant Odds ratio est

Effect Point estimate 

Nitrate concentration > 1 mg/L as N Intercept -3.9552 0.762 26.931 <.0001 — — 

WTDEPAVE 0.7219 0.140 26.788 <.0001 WTDEPAVE 2.058 SILTAVE 0.0356 0.011 10.728 0.001 SILTAVE 1.036 ORDA -0.0164 0.004 13.631 0.0002 ORDA 0.984 DEPTH_TOI_ -0.0012 0.000 23.397 <.0001 DEPTH_TOI_ 0.999 OILENGTH_I 0.00309 0.001 4.554 0.033 OILENGTH_I 1.003 

Nitrate concentration > 2 mg/L as N Intercept -5.1108 0.908 31.697 <.0001 — — 

WTDEPAVE 0.8013 0.163 24.285 <.0001 WTDEPAVE 2.228 SILTAVE 0.0535 0.013 17.970 <.0001 SILTAVE 1.055 ORDA -0.0188 0.005 14.563 0.0001 ORDA 0.981 DEPTH_TOI_ -0.00152 0.000 26.045 <.0001 DEPTH_TOI_ 0.998 OILENGTH_I 0.000985 0.001 0.615 0.433 OILENGTH_I 1.001 

Nitrate concentration > 3 mg/L as N Intercept -4.6698 0.944 24.479 <.0001 — — 

WTDEPAVE 0.6468 0.168 14.765 0.0001 WTDEPAVE 1.909 SILTAVE 0.0481 0.013 12.955 0.0003 SILTAVE 1.049 ORDA -0.0156 0.005 8.845 0.003 ORDA 0.985 DEPTH_TOI_ -0.00165 0.000 23.763 <.0001 DEPTH_TOI_ 0.998 OILENGTH_I 0.00111 0.001 0.790 0.374 OILENGTH_I 1.001 

1. For continuous explanatory variables, the odds ratios correspond to a unit increase in the risk factors. For continuous explanatory variables, t

to the odds ratio for a unit increase of the corresponding effect variable. Odds ratios are computed only for variables not involved in an interactio

2. See Appendix 1 for a description of the coefficient variables.
Appendix 5. Logistic regression parameter estimates and odds ratio estimates for each of 10 logistic regression models.—[<, less than; >, greater than; mg/L, milligrams per liter; N, nitrogen; —, not applicable; see Appendix 6 for scatter plots of the relation between prabilities for each logistic regression model]

Coefficient2 Value Standard 

error

Chi-square 

value

Probability the 

coefficient is 

significant

Odds ratio est

Effect Point estimate 

Nitrate concentration > 4 mg/L as N

Intercept -5.3277 1.014 27.600 <.0001 — — 

NFARM_10YR 0.000211 0.000 6.100 0.014 NFARM_10YR 1 OI_CASE_DI 0.0151 0.022 0.465 0.496 OI_CASE_DI 1.015 DEPTH_TOI_ -0.00187 0.000 16.159 <.0001 DEPTH_TOI_ 0.998 ORDA -0.0127 0.006 4.905 0.027 ORDA 0.987 SILTAVE 0.0326 0.014 5.137 0.023 SILTAVE 1.033 WTDEPAVE 0.7355 0.192 14.668 0.0001 WTDEPAVE 2.086 

Nitrate concentration > 5 mg/L as N

Intercept -6.8249 1.296 27.746 <.0001 — — 

DEPTH_TOI_ -0.004 0.001 11.821 0.0006 — — NFARM_10YR 0.00042 0.000 13.843 0.0002 NFARM_10YR 1 OI_CASE_DI -0.05 0.042 1.437 0.231 — — ORDA -0.019 0.007 6.943 0.008 ORDA 0.981 SILTAVE 0.039 0.018 4.927 0.026 SILTAVE 1.04 WTDEPAVE 0.8839 0.251 12.409 0.0004 WTDEPAVE 2.42 DEPTH_TOI*OI_CASE_DI 0.000367 0.000 3.839 0.050 — — 

1. For continuous explanatory variables, the odds ratios correspond to a unit increase in the risk factors. For continuous explanatory variables, t

to the odds ratio for a unit increase of the corresponding effect variable. Odds ratios are computed only for variables not involved in an interactio

2. See Appendix 1 for a description of the coefficient variables.
Appendix 5. Logistic regression parameter estimates and odds ratio estimates for each of 10 logistic regression models.—[<, less than; >, greater than; mg/L, milligrams per liter; N, nitrogen; —, not applicable; see Appendix 6 for scatter plots of the relation between pabilities for each logistic regression model] Coefficient2 Value Standard error Chi-square value Probability the coefficient is significant Odds ratio es

Effect Point estimate 

Nitrate concentration > 6 mg/L as N Intercept -4.7459 1.240 14.648 0.0001 — — 

NFARM_10YR 0.000555 0.000 15.837 <.0001 NFARM_10YR 1.001 OI_CASE_DI -0.0909 0.052 3.024 0.082 — — WTDEPAVE 0.7818 0.277 7.982 0.005 WTDEPAVE 2.185 ORDA -0.0211 0.009 5.567 0.018 ORDA 0.979 DEPTH_TOI_ -0.00563 0.002 11.507 0.001 — — OI_CASE_D*DEPTH_TOI_ 0.000541 0.000 4.003 0.045 — — 

Nitrate concentration > 7 mg/L as N Intercept -1.187 1.012 1.375 0.241 — — 

NFARM_10YR 0.000422 0.000 8.746 0.003 NFARM_10YR 1 OI_CASE_DI -0.1599 0.067 5.694 0.017 — — DEPTH_TOI_ -0.00793 0.003 9.660 0.002 — — OI_CASE_D*DEPTH_TOI_ 0.000772 0.000 5.072 0.024 — — 

Nitrate concentration > 8 mg/L as N Intercept -1.396 1.076 1.684 0.194 — — 

NFARM_10YR 0.00047 0.000 9.257 0.002 NFARM_10YR 1 OI_CASE_DI -0.1614 0.068 5.608 0.018 — — DEPTH_TOI_ -0.00812 0.003 9.385 0.002 — — OI_CASE_D*DEPTH_TOI_ 0.000776 0.000 4.992 0.026 — — 

1. For continuous explanatory variables, the odds ratios correspond to a unit increase in the risk factors. For continuous explanatory variables, 

to the odds ratio for a unit increase of the corresponding effect variable. Odds ratios are computed only for variables not involved in an interacti

2. See Appendix 1 for a description of the coefficient variables.
Appendix 5. Logistic regression parameter estimates and odds ratio estimates for each of 10 logistic regression models.—[<, less than; >, greater than; mg/L, milligrams per liter; N, nitrogen; —, not applicable; see Appendix 6 for scatter plots of the relation between pabilities for each logistic regression model]

Coefficient2 Value Standard 

error

Chi-square 

value

Probability the 

coefficient is 

significant

Odds ratio es

Effect Point estimate 

Nitrate concentration > 9 mg/L as N

Intercept -1.0447 1.223 0.729 0.393 — — 

NFARM_10YR 0.000474 0.000 7.496 0.006 NFARM_10YR 1 OI_CASE_DI -0.2021 0.078 6.721 0.010 — — DEPTH_TOI_ -0.0104 0.003 10.107 0.002 — — OI_CASE_D*DEPTH_TOI_ 0.00103 0.000 6.656 0.010 — — 

Nitrate concentration > 10 mg/L as N

Intercept -2.1454 1.724 1.549 0.213 — — 

NFARM_10YR 0.000658 0.000 5.970 0.015 NFARM_10YR 1.001 OI_CASE_DI -0.26 0.095 7.482 0.006 — — DEPTH_TOI_ -0.0123 0.004 8.785 0.003 — — OI_CASE_D*DEPTH_TOI_ 0.00135 0.000 8.276 0.004 — — 

1. For continuous explanatory variables, the odds ratios correspond to a unit increase in the risk factors. For continuous explanatory variables, 

to the odds ratio for a unit increase of the corresponding effect variable. Odds ratios are computed only for variables not involved in an interacti

2. See Appendix 1 for a description of the coefficient variables.
Appendix 6.

0.6

0.4

0.2

0

1.0

0.8

0 0.2 0.4 0.6 0.8 1.0

1:1 line

R-squared: 0.95

Concentration

greater than

1 milligram per

liter as nitrogen

0.6

0.4

0.2

0

1.0

0.8

0 0.2 0.4 0.6 0.8 1.0

1:1 line

R-squared: 0.92

Concentration

greater than

2 milligrams per

liter as nitrogen

0.6

0.4

0.2

0

1.0

0.8

0 0.2 0.4 0.6 0.8 1.0

R-squared: 0.89

1:1 line

Concentration

greater than

3 milligrams per

liter as nitrogen

1:1 line 0.6

0.4

0.2

0

1.0

0.8

0 0.2 0.4 0.6 0.8 1.0

R-squared: 0.95

Concentration

greater than

4 milligrams per

liter as nitrogen

0.6

0.4

0.2

0

1.0

0.8

0 0.2 0.4 0.6 0.8 1.0

1:1 line

R-squared: 0.96

Concentration

greater than

5 milligrams per

liter as nitrogen

0.6

0.4

0.2

0

1.0

0.8

0 0.2 0.4 0.6 0.8 1.0

R-squared: 0.93

1:1 line

Concentration

greater than

6 milligrams per

liter as nitrogen

0.6

0.4

0.2

0

1.0

0.8

0 0.2 0.4 0.6 0.8 1.0

1:1 line

R-squared: 0.99

Concentration

greater than

7 milligrams per

liter as nitrogen

0.6

0.4

0.2

0

1.0

0.8

0 0.2 0.4 0.6 0.8 1.0

1:1 line

R-squared: 0.98

Concentration

greater than

8 milligrams per

liter as nitrogen

0.6

0.4

0.2

0

1.0

0.8

0 0.2 0.4 0.6 0.8 1.0

1:1 line

R-squared: 0.98

Concentration

greater than

9 milligrams per

liter as nitrogen

0.6

0.4

0.2

0

1.0

0.8

0 0.2 0.4 0.6 0.8 1.0

1:1 line

R-squared: 0.98

Concentration

greater than

10 milligrams per

liter as nitrogen

OBSERVED PROBABILITY THAT THE

NITRATE CONCENTRATION IS

GREATER THAN THE

CONCENTRATION

SPECIFIED

PREDICTED PROBABILITY THAT THE NITRATE CONCENTRATION IS GREATER THAN THE SPECIFIED CONCENTRATION

OBSERVED PROBABILITY THAT THE

NITRATE CONCENTRATION IS

GREATER THAN THE

CONCENTRATION

SPECIFIED

OBSERVED PROBABILITY THAT THE

NITRATE CONCENTRATION IS

GREATER THAN THE

CONCENTRATION

SPECIFIED

66 Relations That Affect the Probability and Prediction of Nitrate Concentration in Private Wells, Glacial Aquifer System

Appendix 6. Scatterplots showing predicted and observed probabilities of nitrate concentration greater than the specified 

concentration in private wells in the glacial aquifer system for all 10 logistic regression models developed for this study. 
Appendix 7. Spearman rank correlations of nitrate concentration with selected variables, probability significance (p), and number of samples.—Con[mg/L as N, milligrams per liter as nitrogen; %, percent; >, greater than; in., inches; ft, feet; ln(m), natural log of value in meters; km, kilometers; kg/km2/yr, kilograms per squarkilograms per square kilometer; km2, square kilometers; in./hr, inches per hour; NAWQA, National Water-Quality Assessment Program; DEM, digital elevation model; gray shacorrelations; bold indicates correlations significant at the 95-percent confidence level; plain text indicates correlations significant at the 90-percent confidence level]

Variable

Spearman 

correlation 

coefficient

Probability of 

a significant 

correlation

Number of 

samples Variable description Original data source or variable Desc

A00631 1 NA 379 Nitrate (mg/L as N) NAWQA data warehouse 

(http://infotrek.er.usgs.gov/traverse/f?p=NAWQA:HOME:1931200546639998)

Value at 

PCTAG -0.096 0.063 379 Agricultural land use (%) Nakagaki and others (2007) Area-we

within 

PCTFOR 0.098 0.056 379 Forest land use (%) Nakagaki and others (2007) Area-we

within 

PCTURBAN 0.088 0.089 379 Urban land use (%) Nakagaki and others (2007) Area-we

within 

AGGT50 -0.040 0.433 379 Agricultural land use > 50 % of area 

within 1,640 ft of a well, true/false binary indicator

Calculated for this report from 

Nakagaki and others (2007)

Determi

averathe w

FORGT50 0.083 0.105 379 Forest land use > 50 % of area 

within 1,640 ft of a well, true/false binary indicator

Calculated for this report from 

Nakagaki and others (2007)

Determi

averathe w

URBGT50 0.061 0.237 379 Urban land use > 50 % of area 

within 1,640 ft of a well, true/false binary indicator

Calculated for this report from 

Nakagaki and others (2007)

Determi

averathe w

MIXEDLU -0.063 0.224 379 Mixed land use, no land use greater 

than 50 % of within 1,640 ft of a well, true/false binary indicator

Calculated for this report from 

Nakagaki and others (2007)

Determi

averathe w

AWCAVE 0.054 0.305 357 Mean available water capacity 

(fraction)

Wolock (1997) Average

area w

BDAVE -0.291 <0.0001 357 Mean bulk density 

(grams per cubic centimeter)

Wolock (1997) Average

area w

CLAYAVE -0.007 0.902 357 Mean clay content (%) Wolock (1997) Average

area w

SANDAVE -0.103 0.051 357 Mean sand content (%) Wolock (1997) Average

area w
Appendix 7. Spearman rank correlations of nitrate concentration with selected variables, probability significance (p), and number of samples.—Con[mg/L as N, milligrams per liter as nitrogen; %, percent; >, greater than; in., inches; ft, feet; ln(m), natural log of value in meters; km, kilometers; kg/km2/yr, kilograms per squar

kilograms per square kilometer; km2, square kilometers; in./hr, inches per hour; NAWQA, National Water-Quality Assessment Program; DEM, digital elevation model; gray shadcorrelations; bold indicates correlations significant at the 95-percent confidence level; plain text indicates correlations significant at the 90-percent confidence level] Variable Spearman correlation coefficient Probability of a significant correlation Number of samples Variable description Original data source or variable Desc

SILTAVE 0.159 0.003 357 Mean silt content (%) Wolock (1997) Average

area w

RECHARGEBF -0.004 0.945 356 Mean annual recharge from base- flow analysis and Gebert runoff (in.) Wolock (2003) Area-we

within 

RUNOFF 0.049 0.353 356 Mean annual runoff (1951–80) from Gebert (in.) Gebert and others (1987) Area-we

within 

CONTACT -0.067 0.212 350 Subsurface flow contact time (days) Wolock and others (1997) Area-we

within 

DEPMIN -0.103 0.051 357 Depth to minimally permeable soil layer (in.) Wolock (1997) Average

area w

HGA 0.044 0.404 357 Soil hydrologic group A (%) Wolock (1997) Average

area w

WTDEPAVE 0.246 <0.0001 357 Mean depth to saturated soil (ft) Wolock (1997) Average

area w

OMAVE -0.135 0.011 357 Soil organic-matter content (%) Wolock (1997) Average

area w

ORDA -0.213 <0.0001 357 Soil order A (alfisols) (%) Wolock (1997) Average

area w

PCTCOARSE 0.059 0.252 379 Coarse-grained surficial material (%) Fullerton and others (2004); and Clawges and Price (1999); and National Park Service (1999). Average 

the w

PCTFINE -0.087 0.090 379 Percent fine-grained surficial material (%) Fullerton and others (2004); and Clawges and Price (1999); and National Park Service (1999). Average 

the w

SLOPE 0.159 0.003 356 Slope from 1-km-resolution DEM (%) K.J. Hitt, U.S. Geological Survey, written commun., 2006 Average

area w

TWI -0.068 0.199 356 Topographic wetness index from 1-km-resolution DEM (ln(m)) K.J. Hitt, U.S. Geological Survey, written commun., 2006 Average

area w
Appendix 7. Spearman rank correlations of nitrate concentration with selected variables, probability significance (p), and number of samples.—Con[mg/L as N, milligrams per liter as nitrogen; %, percent; >, greater than; in., inches; ft, feet; ln(m), natural log of value in meters; km, kilometers; kg/km2/yr, kilograms per squarkilograms per square kilometer; km2, square kilometers; in./hr, inches per hour; NAWQA, National Water-Quality Assessment Program; DEM, digital elevation model; gray shacorrelations; bold indicates correlations significant at the 95-percent confidence level; plain text indicates correlations significant at the 90-percent confidence level]

Variable

Spearman 

correlation 

coefficient

Probability of 

a significant 

correlation

Number of 

samples Variable description Original data source or variable Desc

PERDUN -0.022 0.673 356 Percent Dunne overland flow (%) K.J. Hitt, U.S. Geological Survey, 

written commun., 2006

Average

area w

PERHOR 0.077 0.154 349 Percent Hortonian overland flow 

(%)

K.J. Hitt, U.S. Geological Survey, 

written commun., 2006

Average

area w

PERMAVE 0.027 0.618 357 Average soil permeability (in./hr) Wolock (1997) Average

area w

ROCKDEPAVE -0.192 0.000 357 Average total soil thickness 

examined (in.)

Wolock (1997) Average

area w

DEPTH_TOI_ -0.240 <0.0001 347 Depth to top of open interval (ft) NAWQA data warehouse 

(http://infotrek.er.usgs.gov/traverse/f?p=NAWQA:HOME:1931200546639998)

Value at 

DEPTHBOI_F -0.198 0.000 314 Depth to bottom of open interval (ft) NAWQA data warehouse 

(http://infotrek.er.usgs.gov/traverse/f?p=NAWQA:HOME:1931200546639998)

Value at 

OILENGTH_I 0.125 0.027 314 Open interval length (in.) NAWQA data warehouse 

(http://infotrek.er.usgs.gov/traverse/f?p=NAWQA:HOME:1931200546639998)

Value at 

OI_CASE_DI 0.228 <0.0001 371 Diameter of open interval (in.) NAWQA data warehouse 

(http://infotrek.er.usgs.gov/traverse/f?p=NAWQA:HOME:1931200546639998)

Value at 

WELLDPTH_I -0.240 <0.0001 378 Well depth (ft) NAWQA data warehouse 

(http://infotrek.er.usgs.gov/traverse/f?p=NAWQA:HOME:1931200546639998)

Value at 

NDEP_10YRA -0.253 <0.0001 357 10-year mean nitrogen atmospheric 

deposition (kg/km2/yr)

Calculated for this report from 

Ruddy and others (2006)

Average 

the w
Appendix 7. Spearman rank correlations of nitrate concentration with selected variables, probability significance (p), and number of samples.—Con[mg/L as N, milligrams per liter as nitrogen; %, percent; >, greater than; in., inches; ft, feet; ln(m), natural log of value in meters; km, kilometers; kg/km2/yr, kilograms per squar

kilograms per square kilometer; km2, square kilometers; in./hr, inches per hour; NAWQA, National Water-Quality Assessment Program; DEM, digital elevation model; gray shadcorrelations; bold indicates correlations significant at the 95-percent confidence level; plain text indicates correlations significant at the 90-percent confidence level] Variable Spearman correlation coefficient Probability of a significant correlation Number of samples Variable description Original data source or variable Desc

NFARM_10YR -0.074 0.162 357 10-year mean nitrogen fertilizer applied to farms (kg/yr) Calculated for this report from Ruddy and others (2006) Average 

the w

NNONF_10YR 0.015 0.778 357 10-year mean nitrogen fertilizer applied to other than farms (kg/yr) Calculated for this report from Ruddy and others (2006) Average 

the w

PDENS00 0.019 0.718 379 2000 population density (people/km2) U.S. Census Bureau (2004) Average 

the w

PDENS90 0.003 0.949 379 1990 population density (people/km2) U.S. Census Bureau (1992) Average 

the w

SEWPUB 0.127 0.014 379 Public sewer (% of housing units) U.S. Census Bureau (1992) Average 

the w

SEWSEP -0.131 0.010 379 Septic tank or cesspool (% of housing units) U.S. Census Bureau (1992) Average 

the w

MEDYRBLT -0.054 0.297 379 Median year housing built U.S. Census Bureau (1992) Average 

the w

WATDRWEL -0.257 <0.0001 379 Individual well, drilled (% of housing units) U.S. Census Bureau (1992) Average 

the w

WATDUWEL 0.124 0.016 379 Individual well, dug (% of housing units) U.S. Census Bureau (1992) Average 

the w

WATPUBPV 0.199 <0.0001 379 Public system or private company (% of housing units) U.S. Census Bureau (1992) Average 

the w
Appendix 8. Variables selected in each of three iterations of the development of the 10 logistic regression models developed for this study.—Contin[>, greater than; mg/L as N, milligrams per liter as nitrogen; grey shaded indicates selected; grey shaded and crossed out indicates selected but later omitted from subsequent iteindicates not selected; ROC, Receiver Operating Characteristic Curve statistic; H-L, Hosmer-Lemeshow chi-square goodness-of-fit statistic; see Appendix 1 for description of v

Logistic regression models

Variable, 

goodness-of-fit

statistics, and 

number of wells

Nitrate 

concentration 

> 10 mg/L as N

Nitrate 

concentration 

> 9 mg/L as N

Nitrate 

concentration 

> 8 mg/L as N

Nitrate 

concentration 

> 7 mg/L as N

Nitrate 

concentration 

> 6 mg/L as N

Nitrate 

concentration 

> 5 mg/L as N

Nitrate 

concentration 

> 4 mg/L as N

Nitrate 

concentration 

> 3 mg/L as N

co

> 

First iteration of variable selection

interceptnfarm_10yrwelldpth_ioi_case_diwtdepaveordadepthtoi_irockdepavesiltaveoilength_ibdavedepthtoi*oi_case_diROC 0.86 0.929 0.901 0.892 0.863 0.851 0.797 0.825 

Second iteration of variable selection

interceptdepthtoi_ioi_case_dinfarm_10yrwtdepaveordasiltaveoilength_idepthtoi*oi_case_diROC 0.952 0.918 0.901 0.89 0.877 0.87 0.797 0.819 
Appendix 8. Variables selected in each of three iterations of the development of the 10 logistic regression models developed for this study.—Contin[>, greater than; mg/L as N, milligrams per liter as nitrogen; grey shaded indicates selected; grey shaded and crossed out indicates selected but later omitted from subsequent iteindicates not selected; ROC, Receiver Operating Characteristic Curve statistic; H-L, Hosmer-Lemeshow chi-square goodness-of-fit statistic; see Appendix 1 for description of v

Logistic regression models Variable, goodness-of-fit statistics, and number of wells Nitrate concentration > 10 mg/L as N Nitrate concentration > 9 mg/L as N Nitrate concentration > 8 mg/L as N Nitrate concentration > 7 mg/L as N Nitrate concentration > 6 mg/L as N Nitrate concentration > 5 mg/L as N Nitrate concentration > 4 mg/L as N Nitrate concentration > 3 mg/L as N 

co

> 

Third iteration of variable selection and final models intercept depthtoi_i oi_case_di nfarm_10yr wtdepave orda siltave oilength_i depthtoi*oi_case_di ROC 0.948 0.918 0.901 0.890 0.877 0.870 0.820 0.815 

H-L 2.0 5.3 6.5 4.0 9.6 4.4 4.9 6.0 H-L probability 0.9 0.6 0.6 0.9 0.3 0.8 0.8 0.6 H-L degrees of freedom 6 7 8 8 8 8 8 8 Number of wells used in each model 14 19 21 22 26 36 50 68 
Appendixes 1–9 73

Appendix 9. Linear regression to predict network mean nitrate concentration using the same variables 

used in the logistic regression models. The variables were used because they were used in the logistic 

regression models. The significance level of variables was not a consideration for this model.

[NA, not applicable; see figure 10.1 for scatter plot of relation between observed and predicted probabilities; see appendix 

1 for description of variables; multiple R-squared = 0.83; F-statistic = 5.45 on 7 and 8 degrees of freedom and p-value = 

0.02; the variables were used because they were used in the logistic regression models and the significance level of variables was not a consideration for this linear regression model]

Coefficient variables Value Standard error

Probability the 

coefficient is 

significant

Probability of 

significance 

if coefficient 

variable is added 

sequentially, 

first to last

Intercept (NULL Model) -2.184 1.420 0.16 NA

mDiamOIin 0.158 0.081 0.09 0.00

mwtdepave 0.479 0.320 0.17 0.12

morda -0.017 0.011 0.17 0.61

msiltave 0.054 0.029 0.10 0.40

mnfarm.10y 0.000 0.000 0.19 0.41

moilength -0.003 0.006 0.64 0.82

mdepthtoi -0.001 0.001 0.07 0.07


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d—Relations That Affect the Probability and Prediction of Nitrate Concentration in Private Wells, Glacial Aquifer System—SIR 2010–5100

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