Lake Sna

Walcott ke River

Big

River

Little River

Wood Wood

Water-Resources Investigations Report 03–4143

U.S. Department of the Interior

U.S. Geological Survey

Prepared in cooperation with

Idaho Department of Environmental Quality and 

Probability of Detecting Elevated Concentrations

of Nitrate in Ground Water in a Six-County Area

of South-Central Idaho

Cassia, Gooding, Jerome, Lincoln, Minidoka, and Twin Falls Counties

Version 1.1
Probability of Detecting Elevated Concentrations of 

Nitrate in Ground Water in a Six-County Area of 

South-Central Idaho

By Kenneth D. Skinner and Mary M. Donato

Water-Resources Investigations Report 03–4143

Prepared in cooperation with 

IDAHO DEPARTMENT OF ENVIRONMENTAL QUALITY and

CASSIA, GOODING, JEROME, LINCOLN, MINIDOKA, AND TWIN FALLS COUNTIES

Boise, Idaho

2003

NOTE: On June 23, 2005, a correction was made on page 10, third

paragraph, first sentence, by the addition of the line, "...from the 

ISDA for 1998. Crops belonging to the legume... "
U.S. DEPARTMENT OF THE INTERIOR

Gale A. Norton, Secretary

U.S. GEOLOGICAL SURVEY

Charles G. Groat, Director

The use of firm, trade, and brand names in this report is for identification purposes

only and does not constitute endorsement by the U.S. Government.

Additional information can be 

obtained from:

District Chief

U.S. Geological Survey

230 Collins Road

Boise, ID 83702-4520

http://idaho.usgs.gov

Copies of this report can be 

purchased from:

U.S. Geological Survey

Information Services

Box 25286

Federal Center

Denver, CO 80225

e-mail: infoservices@usgs.gov

Copies of this report also are 

available in PDF format, which can 

be viewed using Adobe Acrobat 

Reader, at URL:

http://idaho.usgs.gov/public/reports.html 
Contents iii

CONTENTS

Contents

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

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

Background. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2

Purpose and scope. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2

Acknowledgments . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2

Study area description and geohydrology . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3

Snake River Plain aquifer . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3

Perched aquifer . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3

Tributary valley aquifers. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3

Model development approach . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5

Ground-water quality data. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5

Hydrogeologic and anthropogenic data. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8

Estimating the probability of detecting elevated nitrate concentrations in ground water . . . . . . . . . . . . . . . . . . . 11

Statistical methods and the logistic regression model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13

Univariate analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13

Multivariate logistic regression analysis. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15

Construction of the elevated nitrate concentration probability map. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16

Evaluation and testing of probability models . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16

Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21

References cited . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21

FIGURES

1–5. Maps showing:

1. Location of the study area and the perched aquifer in the Burley area, 

south-central Idaho. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4

2. Sources and locations of ground-water samples analyzed for nitrate, 

south-central Idaho. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6

3. Elevated nitrate concentrations detected or not detected in ground-water samples used 

to construct and verify the probability model, south-central Idaho . . . . . . . . . . . . . . . . . . . . . . . 7

4. Nitrogen input, south-central Idaho . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9

5. Location of the flow-model boundary and rates of ground-water velocity, 

south-central Idaho. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12

6. Boxplots showing correlation between nitrate concentrations and land use classified by the 

Bureau of Reclamation and the Idaho Department of Water Resources, south-central Idaho . . . . . . . 15

7. Map showing probability of detecting elevated nitrate concentrations in ground water, 

south-central Idaho . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17

 8. Graph and boxplot showing correlation between groups of predicted probabilities of detecting 

elevated nitrate concentrations and actual detections of elevated nitrate concentrations in 

ground-water samples used in the model data set, south-central Idaho . . . . . . . . . . . . . . . . . . . . . . . . 18

9. Graph and boxplot showing correlation between groups of predicted probabilities of detecting 

elevated nitrate concentrations and actual detections of elevated nitrate concentrations in 

ground-water samples used in the verification data set, south-central Idaho . . . . . . . . . . . . . . . . . . . . 19

 10. Map showing correctly and incorrectly predicted detections of elevated nitrate 

concentrations in ground water using a probability cutpoint of 0.50, south-central Idaho. . . . . . . . . . 20
iv Probability of Detecting Elevated Concentrations of Nitrate in Ground Water in a Six-County Area of South-Central Idaho

75th percentile plus

 1.5 times the IQR

25th percentile minus

 1.5 times the IQR

Interquartile range

(IQR)

Outlier

75th percentile

Median (50th percentile)

25th percentile

Outlier

EXPLANATION

for boxplots shown in

figures 6, 8 and 9

Number of measurements

 or samples

27

TABLES

1. Results from univariate correlations between independent variables and elevated nitrate 

detections or nitrate concentrations in ground water, south-central Idaho . . . . . . . . . . . . . . . . . . . . . . 14

 2. Variables selected for use in the final probability model, south-central Idaho. . . . . . . . . . . . . . . . . . . 16

CONVERSION FACTORS, ABBREVIATED WATER-QUALITY UNIT, AND BOXPLOT EXPLANATION

Multiply By To obtain

acre 4,047 square meter (m2)

foot (ft) 0.3048 meter (m)

foot per hour (ft/hr) 0.3048 meter per hour (m/hr)

foot squared per day (ft2/d)1 0.09290 meter squared per day (m2/d)

gallon per minute (gal/min) 0.06309 liter per second (L/s)

inch (in.) 25.4 millimeter (mm)

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

mile (mi) 1.609 kilometer (km)

pound (lb) 0.4536 kilogram (kg)

pound per acre (lb/acre) 1.121 kilogram per square meter (kg/m2)

pound per acre per year [(lb/acre)/yr] 1.121 kilogram per square meter per year [(kg/m2)/yr]

pound per day (lb/d) 0.4536 kilogram per day (kg/d)

square mile (mi2) 2.590 square kilometer (km2)

1 The standard unit for transmissivity is cubic foot per day per square foot times foot of aquifer thickness [(ft3/d)/ft2]ft. This mathematical expression reduces to foot squared per day (ft2/d).

Abbreviated water-quality unit:

mg/L milligram per liter
Introduction 1

Probability of Detecting Elevated Concentrations of 

Nitrate in Ground Water in a Six-County Area of 

South-Central Idaho

By Kenneth D. Skinner and Mary M. Donato

Abstract

A probability map constructed for this study 

identi ed se veral areas in a six-county region of 

south-central Idaho with high probabilities of 

detecting elevated concentrations (greater than 

2 milligrams per liter) of nitrate. An increasing 

proportion of Idaho’s ground water being used 

for drinking water and large increases in the inputs 

of nitrogen to ground water in Cassia, Gooding, 

Jerome, Lincoln, Minidoka, and Twin Falls Counties have prompted concerns about the quality of 

the resource. The probability map was constructed 

to assist regulatory and resource agencies in managing land use and protecting water resources.

To construct the probability map, hydrogeologic and anthropogenic data were integrated with 

ground-water quality data in a geographic information system. The resulting data set contained 

land use, geology, precipitation, soil characteristics, depth to ground water, nitrogen input, and 

ground-water velocity information for each of the 

1,365 samples collected from 1991 to 2001. Logistic regression analysis was used to determine the 

most statistically signi cant v ariables related to 

the detection of elevated nitrate concentrations.

The resulting multivariate probability model 

showed that ground-water velocity, nitrogen input, 

precipitation, soil drainage, land use, and depth to 

ground water were signi cantly correlated with 

elevated nitrate concentrations. A subset of the 

water-quality data set was used to verify these 

results. Linear regression of the percentage of predicted probabilities of elevated nitrate concentrations and the actual percentage of elevated nitrate 

concentrations with the model data set and the veri cation data set both sho wed good correlations: 

r-squared values were 0.96 and 0.97, respectively. 

Statistical comparisons of both data sets showed 

that ground-water samples containing elevated 

nitrate concentrations had signi cantly higher 

probabilities of detection (p < 0.001) than samples 

without elevated nitrate concentrations. On the 

basis of these results, a map identifying the probability of detecting elevated nitrate concentrations 

was constructed. High-probability areas on the 

map coincided with regions of agricultural land 

use and high nitrogen input, except in southern 

Gooding County and western Jerome County. In 

these areas, high ground-water velocities representing a predominance of regional ground water 

resulted in a low probability of detecting elevated 

nitrate concentrations. Areas of poor prediction 

tended to be congregated along the transition zone 

between high and low ground-water velocities in 

Jerome and Gooding Counties, indicating a mix of 

regional and recently recharged ground water.

INTRODUCTION

Introduction

Ground-water quality is an ongoing concern in 

Idaho. In 1990, ground water accounted for nearly 

85 percent of the State’s drinking water; in 1995, it 

accounted for almost 95 percent (Solley and others, 

1993, 1998). Previous studies have detected high concentrations of nitrate in many aquifers in the State 

(Rupert, 1994; Crockett, 1995; Rupert and others, 

1996). Predominant sources of nitrate in much of the 

State are inorganic fertilizer, cattle manure, and legume 

crops (Rupert, 1997). Because of the stable agricultural 

industry and large increases in the dairy industry, especially in Gooding, Jerome, and Twin Falls Counties 

(Idaho Agricultural Statistics Service, 1999; U.S. 

Department of Agriculture, 1999), resource managers 

and planners are in need of tools to aid in land-use planning and water-resource management and protection.
2 Probability of Detecting Elevated Concentrations of Nitrate in Ground Water in a Six-County Area of South-Central Idaho

Maps showing the probability of detecting elevated 

nitrate concentrations can be important tools to aid regulatory and resource-protection agencies. Ground-water 

probability maps indicate the predisposition of areas to 

ground-water contamination on the basis of natural and 

anthropogenic factors. These maps also can assist other 

organizations such as agricultural producers; city governments; planning and zoning commissions; and State 

programs related to Wellhead Protection, Drinking 

Water, and Best Management Plans. 

For this study, elevated nitrate concentrations or 

nitrate detections are considered greater than 2 mg/L. A 

nitrate concentration of 2 mg/L was chosen because it 

was the concentration used in other similar studies in 

the area (Rupert, 1998; Donato, 2000) and is high 

enough above local background concentrations, typically below 1 mg/L, to indicate an anthropogenic in uence on ground water.

Background

Most maps showing the vulnerability of areas to 

ground-water contamination are created using a geographic information system (GIS) to combine hydrogeologic and anthropogenic data such as land use, soil 

properties, and depth to ground water. One of the most 

widely used methods for producing such maps is the 

DRASTIC model (Aller and others, 1985). The DRASTIC model uses point ratings assigned to seven factors: 

Depth to ground water, net Recharge, Aquifer media, 

Soil media, Topography, Impact of vadose zone media, 

and hydraulic Conductivity of the aquifer. The ratings 

are added together in data layers in a GIS to make a vulnerability map. DRASTIC models usually are not calibrated to actual ground-water contaminant concentrations.

Another method of vulnerability mapping uses statistical correlations between environmental factors and 

water-quality data. A statistical method used to calibrate 

nitrate vulnerability maps with water-quality data was 

developed by the U.S. Geological Survey (USGS) 

National Water-Quality Assessment (NAWQA) Program for the upper Snake River Basin, southeastern 

Idaho (Rupert, 1997). This method differs from the 

DRASTIC method by calculating the probability of 

contamination on the basis of statistical correlations 

between measured nitrate concentrations in ground 

water and land use, soils, and depth to ground water.

The statistical method was improved by using 

logistic regression to relate water-quality data to hydrogeologic and anthropogenic data. Two probability maps 

for detecting the herbicide atrazine have been created, 

one for the upper Snake River Basin and one for the 

western Snake River Plain (Rupert, 1998; Donato, 

2000). These maps are called probability maps because 

they delineate areas according to the probability of 

detecting a contaminant in that area. Calibrated contaminant probability maps are a superior predictive tool 

over maps produced using the modi ed DRASTIC 

method because the actual probabilities of contaminant 

detection can be quanti ed.

The probability map developed in this study 

encompasses a smaller area than those of Rupert (1998) 

and Donato (2000). To compensate for the difference in 

study area size, a larger scale soil data set was used than 

in the previous two studies. In addition, an aquifer property data layer was incorporated to provide another 

explanatory factor for the probability of detecting elevated nitrate concentrations in ground water.

Purpose and Scope

The main purpose of this report is to document the 

construction and veri cation of a map sho wing the 

probability of detecting elevated nitrate concentrations

in ground water in south-central Idaho. A GIS was utilized to examine relations between elevated nitrate in 

ground water and hydrogeologic and anthropogenic factors. The data set consisted of 1,365 ground-water samples collected from 1991 to 2001. This report also documents the construction of three GIS layers—a nitrogen 

input layer, a ground-water velocity layer, and a depthto-water layer—used to construct the probability map. 

Logistic regression was used to develop the statistical 

model that predicts the probability of detecting elevated 

nitrate concentrations in ground water.

Acknowledgments

The author wishes to thank the following people 

and agencies: Dave Clark and Patrick Lambert (USGS) 

for valuable discussions leading to improvements in the 

probability model, and Idaho State Department of Agriculture (ISDA) and Idaho Department of Environmental 

Quality (IDEQ) for providing an extensive additional 

nitrate concentration data set.
Study Area Description and Geohydrology 3

STUDY AREA DESCRIPTION AND 

GEOHYDROLOGY

Study Area Description and Geohydrology

Cassia, Gooding, Jerome, Lincoln, Minidoka, and 

Twin Falls Counties compose the study area, approximately 7,800 mi2 ( g. 1) in south-central Idaho. Most 

of the study area is in the downstream part of the eastern Snake River Plain and is bounded on the south by 

mountains and tributary valleys. About 57 percent of the 

area is rangeland, 17 percent is ood-irrig ated land, 

11 percent is sprinkler-irrigated land, and the remaining 15 percent is composed of six other land-use types. 

Most of the agricultural land in the study area is near 

the Snake River. The area is predominantly semiarid; 

mean annual precipitation ranges from 10 in. on the 

Snake River Plain to 40 in. on the mountains in central 

Cassia County.

The study area ground-water system is made up of 

three types of aquifers: a regional basalt aquifer, a local 

perched alluvial aquifer, and tributary valley aquifers. 

The regional basalt aquifer underlying the eastern 

Snake River Plain provides most of the ground water 

that moves through the study area. The local perched 

alluvial aquifer ( g. 1) o verlying the eastern Snake 

River Plain near Minidoka and Cassia Counties and the 

tributary valley aquifers in the southern part of the study 

area are lesser sources of ground water.

Snake River Plain Aquifer

North of the Snake River in the study area is the 

eastern Snake River Plain aquifer, composed primarily 

of vesicular and fractured olivine basalt o ws (Quaternary age) of the Snake River Group (Whitehead, 1992). 

Individual o ws average 20 to 25 ft in thickness. The 

top of the basalt is generally less than 100 ft below land 

surface throughout this part of the plain, and the thickness of the basalt is more than 1,000 ft in places.

Layered basalt o ws in the eastern Snake River 

Plain aquifer yield exceptionally large volumes of water 

to wells and springs. Individual well yields are some of 

the highest in the Nation and typically range from 2,000 

to 3,000 gal/min to 7,000 gal/min with minimal drawdown (Whitehead, 1992; Lindholm, 1996). Transmissivity can be as high as 1,000,000 ft2/d and is commonly 100,000 ft2/d (Whitehead, 1992). Locally, aquifer properties can vary greatly; however, on a regional 

scale, the variability is minimal.

Regional ground-water movement in the eastern 

Snake River Plain aquifer is from the northeast to the 

southwest (Rupert, 1997). Ground water is discharged 

as springs and seeps to the Snake River along the reach 

bordering Twin Falls, Jerome, and Gooding Counties. 

Ground-water discharge to this reach of the Snake River 

increased considerably from about 1910 through the 

early 1950s (Kjelstrom, 1992). The increase is attributed to recharge from surface-water irrigation north of 

the Snake River. Since the early 1950s, ground-water 

discharge to the Snake River has decreased as a result 

of increased ground-water withdrawals for irrigation 

(Moreland, 1976), the introduction of more ef cient 

irrigation practices such as conversion from ood to 

sprinkler irrigation, and local droughts (Kjelstrom, 

1992). Changes in ground-water levels re ect the same 

long-term downward trend as does spring discharge 

(Kjelstrom, 1992; Rupert, 1997). 

Perched Aquifer

An alluvial aquifer is perched above a blue-clay 

layer about 60 to 120 ft below land surface in the Burley 

area ( g. 1) (Rupert, 1997). The top of the clay layer 

was previously mapped on the basis of data from several hundred well-driller records. Water in the perched 

aquifer moves northward at the southern boundary of 

the perched aquifer and westward near the western 

boundary. The water level in the perched aquifer is 

about 100 ft above that of the Snake River Plain aquifer. 

Recharge to the perched aquifer is predominantly in ltration of irrigation water. According to local accounts, 

the perched aquifer was formed in 1907 when a canal 

network was constructed through the area to transport 

irrigation water. Reportedly, several wells completed in 

this aquifer go dry seasonally after irrigation ceases and 

become operational again after the start of the next irrigation season.

Tributary Valley Aquifers

Tributary valley aquifers south of the Snake River 

recharge the regional Snake River Plain aquifer in the 

study area. They are predominantly alluvial deposits 

that inter nger with the Snak e River Group near the 

mouths of the valleys. A more complete description of 

these valley aquifers is provided by Mundorff and others (1964).
Base from U.S. Geological Survey

digital data, Hydrography 1:2,000,000,

1995; Urban areas 1:2,000,000, 1994;

Transverse Mercator projection

Factor at central meridian: 0.99960

Longitude of central meridian:

-114∞00'; Latitude of origin: 42∞00'

False easting (meters): 500,000

False northing (meters): 100,000

115∞00' 114∞30' 114∞00' 113∞30'

43∞00'

42∞30'

42∞00'

Twin Falls Kimberly

Oakley

Filer Paul

Buhl

Wendell

Jerome

Gooding

Burley

Rupert Lake Walcott

Snake

River

Big

River

Little

River

Wood Wood

Raft

River

Snake

River

LINCOLN

GOODING

MINIDOKA

JEROME

TWIN

FALLS

CASSIA

0

0

5

5

15

15

10

10

20 MILES

20 KILOMETERS

EXPLANATION

Perched aquifer

Not delineated

IDAHO

WYOMING

NEVADA UTAH

Western Snake River Plain

Eastern Snake River Plain

Upper Snake River Basin

Study

area

Figure 1. Location of the study area and the perched aquifer in the Burley area, south-central Idaho.

4 Probability of Detecting Elevated Concentrations of Nitrate in Ground Water in a Six-County Area of South-Central Idaho
5

MODEL DEVELOPMENT APPROACH

The creation of the elevated nitrate probability 

model closely followed the methodologies of Rupert 

(1998) and Donato (2000). These studies were based on 

water-quality data from the Idaho Statewide GroundWater Monitoring Program (ISGWMP), a cooperative 

program between the USGS and the Idaho Department 

of Water Resources (IDWR). Rupert (1998) used additional data collected as part of the USGS NAWQA Program. Because of poor spatial distribution of ISGWMP 

and NAWQA nitrate data in the study area, it was uncertain whether a statistically valid model for producing 

the probability maps could be built. Thus, additional 

nitrate data from the USGS National Water Information 

System (NWIS) data base, the IDEQ, and the ISDA 

were used for this study.

The elevated nitrate probability map was constructed using mostly existing data and published interpretation of o w, statistical methods that model the 

probability, and a GIS to process the data and produce 

the nal map. First, all the nitrate data from the multiple 

data bases were combined. Next, relations between the 

occurrence of elevated nitrate concentrations and 

hydrologic and anthropogenic data were evaluated 

using a GIS and statistical methods, including logistic 

regression. Univariate relations between elevated nitrate 

concentrations and land use, geology, precipitation, soil 

characteristics, depth to ground water, nitrogen input, 

and ground-water velocity were examined to identify 

explanatory variables. Multivariate logistic regression 

was used to determine the best probability model using 

a forward-stepwise approach with a backward check for 

elimination. The nal model then w as entered into a 

GIS to produce the probability map.

GROUND-WATER QUALITY DATA

Ground-Water Quality Data

Initial phases of model development incorporated 

nitrate data collected as part of the ISGWMP, the USGS 

NAWQA Program, and a 70-well network established 

in Cassia and Twin Falls Counties speci cally for this 

study. Primary objectives of the ISGWMP are to characterize the quality of water in Idaho’s aquifers, identify 

temporal trends in water quality in individual aquifers, 

and identify potential ground-water quality problem 

areas (Idaho Department of Water Resources, 1995; 

Neely, 2001). The goals of the NAWQA Program are to 

(1) describe current water-quality conditions for a large 

part of the Nation’s freshwater streams, rivers, and aquifers; (2) describe water-quality trends; and (3) improve 

understanding of the primary natural and human factors 

that affect water-quality conditions. The purpose of the 

additional 70-well network was to aid in calibrating 

nitrate probability maps in areas of Cassia and Twin 

Falls Counties where the data were sparse. All the 

nitrate data used for this study were collected during 

1993 to 2001. If multiple data were available from a single well, the most recent data value was used. All programs used a random well-selection process and similar 

sampling methods. 

Spatial distribution of wells in the data sets indicated that most of the sampled wells were located in 

agricultural and urban areas. Thus, initial statistical 

models based on these data were of limited use for 

describing the probability of detecting elevated nitrate 

concentrations in other land-use areas. To create a more 

robust statistical model, additional nitrate data collected 

during previous USGS studies and stored in the USGS 

NWIS data base were used. Nitrate data from the following data bases also were added to the data set used 

in nal statistical modeling: ISD A — ground-water 

monitoring networks and a one-time analysis of water 

from wells at dairies statewide; and IDEQ — individual 

ground-water quality investigations statewide and the 

Drinking Water Information Management System public water-supply data base ( g. 2). Samples collected 

and analyzed by the USGS were reported as nitrite plus 

nitrate as nitrogen (NO2 + NO3–N), whereas the 

remainder of the samples were analyzed by the Idaho 

State Laboratory and reported as nitrate as nitrogen 

(NO3 – N). Concentrations of nitrite in ground water in 

the study area are typically negligible; therefore, USGS, 

IDEQ, and ISDA analyses were considered equivalent. 

Some of the additional nitrate data did not have associated well depths and water levels, so a generalized 

depth-to-water map was used instead of well depth and 

water-level measurements during statistical analysis. 

Also, some of the additional samples were collected 

from wells that were not randomly selected; however, 

these samples accounted for only a small proportion of 

the total data set. The entire data set consisted of 1,365 

samples, collected from 1991 to 2001.

A random selection process in the statistical software was used to extract 20 percent of the sample set 

for external veri cation of the statistical model. The 

veri cation data set w as viewed in a GIS to ensure a 

good spatial distribution.

Ground-Water Quality Data
115∞00' 114∞30' 114∞00' 113∞30'

43∞00'

42∞30'

42∞00'

Lake

Walcott

Snake River

Big

River

Little

River

Wood Wood

Raft

River

Snake

River

LINCOLN

GOODING

MINIDOKA

JEROME

TWIN

FALLS

CASSIA

0

0

5

5

15

15

10

10

20 MILES

20 KILOMETERS

EXPLANATION

Perched aquifer

Not delineated

U.S. Geological Survey nitrate sample

Idaho State Department of Environmental Quality nitrate sample

Idaho Department of Agriculture

nitrate sample

Figure 2. Sources and locations of ground-water samples analyzed for nitrate, south-central Idaho.

6 Probability of Detecting Elevated Concentrations of Nitrate in Ground Water in a Six-County Area of South-Central Idaho
115∞00' 114∞30' 114∞00' 113∞30'

43∞00'

42∞30'

42∞00'

115∞00' 114∞30' 114∞00' 113∞30'

43∞00'

42∞30'

42∞00'

LINCOLN

GOODING

MINIDOKA

JEROME

TWIN

FALLS

CASSIA

LINCOLN

GOODING

MINIDOKA

JEROME

TWIN

FALLS

CASSIA

0

0

5

5

15

15

10

10

20 MILES

20 KILOMETERS

Samples used to construct

the probability model

Samples used to verify

the probability model

EXPLANATION

Not delineated

Nitrate concentration greater

than 2 milligrams per liter

Nitrate concentration equal to

or less than 2 milligrams

per liter

Figure 3. Elevated nitrate concentrations detected or not detected in ground-water samples used to construct and verify the

probability model, south-central Idaho. (Elevated, greater than 2 milligrams per liter)

Ground-Water Quality Data 7
8 Probability of Detecting Elevated Concentrations of Nitrate in Ground Water in a Six-County Area of South-Central Idaho

Of the 1,095 samples used to create the statistical 

model and probability map, 656 contained an elevated 

nitrate concentration; 161 out of 270 samples in the veri cation data set contained an ele vated nitrate concentration ( g. 3). Nitrate concentrations in both data sets 

ranged from less than 0.05 to 26 mg/L as N; concentrations in 56 of the 1,365 samples exceeded the U.S. 

Environmental Protection Agency (EPA) maximum 

contaminant level of 10 mg/L. 

HYDROGEOLOGIC AND ANTHROPOGENIC DATA

Hydrogeologic and Anthropogenic Data

Hydrogeologic and anthropogenic data used in this 

study included land use, precipitation, sur cial geology , 

soil characteristics, nitrogen input, relative groundwater velocity, and depth to water. These data are available in GIS format from a variety of sources. 

Two sets of land-use data were evaluated for use in 

the probability model, one from IDWR and one from 

the Bureau of Reclamation (BOR). The IDWR land-use 

data were combined from three maps: one showing vegetation type, one differentiating between sprinkler and 

 ood irrig ation, and one differentiating between dryland and irrigated agriculture. The BOR mapped land 

cover at 1:40,000 scale from digitized high-altitude 

aerial photographs taken in 1987 and eld check ed in 

1992. Each land-use data set has unique advantages. 

The IDWR data were mapped at a scale of 1:100,000 

and included classi cations for la va o ws, dryland agriculture, rangeland, and forest land. The BOR data were 

mapped at a larger scale but combined forest, lava 

 o ws, and rangeland into one classi cation, nati ve 

lands. Each land-use data set was evaluated separately 

to determine which produced the best correlation with 

elevated nitrate concentrations.

A precipitation GIS data set (1:250,000) was 

obtained from the Water and Climate Center of the Natural Resources Conservation Service (NRCS) and represents mean annual precipitation from 1961 to 1990. 

The sur cial geology GIS data set is from a digitized geologic map by Whitehead (1986) at a scale of 

1:100,000.

Soils data were obtained from the NRCS Soil Survey Geographic (SSURGO) data base. SSURGO soil 

maps are made at scales ranging from 1:12,000 to 

1:63,360. Previous analyses of the Snake River Plain by 

Rupert (1998) and Donato (2000) incorporated data 

from the State Soil Geographic Database (STATSGO), 

which are mapped at a scale of 1:250,000. Use of the 

SSURGO soils data set provided a signi cant impro vement over the STATSGO data set as a result of the small 

size of the study area. The soil characteristics evaluated 

in the statistical model were percentage of clay content, 

drainage, hydrologic group (in ltration), percentage of 

organic matter, permeability, and soil depth. Clay content, organic matter, and permeability were assigned 

values for each soil horizon. A weighted average for the 

entire soil column was used for the statistical analysis.

The method used to estimate nitrogen input and 

losses for the study area followed that of Rupert (1996). 

Five sources of nitrogen were considered: fertilizer, 

cattle manure (dairy and beef), septic systems, atmospheric deposition (precipitation), and legume crops. 

Nitrogen losses resulting from crop uptake; decomposition of previous-year nonleguminous crop residue 

(chaff); and storage, volatilization, denitri cation, and 

inorganic nitrogen availability of cattle manure were 

estimated. 

Most nitrogen sources, including cattle inventories 

and crop acreages, were determined using 1998 data. 

Exceptions were fertilizer sales data, which were available only for 1997, and population household estimates 

for septic systems, which were adjusted to approximate 

1998 data.

Because speci c nitrogen application maps were 

not available, nitrogen input values were distributed 

according to the BOR’s land-use coverage. For example, nitrogen input from fertilizer was applied only to 

land classi ed as residential or agricultural (dry f armed 

and ood- or sprinkler -irrigated land), whereas nitrogen 

from septic systems was applied only to residential or 

commercial land, because actual septic system locations 

are not available. The nitrogen input categories are 

county-level estimates distributed by land-use type in 

each county, so arti cial discontinuities occur at county 

boundaries ( g. 4).

Nitrogen fertilizer use for the six counties in the 

study area were estimated using a method similar to that 

of Battaglin and Goolsby (1995). The ratio of expenditures for commercial fertilizer in the county to expenditures for commercial fertilizer in the State was multiplied by the number of pounds of nitrogen applied in 

the entire State to obtain the number of pounds of nitrogen applied in each county, as follows:

$ spent in county

$ spent in State 

= pounds of nitrogen applied in 

county (1)

( ) X pounds of nitrogen applied in State
115° 00' 114° 30' 114° 00' 113° 30'

43° 00'

42° 30'

42° 00'

00

5

Figure 4. Nitrogen input, south-central Idaho.

Hydrogeologic and Anthropogenic Data 9
10 Probability of Detecting Elevated Concentrations of Nitrate in Ground Water in a Six-County Area of South-Central Idaho

The calculations of nitrogen fertilizer use are based 

on State and county fertilizer sales gures from the 

1997 U.S. Department of Agriculture’s Census of Agriculture. The nitrogen from fertilizer data then were 

divided by the total number of agricultural and residential acres in each county to obtain the number of pounds 

of nitrogen applied per acre. The resulting county-level 

nitrogen inputs for the six counties in the study area are 

reasonable when compared with those reported for the 

six-county study area in 1991 by Battaglin and Goolsby 

(1995). 

Nitrogen losses from crop uptake were applied 

only to agricultural land-use types. Estimated nitrogen 

losses from crop uptake were calculated by determining 

the amount of nitrogen required for a given crop and 

yield and dividing by the acres of that crop in a county. 

Crop uptake was estimated for the major crops grown in 

each county based on 1998 data (barley, sugar beets, 

potatoes, oats, wheat, and corn).

For this study, nitrogen input from legumes was estimated using alfalfa and dry bean crop data by county 

family, such as clovers, alfalfa, and beans, establish a 

symbiotic relationship with microbes that reside in nodules on the roots of the host plant and x atmospheric 

nitrogen. The nitrogen xation rates were from a report 

by Goolsby and others (1999): 194.5 lb/acre for alfalfa 

and 53.7 lb/acre for dry beans.

Nitrogen input resulting from dairy cattle was 

estimated for areas with known dairy operations and 

weighted by the average number of dairy cattle per 

facility. These data were provided by ISDA for 429 

dairies in the study area, probably a fraction of the total 

number of dairies (Danielle Bruno, Idaho State Department of Agriculture, oral commun., 2000). A contour 

map, based on the dairy locations and number of dairy 

cattle, was created in intervals of 50 animals, ranging 

from 1 to 450 animals/mi2. This allowed a range of 

nitrogen input values, in pounds per acre, to be assigned 

spatially on the basis of the estimated number of animals per acre. It was assumed that dairy cattle produce 

0.45 lb/d of nitrogen per animal (Lander and others, 

1998).

Ranges of nitrogen losses from storage and application of dairy cattle manure summarized by Rupert 

(1996) were used. The type of manure storage system 

determines the amount of loss, ranging from 80 percent 

in open lagoons to 15 percent by spreading. Volatilization losses (mostly as ammonia) during eld application 

range from 5 to 30 percent. Denitri cation losses (loss 

of inorganic nitrogen by biological conversion to nitrogen gas) range from 0 to 40 percent depending upon 

soil drainage properties. Rupert (1996) summarized 

a range of estimates of organic nitrogen from cattle 

manure that is not available for plant uptake or leaching. 

This organically bound nitrogen breaks down in the soil 

over time and forms inorganic nitrogen, which then is 

available for plant uptake and leaching. Nitrogen availability ranges from 45 to 96 percent after the rst year 

of application. The mean of these nitrogen loss ranges 

was subtracted from the nitrogen inputs. 

Because information on the spatial distribution of 

beef cattle was not available, it was assumed that all 

beef cattle were located on agricultural land, although 

this necessary simpli cation does not account for cattle 

on rangeland. The number of beef cattle in each county, 

obtained online from the Idaho Agricultural Statistics 

Service, was multiplied by the average daily amount of 

total nitrogen in feces and urine produced by each animal (0.305 lb/d/animal). 

Nitrogen losses from beef cattle manure differ 

from those of dairy cattle manure only in the method of 

manure storage and application. Losses resulting from 

storage of cattle manure range from 0 to 80 percent, 

depending on whether the cattle were grazing on open 

rangeland or in feedlots and pens. Rupert (1996) indicated that 85 percent of the total nitrogen remains when 

manure is applied directly to the ground. This is between the range of 70 to 95 percent retained by mechanical spreading methods. Because denitri cation and 

organic nitrogen losses occur once the manure is 

applied to the ground, they are the same for both dairy 

and beef cattle. 

Nitrogen concentration data from the National 

Atmospheric Deposition Program/National Trends Network were combined with long-term average precipitation data to compute the annual amount of nitrogen 

input by precipitation at any point in the study area. 

Precipitation contains small but measurable amounts 

of nitrogen. The GIS data set (Molnau, 1995) showing 

30-year average precipitation ranging from less than 

5 to 40 in/yr was used to calculate a precipitationweighted mean deposition of nitrogen, in pounds per 

acre.

Total nitrogen input from domestic septic tank systems was estimated by multiplying the average amount 

of total nitrogen generated per person by the average 

number of persons per household and the number of 

households using domestic septic systems in each 

county. Estimates for the number of households were 

based on 1990 census data and 1998 updated population 

from the ISDA for 1998. Crops belonging to the legume
Estimating the Probability of Detecting Elevated Nitrate Concentrations in Ground Water 11

estimates. The exact distribution of septic systems in the 

study area is not well known. Therefore, it was assumed 

that nitrogen input from domestic septic systems occurs 

chie y in areas designated as residential or commercial 

lands, according to the BOR land-use maps.

Relative ground-water velocity data were obtained 

from an adaptation of a three-dimensional, nite-dif ference, numerical model of the eastern Snake River Plain 

regional aquifer system (Garabedian, 1992; David 

Clark, U.S. Geological Survey, written commun., 

2002)( g. 5). Velocity data had not been used in previous probability models for the Snake River Plain 

(Rupert, 1998; Donato, 2000). However, it was hypothesized during this study that the probability of detecting 

elevated nitrate concentrations at any given location in 

the study area might be related to the rate of groundwater and solute movement through the study area’s 

aquifer systems. Conceptually, areas of high groundwater velocity result in a greater amount of regional 

ground water containing low nitrate concentrations that 

mixes with surface recharge containing higher nitrate 

concentrations. Thus, areas of high nitrogen input and 

high ground-water velocity will result in a lower nitrate 

concentration than will areas of high nitrogen input and 

low ground-water velocity. Water-quality samples collected from spring discharge originating from high 

ground-water velocity areas indicate a greater proportion of regional water than do samples from spring discharge originating from middle to low ground-water 

velocity areas (Clark and Ott, 1996). 

Ground-water velocity values for the areas outside 

the o w model were determined by visually de ning 

aquifer boundaries based on topography and using ordinary kriging to statistically interpolate velocity values 

from the o w model to the outside areas. The nal 

ground-water velocity layer resulted in either high 

or low velocity values with a small transitional zone 

( g. 5). 

Depth to ground water was based on a map developed from more than 1,000 water-level measurements. 

The water-level data were compiled from the USGS 

NWIS data base. Water-level measurement reselection 

followed the methods of Maupin (1991). Ordinary kriging then was used to interpolate water-level values at 

0.5-mi grid intersections. The resulting raster data set 

was converted to a vector GIS data set, and 20-ft waterlevel contours were created.

ESTIMATING THE PROBABILITY OF DETECTING 

ELEVATED NITRATE CONCENTRATIONS IN 

GROUND WATER

Estimating the Probability of Detecting Elevated Nitrate Concentrations in Ground Water

A map showing the probability of detecting elevated nitrate concentrations was constructed using a 

GIS and logistic regression statistical methods (Hosmer 

and Lemeshow, 2000) in the following steps:

1. Data describing nitrate concentrations and 

hydrogeologic and anthropogenic variables 

were combined into one GIS data set providing each sample location with all of the corresponding GIS data. The GIS data set was then 

exported to a statistical software program for 

logistic regression analysis.

2. The data set was statistically analyzed to evaluate individual (univariate) correlations between nitrate in ground water and hydrologic 

and anthropogenic characteristics and to identify those variables that correlated signi -

cantly with elevated nitrate concentrations.

3. Multivariate forward-stepwise regression 

with a backward check for elimination was 

performed to identify the most signi cant 

variables to include in the probability model, 

after which each variable’s signi cance w as 

veri ed.

4. Various tests, including an external data veri-

 cation check, were conducted to determine 

how well the probability model represented 

the data.

5. The nal multi variate model was entered 

into a GIS and the probability map was constructed.

For this study, the nitrate concentration in ground 

water was converted to a binary dependent variable, elevated nitrate detection, whereby the nitrate concentration was either greater than 2 mg/L or less than or equal 

to 2 mg/L. For logistic regression analysis, the dependent variable is categorical. 

Independent categorical variables included geology, land use, soil hydrologic group, and soil drainage. 

To prevent divergence of the logistic regression model 
115° 00' 114° 30' 114° 00' 113° 30'

43° 00'

42° 30'

42° 00' 0

0

Figure 5. Location of the flow-model boundary and rates of ground-water velocity, south-central Idaho.

12 Probability of Detecting Elevated Concentrations of Nitrate in Ground Water in a Six-County Area of South-Central Idaho
Estimating the Probability of Detecting Elevated Nitrate Concentrations in Ground Water 13

p= (2)

resulting from small populations of data in some categories, similar categories within the geology and landuse data sets were combined to provide an approximately even distribution of data per independent variable. For example, the BOR’s land-use categories — 

native, gravel pit, idle, and public land — each contained few nitrate samples but, when combined into one 

category termed native, the amount of samples was adequate to compare with the agricultural categories. By 

generalizing some of the categories, a meaningful logistic regression model was obtained. 

The other independent variables were modeled as 

continuous; therefore, precipitation and depth-to-water 

values at sample sites were assigned midpoint values 

between contours. For example, sample locations 

between depth-to-water contours of 40 and 60 ft were 

assigned a depth-to-water value of 50 ft.

Statistical Methods and the Logistic Regression 

Model

A variety of statistical methods was used to evaluate correlations between the nitrate concentration, or the 

binary-variable elevated nitrate detection, and the independent variables. Spearman correlation tests were used 

to determine signi cant correlations between continuous variables and nitrate concentrations or elevated 

nitrate detections. The Wilcoxon rank-sum test (Ott, 

1993) was used to determine whether differences 

between nitrate concentrations and the different categories of a variable were signi cant (for e xample, signi -

cant differences between nitrate concentrations and different land-use types). This test also evaluated whether 

differences between elevated nitrate detections and nondetections for a continuous variable were signi cant.

Logistic regression was used to predict the probability of detecting nitrate concentrations greater than 2 

mg/L in ground water. Logistic regression is a statistical 

method similar to linear regression. However, in logistic 

regression, the output variable is binary, and any number of the independent variables can be categorical (discrete). 

Multiple logistic regression (more than one independent variable) software generates several parameters 

that determine the predictive success of the model, 

including the likelihood ratio statistic (LR), rho-squared 

value (similar to an r-squared value in linear regression), standard error, and p-value of the model parameter coef cients. The model prediction success table also 

was used to evaluate the probability model’s classi catory power. These evaluation parameters are described 

in a report by Rupert (1998). For a thorough description 

of how these parameters are created, refer to Hosmer 

and Lemeshow (2000) or SPSS Inc. (2000). An example 

multiple regression model follows, showing the calculation of the probability of detecting elevated nitrate concentrations in ground water:

where

p=the probability of detecting elevated nitrate 

concentration in ground water;

a=intercept;

b

1=slope coef cient for ground-w ater velocity;

V=ground-water velocity;

b

2=slope coef cient for land-use type 1;

LU

1=land-use type 1;

b

3=slope coef cient for land-use type 2;

LU

2=land-use type 2;

b

4=slope coef cient for soils property;

S=soils property;

b

5=slope coef cient for depth to w ater; and 

WL=depth to water.

Univariate Analysis

Univariate analysis was performed on all variables 

to determine initial correlations with nitrate concentrations and elevated nitrate detections and to identify key 

variables that were likely to be signi cant in the nal 

model. Logistic regression, Spearman correlation tests, 

and the Wilcoxon rank-sum test were performed on all 

data (table 1). After the land-use categories were 

regrouped to account for small populations of wells in 

certain land-use types, comparisons were made to determine whether statistical differences between nitrate 

concentrations among the land-use categories were signi cant (p < 0.05). Dif ferences between nitrate concentrations and each of the three land uses classi ed by 

BOR, and between nitrate concentrations and two of the 

three land uses classi ed by ID WR were statistically 

signi cant ( g. 6); ho wever, the IDWR data resulted in 

a better t of the logistic re gression model.

e [a + b

1

(V) + b

2

(LU

1

) + b

3

(LU

2

) + b

4

(S) + b

5

(WL)]

1+e [a + b

1

(V) + b

2

(LU

1

) + b

3

(LU

2

) + b

4

(S) + b

5

(WL)]
14 Probability of Detecting Elevated Concentrations of Nitrate in Ground Water in a Six-County Area of South-Central Idaho

Table 1. Results from univariate correlations between independent variables and elevated nitrate detections or nitrate concentrations in

ground water, south-central Idaho

[Q-T, Quaternary-Tertiary; ref, reference; BOR, Bureau of Reclamation; IDWR, Idaho Department of Water Resources]

Independent variable

Logistic 

regression 

coefficient

Logistic 

regression 

coefficient 

p-value

Likelihood 

ratio

Likelihood 

ratio

p-value

McFadden's 

rho-squared

Degrees 

of 

freedom

Spearman's 

correlation 

coefficient

Wilcoxon 

p-value

Nitrogen input. . . . . . . . . . . . 0.004 0.000 17.184 0.000 0.012 1 0.085 0.059

Ground-water velocity . . . . . -0.665 0.000 151.460 0.000 0.103 1 -0.310 0.000

Geology (Q-T basalt) . . . . . . 1.389 0.026 0.315 0.000

Geology (Q-T sediments) . . . 0.413 0.505 0.051 0.000

Geology (other). . . . . . . . . . . 0.000 ref . -0.011 0.357

Geology (Q basalt) . . . . . . . . -0.682 0.267 -0.357 0.000

Geology (Q sediments) . . . . . 0.464 0.482 170.896 0.000 0.116 4 0.029 0.789

Gravity-irrigated land 

(BOR) . . . . . . . . . . . . . . . . 0.458 0.001 0.157 0.000

Native land (BOR) . . . . . . . . -0.567 0.001 -0.160 0.000

Sprinkler-irrigated land 

(BOR) . . . . . . . . . . . . . . . . 0.000 ref. 38.039 0.000 0.026 2 -0.032 0.459

Flood-irrigated land 

(IDWR). . . . . . . . . . . . . . . 1.116 0.000 0.265 0.000

Rangeland (IDWR) . . . . . . . . -0.122 0.597 -0.145 0.000

Sprinkler-irrigated land 

(IDWR). . . . . . . . . . . . . . . 0.000 ref. 76.862 0.000 0.052 2 -0.193 0.000

Precipitation . . . . . . . . . . . . . -0.205 0.000 13.881 0.000 0.009 1 -0.118 0.004

High in ltration rates (soil 

hydrologic group) . . . . . . . -1.113 0.001 -0.060 0.074

Moderate in ltration rates 

(soil hydrologic group) . . . -0.516 0.005 0.005 0.428

Slow in ltration rates (soil 

hydrologic group) . . . . . . . -0.716 0.000 -0.071 0.009

Very slow in ltration rates 

(soil hydrologic group) . . . 0.000 ref. 19.240 0.000 0.013 3 0.113 0.001

Excessively drained (soil 

drainage) . . . . . . . . . . . . . . 0.000 ref. -0.016 0.159

Well drained (soil 

drainage) . . . . . . . . . . . . . . 0.179 0.506 0.071 0.005

Poorly drained (soil drainage) -0.226 0.497 3.733 0.155 0.003 2 -0.055 0.121

Soil layer depth . . . . . . . . . . . 0.000 0.994 0.000 0.994 0.000 1 -0.008 0.151

Soil clay content . . . . . . . . . . -0.030 0.003 9.071 0.003 0.006 1 -0.106 0.000
Estimating the Probability of Detecting Elevated Nitrate Concentrations in Ground Water 15

30

25

20

15

10

5

0

FLOODIRRIGATED

LAND

SPRINKLERIRRIGATED

LAND

NATIVE

LAND

FLOODIRRIGATED

LAND

SPRINKLERIRRIGATED

LAND

RANGELAND

NITRATE CONCENTRATION, IN

MILLIGRAMS PER LITER

LAND USE

Bureau of Reclamation data Idaho Department of Water Resources data

p<0.001

p<0.001

p=0.005

p<0.001

p=0.483

p<0.001

Figure 6. Correlation between nitrate concentrations and land use classified by the Bureau of Reclamation and the Idaho Department of Water Resources, south-central Idaho.

Among the best predictors of detecting elevated 

nitrate concentrations using univariate analysis were 

ground-water velocity, geology, both land-use data sets, 

depth to water, and soil organic matter content (table 1). 

Except for soil depth, the other variables were weak 

predictors of elevated nitrate concentrations. Due to a 

logistic regression coef cient p-v alue of 0.994 and 

Spearman and Wilcoxon p-values of 0.155 and 0.151, 

respectively, soil depth was omitted from further analysis. The remaining variables were carried forward for 

multivariate logistic regression analysis.

Multivariate Logistic Regression Analysis

Several methods can be used to create a multivariate logistic regression model. Most involve a stepwise 

procedure, whereby variables are added to or deleted 

from the model one at a time on the basis of statistical 

signi cance until the model that best ts the data is 

achieved. Statistical signi cance is assessed by the lik elihood ratio chi-square test (Hosmer and Lemeshow, 

2000), which commonly is used to compare nested 

models. 

Soil organic matter content . . 1.118 0.000 24.493 0.000 0.017 1 0.183 0.000

Soil permeability. . . . . . . . . . -0.013 0.185 1.744 0.187 0.001 1 -0.074 0.000

Depth to water. . . . . . . . . . . . -0.004 0.000 29.422 0.000 0.020 1 -0.176 0.000

Independent variable

Logistic 

regression 

coefficient

Logistic 

regression 

coefficient 

p-value

Likelihood 

ratio

Likelihood 

ratio

p-value

McFadden's 

rho-squared

Degrees 

of 

freedom

Spearman's 

correlation 

coefficient

Wilcoxon 

p-value

Table 1. Results from univariate correlations between independent variables and elevated nitrate detections or nitrate concentrations in

ground water, south-central Idaho—Continued
16 Probability of Detecting Elevated Concentrations of Nitrate in Ground Water in a Six-County Area of South-Central Idaho

Table 2. Variables selected for use in the final probability model, 

south-central Idaho

[IDWR; Idaho Department of Water Resources]

Variable

Coefficient

Standard 

error Wald test (z)

pvalue

Ground-water 

velocity . . . . . . . . . . -0.860 0.073 -11.781 0.000

Nitrogen input . . . . . . . -0.006 0.001 -04.661 0.000

Well drained (soil 

drainage) . . . . . . . . . -0.559 0.315 0-1.775 0.076

Poorly drained (soil 

drainage) . . . . . . . . . -2.454 0.393 0-6.244 0.000

Precipitation . . . . . . . . -0.357 0.081 0-4.407 0.000

Flood-irrigated land 

(IDWR) . . . . . . . . . . -0.583 0.180 -03.239 0.001

Rangeland 

(IDWR) . . . . . . . . . . -0.106 0.276 0-0.384 0.701

Depth to water. . . . . . . -0.002 0.001 0-2.489 0.013

Constant . . . . . . . . . . . -4.671 0.840 -05.561 0.000

The method utilized to develop the preliminary 

model was a manual forward-stepwise selection of variables with a backward test for elimination. This method 

uses a statistical algorithm to determine the initial variable with the highest statistical signi cance to create the 

best single-variable model. A two-variable model then 

is created by adding each of the remaining variables one 

at a time to the single-variable model and determining 

which, if any, signi cantly impro ved the one-variable 

model’s predictive capabilities. This process of adding 

variables continues until no remaining variables signi -

cantly improve the model. After each successive variable is added, each variable included in the present 

model is individually tested for removal, because a 

variable found to be signi cant at an early step could 

become insigni cant at a later step. In de veloping the 

model, variables were considered signi cant at the 95-

percent con dence le vel (p-value < 0.05). 

The variables selected for the preliminary model 

were ground-water velocity, nitrogen input, precipitation, soil drainage, land use (IDWR), and depth to 

water. After the preliminary model was created, several 

steps were taken to verify the suitability of the selected 

variables. First, the variable coef cients were compared 

with those produced by the univariate model to check 

for large differences in magnitude that would indicate 

that an excluded variable was needed to adjust the t of 

the variables that remained in the model. Another 

method to identify intervariable in uences is to reenter 

all the unselected variables one at a time into the model 

to check for large changes in coef cient magnitudes, 

then reevaluate the likelihood ratio test to check for signi cant model impro vement from the unselected variables. Each continuous variable then is checked for linearity in the logit (a transformation of equation 2). Linearity in the logit is assumed in the beginning stages of 

model development and needs to be veri ed for the continuous variables in the nal model. Lastly , interactions 

between variables are checked. Variables interact when 

one independent variable is not constant over levels of 

another independent variable (Hosmer and Lemeshow, 

2000). Interactions are checked by adding an interaction 

term into the model and checking for a statistically signi cant impro vement by the likelihood ratio chi-square 

test. Interactions need to be scienti cally sound to 

remain in the probability model. For the present model, 

all the preselected variables remained after the veri cation tests were conducted and no interactions were 

added. The nal probability model is listed in table 2.

Construction of the Elevated Nitrate 

Concentration Probability Map

Multivariate analysis resulted in a best- t probability regression model that incorporated variables for 

ground-water velocity, nitrogen input, precipitation, soil 

drainage, land use (IDWR), and depth to water. The 

regression model then was used to construct the probability map. Each of the nal data layers were combined 

into one GIS data set, and a probability value was calculated using equation 2 for each of the 251,000 polygons 

that resulted from intersecting the GIS data layers 

( g. 7).

EVALUATION AND TESTING OF PROBABILITY 

MODELS

Evaluation and Testing of Probability Models

Several tests were conducted to evaluate how well 

the model t the data as a whole. The likelihood ratio 

statistic tests the hypothesis that all coef cients e xcept

the constant are zero, similar to the F test reported for 

linear regression. The log likelihood ratio for the nal 

probability model was 297.305, which is chi-squared 

with eight degrees of freedom and a p-value of < 0.001, 

indicating a signi cance le vel greater than 99 percent. 
115° 00' 114° 30' 114° 00' 113° 30'

43° 00'

42° 30'

42° 00'

Twin

Falls Kimberly

Oakley

Paul

Filer

Buhl

Wendell

Jerome

Gooding

Burley

Rupert

Lake

Walcott

Snake

River

Big

River

Little

River

Wood Wood

Raft

River

Snake

River

LINCOLN

GOODING

MINIDOKA

JEROME

TWIN

FALLS

CASSIA

00

5

P

Figure 7. Probability of detecting elevated nitrate concentrations in ground water, south-central Idaho. (Elevated, greater than 2 milligrams per liter)

Evaluation and Testing of Probability Models 17
18 Probability of Detecting Elevated Concentrations of Nitrate in Ground Water in a Six-County Area of South-Central Idaho

100

90

80

70

60

50

40

30

20

10

0

1.0

0.9

0.8

0.7

0.6

0.5

0.4

0.3

0.2

0.1

0

0 0.1 0.2 0.3 0.4 0.5 NITRATE CONCENTRATION

GREATER THAN 2

MILLIGRAMS PER LITER

NITRATE CONCENTRATION

EQUAL TO OR LESS THAN

2 MILLIGRAMS PER LITER

0.6 0.7 0.8 0.9 1.0

PREDICTED PROBABILITY OF

ELEVATED NITRATE DETECTION

PERCENT OF ACTUAL ELEVATED

NITRATE DETECTIONS

y=0.958x + 0.007

r2=0.959

656

439

PREDICTED PROBABILITY OF

ELEVATED NITRATE DETECTION

Wilcoxon

rank-sum

test p-value

<0.001

Figure 8. Correlation between groups of predicted probabilities of detecting elevated nitrate concentrations and actual detections

of elevated nitrate concentrations in ground-water samples used in the model data set, south-central Idaho.

McFadden’s rho-squared is a transformation of the likelihood ratio and is similar to the r-squared value in linear regression. McFadden’s rho-squared values between 

0.20 and 0.40 are considered satisfactory (SPSS Inc., 

2000). The rho-squared value for the nal probability 

model was 0.202. For the 1,095 samples in the model 

data set, the model correctly predicted 64 percent of the 

data; 70 percent of the samples that contained elevated 

nitrate concentrations were correctly predicted and 55 

percent of the samples that did not contain elevated 

nitrate concentrations were correctly predicted, also 

known as the sensitivity and speci city , respectively. A 

probability cutpoint of 0.50 was used to determine the 

data set’s sensitivity and speci city . Probability values 

ranged from 0.04 to 0.95. The results of this model 

closely match those of Rupert (1998) and Donato 

(2000).

The range of the model’s predicted probabilities of 

detecting elevated nitrate was evaluated by comparing 

groupings of predicted probabilities with percentages of 

actual elevated nitrate detections in each group. This 

was done by performing a linear regression between the 

percentage of actual elevated nitrate detections in a 

group and the predicted probability of elevated nitrate 

detections in a group. The probability of detecting elevated nitrate concentration was calculated for each sample, and the data set was sorted by ascending probability 

and divided into categories of 10 percent (0 to 9, 10 to 

19, 20 to 29, and so on). The percentage of elevated 

nitrate detections in each group was calculated, and linear regression was used to compare the percentage of 

actual elevated nitrate detections with the predicted 

probability of elevated nitrate detections in each group 

( g. 8). A perfectly t model is one in which linear 

regression produces a slope = 1, y-intercept = 0, and an 

r-squared value of 1. The probability model resulted in a 

slope = 0.958, y-intercept = 0.007, and an r-squared 

value of 0.959. The Wilcoxon test was used to determine whether differences in probability ratings between 

samples with elevated nitrate detections and samples 

without elevated nitrate detections were signi cant 

( g. 8). The difference between the high-probability 

values for elevated nitrate detections and the lowprobability values for nondetections was signi cant 

(p < 0.001).

The probability model also was compared with the 

extracted veri cation data set of 270 samples. The veri-

 cation data set w as randomly selected from the combined data sets of the USGS, ISDA, and IDWR. The 

veri cation samples were combined with the GIS data 

sets, and the probability for detecting nitrate was calculated for each sample using the logistic regression 
Evaluation and Testing of Probability Models 19

100

90

80

70

60

50

40

30

20

10

0

0 0.1 0.2 0.3 0.4 0.5 NITRATE CONCENTRATION

GREATER THAN 2

MILLIGRAMS PER LITER

NITRATE CONCENTRATION

EQUAL TO OR LESS THAN

2 MILLIGRAMS PER LITER

0.6 0.7 0.8 0.9 1.0

1.0

0.9

0.8

0.7

0.6

0.5

0.4

0.3

0.2

0.1

0

PERCENT OF ACTUAL ELEVATED

NITRATE DETECTIONS

PREDICTED PROBABILITY OF

ELEVATED NITRATE DETECTION

PREDICTED PROBABILITY OF

ELEVATED NITRATE DETECTION

y=1.060x + 0.039 109

r2=0.973

161

Wilcoxon

rank-sum

test p-value

<0.001

Figure 9. Correlation between groups of predicted probabilities of detecting elevated nitrate concentrations and actual detections

of elevated nitrate concentrations in ground-water samples used in the verification data set, south-central Idaho.

ing probability of elevated nitrate detection, and the percentage of actual elevated nitrate detections in each 

interval was calculated. Linear regression was used to 

compare the predicted probability of detection in each 

group with the actual percentage of detections. The predicted and detected values ( g. 9) were strongly correlated with a slope = 1.060, y-intercept = -0.039, and an 

r-squared value of 0.973. The Wilcoxon rank-sum test 

for the veri cation data set, as for the model data set, 

indicated that the difference between the high-probability values for elevated nitrate detections and the lowprobability values for nondetections was signi cant 

(p < 0.001). For the 270 samples in the veri cation data 

set, the model correctly predicted 74 percent of the data; 

83 percent of the samples with elevated nitrate were 

correctly predicted, and 63 percent of the samples without elevated nitrate were correctly predicted. Probability values for the veri cation data set ranged from 0.06 

to 0.91. As with the model data set, a probability cutpoint of 0.50 was used in determining a correct or 

incorrect prediction.

Although the study areas and data sets for developing probability models in the two previous studies 

(Rupert, 1998; Donato, 2000) were different from those 

used for this study, several of the signi cant e xplanatory 

variables were the same—land use, soil drainage, and 

depth to water.

The areas of predicted high probability for elevated 

nitrate detection ( g. 6) coincide with areas of high 

nitrogen input and agricultural land use in northern 

Twin Falls, northern Cassia, and southern Minidoka 

Counties. An exception to the correlation between predicted high probability of elevated nitrate detection and 

areas of high nitrogen input occurs in southern Gooding 

and western Jerome Counties. This area is characterized 

by agricultural land use and high nitrogen input but was 

predicted by the model to have a low probability for elevated nitrate detection. The low-probability prediction 

is a result of high ground-water velocity, which represents the large amount of regional ground water moving 

through the aquifer. The model correctly predicted that 

high nitrate concentrations are less likely to occur in 

areas where regional ground water predominates and 

moves relatively faster through the aquifer than in areas 

where ground water moves slower and has a larger component of recent recharge from the surface.

Areas of lowest probability, primarily in Cassia 

and Twin Falls Counties, relate to high-precipitation, 

high-elevation areas with no agricultural land use, but 

the low-probability areas in northern Minidoka County 

and northeastern Lincoln County result from deeper 

ground water.

The effect of the soil drainage variable is most 

prominent in southern Minidoka County, a region of 
20 Probability of Detecting Elevated Concentrations of Nitrate in Ground Water in a Six-County Area of South-Central Idaho

115° 00' 114° 30' 114° 00' 113° 30'

43° 00'

42° 30'

42° 00'

115° 00' 114° 30' 114° 00' 113° 30'

43° 00'

42° 30'

42° 00'

LINCOLN

GOODING

MINIDOKA

JEROME

TWIN

FALLS

CASSIA

LINCOLN

GOODING

MINIDOKA

JEROME

TWIN

FALLS

CASSIA

0

0

5

5

15

15

10

10

20 MILES

20 KILOMETERS

Correctly predicted

detections of

elevated nitrate

concentrations

Incorrectly predicted

detections of

elevated nitrate

concentrations

EXPLANATION

Not delineated

Perched aquifer

Nitrate concentration greater

 than 2 milligrams per liter

Nitrate concentration equal to

 or less than 2 milligrams

 per liter

Figure 10. Correctly and incorrectly predicted detections of elevated nitrate concentrations in ground water using a probability

cutpoint of 0.50, south-central Idaho. (Elevated, greater than 2 milligrams per liter)
Summary 21

The effect of the soil drainage variable is most 

prominent in southern Minidoka County, a region of 

predicted low probability, where the soil above the 

perched aquifer is poorly drained. Soil drainage describes the frequency and duration of wet periods of the 

soil (U.S. Department of Agriculture, 1995). Soils with 

poor drainage are typically water saturated and can have 

reducing conditions that may lead to denitri cation, 

which reduces nitrate concentration (Goolsby and others, 1999).

Incorrectly predicted elevated nitrate detections 

tend to congregate along a transition zone between high 

and low ground-water velocity areas in Jerome and 

Gooding Counties, where the probability model underpredicts the probability of detecting elevated nitrate 

concentrations ( g. 10). Although this area does have 

high nitrogen input, the ground-water velocities are in 

the middle range, which indicates a mix of regional 

ground water and surface recharge that results in nitrate 

concentrations above 2 mg/L. 

The probability model slightly overpredicts elevated nitrate detections in the perched aquifer area 

( g. 10). Probability v alues in this area range between 

0.50 and 0.60, just slightly over the cutpoint of 0.50 for 

correctly predicted elevated nitrate detections.

SUMMARY

Summary

Ground-water quality is an ongoing concern in 

Idaho because of rising nitrate concentrations in an 

increasing number of wells. The concentration of nitrate 

in ground water is related to anthropogenic factors; 

therefore, planning tools are needed to aid local managers in assessing the potential effects of land-use decisions on nitrate concentrations in ground water.

Ground-water probability maps can be an important tool for resource-protection and regulatory agencies 

to help protect ground-water quality. In previous studies 

(Rupert, 1998; Donato, 2000), the U.S. Geological Survey developed preliminary maps showing the probability of detecting elevated nitrate in ground water of the 

upper Snake River Basin and the western Snake River 

Plain. This study used similar methodologies while 

compensating for differences in study area scale. The 

resultant probability map provides an additional tool for 

managing the increase of nitrate concentrations in 

south-central Idaho ground water.

The elevated nitrate probability map was produced 

by overlaying ground-water quality data on hydrogeologic and anthropogenic geographic information system 

(GIS) layers. The GIS layers consisted of two land-use 

data sets (Bureau of Reclamation and Idaho Department 

of Water Resources), precipitation, geology, nitrogen 

input, six soil characteristics, ground-water velocity, 

and depth to water. A statistical software program was 

used to conduct a variety of statistical tests, including 

logistic regression and the Wilcoxon rank-sum test. A 

forward-stepwise logistic regression and subsequent 

model- t assessment with model diagnostic e valuations 

resulted in a nal probability model based on groundwater velocity, nitrogen input, precipitation, soil drainage, land use (Idaho Department of Water Resources), 

and depth to water. 

The nal probability model performed well in predicting areas of elevated nitrate concentration (greater 

than 2 mg/L). A linear regression of the grouped predicted probabilities of detecting elevated nitrate concentrations with the percentage of actual elevated nitrate 

detections showed strong correlation with an r-squared 

value of 0.96. A similar linear regression of a veri cation data set also showed a strong correlation with an rsquared value of 0.97. There was a signi cant dif ference (p < 0.001) between samples with and without elevated nitrate detections for both the model data set and 

the veri cation data set. Areas of high probability of 

elevated nitrate detections coincide with areas of agricultural land use and high nitrogen input except in 

southern Gooding and western Jerome Counties, where 

high ground-water velocities predominate resulting in 

low probabilities of elevated nitrate detection. This nding reinforces the concept that high nitrate concentrations are less likely to occur in areas where regional 

ground water moves relatively quickly through the aquifer than in areas where ground water moves more 

slowly and is recharged from the surface. Incorrectly 

predicted elevated nitrate detections tend to be congregated along a transition zone between areas of high and 

low ground-water velocity in Jerome and Gooding 

Counties indicating a mix of regional ground water and 

surface recharge.

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nato—Probability of Detecting Elevated Concentrations of Nitrate in Ground Water in a Six-County Area of South-Central Idaho—

U.S. Geological Survey Water-Resources Investigations Report 03–4143