Estimating the Probability of Elevated Nitrate Concentrations 

in Ground Water in Washington State

Scientific Investigations Report 2008–5025

U.S. Department of the Interior

U.S. Geological Survey

Prepared in cooperation with the Washington State Department of Health
Cover:

Top: Photograph showing example of agricultural land use. (Photograph taken by 

Anthony Grillo, private citizen, February 26, 2008.)

Bottom left: Photograph showing fertilizer being applied in a residential area. 

(Photograph taken by Lonna Frans, U.S. Geological Survey, February 26, 2008.)

Bottom right: Photograph showing USGS scientist determining a well location. 

(Photograph taken by U.S. Geological Survey staff.)
Estimating the Probability of Elevated 

Nitrate Concentrations in Ground Water in 

Washington State

By Lonna M. Frans

Prepared in cooperation with the Washington State Department of Health

Scientific Investigations Report 2008–5025

U.S. Department of the Interior

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

DIRK KEMPTHORNE, Secretary

U.S. Geological Survey

Mark D. Myers, Director

U.S. Geological Survey, Reston, Virginia: 2008

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U.S. Government.

Although this report is in the public domain, permission must be secured from the individual copyright owners to 

reproduce any copyrighted materials contained within this report.

Suggested citation:

Frans, L.M., 2008, Estimating the probability of elevated nitrate concentrations in ground water in Washington State: 

U.S. Geological Survey Scientific Investigations Report 2008–5025, 22 p.
iii

Contents

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

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

Background............................................................................................................................................3

Purpose and Scope ..............................................................................................................................3

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

Methods of Investigation..............................................................................................................................5

Description of Logistic Regression ...................................................................................................5

Compilation of Nitrate Concentration Data into a Response Variable.........................................7

Compilation of Anthropogenic and Hydrogeologic Data into Explanatory Variables................7

Logistic Regression Results ......................................................................................................................11

Validation of Nitrate Models .............................................................................................................13

Estimating the Probability of Elevated Nitrate Concentrations in Ground Water.............................13

Appropriate Uses of the Probability Maps .....................................................................................20

Summary........................................................................................................................................................20

References Cited..........................................................................................................................................20

Figures

Figure 1. Map showing location of counties and major cities in Washington .................. 2

Figure 2. Map showing hydrogeomorphic regions in Washington .............................. 4

Figure 3. Map showing nitrate concentrations in water from wells in Washington from

the Washington State Department of Health database (1995–2006) .................. 8

Figure 4. Graph showing nitrate concentrations in ground-water samples collected in

hydrogeomorphic regions in Washington from the Washington State

Department of Health database (1995–2006) ............................................. 9

Figure 5. Map showing nitrate concentrations in water from wells in Washington

from the U.S. Geological Survey and Washington State Department of

Ecology databases (1995–2006)............................................................ 9

Figure 6. Graph showing McFadden’s rho squared from relations of amount of nitrogen

application and percentage of agricultural, urban, and undeveloped lands

within circular buffers around wells with nitrate concentrations greater than

2 milligrams per liter in ground water in Washington ................................. 10

Figure 7. Graphs showing percentage of actual nitrate concentrations greater than

2 milligrams per liter (mg/L) and the estimated probability of nitrate

concentrations greater than 2 mg/L in the calibration dataset ........................ 12

Figure 8. Graphs showing percentage of actual nitrate concentrations greater than 2

milligrams per liter (mg/L) and the estimated probability of nitrate

concentrations greater than 2 mg/L in the validation dataset ........................ 13
iv

Tables

Table 1. Summary of anthropogenic and natural explanatory variables used for model

development ................................................................................. 10

Table 2. Regression coefficients and individual p-values of independent variables for

the two logistic regression models with and without hydrogeomorphic

regions that were significantly related with nitrate concentrations greater

than 2 milligrams per liter in ground water in Washington ........................... 11

Table 3. Statistical results from models that estimate the probability of nitrate

concentrations exceeding 2 milligrams per liter in ground water in Washington ... 11

Figure 9. Maps showing probability of detecting nitrate concentrations greater than 2

milligrams per liter in ground water at a depth of 145 feet below land surface

for the two logistic regression models with and without hydrogeomorphic

regions, Washington ........................................................................ 14

Figure 10. Maps showing probability of detecting nitrate concentrations greater than 2

milligrams per liter in ground water at a depth of 145 feet below land surface

for the two logistic regression models with and without hydrogeomorphic

regions, Puget Sound region, Washington ............................................. 16

Figure 11. Maps showing depth to which wells need to be drilled for at least a

90-percent probability of detecting a nitrate concentration less than 2

milligrams per liter in ground water for the logistic regression model without

hydrogeomorphic regions, State of Washington and Puget lowlands ............... 18

Figures—Continued
v

Conversion Factors and Datums

Conversion Factors

Inch/Pound to SI

Multiply By To obtain

Length

inch (in.) 2.54 centimeter (cm)

inch (in.) 25.4 millimeter (mm)

foot (ft) 0.3048 meter (m)

Area

acre 0.004047 square kilometer (km2

)

square mile (mi2

) 2.590 square kilometer (km2) 

SI to Inch/Pound

Multiply By To obtain

Length

meter (m) 3.281 foot (ft) 

kilometer (km) 0.6214 mile (mi)

kilometer (km) 0.5400 mile, nautical (nmi) 

meter (m) 1.094 yard (yd) 

Area

square kilometer (km2

) 247.1 acre

square kilometer (km2

) .0386 square mile (mi2)

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

°F=(1.8×°C)+32.

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

°C=(°F-32)/1.8.

Concentrations of chemical constituents in water are given either in milligrams per liter (mg/L) 

or micrograms per liter (μg/L). 

Datums

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

(NAVD 88).

Horizontal coordinate information is referenced to the North American Datum of 1983 (NAD 83).

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

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Estimating the Probability of Elevated Nitrate 

Concentrations in Ground Water in Washington State

By Lonna M. Frans

Abstract

Logistic regression was used to relate anthropogenic 

(manmade) and natural variables to the occurrence of elevated 

nitrate concentrations in ground water in Washington State. 

Variables that were analyzed included well depth, groundwater recharge rate, precipitation, population density, fertilizer 

application amounts, soil characteristics, hydrogeomorphic 

regions, and land-use types. Two models were developed: 

one with and one without the hydrogeomorphic regions 

variable. The variables in both models that best explained 

the occurrence of elevated nitrate concentrations (defined as 

concentrations of nitrite plus nitrate as nitrogen greater than 

2 milligrams per liter) were the percentage of agricultural 

land use in a 4-kilometer radius of a well, population density, 

precipitation, soil drainage class, and well depth. Based on 

the relations between these variables and measured nitrate 

concentrations, logistic regression models were developed 

to estimate the probability of nitrate concentrations in 

ground water exceeding 2 milligrams per liter. Maps 

of Washington State were produced that illustrate these 

estimated probabilities for wells drilled to 145 feet below 

land surface (median well depth) and the estimated depth to 

which wells would need to be drilled to have a 90-percent 

probability of drawing water with a nitrate concentration 

less than 2 milligrams per liter. Maps showing the estimated 

probability of elevated nitrate concentrations indicated that 

the agricultural regions are most at risk followed by urban 

areas. The estimated depths to which wells would need to be 

drilled to have a 90-percent probability of obtaining water with 

nitrate concentrations less than 2 milligrams per liter exceeded 

1,000 feet in the agricultural regions; whereas, wells in urban 

areas generally would need to be drilled to depths in excess of 

400 feet. 

Introduction

Ground water is a significant source of drinking water 

in Washington State (fig. 1), where more than 60 percent of 

the population uses ground water for domestic needs (Ron 

Lane, U.S. Geological Survey, oral commun., August 2007). 

Nitrate concentrations in ground water are elevated in parts of 

the State as a result of various land-use practices, including 

fertilizer application, dairy operations and ranching, and 

septic-system use (Williamson and others, 1998; Ebbert 

and others, 2000). Consumption of water with elevated 

nitrate concentrations is linked to methemoglobinemia, or 

“blue baby” disorder, a potentially fatal condition caused 

by low oxygen levels in the blood of infants (Fewtrell, 

2004) and spontaneous abortion among some women 

(Centers for Disease Control and Prevention, 1996). High 

nitrate concentrations also have been linked to bladder and 

ovarian cancer (Weyer and others, 2001) and non-Hodgkin’s 

lymphoma (Ward and others, 1996). 

To help assure the quality of the State’s drinking-water 

supply, the Washington State Department of Health (WDOH) 

requires that public-supply water systems regularly measure 

nitrate concentrations. However, such testing is only required 

of public-supply systems and, as a result, citizens and public 

health officials have only limited information about the 

potential exposure to elevated nitrate concentrations for 

people whose primary drinking-water sources are private 

wells. To assist public health officials, WDOH asked the 

U.S. Geological Survey (USGS) to develop maps that show 

the relation between elevated nitrate concentrations and the 

locations and depths of wells. This information could be used 

to help estimate exposure to nitrate in drinking water in areas 

without measurements of nitrate concentrations in ground 

water.
2 Estimating the Probability of Elevated Nitrate Concentrations in Ground Water in Washington State

wa19-0163_fig01

0 20 40 60 80 100 MILES

0 20 40 60 80 100 KILOMETERS

124° 122° 120° 118°

48°

46°

GRAYS 

HARBOR

PACIFIC LEWIS

SKAMANIA COWLITZ

CLARK KLICKITAT

YAKIMA

KITTITAS

PIERCE

THURSTON

SAN 

JUAN

ISLAND

KITSAP

MASON

CLALLAM

JEFFERSON

KING

SNOHOMISH

SKAGIT

WHATCOM

OKANOGAN

CHELAN

DOUGLAS

GRANT

BENTON WALLA WALLA

COLUMBIA

GARFIELD

ASOTIN

WHITMAN ADAMS

FRANKLIN

LINCOLN SPOKANE

FERRY

STEVENS

PEND 

OREILLE

WAHKIAKUM

Bellingham

Everett

Seattle

Tacoma

Olympia

Vancouver

Richland

Spokane

IDAHO

OREGON

BRITISH COLUMBIA CANADA

Base from U.S. Geological Survey digital data

Universal Transverse Mercator projection, Zone 10

Horizontal Datum: North American Datum of 1983 (NAD 83)

Figure 1. Location of counties and major cities in Washington.
Introduction 3

Background

Ground-water vulnerability maps are designed to estimate 

the potential for contamination of ground water in an area 

based on anthropogenic and hydrogeologic factors. Multiple 

definitions exist for the term “ground-water vulnerability” 

depending on the research objectives. For this study, we use 

the definition from the National Research Council (1993), 

which states that ground-water vulnerability to contamination 

is 

“...the tendency or likelihood for contaminants 

to reach a specified position in the ground-water 

system after introduction at some location above the 

uppermost aquifer.” 

The National Research Council (1993) refined the 

definition on the basis of whether the assessment was 

contaminant specific, defined as “specific vulnerability,” or for 

any contamination in general, “intrinsic vulnerability.”

Three previous studies, Tesoriero and others (1998), 

Frans (2000), and Nolan and others (2002), partially estimated 

ground-water vulnerability of the State of Washington to 

nitrate contamination. Tesoriero and others (1998) developed 

a logistic regression model to estimate the probability of 

nitrate contamination exceeding 3 mg/L in the Puget lowland. 

Well depth, surficial geology, and land use (forest, urban, and 

agriculture) in a 3.2-km radius of a well were identified as the 

significantly related variables.

In Frans (2000), logistic regression models were 

developed to estimate the probability of nitrate contamination 

exceeding 3 and 10 mg/L for Grant, Franklin, and Adams 

Counties in eastern Washington. In those models, well casing 

depth, fertilizer application amounts, and the mean soil 

hydrologic group were identified as the significantly related 

variables.

Nolan and others (2002) developed a logistic regression 

model to estimate the probability of nitrate contamination 

exceeding 4 mg/L in predominantly shallow, recently 

recharged ground waters of the conterminous United States. 

The significantly related variables were nitrogen fertilizer 

loading, percentage of cropland as pasture, natural log of 

human population density, percentage of well-drained soils, 

depth to seasonally high water table, and presence or absence 

of unconsolidated sand and gravel aquifers. Although this 

model was applied to the conterminous United States, few data 

used to calibrate the model were from the State of Washington 

(Nolan and others, 2002).

Purpose and Scope

This report presents the results of an analysis relating 

anthropogenic and natural factors to the occurrence of 

elevated nitrate concentrations in ground water of Washington 

State. The probability of elevated nitrate concentrations at a 

particular location was estimated using a logistic regression 

model. The logistic regression model was entered into a 

geographic information system (GIS) to produce maps that 

display the probability of elevated nitrate concentrations 

throughout Washington State. In this report, nitrate 

concentration refers to the concentration of nitrite plus 

nitrate measured as nitrogen, and the term elevated nitrate 

concentrations refers to those concentrations that exceed 

2 mg/L (as N).

Description of Study Area

The State of Washington (fig. 1) has a very diverse 

climate. The north-south trending Cascade Mountains divide 

the State into a humid western half and a semiarid eastern 

half. On average, the annual precipitation is about 70 in. in 

western Washington and 20 in. in eastern Washington. Locally, 

annual precipitation ranges from about 20 to 200 in. in western 

Washington and about 7 to 40 in. in eastern Washington. 

 The surficial geology of Washington also is diverse. 

Bedrock is exposed in the Cascade and Olympic Mountains 

in northeastern Washington, and the Columbia River basalt 

flows cover the southeastern part of the State. Unconsolidated 

alluvial materials fill in the bottoms of many bedrock 

valleys and overlie much of Columbia River basalts, and 

unconsolidated glacial materials cover most of the Puget 

lowland region. 

A map of hydrogeomorphic regions was developed 

specifically for this study, because a highly detailed map of 

regional aquifers for Washington was not available (fig. 2). 

According to Rupert (2003), 

“...hydrogeomorphic regions are similar in concept 

to regional aquifers, but are distinguished from 

regional aquifers in that hydrogeomorphic regions 

are delineated on the basis of general geographic 

locations of geologic materials and not on actual 

aquifer locations.” 
4 Estimating the Probability of Elevated Nitrate Concentrations in Ground Water in Washington State

wa19-0163_fig02

EXPLANATION

Hydrogeomorphic region

Western Washington

 alluvial fill

Willamette lowland

Columbia basalt flows

Bedrock

Eastern Washington

 alluvial fill

Puget lowland

0 20 40 60 80 100 MILES

0 20 40 60 80 100 KILOMETERS

124° 122° 120° 118°

48°

46°

Bellingham

Everett

Seattle

Tacoma

Olympia

Vancouver

Richland

Spokane

GRAYS 

HARBOR

PACIFIC LEWIS

SKAMANIA COWLITZ

CLARK KLICKITAT

YAKIMA

KITTITAS

PIERCE THURSTON

SAN 

JUAN

ISLAND

KITSAP

MASON

CLALLAM

JEFFERSON

KING

SNOHOMISH

SKAGIT

WHATCOM

OKANOGAN

CHELAN

DOUGLAS

GRANT

BENTON WALLA WALLA

COLUMBIA

GARFIELD

ASOTIN

WHITMAN ADAMS

FRANKLIN

SPOKANE

LINCOLN

FERRY

STEVENS

PEND 

OREILLE

WAHKIAKUM

Figure 2. Hydrogeomorphic regions in Washington.
Methods of Investigation 5

The hydrogeomorphic regions were delineated 

based on the surficial geologic map of Washington 

(Washington Department of Natural Resources, 2005). The 

hydrogeomorphic regions that were delineated include the 

glacial material of the Puget lowland, alluvial fill in western 

and eastern Washington, the Columbia basalt flows, the 

alluvial material of the Willamette lowland, and the bedrock 

of northern Washington, the Cascades, and Olympics. In 

eastern Washington, the alluvial fill hydrogeomorphic region 

lies on top of the basalt and bedrock units. Therefore, wells in 

the eastern Washington alluvial fill region were stratified by 

depth to determine if the wells were deep enough to penetrate 

the underlying regions. Where possible, well depths were 

compared to sediment thickness maps (Jones and others, 2006, 

and Susan Loper, Franklin Conservation District, written 

commun., 2007) to determine if the wells penetrated the 

alluvial fill. If such sediment thickness maps were unavailable, 

wells with depths less than 150 ft were assumed to be in the 

alluvial fill region. Wells with depths greater than 150 ft were 

assumed to penetrate into the underlying regions. 

Most of the population in Washington resides in the Puget 

lowland region. Eastern Washington is generally sparsely 

populated with the exception of a few cities such as Spokane. 

Methods of Investigation

Maps showing the probability of elevated nitrate 

concentrations in ground water in Washington State were 

developed in several steps:

1. Relevant anthropogenic, hydrogeologic, and nitrate 

concentration data were compiled. 

2. Nitrate concentrations in ground-water data were overlaid 

with anthropogenic and hydrogeologic data using a GIS 

to produce a dataset in which each well with a measured 

nitrate concentration was attributed with population, 

land cover, precipitation, recharge, soils, and well depth. 

These data then were downloaded to a statistical software 

package for analysis. 

3. Several preliminary multivariate models with various 

combinations of explanatory variables were calibrated. 

4. The performance of the multivariate models that best 

estimated the probability of elevated nitrate concentrations 

in ground water was evaluated and validated. 

5. The multivariate models were entered into the GIS, and 

the probability maps were constructed. 

Description of Logistic Regression 

Logistic regression was selected for this analysis because 

logistic regression quantifies the relation between a variable 

of interest (response variable) and one or more variables that 

affect the variable of interest (explanatory variables). This is 

conceptually similar to multiple linear regression. However, 

the response variable in logistic regression is transformed into 

a binary response (yes or no) variable. This makes logistic 

regression an excellent tool for modeling aquifer vulnerability 

to nitrate contamination because logistic regression can 

quantify the probability that nitrate will exceed a specified 

concentration. According to Tesoriero and others (1998), 

“Logistic regression may identify relations between 

the occurrence of a constituent and explanatory 

variables when other methods do not because 

logistic regression answers a simpler question—

whether a well is expected to have water with a 

concentration greater than a specified value. In 

contrast, other methods (e.g., linear regression) try to 

estimate the absolute concentration of a constituent. 

Given the many factors related to the source and 

transport of a constituent in ground water, it is often 

impossible to predict its concentration; however, it 

may be possible to predict the probability that the 

concentration is above a specified level.”

In this study, logistic regression models were used to 

determine the probability of exceedance of 2 mg/L of nitrite 

plus nitrate as nitrogen in ground water. For the models, a 

binary response variable was defined by dividing the measured 

nitrate concentrations into two groups: those greater than or 

equal to 2 mg/L (exceedances) and those less than 2 mg/L 

(nonexceedances). The threshold of 2 mg/L was selected 

because nitrate concentrations that exceed 2 mg/L generally 

are the result of anthropogenic effects (Nolan and others, 

1998).

The logistic regression models take the form of

 

P e

e

P

b b X

b b X =

+

+

+ ( )

0

0 1

( )

,

where

is the probability of an exceedance,

is the base of the natural logarithm,

is the inter

e

b0 cept,

represents a set of explanatory variables such as

l

X

and use, soils, or well depth, and

b represents the slope for each of the explanatory

variables so that b X( ) = [b (lan 1 d use) + 

(soils) + (well depth) +.....] (Hosmer and

2

3

b

b

Lemeshow, 1989; Helsel and Hirsch, 1992).

(1)
6 Estimating the Probability of Elevated Nitrate Concentrations in Ground Water in Washington State

When the probability of an exceedance is plotted versus 

an explanatory variable, the result is an S-shaped curve with 

the probability being bounded by 0 on the lower end and 1 

on the upper end. The SAS statistical software was used to 

determine (calibrate) values of b0 and b that best fit the data 

using an iteratively reweighted least-squares algorithm (SAS 

Institute, 1990).

Model performance was evaluated using several statistical 

measures. Logistic regression calculates several statistical 

parameters that determine the predictive success of the model. 

The log-likelihood ratio measures the success of the model 

as a whole by comparing measured with estimated values 

(Hosmer and Lemeshow, 1989); specifically, it tests whether 

model coefficients of the entire model are significantly 

different from zero. The most significant model is the one 

with the highest log-likelihood ratio, taking into account the 

number of explanatory variables (degrees of freedom) used in 

the model. The log-likelihood ratio can be approximated by a 

chi-squared distribution, and the computed p-value reflects the 

degree of certainty (significance level) that model coefficients 

as a whole are different from zero. A p-value of 0.05 indicates 

a significance level of 95 percent, a p-value of 0.01 indicates 

a significance level of 99 percent, and the smallest p-value 

indicates the best model. McFadden’s rho-squared (SPSS, Inc., 

2000) is a transformation of the log-likelihood statistic and is 

intended to mimic the R2

 metric of linear regression. Rhosquared is always between 0 and 1; a rho-squared closer to 1 

corresponds to a better fit. Rho-squared tends to be smaller 

than R2, so a small number does not necessarily imply a poor 

fit. Values between 0.2 and 0.4 indicate good results (SPSS, 

Inc., 2000). The percentage of correct responses is a measure 

of how many actual nitrate exceedances and nonexceedances 

are present, compared with what was estimated by the model; 

the largest number denotes the best model. The percentage 

of correct responses is calculated as the number of measured 

exceedances estimated by the model as exceedances, plus 

the number of measured nonexceedances estimated by the 

model as nonexceedances, divided by the combined number 

of measured exceedances and nonexceedances (Nolan and 

Clark, 1997). Additional information regarding these statistical 

measures is available in Hosmer and Lemeshow (1989) and 

Helsel and Hirsch (1992).

 The partial-likelihood ratio was used to compare nested 

models to determine the significance of adding one or more 

new variables (Helsel and Hirsch, 1992; Nolan and Clark, 

1997). A nested model contains all explanatory variables in 

the original model, plus one or more additional explanatory 

variables. To determine whether the model is improved by 

adding the explanatory variable, the logistic regression model 

is calculated without that new variable. Logistic regression 

calculates a partial-likelihood ratio. The logistic regression 

model then is rerun with the additional new explanatory 

variable; the second model also calculates a partial-likelihood 

ratio. The difference in partial-likelihood ratios between the 

two models is calculated and a chi-squared approximation is 

calculated with degrees of freedom equal to the number of 

additional variables in the new model. If the p-value from the 

chi-squared distribution is less than 0.05, the model has been 

significantly improved at the 95-percent level.

For individual explanatory variables, the p-value for 

the Wald statistic is reported. The Wald statistic can be 

approximated by a chi-squared distribution and is used 

to indicate whether individual model coefficients are 

significantly different from zero. Individual coefficients were 

considered to be statistically significant if the p-value of the 

Wald statistic was less than or equal to 0.05. The p-value for 

the Wald statistic can be considered similar to the p-value for 

the slope of a line in linear regression. In linear regression, the 

slope of the line is considered to be statistically different from 

a horizontal line (with a slope of zero) if the p-value is less 

than 0.05. Similarly, the regression coefficients are considered 

to be statistically different from zero if the p-values are less 

than 0.05.

Multicollinearilty is the result of strong correlation 

between explanatory variables, and is a major concern for 

multivariate logistic regression models. Multicollinearity 

may result in incorrect signs and magnitudes of regression 

coefficients, thereby, leading to incorrect conclusions about 

relations between explanatory and response variables. Pearson 

correlation coefficients and multicollinearity diagnostic 

statistics were examined to assess the multicollinearity in 

the models. A strong correlation between two variables 

was indicated if the correlation coefficient was greater than 

0.7. However, Pearson correlation coefficients would not 

detect cases where multiple explanatory variables may be 

interdependent. In these cases, the Tolerance and Variance 

Inflation Factor (VIF) can be used to detect multicollinearity. 

According to Gurdak and Qi (2006), the Tolerance and 

VIF are based on linear regression analysis of explanatory 

variables. The Tolerance is defined as 1 – R2

, where R2 is 

the coefficient of determination for the regression of one 

independent variable on all remaining independent variables 

(Allison, 1991; Menard, 2002). The VIF is equal to the 

reciprocal of the tolerance and describes how inflated the 

variance of coefficient is compared to what it would be if there 

were no multicollinearity (Allison, 1991). Although no formal 

thresholds exist to use for the Tolerance or VIF in detecting 

the presence of multicollinearity, Allison (1991) suggests that 

Tolerance values less than 0.4 (VIF greater than 2.5) may 

indicate the presence of multicollinearity.
Methods of Investigation 7

Compilation of Nitrate Concentration 

Data into a Response Variable

The binary response variable of nitrate concentrations 

exceeding or not exceeding a selected concentration 

(exceedances and nonexceedances, respectively) was 

computed from the WDOH public-water supply system 

database. The WDOH dataset contained more than 60,000 

nitrate analyses from samples collected between April 1979 

and September 2006. Because nitrate concentrations and landuse characteristics would be expected to have changed over 

such a long period, the dataset was reduced to include only the 

samples collected after January 1, 1995. Reporting level limits 

in this smaller dataset ranged from less than 0.001 to less than 

7 mg/L. Because the wide range of reporting levels would 

adversely affect the computation of the response variable, 

analyses with reporting levels greater than 0.5 mg/L were 

omitted, which resulted in the exclusion of about 850 samples. 

Once the dataset of nitrate analyses was finalized, a 

single nitrate concentration was calculated for each water 

source, as many of the sources had multiple samples. This 

was accomplished by computing the median value of all 

samples for each water source. The resulting dataset then was 

further reduced to exclude all water sources that were not 

from an individual well, had no location information, or had 

location information of questionable quality. The final dataset 

contained median nitrate concentrations for about 12,600 

wells. 

The final dataset contains far fewer wells in eastern 

Washington than in western Washington, but nitrate 

concentrations were elevated in a larger percentage of wells 

in eastern Washington (fig. 3). Nitrate concentrations were 

higher in wells in the Columbia basalt flow and the eastern 

Washington unconsolidated hydrogeomorphic regions than 

the other regions of the State (fig. 4). The regional median 

nitrate concentrations ranged from 1.4 mg/L in the eastern 

Washington alluvial fill region to the reporting limit of 0.5 

mg/L in the western Washington alluvial fill, bedrock, and 

Puget lowland regions. 

Nitrate concentrations in ground water from wells in 

the USGS and Washington State Department of Ecology 

databases (fig. 5) were used as the model validation dataset 

(1,813 wells). Only data collected after 1995 were used, and 

all known public-supply well samples were excluded so no 

data were duplicated in the calibration dataset. As with the 

calibration dataset, nitrate concentrations in the validation 

dataset were elevated in a larger percentage of wells in eastern 

Washington.

Compilation of Anthropogenic and 

Hydrogeologic Data into Explanatory Variables

Explanatory variables that were compiled and evaluated 

included well depth (depth to bottom of well from land 

surface), ground-water recharge rate, average annual 

precipitation, population density, land use, nitrogen application 

amounts, soil available water capacity, soil hydrologic group, 

soil drainage group, soil permeability, soil clay content, 

amount of organic matter in soil, and hydrogeomorphic region 

(table 1). Data for explanatory variables were obtained from 

several sources.

Well depth was obtained for each wells, if available, from 

the WDOH well database. Ground-water recharge rates were 

taken from Wolock (2003) and average annual precipitation 

was from Spatial Climate Analysis Service-Oregon State 

University (2006). Population density was retrieved from the 

U.S. Bureau of the Census for the 2000 (GeoLytics, 2001) 

census year. Land-use data were compiled from the 1992 

National Land Cover Dataset (Vogelmann and others, 2001), 

which was enhanced with GIRAS land use/land cover data 

modified as described in Price and others (2003) to more 

accurately represent alpine tundra, orchards, vineyards, and 

residential areas. Areas were classified as urban, agricultural, 

or other (which includes forest, rangeland, wetlands, and 

barren areas). All soil criteria (available water capacity, 

hydrologic group, drainage group, clay content, permeability 

rate, and organic matter content) were obtained from Schwarz 

and Alexander (1995), which utilizes the STATSGO soil 

database (U.S. Department of Agriculture, 1993). The soil 

data include weighted vertical averaging of many of the soil 

characteristics contained in the database.

Estimates of agricultural and urban nitrogen fertilizer 

application amounts were computed as the product of the 

rate of nitrogen fertilizer application (in kilograms per square 

kilometer per year) and the total applicable land use area 

within a specified radius of each well. Nitrogen application 

rates were determined by allocating the farm and nonfarm 

county-level nitrogen application amounts of Ruddy and 

others (2006) to the compiled land-use data. For each county, 

the approximate average nitrogen mass from 1995 to 2004 was 

divided by the total area of allocated land cover to determine 

the nitrogen application rate. 

The percentage of each land-use type and the amount of 

nitrogen fertilizer applied within a specified radius (buffer) 

of each well were calculated and then related to nitrate 

concentrations. The optimal radius to use for the land-use 

and fertilizer application data was determined by performing 

logistic regression analyses at different radii around the wells. 
8 Estimating the Probability of Elevated Nitrate Concentrations in Ground Water in Washington State

wa19-0163_fig03

124° 122° 120° 118°

48°

46°

EXPLANATION

Nitrate concentration, in 

 milligrams per liter

0 – 1.99

Greater than or

 equal to 2 

0 20 40 60 80 100 MILES

0 20 40 60 80 100 KILOMETERS

0 20 40 60 MILES

0 20 40 60 KILOMETERS

GRAYS 

HARBOR

PACIFIC LEWIS

SKAMANIA COWLITZ

CLARK KLICKITAT

YAKIMA

KITTITAS

PIERCE

THURSTON

SAN 

JUAN

ISLAND

KITSAP

MASON

CLALLAM

JEFFERSON

KING

SNOHOMISH

SKAGIT

WHATCOM

OKANOGAN

CHELAN

DOUGLAS

GRANT

BENTON WALLA WALLA

COLUMBIA

GARFIELD

ASOTIN

WHITMAN ADAMS

FRANKLIN

LINCOLN SPOKANE

FERRY

STEVENS

PEND 

OREILLE

WAHKIAKUM

Bellingham

Everett

Seattle

Tacoma

Olympia

Vancouver

Richland

Spokane

Bellingham

Everett

Seattle

Tacoma

Olympia

Figure 3. Nitrate concentrations in water from wells in Washington from the Washington State Department of Health database 

(1995–2006).
Methods of Investigation 9

EXPLANATION

Nitrate concentration, in

 milligrams per liter

0 – 1.99

Greater than or

 equal to 2 

0 20 40 60 80 100 MILES

0 20 40 60 80 100 KILOMETERS

124° 122° 120° 118°

48°

46°

GRAYS 

HARBOR

PACIFIC LEWIS

SKAMANIA COWLITZ

CLARK KLICKITAT

YAKIMA

KITTITAS

PIERCE

THURSTON

SAN 

JUAN

ISLAND

KITSAP

MASON

CLALLAM

JEFFERSON

KING

SNOHOMISH

SKAGIT

WHATCOM

OKANOGAN

CHELAN

DOUGLAS

GRANT

BENTON WALLA WALLA

COLUMBIA

GARFIELD

ASOTIN

WHITMAN ADAMS

FRANKLIN

LINCOLN SPOKANE

FERRY

STEVENS

PEND 

OREILLE

WAHKIAKUM

Bellingham

Everett

Seattle

Tacoma

Olympia

Vancouver

Richland

Spokane

Figure 4. Nitrate concentrations in 

ground-water samples collected in 

hydrogeomorphic regions in Washington 

from the Washington State Department of 

Health database (1995–2006).

Figure 5. Nitrate concentrations in water from wells in Washington from the U.S. Geological Survey and Washington State 

Department of Ecology databases (1995–2006).

Western

Washington

alluvial fill

Willamette

lowland

Columbia

basalt

flows

Eastern Bedrock

Washington

alluvial fill

Puget

lowland

HYDROGEOMORPHIC REGION

NITRATE CONCENTRATION, IN MILLIGRAMS PER LITER

0

10

20

30

40

50

Outlier

1.5 times interquartile range

75th percentile

Median

25th percentile

EXPLANATION
10 Estimating the Probability of Elevated Nitrate Concentrations in Ground Water in Washington State

McFadden’s rho-squared 

was calculated for each 

buffer size to determine the 

most significant relation 

(fig. 6). The optimum 

buffer sizes were 4,000 m 

for agricultural lands, 2,000 

m for undeveloped lands, 

500 m for urban lands, 

and 2,000 m for nitrate 

application amounts.

Percentage of land 

cover, nitrate application 

amounts, recharge, 

precipitation, population 

density, soils, and well 

depth were modeled as 

continuous variables. 

Because of their categorical 

nature, hydrogeomorphic 

regions were modeled as 

discrete variables. Discrete 

variables were coded as “1” 

Table 1. Summary of anthropogenic and natural explanatory variables used for model development.

Variable Number of 

samples

Minimum 

value

Median 

value

Maximum 

value Source of data

Well depth (feet) 12,601 1 145 2,200 Washington Dept. of Health data base

Average annual precipitation (inches) 12,601 5.7 43.23 171.9 Spatial Climate Analsyis Service–

Oregon State University, 2006

Recharge 11,655 3 354 1,982 Wolock, 2003

2000 population density at the well location 

(people per squared kilometer)

12,560 0 675 39,263 GeoLytics, 2001

Urban land use within 500 meters of well 

(percent)

12,601 0 16.12 100 Vogelmann and others, 2001; 

Price and others, 2003

Agricultural land use within 4 kilometers of 

well (percent)

12,601 0 7.52 98.87 Vogelmann and others, 2001; 

Price and others, 2003

Undeveloped land use within 2 kilometers 

of well (percent)

12,601 0 68.5 100 Vogelmann and others, 2001; 

Price and others, 2003

Nitrate application within 2 kilometers of 

well (kilograms per year)

12,601 0 6,295 153,047 This study

Available water capacity (inch per inch) 12,464 .03 .09 .21 Schwarz and Alexander, 1995

Clay content (in percent) 12,464 0 8.20 44.3 Schwarz and Alexander, 1995

Organic matter (percent by weight) 12,464 .1 1.30 10.9 Schwarz and Alexander, 1995

Permeability (inches per hour) 12,464 .25 3.81 17.14 Schwarz and Alexander, 1995

Hydrologic group [rated 1 (high infiltration) 

to 4 (very slow infiltration)]

12,464 1 2.5 4 Schwarz and Alexander, 1995

Soil drainage [rated 1 (excessive) to 7 (very 

poorly drained)]

12,464 1.3 3.1 6.9 Schwarz and Alexander, 1995

Nitrate application

Agriculture

Urban

Other

MCFADDEN’S RHO-SQUARED, UNITLESS

0

0.02

0.04

0.06

0.08

0.10

0.12

0 1,000 2,000 3,000 4,000 5,000 6,000

BUFFER RADIUS, IN METERS

Figure 6. McFadden’s rho squared from relations of amount of nitrogen application and 

percentage of agricultural, urban, and undeveloped lands within circular buffers around wells 

with nitrate concentrations greater than 2 milligrams per liter in ground water in Washington.

if a well was located in a particular region and coded “0” if the well was not located in that region. For example, if a well was 

located in the western Washington alluvial fill region, then those wells in that region would be coded 1 and all other wells would 

be coded 0. Hosmer and Lemeshow (1989) further describe the use of continuous and discrete variables in logistic regression. 

Reference cell coding was used with the Puget lowland region as the reference variable.
Logistic Regression Results 11

Logistic Regression Results 

Based on the relations between the explanatory variables 

and the measured elevated nitrate concentrations, various 

logistic regression models were developed to estimate 

the probability that ground water will exceed a nitrate 

concentration of 2 mg/L. All possible combinations of the 

explanatory variables were evaluated to develop the models. 

The performance of these models was evaluated using the 

log-likelihood ratio, McFadden’s rho-squared, the p-values for 

each variable included in the models, and the percentage of 

correct responses. 

The two best performing models—one with and one 

without hydrogeomorphic regions—for estimating the 

probability of nitrate concentrations exceeding 2 mg/L 

were identified. Models with and without hydrogeomorphic 

regions were developed because of the possibility that 

Table 2. Regression coefficients and individual p-values of independent variables for the two logistic 

regression models with and without hydrogeomorphic regions that were significantly related with nitrate 

concentrations greater than 2 milligrams per liter in ground water in Washington.

[Abbreviation: –, no data; <, less than.]

Independent variable

With hydrogeomorphic region Without hydrogeomorphic region

Regression 

coefficients p-values Regression coefficients p-values

Logistic regression constant 1.6132 <0.0001 1.3857 <0.0001

Well depth, in feet -.00436 <.0001 -.00388 <.0001

Average annual precipitation, in inches -.0252 <.0001 -.026 <.0001

Percentage of agricultural land within a 

4-kilometer buffer

.0276 <.0001 .0275 <.0001

2000 population density .000064 <.0001 .00007 <.0001

Soil drainage -.5796 <.0001 -.5554 <.0001

Hydrogeomorphic region

Eastern Washington basin fill -.3349 .0011 – –

Columbia basalts .1583 .128 – –

Bedrock -.4621 <.0001 – –

Willamette basin .0337 .7963 – –

Western Washington basin fill -.7302 <.0001 – –

different relations between explanatory and response variables 

may occur in each of the hydrogeomorphic regions. This 

allowed a comparison between the model that included 

the hydrogeomorphic regions with the one that did not to 

determine if inclusion of the hydrogeomorphic regions 

significantly improved model performance. 

Well depth, average annual precipitation, percentage 

of agricultural land within a 4-km buffer around the well, 

population density, and soil drainage were the significant 

explanatory variables in both of the best performing models 

(table 2). Overall performance of both models was good, with 

the chi-squared p-value calculated from the log-likelihood 

ratio of the entire model less than 0.001, McFadden’s rhosquared of about 0.19, and the percentage of correct responses 

greater than 81 percent (table 3). The two models performed 

equally well, with identical percentages of correct responses. 

Table 3. Statistical results from models that estimate the probability of nitrate 

concentrations exceeding 2 milligrams per liter in ground water in Washington.

[Abbreviation: <, less than.]

Statistical results

Model

With 

hydrogeomorphic 

region

Without 

hydrogeomorphic 

region

Log-likelihood ratio 2,452 2,378

p-value <.0001 <.0001

McFadden’s rho-squared .193 .187

Percentage of correct responses 81.33 81.33
12 Estimating the Probability of Elevated Nitrate Concentrations in Ground Water in Washington State

The positive and negative signs of the model coefficients 

were as expected. Well depth showed a negative correlation 

with elevated nitrate concentrations as nitrate concentrations 

usually decrease with depth below land surface. The relation 

between percentage of agricultural land use near a well and 

elevated nitrate concentrations was positive. This indicates 

that agricultural fertilizer is a large source of nitrate to ground 

water. The relation between population density and elevated 

nitrate concentrations also was positive, which is likely the 

result of residential fertilizer usage and septic system inputs. 

The relation between elevated nitrate concentrations and 

soil drainage was negative indicating that the probability of 

elevated nitrate concentrations increases beneath soils that 

are well drained. Soils that are poorly drained may have an 

increased likelihood of fostering denitrifying conditions, 

thereby decreasing the amount of nitrate available to leach 

into the ground water. The relation between elevated nitrate 

concentrations and precipitation also was negative, which 

is likely due to the larger percentage of elevated nitrate 

concentrations in eastern Washington, which receives less 

precipitation than western Washington.

y = 1.0084x – 0.0042

R 2

 = 0.9792

0

10

20

30

40

50

60

70

y = 0.998x – 0.0004

R 2

 = 0.9748

0

10

20

30

40

50

60

70

0 10 20 30 40 50 60 70

ESTIMATED PROBABILITY, IN PERCENT

ACTUAL PROBABILITY, IN PERCENT

B. Without hydrogeomorphic regions 

A. With hydrogeomorphic regions 

1:1 line

Figure 7. Percentage of actual nitrate concentrations greater than 2 milligrams per liter 

(mg/L) and the estimated probability of nitrate concentrations greater than 2 mg/L in the 

calibration dataset.

Alternative measures of model performance were 

generated regressing the measured and estimated probabilities 

of elevated nitrate concentrations from wells included in the 

calibration dataset (fig. 7). Nitrate concentrations from the 

calibration wells were converted to a binary classification 

of 0 for nitrate concentrations less than 2 mg/L and 1 for 

those greater than 2 mg/L. This binary conversion allowed 

the percentage of actual detections to be calculated and 

compared to the estimated probabilities for each 10 percent 

decile. The estimated and measured number of exceedances 

and nonexceedances were similar for both models with and 

without hydrogeomorphic regions, as indicated by R2 values 

of 0.9748 and 0.9792, respectively, with no systemic bias 

as shown by the 1:1 line in figure 7. Pearson’s correlation 

coefficients and Tolerance and VIF statistics detected no 

multicollinearity for the explanatory variables included in the 

models. Pearson’s correlation coefficients were all less than 

0.5, tolerance was greater than 0.67, and VIF less than 1.5.
Estimating the Probability of Elevated Nitrate Concentrations in Ground Water 13

Validation of Nitrate Models

To validate the models, the estimated 

probabilities of elevated nitrate concentrations 

for wells in the validation dataset from USGS 

and Department of Ecology were computed and 

compared to the actual probabilities (fig. 8). 

Nitrate concentrations from the validation wells 

were converted to a binary classification of 0 for 

nitrate concentrations less than 2 mg/L and 1 for 

concentrations greater than 2 mg/L. This binary 

conversion allowed the percentage of measured 

detections to be calculated and compared 

to the estimated probabilities for each 10 

percent decile. The relation between the actual 

percentage of wells with a nitrate concentration 

greater than 2 mg/L and the estimated 

probabilities had an R2

 of 0.9061 for the model 

without hydrogeomorphic regions and 0.9173 

for the model with hydrogeomorphic regions. 

The validation of the model that included 

hydrogeomorphic regions was not as strong 

because some regions had few data points. 

Overall, both logistic regression models tended 

to underestimate the actual probability for the 

validation dataset by about 10 percent. 

wa19-0163_fig08 

0

20

40

60

80

100

0 20 40 60 80 100

0

20

40

60

80

100

ESTIMATED PROBABILITY, IN PERCENT

ACTUAL PROBABILITY, IN PERCENT

y = 0.913x + 0.0919

R 2

 = 0.9173

y = 0.8748x + 0.1147

R 2

 = 0.9061

B. Without hydrogeomorphic regions 

A. With hydrogeomorphic regions 

Figure 8. Percentage of actual nitrate concentrations greater than 

2 milligrams per liter (mg/L) and the estimated probability of nitrate 

concentrations greater than 2 mg/L in the validation dataset.

Estimating the Probability of 

Elevated Nitrate Concentrations in 

Ground Water

Maps showing the probability of detecting elevated 

nitrate concentrations in ground water throughout Washington 

State were generated using the logistic regression models and 

a GIS (figs. 9–10). To generate the maps, a 500 × 500-meter 

grid was constructed that covered the entire State. A well was 

assumed to be in the center of each grid cell and the nitrate 

concentration in each well was assumed to represent the nitrate 

concentrations in ground water for the entire grid cell. For the 

model without hydrogeomorphic regions (fig. 9A), the amount 

of agricultural land use within a 4-km radius from the center 

of each cell was calculated; the annual average precipitation, 

population density, and soil drainage class were determined; a 

well depth of interest was selected; and probabilities of nitrate 

concentration exceedances were determined using equation 

(1) and the coefficients in table 2. The probabilities were 

then mapped using a GIS. The process for the model with 

hydrogeomorphic regions (fig. 9B) was similar, but included 

the hydrogeomorphic region of each cell.

Estimated probabilities of nitrate concentrations 

exceeding 2 mg/L in wells drilled to 145 ft below land surface 

(the median well depth for the calibration dataset) range from 

0 to greater than 95 percent for both models with and without 

hydrogeomorphic regions (fig. 9). The high probabilities 

of elevated nitrate concentrations are most widespread in 

areas of eastern Washington that have a high density of 

agricultural land use. The high probabilities of elevated 

nitrate concentrations beneath the urban and agricultural 

areas in the Puget lowland are less widespread than in the 

agricultural areas of eastern Washington, but probabilities 

do exceed 50 percent in selected areas (fig. 10). Conversely, 

regions of the State with little agriculture or urban land use 

have less probability of exceeding a nitrate concentration of 

2 mg/L. These types of maps can be generated for any depth 

of interest, with probabilities of elevated nitrate concentrations 

decreasing with increasing well depth.
14 Estimating the Probability of Elevated Nitrate Concentrations in Ground Water in Washington State

wa19-0163_fig09a

Probability of detecting elevated nitrate

 concentrations in ground water, in percent

A. Without hydrogeomorphic regions.

0 20 40 60 80 100 MILES

0 20 40 60 80 100 KILOMETERS

124° 122° 120° 118°

48°

46°

EXPLANATION

100

50

0

GRAYS 

HARBOR

PACIFIC LEWIS

SKAMANIA COWLITZ

CLARK KLICKITAT

YAKIMA

KITTITAS

PIERCE

THURSTON

SAN 

JUAN

ISLAND

KITSAP

MASON

CLALLAM

JEFFERSON

KING

SNOHOMISH

SKAGIT

WHATCOM

OKANOGAN

CHELAN

DOUGLAS

GRANT

BENTON WALLA WALLA

COLUMBIA

GARFIELD

ASOTIN

WHITMAN ADAMS

FRANKLIN

LINCOLN SPOKANE

FERRY

STEVENS

PEND 

OREILLE

WAHKIAKUM

Bellingham

Everett

Seattle

Tacoma

Olympia

Vancouver

Richland

Spokane

Figure 9. Probability of detecting nitrate concentrations greater than 2 milligrams per liter in ground water at a depth of 145 

feet below land surface for the two logistic regression models with and without hydrogeomorphic regions, Washington.
Estimating the Probability of Elevated Nitrate Concentrations in Ground Water 15

wa19-0163_fig09b

Probability of detecting elevated nitrate

 concentrations in ground water, in percent

B. With hydrogeomorphic regions.

0 20 40 60 80 100 MILES

0 20 40 60 80 100 KILOMETERS

124° 122° 120° 118°

48°

46°

EXPLANATION

100

50

0

GRAYS 

HARBOR

PACIFIC LEWIS

SKAMANIA COWLITZ

CLARK KLICKITAT

YAKIMA

KITTITAS

PIERCE

THURSTON

SAN 

JUAN

ISLAND

KITSAP

MASON

CLALLAM

JEFFERSON

KING

SNOHOMISH

SKAGIT

WHATCOM

OKANOGAN

CHELAN

DOUGLAS

GRANT

BENTON WALLA WALLA

COLUMBIA

GARFIELD

ASOTIN

WHITMAN ADAMS

FRANKLIN

LINCOLN SPOKANE

FERRY

STEVENS

PEND 

OREILLE

WAHKIAKUM

Bellingham

Everett

Seattle

Tacoma

Olympia

Vancouver

Richland

Spokane

Figure 9.—Continued.
16 Estimating the Probability of Elevated Nitrate Concentrations in Ground Water in Washington State

wa19-0163_fig10a

A. Without hydrogeomorphic regions.

Greater than 50

25

0

EXPLANATION

Probability of detecting elevated

 nitrate concentrations in ground

 water, in percent

0 20

0

40 60 MILES

20 40 60 80 KILOMETERS

124°

48°

122°

GRAYS 

HARBOR

PIERCE

THURSTON

SAN 

JUAN

ISLAND

KITSAP

MASON

CLALLAM

JEFFERSON

KING

SNOHOMISH

SKAGIT

WHATCOM

Figure 10. Probability of detecting nitrate concentrations greater than 2 milligrams per liter in ground water at a depth of 145 

feet below land surface for the two logistic regression models with and without hydrogeomorphic regions, Puget Sound region, 

Washington. 
Estimating the Probability of Elevated Nitrate Concentrations in Ground Water 17

wa19-0163_fig10b

B. With hydrogeomorphic regions.

Greater than 50

25

0

EXPLANATION

Probability of detecting elevated

 nitrate concentrations in ground

 water, in percent

0 20

0

40 60 MILES

20 40 60 80 KILOMETERS

124°

48°

122°

GRAYS 

HARBOR

PIERCE

THURSTON

SAN 

JUAN

ISLAND

KITSAP

MASON

CLALLAM

JEFFERSON

KING

SNOHOMISH

SKAGIT

WHATCOM

Figure 10.—Continued.
18 Estimating the Probability of Elevated Nitrate Concentrations in Ground Water in Washington State

In addition to maps displaying the probability of elevated 

nitrate concentrations, the logistic regression models can 

be used to generate maps showing the depth to which wells 

need to be drilled to have a specific probability of obtaining 

water with a nitrate concentration less than 2 mg/L. This can 

be done by selecting the probability of a specific elevated 

nitrate concentration, using the coefficients in table 2, and 

solving equation (1) for the well depth. For example, by 

fixing the probability of exceeding nitrate concentrations 

Figure 11. Depth to which wells need to be drilled for at least a 90-percent probability of detecting a nitrate concentration 

less than 2 milligrams per liter in ground water for the logistic regression model without hydrogeomorphic regions, State of 

Washington and Puget lowlands.

of 2 mg/L at 10 percent, wells would need to be drilled to a 

depth of more than 1,000 ft in some regions in order to have 

a 90-percent probability of obtaining ground water with 

nitrate concentrations less than 2 mg/L (fig. 11A). In general, 

wells installed in the agricultural areas of eastern Washington 

need to be drilled to a depth of at least 750 to 1,500 ft to 

have a 90-percent probability of obtaining water with nitrate 

concentrations less than 2 mg/L. Likewise, wells in the urban 

and agricultural areas of the Puget lowlands would need to 

A. Without hydrogeomorphic regions—State of Washington.

Estimated well depth, in feet 0 20 40 60 80 100 MILES

0 20 40 60 80 100 KILOMETERS

124° 122° 120° 118°

48°

46°

EXPLANATION

1,500

1,000

500

0

GRAYS 

HARBOR

PACIFIC LEWIS

SKAMANIA COWLITZ

CLARK KLICKITAT

YAKIMA

KITTITAS

PIERCE

THURSTON

SAN 

JUAN

ISLAND

KITSAP

MASON

CLALLAM

JEFFERSON

KING

SNOHOMISH

SKAGIT

WHATCOM

OKANOGAN

CHELAN

DOUGLAS

GRANT

BENTON WALLA WALLA

COLUMBIA

GARFIELD

ASOTIN

WHITMAN ADAMS

FRANKLIN

LINCOLN SPOKANE

FERRY

STEVENS

PEND 

OREILLE

WAHKIAKUM

Bellingham

Everett

Seattle

Tacoma

Olympia

Vancouver

Richland

Spokane
Estimating the Probability of Elevated Nitrate Concentrations in Ground Water 19

B. Without hydrogeomorphic regions—Puget lowlands.

EXPLANATION

Estimated well depth, in feet

750

0

250

500

0 20

0

40 60 MILES

20 40 60 80 KILOMETERS

124°

48°

122°

GRAYS 

HARBOR

PIERCE

THURSTON

SAN 

JUAN

ISLAND

KITSAP

MASON

CLALLAM

JEFFERSON

KING

SNOHOMISH

SKAGIT

WHATCOM

Figure 11.—Continued.

be drilled to a depth of at least 400 ft (fig. 11B). Of course in 

some areas, it may not be possible to obtain drinkable water 

from a well drilled that deep so the probability of obtaining 

water with nitrate concentrations less than 2 mg/L would 

be less in a shallower well. Additionally, the inclusion of 

wells that are open to multiple hydrogeologic units could 

bias the estimated depths. In these cases, ground water with 

high nitrate concentrations enter the well from open intervals 

located at shallower depths. For example, many wells on the 

Columbia Plateau have wells that are only cased to the top of 

the basalts with very long uncased sections continuing down 

through the basalts. These shallow casings allow shallow 

ground water to enter the deeper wells. Casing depth has been 

shown to be preferable explanatory variable in these situations 

(Frans, 2000); however, casing depths were not available as 

part of the WDOH database.
20 Estimating the Probability of Elevated Nitrate Concentrations in Ground Water in Washington State

Appropriate Uses of the Probability Maps

The probability maps developed for this study illustrate 

the estimated probability of nitrate concentrations exceeding 

2 mg/L in ground water in Washington. The probability maps 

do not show actual nitrate contamination of ground water. 

In addition, inherent uncertainty is associated with these 

maps. Uncertainty in the estimates is the result of data errors 

in the well database and GIS-based explanatory variables 

and estimated error in developing the logistic regression 

coefficients. Higher resolution data, particularly for the soils 

and nitrate application data, would improve the models.

The maps in this report are intended for regional scale 

use only and have limitations for use at the field-scale. The 

maps are not appropriate at any scale larger than 1:250,000, 

as determined by the STATSGO soil data, which has the 

smallest scale of the explanatory variables used in the models. 

Many unaccounted for field-scale complexities affect the 

concentration of nitrate in ground water and in a given well. 

For example, the models do not account for point sources of 

nitrate or preferential pathways in the soil. Although a well 

may be installed in a region with an estimated high probability 

of elevated nitrate concentration, the well may in fact actually 

yield water with low nitrate concentrations due to complexities 

that cannot be represented in regional-scale models such as 

those developed in this study. 

In addition to the significant explanatory variables 

of agricultural land use amounts, population density, 

precipitation, well depth, and soil drainage group, other 

variables also can have an important effect on nitrate 

concentrations. The absence of an explanatory variable from 

the model does not mean that the variable does not have an 

important effect on nitrate concentrations. In many cases, if 

two or more explanatory variables are closely correlated with 

each other, only one of the variables will be incorporated into 

the model to account for the effects of both variables. For 

example, soil drainage class and soil hydrologic group are well 

correlated, therefore, only one of the variables was included. 

Summary

Logistic regression was used to relate anthropogenic 

and natural factors to the occurrence of elevated nitrate 

concentrations in the State of Washington and develop models 

that estimate the probability of nitrate concentrations in 

ground water exceeding 2 milligrams per liter. Explanatory 

variables that were considered for inclusion in the models 

included hydrogeomorphic regions, soil characteristics, 

ground-water recharge rates, precipitation, land use, well 

depth, population density, and the amount of fertilizer applied 

annually near the well. 

Two models that best estimate the probability of 

elevated nitrate concentrations were selected: one with and 

one without hydrogeomorphic regions. Other variables that 

were included in these models were well depth, percentage 

of agricultural land use within 4 kilometers of a well, average 

annual precipitation, population density, and soil drainage 

class. Relations between the estimated probability of detecting 

elevated nitrate and the actual percentage of wells with 

elevated nitrate concentrations were good for both models 

with R2

 values greater than 0.9. 

Maps showing the estimated probability of detecting 

elevated nitrate concentrations indicate that the agricultural 

regions are most at risk followed by urban regions. Areas of 

the State that are not affected by agricultural or urban areas 

had much lower probabilities of detecting elevated nitrate 

concentrations. Maps also were generated that show the 

estimated depths to which wells would need to be drilled in 

order to have a 90-percent probability of obtaining water with 

nitrate concentrations less than 2 milligrams per liter. These 

depths frequently exceed 1,000 feet in the agricultural regions, 

although wells in urban areas generally would need to be 

drilled to depths in excess of 400 feet. 

References Cited

Allison, P.D., 1991, Logistic regression using the SAS 

system—Theory and application: Cary, N.C., SAS Institute 

Inc., 288 p. 

Centers for Disease Control and Prevention, 1996, 

Spontaneous abortions possibly related to ingestion of 

nitrate-contaminated well water, La Grange County, 

Indiana, 1991–1994: Morbidity and Mortality Weekly 

Report, v. 45, p. 569–572.

Ebbert, J.C., Embrey, S.S., Black, R.W., Tesoriero, A.J., and 

Haggland, A.L., 2000, Water quality in the Puget Sound 

Basin, Washington and British Columbia, 1996–98: U.S. 

Geological Survey Circular 1216, 31 p.

Fewtrell, Lorna, 2004, Drinking-water nitrate, 

methemoglobinemia, and global burden of disease—A 

discussion: Environmental Health Perspectives, v. 112, no. 

14, p. 1371–1374.

Frans, L.M., 2000, Estimating the probability of elevated 

nitrate (NO2 + NO3 - N) concentrations in ground water 

in the Columbia Basin Ground Water Management Area, 

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22 Estimating the Probability of Elevated Nitrate Concentrations in Ground Water in Washington State

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Manuscript approved for publication, February 22, 2008

Prepared by the USGS Publishing Network, 

Bob Crist 

Bill Gibbs

Lyn Osburn

Bobbie Jo Richey

Linda Rogers

Sharon Wahlstrom

For more information concerning the research in this report, contact the 

Director, Washington Water Science Center

U.S. Geological Survey, 934 Broadway — Suite 300

Tacoma, Washington 98402

http://wa.water.usgs.gov
Frans— Estimating the Probability of Elevated Nitrate Concentrations in Ground Water in Washington State—Scientific Investigations Report–2008–5025