National Water Quality Assessment Program

Comparison of Two Methods for Delineating 

Land Use Near Monitoring Wells Used for 

Assessing Quality of Shallow Ground Water

Water-Resources Investigations Report 03–4067

U.S. Department of the Interior

U.S. Geological Survey

Aquifer

Unsaturated zone

Confining unit

Water table

Flow path to 

well bottom

Land surface

Well screen

General direction 

of ground-water 

flow

Well

3-16 yrs.

1 yr.

200-meter sector

500-meter diameter 

circle
U.S. Department of the Interior 

U.S. Geological Survey

Comparison of Two Methods for Delineating 

Land Use Near Monitoring Wells Used for 

Assessing Quality of Shallow Ground Water

By D.L. Lorenz, R.M. Goldstein, T.K. Cowdery, and J.D. Stoner

Water-Resources Investigations Report 03-4067

Contribution from the National Water-Quality Assessment Program
U.S. DEPARTMENT OF THE INTERIOR

Gale A. Norton, Secretary

U.S. GEOLOGICAL SURVEY

Charles G. Groat, Director

Use of firm, trade, and brand names in this report is for identification purposes only and does not 

constitute endorsement by the U.S. Geological Survey.

For additional information write to:

Chief, NAWQA Program

U.S. Geological Survey

12201 Sunrise Valley Drive, MS 413

Reston, VA 20192

Copies of this report can be purchased from:

U.S. Geological Survey

Branch of Information Services

Box 25286, MS 517

Federal Center

Denver, CO 80225

Information regarding the National Water-Quality Assessment (NAWQA) Program is available on the Internet via the World Wide Web. 

You may connect to the NAWQA Home Page using the Universal Resource Locator (URL) at: 

http://wwwrvares.er.usgs.gov/nawqa/nawqa_home.html

Information about the Red River of the North River Basin Project of the NAWQA Program is available at:

http://mn.water.usgs.gov/redn/index.html

Water-Resources Investigations Report 03-4067
FOREWORD

The U.S. Geological Survey (USGS) is committed to serve the 

Nation with accurate and timely scientific information that helps 

enhance and protect the overall quality of life, and facilitates 

effective management of water, biological, energy, and mineral 

resources. (http://www.usgs.gov/). Information on the quality of 

the Nation’s water resources is of critical interest to the USGS 

because it is so integrally linked to the long-term availability of 

water that is clean and safe for drinking and recreation and that is 

suitable for industry, irrigation, and habitat for fish and wildlife. 

Escalating population growth and increasing demands for the 

multiple water uses make water availability, now measured in 

terms of quantity and quality, even more critical to the long-term 

sustainability of our communities and ecosystems.

The USGS implemented the National Water-Quality 

Assessment (NAWQA) Program to support national, regional, 

and local information needs and decisions related to waterquality management and policy. (http://water.usgs.gov/nawqa/). 

Shaped by and coordinated with ongoing efforts of other Federal, 

State, and local agencies, the NAWQA Program is designed to 

answer: What is the condition of our Nation’s streams and ground 

water? How are the conditions changing over time? How do 

natural features and human activities affect the quality of streams 

and ground water, and where are those effects most pronounced? 

By combining information on water chemistry, physical 

characteristics, stream habitat, and aquatic life, the NAWQA 

Program aims to provide science-based insights for current and 

emerging water issues and priorities. NAWQA results can 

contribute to informed decisions that result in practical and 

effective water-resource management and strategies that protect 

and restore water quality.

Since 1991, the NAWQA Program has implemented 

interdisciplinary assessments in more than 50 of the Nation’s 

most important river basins and aquifers, referred to as Study 

Units. (http://water.usgs.gov/nawqa/nawqamap.html). 

Collectively, these Study Units account for more than 60 percent 

of the overall water use and population served by public water 

supply, and are representative of the Nation’s major hydrologic 

landscapes, priority ecological resources, and agricultural, urban, 

and natural sources of contamination. 

Each assessment is guided by a nationally consistent study 

design and methods of sampling and analysis. The assessments 

thereby build local knowledge about water-quality issues and 

trends in a particular stream or aquifer while providing an 

understanding of how and why water quality varies regionally 

and nationally. The consistent, multi-scale approach helps to 

determine if certain types of water-quality issues are isolated or 

pervasive, and allows direct comparisons of how human 

activities and natural processes affect water quality and 

ecological health in the Nation’s diverse geographic and 

environmental settings. Comprehensive assessments on 

pesticides, nutrients, volatile organic compounds, trace metals, 

and aquatic ecology are developed at the national scale through 

comparative analysis of the Study-Unit findings. 

(http://water.usgs.gov/nawqa/natsyn.html). 

The USGS places high value on the communication and 

dissemination of credible, timely, and relevant science so that the 

most recent and available knowledge about water resources can 

be applied in management and policy decisions. We hope this 

NAWQA publication will provide you the needed insights and 

information to meet your needs, and thereby foster increased 

awareness and involvement in the protection and restoration of 

our Nation’s waters. 

The NAWQA Program recognizes that a national assessment 

by a single program cannot address all water-resource issues of 

interest. External coordination at all levels is critical for a fully 

integrated understanding of watersheds and for cost-effective 

management, regulation, and conservation of our Nation’s water 

resources. The Program, therefore, depends extensively on the 

advice, cooperation, and information from other Federal, State, 

interstate, Tribal, and local agencies, non-government 

organizations, industry, academia, and other stakeholder groups. 

The assistance and suggestions of all are greatly appreciated.

Robert M. Hirsch

Associate Director for Water

v

CONTENTS

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

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

Land-use categorization........................................................................................................................................................................... 2

Land-use delineation methods................................................................................................................................................................. 6

Methods of comparison ........................................................................................................................................................................... 7

Comparison of land uses based on the sector and the circle methods..................................................................................................... 8

Implications for relating land use to ground-water quality ..................................................................................................................... 9

Summary................................................................................................................................................................................................ 12

References ............................................................................................................................................................................................. 13

ILLUSTRATIONS

Figures 1-2. Maps showing:

1. Study area locations, Red River of the North Basin Study Unit ............................................................................................ 3

2. Land-use study areas and well networks, Red River of the North Basin Study Unit............................................................. 4

Figure 3. Conceptual diagram of two methods for delineating land use of areas contributing recharge to a well screened just 

below the water table.............................................................................................................................................................. 6

Figure 4. Graphical representation of cosine similarity .......................................................................................................................... 8

5. Nitrate concentration variation through time at selected wells. ............................................................................................11

TABLES

Table 1. Land-use categories aggregated to the common categories used in this study.......................................................................... 5

2. Ground-water modeling factors for flow in the study areas, Red River of the North Basin.................................................... 7

3. Estimated land-use percentages by the delineation method..................................................................................................... 9

4. Similarity values of land use near wells between each method and the general land use for each study area, measured 

by the cosine method. ............................................................................................................................................................. 9

5. Similarity values between land uses near each well within the sector and the 500-meter circle, by study area.................... 10

6. Results of the regression relating land use to nitrate concentration. .......................................................................................11

CONVERSION FACTORS AND ABBREVIATIONS

Multiply metric unit by to obtain inch-pound unit

meter (m) 3.281 foot

kilometer (km) 0.6214 mile

square kilometer (km2

) 0.3861 square mile

Abbreviated water quality units: Chemical concentrations are given in milligrams per liter (mg/L), a unit expressing the 

concentration of chemical constituents in solution as mass (milligrams) per unit volume (liter) of water.
vi

ACKNOWLEDGMENTS

TECHNICAL REVIEWERS

Geoffrey Delin, Hydrologist; U.S. Geological Survey, Mounds View, Minnesota

Bernard T. Nolan, Research Hydrologist, U.S. Geological Survey, Reston, Virginia

EDITORIAL AND GRAPHICS

Carol Anderson, Editor, U.S. Geological Survey, Lakewood, Colorado

Ginger Amos, Editor, U.S. Geological Survey, Mounds View, Minnesota

Robert Borgstede, Illustrator, U.S. Geological Survey, Mounds View, Minnesota

Gerhard Kuhn, Hydrologist, U.S. Geological Survey, Lakewood, Colorado

APPROVING OFFICIAL 

George Garklavs, Reports Improvement Advisor, St. Paul, Minnesota
1

Comparison of Two Methods for Delineating 

Land Use Near Monitoring Wells used for 

Assessing Quality of Shallow Ground Water

By David L. Lorenz, Robert M. Goldstein, Timothy K. Cowdery, and Jeffrey D. Stoner

ABSTRACT

Two methods were compared for delineating land use near shallow monitoring wells. These wells were used to assess 

the effects of agricultural cropland on the quality of recently recharged ground water in two sand and gravel aquifers 

located near land surface. The two methods for delineating land use near wells were (1) the sector method, which used 

potentiometric-surface maps to estimate average flow direction and a ground-water-flow model to estimate maximum 

length of contributing area to the monitoring well within an upgradient sector; and (2) the circle method, which used a 500-

meter radius circle around the well based on a national empirical analysis. Land uses were compiled for 29 wells in each of 

two surficial aquifers in the Red River of the North Basin within the area defined by each method. Land use near each well 

was interpreted from orthorectified photographs and site inspection for both delineation methods. Land use near individual 

wells characterized by each method varied greatly, which can affect the results of statistical correlations between land use 

and water quality. Land use determined by the circle method related more closely to the land use for each entire study area. 

Land use determined by the sector method (within 200 meters from the wells) compared more favorably to ground-water 

quality based on nitrate concentrations. The maximum length of contributing areas to wells estimated in this study may be 

of value for other studies of unconsolidated sand and gravel aquifers with similar hydrogeological characteristics of permeability, water-table slopes, recharge, and depth to water. The additional effort required for estimating the model delineation 

of land use and land cover for the sector method must be weighed against the improved confidence in statistical correlation 

between land use and the quality of shallow ground water. Improved scientific confidence and understanding of relations 

between land use and quality of ground water may encourage more effective implementation of land and water management for protecting water quality.

INTRODUCTION

Goals of the U.S. Geological Survey’s (USGS) National Water-Quality Assessment (NAWQA) Program 

are achieved through investigation of 

the Nation’s most important river 

basins and aquifer systems, which are 

referred to as “Study Units” (Gilliom 

and others, 1995). These Study Units 

are distributed throughout the Nation 

and encompass diverse hydrologic 

settings. National synthesis of 

NAWQA data, based on aggregation 

of comparable information obtained 

from the Study Units, is a major component of the program. This effort 

focuses on selected water-quality topics (water chemistry and aquatic biological communities) using nationally 

consistent information and methods. 

Comparative studies (1) explain differences and similarities in the status 

of water quality among Study Units, 

and (2) identify changes, trends, and 

associated causes.

The ground-water component of 

the NAWQA Program assesses 

ground-water quality at three spatial 

scales: (1) in the major aquifers of the 

Study Unit, surveys assess water quality commonly used for drinking water, 

(2) in specific land-use areas, studies 

assess the effects of land use on the 

quality of recently recharged shallow 

ground water associated with a specific and hydrogeologic conditions, 

and (3) along a specific ground-water 

flow transect, studies examine the 

relations among land use, groundwater flow, contaminants, and surface/ground-water interactions (Gilliom and others, 1995). Analysis of 

results from geographic nesting of a 

land-use study within a survey of a 

major aquifer can provide useful 

insights into future effects of land-use 

activities on the quality of drinking 

water.

The land-use studies are used to 

evaluate the quality of recently 

recharged ground water (generally 

less than 10 years old) in regions that 

represent the intersection of a targeted 

land use and an aquifer of interest. 

The targeted land use may be a specific group of crops and associated 

agricultural practice or residential and 

commercial development of a certain 

age (Squillace and Price, 1996). The 

aquifers of interest typically are 

unconfined and near the land surface. 

These studies attempt to determine 
2

what land-use-derived contamination 

is reaching the youngest ground water 

in the area. 

Preliminary national synthesis of 

results from various land-use studies 

completed within the first 20 Study 

Units indicated a problem correlating 

the overall targeted land use with the 

observed ground-water quality (Bernard T. Nolan, U.S. Geological Survey, oral commun., 2000). The 

problem was that the methods for 

delineating land use within a targeted 

land-use area were not finalized and 

there was some variability in this 

delineation among the Study Units. 

Many Study Units targeted agricultural land. The targeted agricultural 

land-use area generally included a 

mixture of a specific cropland group 

and non agricultural land, such as forest or wetland. Individual investigators may or may not have included the 

non agricultural land within the definition of the land-use study area. Well 

locations were randomly selected 

throughout the targeted land-use area 

and hydrogeologic setting specific to 

the Study Unit using an equal-area 

grid method and computer program 

(Scott, 1990). For example, given the 

same targeted land-use area for well 

placement, one investigator may have 

classified the area as 40-percent cropland, whereas another could have 

found 95-percent cropland, depending 

on the geographic scale at which the 

land use was implemented. That variability in interpretations resulted in 

the problem correlating the targeted 

land use to observed water quality 

from those wells. After the preliminary national synthesis analysis identified this problem, guidance was 

developed to foster more consistent 

land-use delineation around the monitoring wells regardless of the interpretation of overall landscapes across the 

Nation. Although draft NAWQA 

guidance and recommendations for 

determining land use near individual 

wells were available before 1998, the 

procedures were not finalized until 

published in Koterba (1998). The Red 

River of the North Study Unit characterized land use at the study areas and 

near the individual wells (Cowdery, 

1997) before finalizing the revised 

methods presented in Koterba (1998).

This report (1) compares two 

methods of delineating land use 

around monitoring wells and (2) 

examines the applicability of each 

method for assessing land-use effects 

on the quality of shallow ground 

water. For reference in this report, the 

approach used by the Red River of the 

North Study Unit (Cowdery, 1997) is 

referred to as the “sector method” and 

the national approach (Koterba, 1998) 

is referred to as the “circle method”. 

Land uses delineated by the two 

methods are compared at two of the 

three spatial scales used in NAWQA 

ground-water studies: (1) targeted 

land use within specific study areas 

compared to the land use near individual wells determined by each method, 

and (2) comparison of land use near 

individual wells determined by each 

method. Applicability of each method 

for evaluating the quality of shallow 

ground water is accomplished by 

evaluating the correlations of nitrate 

concentrations with land use relative 

to the spatial scales of the two methods. 

The Red River of the North Basin 

Study Unit encompasses 90,000 km2

in Minnesota, North Dakota, and 

South Dakota (fig. 1). Within the 

Study Unit, the hydrogeologic settings for the ground-water land-use 

study areas were the two largest surficial aquifers: the Sheyenne Delta and 

the Otter Tail Outwash (Cowdery, 

1997). The Sheyenne Delta is an 

underflow delta and consists of fine 

and very fine sand in the southwest 

grading to silt and clay in the northeast. The Otter Tail Outwash is an 

intramorainal outwash plain consisting primarily of fine to coarse sand. 

Typical depth to the water table is 

about 1.5 m in the Sheyenne Delta 

and about 4.5 m in the Otter Tail Outwash. Although the Study Unit is 

mostly agricultural (Lorenz and 

Stoner, 1996), cropping patterns differ 

throughout the area. In the Sheyenne 

Delta study area, the dominant crops 

were corn, hay, and sunflowers and 

grazing was a major land use (about 

25 percent of the area). In the Otter 

Tail Outwash study area, the major 

crops were corn, hay, beans, with 

some potatoes. Much more cropland 

is irrigated in the Otter Tail Outwash 

study area than in the Sheyenne Delta 

study area. For additional information 

see Stoner and others (1993), Lorenz 

and Stoner (1996), and Cowdery 

(1997). 

The targeted land use was agricultural, which for this study meant that 

at least 80 percent of the land use of 

the study areas was cropland, pasture, 

or grazing, or contained the infrastructure necessary to support those 

activities (farmsteads and roads). The 

study areas that were selected are 

shown in figure 2. The land use within 

each study area was not completely 

homogeneous. Within an area generally regarded as agricultural, there can 

be wetlands, lakes, forests and small 

villages. Although the general land 

use was agricultural, other land uses 

may account for up to 20 percent of 

the total area. 

LAND-USE CATEGORIZATION

Digital land-cover and land-use 

(hereinafter referred to as “land use”) 

data (LUDA) are available from the 

U.S. Geological Survey (1986). These 

data were augmented by direct-observation field surveys from 1993-95 and 

interpretation of aerial photographs 

(1987-93). The Anderson Level II 

(Anderson and others, 1976) classification system was used as a basis to 

define land-use categories for these 

data.

The Anderson Level II classification system was modified for use in 
3

the land-use study areas in the Red 

River of the North Study Unit. Agricultural land class 21 (cropland and 

pasture) (Anderson and others, 1976) 

was divided into four categories: dryland cropland, irrigated cropland, pasture, and hay. A fifth category was 

added for the Sheyenne National 

Grassland to better define the boundary of that area.

Koterba (1998) identified hundreds of detailed land-use categories 

for a national (NAWQA) system 

using the broad categories of agricultural, urban, mining, and general. 

Examples in the general category 

include open water, forests, and wetlands. The agricultural land use 

includes separate subcategories for 

each possible crop or type of livestock. That system also uses a special 

code to indicate whether the land is 

irrigated. The detail provided by the 

NAWQA system was designed to 

enable correlation of the occurrence 

of specific contaminants associated 

with a unique crop or land use. 

In this study, 37 categories from 

Koterba (1998) were used to define 

the land use delineated by the circle 

method in the study area. Earlier, the 

Red River of the North Study Unit 

defined 15 land-use categories (Cowdery, 1997); however, the two sets of 

land-use categories were not entirely 

compatible. To make comparisons 

between the land uses delineated by 

the two methods, a common set of 

nine land-use categories was constructed (table 1).

The land use for each study area 

was compared to the land use near 

each randomly placed well within that 

study area. Open water was originally 

not considered part of the study area 

because most open water (streams and 

lakes) were assumed to not contribute 

recharge, and therefore, not affect 

ground-water quality. Concentrated 

livestock also were not part of the 

original classification because none 

Sheyenne

Delta

study area

Otter Tail

outwash

study area

CANADA

NORTH

DAKOTA

SOUTH

DAKOTA MINNESOTA

Red River of the North

Basin Study Unit

98° 96° 100° 49°

48°

47°

46°

Base from U.S. Geological

Survey digital data 1:2,000,000

1972 Albers Equal Area Conic

projection. Standard Parallels

29°30' and 45°30'

central meridian -97°

CANADA

NORTH DAKOTA

SOUTH DAKOTA

0

0 50 100 MILES

50 100 KILOMETERS

Figure 1. Study area locations Red River of the North Basin Study Unit.

MINNESOTA

Red

River

of

the

North

Sheyenne

River

Otter

Tail

River
4

OT06

OT05

OT04 OT16

OT17

OT07 OT15

OT08

OT09

OT03

OT14 OT18

OT30

OT19

OT10

OT13

OT02

OT01

OT20

OT21

OT28

OT29

OT27

OT25

OT26

OT12

OT22

OT23

OT24

SD17

SD18

SD16 SD19

SD30

SD28

SD20

SD27

SD25 SD26

SD23

SD15

SD21

SD14

SD22

SD24

SD06

SD07

SD08

SD05

SD04

SD03

SD09

SD10

SD13

SD11

SD12

SD02

SD01

CASS CO. RANSOM CO. RICHLAND CO.

BECKER CO.

OTTER TAIL CO.

to Detroit Lakes

to Wadena

to Casselton

to Lisbon

to Wyndmere

Sheldon

Kindred

Mc Leod

Perham

46°38'

46°20'

97°30' 97°

95°40' 95°30'

46°40'

46°30'

Sheyenne

River

Otter

Tail

River

Toad

River

Murphy

Big

Pine

Lake

Rush Lake

Lake Marion

Lake

Sheyenne Delta Study Area

Otter Tail Outwash Study Area

Figure 2. Land-use study areas and well networks,

Red River of the North Basin Study Unit.

EXPLANATION

National Grassland (Not a part of the Sheyenne

Delta Study Area)

Well location and well number OT20

Base from U.S. Geological Survey

digital data 1:100,000, 1976-1986

Albers Equal Area Conic projection

Standard parallels 29°30' and 45°30'

central meridian -97°

0

0

5 10 MILES

5 10 KILOMETERS
5

Table 1. Land-use categories aggregated to the common categories used in this study

Red River of the North 

land-use categories

Common land-use categories 

(this study) National (NAWQA) land-use categories

Dryland cropland non-irrigated cropland cropland, nonproductive

Hay cropland, barren

alfalfa hay or feed

alfalfa seed

field corn

corn, unknown use

small grain, unknown

oats

potatoes

sunflowers

sorghum

soybeans

wheat

Irrigated cropland irrigated cropland special code for any of the above categories

Grazing, grassland, or pasture grassland and pasture general rangeland

Grazing, mixed shrub and field horses, pasture

National grassland mixed domestics, pasture

Deciduous forest forest coniferous, managed

Evergreen forest coniferous, unmanaged

Mixed forest deciduous, managed

deciduous, unmanaged

mixed forest, unmanaged

Nonforest wetland wetlands general wetland

lacustrine wetland

Forested wetland riverine wetland

Roadway transportation transportation road

railway

Farmstead farmstead agricultural related

development

Urban residential urban urban, residential

Urban commercial urban, commercial

1

1

Category not used in original study

open water open water

1 concentrated livestock feedlot or confined

domestic livestock

cattle, beef

cattle, dairy

swine
6

were identified in the land-use and 

land-cover data collected in the 

1970’s. Open water and concentrated 

livestock were included as categories 

for this study because they do occur 

within the 500-m circles around wells.

LAND-USE DELINEATION 

METHODS

In the land-use studies for the Red 

River of the North Study Unit, the 

land-use area (with its associated land 

uses) contributing recharge to a well 

was estimated using ground-water 

models that determine traveltimes of 

water to a well under natural flow 

conditions (Cowdery, 1997). The 

method, referred to as the “sector 

method”, produced either a pieshaped sector of the land upgradient 

from the well if the direction of 

ground-water flow was known, or a 

circle of land surrounding the well if 

the direction of flow could not be 

determined. The length of the radius 

of each sector (or circle if direction 

was not known) was determined using 

a ground-water model to backtrack 

water from the bottom of the screened 

interval to the water table (path b in 

figure 3). The sector shape was chosen as a simple approximation of the 

zone of influence for potential 

Aquifer

Unsaturated zone

Confining unit

Water table

Flow path to 

well bottom

Land surface

Well screen

General direction 

of ground-water 

flow

Well

3-16 yrs.

1 yr.

200-meter sector

500-meter diameter 

circle

Figure 3. Conceptual diagram of two methods for delineating land use of areas contributing recharge to a well 

screened just below the water table. [3-16 yrs. is the range in estimated maximum time for a water particle to

travel from water table to bottom of monitoring well.]
7

recharge. A 90-degree angle was 

selected to account for seasonal 

uncertainty in the regional groundwater flow direction. In low watertable gradient areas, the radii were 50 

and 150 m, and in high water-table 

gradient areas were 125 and 200 m in 

the Sheyenne Delta and the Otter Tail 

Outwash study areas, respectively 

(table 2). These radii represent distance of recharge influence estimates 

of the maximum for each study area. 

Table 2 is a summary of the hydrologic factors used in ground-waterflow models to estimate the radii of 

sectors for the study areas (Cowdery, 

1997). The model estimates of traveltime within the saturated zone compared favorably with ages of ground 

water measured by chlorofluorocarbon dating methods of selected 

ground-water samples (Stoner and 

others, 1998). 

An evaluation of previous studies 

by Koterba (1998) suggested that the 

best compromise for defining landuse characteristics around monitoring 

wells in a wide variety of hydrogeologic settings across the Nation would 

be a circular buffer with a 500-m 

radius from the well. Koterba (1998) 

reported that for many study areas, the 

direction of ground-water flow and 

hydraulic characteristics of the aquifer 

may not be well defined or known. 

Figure 3 highlights the major differences between the methods proposed 

by Koterba (1998) and that used in the 

Red River of the North for a 200 m 

radius sector. For well sites where the 

general direction of ground-water 

flow is known, the 90-degree sectors 

are expected to better estimate the 

contributing area of recharge and 

associated land use for these wells 

than the 500-m circles used as buffers 

for national statistical comparisons. 

METHODS OF COMPARISON

To determine how well the sector 

and circle methods characterized the 

general land use for the two study 

areas, the land use for all wells for 

each study area was computed by calculating the mean of each percentage 

land use for each method. Those 

means were compared to the land-use 

composition of each respective study 

area. Land use from each well was 

determined by the two methods, giving one similarity comparison for 

each well in each study area. If both 

methods measure the same land uses, 

the similarity values should be classed 

as very similar.

Several methods can be used to 

calculate similarity values for comparing percentage data that belong to 

mutually exclusive and exhaustive 

categories. This means that the percentages of the categories for an 

observation (land use within a circle 

or sector) always sum to 100 percent. 

For this report, the categories are 

those listed in table 1 (common landuse categories). One difficulty with 

percentage data is that the values are 

Table 2. Ground-water modeling factors for flow in the study areas, Red River of the North Basin 

 [modified from Cowdery, 1997; m, meter; m/y, meter per year; WT, water table.]

Study Area 

Factor Sheyenne Delta Otter Tail Outwash Data Source

Aquifer thickness (m) 19.5-26.5 13.4-14.9 well logs

Porosity 0.35 0.25 estimated from grain-size distribution

Effective recharge rate (m/y) 0.076 0.177 model calibration

Horizontal hydraulic conductivity (m/day) 1.5-3.0 31-73 aquifer tests and model adjustments

Ratio of horizontal to vertical hydraulic conductivity 10 5 assumed from inspection of core samples

Low water-table gradient conditions

Gradient range (dimensionless) 0.0008-0.0015 0.00019-00044 water table map

Number of wells in low gradient conditions 26 21 --

Radius of influence for 1.5 m depth below WT (m) 21-24 85-111 model results

Maximum traveltime (years) 8.0 2.5 model results

Radius of influence for 3 m depth below WT (m) 40-49 159-229 model results

Maximum traveltime (years) 15.6 4.8 model results

Radius chosen to characterize land use (m) 50 150 model results

High water-table gradient conditions

Gradient range 0.0015-0.011 0.00077-0.0017 water table maps

Number of wells in high gradient conditions 3 8 --

Radius of influence for 1.5 m depth below water 117-120 168-192 model results

Maximum traveltime (years) model 7.6 2.5 model results

Radius chosen to characterize land use (m) 125 200 model results
8

Figure 4. Graphical representation of cosine

similarity. [The percentage difference a and

a are projected onto an arc giving angular

differences and . Line segments a and

a are equal in length (represent the same

percentage difference). But, is greater

than . This demonstrates the reduction in

edge effect using cosine similarity].

1

2

12 1

2

1

2

 







2

1

a

a 2 1 The sum to 100 percent line

not independent; if the value in one 

category increases, then values within 

the other categories must decrease. 

Because of the relations of these data, 

the usual methods of comparison 

(such as computing Euclidean distances) are not appropriate. One 

appropriate method is to describe the 

difference between two observations 

by the angle between them (Philip and 

Watson, 1988). In this comparison, the 

particular advantage for using angles 

is that they reduce edge effects—differences between small values are 

downweighted using this method 

compared to Euclidean distances (fig. 

4). Thus, this method emphasizes the 

differences between the major landuse categories in the observations. It is 

more common to express the angle 

between points as a similarity in terms 

of the cosine of the angle. Values of 

the cosine range from 1 (identical 

composition) to 0 (no categories in 

common). The cosine of the angle 

between observations then becomes a 

measure of similarity, analogous to a 

correlation coefficient in correlation 

analysis. The cosine of the angle hereinafter will be referred to as the “similarity value”.

The similarity value between 

observations is given by:

Skl = Σ cik*cil / (Σ cik

2 * Σ cil2

)

1/2,

where Skl is the similarity value 

between observation k and l,

cik and cil are the percentage values 

for category i for observations k and l,

and the summation is performed over 

all categories.

Observations were classified as 

“very similar” if the similarity value 

was greater than 0.95 (corresponding 

to angles less than 18 degrees). Observations were classified as “different” 

if the similarity value was less than 

0.75 (corresponding to an angle 

greater than 41 degrees) and “similar” 

if between 0.95 and 0.75. These criteria are round numbers close to 95th

and 50th (median) percentile values of 

a cumulative cosine distribution 

(0.948 and 0.731).

COMPARISON OF LAND USES 

BASED ON THE SECTOR AND 

CIRCLE METHODS

The process of randomly selecting 

well locations within the targeted land 

use of the study area was assumed to 

produce a representative sampling of 

land use near the selected well. Targeted land uses within the two study 

areas (table 3) were compared to the 

land use near each well as determined 

by both methods. The general land use 

represents all of the land uses within 

each study area, determined by using 

the augmented LUDA data. 

The results of the comparison 

between the mean percentage for each 

method and the general land use for 

the study area are summarized in table 

4. The sector method for the Sheyenne Delta has a similarity value less 

than all other values because the area 

of the sectors in the Sheyenne Delta is 

relatively small, and land use categorized as “transportation” composes a 

substantial percentage of the area of 

the sector. All other similarity values 

are greater than 0.95, indicating similar comparison.

The similarity values for comparing land-use delineation (sectors and 

500-m circles) varied greatly. For the 

Sheyenne Delta study area, similarity 

values ranged from 0.17 to 0.99, 

whereas the range of similarity values 

for wells on the Otter Tail Outwash 

study area was slightly greater, ranging from 0.10 to 0.99 (table 5). The 

two methods produced similar results. 

There would be no wells with similarity values less than 0.75. In the Sheyenne Delta, however, 13 of 29 

similarities were less than 0.75, and in 

the Otter Tail Outwash, 11 of 29 similarities were less than 0.75, indicating 

that the land use determined by the 

two methods for the same well could 

be quite different. 

Approximately 40 percent of the 

comparisons between the two methods produced low similarity values 

that can be attributed to the large differences in areas delineated by the 

two methods. The areas included in 

the 90-degree sectors ranged from 

0.25 to 1.56 percent (median of 0.25 

percent) of the total area within a 500-

m circle for the Sheyenne Delta well 

sites. The areas included in the 90-

degree sectors ranged from 2.25 to 

4.00 percent (median of 2.25 percent) 

of the total area within a 500-m circle 

for the Otter Tail Outwash well sites. 

The largest median of 2.25 percent 

represents a difference in land area of 

767,700 m2 between the two delineation methods. The difference in the 

median sector areas between study 

areas was only 15,700 m2

. The location of the sector within the 500-m 
9

Table 3. Estimated land-use percentages for the study areas by the delineation method

[Values for circle and sector methods are the means for each category from all 29 wells in each study area]

Sheyenne Delta study area Otter Tail Outwash study area

Land use Study-area target Circle Sector Study-area target Circle Sector

Non-irrigated cropland 60 49 37 46 49 43

Irrigated cropland 4 3 1 27 21 18

Grassland and pasture 25 32 26 8 3 13

Forest 5 10 2 11 11 7

Wetlands 4 0 0 4 5 0

Transportation 1 4 32 1 4 9

Farmstead 1 2 3 2 2 7

Urban 0 0 0 1 2 3

Open water 0 0 0 0 1 0

Concentrated livestock 0 0 0 0 10

1

 Concentrated livestock was 3 percent at two wells

0

Total 100 100 101 100 98 100

circle also could have a significant 

effect on the comparison of resulting 

land use between the two methods. 

For example, in figure 3, by rotating 

the sector 180 degrees in any direction, transportation would be part of 

the delineated land use.

IMPLICATIONS FOR 

RELATING LAND USE TO 

GROUND-WATER QUALITY

For agricultural areas, land use is 

assumed to be a reasonable surrogate 

for the timing and intensity of chemicals applied to the land. The potential 

for any chemical to reach shallow 

ground water depends on the hydrogeology, weather conditions, agricultural practices, and characteristics of 

the chemical. However, the land-use 

studies are also a means for understanding how land use, chemical 

application, and hydrogeologic conditions affect water quality spatially and 

temporally. Use of chemicals in agricultural areas usually is consistent 

with crop type. Where the same land 

use (cropping pattern and chemical 

use) occurs across several Study 

Units, the effects of hydrogeologic 

conditions can be examined by determining the quality of the shallow 

ground water. 

Shallow ground-water quality in 

the two study areas was significantly 

different (Cowdery, 1997) even 

though the general land use was similar (similarity value is 0.87). Significant differences were observed in 

median concentrations of oxygen, 

nitrate, and ammonia. The number of 

herbicides detected was different, as 

were the median total pesticide concentrations. Cowdery (1997) attributed the differences in water quality 

to differences in hydrogeology, rainfall, and biological activity as well as 

land use, and states that these factors 

magnified the differences in water 

quality that may have been expected 

from land use alone.

Because the two methods are 

expected to measure the land use near 

each well that affects ground-water 

quality, the application of one or the 

other method will change the perspective of such an analysis. About 45 percent of the similarity values between 

the two methods from the Sheyenne 

Delta study area and 38 percent from 

the Otter Tail Outwash study area are 

different. For the Sheyenne Delta 

study area, one reason for the differences between the two methods results 

from large areas of land use near some 

wells that are not representative of 

general land use. In particular, several 

wells are located near the periphery of 

the Sheyenne National Grassland (fig. 

2). The 500-m circles include relatively large areas that are grassland, 

grazing, forests, or wetlands, which 

are the dominant land uses of the 

Sheyenne National Grassland. The 

short radii of influence used for the 

Sheyenne Delta sectors also resulted in 

a larger percentage of land area classified as “transportation” (a road may 

account for 5 to 10 percent of the area 

of a sector). For the Otter Tail Outwash study area, the larger dissimilarities are caused by smaller scale 

heterogeneities that affect the land use 

near some wells but not others.

The large dissimilarities between 

the methods can lead to misinterpretation of the relation of land use to water 

quality. Theoretically, the sector 

method should provide the more accurate determination of the land area 

Table 4. Similarity values of mean land use near wells for each method and the general 

land use for each study area, measured by the cosine method

Study area Sector Circle

Sheyenne Delta 0.80 0.98

Otter Tail outwash 0.96 0.99
10

Table 5. Similarity values (cosine of the angle) between land uses near each well within the sector and the 500-meter circle, by study 

area 

 [n/a, not available: Percent of area is the area of the sector compared to the 500-m circle expressed as percent]

Sheyenne Delta study area Otter Tail Outwash study area

Well number

Similarity value 

between sector and 

circle methods

Sector percent of 

area of the 500-m 

circle

Similarity value 

between sector and 

circle methods

Sector percent 

of area of the 

500-m circle

1 0.90 1

1.00

1Denotes contributing sector is a circle.

0.99 2.25

2 0.75 0.25 0.67 19.00

3 0.98 1.56 0.94 2.25

4 0.85 1.56 0.68 2.25

5 0.93 0.25 0.94 2.25

6 0.40 0.25 0.96 2.25

7 0.94 0.25 0.80 4.00

8 0.99 0.25 0.18 4.00

9 0.83 0.25 0.93 2.25

10 0.99 0.25 0.94 2.25

11 0.20 0.25 n/a n/a

12 0.32 0.25 0.99 2.25

13 0.17 0.25 0.45 2.25

14 0.35 0.25 0.17 2.25

15 0.39 0.25 0.91 2.25

16 0.38 0.25 0.92 2.25

17 0.80 1

1.00 0.55 2.25

18 0.70 0.25 0.35 4.00

19 0.96 0.25 0.86 2.25

20 0.20 0.25 0.68 2.25

21 0.18 0.25 0.10 4.00

22 0.99 0.25 0.98 1

9.00

23 0.77 0.25 0.80 4.00

24 0.79 0.25 0.62 4.00

25 0.25 0.25 0.82 2.25

26 0.67 0.25 0.80 2.25

27 0.41 1.56 0.62 2.25

28 0.94 0.25 0.85 4.00

29 n/a n/a 0.86 2.25

30 0.80 0.25 0.86 4.00

Mean 0.65 0.73

Median 0.77 0.25 0.82 2.25

contributing recharge near the well 

(Koterba, 1998), and a better relation 

between land use and water quality 

because it is not known exactly what 

area of the 500-m circle actually contributes to water quality at the well. 

An analysis of the nitrate concentration highlights the change in the 

relation between water quality and 

land use with increasing uncertainly 

about the area contributing recharge. 

The Otter Tail Outwash study area 

offers the opportunity to examine the 

variability of nitrate conditions within 

a single aquifer system where many 

other factors that can affect water 

quality are fairly constant. A regression analysis was performed relating 

nitrate concentration to cropland, 

defined as the sum of the percentages 

of dryland and irrigated cropland. The 

nitrate concentration data from 27 

wells were log-transformed to linearize the relation. The remaining two 

wells from the study area were 

excluded because one well did not 

have nitrate concentration data and 

the other because general water 

chemistry indicated that the well 

water was a mix of recently recharged 

water and older water. The results of 

that regression analysis are presented 

in table 6. The results of the regression analysis between nitrate concentration and percent cropland was 

similar between the two methods (the 
11

coefficients of the regression lines 

were comparable), but the significance 

of the relation changed from a statistically significant p-value of 0.05 for the 

sector method to a statistically nonsignificant p-value of 0.29 for the circle method. In this case, the confounding effect of including a much larger 

area for delineating land use for the 

recharge area of a well is evident in the 

poorer relation between nitrate concentration and percentage of cropland 

land use.

Analysis of pesticide detections to 

evaluate the usefulness of the two 

methods for delineating land use near 

monitoring wells was inconclusive. 

Pesticide concentrations were low for 

many samples and many pesticides 

that were analyzed for were not 

detected at all for many wells (Cowdery, 1997). Relating pesticide detections to the area of cropland near wells, 

therefore, was ineffective.

The results of this analysis of contributing areas near shallow monitoring wells compared favorably to a 

NAWQA study in New Jersey, in 

which Kauffman and others (2001) 

investigated the effects of urban, suburban, and agricultural land use on the 

quality of ground water in an unconsolidated sand and gravel aquifer with 

a comprehensive model analysis for 70 

wells. The effective maximum distance of influence from the New Jersey 

land-use study wells ranged from 37 to 

480 m with a median distance of 147 

m, which is quite comparable to the 

distance of maximum influence used 

in the sector method for the Otter Tail 

Outwash study area (table 2). Also 

comparable between these two different study areas was the measured maximum ground-water age. Ground water 

sampled from the New Jersey wells 

was slightly younger than that measured for the Otter Tail Outwash study 

(Stoner and others, 1998), but this difference could be explained by the 

slightly higher average hydraulic conductivity and recharge rate in the New 

Jersey aquifer (the Kirkwood-Cohansey aquifer system). 

Effective distances of influence 

reported from these studies derived 

from a ground-water flow model, such 

as the sector method, are transferable 

to aquifers with similar hydrogeologic 

settings. In vastly differing aquifer 

settings, it would be more prudent to 

construct conceptual flow models fitted to local conditions of hydraulic 

conductivity, porosity, recharge, 

water-table gradients, and depth to 

water. Because of the few number of 

intervening clay lenses observed in 

drilling cores from the Otter Tail Outwash and Kirkwood-Cohansey aquifers, limited horizontal flow was 

assumed within these unsaturated 

zones, further simplifying the links 

between ground-water quality and 

activities at land surface. Caution also 

is suggested for transferring results 

from these studies to areas of different 

aquifer materials and conditions that 

would affect the transport of nitrate 

and pesticides from land surface to 

and through shallow ground water. 

For example, Cowdery (1997) 

described some differences in the relations between land use and shallow 

ground-water quality between the 

Sheyenne Delta and Otter Tail Outwash aquifers attributed to differences 

in soil and aquifer materials and redox 

conditions. 

At an individual well, factors that 

can affect water quality include soil 

characteristics, seasonal recharge, and 

geology. Several wells in both study 

areas were sampled repeatedly to 

assess the variation in water quality 

occurring through time (fig. 5). On 

average, nitrate concentrations gener0

10

20

30

40

50

60

OT01

OT06

OT09

OT28

SD16

DISSOLVED NITRATE, IN MILLIGRAMS PER LITER

SAMPLE DATE

1994 1995 1999 2000

Figure 5. Nitrate concentration variation through time at selected wells.

[OTO, Otter Tail Outwash wells; SD, Sheyene Delta well.]

Table 6. Results of the regression relating land use to nitrate concentrations 

Regression results

Cropland estimate Intercept Cropland 

coefficient

P-value of the 

model

Sector method -0.560 0.0261 0.05

Circle method -0.777 0.0259 0.29
12

ally remained high over a 6-year 

period in the Otter Tail Outwash wells 

and remained low in the Sheyenne 

Delta well example. However, nitrate 

concentration fluctuated widely over 

periods of months in all of these 

wells. This fluctuation implies that to 

characterize the quality of the water 

withdrawn from a specific well, 

detailed knowledge on the size of the 

contributing area and its land use are 

required along with application rates, 

timing, and selection of agricultural 

chemicals; amounts and timing of 

recharge events; soil; and geology. 

However, analysis of water quality 

from a collection of wells in similar 

hydrogeological and agricultural conditions presents the opportunity to 

assess the effects of land use integrated over the past approximately 10 

years. Information about general patterns of land use and land-use change 

becomes the more desirable method 

for assessing the effects of land use on 

the quality of ground water than information on specific crop type or land 

use in any given year. General conclusions for effective local land and 

water management to improve the 

quality of ground water might best be 

drawn from these principles of timeintegration of land use and the best 

available information for delineating 

the land area most likely to contribute 

recharge to the monitoring wells. 

Improved scientific confidence and 

understanding of relations between 

land use and quality of ground water 

may encourage more effective implementation of land and water management for protecting water quality.

SUMMARY

A component of the National Water Quality Assessment 

Program is to examine ground-water quality in relation to 

land use. The objectives of the land-use studies are to 

assess land-use practices and human and natural factors 

that affect water quality in recently recharged ground water. 

The land-use studies concentrate on a targeted land use and 

hydrogeological conditions. Wells selected for the land-use 

studies are randomly distributed throughout the targeted 

land use and hydrogeologic setting specific to the Study 

Unit. 

A critical aspect of data analysis is accurate determination of the characteristic land use that potentially affects the 

quality of shallow ground water. In the Red River of the 

North Study Unit, land use at individual wells in two surficial aquifers, the Sheyenne Delta and the Otter Tail Outwash, was determined using two methods. The sector 

method uses potentiometric surfaces to estimate the direction of ground-water flow and simple flow models to estimate the distance from the well that encompasses 

contributing recharge to that well. This method produced 

either a pie-shaped 90-degree section of land upgradient 

from the well if the direction of ground-water flow was 

known, or a circle of land surrounding the well if the direction of flow could not be determined. The length of the arm 

of the sector or radius of the circle ranged from 50 to 200 m 

on the basis of particle tracking from bottom of well-screen 

depths backwards though time to the intersection with the 

water table. These 90-degree sectors or circles defined the 

estimated contributing area of recharge for the monitoring 

well. The circle method of determining the land area affecting a well considers a circular buffer of 500-m radius from 

the well, which was empirically based on national and 

regional analysis of statistical correlation between general 

land use and measured water quality for hundreds of wells 

in a variety of hydrogeologic and land-use settings across 

the nation. Generally, the area included in the sectors was 

only 0.25 to 9.0 percent of the area in the 500-m circle. 

Land use was interpreted from orthorectified photographs 

and verified in the field by site inspection. Data were compiled by the two methods for 29 wells, each randomly 

selected near targeted cropland overlying the Sheyenne 

Delta and Otter Tail Outwash surficial aquifers.

Comparisons of the two methods were made between: 

(1) land use within the targeted study area and land use near 

individual wells delineated by each method, and (2) land 

use within the sectors and the land use within the 500-m 

circle for each well in each area. The results of the comparisons were: (1) for the Sheyenne Delta and Otter Tail Outwash study areas, the average percentage of land in each of 

the land-use categories determined by the circle method 

was more similar to the targeted land use within the general 

study area than that determined by the sector method; (2) 

the median similarity value between methods (similarity 

values range from 0.00 – no similarity to 1.00 complete 

similarity) was 0.77 within the Sheyenne Delta study area, 

whereas the median similarity value for wells in the Otter 

Tail Outwash study areas was slightly greater (0.82). 

Where sufficient hydrogeological data are available, the 

sector method presents a more accurate estimate of the land 

use affecting an individual monitoring well than the circle 

method. On the basis of cropland area estimated collectively for each study area by the two methods, the sector 

method provides a better correlation to nitrate concentrations in the ground water than the circle method. The sector 

method, or any procedure that incorporates hydrologic 

sense toward estimating the land area of contributing 

recharge to a network of monitoring wells should provide 

more compelling information from which to suggest land 

and water-management practices for improving quality of 

shallow ground water. 

The distances of land-use influence from wells in this 

study compared closely with a comprehensive analysis of a 

similar hydrogeologic setting in the Kirkwood-Cohansey 
13

REFERENCES

Anderson, J.R., Hardy, E.E., Roach, 

J.T., and Witmer, R.E., 1976, A 

land use and land cover classification system for use with remote 

sensor data: U.S. Geological Survey Professional Paper 964, 28 p.

Cowdery, T.K., 1997, Shallow 

ground-water quality beneath 

cropland in the Red River of the 

North Basin, Minnesota and North 

Dakota, 1993-95: U.S. Geological 

Survey Water-Resources Investigations Report 97-4001, 52 p.

Gilliom, R.J., Alley, W.M., and 

Gurtz, M.E., 1995, Design of the 

National Water-Quality Assessment Program—Occurrence and 

distribution of water-quality conditions: U.S. Geological Survey 

Circular 1112, 40 p.

Kauffman, L.J., Baehr, A.L., Ayers, 

M.A., Stackelberg, P.E., 2001, 

Effects of land use and travel time 

on the distribution of nitrate in the 

Kirkwood-Cohansey Aquifer System in southern New Jersey: U.S. 

Geological Survey WaterResources Investigations Report 

01-4117, 90 p.

Koterba, M.T., 1998, Ground-water 

data-collection protocols and procedures for the National WaterQuality Assessment Program—

Collection, documentation, and 

compilation of required site, well, 

subsurface, and landscape data for 

wells: U.S. Geological Survey 

Water-Resources Investigations 

Report 98-4107, 91 p.

Lorenz, D.L., and Stoner, J.D., 1996, 

Sampling design for assessing 

water quality in the Red River of 

the North Basin, North Dakota, 

South Dakota, and Minnesota, 

1993-95: U.S. Geological Survey 

Water-Resources Investigations 

Report 96-4129, 2 plates.

Philip, G.M., and Watson, D.F., 1988, 

Angle measure compositional differences: Geology, v. 16, p. 976-

979.

Scott, J.C., 1990, Computerized random site-selection approaches for 

design of a ground-water-quality 

sampling network: U.S. Geological Survey Water-Resources 

Investigations Report 90-4101, 

109 p. 

Squillace, P.J., and Price, C.V., 1996, 

Urban land-use study plan for the 

National Water-Quality Assessment Program: U.S. Geological 

Survey Open-File Report 96-217, 

19 p.

Stoner, J.D., Cowdery, T.K., and 

Puckett, L.J., 1998, Ground-water 

age dating and other tools used to 

assess land-use effects on water 

quality: U.S. Geological Survey 

Water-Resources Investigations 

Report 97-4150, 6 p.

Stoner, J.D., Lorenz, D.L., Wiche, 

G.J., and Goldstein, R.M., 1993, 

Red River of the North Basin, 

Minnesota, North Dakota, and 

South Dakota: Water Resources 

Bulletin, v. 29, p. 575-615.

U. S. Geological Survey, 1986, Land 

use and land cover digital data 

from 1:250,000-and 1:100,000-

scale maps: U.S. Geological Survey Data User’s Guide 4, 40 p.

aquifer in New Jersey and suggests that these results may 

be of value for other unconsolidated sand and gravel aquifers with similar hydrogeological characteristics of permeability, water-table slopes, recharge, and depth to water. 

The additional effort required for estimating the sector 

delineation of land use and land cover must be weighed 

against the improved confidence in statistical correlation 

between land use and the quality of shallow ground water. 

Relating land use to water quality in a well is complicated 

by several factors other than land use such as soil characteristics, seasonal recharge, and local geology. Variation in 

ground-water quality may occur with location, depth, and 

through time. These factors become more important for 

more detailed deterministic assessments of land-use effects 

on the quality of ground water in a specific aquifer. 

Improved scientific confidence and understanding of relations between land use and quality of ground water may 

encourage informed implementation of land and water 

management for protecting water quality.