An Interdisciplinary Assessment of RegionalScale Nonpoint Source Ground-Water 

Vulnerability: Theory and Application

By Richard L. Bernknopf, Laura B. Dinitz, and Keith Loague

Professional Paper 1645

U.S. Department of the Interior

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

Gale A. Norton, Secretary

U.S. Geological Survey

Charles G. Groat, Director

Any use of trade, product, or fi rm names in this publication

is for descriptive purposes only and does not imply endorsement 

by the U.S. Government.

United States Government Printing Offi ce: 2001

For additional copies please contact:

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This report and any updates to it are available online at

http://geopubs.wr.usgs.gov/prof-paper/pp1645/

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Text edited by Ann Yaeger and Sean Murphy Stone

Layout and design by Stephen L. Scott 

Manuscript approved for publication, June 20, 2001

 

FRONT COVER

Aerial photograph of Pearl Harbor basin, O‘ahu, Hawai‘i taken in 1977.

Library of Congress Cataloging-in-Publication Data

Bemknopf, Richard L. (Richard Lewis)

An interdisciplinary assessment of regional-scale nonpoint ground-water vulnerability:

theory and application / by Richard L. Bemknopf, Laura B. Dinitz, and Keith Loague. 

p. cm. -- (Professional paper; 1645)

Includes bibliographical references.

 1. Water--Pollution potential--United States. 2. Agricultural chemicals--Environmental 

aspects--United States. 3. Nonpoint source pollution--United States. 4. Geographic 

information systems--United States. 5. Water quality management--United 

States--Decision making. 6. Water quality management--Hawaii--Pearl Harbor 

Region--Decision making--Case studies. I. Dinitz, Laura B. II. Loague, Keith M. (Keith 

Michael), 1951- III. Title. IV. Professional paper (Geological Survey (U.S.)); no. 1645.

QE75 .P9 no. 1645

[TD223]

557.3 s--dc2l

[363.7394]
CONTENTS

Abstract--------------------------------------------------------------------------------------------- 1

Introduction---------------------------------------------------------------------------------------- 1

An Integrated Earth Science–Economics Framework----------------------------------------- 2

 Regulatory Model-------------------------------------------------------------------------- 2

 Risk Assessment--------------------------------------------------------------------------- 2

 Risk Management-------------------------------------------------------------------------- 4

 The Value of ESI: V(θ )-------------------------------------------------------------------- 4

A Method for Estimating ESI Benefits--------------------------------------------------------- 5

Application of the IESEM, Pearl Harbor Basin, O‘ahu, Hawai‘i--------------------------- 6

 Alternative A-------------------------------------------------------------------------------- 6

 Alternative B------------------------------------------------------------------------------- 6

 Cost-Effectiveness Analysis--------------------------------------------------------------- 8

Discussion------------------------------------------------------------------------------------------ 8

Conclusions----------------------------------------------------------------------------------------- 10

Acknowledgments--------------------------------------------------------------------------------- 10

References Cited----------------------------------------------------------------------------------- 10

 

III

FIGURES

1. Impact of reducing σ(RF), the standard deviation of RF, and of using information structure RF2 ------------------------ 5

2. Soil orders for the Pearl Harbor basin, Island of O‘ahu, Hawai‘i---------------------------------------------------------------- 7

3. Cost effectiveness of earth science information (ESI) in million dollars------------------------------------------------------- 8

4. Ground-water vulnerability maps for the Pearl Harbor basin, Island of O‘ahu, Hawai‘i------------------------------------- 9

TABLES

 1. Classification scheme used for the AF and RF indices for pesticide movement in soils (Khan and others, 1986)-------- 14

 2. The 10 pesticides included in the study, which are (or have been) used in Hawai‘i for sugarcane and pineapple 

 (after Kleveno and others, 1992)----------------------------------------------------------------------------------------------------- 15

 3. The mean E(AF ) and standard deviation σ(AF) of the Attenuation Factor for the 10 selected pesticides for 

the 5 major O‘ahu soil orders---------------------------------------------------------------------------------------------------------- 16

 4. The mean E(RF ) and standard deviation σ(RF) of the Retardation Factor for the 10 selected pesticides for 

the 5 major O‘ahu soil orders---------------------------------------------------------------------------------------------------------- 17

 5. Reductions in the components of σ(AF) by 10 percent to 0.9σ(AF) and by 90 percent to 0.1σ(AF) for the 

10 selected pesticides for the 5 major O‘ahu soil orders--------------------------------------------------------------------------- 18

 6. Reductions in the components of σ(RF) by 10 percent to 0.9σ(RF) and by 90 percent to 0.1σ(RF) for the 

10 selected pesticides for the 5 major O‘ahu soil orders--------------------------------------------------------------------------- 19

 7. Expected present value of net benefits of agricultural production and cost effectiveness of the ESI in millions 

of dollars to produce pineapple on 32,226 hectares in the Pearl Harbor basin, Island of O‘ahu, Hawai‘i------------------ 20

 8. Number of hectares acceptable for pesticide use without wellhead treatment for insecticide-herbicide 

combinations at 3 levels of uncertainty for the 10 selected pesticides for the 5 major soil orders--------------------------- 21

 
IV

Notation used in text and equations

a action by a decisionmaker [a = 1, . . . , A]

[Bγ θ(Q)] expected present value of net benefits of agricultural production using γ θ [$]

[Bγ θ

(∆Q)] expected present value of marginal net benefits of agricultural production from a refinement in γθ [$]

C(θ ) cost of regional-scale vulnerability assessment θ [$]

C1(θ ) cost of improved understanding of physical process model [$]

C2(θ ) cost of increased statistical accuracy [$]

Cj cost of using pesticide j [$]

Cw investment, operating, and maintenance costs for a wellhead treatment program [$]

d distance to ground water (or some compliance depth) from the surface [m]

dγ admissible decisions based on γ [dγ = 0, . . . , D]

foc soil organic carbon [0]

Fj fraction of the total area treated with pesticide j [0 ≤ Fj ≤ 1]

F(P) critical value of the standard normal distribution exceeded only with probability 1 - P [0]

G vector of agricultural policy variables

h number of planted hectares [ h = 0, . . . , H]

i agricultural commodity [i = 1, . . . , I]

j pesticide type [ j = 0, . . . , J ]

k soil type [k = 1, . . . , K]

Koc pesticide sorption coefficient [m3/kg]

 set of natural numbers [ = {1, 2, 3,...}]

NV(θ ) maximum net benefit of ESI [$]

P confidence level of decisionmaker in applying a regional ground-water vulnerability assessment [0≤ P≤ 1]

ps(k)γ θ conditional probability of γθ given that the true state of nature is s(k) [0≤ ps(k)γ θ≤ 1]

q net ground-water recharge [m/day]

Q supply of agricultural commodity [tons]

R0 regulatory standard for ground-water contamination based on a physical threshold [0]

s state of the environment [s = 1, . . . , S]

T agricultural production time period [years]

t1/2 pesticide half-life [years]

u payoff or utility to the decisionmaker [0]

V(θ ) benefit of regional-scale vulnerability assessment θ [$]

V1(θ ) benefit of improved understanding of physical process model [$]

V2(θ ) benefit of increased statistical accuracy [$]

Y total yield per hectare [tons/hectare]

yj average yield per hectare when using pesticide j [tons/hectare]

γ NPS vulnerability assessment, or information signal, based on ESI [γ = 1, . . . , Γ ]

θ index of information uncertainty, or information structure [θ = 1, . . ., θ1]

θFC soil-water content at field capacity [0]

Πi expected net revenue of crop i [$]

ρ correlation of observed and predicted ground-water condition [-1 ≤ ρ ≤ 1] 

ρb soil bulk density [kg/m3]
1

Abstract

The availability of potable ground-water supplies is 

a major environmental quality and human health concern 

throughout the United States. In the study reported here, a 

geographic information system (GIS) environment is used 

to apply an Integrated Earth Science–Economics Model 

(IESEM) that combines a regional-scale nonpoint source vulnerability assessment tool with a specific remediation measure 

to avoid unnecessary agricultural production costs related to 

the use of agrochemicals. Based on two screening indices that 

utilize earth science information, the vulnerability assessment 

tool functions in a spatial analysis to target areas vulnerable 

to ground-water contamination. This coordinated approach 

forms the core of a risk-based regulatory standard for the 

application of agrochemicals. The application of the IESEM 

in a cost-effectiveness analysis for 17 coordinated programs 

showed that 12 of the programs demonstrated substantial cost 

savings, ranging from $8.0 million to $244.0 million, that 

could accrue to producers if a regional vulnerability assessment were coordinated with a wellhead treatment program. 

The coordinated approach was not cost effective for the 

remaining five programs. The case study was conducted for 

the Pearl Harbor basin on the island of O‘ahu, Hawai‘i. The 

IESEM approach was developed as a spatial analysis tool 

to estimate the benefits of an information-based approach to 

decisionmaking.

Introduction

Governmental intervention in the U.S. agriculture industry results in a variety of policies and regulations. Some 

policies, such as the promotion and use of agrochemicals, 

are designed to enhance farm productivity, but others involve 

the regulation of chemical use to protect common property 

resources, such as ground water. These interventions appear 

contradictory, because although pesticide application can 

An Interdisciplinary Assessment of Regional-Scale 

Nonpoint Source Ground-Water Vulnerability: 

Theory and Application

By Richard L. Bernknopf1, Laura B. Dinitz2, and Keith Loague3

increase producers’ crop yields, it can also create an unwanted 

byproduct of polluted ground water. There are several ways 

to approach this externality problem and act to reduce the 

adverse impacts of ground-water contamination. This study 

focuses on the analytical application of geographic information science for making policy choices in a decision framework. Two policy options are (1) to prevent contamination 

by restricting or eliminating agrochemical application using 

a screening model based on earth science information (ESI) 

(that is, an adaptation program) and (2) to remediate contaminated ground water with a granulated activated carbon wellhead treatment system in the agricultural producing region 

(that is, a mitigation program). Although each option has 

risks to both water consumers and decisionmakers, option 2 

is the focus of this study. Separate regulatory policies that 

enhance farm production or reduce ground-water pollution 

could result in either an underestimate or overestimate of the 

benefits associated with agricultural productivity (crop yield) 

or environmental protection (contamination of the groundwater resource). Alternatively, using a geographic information 

system (GIS) with a coordinated agricultural and resource 

policy that combines a regulatory screen and a remediation 

program would provide a more socially beneficial framework 

by permitting the application of agrochemicals and implementing wellhead treatment in locations deemed appropriate 

by the screen.

The design of an efficient regional-scale ground-water 

quality protection program is contingent upon an accurate 

spatial representation of the hazard. Accurate scientific information is necessary to avoid resource allocation mistakes, 

such as inappropriately permitting or restricting agrochemical 

use or imposing additional production costs. Based upon a 

regional ground-water vulnerability assessment, the application of a decision rule provides a convenient mechanism to 

apportion the financial burden of the regulation to producers. 

This method distinguishes producers located in vulnerable 

areas who should incur the additional cost of a wellhead treatment program from those who should not. The framework 

provides a means to conduct a location-based comparison 

of alternative policy choices. Because the framework is integrated into the GIS, the benefits of a particular program can 

be evaluated.

The focus of this study was the estimation of an economic value for ESI to concurrently support agricultural production and protect ground-water resources. The analysis 

was conducted in a GIS environment to identify places that, 

1U.S. Geological Survey, Menlo Park, CA 94025 and Department of 

Geological and Environmental Sciences, Stanford University, Stanford, CA 

94305.

2U.S. Geological Survey, Menlo Park, CA 94025.

3Department of Geological and Environmental Sciences, Stanford University, Stanford, CA 94305.

Introduction
2 Assessment of Regional-Scale Nonpoint Source Ground-Water Vunerability

depending on soil and chemical properties and their interactions, are vulnerable to ground-water contamination, require 

ground-water remediation, and are subject to increased farm 

production costs, and those that are not. In the latter case, 

there is potential for an improvement in resource allocation 

that can be exploited by reducing the uncertainty of information associated with the application of agrochemicals.

The remainder of this paper is divided into five sections: 

(1) development of an Integrated Earth Science–Economics 

Model (IESEM) that characterizes a regulatory decision 

framework, (2) a method for estimating the benefits of using 

ESI, at different levels of uncertainty, to make decisions 

regarding the use of agrochemicals, (3) a case study for pineapple production, in an area within the Pearl Harbor basin 

on the island of O‘ahu, Hawai‘i, using alternative ESI information structures to support a coordinated agricultural and 

resource policy, (4) a discussion of the benefits and costs 

associated with using ESI for policy analysis and the inherent 

risks of scientific uncertainty, and (5) conclusions.

An Integrated Earth Science–

Economics Framework

Agrochemicals have been used extensively in the United 

States for several decades. As a result, the economic consequences of nonpoint source (NPS) ground-water contamination, even at very low concentrations, cannot be ignored 

(Loague and others, 1998). Leon-Guerrero and others, (1994) 

reported on the occurrence of ground-water contamination in 

the Pearl Harbor basin of O‘ahu, Hawai‘i. In response to 

this type of threat to a common property resource, public programs for mitigating losses associated with ground-water contamination have consisted of either safety rules that restrict 

or tax the use of hazardous chemicals (Wise and Johnson, 

1991), or additional production costs for wellhead treatment 

(Leon-Guerrero and others,1994). The regulations that are 

promulgated to protect ground-water resources affect individual agricultural producers (Antle and Capalbo, 1993; Reicheldorfer and Kramer, 1993).

For the IESEM framework, the economic objective is 

to maximize agricultural output while maintaining a potable 

ground-water supply. The IESEM incorporates ESI directly 

into the constrained optimization problem: 

max B(Q), subject to: γ ≤ or ≥ R0 (1)

 Q

where B(Q) is the economic benefit of agricultural production, 

Q is the supply (quantity produced) of an agricultural commodity, γ is an NPS vulnerability assessment based on ESI, 

and R0 is a regulatory standard for ground-water contamination based on a physical threshold. The IESEM framework 

has four parts: (1) a regulatory model to characterize economic activities, (2) a risk assessment tool to identify the 

environmental hazard, (3) a risk management tool to choose a 

mitigation action, and (4) a valuation method to estimate the 

value-in-use of the scientific information. 

Regulatory Model

Regulators attempt to maximize social welfare by imposing rules to achieve an optimal level of safety for the application of a pesticide j that could increase crop yield and so also 

increase income. The benefits of agricultural production B(Q) 

are derived from the supply Q, total crop yield per hectare 

Y, and number of planted hectares h of H total available 

hectares of arable land. The optimal benefit, max B(Q) where 

Q = hY (Carlson and Wetzstein, 1993), is achieved when the 

greatest number of land parcels are permitted agrochemical 

application. Yield in the region is represented by Y = ∑yjFj, 

where yj is the average yield per hectare and Fj = hj/H jis the 

fraction of the total area treated with the jth pesticide. Acreage 

is represented by h = h(H,Πi, G), where Πi is the expected 

net revenue of crop i and G is a vector of agricultural policy 

variables. The vector G contains a regulatory standard, a 

regional ground-water vulnerability assessment, and, if necessary, the requirement of mitigation (for example, wellhead 

treatment).

The yield per hectare for a commodity varies according 

to the type and intensity of pesticide application. Many States 

use a regional-scale vulnerability assessment as the basis for 

determining whether a regulatory action would affect the use 

of specific chemicals (Barbash and Resek, 1996). Depending 

on the regulatory action, the number of chemicals used can 

alter Q. If the application of pesticide j is permitted, the 

benefit B(∆Q) increases as a result of the increase in Q. The 

new supply will be:

(Q + ∆Q) = (h + ∆h) (Y+∆Y ). (2)

Substituting for Y and h in equation 2 yields:

 (Q + ∆Q) = [h(H,Πi,G) + ∆h(H,Πi,G)] . [∑yjFj + ∑yj∆Fj]. (3)

 j j

Equation 3 reveals that the quantity supplied depends on, 

among other things, the area Fj, the ESI, and the regulator risk 

associated with policy G.

Risk Assessment

Risk to farmers and regulators is an outgrowth of the 

uncertainties related to maximizing agricultural output while 

sustaining a potable ground-water supply. In this context, the 

foundation for resource management actions is the translation 

of ESI into a ground-water vulnerability assessment. Assessments are made available in a variety of ways, ranging from 

site-specific evaluations to national assessments (National 

Research Council, 1993). These assessments combine hydrologic and chemical processes to produce a relative risk indicator of ground-water vulnerability that can be communicated 

using a map. For example, index-based methods used to 

estimate regional-scale ground-water vulnerability have been 

developed to determine, in a relative sense, if a specific agrochemical can be applied to a specific soil type on a particular 

tract of land without leaching to and subsequently contaminating ground water (see Khan and Liang, 1989).
3

Risk is a function of a regulatory standard and the information available from a ground-water vulnerability assessment:

1-P = f (R0, γ) (4)

where 1-P is the risk of choosing the appropriate mitigation 

strategy. It should be noted that all of the currently available 

vulnerability assessment methods contain considerable uncertainty in targeting areas that are more vulnerable to contamination (National Research Council, 1993). The uncertainties 

inherent in these estimates can alter mitigation outcomes. The 

risk-averse decisionmaker invariably will choose the “safe 

way out” and either restrict chemical application or require 

wellhead treatment. In some cases, this approach could be 

suboptimal. To reduce risk, the decisionmaker’s confidence 

level P about the information that supports a mitigation choice 

must increase (Lichtenberg and others, 1989; Bernknopf and 

others, 1997).

Consider the decisionmaker who has to choose among A

actions as a means to ensure consumers of a potable water 

supply. There are two possible states of the environment s: 

(1) the agrochemical is mobile and is likely to contaminate 

ground water (s = 1), and (2) the agrochemical is immobile 

and is unlikely to contaminate ground water (s = 2). The 

payoff u depends on the true state of the environment s and 

the action a:

u = u(a, s). (5)

The true state of pesticide contamination in space and 

time at the regional scale is unknown. There exists some 

conditional probability distribution psγ , which is assumed to 

be known to the decisionmaker (Nelson and Winter, 1964) 

and consists of three elements (Phlips, 1988): (1) the set of 

possible states of the environment s, (2) the set of possible 

information signals γ, and (3) the probability p that a signal 

is observed, given that a particular state of the environment 

prevails.

Concerns have been expressed about the effectiveness 

and reliability of regulatory standards that are based on vulnerability assessments (National Research Council, 1993). 

The most obvious concern is the uncertainty of the ESI that 

supports γ . If γ were to be used to make regulatory decisions, 

it should correlate strongly with s. However, for a variety 

of reasons, it is extremely difficult to verify or validate the 

accuracy of γ (Konikow and Bredehoeft, 1992; Barbash 

and Resek, 1996). Although analyses show that reliance on 

γ is problematic, there is evidence of statistical correlation 

between an ESI prediction and observed values of groundwater contamination (Barbash and Resek, 1996).

The correlation coefficient is expressed as ρ = Corr(γ, s), 

where the higher the ρ, the more closely γ correlates with s

and hence, the more value accrues to γ. If ρ = 1, γ contains 

no noise and is a perfect predictor of s. However, because this 

is usually not the case, there is a risk in applying ESI in a 

regulatory decision. Let θ represent ρ (Radner and Stiglitz, 

1984), where θ is an index of information uncertainty associated with γ .

Reductions in the ESI uncertainty and improvements in 

ρ result from a better understanding of the underlying physical processes and help reduce risk management uncertainty 

(Barbash and Resek, 1996). Refinements in ESI data collection (for example, greater sampling density) also reduce 

decisionmaking uncertainty (Bernknopf and others, 1999). A 

decrease in the uncertainty of the vulnerability assessment 

leads to a change in the area acceptable for agrochemical 

use. Any changes are benefits to the use of the regulatory 

standard and provide a means to measure the value of the 

improved ESI. However, less uncertainty resulting from a 

refined process model and/or from greater density of data 

collection comes at an increased cost.

There are Γ assessments of regional-scale ground-water 

vulnerability of increasing complexity in terms of both the 

physical processes and their data requirements (National 

Research Council, 1993). Among the various vulnerabilityassessment methods, the process-based approach is, in theory, 

the best to apply. However, the regional-scale data requirements and costs for process-based simulations can be staggering (Loague and others, 1990). Another approach, the index 

method, is a calculation of the relative degree of vulnerability 

among different areas in a region, or the relative tendency for 

different compounds to contaminate ground water (Barbash 

and Resek, 1996).

A good vulnerability assessment attempts to characterize 

six physical processes associated with the leaching of organic 

chemicals. The first three, advection, dispersion, and diffusion, apply to the flux of contaminants through a subsurface 

environment. They account for the movement of a contaminant owing to the flow of water, the mixing of water caused 

by different flow paths through a porous medium, and the 

tendency for dissolved particles to disperse in an aqueous 

environment following the principles of Brownian motion. 

The latter three, decay, sorption, and volatilization, apply to 

the mass balance of contaminants in a subsurface environment. They account for the chemical or biochemical transformation of a contaminant into a different form, the attachment 

of a contaminant onto solid particles where it is no longer 

available in the aqueous solution, and the transformation 

of the contaminant from its dissolved or liquid form to a 

gaseous form. Several leaching indices (or screening models) 

that include some of these processes are currently used 

in regional-scale ground-water vulnerability assessments (for 

example, Diaz-Diaz and others, 1999; Jury and others, 1987; 

Rao and others, 1985).

Two indices of pesticide mobility are included in this 

study. The first index, the Retardation Factor (RF), is a linear 

measure of pesticide mobility with a numerical range between 

one and infinity. The RF index estimates pesticide mobility on 

the basis of only one of the six processes: sorption. The larger 

the RF value, the more likely it is that the pesticide will be 

sorbed by the soil. The second index, the Attenuation Factor 

(AF), is an exponential measure of pesticide leaching relative 

to a compliance depth, with a numerical range between zero 

and one. The AF index estimates pesticide mobility on the 

basis of three of the six processes listed above: advection, 

decay, and sorption. The larger the AF value, the more likely 

An Integrated Earth Science–Economics Framework
4 Assessment of Regional-Scale Nonpoint Source Ground-Water Vunerability

it is that the pesticide will leach. Because the AF index takes 

into account a greater number of physical processes, it is a 

more rigorous approach for estimating pesticide leaching than 

the RF index.

The AF index, originally proposed by Rao and others 

(1985), can be expressed as:

AF = exp ( -0.69 d RFθFC ) 

 q t1/2 

(6)

where d is distance to ground water (or a compliance depth) 

from the surface, θFC is the soil-water content at field capacity, q is net ground-water recharge, and t

1/2 is pesticide halflife. The RF index is defined as:

RF = 1 + ρ b f

ocKoc

 θ FC 

(7)

where ρ b is soil bulk density, foc is soil organic carbon, and 

Koc is the pesticide sorption coefficient. The scales used to 

subdivide the AF and RF estimates into ranges are subjective. 

Khan and others (1986) adopted the schemes shown in table 

1 for making relative assessments of pesticide mobility with 

the AF and RF indices.

Risk Management

For the application presented here, consider a population 

of K soil orders with varying degrees of vulnerability to J

pesticides. Let hk be the number of planted hectares of soil 

order k in the study area, and assume that the θth ESI signal 

is distributed as a uniform distribution; that is, γ θ~ U(α, β) 

with mean (α + β) / 2 and variance (β - α)

2

 / 12. For each soil 

order, vulnerability examination γ θ is applied to each hectare 

that results in an expected value and a variance:

AFθ = (E(AFθ), σ2 (AFθ)) (8)

and

RFθ = (E(RFθ), σ2 (RFθ)). (9)

The first two moments of the AF distribution in a firstorder uncertainty analysis (FOUA) have been used to characterize uncertainty for the AF and RF indices (Kleveno and 

others, 1992; Loague, 1991, 1994; Loague and Green, 1988, 

1990a, b, c; Loague and others, 1989, 1990, 1996). The regulatory standard R0 defines a threshold of contamination based 

on the AF and RF estimates. A standard R0 is determined for 

confidence level P (Lichtenberg, 1991):

Prob[γ θ < or > R0 ] > P. (10)

The vulnerability assessment γ θ

 is compared with R0. In 

response, the decisionmaker associates the vulnerability index 

for soil order k with the admissibility of the application of 

pesticide j and chooses an action a from a decision function 

dγ ∈D that relates the signal from γ θ to a∈A. The decision 

rule states:

 1, if γθ meets the standard R0 for pesticide

 j on soil type k and is less than the margin (11) 

of error; application is permitted 

0, otherwise.

The decision rule is illustrated for the RF in figure 1. To 

the right of R0, the application of the jth pesticide is permitted 

without treatment; to the left of R0, treatment is necessary.

Assume there are existing data to estimate a prior probability φs ∈[0,1] of state s for pesticide j in soil k. Any 

refinement in γ suggests either an increase in the number of 

physical processes included in the vulnerability assessment or 

a decrease in its variance. The information structure θ∈[0,θ 1], 

associated with γ , is a Markov matrix of the conditional probability ps(k)γ θ

of ground-water contamination:

 ps(k)1

γ 1

 ps(k)1

γ 2

 

=

 p11 p12

 ps(k)γ θ 

= 

 ps(k)2

γ 1

 ps(k)2

γ 2

 p21 

p22 

(12)

where p11 is the probability that γθ indicates that ground-water 

contamination will occur given that the agrochemical is 

mobile, p12 is the probability that γ θ

 indicates that groundwater contamination will not occur given that the agrochemical is mobile, p21 is the probability that γθ indicates that 

ground-water contamination will occur given that the agrochemical is immobile, and p22 is the probability that γ θ

 indicates that ground-water contamination will not occur given 

that the agrochemical is immobile.

The payoff to the decisionmaker is us(a,θ ). The expected 

value of a decision rule d, given θ, is:

U(d,θ ) ≡ ∑ φ s ps(k)γ θus(dγ ,θ ). (13)

 s,γ

The value of a particular θ is the maximum expected 

utility that can be achieved using the dγ , as defined by Radner 

and Stiglitz (1984), and is given by:

max V(θ ) ≡ sup [U(d,θ ): d∈D(θ)]. (14)

 θ

D(θ ) is the set of admissible decision functions, and 

its expected value achieves the supremum of V(θ ). For the 

decision rule for θ to be optimal, dγ must translate to an 

action that maximizes ∑ φs ps(k)γ θus(a, θ) subject to a ∈A(θ ). 

This function establishses a relative value for different γ θ in 

a risk-decision framework. To demonstrate the value of ESI, 

the Bayesian screening model is applied in the case study 

section.

The Value of ESI: V(θ)

The relative value of a refinement in ESI is estimated 

as the difference in the expected payoffs of decisions for 

different θ. An increase in supply and hence in the value 

of agricultural production, without increasing the potential 

for ground-water contamination, accrues benefits to the ESI. 

Then, the benefit of θ is:

V(θ ) = U(d,θn+1) –U(d,θn) ≥ 0, for any n ∈ . (15)

dγ jk =
5

The benefits V(θ ) = V1(θ ) + V2(θ ) and costs C(θ )

= C1(θ ) + C2(θ ) associated with the implementation of 

a regional vulnerability assessment are composed of the 

benefits and costs from improved characterization of the physical processes, V1 and C1, and the benefits and costs from 

increased statistical accuracy, V2 and C2. It is assumed that the 

benefit of an improvement in θ meets the conditions dV(θ )/dθ

> 0 and d2V(θ )/dθ2 < 0. The cost of supplying the information increases at an increasing rate, and therefore dC(θ ) /dθ

> 0 and d 2C(θ)/dθ2 > 0. Although the benefits from ESI 

seem obvious, making decisions about “how much” ESI is 

less obvious. This decision involves estimating the benefits of 

each θ for a given P and then choosing the θ that maximizes 

the value of ESI. The maximum net benefit of ESI is defined 

as:

NV(θ ) = max [(V1(θ ) + V2(θ )) - (C1(θ ) + C2(θ))]. (16)

 θ

A Method for Estimating ESI 

Benefits

The ESI is used to screen areas for ground-water vulnerability. To estimate V(θ ), the location of vulnerable and “safe” 

areas must be identified. Improvements in the ESI may or 

may not have value in the decisionmaking process. Figure 1 

shows the impact of changes in RFθ . Because the information 

signal RF1 crosses the threshold R0, it is too uncertain to allow 

the use of pesticide j in soil k without the cost of wellhead 

treatment, and V(θ) = 0. On the other hand, a refinement 

of RFθ in the form of a reduction in the standard deviation 

σ(RFθ) may yield an information signal RF2, which does not 

cross R0. Thus, the reduction in uncertainty allows the use of 

the pesticide without production costs for wellhead treatment, 

and V(θ ) > 0. This process yields ∆Fj (from equation 3), the 

change in the fraction of hectares that are permitted pesticide j

without wellhead treatment: 

∆Fj = hj(γθ +1) – hj(γθ) (17)

 H .

The ∆Fj bridges a gap between ESI and the regulatory 

model.

Cost-benefit analysis helps with the decision on whether 

the public should invest in the reduction of ESI uncertainty 

to potentially increase agricultural productivity. The value of 

ESI is estimated using the following three-step procedure:

Step 1.—Estimate the AF and RF Values and Uncertainties: Apply a regional leaching model γθ to estimate groundwater vulnerability, including uncertainty, in a GIS. This 

step incorporates a description of the physical environment 

and the interaction of chemicals, soils, and water recharge. 

Regional-scale ground-water vulnerability estimates and 

their associated uncertainties are assigned to each hectare 

of land that is available for agricultural production. The 

parameters that make up the AF and RF indices (see equations 6 and 7) generally can be divided into three groups: 

(1) soil properties (foc, θFC, and ρb), (2) hydrogeologic and 

climate characteristic parameters (d, q), and (3) chemical 

coefficients (Koc and t1/2). The soil database, at the order 

taxonomic category, and the recharge rates for the five 

major soil orders in the Pearl Harbor basin, Hawai‘i, have 

been reported by Loague and others (1990) and Loague 

(1991). For this study (following Loague and others, 

1990), a very conservative estimate of the depth to the 

water table of 0.5 meter was used. The names and uses 

for the 10 pesticides included in this study, all of which 

are currently (or have been in the past) used in Hawai‘i, 

are listed in table 2. The statistical properties for the 10 

pesticides have been reported in Diaz-Diaz and others 

(1998).

The E(AF) and E(RF) estimates for the 10 selected 

pesticides for the 5 major soil orders are calculated using 

equations 6 and 7. The associated uncertainties, σ(AF) 

and σ(RF), are estimated using the FOUA for each of the 

soil parameters and recharge rates. The resulting values 

for the means and standard deviations of the AF and RF

are reported in tables 3 and 4. To examine the impact 

of a reduction in ESI uncertainty on decisionmaking, the 

standard deviations of the parameters that make up the 

AF and RF indices in equations 6 and 7 are artificially 

reduced by 10 percent and 90 percent. The revised σ(AF) 

and σ(RF) values are listed in tables 5 and 6. The values 

in tables 3, 4, 5, and 6 are used with the classification 

scheme in table 1 to illustrate the impact of increased 

statistical accuracy of the ESI in the application of the 

regulatory model described below.

Figure 1.—Impact of reducing σ(RF), the standard deviation of RF, 

and of using information structure RF2 relative to information structure RF1. The decision dγ jk is based on information signal γ, pesticide j, and soil type k. R0 is the regulatory standard for ground-water 

contamination, and θ is an index of earth science information (ESI) 

uncertainty. It is assumed that RF ~ U(α, β).

A Method For Estimating ESI Benefi ts

α1

α2

β1

β2

R0 > RF ; d jk = 0 R0 RF ; d jk = 1

R0 RF

[ E(RF2); σ2(RF2) ]

[ E(RF1

); σ2(RF1) ]

< θ γ

θ γ

θ
6 Assessment of Regional-Scale Nonpoint Source Ground-Water Vunerability

Step 2.—Apply the Regulatory Model: Using a GIS, 

apply γ θ in agricultural areas to decide which hectares 

of land should require wellhead treatment with pesticide 

use based on R0. For a strategy to be efficient, the value 

of agricultural production bijk = pricei × Qijk, or any additional benefits based on ∆Qijk, must offset the costs of 

either the collection of additional ESI or the wellhead 

treatment program. The standard R0 is applied to determine the location of vulnerable and “safe” areas when pesticide j is applied to soil order k. For this demonstration, 

the standard for pesticide use to be considered safe is in 

the very immobile or very unlikely classification (see table 

1). It is assumed that the decisionmaker is risk averse and 

only allows application of a pesticide without wellhead 

treatment if E(γ θ) ± F(P)σ(γ θ) meets R0, where F(P) is the 

critical value of the standard normal distribution exceeded 

only with probability 1 - P (Lichtenberg and others, 1989). 

Confidence levels of P = 0.67, 0.95, and 0.99 are evaluated to represent three levels of risk for the decisionmaker.

Step 3.—Adopt a Loss-Reduction Strategy: Apply a 

place-based Bayesian decision model to evaluate the costs 

and benefits of the societal impacts of using different γ θ

with a regulatory standard. Based on Q for commodity i, 

the expected present value of net benefits Bγ θ(Q) over the 

production time period T are:

 T

Bγ θ(Q) = ∫ [∑ (bijk – Cij) – Cw – C(θ)]e –rt dt (18)

 0 i,j,k

where Cij is the cost of producing crop i using pesticide 

j, and Cw is the investment and operating costs of a wellhead treatment program. The expected present value of 

marginal net benefits Bγ θ (∆Q) of a refinement in γ θ is 

measured in terms of the additional number of hectares 

on which pesticide j is allowed without wellhead treatment. The value-in-use of ESI in terms of the benefits per 

hectare is the difference in the base level of Bγ θ(Q) and 

the additional benefits that accrue with a refinement in the 

ESI, [Bγ θ(∆Q)] , where

bijk . ∆Fj = [Bγ θ(∆Q)] – Bγ θ(Q). (19)

The optimal benefit of a regional vulnerability assessment 

is achieved by using the θ that maximizes crop production 

while meeting the decision criterion:

NV(θ) = max (bijk . ∆Fj), subject to dγ jk = 1. (20)

 j

Application of the IESEM, Pearl Harbor 

Basin, O‘ahu, Hawai‘i

To demonstrate the potential cost effectiveness of alternative strategies for mitigating ground-water contamination 

from pesticide use, the IESEM is applied to a hypothetical 

pineapple production example for the Pearl Harbor basin 

on the island of O‘ahu, Hawai‘i. In comparing these alternative strategies, it was assumed that ESI can be used to 

determine where ground-water contamination will not occur 

and therefore where the need for wellhead treatment can be 

eliminated. It was assumed that the application of a pesticide 

combination increases yield by 90 percent. The regulatory 

screen is applied to a 100-m × 100-m (1 hectare) grid in a 

GIS for the 5 soil orders found in the study area as shown in 

figure 2. There are 32,226 hectares in the Pearl Harbor basin 

study area. When this number is broken down by soil order, 

there are 4,606 ha for Inceptisols, 6,210 ha for Mollisols, 

12,450 ha for Oxisols, 3,186 ha for Ultisols, and 5,774 ha 

for Vertisols.

For the Pearl Harbor case study, there are two alternatives for reducing the environmental hazard: Alternative A, 

conduct a regionwide wellhead treatment program over the 

productive lifetime of the resource to remove all pesticides 

from the ground water before consumption; Alternative B, 

target areas of vulnerability by increasing the amount of scientific information collected and decreasing the uncertainty 

of the components of γθ. Areas that meet the regulatory standard do not require wellhead treatment, whereas the remaining vulnerable areas do. It was assumed that maintaining a 

viable ground-water resource is of great value.

Alternative A

Wellhead treatment is an investment to remediate contaminated ground water that results from pesticides used in 

agricultural production. The expected payoffs of ground-water 

treatment result from the unrestricted application of pesticides 

to maximize agricultural output and having no restrictions 

on where pineapple can be planted. In the production scenarios that follow, pineapple is assumed to be produced on all 

32,226 hectares and to have a 3-year production cycle (LeonGuerrero and others, 1994). The wellhead treatment alternative is considered a noninformative information structure (that 

is, θ = 0) because ps(k)γ 0is independent of s(k) for each γ. In 

this case, no regional vulnerability assessment is used to make 

decisions (that is, C(θ) is zero and B(Q) is independent of 

γθ), and all ground water must be treated. For Alternative A, 

the benefits and costs of agricultural production are contained 

in table 7. The present value of the agricultural benefits bijk

is estimated as $4.8 billion, and the production and wellhead 

treatment costs, Cij and Cw, are estimated as $2.2 billion and 

$336 million, respectively. The expected present value of net 

benefits of using wellhead treatment over a production period 

of T = 24 years (or 8 production cycles) is calculated using 

equation 18 and is listed in column 5 of table 7. Alternative A 

has an expected present value of net benefits of $2.3 billion, 

or $11.7 million annually.

Alternative B

By determining locations that meet the regulatory standard, ESI is incorporated in the decision to permit pesticide 
7

application without wellhead treatment. As in Alternative A, 

pineapple is assumed to be produced on all 32,226 hectares. 

The expected payoffs of γθ result from the reduction in the 

uncertainty associated with decisions concerning the application of pesticides and the potential decrease in production 

costs (that is, a reduction in Cw from equation 18). For this 

alternative, θ = ρ, and ps(k)γθ is an informative information 

structure that depends on s(k) for each γ (Radner and Stiglitz, 

1984).

R0 consists of an implementation protocol that relates 

γθ to a soil order. The risk of making the wrong decision is 

a strong motivation to be conservative in the application of 

the protocol. It is assumed that the decisionmaker applies γθ

with confidence level P. For the protocol, based on the RF

standard of 10.0 and a critical value of F(P) = 1, an action 

to require wellhead treatment occurs if E(RF) - F(P)σ(RF) 

< 10.0; this is referred to as the screen and is meant to 

be only illustrative. Initially, it is assumed that owing to 

pesticide application, ground water must be treated at all 

wellheads. However, if in some locations the RF signal meets 

the standard, that is, E(RF) - F(P)σ(RF) ≥ 10, then production can occur without treatment in those locations. For each 

hectare, the RF value is compared with R0 to identify which 

soil orders are potentially suitable for application of the jth

pesticide. Table 8 lists, for each pesticide combination and 

information structure, the number of hectares acceptable for 

pesticide use without wellhead treatment. The application of 

the standard for the chemical combinations in table 8 results 

in a range from 0 ha for the RF index to 32,226 ha for 

the AF index of areas that are acceptable for pesticide use 

without wellhead treatment . It was assumed that 8 of the 10 

chemicals listed in table 2 were in use within the study area. 

The remaining two chemicals (DBCP and EDB), though no 

longer used, were included to examine whether banning them 

was a good policy decision.

An example illustrates how Alternative B works (following Bernknopf and others, 1997). Consider the following 

values: E(RF) = 11.0; R0 = 10.0; F(P) = 1; σ(RF) = 3.0; 

0.9σ(RF) = 2.7; and 0.1σ(RF) = 0.3. For the 0 percent reduction and 10 percent reduction cases, E(RF) - F(P).

1σ(RF) 

= 11.0 - 3.0 = 8.0 < 10.0, and E(RF) - F(P).0.9σ(RF) = 

11.0 - 2.7 = 8.3 < 10.0. Neither case meets the standard 

R0, so dγ jk = 0, and the application of pesticide j requires 

wellhead treatment and its associated production costs. This 

corresponds to the distribution RF1 ~ U[α1 , β1] in figure 1. 

On the other hand, for the 90 percent reduction case, E(RF) 

- F(P).0.1σ(RF) = 11.0 - 0.3 = 10.7 > 10.0, as illustrated by 

the distribution RF2 ~ U[α2 , β2] in figure 1. R0 is now met 

and dγ jk = 1, so the application of pesticide j is permitted 

without requiring wellhead treatment. Because of the reduction in treatment costs in areas for which γθ meets the standard, the γ -based model yields an increase in net revenue 

from agricultural production. Fewer hectares require treatment in Alternative B than in Alternative A in nearly every 

case.

The 10 pesticides that can be or have been used in 

the study area are divided into 2 groups: herbicides (Ametryn, Atrazine, Bromacil, Diuron, Hexazinone, and Simazine) 

and insecticides (DBCP, EDB, Fenamiphos, and Oxamyl). It 

is assumed that production requires a combination of one 

chemical from each group. The success of a pesticide combination is measured by the number of hectares permitted 

Figure 2.—Soil orders for the Pearl Harbor basin, Island of O‘ahu, Hawai‘i.

Application Of The IESEM, Pearl Harbor Basin, O‘ahu, 

158°05' 158°00' 157°55' 157°50'

158°05'

21°25'

21°20'

21°25'

21°20'

158°00'

0

0

5 

5 10 Kilometers

10 Miles

157°55' 157°50'

Soil Orders

Inceptisols

Mollisols

Oxisols

Ultisols

Vertisols

Excluded area 

Oahu
8 Assessment of Regional-Scale Nonpoint Source Ground-Water Vunerability

for pesticide application that do not require ground-water 

treatment (see table 8). For any AFθ, without treatment, the 

application of any EDB combination is permitted on zero 

hectares, while the application of Fenamiphos or Oxamyl 

with Ametryn or Diuron is permitted on all 32,226 hectares. 

The agricultural benefits and the costs of production associated with γθ are estimated to be $4.8 billion and $2.2 billion, 

respectively. The costs of the screen and wellhead treatment 

for Alternative B range from $92 million to $403 million (see 

Leon-Guerrero and others, 1994, for details on monitoring 

and sampling costs for C(θ )). Using equation 18, depending 

on the choice of γθ from Alternative B, the expected present 

value of net benefits Bγ θ (Q) ranges from $2.2 billion to $2.5 

billion as displayed in table 7.

Cost-Effectiveness Analysis

After the payoffs have been estimated for Alternatives 

A and B, the decisionmaker must decide which program 

is most cost effective. The GIS was used over the entire 

study area to compare Alternative B with Alternative A in 

a very straightforward manner. The difference between the 

expected present values of net benefits of the two alternatives 

represents the cost effectiveness of Alternative B. The regulatory program with the maximum positive expected present 

value of net benefits is the most efficient and should be 

implemented. Figure 3, a bar graph of the last column of 

table 7, shows, in ascending order, the difference between 

the expected present value of net benefits of each Alternative 

B program and the Alternative A program (the $0 line). 

The most cost-efficient program (Alternative B, Program 17) 

was based on combinations of Fenamiphos or Oxamyl with 

Ametryn or Diuron. Over a 24-year period, its total savings 

amounted to $244 million, or $10.1 million annually. On the 

other hand, the least cost-efficient program (Alternative B, 

Program 1) was based on all six of the DBCP combinations. 

Over the same 24-year period, its total net loss was $ -66.4 

million, or $ -2.8 million annually. Of course, these findings 

are meant only to demonstrate the cost effectiveness of the 

coordinated agricultural and resource programs and do not 

reflect economies of scale or the value of ground water lost.

Discussion

The number of hectares acceptable for pesticide use without wellhead treatment ranges from 0 ha for all chemical 

combinations using the RF index to 32,226 ha for combinations of Fenamiphos or Oxamyl with Ametryn or Diuron 

using the AF index (see table 8). For these combinations, the 

expected present values of net benefits B(Q), listed in table 7, 

are $2.2 billion (Alternative B, Program 2) and $2.5 billion 

(Alternative B, Program 17). For each chemical combination, 

a reduction in the aleatory uncertainty changed the designation of at least 4,606 ha from vulnerable to “safe.”

A specific comparison of the benefits of improving the 

epistemic uncertainty for the Oxamyl/Bromocil combination 

is shown in figure 4. Figure 4A is a map of the application 

of Step 1, the method to determine the AF categories for the 

Pearl Harbor basin. The outline of an area of approximately 

12,958 ha was sketched onto figure 4 as the active pineappleand sugar-producing region in 1980 (Armstrong, 1983). On 

the basis of the outline, there were about 10,423 ha of pineapple production and about 1,709 ha of sugar production. 

The remaining 826 ha could not be classified. It should be 

noted that the following results illustrate an example based on 

historical cultivation and do not imply that this area would 

be planted exclusively with pineapple. Figure 4B is a map of 

the outcome of using the AF classification scheme in table 

1, applying the decision rule from equation 11, and applying 

Steps 1 and 2 of the method for estimating ESI benefits. 

The map shows that without treatment, 16,590 ha are acceptable and 15,636 ha are unacceptable for the application of 

the Oxamyl/Bromacil combination. A comparison of figures 

4B and 4C illustrates the impact of a reduction in statistical 

uncertainty and the potential economic benefits described in 

Step 3 of the method. With a 90 percent reduction in uncertainty, 12,450 ha are added to the acceptable category for 

a total of 29,040 ha as shown in figure 4C. Only 3,186 ha 

remain unacceptable.

The maps in figure 4 illustrate that the risk of using 

the Oxamyl/Bromacil chemical combination would have been 

real. Even though the “safe” areas increased from figure 

4B to figure 4C, vulnerable areas remain and reduce the 

possibility of avoiding future NPS contamination. For the 

Oxamyl/Bromacil combination, using the AF index, the 90 

percent reduction in uncertainty provides a potential decrease 

in income from pineapple production of $36.5 million; that 

is, $44.2 million (Alternative B, Program 9) - $80.7 million 

(Alternative B, Program 11); thus, Alternative B, Program 11 

would be preferred. On the other hand, for the combinations 

of Fenamiphos or Oxamyl with Ametryn or Diuron, for both 

the 1.0AF (Alternative B, Program 17) and 0.1AF (Alternative 

Figure 3.—Cost effectiveness of earth science information (ESI) in 

million dollars.

-$100

-$50

$0

$50

$100

$150

$200

$250

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17

COORDINATED PROGRAM

B (Q) - B (Q), IN MILLION DOLLARS γ

θ

γ0
9

Figure 4.—Ground-water vulnerability maps for the Pearl Harbor basin, Island of O‘ahu, Hawai‘i, for the Oxamyl/Bromocil combination based upon the AF. A, spatial representation of the AF categories; B, decision rule (dγ ) to accept or reject the application of 

a pesticide without wellhead treatment based on the rule E(AF ) + σ(AF ) < 0.0001; C, decision rule (dγ ) to accept or reject the 

application of a pesticide without wellhead treatment based on the rule E(AF ) + 0.1σ(AF ) < 0.0001. Outlined areas represent 

active pineapple and sugar production in 1980 (Armstrong, 1983).

Discussion

A

B

C

Attenuation Factor (AF)

Categories

Excluded area

Acceptable

Unacceptable

Excluded area





Acceptable

Unacceptable

Excluded area





Decision Rule (d )

Decision Rule (d )

Historical Cultivation Area

Very likely

Likely

Unlikely

Very unlikely

Moderately likely

Pineapple

Sugarcane

γ

γ

(E (AF) + σ(AF) <0.0001)

(E (AF) + σ(AF) ≥0.0001)

(E (AF) + 0.1σ(AF) <0.0001)

(E (AF) + 0.1σ(AF) ≥0.0001)
10 Assessment of Regional-Scale Nonpoint Source Ground-Water Vunerability

B, Program 12) cases, the expected present values of net 

benefits of $244.0 million and $96.1 million, respectively, are 

greater than those of Alternative B, Program 11. Furthermore, 

for all six of the DBCP combinations, Alternative A is more 

cost effective than Alternative B, Programs 1 and 3 (with 

expected present values of net benefits of $ -66.4 million and 

$ -44.3 million, respectively) and would be preferred; these 

are the only two programs for which Alternative A is more 

cost effective than Alternative B. Depending on the availability, effectiveness, and price of the chemicals, conclusions 

about the efficacy of their use can vary.

The application of the regulatory model demonstrated 

that the RF and AF indices behaved differently. The RF estimates were affected by changes in the levels of uncertainty far 

more than the AF estimates. However, in nearly every case, 

the AF estimates resulted in fewer hectares that would require 

wellhead treatment than did the RF estimates. This model 

indicates that the application of the AF consistently allows 

greater use of chemicals.

The regulator’s level of risk aversion moderately affects 

the outcomes of the regulatory model and the actions to be 

taken. For the RF index, a change in the confidence level 

P from 0.67 (F(P) = 1) to 0.95 (F(P) = 2) decreases the 

number of hectares exempt from wellhead treatment from 

4,606 ha to 0 ha for combinations of DBCP or Fenamiphos 

with Simazine. For the regulator who requires P = 0.99 (F(P) 

= 3), the number of hectares that do not require wellhead 

treatment decreases from 4,606 ha to 0 ha for combinations 

of DBCP with Ametryn, Atrazine, and Diuron, and from 

26,452 ha to 14,002 ha for combinations of Fenamiphos with 

Ametryn, Diuron, and Simazine. An increase in P for the 

AF index results in only one change in farm productivity 

for pineapple production. When P = 0.99 for the 1.0AF

case, the number of hectares exempt from wellhead treatment 

decreases from 16,590 ha to 10,816 ha for combinations 

of Fenamiphos or Oxamyl with Hexazinone, reducing the 

expected present value of net benefits from $80.7 million to 

$20.5 million. These results demonstrate that the IESEM is 

capable of representing changes in decisionmaker risk and in 

reductions of ESI uncertainty. Finally, the application of the 

IESEM showed that the policy to restrict the application of 

DBCP and EDB in areas of historical production was a wise 

decision. When the ESI for these two insecticides was used 

in the application of the implementation protocol, the model 

result was too uncertain to permit the use of these chemicals 

without wellhead treatment.

Conclusions

This study demonstrates that using an IESEM in a GIS 

framework provides an ability to assess, at a regional scale, 

the tradeoffs among pesticide use, crop yield, and groundwater treatment. The cost-effectiveness analysis described 

here allowed an assessment of alternative policy choices. The 

results indicated that a coordinated information-based screening and wellhead treatment program could be cost effective. 

Extensions to the method developed in this paper can be 

made to accommodate a physics-based model with more realistic delineations of known agricultural regions or recreational 

areas (for example, golf courses).

The IESEM has been developed to estimate the value of 

ESI in a decision framework using a GIS. The two contributions of the decision framework reported here are understanding the physical processes at work in the shallow soil 

subsurface and refining the accuracy of ESI predictions on the 

basis of regional-scale vulnerability assessments. However, 

the estimation of ρ remains problematic. Further research 

must improve the correlation between an ESI prediction and 

observed ground-water contamination to demonstrate the utility of the regional vulnerability measure as a regulatory tool. 

Before the application of regional models becomes routine, 

additional regional vulnerability assessment measures, including chemical concentrations, will be necessary for a successful regulatory program.

Acknowledgments

The effort described in this paper is a CESIR (Center for 

Earth Science Information Research) contribution. Thanks to 

Brian Bennett, Connie Hoong, Susan Landsittel, K. Allison 

Lenkeit, Roberto Lugo, and John Tracy for their help with 

technical aspects of the paper, and to Susan Benjamin, Rick 

Champion, and Lee De Cola for their reviews. We are grateful 

to Pat Shade, of the USGS in Honolulu, for providing us with 

a digital version of the O‘ahu soil survey. The views expressed 

here are solely those of the authors and may not represent the 

opinions of others. 

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Reicheldorfer, K., and Kramer, R.A., 1993, Agricultural resource 

policy, in Carlson, G.A., Zilberman, D., and Miranowski, 

J.A., eds., Agricultural and environmental resource economics: New York, Oxford University Press.

U.S. Department of Agriculture, 1999, State statistical report 

[Online]. Available HTTP: http://www.nass.usda.gov/hi/stats/

stat-26.htm.

Wise, S., and Johnson, S.R., 1991, A comparative analysis of state 

regulations for use of agricultural chemicals, in Just, R.E., 

and Bockstael, N., eds., Commodity and resource policies in 

agricultural systems: Berlin, Springer-Verlag.

References Cited
12 Assessment of Regional-Scale Nonpoint Source Ground-Water Vunerability
13

 TABLES 1–8
14 Assessment of Regional-Scale Nonpoint Source Ground-Water Vunerability

Table 1.—Classifi cation scheme used for the AF and RF indices for pesticide movement in 

soils (Khan and others, 1986).
15

Table 2.—The 10 pesticides included in this study, which are (or have been) used in Hawai‘i for sugarcane and pineapple (after Kleveno 

and others, 1992).

Common and chemical names Use in Hawai‘i

Ametryn herbicide

2-(ethylamino-4-(isopropylamino)-6-methylthio)-s-triazine 1964–present

Atrazine herbicide

2-chloro-4-ethylamino-6-isopropylamino-s-triazine 1958–present

Bromacil herbicide

5-bromo-3-sec-butyl-6-methyluracil 1963–present

DBCP soil fumigant

1,2-dibromo-3-chloropropane 1955–1984

Diuron herbicide

3-(3,4-dichlorophenyl)-1,1-dimethylurea 1954–present

EDB insecticidal fumigant

ethylene dibromide 1946–1983

Fenamiphos nematicide

ethyl 3-methyl-4-(methylthio) phenyl (1-methyl) phosphoramidate 1969–present

Hexazinone herbicide

3-cyclohexyl-6-(dimethylamino)-1-methyl-s-triazine-2,4-(1H,3H)-dione 1976–present

Oxamyl insecticide/nematicide

methyl N ́, N ́-dimethyl-N-[(methylcarbomoyl)-oxy]-1-thiooxamimidate 1969–present

Simazine herbicide

2-chloro-4,6-bis-(ethylamino)-s-triazine 1956–present
16 Assessment of Regional-Scale Nonpoint Source Ground-Water Vunerability

Table 3.—The mean E(AF ) and standard deviation σ(AF ) of the Attenuation Factor for the 10 selected pesticides for the 5 major O‘ahu soil 

orders.

Chemicals Soil orders

 

Inceptisols Mollisols Oxisols Ultisols Vertisols

E(AF) E(AF) E(AF) E(AF) E(AF)

σ(AF) σ(AF) σ(AF) σAF) σ(AF)

Ametryn 4.4x10-54 8.3x10-33 1.3x10-18 2.8x10-6 5.4x10-26

4.1x10-52 3.4x10-31 3.3x10-17 1.8x10-5 1.8x10-24

Atrazine 3.0x10-33 6.4x10-21 5.2x10-12 3.8x10-4 4.7x10-17

1.7x10-31 1.6x10-19 8.3x10-11 1.4x10-3 9.9x10-16

Bromacil 4.9x10-12 1.0x10-8 3.2x10-5 5.8x10-2 8.5x10-8

1.3x10-10 1.4x10-7 2.6x10-4 1.4x10-1 9.2x10-7

DBCP 3.3x10-8 1.5x10-5 2.0x10-3 1.6x10-1 9.5x10-5

4.3x10-7 8.8x10-5 7.4x10-3 1.7x10-1 4.6x10-4

Diuron 7.4x10-96 3.3x10-57 3.5x10-32 1.4x10-10 9.8x10-45

1.4x10-93 3.1x10-55 2.0x10-30 2.2x10-9 7.4x10-43

EDB 3.3x10-1 4.6x10-1 6.4x10-1 8.9x10-1 5.0x10-1

4.5x10-1 2.7x10-1 3.6x10-1 3.0x10-1 2.4x10-1

Fenamiphos 2.6x10-57 3.1x10-35 5.6x10-20 1.2x10-6 3.2x10-28

2.8x10-55 1.6x10-33 1.7x10-18 1.0x10-5 1.3x10-26

Hexazinone 3.3x10-9 1.3x10-6 4.9x10-4 1.2x10-1 6.9x10-6

4.3x10-8 7.5x10-6 1.8x10-3 1.0x10-1 3.3x10-5

Oxamyl 1.6x10-139 1.5x10-102 3.8x10-58 4.2x10-16 6.1x10-93

3.2x10-137 1.3x10-100 2.1x10-56 4.9x10-15 4.4x10-91

Simazine 9.0x10-41 1.7x10-25 1.5x10-14 6.3x10-5 1.1x10-20

3.9x10-38 4.3x10-23 2.1x10-12 2.8x10-3 2.1x10-18
17

Table 4.—The mean E(RF ) and standard deviation σ(RF ) of the Retardation Factor for the 10 selected pesticides for the 5 major O‘ahu soil orders.

Chemicals Soil orders

Inceptisols Mollisols Oxisols Ultisols Vertisols

E(RF) E(RF) E(RF) E(RF) E(RF)

σ(RF) σ(RF) σ(RF) σ(RF) σ(RF)

Ametryn 41.7 19.2 18.6 31.0 13.3 

29.6 10.1 11.1 12.3 7.5

Atrazine 19.4 9.3 9.0 14.6 6.6 

14.0 4.9 5.3 6.3 3.6

Bromacil 5.9 3.2 3.1 4.6 2.5 

 5.7 2.3 2.3 3.6 1.6

DBCP 11.7 5.8 5.6 8.9 4.2 

 8.4 3.0 3.2 3.9 2.2

Diuron 74.3 33.8 32.6 55.0 23.1

63.5 23.8 24.9 33.6 17.1

EDB 6.2 3.3 3.2 4.8 2.6

5.8 2.4 2.4 3.6 1.6

Fenamiphos 27.8 13.0 12.6 20.7 9.1

22.2 8.2 8.6 11.2 5.9

Hexazinone 6.5 3.5 3.4 5.0 2.7

4.1 1.4 1.5 1.7 1.0

Oxamyl 4.8 2.7 2.6 3.8 2.2

2.8 1.0 1.1 1.2 0.7

Simazine 20.8 9.9 9.6 15.6 7.0

97.7 43.5 42.1 71.4 29.4
18 Assessment of Regional-Scale Nonpoint Source Ground-Water Vunerability

Table 5.—Reductions in the components of σ(AF ) by 10 percent to 0.9σ(AF ) and by 90 percent to 0.1σ(AF ) for the 10 selected pesticides for the 

5 major O‘ahu soil orders.
19

Table 6.—Reductions in the components of σ(RF ) by 10 percent to 0.9σ(RF ) and by 90 percent to 0.1σ(RF ) for the 10 

selected pesticides for the 5 major O‘ahu soil orders.
20 Assessment of Regional-Scale Nonpoint Source Ground-Water Vunerability

Table 7.—Expected present value of net benefi ts of agricultural production and cost effectiveness of the ESI in millions of dollars to produce pineapple1 on 32,226 hectares in the Pearl Harbor basin, Island of O‘ahu, Hawai‘i.2 Assume production area, 

estimated yields, and income (bijk)3 of $4,832.2 million at a production cost (Cij)

4 of $2,213.0 million.

1 A growing cycle is 3 years (Leon-Guerrero and others, 1994).

2

 All prices and costs are in 1999 dollars.

3 Assumes benefi ts per hectare are $11,324 for pineapple (U.S. Department of Agriculture, 1999).

4 Production costs are based on Philipp and Baker (1975).

5 Present value of costs for Alternative A includes capital investment ($5,850/ha) and operating costs ($400/ha/yr) discounted at 7 percent annually. 6 Present value of costs for Alternative B includes monitoring and sampling for the RF ($150/ha/yr), 0.9RF ($150/ha/yr + $10/j/ha/yr), 0.1RF ($150/ha/yr + $100/j/ha/yr), 

 and for the AF ($250/ha/yr + $1,000/j ), 0.9AF ($250/ha/yr + $10/ha/yr + $1,000/j ), and 0.1AF ($250/ha/yr + $100/ha/yr + $1,000/j ).

 Program Cw C( ) B (Q) 6 Number of

ha permitted

without treatment

5 θ

γθ

γθ B (Q) − B (Q) γ 0

$

$

$

$

$

$

$

$

$

$

$

$

$

$

$

$
21

______________________________________________________________________________

Combinations 1.0RF 0.9RF 0.1RF 1.0AF 0.9AF 0.1AF

Insecticide Herbicide ______________________________________________________________________________

DBCP Ametryn 0 0 4,606 4,606 10,816 10,816

DBCP Atrazine 0 0 4,606 4,606 10,816 10,816

DBCP Bromacil 0 0 0 4,606 10,816 10,816

DBCP Diuron 0 0 4,606 4,606 10,816 10,816

DBCP Hexazinone 0 0 0 4,606 10,816 10,816

DBCP Simazine 0 0 4,606 4,606 10,816 10,816

Fenamiphos Ametryn 0 3,186 26,452 32,226 32,226 32,226

Fenamiphos Atrazine 0 0 7,792 29,040 29,040 29,040

Fenamiphos Bromacil 0 0 0 16,590 16,590 29,040

Fenamiphos Diuron 0 3,186 26,452 32,226 32,226 32,226

Fenamiphos Hexazinone 0 0 0 16,590 16,590 16,590

Fenamiphos Simazine 0 0 4,606 29,040 29,040 29,040

Oxamyl Ametryn 0 0 0 32,226 32,226 32,226

Oxamyl Atrazine 0 0 0 29,040 29,040 29,040

Oxamyl Bromacil 0 0 0 16,590 16,590 29,040

Oxamyl Diuron 0 0 0 32,226 32,226 32,226

Oxamyl Hexazinone 0 0 0 16,590 16,590 16,590

Oxamyl Simazine 0 0 0 29,040 29,040 29,040 ______________________________________________________________________________

Table 8.—Number of hectares acceptable for pesticide use without wellhead treatment for insecticide–herbicide combinations at 3 levels of uncertainty for the 10 selected pesticides for the 5 major soil orders (hj). 

The total number of hectares (H) in the study area is 32,226. There were no EDB combinations with positive 

acreage.
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