Integrating economic, environmental and GIS modeling to target cost effective land retirement in...

ANALYSIS

Integrating economic, environmental and GIS modeling totarget cost effective land retirement in multiple watersheds

Wanhong Yang a,*, Madhu Khanna b, Richard Farnsworth c, Hayri Onal b

a Department of Geography, University of Guelph, Guelph, Ontario, Canada N1G 2W1b Department of Agricultural and Consumer Economics, University of Illinois at Urbana-Champaign, Urbana, IL 61801, USA

c Department of Forestry and Natural Resources, Purdue University, West Lafayette, IN 47907-2033, USA

Received 26 September 2002; received in revised form 13 April 2003; accepted 15 May 2003

Abstract

An integrated framework of economic, environmental and GIS modeling is developed to study cost-effective

retirement of cropland within and across multiple watersheds to achieve environmental goals. This framework is

applied to 12 contiguous agricultural watersheds in the Illinois Conservation Reserve Enhancement Program region of

the United States. A key goal of this program is to reduce sediment loadings in the Illinois River by 20% by retiring land

from crop production. The characteristics of land parcels to be targeted for retirement within each watershed and the

criteria for cost-effective allocation of abatement responsibility across watersheds are analyzed. Our analysis suggests

that program costs are minimized when the abatement standard is set for the region rather than uniformly for each

watershed. For both policy scenarios, the land parcels targeted for retirement should be those that are highly sloping

and adjacent to a water body.

Keywords: Cost effectiveness; Land retirement; Multiple watersheds; Uniform and non-uniform standards

1. Introduction

Increasing emphasis on protecting water quality

from nonpoint pollution sources has led to a shift

in the policy objectives of conservation programs,

such as, the Conservation Reserve Program

(CRP), from on-site erosion control towards

controlling off-site sediment loadings. More re-

cently, with the development of the Conservation

Reserve Enhancement Program (CREP) the focus

of these programs has shifted towards achieving

explicitly defined goals for water quality in locally

identified environmentally sensitive river basins.

The goals of the CREP in Illinois include a 20%

reduction in sediment loadings, a 10% reduction in

nitrogen and phosphorus loadings and an increase

in aquatic and wildlife populations in the Illinois

River (USDA, 1998). The program seeks to

achieve these goals by retiring about 94 thousand

hectares of cropland in the Illinois River Basin for

at least 15 years and possibly for 35 years or

* Corresponding author. Tel.: �/1-519-824-4120x53090; fax:

�/1-519-837-2940.

E-mail address: wayang@uoguelph.ca (W. Yang).

Ecological Economics 46 (2003) 249�/267

www.elsevier.com/locate/ecolecon

doi:10.1016/S0921-8009(03)00141-1

permanently through offering rental payments to

landowners based on soil productivity. Eligible

land for enrollment is defined as cropland within

the basin’s 100-year floodplains, highly erodible

cropland adjacent to riparian areas, and cropland

where landowners are willing to create wetlands. A

secondary program restriction requires that 85%

of the land enrolled be within the basin’s envir-

onmentally sensitive riparian areas defined above

as 100-year floodplains. The amount of eligible

land is spread out over 100 sub-watersheds1 and is

more than six times larger than the program’s

acreage enrollment goal of 94 thousand hectares.

This raises two program implementation issues

on which the program description itself is silent.

First, should land enrollment be targeted to

achieve the environmental goals of the program

at the sub-watershed level or in the aggregate for

the river basin as a whole? Second, what types of

land parcels should be selected for enrollment in

each sub-watershed to achieve the environmental

goals cost-effectively?

The literature in environmental economics sug-

gests that when polluters are heterogeneous, an

aggregate abatement goal can be achieved cost-

effectively if each polluter undertakes pollution

abatement such that the cost of the last unit of

abatement is equalized throughout the river basin

(Baumol and Oats, 1971). This concept implies

that more abatement will occur in sub-watersheds

with low abatement costs, and less abatement will

occur in high abatement cost sub-watersheds;

implying that a non-uniform performance stan-

dard will be more cost effective than a uniform

standard. However, a social planner may prefer a

uniform performance standard where the same

abatement goal must be achieved in every sub-

watershed, for equity reasons (Schleich et al.,

1996), or to reduce transaction costs. The firstobjective of this paper is to estimate and compare

differences in costs, hectares retired and land

retirement patterns between the two performance

standards on sediment loadings.

The second objective is to develop criteria for

the land parcels that should be selected for

enrollment to meet the sediment abatement goals

of the program cost-effectively. Land parcels evenwithin a watershed are heterogeneous in their

characteristics and differ in their opportunity costs

of retirement (that is the forgone profits from crop

production) and in the extent to which their

retirement would reduce off-site sediment loadings

in the water body. Babcock et al. (1996, 1997)

suggest that land with the highest abatement

benefits to opportunity cost ratio should beselected to achieve abatement goals efficiently.

Determining the contribution of each land parcel

to off-site sediment loading requires estimation of

its sediment-trapping coefficient, and those of the

downslope parcels. Each parcel’s coefficient de-

pends on that parcel’s site-specific characteristics

(slope, soil characteristics, and distance from the

water body) and land use decision (crops, trees,pasture or grass) as well as highly complex

interdependencies between land use and sediment

trapping efficiencies of upslope and downslope

land parcels. Thus, the sediment deposition coeffi-

cient of a land parcel needs to be determined

endogenously with the land use decisions upslope

and downslope parcels.

To address these issues we develop an integratedeconomic, environmental and GIS modeling

framework that includes an endogenously deter-

mined sediment transport process and incorpo-

rates the micro-economic decision by a farmer to

retire land or continue crop production and the

environmental impacts of such decisions. This

framework extends the model development in

Khanna et al. (2003) and applies it to comparecost, acreage, location and parcel differences

between a non-uniform and uniform standard

across twelve sub-watersheds in the Illinois River

Basin.

Our research builds upon previous studies of

environmental programs on land use and farming

practices in several ways. A few studies have

1 A sub-watershed is defined as an 11-digit watershed.

Watersheds are delineated by USGS using a nationwide system

based on surface hydrologic features. Regions are defined using

a 2-digit classification, subregions are defined at the 4-digit level

accounting units and cataloguing units are defined as the 6 and

8 digit levels. A watershed is defined using an 11-digit

classification system and its size can vary between 16,000 and

101,000 hectares. For details, see http://www.ftw.nrcs.usda.gov/

UC/ni170304.html.

W. Yang et al. / Ecological Economics 46 (2003) 249�/267250

compared the efficiency and distributional impli-

cations of setting environmental standards at a

field/farm/watershed level or analyzed crop man-

agement strategies at a watershed level to reduce

pollution loadings. However, these studies as-

sumed that the relationship between on-site pollu-

tion generation and off-site pollution loadings is

dependent on exogenously given site-specific fac-

tors (Kramer et al. 1983; Ribaudo, 1986, 1989;

Prato and Wu, 1996; Carpentier et al., 1998).

Braden et al. (1989) assumed a more complex

pollution transport process in which the portion of

pollution trapped depends not only on the site-

specific characteristics but also on the manage-

ment practices of downslope parcels. However,

they did not incorporate the effect of the volume of

runoff flowing from upslope parcels on the trap-

ping capacity of downslope land parcels and

therefore ignored the impact of land use changes

upslope on sediment transport coefficients. Lint-

ner and Weersink (1999) was one of the few studies

incorporating economic, environmental and spa-

tial analyses to examine policies to reduce nitrogen

and phosphorus runoff. They incorporated the

interdependence between sediment deposition

coefficients and fertilizer-use decisions of all par-

cels in a flow path, but they assumed that all

parcels were identical. This assumption allowed

the sediment deposition ratio of a parcel to be

dependent only on its own characteristics and

reduced the true complexity of the problem. The

approach we present in this paper offers a more

realistic simulation of the sediment generation and

transport process by simultaneously determining

heterogeneous land use decisions and off-site

sediment abatement for all parcels in a flow path.

In Section 2, we present the conceptual frame-

work underlying the empirical model described in

Section 3. In Sections 4 and 5, we describe the data

used for 12 sub-watersheds in the study area

targeted under Illinois’ CREP and the results

obtained under both non-uniform and uniform

performance standards. In Section 6, we discuss

the policy implications and conclusions from this

research.

2. Conceptual framework

We assume a social planner who wants to

achieve a given sediment abatement target at

least-cost by selecting the land parcels to be retired

from crop production in a region with multiple

watersheds. The aggregate cost of abatement is

represented by the sum of abatement costs in-

curred by the owners of individual parcels whohave a choice of whether to retire their land from

crop production or to continue production. The

stringency of the sediment abatement objective

influences the amount the social planner would be

willing to compensate the landowners for retiring

their land from crop production and the parcels

that would be offered for enrollment in the land

retirement program.Consider a region with n�/l, 2, . . ., N water-

sheds, where each watershed is divided into j�/

1, . . ., Jn surface runoff channels by which pollu-

tants are transported from land to a river. Each

runoff channel comprises of i�/1, . . ., Ijn land

parcels of equal size, say a , with parcel i�/1 being

the closest to the river. The runoff channels are

independent of each other and each land parcel isassumed to be homogeneous in terms of its site-

specific characteristics such as slope, soil type, and

productivity. For each land parcel we have two

choices, either retire the land or continue crop

production on that parcel. Let pnijk be the per acre

quasi-rent earned on the ith land parcel in the jth

channel with the k th activity in watershed n , where

k�/0 indicates retirement of land and k�/1indicates crop production. The quasi-rent is de-

fined as total revenue minus total variable costs

(Just et al., 1982). For activity k , sediment

generated per land unit is denoted by snijk .

The total amount of sediment produced by the

ith parcel is given by a1k�0 snijkXnijk; where Xnijk

denotes the amount of land in that parcel allocated

to activity k . Determining the portion of thissediment that is transported to the river is a

complex process. If one parcel in a runoff channel

is converted into grass cover, not only the sedi-

ment generation and deposition ratio of that

parcel are affected, but also the deposition ratios

of all downslope parcels are affected because of the

reduced runoff volume and velocity.

W. Yang et al. / Ecological Economics 46 (2003) 249�/267 251

A fraction of the sediment produced by the ithparcel, denoted by dn ,i ,i�m ,j , is deposited in each

of the i�/m downslope parcels in flow path j ,

where m�/0, . . ., i�/1. This is referred to as the

deposition ratio of land parcel i�/m which is a

function of its site-specific characteristics, Lnij ;

land use activities, Xnijk ; and the amount of

sediment inflow, Sn ,i�1,j , from upland parcels.

Thus, we have the functional relationship:

dn;i;i�m;j �d(Ln;i�m;j; Xn;i�m;j;k; Sn;i�m;j)

for m�0; . . . ; i�1; Where:(1)

Sn;i�m;j�s(Ln;i;m�1;j ; . . . ; Ln;Ij ;j; Xn;i;m�1;j;k; . . . ; Xn;Ijn;j;k

As Sn ,i�m ,j increases, the deposition ratio

dn ,i ,i�m ,j in Eq. (1) is expected to decrease. The

amount of sediment Sn ,i�m ,j flowing into the (i�/

m )th parcel also depends on the site-specificcharacteristics and land use decisions by all parcels

in the channel. Thus, the fraction of sediment

deposited on the land parcels in the flow channel

and not loaded into the water body is

ai�1m�0 dn;i;i�m;j 51: From (1) and (2) we see that

the deposition ratios dn ,i ,i�m ,j (for m�/0,. . .i�/1)

of each land parcel is simultaneously determined

with the land use decision of all parcels,Xn;i;m�1;j;k; . . . ; Xn;Ijn;j;k

; in the jth flow path.

The social planner seeking to meet a sediment

abatement target A at least-cost faces a twofold

decision problem: (a) to determine the amount of

abatement to be undertaken by each of the N

watersheds such that the aggregate abatement

target is met; and (b) to select the land parcels to

be targeted for enrollment in the land retirementprogram in each watershed. Assume that S0

n is the

level of sediment loading in watershed n before

land retirement. The ocially optimal land retire-

ment pattern can be determined by solving the

following optimization problem:

pnij1Xnij1�XN

pnijkXnijk (3)

Subject to

Xnijk�a; �n; i; j; (4)

S0n�

�1�

Xi�1

dn;i;i�m;j

snijkXnijk

]A: (5)

The first order optimality conditions of the

Lagrangian are

@Xnijk

��pnijk

��1�

Xi�1

dn;i;i�m;j

�snijk�

Xi�1

� @dn;i;i�m;j

@Xnijk

snijkXnijk�XIjn�i

@dn;i�m;i;j

@Xnijk

snijkXnijk

��mnij

]0 (6)

@Xnijk

Xnijk�0; �n; i; j and k

where l and mnij are the Lagrange multipliers

associated with constraints (4) and (5).

From the social planner’s perspective it is

optimal to retire a land parcel from production,that is X nij1� �0; if @L /@Xnij 1�/0. In this case,

according to Eq. (4) we have X nij0� �a�0; which

implies that @L=@Xnij0�0: These two conditions

can be rearranged to show that retirement of land

parcel i from crop production is socially preferable

if the net social cost of land retirement is less than

the value of crop production on that parcel:

l��

1�Xi�1

dn;i;i�m;j��

(snij1�snij0)�2snij0aXi�1

@dn;i;i�m;j

@Xnij0

�2snij0aXIjn�i

@dn;i�m;i;j

@Xnij0

��pnij1: (7)

l* represents the marginal value per ton of the

abatement achieved by retiring a land parcel,which is the value that the planner would be

willing to pay per ton of abatement to induce

voluntary land retirements by farmers. With an

aggregate abatement constraint, this marginal

value is the same for all watersheds, implying

that a ton of abatement from any watershed

should be valued equally. If the watersheds differ

in their costs of abatement due to differences intheir land quality and topology, this equi-marginal

principle for cost-effective abatement will result in

a non-uniform allocation of abatement responsi-

bility across the watersheds. More abatement will

occur in watersheds where abatement costs are low

compared to watersheds where abatement costs

are higher.

To examine the type of land parcels within awatershed that should be retired from crop pro-

duction we examine each of the terms in Eq. (7).

The term (1�ai�1m�0 dn;i;i�m;j� )(snij1�snij0) shows the

off-site abatement of sediment generated on parcel

i due to a change in its land use. This term is likely

to be large if retirement by the ith parcel leads to a

large reduction in its sediment generation per acre

(that is, if (snij 1�/snij 0)�/0 is large) or ifai�1

m�0 dn;i;i�m;j� is small. The latter is the case if:

(1) there are few or no downslope parcels which

can trap the sediment generated by the i th parcel

or if the deposition capability of the downslope

parcels is small; or (2) the amount of sediment

flowing in from upslope parcels in the interior

of the watershed is large. The term

ai�1m�0 (@dn;i;i�m;j=@Xnij0) represents the effect of a

change in land use decision on the ith parcel on

deposition ratios of (i�/m ) downslope parcels2.

The indirect benefit of land retirement by the ith

parcel is large if the extent to which it raises

deposition ratios of downslope parcels by reducing

sediment runoff is large3. The benefits of increased

trapping of sediment flows on downslope parcels

become particularly important if the volume of

sediment generated by the ith parcel even after

land retirement is large. The third term

aIjn�i

m�1 (@dn;i�m;i;j=@Xnij0) represents the effect of

land retirement on the ability of the ith parcel to

capture sediment from upland parcels and it is

positive. The ith land parcel provides an external

benefit to upland parcels by trapping a portion of

their sediment and preventing it from being loaded

into the water body. Together the terms on the

left-hand side of Eq. (7) indicate the marginal

value per acre of retiring a land parcel from

cropping.

Based on the terms in Eq. (7), we can identify

two types of parcels that would be good candi-

dates for retiring from crop production. Any

cropland parcel that is close to a river, generating

a large amount of eroded soil and capable of

trapping sediment from upslope parcels when

converted to permanent cover makes a good

candidate for a land retirement program. Second,

upland parcels that substantially improve the

sediment trapping efficiencies of downslope par-

cels when taken out of crop production also make

good candidates for a retirement program. In

either case, land retirement is optimal if the

forgone quasi-rent from crop production is low.

Note that due to the homogeneity assumption, in

the optimal solution each parcel is either fully

retired or fully under crop production.

For equity reasons, or to keep transactions costs

low, social planners sometimes prefer to distribute

gains and losses proportionally. In that case,

instead of setting an abatement target for the

whole region and allocating abatement responsi-

bility non-uniformly across watersheds, the social

planner could set a uniform performance standard

for each watershed. This is represented by repla-

2 This term is positive because an increase in the retired

portion of the i th land parcel reduces the volume of sediment

runoff flowing to downslope parcels, thereby increasing the

deposition ratio of each of the i�/m parcels.

3 Hydrological models indicate that large sediment inflow

from upland parcels reduces the capacity of a land parcel to

deposit sediment.

cing constraint (5) by N constraints as follows

S0n�

�1�

Xi�1

dn;i;i�m;j

snijkxnijk]An

for n�1; . . . ;N

The optimal solution would now consist of N

values of l , which would be different in most cases

because of differences in land characteristics

among watersheds. Even though the same abate-

ment goal can be achieved either with an aggregate

abatement constraint or with a uniform standard

for each watershed, having N abatement con-

straints will increase the costs of abatement

according to the LeChatelier’s principle (Varian,1992).

3. Empirical model

The endogenous sediment transport process

causes high nonlinearity of the sediment abate-

ment constraint in the theoretical model and

precludes its use in an empirical analysis4. To

cope with this complexity, we modify the theore-tical model in two ways. First, we restrict any

possible changes in land use to only the first three

parcels of every runoff channel nearest or adjacent

to a water body. The defined area is a stylized

representation of the eligible land in the Illinois

CREP5. Justifications of this restriction are pro-

vided in the next section. Second, we consider

three-parcel chains in each runoff channel ratherthan individual parcels as the primary decision

units. For each three-parcel chain, we define

alternative land retirement scenarios that represent

all possible combinations of land management

decisions, such as crop �/crop �/crop or crop �/re-

tire �/crop , etc. If for instance, all the three parcels

that make up a chain are agricultural land, this

defines eight (�/23) combinations. For each op-

tion, the sediment flow from upland parcels is

exogenous because those parcels are not part of

the decision space. Note that the three-parcel

chains in the buffer region are linked to the inland

watershed so that runoff and sediment transport

from upland parcels beyond the eligible region are

tracked and incorporated into the sediment trans-

port process within the eligible region.

The decision problem for the social planner is to

select one of the eight land management options

for every flow channel so that a specified sediment

abatement goal is reached and the sum of forgone

quasi-rents is minimized in the program area. This

problem can be formulated as an integer program-

ming model by defining a binary selection variable

for each channel and each management option.

Although this would eliminate the endogeneity of

sediment deposition ratios of individual land

parcels, we would still have a computationally

difficult problem because even for a small wa-

tershed a large number of parcels and even more

land retirement scenarios would be involved and

therefore the resulting integer programming model

would not be tractable. However, it turns out that

even if we define the selection variables as con-

tinuous variables, which would lead to a linear

programming model, the optimal solution of the

model involves only binary values for all but at

most one pair of management alternatives for one

flow chain6. By rounding the solution for that pair

to the nearest binary values, an approximately

optimal solution is obtained. The approximation

error is extremely small and can be ignored, but

4 Optimization problems with too many nonlinear

constraints are in general harder to solve than problems with

a nonlinear objective and linear constraints (McCarl and Onal,

1989). Also, in order to define a convex programming problem

and guarantee the numerical solutions to be optimal, the

nonlinear constraint functions are required to possess certain

convexity properties (Bazaraa et al., 1993). In this particular

application, the AGNPS relations describing the sediment

deposition/transport process for multi-parcel flow chains are

highly complex and violate those requirements. Therefore, the

original nonlinear problem is computationally unmanageable.5 The defined area is 21% of the entire watershed area.

6 This is based on the theory of linear programming. A

rigorous proof is not given here for the sake of space, but it is

available from the authors upon request. Empirical results also

verified this theoretical fact. In most cases, the linear

programmiing model solutions were purely binary. Such

models are sometimes called ‘integer friendly’ linear programs

in the operations research literature.

the advantages of this method are enormous. First,we benefit from the computational convenience of

linear programming. Second, as will be elaborated

later, linear programming provides valuable sha-

dow price information that can be used to

determine economic incentives for voluntary land

retirement, which would not be possible if an

integer programming formulation was used.

An algebraic description of the linear program-ming model for finding the least-cost solution is

relatively straightforward. For watershed n , let

Znpj denote whether or not land retirement sce-

nario p is selected for channel j , and rnpj and snpj

denote the forgone quasi-rent and sediment abate-

ment, respectively, relative to the option where all

parcels are under crop production7. The model

below determines a cost-effective pattern of landretirement in multiple watersheds under an aggre-

gate sediment abatement target in the region, A:

rnpjZnpj (9)

Subject to

snpjZnpj ]A (10)

Znpj �1 for all j�1; . . . ; J (11)

Znpj ]0

for all j�1; . . . ; J and p�1; . . . ; 8:(12)

The empirical model for a uniform standard in

multiple watersheds is structurally the same as the

above model except that the aggregate sedimentabatement constraint (10) should be defined for

each watershed, that is

j�1 a8p�1 snpjZnpj ]An; for all n�1; . . . ; N:/

Note that in the above formulation the selection

variables, Znpj are defined as continuous variables

rather than binary variables. Therefore, Eq. (9)

through Eq. (12) define a linear programming

model. The shadow price, s , associated withconstraint (10) represents the marginal cost of

sediment abatement at the constrained level. It canbe shown that it would be optimal for the land-

owner to select enrollment option p for channel j if

an economic incentive equal to sspj was offered8.

Therefore, the term sspj represents the maximum

payment a social planner would be willing to offer

for a voluntary enrollment schedule that is con-

sistent with the socially optimal solution.

4. Data description

We apply the framework described above to an

area consisting of 12 contiguous watersheds inIllinois’ designated CREP region in the United

States (Fig. 1). This area lies within the boundaries

of Brown, Cass, Mason, Menard, Morgan, and

Sangaman counties in Illinois. Totaling about 250

thousand hectares, these watersheds adequately

represent the soil, terrain, crops, farming systems,

and climate found in the Illinois CREP region. For

the analysis, we partition the entire study regioninto 91-by-91 m (300-by-300 foot) parcels with

each parcel being 0.84 hectare and set the buffer

width eligible for enrollment in CREP equal to 274

meters (900 feet) along all streams and tributaries.

This parcel size matches the resolution of available

GIS data, thus minimizing problems associated

with heterogeneous characteristics within land

parcels. This definition of eligible land differsfrom the definition of riparian areas considered

to be eligible for enrollment in CREP (that is, the

100-year floodplain). For small streams in the

Illinois River Basin, this 274-in buffer generally

exceeds the 100-year floodplain boundaries, while

for major tributaries and the main Illinois River,

this buffer could be narrower than the floodplain9.

Although, for most part, this buffer closelyapproximates the floodplain eligibility require-

7 Note that rnpj and snpj are both zero for p�/1.

8 Proof of this is a straightforward matter and requires

standard linear programming theory and optimality conditions.

Therefore, it is not explained in detail here, but available upon

request.9 A 600 feet buffer is typically considered as sufficient to

meet the needs of many wildlife species, such as large mammals,

heron rookeries, bald eagles or cavity nesting birds USDA,

ment in the Illinois CREP program, it also

includes highly sloping land adjacent to streams

that is typically outside the 100-year floodplain.

The definition of the buffer area in our model is

therefore broader than the floodplain and is not

constrained by program requirements (Yang,

2000).

Several sources are used to construct the base

scenario. We assign land use to every parcel based

on a digitized land cover map from the Illinois

Department of Natural Resources (1996). For the

parcels identified as cropland, we use a crop

budget model (FaRM Laboratory, 1995) to simu-

late the input�/output relationship of crop produc-

tion and estimate cropland quasi-rents by soil

types for a typical 283-ha (700 acre) reduced-

till10 grain farm with a corn and soybean rotation.

Quasi-rents of crop production are defined as total

revenues minus total variable costs (Just et al.,

1982) and represent a farmer’s opportunity cost

for taking the land out of crop production.

Variable costs include seed, fertilizer, pesticide,

herbicide, machinery repair, labor and other

expenses that vary with crop production. Because

machinery might not be downsized or sold when

land retirement is a small portion of a farm’s land

base, fixed annualized machinery costs are in-

cluded in the quasi-rents.

The data to develop the crop budgets are

obtained or adjusted to the base program year,

1998, when the Illinois CREP started. The soil

productivity estimates by Olson and Lang (1994)

are used to determine potential crop yields. The

Illinois Agronomy Handbook (Cooperative Ex-

tension Service, 1999) is used to identify seed,

fertilizer, pesticide, herbicide and other input

requirements for representative farms. Machinery

and labor use and expenses are calculated by using

a machinery program developed by Siemens

(1998). Input and output prices, crop insurance,

and interest rates and payments for 1998 are

obtained from published sources (Illinois Farm

Business Farm Management Association, 1999;

Pike, 1999). All of the above data are used to

estimate quasi-rents per hectare by soil type and

the data are assigned to cropland parcels through-

out the watersheds using GIS.

We use the Agricultural Non-point Source

Pollution (AGNPS) model (Young et al., 1994,

1995), a storm event hydrologic model used by

Fig. 1. Study area: 12 watersheds in the State of Illinois, USA.

10 Reduced-till systems reduce the number of soil disturbing

activities or use equipment that disturb less of the soil surface.

many researchers, to estimate erosion, sediment

and other hydrological variables. A GIS interface

originally developed by Liao (1997) is modified to

prepare parcel-specific input data (obtained from

GIS data layers) for the simulation model.

AGNPS requires input data for five parameters

at the regional (or watershed) level and 23 para-

meters at the parcel level11 (Young et al., 1994,

1995). Rainfall data from the Illinois State Survey

(Huff and Angel, 1989) are used to construct a

typical 5-year storm event (9.47 cm of rainfall for

12 h) for the study area12. The 23 parameters

required by the AGNPS model for every parcel are

derived from elevation (U.S. Geological Survey,

1997), soil (USDA, 1997) and land cover (Illinois

Department of Natural Resources, 1996) GIS data

layers and other published sources. Using the

elevation data, we assign surface runoff direction

(aspect) and slope to every parcel in each wa-

tershed. Then we associate every parcel with a

unique runoff channel, the end result being about

33 thousand channels in the 12 watersheds. The

soils data layer is used to assign soil texture,

erodibility, and soil hydrologic group to individual

parcels. Similarly, we use the land cover layer to

decide Manning’s roughness coefficient, surface

condition coefficient, cropping management fac-

tor, conservation practice factor and chemical

oxygen factor for every parcel (for definitions of

these parameters see Young et al., 1994; Wisch-

meier and Smith, 1978; Walker and Pope, 1983).

The Illinois Natural Resource Conservation Ser-

vice provided the required slope-based slope length

data and runoff curve number (USDA, 1972,1986). AGNPS defaults are employed for the

remaining parameters.

Summary statistics for the study area before the

introduction of a buffer program are shown in

Table 1. The base sediment loading, obtained from

AGNPS for the specified 5-year storm event, is

about 160 thousand tons. The contributions of

individual sub-watersheds to the total sedimentloading range from 3.3 thousand to 23.7 thousand

tons. Eligible cropland within the 274-m (900-foot)

buffer along streams equals 53 thousand hectares,

which corresponds to 33% of the total cropland in

the area and 21% of the region’s total area. For the

eligible cropland, calculated averages for slope,

on-site erosion, upland sediment inflows, and

quasi-rents vary across the 12 watersheds. Forinstance, the average slopes vary between 0.9 and

3% across watersheds, while erosion generation

varies between 3 and 11 tons per hectare. There is

also considerable variability in the characteristics

of land parcels within each watershed. Variations

in two of these characteristics, slope and quasi-

rents, are shown in Fig. 2A and B. For example,

while a large percentage of the eligible land inwatersheds 1 and 2 is relatively flat (with a slope of

less than 2%), much of the lands in watersheds 11

and 12 are highly sloping. The land in watersheds

1 and 2 is also relatively more expensive (with a

quasi-rent above $360 per hectare), while a con-

siderable portion of the land in watersheds 10, 11

and 12 has a quasi-rent between $260 and $360 per

hectare.

5. Empirical results

The empirical model is implemented with a

mathematical programming software GAMS

(McCarl, 2003). For the analysis, we consider an

aggregate sediment abatement goal of 20% and

limit enrollment in the program to the croplandwithin a 274-m buffer along streams and tribu-

taries. We first examine the cost-effective alloca-

tion of abatement responsibility across watersheds

to achieve the aggregate sediment abatement goal

and its implications for the design of a non-

uniform abatement standard for the 12 sub-water-

11 The five parameters at watershed level are watershed

name, cell area, total number of cells, precipitation and rainfall

energy-intensity value. The 23 parameters at parcel level are cell

number, aspect (flow direction), receiving cell number, channel

indicator, runoff curve number (CN), slope, slope length, slope

shape, channel slope gradient, channel side slope, Manning’s

roughness coefficient, soil texture, soil erodibility (K), cropping

management factor (C), conservation practice factor (P),

surface condition coefficient (SC), fertilization application

level, chemical oxygen demand factor (COD), point source

indicator, erosion from other sources, terrace impoundments

and feedlots. Source: Young et al., 1994, 1995.12 The average annual rainfall in the Illinois is about 34

inches per year. One 5-year storm event constitutes about 10%

of the cumulative annual rainfall.

Table 1

Characteristics of the study area and individual watersheds

Characteristics of eligible croplandb

Watershed Total area (ha) Sediment loading (tons)a Eligible cropland (ha) Slope (%) Upland sediment inflow

(tons/ha)

On-site erosion

(tons/ha)

Quasi-rent

($/ha)

1 25,263 11,565 5261 1.2 3.3 4.1 438.8

2 18,193 3335 2725 0.9 1.7 3.0 360.5

3 25,951 14,796 5986 1.7 2.0 5.7 424.0

4 26,459 16,763 5310 2.0 2.6 6.6 443.1

5 18,519 9770 3686 1.7 2.6 5.7 392.4

6 12,139 9364 2103 3.2 2.6 9.4 400.5

7 28,672 20,049 6436 2.1 2.5 6.8 401.8

8 18,024 8369 4145 1.7 2.3 5.4 393.9

9 22,118 14,301 5066 2.2 2.5 6.9 413.9

10 18,758 16,899 3293 3.7 3.0 11.0 375.1

11 12,659 10,623 2144 2.9 3.9 9.5 392.4

12 23,605 23,706 6436 3.0 3.5 9.8 416.6

Total 250,360 159,540 52,591 2.2 2.7 7.0 404.5

a The sediment loading into the water bodies before land retirement under a 5 year storm even (9.47 cm in 12 h).b Average values of characteristics of eligible land parcels.

sheds. We then compare the implications of this

policy vis-a-vis the uniform abatement standard

that imposes a 20% sediment abatement goal for

each of the 12 watersheds13. The costs, hectares

retired, land retirement patterns and other results

obtained from the two model runs follow.

Given the base scenario and the specified 5-year

storm event, a 20% abatement goal translates into

a 32 thousand ton reduction in the sediment

loading in the region. As shown in Table 2

columns (2) and (4), the least-cost solution for

achieving 20% sediment abatement at the aggre-

gate level results in a fairly non-uniform allocation

of abatement across the watersheds. Watersheds 1

through 7 should abate less than 20% while

watersheds 8 through 12 should abate more than

20% of the base sediment loadings. It would be

cost-effective for watershed 1 to abate the least

(4% of base loadings) and for watershed 12 to

abate the most (33% of base loadings). This least-

cost approach would result in the retirement of

almost 3.7 thousand hectares throughout the study

area (column 6) at an aggregate abatement cost

Fig. 2. Slopes of eligible land (A) and quasi-rents (B) within and across 12 watersheds.

13 Under a non-uniform standard, the model is run for a

total of 62,816 eligible land parcels in the 12 watersheds. Under

a uniform standard, the model is run for each watershed with

land parcels ranging from 2510 to 7683.

slightly less than $1.25 million per year (column 8).As expected (see Section 2), this approach

equalizes the marginal costs of abatement across

watersheds. The equalized marginal cost per ton of

sediment abatement was found to be $71 per ton.

The marginal cost of sediment abatement multi-

plied by the sediment abatement achieved by each

land parcel determines the rental payment a

planner would be willing to make to induce thelandowner to retire that parcel from crop produc-

tion. Therefore, the payments to individual parcels

will vary from one parcel to another depending on

each parcel’s ability to trap sediment.

In contrast to the least-cost approach, a uniform

standard of 20% abatement by each watershed

would entail the retirement of about 4.3 thousand

hectares with quasi-rent losses amounting tonearly $1.53 million per year. The cost difference

between these two standards, namely $0.28 million

per year, results from enrolling more land (625

hectares) with the uniform standard. This can be

expected because imposing abatement constraints

for individual watersheds moves the optimal solu-

tion away from the least-cost solution with an

aggregate abatement constraint. The uniformstandard requires watersheds 1 through 6 to

increase their abatement and to retire more

hectares compared to the non-uniform standard,

whereas watersheds 8 through 12 would need to

retire fewer hectares than with the non-uniform

standard. Variability in land characteristics and

land use make it more expensive to retire land in

watersheds 1 through 7 than in watersheds 8through 12. Requiring all watersheds to abate to

the same extent results in varying marginal costs

across watersheds, as the conceptual framework

implies. Our empirical results show that watershed

1 would have the highest marginal cost, $256 per

ton, whereas watershed 12 would have a substan-

tially less marginal cost, $42 per ton. The largest

increases in cropland retired, sediment abated, andquasi-rent losses relative to a non-uniform stan-

dard occur in watershed 1 followed by watersheds

2 through 7. On the other hand, the marginal cost

of sediment abatement with a uniform standard

falls below $71 per ton in watersheds 8 through 12;

sediment abatement and acreage retired fall in

these watersheds, with the largest decreases inTa

($’0

.2� /

cropland retired and quasi-rent losses occurring inwatershed 12.

A closer examination of the characteristics of

cropland parcels selected and those not selected for

retirement under a non-uniform standard (see

Table 3) provides useful insights about the types

of land parcels that should be targeted for enroll-

ment. Regardless of the variability across water-

sheds, cropland selected for retirement in allwatersheds is closer to water bodies, more sloping,

more erosive, and more likely to receive larger

volumes of upland sediment flows than the crop-

land not selected for retirement. In addition, the

selected cropland parcels have lower quasi-rents.

For example, the average distance between se-

lected parcels to the river is 72 m, whereas it is 125

m for non-selected parcels. The correspondingaverages for slope are 8 and 2%; for on-site

erosion, 27 and 6 tons per hectare; for upland

sediment inflow, 7 and 5 tons per hectare; and for

quasi-rent losses, $341 and $420 per hectare,

respectively. Examining the land parcels selected

for enrollment under the uniform standard (see

Table 4), we find that their average characteristics

are similar to those obtained under the non-uniform standard, but with a generally stronger

contrast between targeted and non-targeted land.

This is again expected, because under the non-

uniform standard selection is not constrained by

the 20% abatement requirement in each watershed,

hence there is greater flexibility in selecting land

parcels to obtain the desired environmental bene-

fits at lower cost irrespective of the watershed inwhich they are located.

In Fig. 3, we compare the distribution of crop-

land selected and summarize other key character-

istics of the study area by performance standard.

Cropland parcels adjacent to streams comprise the

vast majority of land identified for retirement

under both standards. Furthermore, cropland

parcels selected in all three positions tend to bethe sloping, more erodible, less productive crop-

land. Given our study area and the complex

interactions among land use, the sediment trans-

port process and impacts on water quality, the

combination of sloping, less productive cropland

close to streams figures prominently in reducing

sediment and minimizing costs. This conclusion is

consistent with the optimality condition in Eq. (7)and the discussion of the equation’s first and third

terms and should hold across widely diverse

watersheds.

We use this insight to further understand the

factors driving the differences in costs of abate-

ment across watersheds by examining the joint

distribution of two characteristics, slope and

quasi-rents. Here, we compare watersheds 1 and12 for this purpose. Watershed 1 has the highest

marginal cost of abatement under a uniform

standard while watershed 12 has the lowest. We

find that in watershed 1, 82% of the eligible land

parcels have a slope less than 0.02 and a quasi-rent

more than $360 per hectare. Only 1% of the

eligible parcels in that watershed have a slope

greater than 0.02 and quasi-rent less than $360 perhectare. The corresponding percentages for wa-

tershed 12 are 38 and 27% (compared to 82 and 2%

for watershed 1). Thus, watershed 12 has more

eligible land that is highly sloping and cheaper (as

can also be seen in Fig. 2B) than in watershed 1.

Watershed 12 therefore provides more options for

retiring parcels with larger environmental benefits

at lower cost and this keeps its cost of abatementlower than that of watershed 1.

The results obtained above can be used to derive

some policy implications for the implementation

of CREP in Illinois. As mentioned above, land in

the 100-year floodplain is considered eligible for

CREP. Our analysis, however, shows that to

achieve the sediment abatement goal in a cost-

effective manner, highly sloping cropland adjacentto the water should be selected for retirement.

These cropland parcels often lie outside the 100-

year floodplains in the watersheds in our study

area; because of their height above the water these

land parcels seldom gets flooded although they are

adjacent to the water body and therefore contri-

bute heavily to sediment loadings into the river.

Though the floodplain cropland can be effective intrapping sediment, it is also generally more

productive and therefore more costly to retire.

The map of targeted versus non-targeted land

under a non-uniform standard in watershed 12

(Fig. 4) illustrates this point. The blocks in black

represent the parcels that our empirical model

selects for retirement. The shaded area in grey

Table 3

Characteristics of selected and non-selected parcels under a non-uniform sediment abatement standarda

Watershed Distance from river (m) Slope (%) Upland sediment inflow (tons/ha) On-site erosion (tons/ha) Quasi-rent ($/ha)

Selected Non-selected Selected Non-selected Selected Non-selected Selected Non-selected Selected Non-selected

1 70.2 122.1 7.5 1.1 8.4 3.2 24.0 3.5 390.9 439.3

2 55.5 120.2 5.8 0.8 7.4 1.6 19.7 2.9 360.8 362.2

3 67.8 122.3 8.5 1.3 4.9 1.8 28.2 4.8 342.2 427.7

4 69.4 126.0 8.3 1.6 6.2 2.4 27.5 5.3 351.9 448.7

5 66.0 128.9 6.9 1.4 5.7 2.4 24.8 4.7 331.1 464.5

6 76.2 137.3 8.8 2.6 5.0 2.4 27.2 7.5 326.2 407.7

7 81.7 122.4 9.4 1.5 7.3 2.1 30.8 5.1 341.0 406.2

8 66.7 121.4 7.8 1.4 7.9 1.9 26.9 4.3 348.8 396.1

9 66.8 123.8 7.7 1.8 6.8 2.1 27.5 5.5 347.4 418.3

10 76.1 136.5 9.3 2.8 6.1 2.5 27.8 8.2 329.9 382.8

11 71.6 126.2 7.5 2.1 7.9 3.2 26.0 6.8 332.1 402.5

12 70.8 128.0 7.7 2.2 7.5 2.9 26.9 7.0 343.5 428.5

Total 71.9 125.3 8.2 1.7 6.9 5.3 27.3 5.6 341.0 419.6

a Numbers in the table are average values of the characteristics.

Table 4

Characteristics of selected and non-selected parcels under a uniform sediment abatement standarda

Watershed Distance from river (m) Slope (%) Upland sediment inflow (tons/ha) On-site erosion (tons/ha) Quasi-rent ($/ha)

Selected Non-selected Selected Non-selected Selected Non-selected Selected Non-selected Selected Non-selected

1 71.2 129.6 3.0 0.9 5.0 2.4 9.2 3.2 432.7 439.8

2 56.4 125.2 2.3 0.8 4.9 1.3 6.8 2.6 345.2 362.0

3 76.7 123.3 7.3 1.2 4.8 1.8 23.6 4.3 348.4 430.0

4 75.3 127.2 7.5 1.5 6.0 2.3 24.2 4.9 360.0 451.0

5 69.8 129.8 6.3 1.4 5.5 2.4 22.4 4.4 338.3 466.5

6 81.2 137.9 8.4 2.5 4.9 2.3 25.9 7.3 330.4 409.2

7 84.9 122.5 9.2 1.5 7.2 2.1 30.0 5.0 342.0 406.5

8 66.7 121.3 7.9 1.4 8.0 1.9 27.0 4.3 347.9 396.1

9 67.2 123.6 7.8 1.8 6.9 2.1 27.9 5.5 346.7 418.1

10 74.6 134.7 9.9 2.9 6.3 2.6 29.8 8.6 325.9 381.5

11 65.5 123.8 8.3 2.3 8.4 3.5 29.7 7.5 324.9 399.3

12 56.9 124.3 8.9 2.6 8.7 3.1 32.0 8.2 335.1 422.0

Total 71.6 126.0 7.0 1.7 6.9 2.3 23.2 5.4 357.1 419.3

a Numbers in the table are average values of the characteristics.

adjacent to some of the streams marks the 100-

year floodplain boundary. The close-up views of

two areas in the watershed show that very few of

the selected land parcels lie within the floodplain

boundary. This pattern exists in other watersheds

also, regardless of whether a uniform or a non-

uniform standard is imposed. This result conflicts

with the program’s requirement that 85% of the

enrolled cropland fall within the boundaries of the

100-year floodplains with the remaining 15%

comprised of highly erodible areas. Instead, all

land within a narrow buffer, whether it is within a

floodplain or not, should be considered equally

suitable for enrollment to achieve the sediment

abatement goal cost-effectively.

The map of watershed 12 in Fig. 4 also reveals

another interesting conclusion that applies to

buffer programs such as CREP. The least-cost

solution for the two standards we investigated

does not result in long stretches of continuous

buffers being retired from cropland on both sides

of streams. Instead, we find a few areas of

concentration with the remaining targeted crop-

land dispersed throughout the study area. This

suggests the need for selectivity in retiring land

Fig. 3. Positions and characteristics of selected CREP land

parcels under uniform and non-uniform sediment abatement

standards.

Fig. 4. Eligible cropland and selected CREP land in watershed 12 under a non-uniform standard.

even within a narrow buffer along the water body.Finally, our results show that requiring all water-

sheds to achieve the same level of abatement can

be very costly since costs of abatement can differ

widely across watersheds. Watersheds with larger

portion of less productive cropland adjacent to the

stream and having a relatively high slope should be

required to abate more than watersheds with

largely flat, productive land.

6. Conclusions

In the U.S., policies to reduce non-point source

pollution have generally taken the form of incen-

tives rather than taxation and other ‘polluter pays’

programs. The USDA’s Conservation Reserve

Enhancement Program (CREP), for example,seeks to achieve state-specified numeric environ-

mental goals within an environmentally sensitive

region by providing financial incentives to farmers

to retire cropland. Development of appropriate

criteria for selecting the land to be enrolled in the

program to achieve the program’s goals is a

research problem of theoretical and practical

significance. In this paper, we develop an inte-grated framework that combines economic, envir-

onmental and GIS modeling to examine cost-

effective targeting of land for retirement to achieve

environmental goals in a region with multiple

watersheds. This framework is used to determine

the cost-effective non-uniform sediment perfor-

mance standards for 12 contiguous agricultural

watersheds in the Illinois CREP region and toidentify land parcels that should be enrolled across

watersheds to achieve a sediment abatement goal

of 20%. The framework is also used to compare

the costs of abatement and pattern of land

retirement under a uniform standard and the

same sediment abatement goal of 20% for each

of the 12 watersheds. We also examine the criteria

that should be used to select land parcels forretirement in each watershed under both types of

performance standards.

Consistent with the theoretical framework, a

non-uniform standard results in a lower cost and

smaller amount of cropland retired. The cropland

selected for retirement tends to be adjacent to

streams, sloping, erodible, less productive, and lessprofitable than the cropland not selected. The

runoff channels of the selected parcels also tend to

have greater upland sediment inflow than the

runoff channels where no parcels were selected.

Under a uniform standard policy, selected land

parcels differ from those under a non-uniform

standard policy in that the number of parcels

retired increases in watersheds with higher mar-ginal costs of sediment abatement and it decreases

in watersheds with lower marginal costs. Char-

acteristics of land parcels selected for retirement

mirror those under the non-uniform standard.

Several important policy implications can be

stated given our theoretical framework and em-

pirical analysis. First, the results confirm the

superiority of a non-uniform standard in minimiz-ing costs and land removed from production for

any given sediment abatement goal. With only

slight modifications, however, costs and land

retirement patterns for a uniform standard can

be estimated and compared to the non-uniform

standard, thus giving policy makers the opportu-

nity to assess the costs of policies such as

uniformly applied water quality standards onstreams.

Second, our use of a generic 274-m buffer also

produced some interesting conclusions regarding

eligibility requirements of CREP in Illinois. The

least-cost solution shows that highly sloping, less

productive cropland adjacent to streams with

significant sediment inflow from upland parcels

should be targeted for retirement. The IllinoisCREP program for the most part targets flood-

plain cropland, which is flatter, more productive

and costly. Our results instead suggest that a

buffer program which targets either sloping land

or any cropland within a narrow buffer would

likely decrease costs of sediment abatement and

acreage retired compared to a floodplain buffer

program.This study should be viewed as the first step in

the development and use of spatial economic and

environmental models for improving the design

and implementation of public conservation pro-

grams. Our integrated framework could be ex-

tended in several ways. First, the binary choice of

cropping or retirement could be increased to

include continuous cropping choices with conser-vation practices. Second, our modeling framework

could be extended to examine pollutant trading.

The least-cost non-uniform allocation of land

retirement could be achieved by a program that

allows trading of pollution permits across water-

sheds. Our results show the cost-savings that could

be achieved by allowing trading instead of requir-

ing each watershed to meet the same environmen-tal standard. Third, the hydrologic component

could be expanded to include tile drainage as well

as stream bank and in-stream erosion. There is

considerable debate among researchers regarding

the effectiveness of buffers in watersheds that have

been extensively tiled and watersheds where sedi-

ment from overland sediment flow is considerably

less compared to stream bank and in-streamerosion. Fourth, further research could be con-

ducted to study the implications of characterizing

or simplifying the endogenous pollution transport

process in model estimation. The investigation will

shed light on the errors involved in using exogen-

ously fixed pollution delivery coefficients and

developing simpler models that could be used for

policy analysis on a larger scale. Fifth, the institu-tional barriers to targeting conservation programs

and the transactions costs of targeting could be

incorporated to improve policy analysis. Finally,

more research is needed to examine how the

criteria for land enrollment would change if the

other objectives of CREP are included in our

analysis.

Acknowledgements

The authors would like to thank Hsiu-Hua Liao

for providing a prototype ARC/AGNPS interface

for our study and thank Marie Puddister for

designing figures in the paper. We also acknowl-

edge support from the Illinois Council on Foodand Agricultural Research and the Cooperative

State Research, Education and Extension Service,

U.S. Department of Agriculture, under Project

No. ILLU-05-0305. However, the views expressed

in this article are those of the authors and do not

necessarily reflect those of the Illinois Council on

Food and Agricultural Research or the U.S.Department of Agriculture.

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Integrating economic, environmental and GIS modeling to target cost effective land retirement in...

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