Cost-Effective Targeting of Land Retirement to Improve Water Quality with Endogenous Sediment Deposition Coefficients

Growing concern about the adverse effects of agricultural activities on water quality has redirected the focus of land retirement programs from reducing on-site erosion toward reducing damages to water bodies caused by sediment and chemical laden runoff from fields, and enhancing wildlife habitat. This shift in program emphasis has led to several modifications of the Conservation Reserve Program (CRP) with the most recent being the Conservation Reserve Enhancement Program (CREP). CREP was authorized as part of the 1996 Federal Agriculture Improvement and Reform Act to retire environmentally sensitive cropland in problem areas identified by states. The CRP selects land for enrollment based on their Environmental Benefits Index (EBI) (Farm Service Agency), which assigns scores to land parcels reflecting the expected environmental improvements in on-site soil quality, water quality, and wildlife habitat. The CREP, on the other hand, seeks to enroll land to achieve specific regional environmental goals.

In the case of Illinois, these goals include a 20% reduction in off-site sediment loadings, a 10% reduction in nutrient loadings, increasing populations of waterfowl and State and Federally listed species by 15%, and increasing native fish and mussel stocks in the lower reaches of the Illinois River by 10%. To achieve these goals the Illinois CREP limits enrollment primarily to a narrow buffer zone adjacent to rivers and streams. It seeks to retire 232,000 acres of cropland, 85% of which are to be selected from riparian areas (defined as the 100-year floodplains of the Illinois River and its tributaries, streams and wetlands). The remaining 15% could be selected from highly erodible cropland adjacent to enrolled riparian areas. These criteria make over 5 million acres of cropland eligible for enrollment in the program and CREP does not specify any mechanism for identifying the land parcels that should be retired.

This article develops an analytical framework to determine a cost-effective land enrollment pattern for reducing off-site sediment loadings. Furthermore, it presents a rental payment instrument to create market-based incentives for retiring land parcels from production and achieving the cost-effective pattern voluntarily, in a setting where the government can neither mandate the land parcels that it should retire nor offer payments to only select parcels. A key component of this analysis is to endogenously determine the contribution of each land parcel to off-site sediment loadings. This is a complicated issue for two main reasons. First, it requires estimation of the sediment-trapping coefficient of a land parcel, which depends not only on the characteristics and land use of that parcel, but also on the volume of run-off flowing in from upland parcels. This volume depends on land-use decisions and site-specific characteristics of upslope parcels. Second, it also requires estimation of a sediment transport coefficient that links on-site sediment generation with off-site sediment loading in a water body.

Therefore, the portion of soil transported from a land parcel to a water body depends not only on that parcel's site-specific characteristics (slope, soil characteristics, and distance from a water body) and land-use decision (crops, trees, pasture or grass), but also on highly complex interdependencies between land-use and sediment-trapping coefficients of upslope and downslope land parcels. It cannot be determined exogenously simply based on its own on-site erosion and fixed site-specific characteristics of intervening land. The EBI approach that considers all land within 0.25 miles of the water body as having the same impact on water quality and evaluates each land parcel independently of others is inadequate for this purpose. There is, instead, a need to use more detailed spatial information about the location and other characteristics of land parcels and to determine the benefits provided by each parcel in a flow path jointly or endogenously with the land-use decisions of all parcels in that flow path.

To tackle the complexity described above, this article develops an integrated framework that combines a microeconomic model and a hydrological model. The latter incorporates detailed GIS data about the spatial and physical attributes of heterogeneous land parcels and recognizes the interdependencies between them. This framework is applied to the Court Creek watershed in Illinois to identify the critical attributes of land parcels that should be selected for enrollment to achieve the desired level of watershed sediment abatement at least cost. The above framework is also used to analyze the design of a rental payment policy instrument to replicate the pattern of cost-effective land retirement obtained from a social planner's model.

Difficulties in designing and implementing a site-specific rental payment scheme have led CRP administrators to set a maximum ceiling on soil rental payments for each county (Smith). These rental rates represent the maximum allowable rental rate at which farmers can retire as many of their eligible acres as they want. All eligible offers for rental rates (dollars per acre of land retired) lower than this maximum rate are accepted by the regulator. Due to the inability to observe or measure sediment flows, such a rental rate system is expected to be easier to implement than a parcel-specific rental scheme that requires detailed information about site-specific characteristics of all parcels within a flow path to infer the contribution of a parcel to off-site sediment loading. Farmers may also perceive this system as fair compared to a system where rents vary across parcels due to unobservable differences in their sediment loadings. This may lead to lower resistance from farmers to the enactment of a rental policy based on a ceiling on rental rates per acre for the watershed. However, such a policy creates incentives for enrollment of land with low opportunity costs and not land with the highest abatement benefits to opportunity cost ratio. This can be inefficient (Babcock et al., 1996, 1997). Given the same sediment abatement goal, this article examines differences in abatement costs and in the types of parcels selected under a parcel-specific rental scheme and one establishing a rental cap for the watershed. It provides a measure of the extent to which it might be worth incurring higher transaction costs to realize cost savings by implementing the efficient rental payment policy.

This article contributes to the literature in several ways. First, it presents a conceptual and operational framework by integrating a hydrological model and a detailed GIS database with an economic model that recognizes the interdependence among land parcels when estimating abatement costs. This approach extends the methods used in previous studies, which typically assume that the relationship between on-site pollution generation and off-site loadings is exogenous and dependent on site-specific factors (Carpentier, Bosch, and Batie; Kramer et al.; Ribaudo 1986, 1989) or management practices of downslope parcels (Braden et al.). Second, this article examines the implications of this interdependence among parcels for the design of a rental payment instrument that induces the social planner's preferences in a decentralized decision making setting.¹ Lintner and Weersink also incorporated the interdependence between sediment deposition coefficients and fertilizer-use decisions on all parcels in a flow path, but assumed that all parcels were identical. Their assumption allows the sediment deposition ratio of a parcel to be dependent only on its own characteristics and reduces the true complexity of the problem of simultaneously determining heterogeneous land-use decisions and off-site sediment abatement for all parcels in a flow path.

The results of our empirical analysis have several useful policy implications. They show that the eligibility criteria for land parcels enrolled in CREP should shift from being in the floodplain to one emphasizing erodibility. Additionally, they show how rental payments per acre need to vary across parcels, which are heterogeneous in their spatial and site-specific characteristics, rather than being determined solely by the productivity-based rental cap for the watershed. Finally, the additional costs of abatement incurred by assuming fixed sediment deposition coefficients are not large with low sediment abatement goals but increase substantially as abatement targets increase beyond 20%.

Conceptual Framework

Consider a watershed that is divided into j = 1, …, J run-off channels, or flow paths, by which pollutants are transported from land parcels to a water body. Each flow path is divided into i = 1, …, I_j land parcels of equal size, α, with parcel i = 1 being the closest to the water body. Each flow path is well defined, unique, and independent of others and each land parcel is assumed to be homogeneous in terms of its site-specific characteristics. A land parcel is assumed to have a choice between two activities, denoted by k, where k = 0 indicates retirement of land and k = 1 indicates crop production. The symbol x_ijk denotes the area allocated to the kth activity. Thus we have 0 ≤ x_ijk ≤ α and

(1)

Let π_ijk be the per acre quasi-rent (total revenue minus variable costs) earned on the ith land parcel in the jth channel with the kth activity. Then π_ij0 = 0 because no quasi-rents would be earned if this land parcel is retired from cropping and converted to permanent cover. Because we are focusing on land parcels that are currently under crop production, it is reasonable to assume that π_ij1 > 0. For activity k, sediment flow generated per acre is denoted by s_ijk. The total amount of sediment produced by the ith parcel is given by.

A percentage of the sediment produced by the ith parcel, denoted by d_{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 depends on that parcel's site-specific characteristics, land-use decision, and the amount of sediment flowing into that parcel, denoted by L_i−m,j, x_i−m,j,k and S_{i − m,j}, respectively. Thus we have the functional relationship:

(2)

where

(3)

As S_i−m,j increases, the deposition ratio d_i,i−m,j in (2) is expected to decrease. The amount of sediment S_i−m,j flowing into the i − mth parcel also depends on the site-specific characteristics and land-use decisions by all land parcels that are upslope from it (indexed by i − m + 1, …, I_j).

The total amount of sediment generated in the watershed that is loaded to the water body, S, is the sum of sediment loadings from all run-off channels. With representing the sediment generated by the ith parcel that is deposited on downslope parcels, S can be written as,

(4)

Suppose a social planner seeks to achieve a targeted level of off-site sediment abatement at least cost, where cost is defined as the loss in quasi-rents due to retirement of land from crop production. This problem can be stated as follows:

(5)

subject to

(6)

(7)

where π_ij1α is the quasi-rent per acre earned by the ith parcel in the jth flow path with crop production, S^o is the total sediment loading by the watershed when all land parcels are under crop production, and is the desired sediment abatement level. It should be noted that d_i,i−m,j for the ith parcel in the jth flow path is not a predetermined coefficient, but a function of the parcel's site-specific characteristics and land-use decision and the site-specific characteristics and land-use decisions of all upslope and downslope parcels in that flow path as indicated by (2) and (3).² The Lagrangian for this optimization problem is as follows:

(8)

where λ and µ_ij are the Lagrange multipliers associated with (6) and (7), respectively (λ ≥ 0). The first-order optimality conditions imply that

(9)

and

where λ represents the marginal social cost of sediment abatement (dollars per ton of sediment) and the term in square brackets is the per acre contribution of the ith parcel to off-site sediment loadings. Thus, their product is the marginal cost of sediment abatement per acre. Since the sediment run-off from all flow paths contributes additively to the total sediment loading in the watershed, it is cost effective to pay a uniform price of λ per ton of sediment abatement to each parcel that enrolls. The shadow price, µ_ij, represents the marginal contribution (per acre) of the ith parcel in the jth flow path to the social cost of sediment reduction.

From a social planner's perspective, the net social cost is minimized by fully retiring a land parcel from production, that is, x^*_ij1 = 0, if ∂L/∂x_ij1 > 0. In this case, according to (7) we have x^*_ij0 = α > 0, which implies that ∂L/∂x_ij0 = 0. These two conditions can be rearranged to show that retirement of a land parcel from crop production is socially preferable if

(10)

Because crop production is usually a more erosive activity, we expect that s_ij1 > s_ij0. The difference (s_ij1 − s_ij0) represents the on-site sediment abatement due to retirement of land from production. The term is positive because more sediment cannot be loaded into the water body than was generated on each of the land parcels. Thus, 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 is small while (s_ij1 − s_ij0) is large. The term is small if (1) there are few or no downslope parcels that can trap the sediment generated by the ith 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 (s_ij1 − s_ij0) is large if retirement by the ith parcel leads to a large reduction in its sediment generation per acre.

On the other hand, the term represents the effect of a change in land use on the ith parcel on deposition ratios of (i − m) downslope parcels. This term is positive because an increase in the retired portion of the ith land parcel reduces the volume of sediment flow to downslope parcels, thereby increasing the deposition ratio of each of the i − m parcels. The indirect benefits of land retirement by the ith parcel are large if the extent to which it raises deposition ratios of down-stream parcels is large. These benefits through trapping sediment flows on downslope parcels become particularly important if the volume of sediment generated by the ith parcel is large even after land retirement. The third term,, represents the effect of land retirement on the ability of the ith parcel to capture sediment from upland parcels and 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 (10) indicate the marginal benefits from retiring a land parcel from cropping. They show that a land parcel should be retired from cropping under one of the following two circumstances. First, if the parcel is close to the water body and retirement results in a large decrease in its on-site sediment generation and in its ability to trap sediment flowing from upland parcels, thereby leading to a large decrease in off-site sediment loading. Alternatively, if it is an upland parcel (with many intervening land parcels) and its retirement decision leads to a large improvement in the sediment-trapping efficiencies of downslope parcels and thereby a large reduction in sediment loading in the water body.

The above analysis shows the fallacy of focusing only on retiring land in parcels with high on-site sediment generation irrespective of spatial location, that is, of retiring cropland parcels where (s_ij1 − s_ij0) is large. By ignoring the other terms on the left-hand side of (10), which determine off-site sediment abatement and depend on the location of the parcel in the flow path, the abatement benefits provided by retiring an upslope parcel would be underestimated. This analysis also shows that treating deposition coefficients as fixed rather than endogenous implies that we are setting and equal to zero and thus ignoring the second and third terms on the left-hand side of (10). This would result in an underestimate of the benefits of retiring a parcel. Furthermore, by ignoring the effect of the volume of run-off and land-use decisions of upslope parcels on deposition coefficients of downslope parcels, we may fix the coefficients d^*_i,i−m,j incorrectly and not obtain the correct estimate of the benefits of a retiring a parcel.

The Empirical Model

To apply the conceptual model developed above, the entire watershed is partitioned into parcels or small homogeneous management units that are grouped into flow paths (parcel chains or channels). There is heterogeneity across parcels in terms of soil quality, hydrological, and economic characteristics. In each flow path, only the first three land parcels adjacent to the water body are assumed to be eligible for enrollment. The rationale for this is discussed in the next section. The flow of sediment in any three-parcel chain is independent of the flow in adjacent chains.

In the model, it is reasonable to assume that each land parcel would be either fully cropped or fully retired from production. Typically, this type of “either/or” problem is formulated as a mixed integer programming problem. However, for an average-size watershed, the model would involve a large number of land parcels (if the land parcels are to be sufficiently small and homogenous entities in terms of their economic profitability and contribution to environmental pollution). Moreover, incorporating the nonlinear endogenous relationship between on-site erosion, sediment loading, and land-use decision of all land parcels would lead to a very large-scale nonlinear integer programming model that would be impossible to handle computationally.

To cope with this complexity, we develop a linear programming (LP) approximation that transforms the theoretical model into a computationally convenient empirical model. Instead of defining each land parcel as a decision-making unit, the LP transformation considers every three-parcel chain as a decision-making unit, for which we make a choice (represented by a continuous variable) among alternative land management (enrollment) plans. For each chain, we define 8 ( = 2³) alternative land management plans that represent all possible combinations of discrete enrollment decisions (retire/continue cropping) for the three parcels that make up the chain. These combinations are GGG, GGC, GCG, GCC, CGG, CCG, CGC, and CCC where C denotes crop production, and G denotes enrollment in a land retirement program that requires the planting of permanent grass cover. We denote these eight alternative management plans by p = 1, …, 8, where p = 1 corresponds to the plan with all three parcels under crop production (CCC).

For each channel j, the costs of abatement are defined as the difference in quasi-rents with crop production and those with management plan p, and are denoted by r_pj. Quasi-rents for all parcels outside the buffer are assumed to remain unchanged. Because enrollment decisions for all parcels in channel j are known under management plan p, total sediment abatement achieved by this enrollment option can be determined. This is done by using the hydrological simulation model that incorporates the s_ijk and d_i,i−m,j coefficients described above.

Let e_pj denote the total sediment generated by channel j and loaded to the water body under plan p. These coefficients are determined by site-specific characteristics of the land parcels forming that channel and specified exogenously for each plan p using the hydrological simulation model. While the deposition ratio for each parcel is still dependent on its own characteristics and land-use decision as well as those of the other parcels in the same channel, by changing the level of decision making from the parcel to the chain level we circumvent the computational difficulties arising from the endogeneity of sediment deposition coefficients of individual land parcels. After determining the cost-effective land management pattern for each chain, we determine each parcel's contribution to sediment abatement by the chain and the parcel-specific rental payments per acre required to achieve the desired land-use choices by each parcel.

To choose among the eight alternative land management plans for each chain we introduce an endogenous convex combination (weight) variable associated with the enrollment plan p for channel j, denoted by Z_pj where 0 ≤ Z_pj ≤ 1 with for all j. The algebraic model that determines the cost-effective management plan for the entire watershed is as follows:

(11)

subject to

(12)

(13)

(14)

where S^o is the total sediment loading in the watershed when all land parcels are under crop production, and is the desired sediment abatement level defined above. Note that in the above formulation the endogenous weight variables, Z_pj, are defined as continuous variables. Therefore, 11-14 define a linear program. Equations (13) and (14) imply that each Z_pj can take any arbitrary value in the range of [0, 1]. This means that for each chain the model solution can have a weighted sum of alternative enrollment plans, with the endogenous weights adding up to 1. However, in any optimal solution, all Z_pj except one pair of variables defined for a single channel j, have to take binary values, namely either 0 or 1. The reason for this is that there are 8J variables and J + 1 constraints in the model. Therefore, any basic feasible solution can have at most J + 1 positive variables. Equation (13) implies that there is at least one positive variable for each channel, otherwise the sum cannot be equal to 1. These nonzero variables determine J of the J + 1 basic variables, one variable belonging to each channel, and leave only one remaining basic variable. Thus, except for one pair of management plans for one single channel, all other channels must have Z_pj = 1 for some option p and Z_pj = 0 for all other options.

Binary solutions for the enrollment choice variables for all channels imply that the model may select one of the p plans for channel j rather than a mixed (weighted) enrollment option. Therefore, after rounding the nonbinary solution for that single channel to a binary solution, we obtain a pure binary optimal solution that very closely approximates the true binary solution of the enrollment problem that would be obtained from an integer programming formulation (where Z_pj's would be defined as binary variables).

The error involved in this approximation is negligibly small, but the convenience of the linear transformation procedure is enormous. First, the linear programming formulation enables us to solve the problem even with a large number of channels and choices of management plans per channel. Second, a shadow price interpretation of the optimal solution is now possible, unlike in the case of an integer programming formulation. This is important for determining appropriate economic policy incentives to induce the socially optimum solution. The shadow price σ associated with (12) represents the marginal cost of sediment abatement at the constrained level. It can be shown³ that for each p = 2, …, 8, the term σ(e_1j − e_pj) represents the maximum payment a social planner should offer for the land-use option p > 1 (retiring at least one parcel rather than choosing the CCC option) to the chain in channel j.

The optimal value of σ represents the marginal value payment that the social planner should pay per unit of sediment abatement. To determine the payment per acre that the social planner could offer to each parcel, we first need to disaggregate, ex post, the contribution of each parcel to the total abatement achieved by each three-parcel chain that chooses p > 1. The procedure used to make the allocation is explained here by using a particular example to estimate the contribution of each land parcel for sediment abatement. Suppose, for instance, that plan GGC is found to be optimal for a particular chain. This means that the first two parcels adjacent to the water body should be targeted for retirement and the third parcel (farthest from the water body) should not be targeted. Each parcel's contribution can be identified by examining sediment loading that would have been achieved under plans p = 1, (CCC), p = 2, (CGC) and p = 3, (GGC), with sediment loadings e_1j, e_2j, and e_3j, respectively. The total payment that should be made to the chain in channel j for plan p = 3, (GGC), is σ[e_1j − e_3j]. The difference in sediment loading between plan 1 and plan 2 can be interpreted as the sediment abatement achieved by the land retirement decision of the middle parcel alone. Then the payment for the sediment abatement of the middle parcel is σ[e_1j − e_2j]. Similarly, the sediment abatement contribution of the first parcel (adjacent to the water body) is the difference in the sediment loading between plan 2 and plan 3 and the payment is σ[e_2j − e_3j]. Note that the payments for individual parcels add up to the total payment for the three-parcel chain, that is, σ[e_1j − e_2j] + σ[e_2j − e_3j] = σ[e_1j − e_3j].

Instead of a marginal value payment, the social planner may want to establish a productivity-based rental cap for the entire watershed. Using a heuristic procedure and the relationships and parameters of the above model we determined the rental cap that would yield the targeted abatement. For any specified rental rate per acre of retired land, each three-parcel chain chooses the land management plan that leads to higher quasi-rents (including enrollment payments) than obtained by other plans. These choices in turn determine the aggregate abatement level. Here the policy question is to determine the ceiling on rental rate per acre that meets the abatement goal. To do this, we start from a low value, which does not necessarily meet the abatement goal, and systematically raise the rental rate per acre in small increments until the abatement goal is achieved. The lowest rental rate at which the abatement goal for the watershed is achieved determines the required rental cap.

Data

The framework developed above is applied to the Court Creek watershed located in Knox County, Illinois. The watershed has 61,717 acres, of which 46% is cropland, 24% is grassland, 27% is woodland, and the remaining 3% is urban, water, and miscellaneous land. We partitioned the Court Creek watershed into 300× 300-foot parcels (2.07 acres per parcel), resulting in 29,815 parcels for the entire watershed. This parcel size was chosen because it led to parcels that are relatively homogenous in their soil characteristics and slope. In addition, data could be easily obtained from GIS data sources and matched to this parcel size. Actual enrollment data for Knox County show that the size of the smallest land parcels enrolled in the program was between 1 and 2 acres, suggesting the feasibility of making such small-scale decisions.

We consider land within a 900-foot buffer (the length of the first three parcels) along all streams and tributaries of the Illinois River to be eligible for enrollment. This definition of eligible land differs from the definition of riparian areas (i.e., the 100-year floodplain) considered to be eligible for enrollment in CREP. For small streams in the Illinois River Basin, the 900-foot buffer generally exceeds the 100-year floodplain boundaries while for major tributaries and the main Illinois River, this buffer could be narrower than the floodplain.⁴ For our study, any sloping cropland adjacent to a stream or a riparian buffer within 900 feet of a stream is also considered eligible for enrollment in CREP.⁵

Three types of data were used for this analysis: spatial and topographical data, sediment runoff data, and economic cost data. A satellite image of the Court Creek watershed was used to identify land use in every parcel (Illinois Department of Natural Resources). Publicly available GIS databases were used to obtain elevation data (U.S. Geological Survey), location of streams, the watershed boundary (Illinois Department of Natural Resources), and soils data (Illinois Natural Resource and Conservation Service). These were used to assign slope, distance from the nearest water body, and soil characteristics (soil type and erodibility properties) to every parcel.

Information on each parcel's slope and aspect relative to the stream or river were then used to create flow paths or channels that directed the flow of runoff from upslope areas in the watershed to the nearest water body. We identified 2,318 channels that had an outlet to a water body. Flow channel length varied considerably; 277 channels were only one parcel long, 563 channels were two parcels long and 1,478 channels were three or more parcels long.⁶ The buffer area for the 2,318 channels equaled 5,837 parcels (12,083 acres) of which 3,948 parcels (8,172 acres) were under crop production.

Sediment run-off data for the eight alternative land-use patterns described above were generated by using a hydrological model, Agricultural Non-Point Source Pollution (AGNPS). The model was parameterized to reflect the hydrological conditions in the watershed. Many of the AGNPS parameters such as curve number, Manning's coefficient, surface condition coefficient, cropping factor, conservation factor, and chemical oxygen demand were obtained from USDA publications (U.S. Department of Agriculture 1972, 1986) and adjusted in consultations with state Natural Resource Conservation Service officials to fit the conditions in the Court Creek watershed.

We obtained rainfall data for Illinois from the Illinois State Water Survey (Huff and Angle). These data were used to construct a five-year storm event (3.73 inches of rainfall for twelve hours) for the Court Creek. AGNPS was used to obtain estimates of the channel deposition ratio coefficients d_pj for every land management plan in each flow path.

The opportunity cost of enrolling land in a conservation program is the forgone quasi-rent from crop production, defined as total revenues minus total variable costs. Variable costs included costs of seed, fertilizer, herbicides, costs of machinery repair, labor, crop insurance, and interest. The annualized per acre costs of machinery and equipment were considered fixed costs that did not vary with the land retirement decision and hence were included in the opportunity cost of land retirement. Quasi-rents per acre were estimated for a 700-acre farm, the average-sized commercial operation in Northwestern Illinois, growing corn and soybean using reduced-till and no-till systems,⁷ respectively (details are discussed in Yang). Quasi-rents varied across parcels because crop yields and inputs changed according to each parcel's soil productivity rating. Soil productivity information in Olson and Lang was used to determine maximum potential crop yields. For corn, the estimated crop yields varied between 82 and 188 bushels per acre; for soybeans, between 26 and 60 bushels per acre. These expected yield estimates were used together with recommended input-output ratios based on the Illinois Agronomy Handbook (Cooperative Extension Service) to determine the quantities of seed, various fertilizers, and pesticide inputs required per acre. The costs of machinery and labor required for a 700-acre corn and soybean farming operation were calculated by using a machinery program developed by Siemens. We collected data on output and input prices for 1998 from various state sources (Illinois Farm Business Farm Management Association, Pike). Using all of the above data, we calculated quasi-rents per acre for the 3,948 eligible cropland parcels. Quasi-rents range between $111.3 and $204.9 per acre, with the average quasi-rent being $161.8 per acre.

Summary statistics for the eligible cropland parcels are provided in table 1. Land parcels differ considerably in their slopes, quasi-rents per acre, and on-site erosion. Slopes range between 0.5% and 15%, with 59% of eligible parcels having a slope of 2% or less and only 9% of the parcels having a slope of 10% or more. While some parcels have very erodible soil and generate 26.8 tons of on-site erosion per acre others are less erodible and generate only 0.5 tons of on-site erosion per acre. The amount of sediment from inland areas in the watershed that reaches the parcels in the buffer zone also varies across the flow paths and ranged between 0 and 62.9 tons.

Results

The optimization model was solved with sediment abatement goals of 10%, 15%, 20%, 25%, and 30% relative to the base sediment load for each of the three storm events. The base scenario, with land use according to the satellite image and a five-year storm event resulted in 18,640 tons of sediment being deposited in the watershed's waterways. The 3,948 eligible cropland parcels earned a total quasi-rent of $1,322,675 per year.

To achieve a 20% sediment abatement goal under a five-year storm event (abatement of 3,728 tons of sediment loading), we find that 10.9% of the eligible cropland acreage would need to be targeted for retirement from crop production (table 2). The cost of 20% abatement, measured by the forgone quasi-rents on the retired land parcels is $115,476. Table 2 also shows that the sediment abatement goals of 10% and 30% require 3.7% and 23.8% of cropland within the buffer to be targeted for retirement, respectively. The corresponding estimates for abatement costs are $38,809 and $265,002. The marginal cost of abatement rises steeply as the abatement target becomes more stringent, increasing from $29.2/ton with a 10% abatement target to $54.1/ton and $117.6/ton with 20% and 30% abatement targets, respectively.

For each of the sediment abatement goals considered here our results show that for the Court Creek watershed, the less productive, highly sloping, highly erodible cropland adjacent to streams should be targeted for retirement to achieve cost-effective abatement. For example, with a 20% sediment abatement goal, 22.5% of the parcels adjacent to the water body are selected for enrollment while only 7.6% and 1.7% of the parcels in the second and third positions are selected. Of the parcels selected that were adjacent to the water body, 96% had a slope of 5% to 15% with an average on-site erosion rate of 12.8 tons per acre for the five-year storm event. All of the selected second and third land parcels from the water body had a slope between 5% to 15%. Parcels not selected typically had slopes less than 5% and generated an average on-site erosion of 3.1 tons per acre.

To gain further insight into the site-specific characteristics of land parcels that determine their selection for retirement, we estimate a probit regression equation with the binary choice variable, to crop or retire, as the dependent variable. As shown in table 3, the sloping parcels adjacent to the water body and the parcels belonging to the channels that receive a relatively larger volume of sediment from upland areas are more likely to be selected for land retirement. The regression results show that it is preferable to capture the sediment at the end of the flow channel by retiring parcels adjacent to the water body, rather than to reduce sediment generation by retiring upslope parcels that are further from the water body. Those parcels with high on-site erosion and high sediment trapping efficiency are also given priority.

Both the slope of a land parcel and its soil erodibility index influence on-site erosion generation on a parcel, although the effect of the former is more statistically significant. Since highly sloped parcels next to the water body do not have the benefit of having downslope parcels on which to deposit their own on-site sediment and sediment from upslope parcels, land retirement was an effective way of reducing their sediment loadings in the water body. As a result, retiring these parcels provides relatively larger abatement benefits compared to other parcels that have either a flatter slope or are farther from the water body. The selected parcels also have a relatively lower quasi-rent as compared to the parcels that are not selected for enrollment, but the effect is not statistically significant.

These results have important policy implications. They indicate the importance of both slope and location of the land parcel in determining the abatement benefits it can provide and in influencing the policy maker's criteria of whether to retire that land parcel. The results also show the need for selection criteria to incorporate the volume of sediment flow from upslope parcels as a determinant. More importantly, our findings demonstrate that instead of the entire floodplain being eligible for enrollment in CREP (as is the case for the CREP currently), the eligible area can be restricted to a narrower zone adjacent to the water body if sediment abatement is the primary concern. Additionally, the results show that most of the land selected for enrollment is from the highly sloping and highly erodible areas rather than the flat floodplains that are not highly erodible. This implies that the current operation of CREP that requires the bulk (85%) of the land to be enrolled to be selected from a floodplain and only 15% should be from the highly erodible land category is unduly restrictive and contrary to the enrollment pattern required for cost-effective abatement.

We also examined the impact of incorporating endogenous sediment deposition coefficients on the costs of abatement and the pattern of land retirement vis-à-vis assuming that the deposition coefficients are fixed exogenously. For this, the coefficient for each parcel is fixed at the level that would be obtained if that was the only parcel to enroll and it is maintained at that level irrespective of the land enrollment decisions made by the other two land parcels in that chain. For example, the sediment deposition coefficient of parcel 3 (the parcel furthest from the water body) is fixed at the level determined under the plan GCC. This coefficient is assumed to remain unchanged even if the management plan changes to GGC, GCG, GGG.

Comparing the results obtained with endogenous sediment deposition coefficients, we find that the fixed coefficients assumption implies a significant increase in the abatement cost, $133,681 instead of $115,476 (at the 20% abatement level). This occurs because under the assumption of exogenous coefficients 15% more land parcels need to be enrolled. The fixed coefficient model underestimates the abatement benefits because it ignores two of the three terms in equation (10), specifically a retired parcel's enhanced ability to trap sediment from upland parcels and to increase the deposition coefficients of downslope parcels. The number of additional parcels selected by the fixed coefficient model increases significantly with the abatement goal (see (table 2)). By comparing the results for alternative abatement levels we find that at low sediment abatement goals, incorporating endogeneity has a minor impact on the costs of abatement. However, as the sediment abatement goal increases, endogeneity plays a much greater role, in terms of both the number of parcels enrolled and the abatement costs required to achieve the goals. For example, with a 30% abatement goal, the number of parcels enrolled increases from 940 with the endogenous coefficients model to 1,262 with the fixed coefficient model. Additionally, the number of first parcels enrolled increases more than others. The percentage of first parcels enrolled is 53% with a fixed coefficient model, instead of 41% with the endogenous coefficients model. The corresponding percentage of the second parcels is 28% instead of 20% and of the third parcels is 13% instead of 9%. The relatively large increase in the number of first parcels enrolled with a fixed coefficient model is due to the omission of the positive externality created by retiring upslope parcels on the trapping efficiency of downslope parcels. Many more first layer parcels have to be enrolled to abate sediment flow with a weaker trapping efficiency.

Conclusions

This article develops an integrated modeling framework and a numerical method to identify land parcels that should be targeted for enrollment in a riparian buffer land retirement program seeking to meet specific off-site sediment abatement goals cost-effectively. It combines GIS data with a hydrological model to quantify the sediment transport process and to incorporate interdependence between sediment deposition coefficients and land-use decisions of all parcels in a flow path. We also analyze the design of the cost-effective land rental scheme and show that per acre rental offers should be parcel specific.

The empirical results show that retirement of only 10.9% of the eligible cropland within a 900-foot buffer is sufficient to meet a 20% sediment abatement goal during a typical storm event in that region. The goal was achieved by retiring sloping, less productive cropland with erodible soils adjacent to streams. The parcel-specific rental policy needed to achieve cost-effective land retirement may be politically and administratively difficult (even infeasible). However, under the alternative approach of setting a rental cap per acre for the entire watershed, the social cost of achieving 20% sediment abatement is 38.6% higher than that with the cost-effective rental payment policy. The above analysis also shows that incorporating endogeneity in determining land retirement may not matter much for low sediment abatement goals but as the abatement goal becomes more stringent a larger amount of land would be enrolled unnecessarily if the endogeneity of sediment trapping efficiency is ignored.

These results suggest several ways of modifying CREP to achieve cost-effective abatement. First, the selection of parcels adjacent to a water body indicates the need to restrict the eligible zone for CREP to a buffer area that is narrower than the typical flood plain, particularly along the main tributaries of the Illinois River. In fact, for moderate sediment abatement goals (10–20% in the watershed considered here), the eligible parcels could be restricted to those adjacent to the water body with high erodibility coefficients. Second, the absence of relatively flat cropland parcels (that are typically found in the floodplain) in the selected cropland suggests that it would be preferable not to seek 85% of the enrolled crop land to lie in the flood plains and only 15% to lie in the highly erodible sloping areas. Instead, all land within a narrow buffer, whether it is within a floodplain or not, should be considered equally suitable for enrollment. Finally, the rental payment per acre to induce enrollment should be modified to vary across land parcels at least in a few observable dimensions, such as slope and location of the parcel, rather than being based solely on the productivity potential of the parcel. This increase in the flexibility of the rental instrument could achieve some cost savings while keeping transactions cost low.