A Multi-objective Approach to Integrating Agricultural Economic and Environmental Policies

jem p109

13-11-95 09:38:46

Journal of Environmental Management (1995) 45, 365–378

A Multi-objective Approach to Integrating Agricultural Economic and Environmental Policies P. G. Lakshminarayan∗, S. R. Johnson∗, and A. Bouzaher† ∗Center for Agricultural and Rural Development, Iowa State University, Ames, IA, U.S.A. and †The World Bank, Washington D.C. 20433, U.S.A. Received 15 December 1994

Agricultural nonpoint source pollution of soil and water resources is a major societal concern. Because of unabated NPS pollution, and despite more than a decade of policy, research and intervention, the relationship between agricultural production and environmental performance is still the subject of ongoing debate. Invariably, the environmental objectives conflict with one another and the policy choices involve significant trade-offs. The trade-off between soil erosion and water quality is a typical example of this contradiction. This paper describes a theory and conceptual framework for integrated agricultural economic and environmental modelling using a multicriteria decision-making approach grounded in multi-attribute utility theory. The empirical analysis and policy exercise evaluates policy trade-offs using a watershed-based model. The intent is to develop and implement a framework for policy analysis that provides for a better understanding of why some environmental problems persist despite evolving policies, technologies and market incentives. The multi-objective decision-making model is empirically verified for a specific eastern Iowa watershed. Two key results stand out from empirical analysis. There is a significant trade-off between economic and environmental goals, and even between environmental goals; therefore, a comprehensive analysis with reasonable compromise will give an ideal solution. Incorporating environmental objectives encouraged more environmentally sound cropping practices. In particular, environmentally sustainable crop rotation practices such as corn-soybeans-hay/oats was chosen more frequently by the model.  1995 Academic Press Limited

Keywords: multicriteria, trade-off, soil erosion, agricultural chemicals.

1. Introduction Agricultural nonpoint source (NPS) damage of soil and water resources is a major societal concern. Because of unabated NPS pollution, and despite more than a decade Journal Paper No. J16112 of the Iowa Agriculture and Home Economics Experiment Station, Ames, Iowa. Project No. 3291. 365 0301–4797/95/040365+14 $12.00/0

 1995 Academic Press Limited

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of policy, research and intervention, the relationship between agricultural production and environmental performance is still the subject of ongoing debate. Agricultural NPS policies, which are mostly piecemeal, are directed at protecting a single resource and may have a negative impact on other environmental resources. Invariably, environmental objectives conflict with one another and policy choices involve significant trade-offs. The trade-off between soil erosion and water quality is a typical example of this contradiction (Faeth and Westra, 1993). Increased chemical use with conservation tillage may lead to water quality impairments, suggesting that the soil conservation objective may conflict with the water quality objective. On the other hand, policies imposing water quality standards may shift cultivation practices away from chemicallyintensive conservation tillage. These shifts may lead to increased soil erosion, surface runoff and sediment loading. Theoretical evidence on agricultural and environmental policy conflicts is inconclusive at best (Leathers and Quiggin, 1991). Answers to policy issues involve empirical questions and are crucial for successful NPS pollution policy (Anderson et al., 1985; Bernardo et al., 1993). Mounting environmental concerns and problems of sustainable agriculture linked to improvements in environmental performance underlie the urgent need for added research and methods to support innovative integrated economic and environmental management. Consequently, a comprehensive analytical framework is needed to integrate the environmental effects of agricultural production. For instance, the evaluation of multiple soil and water quality objectives can be an important planning tool when designing innovative programs to promote cost-effective nonpoint source regulations. The integrated economic and environmental systems, for comprehensive public policy evaluation, typically have multiple objectives. In particular, agricultural NPS pollution policy issues involve multiple environmental and economic objectives. There are significant gains from considering all these objectives simultaneously in a multiple objective framework instead of addressing them piecemeal. This paper describes a theory and conceptual framework for integrated agricultural economic and environmental modelling using a multicriteria decision making approach grounded in multi-attribute utility theory. The empirical analysis and policy exercise evaluates policy trade-offs using a watershed-based model. The intent is to develop and implement a framework for policy analysis that provides for a better understanding of why some environmental problems persist despite evolving policies, technologies and market incentives. A major challenge of the policy exercise, however, is obtaining the excessive sitespecific data needed for quantifying selected environmental attributes. A simple and scientifically valid statistical procedure for estimating site-specific attributes and aggregating them to regional levels called metamodelling is used. The metamodel is a simple response function fitted to the biogeophysical outputs from calibrated mathematical simulation models (Bouzaher et al., 1993). Lately, the strategy of combining simulation models with mathematical programming models in order to evaluate alternative resource policy scenarios has become the state-of-the-art technique for integrated assessment (Ellis et al., 1991; Wossink et al., 1992). Conducting site-specific field experiments at various locations within a region to assess environmental impacts of agricultural practices is an immense task. Hence, calibrated biogeophysical process models have been applied to augment this extensive task. Estimating simple response functions to explain the output from complex process models is a powerful tool that simplifies the burden of computation implied by this integrated policy evaluation system. The multi-objective decision making model is empirically verified for a specific

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eastern Iowa watershed. This is an agriculturally important area and a major watershed drained by the two major river systems, the Mississippi and the Des Moines River. It is important both for crop production and nonpoint pollution potential. Comprising nearly 25 million acres of cropland (6% of the national cropped area) it produced $4.3 billion worth of crops, representing about 5% of total U.S. crop receipts. The intensive production and chemical use, coupled with diverse ecosystems, makes this an ideal watershed to study. The U.S. Geological survey (1991) reported that 27% of the samples tested from the river showed concentrations of atrazine, a major corn herbicide, exceeding the maximum contaminant level (MCL) for drinking water. A similar study for groundwater reported 24% of the municipal wells in Iowa had detectable concentrations of atrazine (USGS, 1993). Madison and Brunett (1984) report that 5–10% of the wells sampled in Iowa showed nitrate-nitrogen (NO3−N) concentrations exceeding the MCL (10 mg/l). The annual rate of sediment loading and the associated cost of desilting are also of concern.

2. Theory and conceptual framework Agricultural NPS impacted soil and water resources are externalities characterized by a lack of market and price signals. These generally result in Pareto sub-optimal allocation of resources from society’s point of view (Baumol and Oates, 1975). Optimality requires that the value marginal product of the externality-causing input be set equal to its price and also to the cost of marginal social damage of the externality. Usually, Pigouvian taxes (that is, taxes set equal to the marginal social cost of damage of the effluent, evaluated at the optimum effluent level) achieve socially optimal solutions to externality problems in the absence of other market distortions. The social costs of effluent damage are generally unknown; therefore, quantity-based regulations are usually prescribed for NPS control. In the absence of incentives or any alternative mechanism, the social costs of NPS damage will not be internalized. There are several factors motivating producers to internalize soil erosion damage. Miranda (1992) found that farmers in the midwestern United States incorporate the intertemporal consequences of land management decisions, particularly the on-farm productivity losses from topsoil erosion. In addition to economic motivation, public policy-induced motivation can also be cited. Conservation Compliance, which ties commodity program payments to good stewardship, would be an adequate incentive to minimize soil erosion. Unlike soil erosion, the motivation to internalize externalities from agricultural chemical use is not obvious. The current NPS pollution policy debate, motivated by society’s concern about groundwater and surface water pollution, is likely to mandate specific institutional regulations to internalize agricultural chemical-related externalities. 2.1.      One reason for not being able to alleviate agricultural NPS pollution is the piecemeal approach embodied in resource and environmental policies. That is, the institutionspecific public policies focus on a single attribute on a piecemeal basis, ignoring its relationship to other attributes. Piecemeal policy that generally focuses on a single attribute of a targeted resource, independent of other attributes that are elements of the vector determining the quality of that resource, may lead to elevated levels of

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unregulated attributes. The following proposition characterizes the need for multiple objective treatment of agricultural NPS pollution policy (Lakshminarayan, 1993). Proposition 1. A fundamental assumption in piecemeal NPS regulation is that the externalities addressed by them are independent. This is unrealistic, given the highly interdependent biogeophysical processes determining the performance of environmental resources. Because these are interrelated processes, the regulations must focus on the vector of attributes to minimize unfavorable trade-offs and maximize welfare gains. Assume the existence of a well-defined social utility function U, which is a function of soil quality (L), water quality (W), and economic returns (R), U=u(L, W, R)

(1)

U is an increasing function of L, W and R assumed. Let L, W and R be determined by one or more of the following factors: tillage (t), chemicals (c), and output (Q). L=l(t,c,Q),lt , lQ <0 and lc > 0

(2)

W=w(t,c), wt >0 and wc <0

(3)

R=r(Q), rQ >0

(4)

where the subscripts denote partial derivatives and all the functions are assumed twice differentiable. For sake of simplicity, we assume a direct relationship between the level of chemical input and water quality. The intensity of tillage, which is directly related to soil erosion, could be measured by the amount of surface residue cover. More tillage (meaning less residue cover) impairs land quality by eroding the topsoil at an increased rate. In addition, more tillage implies less chemical use. Increased chemical use under a conservation tillage system may reduce soil erosion but may lead to increased chemical residues. Substituting (2)–(4) into (1), we get: U=u[l(t,c,Q); w(t,c);r(Q)]

(5)

The underlying preferences embodied in U are assumed to satisfy the axiomatic conditions and the function u is assumed smooth and quasi-concave (Varian, 1984). Using the multi-attribute utility function (5) we can graphically show the condition for optimality and trade-off between soil and water quality, holding net returns at a predetermined level, R. Figure 1 illustrates the model for analyzing the trade-off between soil and water quality. Soil and water quality are plotted on the vertical and horizontal axes, respectively. Point B is the initial distribution of soil and water quality. Curve XY is the trade-off frontier or the transformation function, which is an envelop of all feasible Best Management Practices (BMPs) for a given level of net returns. Along this frontier, marginal rate of transformation (MRT) measures the sacrifice of soil quality for a unit increase in water quality; that is, MRTL,W =(dL/dW )=(dh/dW )/(dh/dL)

(6)

where h(W,L;R) is a convex function, the transformation locus. The utility function of the agent, expressed as iso-value utility (indifference) curves, is overlaid on the transformation curve. The indifference curve measures the marginal rate of substitution (MRS) between soil and water quality and is defined as: MRSL,W =−(dL/dW )=(dU/dL)

(7)

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X

A

B

369

T'

C D

U2 T h(L,W;R)

U

U1(L,W;R)

0

T Water quality (W) Figure 1. An illustration of a soil and water quality trade-off.

The initial allocation B is feasible but the agent can move towards the boundary of the feasible set, which is the transformation locus, and achieve higher utility. The agent maximizes his utility at point D, where MRT=MRS; that is, the point of tangency between transformation frontier (XY) and the iso-value utility curve (U1 ). This follows from the separating hyperplane theorem (Varian, 1984). The negative slope of the hyperplane (TT′) that separates the two sets, which is tangent to the transformation locus and indifference curve, indicates the relative marginal values of soil and water quality for a given return R. Denoting the marginal trade-off of soil quality for the water quality as a weight k, then the slope of the indifference curve U1 at point D is the negative of the ratio of the weights attached to soil and water quality in the utility function. Therefore, the transformation frontier can be traced by changing the weights. 2.2.    Agricultural NPS pollution is a multidimensional phenomenon embracing different disciplines, such as physical, natural and socio-political sciences. Therefore, an integrated modelling framework that embraces these disciplines is proposed (Figure 2). The integrated system conceptualized consists of economic, environmental and policy modules. This framework demonstrates the economic relevance of the agricultural production decisions, as well as the environmental consequences of those decisions. It also depicts simultaneous interactions with the policy module and the implications of alternative policy regulations on the economic and environmental systems. The economic module simulates the agricultural economic decisions and the producer’s behavior. The environmental module describes the impact of those production decisions on the resource media. Metamodels play a key role in integrating these two modules. The policy module reflects the public and producer concerns in the form of regulations that balance the interests of conflicting groups.

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Metamodels Crop yield

Policy module Tillage Fertilizer Herbicide

Agri-economic decision model Weed control subsector

Herbicides

Nutrients

Soil erosion

Physical process model (EPIC/WQ)

Multicriteria decision making model

Economic indicators

Environmental indicators

Farm income Crop acreage Tillage

Trade-off analysis

Weather input

Chemical concentration Soil erosion

Soil, Hydrology, Management

Figure 2. A multicriteria decision framework for integrating agricultural and environmental policies.

2.3.       In this section the integrated framework is formalized as a multicriteria decision-making problem and a solution method is presented. Let e be the vector of spatial characteristics impacting the production of both output and nonpoint pollution. The nonpoint pollution functions of each environmental indicator are given by D=d(z, hz , e)

(8)

where D is a vector of resource-specific damage, z is the vector of environmentally benign input levels, and hz is the vector of characteristics (properties) of z including the management conditions that influence emission. This is a simple characterization of the environmental damages as functions of input quantities and the spatial and environmental factors, such as meteorological conditions, local hydrological features and soil properties. Assuming an exogenously given price and policy vector (p, C), the watershed manager’s problem is Maxx,zP=p(x, z, e; p, C,) and

(9)

MinzD=d(z, hz , e)

(10)

subject to resource, technological, physical, and institutional constraints. Equations (9) and (10) are the reduced form representations of the economic and environmental models. Note, that P and D are functions of input use and environmental characteristics. Therefore, the production decisions generate a joint distribution of output, input use and pollution implying that targeting a single factor will affect the joint distribution that may exhibit undesirable trade-offs (Hochman and Zilberman, 1978; Antle and Capalbo, 1991). Hence, solving this problem in a multiple objective framework will be “efficient” in an overall welfare sense. To simultaneously evaluate these conflicting objectives, MCDM tools are required (Cohon, 1978). MCDM represents a useful generalization of the more traditional single-objective problems. Mathematically, the MCDM problem is stated as,

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maximize f(x)=[f1(x), f2(x), . . . , fq (x)] s.t. x M X={x|gj(x)Ζ0, j=1,2, . . . , m; x[0}

(11)

where x is an n-dimensional vector of decision variables. The functions f1, f2, . . . , fq are the q-real valued attribute functions defining the attribute of relevance and x is a non-empty, closed, and compact set defined by a set of m constraints dictated by the physical processes and resource endowments. The feasible set X is convex and fi is smooth and concave supposed. The solution method essentially involves aggregation of these attributes fi by some rule. Unlike in the scalar optimization problems, there is no single “optimum” solution to vector maximization problems because a solution that maximizes one objective will not, in general, maximize any of the other objectives. The vector maximization problem identifies a set of efficient solutions x∗ in the decision space, or equivalently, non-inferior solution f(x∗) in the criterion space. Definition. A point x∗MX is said to be an efficient solution if and only if there does not exist x¯ MX such that f(x¯)[f(x∗) and for at least one value of i, f(x¯ )>f(x∗). That is, any solution for which none of the criterion functions can be improved without causing a degradation in any other is a non-inferior solution. The Kuhn-Tucker conditions for non-inferiority are assumed to hold (Zadeh, 1963). The method employed to solve this problem should be simple and adequately related to the theoretically appealing multi-attribute utility. Because of the simplicity of distancebased methods, their relationship to the multi-attribute utility theory, and the availability of solution algorithms, they are favored by many researchers. More specifically, the distance method minimizes some measure of weighted distance from a reference point. By carefully selecting weights, distance metric and reference point we can adequately relate the resulting method to the preference-based method. Depending on the choice of distance metric and the definition of reference point, the methods differ. The Lpmetric (Minkovsky metric) is the most commonly employed measure. It is represented in its general form as,

C] q

Lp =

i=1

| ai−bi | p

D

1/p

, 1ΖpΖ∞

(12)

where (a1, a2 , . . . , aq ) and (b1, b2 , . . . , bq ) are the coordinates of the two points, the distance between them being minimized. In a multi-objective problem context, the distance between the objective and its reference point is minimized. If the reference points are goal levels for each of the attributes, then it is solved as a goal programming problem (Charnes and Cooper, 1961). Alternatively, if some notion of “ideal” is used as the reference point, then the method is called compromise programming. Both goal and compromise programming have applications in agricultural planning and agricultural policy-related problems (Zeleny, 1982; Lakshminarayan et al., 1991; Romero, 1991). The goal programming technique has widespread application for private and public sector problems. The goal programming technique is often of value in modelling and analyzing multi-objective problems, and it provides a reasonable analytical structure for these, although it is far from a panacea. Goal programming is related to the multi-attribute utility theory in that it embodies additively separable preference structure (Hannan, 1984). Let the goal for the ith objective be denoted as Gi, then the traditional weighted goal programming formulation is:

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min d=Ri ki | Gi−fi(x) | s.t. x M X

(13)

where the objective function minimizes the weighted sum of the absolute deviations of the outcomes from the specified goals for each objective. Thus, the formulation in (13) is identical to the Lp-metric with p=1 and the goals Gi replacing the ideal values f∗i where f∗i is the optimal solution to the single objective problem. A major weakness of the traditional goal programming formulation is that a “good” becomes a “bad” at a critical threshold level. For the case of profit objective, penalizing positive deviation of profit from the goal is equivalent to saying that more profit is bad which is not rational. Rational agents should consider it as “good” if the realized profit exceeds the goal. That is, the agent would be concerned only if the profit fell below the goal. For environmental pollution the agent would likely consider it as “good” if the realized level of pollution was less than the goal, and would be concerned only if the level of pollution realized exceeded the goal. Therefore, a piecewise linear approximation for the formulation in (13), which is an appropriate approximation for most of the economic-environmental policy problems, is − + + min Ri (k− i di +ki di ), s.t. + fi (x)+d− i −di =Gi ,

(14)

x M X, and the nonnegativity. The values of di are associated with positive coefficients in the objective function, which guarantees their status as structural variables, and not slack variables. Therefore, the first line in the “constraint block” is a set of equations, so their corresponding dual variables are not constrained to be non-negative. Charnes and Cooper verify this by solving the dual for a simple goal attainment problem for a machine-loading example (1961, pp. 219–221). The Langrangean for this problem is − + + − + min L=[k− i di +ki di ]+ui [Gi−fi (x)−di +di ].

(15)

The solution follows from the following Khun-Tucker conditions: xk :

−ui (dfi/dxk)=0

d− i :

− − (k− i −ui)≥0 and di (ki −ui)=0

+ i

d :

+ i

(16) + i

+ i

(k +ui)≥0 and d (k +ui)=0

(17) (18)

− + + If d− i >0⇒ki =ui , from (17), then di =0 and (ki +ui)>0; substituting for ui from − + + above get ki >−ki . Thus the solution to (15) requires k− i >−ki and that the product − + of the deviation variables is equal to zero holds for all i(di di =0!i). The later condition, however, need not be imposed for all iterations in the solution of the goal programming problem since only equivalence at an optimum is required. For environmental management problems, this piecewise linear goal programming formulation is ideal. It is not difficult to articulate goals for environmental objectives. Environmental policy includes threshold limits for resource degradation. Therefore, it is reasonable to have a target that the potential for resource degradation is within the threshold limit. Taking the soil erosion example, if erosion exceeds the natural rate of growth for soil, represented by the soil loss tolerance or T-value, then long-term sustainability may be in jeopardy. Accordingly, a typical goal might be to keep soil losses within the threshold limit.

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3. Empirical models and methods 3.1.   A regionally delineated linear programming, comparative static and partial equilibrium model constitute the economic decision model. The economic objective measures shortrun total net profit. The model determines optimal patterns of resource use and production practices, following traditional regional LP models (Hazell and Norton, 1986). A detailed weed control subsector linked to crop production through herbicide management practices, productivity response, resource use and chemical cost is incorporated to simulate substitution between the chemical and mechanical weed control methods (Bouzaher et al., 1992). Activities of the LP model are grouped into four subsectors. The activities in the crop production subsector are defined as acres of non-irrigated crop rotations on highly and non-highly erodible land. Highly and non-highly erodible land are treated separately for modelling Conservation Compliance. Eighteen major crop rotations covering major crops (corn grain, corn silage, soybeans, oats, winter wheat, sorghum, legume hay and non-lugume hay), four tillage practices (conventional till fall plow, conventional till spring plow, reduced till and no till), and two conservation practices (straight row and contour methods) are included. In the government program, subsector activities are defined in relation to production activities. The Conservation Compliance, CRP, deficiency payment and the Normal Flex programs are farm program activities that are defined. In the buy-inputs and marketing subsector, activities are defined for the principal variable inputs of labor, fertilizer and chemicals. In the weed control subsector, activities are modelled as acres of herbicide-treated acres and chemical activities, representing amounts of individual chemicals. Each weed control activity is defined as a strategy, which is a set of information on primary and secondary herbicide treatments including non-chemical control, effectiveness, yield loss and cost (Bouzaher et al., 1992). There are a total of 488 weed control strategies for corn and 148 strategies for sorghum, which allows for substitution between herbicides and between herbicide and mechanical weed control. 3.2.   Monitoring and simulation modelling are two approaches to assessing soil and water quality. Monitoring is the first-best option, but the usefulness of monitoring data depends on the design and implementation of the monitoring effort. For regional soil and water quality assessments, a large network of monitoring stations is required, which makes monitoring impractical because of time and resource limitations. An alternative approach is to use process models. These are mathematical models that describe and simulate the management, physical, chemical and biological processes impacting upon the real-life system being modelled. However, for regional policy evaluation in an integrated framework, thousands of site-specific simulations have to be performed so this is not a practical solution. With the growing focus on ecosystems and policy trade-offs, the tools for analysis must have the capacity to address sitespecific variability, but on a regional scale. A simple and scientifically valid statistical approach called metamodelling is an appropriate tool for such evaluations. By combining process models, statistical design and metamodelling, spatial variability can be integrated. The process model used in this analysis is EPIC (Erosion Productivity Impact

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Calculator) developed by USDA (Jones et al., 1991). EPIC was designed to analyze alternative cropping systems and to project their socio-economic and environmental impacts with specific reference to soil erosion, water quality and crop productivity. Soil erosion, atrazine and nitrate-nitrogen runoff/leaching are obtained by simulating EPIC according to an experiment designed to capture the range of management, soil and weather parameters in the study region. The SOILS-5 (Soil Interpretation Records System [SIRS]) database from which the soil sample was drawn includes layered (soil profile) information. A typical soil in this database is characterized by physical and hydrologic factors, such as percent clay, percent sand, permeability, organic matter, pH, bulk density, percent slope, k-factor, available water and hydrological groups. A stratified random sampling with a complete factorial design was used. Five soil factors—percent clay, bulk density, permeability, pH and k-factor—were used for stratification. The selected factors were stratified into three levels (the soil loss tolerance value—high, medium, and low) and 4 soils were sampled from each of the 15 strata (3 levels and 5 factors) without replacement. In summary, the resulting sample was balanced (soils in all levels of each property are represented at similar proportions), self-weighting (each cropped acre in the watershed had equal probability of selection) and representative of the population of soils in the watershed. EPIC also requires daily weather data such as precipitation, maximum and minimum temperatures, solar radiation and relative humidity. The simulations were conducted over 15 years using historical weather data. The simulation plan also included alternative management and cultural practices. Metamodelling is a statistical method used to approximate outcomes of a process model. While the complex simulation model is a tool to approximate the underlying real-life system, the analytic metamodel attempts to approximate and aid in the interpretation of the simulation model and, ultimately, the real-life system (Kleijnen, 1987). A metamodel is a regression model explaining the input–output relationship of a process model. Ideally, it would be preferable to experiment with the real-life system rather than with a simulation model. In that case, we would have a statistical model of the system rather than a metamodel. This approach is not adopted because it would mean waiting for 15 years of weather to present itself to the real-life system. Metamodels were fitted to EPIC-simulated soil erosion, nitrate-N and atrazine runoff/leaching (Lakshminarayan and Bouzaher, 1992). Regression model development requires close examination of the data so that the prior information contained in the data is fully utilized. Careful data diagnostics were performed to avoid model misspecification and bias. Prior experience in building metamodels for herbicide leaching strongly suggests the need for data transformation to get a good fit (Bouzaher et al., 1993). A linear model for soil erosion indicated that the error terms are non-random, suggesting heteroskedasticity (non-constant variance). This problem was resolved by taking a cubic-root transformation of the data, resulting in the following model: (soil lossCC )1/3 =−5·79+0·20(% slope)+3·86(Kf -factor)+0·07(OM)−0·25(pH) +0·01(rainfall)+0·06(RCN)−0·25(c-prac)−0·12(residue) (Adjusted R2 =0·82, RMSE=0·68) (soil lossCS )1/3 =−5·87+0·23(% slope)+5·23(Kf -factor)+0·07(OM)−0·20(pH) +0·01(rainfall)+0·05(RCN)−0·53(c-prac)−0·06(residue) (Adjusted R2 =0·91, RMSE=0·43) The coefficients in these models were significant at 5%. The subscripts on the dependent variable represent the cropping system (CC is continuous corn and CS is corn-soybeans). Kf -factor is the soil erodibility factor, OM is the percentage of organic

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matter, RCN is the runoff curve number that captures the effect of hydrology and soil cover complexes in controlling runoff, and c-prac is a binary regressor capturing the difference between straight row and contour systems. The residue cover is included to capture tillage effects. Soil erosion increases with slope, erodibility, organic matter, rainfall and RCN. Higher organic matter content of the soil implies greater microbial activity, reducing soil compaction and thereby increasing erosion. The RCN increases for soils with lesser infiltration capacity, which explains the positive sign on this coefficient. Soil pH has a negative sign, implying reduced erosion of alkaline soils because of increased compaction of soils with higher pH. The residue cover, as expected, reduces soil erosion. Chemical runoff/leaching is influenced by several factors including soil, weather, hydrology and agronomic factors. Identifying a simple relationship explaining chemical runoff/leaching is very useful for modelling purposes. A linear model fitted to the untransformed data on nitrate-N leaching did not produce a good fit. The distribution of the error term was skewed, suggesting heteroskedasticity. Data transformation did not solve the problem. A close examination of the data showed that a large number of observations were at or near zero, suggesting an exponential distribution. It is quite common to have such a distribution for chemical and nutrient leaching. Therefore, an exponential model Y(xi; b)=exp(Xb) was fitted as follows: (nitrate-N leachCC )=−18·11+0·24(% slope)+0·21(% clay)+0·51(OM)+0·24(perm) +4·19(bulk dens.)+0·01(rainfall)−0·03(RCN)−0·29(c-prac)−0·12(residue) (Adjusted R2 =0·72, RMSE=1·84) (nitrate-N leachCS )=−7·79+0·00(% slope)+0·03(% clay)+0·21(OM)+0·07(perm) +1·66(bulk dens.)+0·01(rainfall)−0·08(RCN)−0·90(c-prac)+0·18(residue) (Adjusted R2 =0·64, RMSE=4.04) The coefficients of these models were all significant at 5%, except for slope. The negative sign on the RCN coefficient suggests that higher RCN (meaning lower infiltration) results in lower leaching. On the contrary, residue cover increases leaching. Metamodels for other major crops, small grains, sorghum and hay and the metamodels for atrazine runoff/leaching are not shown. 4. Empirical scenarios and results The estimated metamodels were extrapolated for every unique soil and weather observation in the watershed and aggregated using spatial distribution of crop and management practices to provide right-hand side coefficients for the environmental objectives of the MCDM model. Thus, the metamodel-predicted estimates account for site-specific variations in soil, weather and hydrological parameters. Environmental objectives representing (1) soil loss from water erosion (eros), (2) nitrate-N leaching (nlch), and (3) atrazine leaching (alch), are evaluated. These are the principal NPS pollution indicators related to crop production in this study area which are of current concern. The economic objective measures short-run net returns to crop production and program participation. Besides the baseline scenario three alternative scenarios were examined. The baseline is a single objective scenario which maximized profits. The baseline was calibrated to reflect current practices. Scenario S1, which aimed at soil quality protection, minimized the negative deviation of profit and the positive deviation of soil loss from the respective goal levels (p∗, eros∗). Scenario S2, which aimed at groundwater quality, minimized

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T 1. Alternative policy scenario results relative to the baseline Percentage change Indicator

S1

S2

S3

(a) Economic–environmental indicators Net returns Soil loss Nitrate-N runoff Atrazine runoff Nitrate-N leaching Atrazine leaching Nitrogen application

−21·4 −50·0 −19·3 −16·5 +46·1 +18·3 −7·9

−9·5 +35·1 +9·2 +37·2 −50·0 −50·0 −17·3

−43·4 −50·0 −34·5 −15·2 −5·5 −6·6 −18·9

(b) Production indicators Corn acreage Hay acreage Small grains acreage Soybeans acreage

−18·0 +50·2 −32·9 >100·0

−16·3 +31·8 0·0 +14·8

−17·6 >100·0 0·0 -33·1

Conventional tillage Reduced tillage No-till

−25·4 +16·7 +66·7

+35·0 −917·9 ∗

−38·0 +20·4 +74·5

∗ Under this scenario, no-till acreage was totally shifted to conventional tillage.

the negative deviation of profit and the positive deviations of nitrate-N and atrazine leaching from the respective goal levels (p∗, nlch∗, alch∗). The last scenario S3, which aimed at both soil and groundwater quality, minimized the negative deviation of profit and the positive deviations of soil loss and nitrate-N and atrazine leaching from the respective goal levels. Mathematically, − + − + + Min [k− p dp +0dp +0de +ke de ], s.t. − + p(x)+dp −dp =p∗ + e(x)+d− e −de =e∗ Ax=b,

where e represents the environmental indicators. 4.1.  The three alternative scenarios were evaluated relative to the baseline scenario. Table 1 shows the percentage change of economic, environmental and production indicators from the baseline. Soil quality protection scenario (S1) resulted in a 21% reduction in net returns for a 50% reduction in soil loss. In other words, for every ton of soil saved from erosion a loss in net returns equivalent to $1·88 had to be incurred. Because runoff and soil erosion are positively correlated this scenario also resulted in 19% reduction in nitrate-N runoff and 16% reduction in atrazine runoff. However, risk to groundwater quality increased. Nitrate-N and atrazine leaching increased by 46% and 18%, respectively. In spite of 8% reduction in nitrogen fertilizer use the leaching of nitrate-N increased primarily because of shifts in cropping and tillage practices. More

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hay and soybeans were planted under this scenario and conservation tillage (reduced and no-till) increased significantly. On the other hand, groundwater quality scenario (S2) produced results conflicting with the soil erosion goal, net returns decreased by 9% and soil loss increased by 35%. Consistent with increased soil erosion, nitrate-N and atrazine runoff also increased. The increase in hay and soybean acreage was somewhat limited compared to the previous scenario. Conventional tillage increased by 35%, and no-till acreage was totally shifted to conventional tillage. Clearly, the results demonstrate trade-offs between soil and water quality objectives. That is, the soil erosion scenario increased the risk to water quality and vice-versa. Therefore, addressing soil and water quality on a piecemeal basis is sub-optimal because of conflicting relationship between the underlying processes. Scenario (S3), a comprehensive scenario minimizing soil loss that does not allow nitrate-N and atrazine leaching to exceed the baseline, resulted in a 43% decrease in returns. This scenario increased hay production significantly and also increased reduced and no-till acreage. Under this scenario there was no conflict between the environmental objectives, but the producers were subjected to increased economic hardship. The result suggests that compensation, in the form of stewardship payments, is necessary to encourage increased adoption of these practices.

5. Limitations and concluding remarks Two key results stand out of this policy exercise: (1) there was a significant trade-off between the economic and environmental goals, and even between the environmental goals. Therefore, a comprehensive analysis with reasonable compromise will give an ideal solution, (2) incorporating environmental objectives encouraged more environmentally sound cropping practices, In particular, environmentally sustainable crop rotation practices such as corn-soybeans-hay/oats was chosen more frequently by the model. The model and the results are subject to several limitations. The model ignores uncertainty and dynamics. Inclusion of uncertainty will produce a more realistic tradeoff. Because the data on soil, hydrology, weather and production practices are specific to this watershed, the results are not directly applicable to other areas. But the results could be generalized to areas with similar spatial attributes. Furthermore, the results should reflect, in general, sustainable agricultural practices in controlling soil erosion and chemical pollution. Empirical implementation of this integrated modelling system in a multi-objective context is challenging because it requires an enormous amount of data, a wide range of models and research tools, and the coordination of agencies and disciplines. Coordination is defined primarily as a team approach with cost-sharing across agencies so that their decisions are in harmony with the goals of the society. The idea is that the coordination effort must transcend the boundaries of all participants so that the complimentarities, if any, are utilized and contradictions are minimized. The choice of tools and methods in each discipline must be consistent with the goal of integrating various modules.

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