Faculty of Business and Law
SCHOOL OF ACCOUNTING, ECONOMICS AND FINANCE
School Working Paper - Economic Series 2006 SWP 2006/30
Multiple-Criteria Decision Analysis for Integrated Catchment Management
Tony Prato University of Missouri-Columbia, USA and Gamini Herath Deakin University
The working papers are a series of manuscripts in their draft form. Please do not quote without obtaining the author’s consent as these works are in their draft form. The views expressed in this paper are those of the author and not necessarily endorsed by the School.
Multiple-Criteria Decision Analysis for Integrated Catchment Management
Tony Prato and Gamini Herath University of Missouri-Columbia, USA, and Deakin University, Victoria, Australia
ABSTRACT Implementation of Integrated Catchment Management (ICM) is hampered by the lack of a conceptual framework for explaining how landowners select farming systems for their properties. Benefit-cost analysis (a procedure that estimates the costs and benefits of alternative actions or policies) has limitations in this regard, which might be overcome by using multiplecriteria decision analysis (MCDA). MCDA evaluates and ranks alternatives based on a landowner’s preferences (weights) for multiple criteria and the values of those criteria. A MCDA approach to ICM is superior to benefit-cost analysis which focuses only on the monetary benefits and costs, because it: 1) recognizes that human activities within a catchment are motivated by multiple and often competing criteria and/or constraints; 2) does not require monetary valuation of criteria; 3) allows trade-offs between criteria to be measured and evaluated; 4) explicitly considers how the spatial configuration of farming systems in a catchment influences the values of criteria; 5) is comprehensive, knowledge-based, and stakeholder oriented which greatly increases the likelihood of resolving catchment problems; and 6) allows consideration of the fairness and sustainability of land and water resource management decisions. A MCDA based on an additive, multiple-criteria utility function containing five economic and environmental criteria was used to score and rank five farming systems. The rankings were based on the average criteria weights for a sample of 20 farmers in a US catchment. The most profitable farming system was the lowest-ranked farming system. Three possible reasons for this result are
evaluated. First, the MCDA method might cause respondents to express socially acceptable attitudes towards environmental criteria even when they are not important from a personal viewpoint. Second, the MCDA method could inflate the ranks of less profitable farming systems for the simple reason that it allows the respondent to assign non-zero weights to non-economic criteria. Third, the MCDA might provide a better framework for evaluating a landowner’s selection of farming systems than the profit maximization model.
Keywords: Integrated catchment management Multiple-criteria analysis Benefit-cost analysis Ranking farming systems
1. Introduction Managing land and water resources in an economically and ecologically sustainable manner is complex because natural resources are limited, there is competition for the use of natural resources, and there are multiple and interacting sources of land and water degradation. Since the catchment is recognized as an appropriate scale for natural resource planning and management (MacKenzie, 1997), integrated catchment management (ICM) has emerged as the major paradigm for managing land and water resources. Implementation of ICM is hampered by the lack of a conceptual framework for explaining how landowners select land and water resource management systems (LWRMS) for their properties. A LWRMS is a spatial pattern of land uses, soil/water conservation methods, and nutrient/chemical management practices for a property or catchment.
Multiple criteria decision analysis (MCDA) provides a suitable conceptual framework for evaluating landowner selection of LWRMS. In MCDA, a decision-maker, such as a landowner or catchment manager, evaluates alternative management systems based on their preferences for and values of multiple criteria. The best system is the one providing the most preferred combination of criteria. MCDA has been used or proposed for water systems analysis (Haimes and Hall, 1974), environmental management (Bakus et al., 1982; Janssen, 1992), food security (Haettenschwiler, 1994), forest management (Kangas and Kuusipalo, 1993; Kangas, 1994; Penttinen, 1994), agricultural production (Xu et al., 1995; Strassert and Prato, 2002), natural areas (Anselin et al., 1989; Gehlbach, 1975; Sargent and Brande, 1976; Smith and Theberge, 1986; Smith and Theberge, 1987), regional water quality analysis (Makowski et al., 1995), management of agroecosystems (Prato et al., 1996a), wildlife management (Prato et al., 1996b) and soil and water resource management (Prato, 1998).
MCDA approaches to ICM avoid many of the limitations of single-criterion, efficiency-based approaches, such as benefit-cost analysis (BCA). A MCDA approach to ICM is superior to BCA for several reasons: It recognizes that human activities within a catchment are motivated by multiple and often competing objectives and/or constraints, such as maximizing economic returns, reducing soil erosion and water pollution, reducing flood damages, and protecting fish and wildlife habitat. It does not require monetary valuation of criteria, as does BCA. It allows measurement and evaluation of the trade-offs between criteria. It explicitly considers how the spatial configuration of LWRMS in a catchment influences the values of criteria.
It is comprehensive, knowledge-based and stakeholder oriented, which greatly increases the likelihood of resolving catchment problems. It allows consideration of the fairness and sustainability of land and water resource management decisions (Costanza and Folke, 1997). This paper discusses the basic elements of MCDA and applies the approach to a catchment in the United States.
2. Catchment Approach One of the best ways to implement ICM is through a community-based approach that empowers people to make informed management decisions. A top-down approach is unappealing to landowners and rural communities because it generally provides results and recommendations that lack practical significance and broad-based community support. Lee and Stankley (1992) indicate that, “Large-scale (regional) ecological systems can be most effectively regulated by small-scale (local) social organizations.” Naiman et al. (1997) state that, “… watershed management demands unparalleled cooperation between citizens, industry, governmental agencies, private institutions, and academic organizations.” Local social organizations and cooperation require decentralized decision-making. Because BCA is a top-down evaluation technique which does not use individual preferences, it is less compatible with community-based decision making than MCDA (Cameron, 1997).
In many areas of the world, catchment alliances have formed to reduce the adverse cumulative ecological effects of land use and water resource management. Alliances typically include a wide range of stakeholders such as landowners, federal and state resource management agencies, commodity and environmental groups, local government, private industry and others. The basic
premise underlying the formation of catchment alliances is that assessments of sustainable resource management and the design of policies to alleviate unsustainable resource management should occur at the local level. A catchment alliance can utilize MCDA to evaluate the social, economic, and ecological sustainability of resource management (Prato and Hajkowicz, 1999). If a catchment alliance or environmental authority determines that resource management is not sustainable, then it is appropriate for them to evaluate alternative policies (education, technical assistance, and economic incentives) that encourage sustainable resource management.
3. Previous Applications MCDA can be implemented using a variety of methods including multiple-criteria utility functions, Ideal Point, Electre, goal programming, analytical hierarchy process, benefit–cost analysis, and others (Janssen, 1992). These methods differ in terms of how the decision-maker’s preferences for criteria are measured and the way preference information is used to rank alternatives. Because of its simplicity and relevance to real world problems (Keeney and Raiffa, 1976), the following additive multiple-criteria utility function is frequently used to evaluate and rank alternatives (Yakowitz et al., 1993; Foltz et al., 1995; Tecle et al., 1995; Prato, 1999):
vk = ∑ w rsrk ,
where vk is the utility score for the kth LWRMS, srk is the standardized value of the rth criterion (r = 1 ,…, R) with the kth LWRMS (0 ≤ srk ≤ 1), wr is the weight for the rth criterion, and
= 1. vk is a simple weighted additive sum of standardized criteria. An additive utility function
implies that criteria are mutually utility independent, or that the marginal utility of one criterion does not depend on the amounts received of all other criteria.
Criteria weights are typically estimated using three methods: fixed-point scoring, paired comparisons, and judgment analysis. Fixed-point scoring requires the decision-maker to allocate 100 percentage points among the criteria. Criteria weights are set equal to the percentage points. The higher the weight assigned to a criterion, the greater its importance. Fixed-point scoring forces the decision-maker to consider trade-offs among criteria because it is not possible to assign a higher weight to one criterion without reducing the weight assigned to one or more of the other criteria. Paired comparisons are made using the analytic hierarchy process or AHP (Saaty, 1987). AHP is a method for deriving quantitative weights for criteria based on the decision-maker’s qualitative comparison of all pairs of criteria. In making comparisons, the decision-maker evaluates the degree to which one criterion is more, less, or equally important relative to another criterion on a scale of 1 to 9, where 1 designates equally important and 9 indicates extremely more important. Judgment analysis is a statistical method for estimating criteria weights (Cooksey, 1996). It requires the decision-maker to score the feasible alternatives on a scale of 1 to 100 based on criteria values specified by the decision analyst (person assisting the decision-maker in doing MCDA). The relative importance of each criterion is estimated using a multiple linear regression equation in which the scores for alternatives are regressed on the corresponding values of the criteria values for that alternative. Criteria weights are given by the standardized regression coefficients. Other MCDA methods used to evaluate alternatives including the surrogate worth tradeoff method (Haimes and Hall, 1974, 1977), free iterative search (Tecle et al., 1994), the Aspiration-Reservation Based Decision Support System (Fischer et al., 1996; Makowski, 1994) and the balancing and ranking method (Strassert and Prato, 2002).
4. Study area The study area is the Goodwater Creek catchment in northcentral Missouri, USA depicted in Figure 1. Crops grown in the watershed include wheat, sorghum, soybeans, and corn. Extensive uses of fertilizers and/or herbicides on these crops and associated impacts on drinking water quality and aquatic ecosystems have generated considerable local and regional concern. Of particular concern is atrazine and nitrate-nitrogen contamination of surface water. Atrazine is a white, crystalline solid organic compound used to control broadleaf and grassy weeds. Atrazine concentrations in surface water in Goodwater Creek indicated have exceeded the maximum contaminant level (MCL) for drinking water of 3 ppb established by the Environmental Protection Agency. Although water from Goodwater Creek is not used for drinking water, the creek flows into the Mark Twain reservoir which is a major source of drinking water for communities in northeast Missouri (Heidenreich et al., 1996). Nitrate-nitrogen concentrations in Goodwater Creek have not exceeded the drinking water MCL of 10 ppm. However, use of commercial fertilizers in Goodwater Creek watershed and other midwestern watersheds have contributed to low oxygen concentrations (hypoxia) in portions of the Gulf of Mexico (Nelsen et al., 1994). Hypoxia is lethal to fish and other marine organisms. Nitrate-nitrogen contamination of surface water also degrades inland aquatic ecosystems.
5. Procedures Five farming systems were scored and ranked using the additive, multiple-criteria utility function given in equation 1. Each farming system was characterized in terms of crop rotation, tillage method, fertilizer application rate, and pesticide application rate (see Table 1). Use of equation (1) requires data on the average values of the criteria for the five farming systems and average criteria weights. Five economic and environmental criteria were included in the utility function:
increasing net return (NR); reducing economic risk (RI); improving drinking water quality (DW); enhancing aquatic ecosystems (AE); and reducing soil erosion (SE). Economic criteria (NR and RI) were selected because farmers must earn a reasonable income from farming in order to stay in business. Drinking water quality (DW), aquatic ecosystems (AE), and soil erosion (SE) criteria were selected because many nonfarm groups and environmental agencies are concerned about the human and environmental health impacts of farming systems. Average criteria values were calculated using the simulated values of the criteria determined by Wu (1994). Criteria weights were determined based on information obtained in a survey of 20 farmers in Goodwater Creek catchment. The survey employed three criteria weighting methods: fixed-point scoring, paired comparisons (Saaty, 1987), and judgment analysis (Cooksey, 1996). Criteria weights were averaged over the three methods. Hajkowicz and Prato (1998) give more details on the application of the MCDA methods to the results of the farm survey.
6. Results Table 2 lists the average values of the five criteria for the five farming systems. Estimated average weights for the five criteria were wNR = 0.339, wSE = 0.261, wRI = 0.165, wDW = 0.157, wAE = 0.079. Since wNR is the largest weight, the average farmer in Goodwater Creek catchment considers net return to be the most important criterion for selecting a farming system. Increasing net return (profit) is 1.3 times more important than reducing soil erosion, approximately twice as important as reducing economic risk and improving drinking water quality, and more than four times as important as enhancing aquatic ecosystems.
Based on equation (1), utility scores for the five farming systems were: v4 = 0.63, v3 = 0.49, v5 = 0.42, v2 = 0.38, and v1 = 0.35. These scores imply the following ranking of the five farming
systems: FS4 > FS3 > FS5 > FS2 > FS1. Therefore, FS4 (corn-soybean rotation, reduced tillage, medium fertilizer application, and banded pesticide application) is the top-ranked farming system based on the results of the MCDA.
7. Discussion Results for the MCDA indicate that the top-ranked farming system in Goodwater Creek catchment is not the farming system that maximizes profit. FS1 maximizes profit, but FS4 has the highest utility score. Furthermore, even though net return (profit) has the highest average weight, FS1 is the lowest ranked system based on the MCDA model. There are three possible interpretations of these results.
First, the MCDA results may not accurately reflect the private interests of farmers. This interpretation is suggested by the fact that, of the five farming systems, FS1 is closest to the actual farming system used in the Goodwater Creek catchment. In completing the survey, farmers might have felt the need to express socially acceptable attitudes regarding the importance of environmental criteria even though they might not consider them to be important in terms of their farming operation. This form of behavior has been documented for other survey methods such as the contingent valuation method. Survey respondents for contingent valuation surveys tend to express their willingness-to-pay or willingness-to-accept compensation for a good or service from the viewpoint of a concerned citizen rather than as a consumer or user of that good or service (Sagoff, 1988). Cameron (1997) commented that some respondents in a survey of willingness-to-pay for improved water quality in the Hawkesbury-Nepean catchment in Sydney, Australia stated that the payments they would be willing to make were symbolic and like a donation to a worthy cause. This interpretation does not disqualify using MCDA for
gauging the private interests of farmers. Rather, it raises the possibility that MCDA and other valuation methods may give results that reflect the respondents’ social attitudes toward the alternatives being compared.
If the responses of surveyed farmers in Goodwater Creek catchment reflected socially acceptable attitudes toward environmental quality, then there is a greater likelihood that farmers inflated the weights assigned to environmental criteria (soil erosion, drinking water quality, and aquatic ecosystems). Inflation of environmental weights could result in a higher ranking of farming systems that generate higher environmental values. This phenomenon is more likely to occur with the fixed-point scoring and paired comparisons methods because they require farmers to directly reveal their preferences for criteria. It is less likely with Judgment Analysis because criteria weights estimated with this method are based on the scores assigned to farming systems. In other words, it is easier for farmers to ignore environmental criteria without appearing socially irresponsible with Judgment Analysis than with the fixed-point scoring and paired comparisons methods. Despite this argument, there is very little difference in the relative importance of criteria and a negligible difference in the ranking of farming systems with the three criteria weighting methods. If rankings obtained with the MCDA are considered to be unreliable based on the first reason, then it is inappropriate to use MCDA to evaluate the merits of subsidies for encouraging farmer adoption of conservation practices.
A second interpretation is that the MCDA method inflates the ranks of less profitable farming systems for the simple reason that it allows respondents to assign non-zero weights to noneconomic criteria. This possibility exists even when respondents base their evaluation of criteria or farming systems on purely private motivations; that is, when the first interpretation is not
relevant. The second interpretation is more likely when there are trade-offs between the economic and environmental criteria and when the number of economic criteria is greater than the number of non-economic criteria. Although the first condition is satisfied for the five farming systems evaluated here, the second condition is not.
One way to reduce the likelihood of conditions that favor the second interpretation is to use an iterative procedure. Such a procedure allows decision-makers to examine how their responses to survey questions influence the ranking of farming systems. Specifically, the ranking of farming systems implied by a particular set of weights for criteria is shown to the respondent. If the respondent does not agree with the ranking, then s/he is allowed to revise the criteria weights until an acceptable ranking of farming systems is obtained. For example, the AspirationReservation Based Decision Support System (ARBDSS) is an MCDA procedure that utilizes an iterative approach (Fischer et al., 1996; Makowski, 1994).
This study did not use an iterative approach because it was not feasible to determine the ranking of farming systems until after survey responses were enumerated, and it was not feasible to reconvene the respondents after the first survey. An iterative approach can be implemented using a computerized decision support system that allows the decision-analyst to provide immediate feedback to the decision-maker on how revealed preferences for criteria affect criteria weights and the ranking of farming systems.
A third interpretation of differences in the ranking of farming systems is that the MCDA provides a better framework for evaluating the selection of farming systems than the profit maximization model. This interpretation is suggested by the fact that farmers assigned significant
weight to the noneconomic criteria (0.40 on average). Furthermore, if the MCDA provides a better framework than the profit maximization model, then using the latter could distort assessments of the effects of conservation subsidies on the selection of farming systems. In this case, it is prudent to base the design and evaluation of conservation subsidies for agricultural management practices on MCDA.
8. Conclusions Conventional economic approaches to evaluating land and water resource management systems either assign values to environmental impacts (contingent valuation) or evaluate the efficiency of preserving and restoring environmental quality (benefit-cost analysis). A MCDA approach to integrated catchment management is superior to BCA because it: 1) recognizes that human activities within a catchment are motivated by multiple and often competing objectives and/or constraints; 2) does not require monetary valuation of criteria; 3) allows trade-offs between criteria to be measured and evaluated; 4) explicitly considers how the spatial configuration of LWRMS for a catchment influences the values of criteria; and 5) is comprehensive, knowledgebased and stakeholder oriented which greatly increases the likelihood of resolving catchment problems.
The MCDA conducted in this paper models how a landowner selects the most preferred farming system for a farm based on multiple criteria. Scores are used to rank alternative farming systems. The MCDA was used to rank five farming systems based on five economic and environmental criteria in Goodwater Creek catchment located in Missouri, USA. Ranking was based on an additive utility function, which is the sum of the product of criteria weights and standardized criteria values. Results indicate that the highest ranked farming system for Goodwater Creek
catchment is different from the farming system that maximizes profit. The most profitable farming system ranked last. There are several explanations for these results, including the possibility that the MCDA provides a better framework for evaluating the selection of farming systems than the profit maximization model.
REFERENCES Anselin, A., Meire, P.M., Anselin, L., 1989. Multicriteria techniques in ecological evaluation: an example using the Analytic Hierarchy Process. Biological Conservation 49, 215-229. Backus, G.J., Stillwell, W.G., Latter, S.M., and Wallerstein, M.C., 1982. Decision making with applications for environmental management. Environmental Management 6, 493-504. Cameron, J.I., 1997. Applying socio-ecological economics: a case study of contingent valuation and integration watershed management. Ecological Economics 23, 155-165. Cooksey, R.W., 1996. Judgment Analysis: Theory, Methods and Applications. Academic Press, Sydney, Australia. Costanza, R., Folke, C., 1997. Valuing ecosystem services with efficiency, fairness, and sustainability as goals. In: Daily, G.C. (Ed.), Nature’s Services: Societal Dependence on Natural Ecosystems. Island Press, Washington, DC. pp. 49-68. Fischer, G., Makowski, M., Antoine, J., 1996. Multiple criteria land use analysis. Working Paper WP-96-006, International Institute of Applied Systems Analysis, Laxenburg, Austria. Foltz, J.C., Lee, J.G., Martin, M.A., Preckel, P.V., 1995. Multiattribute assessment of alternative cropping systems. American Journal of Agricultural Economics 77, 408-20. Gehlbach, F.R., 1975. Investigation, evaluation, and priority ranking of natural areas. Biological Conservation 8,79-88.
Haimes, Y.Y., Hall, W.A., 1974. Multiobjectives in water resource systems: the surrogate tradeoff method. Water Resources Research 10, 615-624. Haimes, Y.Y., Hall, W.A., 1977. Multiobjective analysis in the Muamee River Basin: a case study on level-B planning. Report SED-WRG-77-1, Case Western University, Cleveland, OH. Haettenschwiler, P., 1994. Decision support systems applied to Swiss federal security policy and food supply. (draft). DSS workshop, International Institute of Applied Systems Analysis Workshop, Laxenburg, Austria. Hajkowicz, S., Prato, T., 1998. Multiple objective decision analysis of farming systems in Goodwater Creek watershed, Missouri, CARES Research Report No. 24, University of Missouri-Columbia, Columbia, MO, June. Heidenreich, L.K., Zhou, Y., Prato, T., 1996. Watershed scale water quality impacts of alternative farming systems, Proceedings for Watershed '96, June 8-12, Baltimore, Maryland. Janssen, R., 1992. Multiobjective Decision Making for Environmental Management. Kluwer Academic Publishers, The Netherlands. Kangas, J., 1994. An approach to public participation in strategic forest management planning. Forest Ecology and Management 70, 75-88. Kangas, J., Kuusipalo, J., 1993. Integrating biodiversity into forest management planning and decision-making. Forest Ecology and Management 61, 1-15. Keeney, R.L., Raiffa, H., 1976. Decisions with Multiple Objectives: Preferences and Value Trade-offs. John Wiley & Sons, New York. Lee, R.G., Stankey, G.S., 1992. Major issues associated with managing watershed resources. In: Adams, P.W., Atkinson, W.A. (Eds.), Balancing Environmental, Social, Political, and
Economic Factors in Managing Watershed Resources. Oregon State University Corvallis, OR. MacKenzie, S.H., 1997. Integrated Resource Planning and Management. Island Press, Washington, DC. Makowski, M., 1994. Methodology and a modular tool for multiple criteria analysis of LP models. Working Paper WP-94-102, International Institute of Applied Systems Analysis, Laxenburg, Austria. Makowski. M., Somlyody, L., Watkins, D., 1995. Multiple criteria analysis for regional water quality management: the Nitra River case. Working Paper WP-95-022. International Institute of Applied Systems Analysis, Laxenburg, Austria. Naiman, R.J., Bisson, P.A., Lee, R.G., Turner, M.G., 1997. Approaches to management at the watershed scale. In: Kohm, K.A., Franklin, J.F. (Eds.), Creating Forestry for the 21st Century: The Science of Ecosystem Management. Island Press, Washington, DC, pp. 239253. Nelsen T.A., Blackwelder, P., Hood, T., McKee, B., Romer, N., Zarikian, A., Metz, C., 1994. Time-based correlation of biogenic, lithogenic and authigenic sediment components with anthropogenic inputs in the Gulf of Mexico. Estuaries 17, 873-885. Penttinen, M., 1994. Forest owner’s decision support systems–a management solution for nonindustrial private forest owners. International Institute of Applied Systems Analysis Workshop, Laxenburg, Austria. Prato, T., Fulcher, C., Wu, S., Ma, J., 1996a. Multiple-objective decision making for agroecosystem management. Agricultural. and Resource. Economics Review 25, 200-212.
Prato, T., Fulcher, C., Zhou, Y., 1996b. Integrated resource management using a decision support system. Southern African Wildlife Management Association Conference, Sustainable Use of Wildlife, University of Cape Town, South Africa, April 9-11, p. 48. Prato, T., 1998. Protecting soil and water resources through multi-objective decision making. In: El-Swaify, S.A., Yakowitz, D.S. (Eds.), Multiple Objective Decision Making for Land, Water and Environmental Management. St. Lucie Press, Delray Beach, FL, pp. 385-394. Prato, T., Hajkowicz, S.. 1999. Selection and sustainability of land and water resource management systems. Journal of the American Water Resources Association 35, 739-752. Prato, T., 1999. Risk-based multiattribute decision making in property and watershed management. Natural Resource Modeling 12, 307-334. Saaty, R.W., 1987. The Analytic Hierarchy Process - what it is and how it is used? Mathematical Modeling 9, 161-176. Sagoff, M., 1988. The Economy of the Earth, Cambridge University Press Cambridge, p. 271. Sargent, F.O., Brande, J.H., 1976. Classifying and evaluating unique natural areas for planning purposes. Journal of Soil and Water Conservation May-June, 113-116. Smith, P.G.R., Theberge, J.B., 1986. A review of criteria for evaluating natural areas. Environmental Management 10, 715-734. Smith, P.G.R., Theberge, J.B., 1987. Evaluating natural areas using multiple criteria: theory and practice. Environmental Management 11, 447-460. Strassert, G. and T. Prato. 2002. Selecting farming systems using a new multiple criteria decision model: the balancing and ranking method. Ecological Economics 40, 269-277. Tecle, A., Duckstein, L., Korhonen, P., 1994. Interactive, multiobjective programming for forest resources management. Applications in Mathematics and Computation 63, 75-93.
Tecle, A., Szidarovszky, F., Duckstein, L., 1995. Conflict analysis in multi-resource forest management with multiple decision-makers. Nature and Resources 31, 8-17. Wu, S., 1994. Economic and water quality impacts of alternative farming systems in Goodwater Creek watershed: A stochastic programming analysis. Ph.D. dissertation, Department of Agricultural Economics, University of Missouri-Columbia, Columbia, MO. Xu, F., Prato, T., Ma, J.C., 1995. A farm-level case study of sustainable agricultural production. Journal of Soil and Water Conservation 50, 39-44. Yakowitz, D.S., Lane, L.J., Szidarovszky, F., 1993. Multi-attribute decision-making: dominance with respect to an importance order of the attributes. Applications in Mathematics and Computation 54, 7-81.
Table 1 - Description of five farming systems _________________________________________________________ Farming Crop Tillage Fertilizer Pesticide system rotation method application application rate rate _________________________________________________________ FS1 CB MT High High FS2 SB MT Low Medium FS3 CBW MT Medium Banded FS4 CB R Medium Banded FS5 CB NT Medium High _________________________________________________________ C = corn, B = soybeans, S = sorghum, W = wheat, MT = minimum tillage, R = reduced tillage, and NT = no tillage.
Table 2 - Average criteria values for five farming systems Farming system Net return ($/ha) Economic risk ($/ha) Drinking water (atrazine applic. rate, L/ha) Aquatic ecosystems Soil erosion (soluble nitrogen rate concentration in (tonnes/ha/yr surface runoff, ppm) ) 12.69 4.66 7.81 8.33 5.70 4.48 6.94 5.15 4.93 1.90
FS1 FS2 FS3 FS4 FS5
328.53 241.39 218.95 296.38 201.82
27.92 20.44 19.68 24.25 23.18
4.68 3.74 1.75 1.75 4.91
Figure 1. Goodwater Creek catchment, northcentral Missouri, USA