An integrated modelling and multicriteria analysis approach to managing nitrate diffuse pollution: 1. Framework and methodology

Science of the Total Environment 359 (2006) 1 – 16 www.elsevier.com/locate/scitotenv

An integrated modelling and multicriteria analysis approach to managing nitrate diffuse pollution: 1. Framework and methodology B.K. Koo a,*, P.E. O’Connell b,1 a The Macaulay Institute, Craigiebuckler, Aberdeen AB15 8QH, UK Water Resource Systems Research Laboratory, School of Civil Engineering and Geosciences, University of Newcastle-upon-Tyne, Newcastle-upon-Tyne, UK

b

Received 29 October 2004; accepted 17 May 2005 Available online 11 July 2005

Abstract As trade-off relationships between the agronomy and the environment are common over land uses within a catchment, one of major concerns of catchment management plans is how to balance the trade-offs over land uses at the catchment-scale. In this two-part paper, an integrated modelling and multicriteria analysis (MCA) methodology is presented which can be used to evaluate a set of land use alternatives and to identify an didealT compromise between economic return and environmental pollution. This didealT compromise here is achieved by land use optimisation of which the objective is to minimise the environmental pollution (nitrate leaching rate) and to maximise the economic return (agronomic gross margin), considering both environmental and economic potential across the catchment in a site-specific manner. The suggested methodology can be used to produce a site-specifically optimised land use scenario that is an didealT compromise between nitrate diffuse pollution and agronomy at the catchment-scales. Some issues on the actual application of the methodology are also discussed. D 2005 Elsevier B.V. All rights reserved. Keywords: Nitrate diffuse pollution; Environmental evaluation; Economic evaluation; Compromise programming; Site-specific land use optimisation

1. Introduction In the UK, there has been a long-term trend of rising nitrate concentrations in rivers in Central and * Corresponding author. Tel.: +44 1224 498200; fax: +44 1224 498207. E-mail addresses: [email protected] (B.K. Koo), p.e.o’[email protected] (P.E. O’Connell). 1 Tel.: +44 191 2226405; fax: +44 191 222 6669. 0048-9697/$ - see front matter D 2005 Elsevier B.V. All rights reserved. doi:10.1016/j.scitotenv.2005.05.042

Southeast England since the 1920s (Nitrate Coordination Group, 1986). Although nitrate levels in many surface water sources have stabilised in recent years (Davies and Sylvester-Bradley, 1995), they still remain high and seasonal variations frequently exceed the EC limit which is 50 mg/l of nitrate (equivalent to 11.3 mg N/l) in drinking water. Nitrate (NO3) itself is not toxic, but it becomes a problem when it is converted to nitrite (NO2) in human guts. Over the last few decades, the potential link

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between high nitrate concentrations in drinking water and fears about human health has been mainly focused on stomach cancer. There are some investigation results that support the positive association of nitrate intake with stomach cancer (Hartman, 1983; Joossens et al., 1996; Hill, 1999) and, on the other hand, there are others that doubt its significance (Davies, 1980; Beresford, 1985; Al-Dabbagh et al., 1986). However, evidence has strengthened to support the theoretical role of nitrate in production of carcinogenic N-nitroso compound in humans, particularly those with low stomach acidity (House of Lords, 1989). Moreover, there is no reason, in view of proven carcinogenic effects on laboratory animals, to believe that humans would not be susceptible. The dose needed to cause stomach cancer in humans is not known, but it is certain that the rate of the reaction increases with increasing nitrite (and therefore nitrate) concentration. Nitrate is also related to environmental problems including eutrophication of fresh waters and depletion of the ozone layer. Elevated nitrate concentrations in surface water can cause qualitative changes in algal communities, for example, from diatoms to blue-green algae which is often toxic to humans. Other adverse effects of eutrophication include severe oxygen depletion at night, which has a detrimental effect on aquatic life, and clogging up of river channels, which increases the risk of flooding. Besides, a nitrogen compound is also known to be one of the causes of depletion of the ozone layer in the stratosphere. Nitrous oxide (N2O) is produced from nitrification and denitrification processes that are boosted by increased use of nitrogenrich fertilisers in agricultural practices. Nitrous oxide from the earth’s surface is transported to the stratosphere by turbulent diffusion and reacts with excited atomic oxygen to produce predominantly N2 and O2 but also some nitric oxide (NO). Nitric oxide is one of the identified important catalysts that removes O3 in the stratosphere (Wayne, 1993). Nitrate in water derives from three main sources: 1) run-off or leaching from agricultural land; 2) sewage effluent; 3) atmospheric deposition, whether in rainfall or in the form of dry deposition. Although atmospheric inputs as a whole are large, inputs directly to surface waters are not large. Inputs from sewage works can be locally important in causing nitrate pollution. However, it is generally accepted that agricultural inputs, more specifically losses of nitrate from agricultural

land, are the main cause of post-war increases in nitrate levels in waters (Royal Society of London, 1983; House of Lords, 1989). It is also noted that by far the most important sources of nitrogen to agricultural land are chemical fertilisers and animal manure, whether applied directly or in the form of slurry or farmyard manure (Royal Society of London, 1983). Nitrogen fertilisers are used in agriculture in order to increase crop yields, but they also increase nitrate leaching rates from the soil column. In principle, the agricultural nitrate pollution control measures can be classified into two groups: curative measures and preventative measures. Curative measures are applied after nitrate polluting activities have occurred and are devised to ’cure’ the pollution that has already occurred. Curative measures currently available are only applicable to drinking water treatment (e.g. water substitution, blending, ion exchange). As these measures cannot contribute to reducing nitrate concentrations in the source waters, the environmental implications of raised nitrate concentrations in waters are ignored. Therefore, even though they may be needed to meet the legislative requirements for drinking water, curative measures are not appropriate for long-term solution of nitrate pollution of waters. On the other hand, preventative measures are applied before or at the same time as nitrate polluting activities are taking place and aim to ’prevent’ the nitrate pollution by acting directly on certain agricultural practices which are likely to cause nitrate pollution. Usually preventative measures are not easy to implement and/or operate as they involve many administrative arrangements between farmers and the authorities such as compensation payment, taxation and monitoring of the practices. Furthermore, it takes a long time (especially for deep aquifers like the chalk where it could take several decades) to see the effects of the measures applied, and this long time-lag makes it complicated to identify and quantify the effects of individual practice measures. However, the sole redeeming feature of preventative measures, which makes them absolutely essential, is that they are fundamental approaches to reducing nitrate concentrations in waters. Thus, preventative measures are appropriate for long-term nitrate control policies. Preventative measures have been the focus of attention since the EC Nitrate Directive (91/676) insisted that nitrate should be controlled by prevention at source and

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gave recommendations for changes in agricultural practice and land use. In terms of implementing preventative measures, more specific approach has been suggested by the Water Framework Directive (2000/60, WFD) which requires that catchment management plans must take into account various stakeholders’ interests in diffuse pollution problems through participatory processes. In developing a catchment management plan, the participation of stakeholders is required to help resolve any conflicts between current land and water management activities, and compliance with the WFD. In this context, a major concern is nitrate pollution from agricultural diffuse sources, which is a consequence of the maximisation of economic returns from intensive agriculture over the past several decades, and the need to achieve a WFD-related compromise between economic return and nitrate pollution of waters. While the objective of stakeholder participation is to facilitate the identification of such a compromise, a participatory process is not in itself sufficient to achieve this. It must be supported by appropriate data, information and knowledge that can steer the deliberations and debate in the direction of a compromise that is acceptable to all. This typically requires the description of a set of land use alternatives, and criteria for evaluating the alternatives. In this two-part paper, an integrated modelling and multicriteria analysis (MCA) methodology is presented which can be used to evaluate a set of land use alternatives and to identify an didealT compromise between economic return and environmental pollution at both local and catchment scales. This didealT compromise here is achieved by land use optimisation of which the objective is to minimise the environmental pollution (nitrate leaching rate) and to maximise the economic return (agronomic gross margin), considering both environmental and economic potential across the catchment in a site-specific manner. It should be noted that this methodology is an academic approach and does not involve any components of the actual participatory process.

incommensurate criteria. As trade-offs are common over land uses within a catchment, it is essential that a land use optimisation methodology should be able to handle multicriteria problems. Thus a MCA method resides in the centre of the land use optimisation approach in this study. A MCA method suitable for land use optimisation at the catchment-scale should be able to handle the nature of the problem:

2. Multicriteria analysis 2.1. MCA for land use optimisation

Alternatives that are closer to the ideal are preferred to those that are farther away. To be as close as possible to the perceived ideal is the rationale of human choice.

Multicriteria analysis (MCA) methods can evaluate a set of alternatives on the basis of conflicting and

The basic idea in compromise programming is to define an ideal solution as a point of reference and

n

n

n

Land use optimisation is to determine the best alternative out of a finite number of discrete, predefined land use alternatives; Criteria are often incommensurable with each other – for example, a criterion for diffuse pollution cannot be directly compared with a criterion for agronomic productivity; Relative importance of criteria may vary across the catchment – a criterion for diffuse pollution potential, for example, may be more important at a place near the water body than at a distant place.

One feasible MCA method that can cover all of the above problems is compromise programming. Compromise programming is a distance-based MCA method and is easy to implement and provide quite robust results. In a study to select the most appropriate MCA method for catchment resources management, Tecle (1992) evaluates compromise programming as the most suitable out of 15 MCA methods. In this study, compromise programming was chosen as the decision rule for land use optimisation. 2.2. Compromise programming In the context of MCA, a compromise can be considered as an effort to approach the ideal solution as closely as possible. Here the ideal solution refers to the mathematically-defined best compromise in a given decision space which may not be feasible in the reality. The core concept of compromise programming is based on Zeleny’s axiom of choice (Zeleny, 1982):

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then identify feasible alternatives according to their relative distances from the ideal solution. Compromise programming assumes that any decision-maker seeks a solution as closely as possible to the ideal point. To achieve this closeness, a distance function is introduced into the analysis. The concept of distance is used here not in its geometric sense, but as a proxy measure for human preferences. The general formula for compromise programming can be given as the following (Zeleny, 1982): Minimise dp ¼

X

kpi



xTi  xi xTi  xoi

p 1=p ð1Þ

where d p is distance measure from the ideal point x*; x*i is the ideal instance of variable x for criterion i; xoi is the nadir or anti-ideal instance of variable x for criterion i; x i is a real instance of variable x for criterion i; k i is the weight for criterion i (k i z 0, P k i = 1); and p is power parameter (z 1). Here, it is noted that power p affects the distance measure d p . For p = 1, d 1 becomes the longest distance between two points in a geometric sense. The shortest distance between any two points is a straight line, and this is achieved for p = 2. For p N 2, distances are based on even shorter measures of distance than a straight line reflecting the importance of the maximal deviation of variables. On the other hand, the weight k reflects the relative importance of the various criteria. Thus within compromise programming a double-weighting scheme exists (Goicoechea et al., 1982). Compromise programming can be adapted to discrete settings as well as continuous settings. The discrete approximation has two possible weaknesses (Romero and Rehman, 1989). First, the compromise set has been determined already. Secondly, the bestcompromise point should always be an extreme point, which is not always the case as in many instances the best-compromises could be interior points. However, the discrete version of compromise programming is a very useful device to rank a finite set of alternatives. Compromise programming combines the best and most useful features of both linear multi-objective programming and goal programming. It is not limited to linear cases and it can be used for identifying nondominated solutions under the most general conditions (Zeleny, 1982).

2.3. Spatial MCA In conventional MCA methods, there is no spatial concept in criterion values or in criterion weights because they are either intrinsically aspatial or aggregated into aspatial numbers. Thus, conventional MCA methods have largely been aspatial in that they assume a spatial homogeneity within the study area. This assumption is unrealistic in many decision situations because evaluation criteria and weights vary in space. On the other hand, spatial MCA methods explicitly represent the geographical dimension by combining GIS and conventional MCA approaches. The combination of GIS and MCA capabilities is of critical importance in spatial MCA. GIS provides capabilities of analysing geographical data to obtain information for making spatial decisions. MCA methods provide tools for aggregating sets of input information along with the decision-maker’s preferences into a set of output information. Consequently, the output of spatial MCA depends not only on the geographical distribution of criterion values but also on the geographical distribution of criterion weights that reflect the decision-maker’s preferences with respect to a set of evaluation criteria. This particular characteristic of spatial MCA forms the basis of the framework for site-specific land use optimisation. There have been a numerous studies combining GIS and MCA methods. Janssen and Rietveld (1990) used MCA approaches combined with GIS to reallocate agricultural land in the Netherlands. Carver (1991) integrated multicriteria evaluation methods with GIS to locate suitable sites for nuclear waste disposal in the UK. Using an MCA toolbox integrated with GIS, Jankowski (1995) evaluated each of the six alternative routes for a primary water transmission line in Seattle, Washington, USA. Tkach and Simonovic (1997) applied a raster GIS-based compromise programming method to the evaluation of floodplain management alternatives in a small town in Canada. Biermann (1999) presented a procedure to integrate GIS’s spatial analysis functions with multicriteria evaluation processes for land suitability assessment in South Africa. More recently, Chen et al. (2001) presented an example of decision-making for determining priority areas for a bush-fire hazard reduction in Australia. All these studies use spatially distributed criterion values and show the potential of a GIS-based

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Table 1 Comparison of aspatial versus spatial MCA approach Items

Aspatial MCA (conventional MCA)

Spatial MCA Partly site-specific (existing approach)

Fully site-specific (proposed approach)

One decision matrix for the entire study area

One decision matrix for each of the grid-cells within the study area

One decision matrix for each of the grid-cells within the study area

One set of criterion weights for the entire study area

One set of criterion weights for the entire study area

Decision rule is applied to the entire study area as a whole

Decision rule is applied to each of the grid-cells within the study area

One set of criterion weights for each of the grid-cells within the study area Decision rule is applied to each of the grid-cells within the study area

Decision matrix

Criterion weights

Decision rule

MCA method as an efficient and powerful tool in the context of spatial decision-making. However, it is noted that very few studies use spatially distributed criterion weights that may have crucial effects on the outcomes of a spatial MCA. In this study, it is suggested that both site-specific criterion values and site-specific criterion weights be used for spatial MCA problems including land use optimisation problems. The rationale for site-specific criterion weights is that the decision-maker’s preferences with respect to evaluation criteria would not be the same for the entire area of interest unless it is of a homogeneous environment. The decision-maker’s preferences are highly likely to be different from one place to another with different environments and, therefore, would have spatial variation within the area of interest.

Thus, in most spatial MCA problems, it is desirable that site-specific criterion weights are used to reflect the spatial variation of the decision-maker’s preferences. The conceptual differences between the conventional MCA approach, the existing spatial MCA approach and the proposed spatial MCA approach are summarised in Table 1 in terms of decision matrix, criterion weights and decision rule implementation.

3. Framework for site-specific land use optimisation Based on the spatial MCA concept, a raster GISbased MCA framework is suggested for site-specific land use optimisation at the catchment-scale (Fig. 1).

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Problem Definition

Land Use Alternatives

Evaluation Criteria

Criterion Value Maps (Decision Matrix)

Criteria

Alternatives

Criterion Weight Maps

Decision Rule: A Raster GIS-based Compromise Programming

Criteria

Weight

Sensitivity Analysis

Site-Specific Land Use Optimisation (Best Land Use Alternatives)

Fig. 1. Framework for site-specific land use optimisation.

In this site-specific approach, not only site-specific criterion values but also site-specific criterion weights are adopted and the compromise programming method is used as the decision rule. It is stressed that the decision-maker here is defined as a hypothetical being that is unbiased and is fully informed of the decision space. This unbiased decision-maker is a core device of the framework to perform land use optimisation objectively. The framework for site-specific land use optimisation is described as follows: Problem Definition – Recognition and definition of the decision problem is the point of start of any

decision making process. Define what the current problem is and investigate what land use activities are causing (or closely related to) the problem. Collect and analyse available information on land use activities that are causing (or closely related to) the problem. Also, considering the characteristics of the problem, determine the suitable size of square grid cells and discretise the study area (a catchment) into square grid cells; Land Use Alternatives – Develop a set of feasible land use alternatives based on information about the land use activities causing (or closely related to) the current problem. The set of land use alternatives

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should cover the dfull rangeT including the worst acceptable and the best possible alternatives; Criterion Value Maps – Specify a set of objectives reflecting major concerns of the problem. Then, as measures for achieving the objectives, define a comprehensive set of evaluation criteria that may have trade-off relationships to one another. For each of the grid cells, estimate criterion values for each of the land use alternatives and generate criterion value maps (i.e. site-specific criterion values); Criterion Weight Maps – Estimate criterion weights for each of the grid cells using environment variables (e.g. such as temperature, ground elevation or soil properties that cannot be controlled by the decisionmaker) that are closely related to the criteria. This is to ensure that the criterion weights are determined in an objective way. Generate criterion weight maps (i.e. site-specific criterion weights); Decision Rule–Implement the compromise programming method to accomplish a site-specific land use optimisation using maps of site-specific criterion values and weights (Eq. (2)): " #1=p X p  xTi  xij p Minimize dp; j ¼ kij ð2Þ xTi  xoi i where d p,j is distance measure from the ideal point x* for grid cell j; x*i is the ideal instance of variable x for criterion i; xoi is the nadir or anti-ideal instance of variable x for criterion i; x ij is a real instance of variable x for criterion i on grid cell P j; k ij is the weight for criterion i on grid cell j (k ij z 0, k i = 1); and p is power parameter (z 1). Note that the conventional aspatial compromise programming approach (Eq. (1)) and the proposed site-specific spatial compromise programming approach (Eq. (2)) are basically the same, but the latter has spatial dimensions with respect to criterion values (x ij ) and criterion weights (k ij ). Site-Specific Land Use Optimisation – The decision rule is applied to each of the grid cells within the catchment and then, consequently, the best land use alternative is determined for each of the grid cells. At the catchment-scale, the best land use alternatives, as a whole, form a land use scenario that is site-specifically optimised. Sensitivity Analysis – A sensitivity analysis aims to identify the effect of changes in the input (criterion

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values and weights) on the output (ranking of land use alternatives at the grid cell scale and land use patterns at the catchment-scale). If changes in the input do not significantly affect the output, the land use optimisation scheme is considered to be robust. Although the land use optimisation methodology is carried out for each of the grid cells within a catchment, changes in land use patterns at the catchment-scale may be more important than changes in the individual grid cells in the context of catchment management. Therefore, it is important to note the changes in land use scenarios at the catchment-scale. If the land use patterns at the catchment-scale are significantly affected by slight changes in criterion values or weights, it may be necessary to return to the problem formulation step and reconsider about evaluation criteria and criterion weights. In the above framework for site-specific land use optimisation, it should be noted that the set of criteria applied to a grid cell may vary according to the criterion weights applied to the given grid cell (e.g. if k ij = 0, criterion i is not applied to grid cell j). So, using criterion weights, the framework is capable of implementing site-specific criteria although it uses a set of fixed criteria. Therefore, the framework can be described as a fully site-specific approach (using site-specific criteria, criterion values and weights).

4. Land use optimisation methodology for reducing nitrate diffuse pollution Based on the site-specific land use optimisation framework proposed above, a land use optimisation methodology is suggested for reducing nitrate diffuse pollution at the catchment-scale. The methodology, as illustrated in Fig. 2, starts with a discretisation of the catchment into grid cells. Then a set of land use alternatives is developed and applied to each of the grid cells. When applied to a given grid cell, every land use alternative is evaluated from two points of view: environmental and economic potential it may have. From environmental and economic evaluations, the N-indicator (Nitrate indicator) and the E-indicator (Economic indicator) are defined to represent respectively the environmental and economic potential. These two indicators are then fed into a raster GIS-

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cator, an evaluation of land use scenarios is carried out and the best land use scenario may be suggested. Here, note that the methodology employs two fixed criteria, i.e. the N–E indicators. Although it uses sitespecific criterion values and weights, the methodology does not allow criteria themselves to vary from one place to another. Thus, in this sense, the methodology is not completely dfully site-specificT. Further details of the methodology are described in the following sub-sections.

Development of Land Use Alternatives

Land Use Alternatives

Environmental Evaluation (Site-Specific Nitrate Leaching Rate Estimation)

Economic Evaluation (Site-Specific Gross Margin Estimation)

N-Indicator

E-Indicator

Land Use Scenarios

Environmental Evaluation (Mean Annual Nitrate Concentrations)

Economic Evaluation (Catchment Mean Gross Margin)

Catchment N-Indicator

Catchment E-Indicator

Catchment Scale

Site-Specific Land Use Optimisation

Grid Scale

4.1. Development of land use alternatives

Land Use Scenario Evaluation

Best Land Use Scenario

Fig. 2. Schematic flow diagram of the approach – site-specific land use optimisation for reducing nitrate pollution from diffuse source.

based compromise programming model to determine the best land use alternative for each of the grid cells. Under a given set of optimisation conditions, the best land use alternatives comprise a land use scenario at the catchment-scale. Different sets of conditions may be applied to generate different sets of land use scenarios. Land use scenarios are then evaluated from environmental and economic points of view. Using a conventional compromise programming method with the catchment N-indicator and the catchment E-indi-

For developing land use alternatives for a given catchment, some aspects of land use should be considered. Firstly, the most important factor to be considered in general situation is the feasibility of land use alternatives. It would be almost meaningless to consider a land use alternative that is not feasible for some reasons. One way of avoiding infeasible land use alternatives would be to look at the various land uses currently being implemented around the region of interest. Assuming that environmental conditions (e.g. climate and landscape) and economic conditions (e.g. prices of goods) are fairly homogeneous at the regional scale, the variety of current land uses within the region would probably provide the possible range of land use alternatives. Secondly, it is important to identify major land uses (or agricultural practices) causing nitrate pollution in the region of interest. Once identified, the major causes should be considered in various land use alternatives within an acceptable range. If a set of land use alternatives fails to include the major causes of nitrate pollution, land use optimisation results would not be very effective in terms of nitrate pollution reduction. So it is essential to include the major causes of nitrate pollution in the region within the land use alternative set. Thirdly, land use alternatives should be developed in line with plans higher in the hierarchy. For example, if a part or whole of the catchment was designated as a nitrate vulnerable zone, any of the land use alternatives within the designated area should comply with the specific regulations given to the designated area. Finally, a set of land use alternatives must have a ‘full range’ from the worst acceptable to the best

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possible alternative so that the effects of various land use alternatives can be compared one another.

simple additive model. Below is the equation for determining DRASTIC Index (DI):

4.2. Environmental evaluation

DI ¼ Dr Dw þ Rr Rw þ Ar Aw þ Sr Sw þ Tr Tw þ Ir Iw þ Cr Cw

4.2.1. Groundwater pollution potential: DRASTIC index DRASTIC index is a numerical ranking system developed by Aller et al. (1987) to assess groundwater pollution potential in various hydrogeologic settings. The DRASTIC methodology assumes that a contaminant will start at the ground surface, enter the soil, travel through the vadose zone and enter the aquifer much like water. It is also based on an assumption that the evaluation area is 100 acres (about 0.4 km2) or larger. In the DRASTIC methodology, groundwater pollution potential is evaluated by seven factors: D – depth to water; R – net recharge; A – aquifer media; S – soil media; T – topography (slope); I – impact of the vadose zone media; and C – hydraulic conductivity of the aquifer. Each of the DRASTIC factors is assigned a relative weight ranging from 1 to 5. The most significant factor has a weight of 5 and the least significant has a weight of 1. Aller et al. (1987) determined the weights using a Delphi (consensus) approach and suggested that these weights be constant and may not be changed (Table 2). According to its value, each of the DRASTIC factors falls into a pre-defined range that is assigned to a rating value with respect to pollution potential. A rating value varies between 1 and 10 and higher ratings imply greater pollution potential and vice versa. This system allows the user to determine a numerical value for any hydrogeologic setting by using a

Table 2 DRASTIC factors and their weights (Aller et al., 1987) DRASTIC factor

Weight

D – depth to water R – (net) recharge A – aquifer media S – soil media T – topography (slope) I – impact of the vadose zone media C – (hydraulic) conductivity of the aquifer

5 4 3 2 1 5 3

ð3Þ

where the subscript r is for rating and the subscript w is for weight. Once the DI has been computed, it is straightforward to identify areas that are more susceptible to groundwater contamination than others. The higher the DI, the greater the groundwater pollution potential. 4.2.2. Nitrate leaching rate Nitrogen in the soil undergoes various processes comprising the nitrogen cycle. Some of the nitrogen, mostly in the form of nitrate, leaches below the root zone and eventually causes nitrate pollution in groundwater and surface water. Major factors affecting the amount of nitrate leaching below the root zone include temperature, precipitation, soil water content, amount of carbon substrate, plant uptake of nitrogen, and nitrogen fertiliser application rate. The interactions between these factors are complex and there are time lags in catchment responses. Thus it is difficult to quantify by field observations the effects of these factors on nitrate leaching rates. Therefore, it is suggested that a mathematical model be used for quantifying the effects of agricultural practices on nitrate leaching rates. To estimate the effects of agricultural practices on nitrate leaching rates, the mathematical model should be able to identify individual processes of the nitrogen cycle in the soil and thus it must be a process-based model. For estimating annual nitrate leaching rates using a model, one grid cell is set up to represent physical conditions of the catchment. Benefits of doing simulations for a representative grid cell are: 1) the same physical conditions are applied to all land use alternatives and, thus, simulation results of nitrate leaching rates are consistent and can be directly compared between land use alternatives; 2) any interactions with surrounding grid cells, which makes it very complicated to estimate nitrate leaching rate from its own cell, can be avoided. If the catchment is comprised of parts with different physical conditions, many representative grid cells can be set up accordingly. In this case, one complete set of simulations of

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nitrate leaching rates should be carried out for each of the representative grid cells. 4.2.3. N-Indicator The N-indicator is devised to represent the inverse of nitrate pollution potential of a land use alternative for a given grid cell. As defined in Eq. (4), the Nindicator is calculated by multiplying the normalised annual nitrate leaching rate with the relative ratio of the DI and then subtracted from 1. mij ¼ 1 

DI j fi  fmin d fmax  fmin DI max

ð4Þ

where m ij is N-indicator of land use alternative i for grid cell j; f i is nitrate leaching rate (kg N/ha/year) of land use alternative i; f max is maximum nitrate leaching rate (the worst acceptable); f min is minimum nitrate leaching rate (the best possible, f min = 0); DIj is DRASTIC index of grid cell j; and DImax is maximum value of the DRASTIC index (DImax = 226). Note that nitrate leaching rates are estimated for a representative grid cell. As nitrate leaching rate approaches to its minimum, m ij becomes 1 regardless of the DI of the grid cell. For a given nitrate leaching rate, m ij varies with the DI: it decreases with a higher DI and increases with a lower DI. The value of m ij becomes 0 when the maximum nitrate leaching rate occurs in the grid cell of the maximum DI. The value of m ij therefore ranges between 0 and 1 with the value 1 being the most favourable and the value 0 being the least favourable alternative for a given grid cell with respect to nitrate pollution potential.

assumed that the ALC grading reflects the overall economic performance of agricultural land. The principal physical factors influencing agricultural production are climate, site and soil. These factors, together with interactions between them, form the basis for classifying land into one of five grades: Grade 1 being the best and Grade 5 being the worst (Table 3). 4.3.2. Agricultural productivity Agricultural productivity of land use alternatives can be estimated using a simple agronomic model based on nitrogen response curves and the ALC grade of the given grid cell. As products from arable land and grassland are not directly comparable (for example, wheat and grass), it is necessary to convert these yields into a commensurable measure, namely money. So the agricultural productivity in the model is represented by annual gross margin. Monetary units are assumed to be constant against time. Below is a brief description of the procedure to estimate annual gross margins of arable land and grassland alternatives, respectively. 4.3.2.1. Gross margins of arable land. For a given land use alternative, the type of crop and nitrogen fertiliser application rates are known. Based on an appropriate nitrogen response function, the crop yield is estimated. The crop yield is then multiplied by the yield factor that reflects the relative performance of arable land according to its ALC grade. The average market price of the crop is applied to the estimated yield and finally the total variable cost is deducted from it to give the annual gross margin.

4.3. Economic evaluation 4.3.1. Agricultural Land Classification The Agricultural Land Classification (MAFF, 1988), ALC hereafter, provides a framework for classifying land according to the extent to which its physical or chemical characteristics impose longterm limitations on agricultural use. The limitations may affect the range of crops that can be grown, the level of yield, the consistency of yield and the cost of obtaining it. Although the ALC grading does not necessarily reflect the level of yield, it is clear that the land with fewer limitations generally incurs less overall management cost. Thus in this study it is

Table 3 Definitions of the ALC grades (MAFF, 1988) Grade/subgrade

Definition

1 2 3 3a 3b 4 5 Others

Excellent quality agricultural land Very good quality agricultural land Good to moderate quality agricultural land Good quality agricultural land Moderate quality agricultural land Poor quality agricultural land Very poor quality agricultural land Other land categories including urban, non-agricultural, woodland, agricultural buildings, open water

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4.3.3. E-Indicator The E-indicator is devised to represent the agronomic potential of a land use alternative for a given grid cell. The E-indicator of a land use alternative for a given grid cell is estimated as the normalised gross margin (Eq. (5)). The higher the gross margin, the higher the E-indicator. lij  lmin eij ¼ ð5Þ lmax  lmin where e ij is the E-indicator of land use alternative i for grid cell j; l ij is gross margin (o/ha/year) of land use alternative i for grid cell j; l max is maximum gross margin (the best gross margin for ALC grade 1); and l min is minimum gross margin (the worst gross margin for ALC grade 5). The value of e ij ranges between 0 and 1, with the value 1 being the most favourable and the value 0 being the least favourable from the agronomic point of view.

alternatives, a two-dimensional N–E diagram can be generated. As illustrated in Fig. 3, the x-axis denotes N-indicator and the y-axis represents E-indicator. Both indicators range from 0 to 1 with the value 0 being the worst and the value 1 being the best. Thus the point (1,1) is defined as the ideal point at which both indicators have their best values. In the N–E diagram, based on the shortest distance concept ( p = 2), the distance measure for each of the alternatives is estimated as follows: dij ¼

qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi  2  2ffi k2Nj 1  mij þ k2Ej 1  eij

ð6Þ

where d ij is distance measure for alternative i for grid cell j; m ij is N-indicator for alternative i for grid cell j; e ij is E-indicator for alternative i for grid cell j; k Nj and k Ej are weights for N-indicator and E-indicator for grid cell j, respectively (k Nj + k Ej = 1). Note that distance measure d ij in Eq. (6) is different from the geometric distance between the ideal point and alternative points in the N–E diagram. The value of d ij largely depends not only on N-indicator and E-indicator values but also on the weights, k Nj and k Ej . In the N–E diagram in Fig. 3, the closest point to the ideal point is the alternative C, but the distance measure of the alternative C may not be the smallest depending on the weights. For example, for a set of

IDEAL POINT (1,1) 1

A B

E-Indicator

4.3.2.2. Gross margins of grassland. A complexity is in estimating the agricultural productivity of grassland alternatives. This is mainly because grass is not the final product but one of the input for livestock farming. In order to estimate the value of grass, it is necessary to identify how the grassland is utilised and what kind of livestock farming is based on the grassland. Based on an assumption that the maximum stocking rate of the livestock is maintained, grassland gross margin is estimated as follows. Firstly, grass yield is estimated using a nitrogen response curve for the type of grassland utilisation and then the yield factor is applied to the estimated yield according to the ALC grade of the given grid cell. Then, the estimated yield and feed requirements of the livestock are used to calculate the maximum stocking rate of the livestock. In the final step, the gross margin of grassland is estimated on an assumption that the gross margin per unit area of grassland is proportional to the total gross margin of the livestock with the ratio of the grass variable cost to the total variable cost.

11

C D E

4.4. Land use optimisation 0

4.4.1. The N–E diagram For a given grid cell, once N-indicator and Eindicator have been estimated for each of land use

1 N-Indicator

Fig. 3. An example of N–E diagram showing alternatives (A – E) and the ideal point.

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weights k N = 0.9 and k E = 0.1, the alternative E would have the smallest distance measure. 4.4.2. Land use optimisation A land use alternative with the smallest d ij is determined as the best land use alternative. At the grid–scale, land use optimisation here technically means to select a land use alternative with the smallest d ij . Thus the land use optimisation model can be described as the following:   ð7Þ Minimise dij If this land use optimisation approach is applied to each of the grid cells within a catchment, the best land use alternative is determined for every grid cell and these best alternatives as a whole form a land use scenario for the catchment. In order to optimise land use at the grid–scale and to draw up a land use scenario at the catchment-scale, the weights k Nj and k Ej need to be known, as well as N-indicator and Eindicator values, for each of the grid cells. Here, this section suggests a method to generate site-specific weights for the catchment land use optimisation. In most cases, a catchment consists of parts with different physical characteristics and this spatial variation needs to be taken into consideration when carrying out catchment land use optimisations. In order to make the weights reflect spatial variations of the nitrate pollution potential and the agronomic potential across the catchment, a pair of weight distribution functions are suggested. The weight distribution function for N-indicator, x N, is defined as a normalised DRASTIC index (Eq. (8)) and, similarly, the weight distribution function for E-indicator, x E, is defined as a normalised ALC grade (Eq. (9)). xNj ¼

DI j  23 226  23

ð8Þ

xEj ¼

6  ALCj 61

ð9Þ

where x Nj and x Ej are weight distribution functions for the N-indicator and the E-indicator of a given grid cell j, respectively. Note that both x Nj and x Ej are standardised to vary from 0 to 1 while the DRASTIC index changes from 23 to 226 and the ALC grade

varies from 6 to 1. These linear weight distribution functions are then used to generate the site-specific weights as in Eqs. (10) and (11). kNj ¼

xNj xNj þ xEj

ð10Þ

kEj ¼

xEj xNj þ xEj

ð11Þ

where k Nj and k Ej are weights for the N-indicator and the E-indicator of a given grid cell j, respectively (k Nj + k Ej = 1). These site-specific weights have two important implications. Firstly, they are objective because they are evaluated using physical characteristics of land rather than subjective preferences of any stakeholders. Secondly, they are dtunedT at the catchment scale in that they reflect relative significance of a land’s potential within a given catchment in terms of DRASTIC index and ALC grade. Thus, these sitespecific weights play a crucial role in generating an objective and efficient land use scenario – an didealT compromise at both local and catchment scale. Once criterion weights are determined, these weights are substituted into Eq. (6) together with N– E indicator values and, consequently, the site-specifically optimised land use scenario is generated. 4.4.3. Sensitivity analysis Sensitivity analysis is a general method used for evaluating how sensitive the model output is to small changes in the input. The idea behind a sensitivity analysis is to check robustness of the model by analysing the effect of perturbed input values on the output. There are two important elements to consider in a sensitivity analysis of MCA: criterion weights and criterion values. Criterion weights are the essence of value judgements and they are often subjective numbers. Therefore criterion weights are more likely to be in dispute than other parameters (Malczewski, 1999). Thus it is suggested that a sensitivity analysis be carried out for the criterion weights. When introducing a perturbation to criterion weights, it is often impractical to apply a certain fixed value of perturbation to the whole catchment. This is particularly so for a system with site-specific criterion weights because criterion weights vary from one grid cell to another. Thus, for valid perturbations,

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it is better to apply a ratio rather than a fixed value and the perturbation ratio needs to be applied to the smaller weight. For example, if the criterion weights are 0.4 and 0.6, respectively, and the perturbation ratio is 0.1, two sets of perturbed weights can be determined by deducting and adding 0.1  0.4 = 0.04 from/to the original weights: 0.36 and 0.64; and 0.44 and 0.56, respectively. The perturbed criterion weights kVNj and kVEj can be described as the following:   ð12Þ kVNj ¼ kNj Frp d min kNj ; kEj kVEj ¼ kEj Frp d minðkN ; kE Þ

ð13Þ

where r p is perturbation ratio. When a set of perturbed criterion weights is applied to a land use optimisation scheme, a corresponding land use scenario is generated. If the resulting land use scenario has no or little change from the original scenario, the optimisation scheme can be described as robust for that range of perturbation. However, if the resulting land use scenario is significantly different from the original scenario, the optimisation scheme cannot be described as robust for that range of perturbation. In the latter case, it is necessary to apply reduced perturbations and examine whether significant changes are made in the resulting land use scenario. Repeating this procedure can provide information on how sensitive the optimisation scheme is to the criterion weights and how precisely the weights need to be defined. 4.5. Evaluation of land use scenarios Depending on the number of sets of criterion weights applied to the land use optimisation, there may be multiple land use scenarios to evaluate. From environmental and economic points of view, every land use scenario may have different potential. If scenarios need to be ranked, or if the best scenario needs to be chosen, this is another MCA problem. In this study, a conventional compromise programming method is applied to this matter. For environmental evaluation, long-term effects of land use scenarios on nitrate concentrations at the catchment outlet are estimated. Here, the range of ’long-term’ could be from several years to several decades depending on the catchment characteristics. From nitrogen simulations for each of the individual

13

land use scenarios, mean nitrate concentrations for a certain period (e.g. the last year of the simulation period) can be calculated. These mean nitrate concentrations are then normalised to define the catchment N-indicator: Ni ¼ 1 

ci  cmin cmax  cmin

ð14Þ

where Ni is catchment N-indicator for land use scenario i; c i is mean nitrate concentrations at the catchment outlet, for land use scenario i; c max is the maximum mean nitrate concentrations at the catchment outlet; and c min is the possible minimum mean nitrate concentrations at the catchment outlet (c min = 0.1 for pristine condition). For economic evaluation, on the other hand, catchment mean agricultural productivity is estimated for each of the land use scenarios. Agricultural productivity here is represented by annual gross margin (o/ ha/year). Catchment mean gross margins are then normalised to define the catchment E-indicator: l  lmin Ei ¼ i ð15Þ lmax  lmin where Ei is catchment E-indicator for land use scenario i; l i is catchment mean gross margin (o/ha/year) for land use scenario i; l max is the possible maximum gross margin (o/ha/year); and l min is the possible minimum gross margin (o/ha/year). Both Ni and Ei vary between 0 and 1, with the value 1 being the most favourable and the value 0 being the least favourable land use scenario from the environmental and the economic points of view, respectively. When Ni and Ei are estimated, the concept of the N–E diagram, described before, is adopted for the evaluation of land use scenarios. Here, the ideal point is again located at (1,1) and the distance measure is estimated as follows: qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi ð16Þ di ¼ ð1  Ni Þ2 þ ð1  Ei Þ2 where d i is distance measure from the ideal point for land use scenario i; Ni is catchment N-indicator for land use scenario i; and Ei is catchment E-indicator for land use scenario i. Note that there are no weighting factors in Eq. (16) – weights are taken into account at individual grid cells and there is no need to consider them at the catchment-scale. Now that the

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value of d i has been estimated for each of the land use scenarios, the land use scenario with the smallest value of d i may be suggested as the best land use scenario.

5. Discussion The framework for site-specific land use optimisation suggested above adopts a compromise programming method as the decision rule. It uses both sitespecific criterion values and site-specific criterion weights, whereas most existing approaches use sitespecific criterion values and global constant criterion weights. What should be noted is that the decisionmaker in this framework is defined as a hypothetical being that is unbiased and is fully-informed of the decision space. Such a decision-maker may not exist in the real world, but it is a key component in this academic approach to producing objective results that may have significant implications in the real situation. Based on the suggested framework, a site-specific land use optimisation methodology has been developed and suggested. The objective of land use optimisation here is to minimise the environmental pollution (nitrate leaching rate) and to maximise the economic return (agronomic gross margin), taking into account both environmental and economic potential of land across the catchment. For this purpose, the N-indicator (Nitrate indicator) and the E-indicator (Economic indicator) are defined to represent the relative potential of nitrate pollution and economy, respectively. Using the N–E indicators and site-specific criterion weights, the methodology can produce a site-specifically optimised land use scenario at the catchment-scale. Unlike in most other approaches where criterion weights are determined subjectively, the site-specific criterion weights in this methodology are objectively determined and are reflecting the relative significance of a land’s potential within a given catchment. Therefore, the outcome of this methodology, i.e. the site-specifically optimised land use scenario, is considered to be objective and efficient at the catchment-scale. There are limitations in the actual use of the methodology. Firstly, the methodology is purely an academic, top-down approach and does not take account of the participatory process. The methodology is not

for directly improving the participatory process, but for indirectly supporting the process by proposing an didealT solution for trade-offs over land uses. Secondly, only two criteria, namely the N–E indicators, are taken into account for land use optimisation and no other criterion is considered in the methodology. Therefore the application of the methodology is limited to nitrate diffuse pollution problems only and this is certainly a significant limitation. However, if modified using a composite programming method, which is an extension of the compromise programming method, the methodology can be extended to be used for multiple pollutants problems. Thirdly, numerous simplifications of complex responses of the agrienvironmental system are included in the mathematical models used for evaluating nitrate leaching rates and economic gross margins. Thus, implications of the final results of the methodology could be significantly affected by certain simplifications in the models. Finally, uncertainties are involved in evaluating DRASTIC index and ALC grades as well as in using mathematical models through equations and parameter values. Thus, the final results of the methodology must be interpreted bearing in mind the uncertainties included. In its present form, the methodology represents a technical contribution towards the process of managing land use in a manner which can help comply with the WFD, while preserving as far as possible its economic production potential. However, the methodology has not been rendered into a form where it could support a participatory stakeholder decisionmaking process using, for example, different multimedia tools to present the information to the stakeholders (e.g. Pereira et al., 2003). This would require a further phase of work not included within the scope of the research reported here.

6. Conclusions The EU Water Framework Directive (WFD) has brought catchment management plans to the interest of various sectors of the society. One of the most probable reasons why catchment management plans attract many interests is that they include land use management plans to tackle diffuse source water pollution. As trade-off relationships between the agrono-

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my and the environment are common over land uses, one of major concerns of catchment management plans is how to balance the trade-offs over land uses at both local and catchment scales. In this paper, an integrated modelling and multicriteria analysis (MCA) methodology is presented which can be used to balance the trade-offs over land uses for reducing nitrate pollution from agricultural diffuse sources. Based on a compromise programming approach, the methodology operates on each of the square grid cells which a given catchment is comprised of. Land use optimisation here is basically to choose out of a given set of land use alternatives the optimum alternative – i.e. the best compromise between the N-indicator (Nitrate indicator) and the E-indicator (Economic indicator) that represent the relative potential of nitrate pollution and economy, respectively. What can be differentiated from other approaches is that the suggested approach employs not only site-specific criterion values but also site-specific criterion weights. Because the site-specific criterion weights are objectively evaluated using physical properties of land rather than subjective preferences of any stakeholders and also because they reflect relative significance of land’s potential across a given catchment, the resultant site-specifically optimised land use scenario is considered to be objective and efficient at the catchment-scale. The methodology has many limitations. It is a purely academic top-down approach taking account of no participatory processes. It is applicable to nitrate diffuse pollution problems only and it involves many simplifications and uncertainties. Despite its limitations, however, the methodology is considered to be useful particularly because its outcome, i.e. a sitespecifically optimised land use scenario, is regarded as an didealT compromise at both local and catchment scales. Therefore, in the WFD-related participatory process, the suggested methodology can be used to help steer the decision-making process towards an didealT compromise between economic return and nitrate diffuse pollution.

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