Selecting irrigation water pricing alternatives using a multi-methodological approach

Mathematical and Computer Modelling 55 (2012) 861–883

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Selecting irrigation water pricing alternatives using a multi-methodological approach Jordi Gallego-Ayala ∗ Water Research Institute of Mozambique, Av. Patrice Lumumba n◦ 770 Maputo, Mozambique

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Article history: Received 25 February 2011 Received in revised form 28 August 2011 Accepted 12 September 2011 Keywords: AHP Compromise solution Irrigated agriculture PMP TOPSIS

abstract Public decision-makers in charge of designing and implementing the irrigation water pricing policy required by the Water Framework Directive have a difficult task to select between a set of possible alternatives. The main objective of this study is to develop a multi-methodological approach that allows supporting decision makers to choose the alternative that achieves the best compromise solution in irrigated areas between a set of socio-economic and environmental attributes. To this end, a case study is applied in two irrigation districts in the province of Palencia (Spain). The proposed approach takes the following steps: (a) selection of potential alternatives to be evaluated, (b) classification of farmers into homogeneous groups, (c) simulation of irrigated farmers behaviour when facing different water pricing alternatives via positive mathematical programming models, (d) selection of the socioeconomic and environmental criteria for the analysis and (e) application of a hybrid multi-criteria decision making model to rank the alternatives integrating the Analytic Hierarchy Process and the modified Technique for Order Preference by Similarity to Ideal Solution. The results show the effectiveness and potential utility of the proposed methodological framework for irrigation water pricing instruments’ selection. The empirical results of this research indicate that those pricing instruments which consider the current consumption of irrigation water allow for a better compromise solution instead of the tools that price water irrespective of current consumption. Furthermore, the results also suggest that the irrigation water pricing policy could be implemented in function of the different farming districts, rather than establishing one single type of irrigation water pricing instrument and tariff level for a whole river basin, as these would not allow to achieve the same degree of compromise solution in different farming-districts. © 2011 Elsevier Ltd. All rights reserved.

1. Introduction European agriculture is undergoing a cycle of continuous changes at the policy level, due to factors both external (globalization, economic development, climate change) and endogenous (new social demands) to the European Union [1]. The growing environmental consciousness of the European society has led to a change in the policies direction of the Union, so it has come to assign greater weight to environmental objectives pursued by the policies of the Union [2]. In the field of water policy, the Water Framework Directive (WFD)—Directive EC/60/2000—requires implementing new management plans aiming to achieve ‘‘good ecological status of water bodies’’, to reach a rational use and management of water resources,

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from a perspective of sustainable development. To this end, the WFD will introduce a series of measures and economic instruments that affect irrigated agriculture directly and significantly [3]. In line with this, irrigated agriculture will be affected by the implementation of economic instruments based on a water pricing policy (Article 9), aimed to improve irrigation water management through the imposition of a water pricing tariff that enables the cost-recovery of water-related services [4–7]. If the irrigation water pricing policy is applied exhaustively in financial, environmental and resource cost-recovery terms, it could jeopardize the sustainability of irrigated agriculture, bearing in mind that it will produce negative effects from the economic (economic profitability of farms) and social (decrease of labour demand) points of view [8,9]. Indeed, in rural areas with low profitable irrigation performance, the successful achievement of environmental objectives aimed by the WFD without compromising the economic and social viability of this multifunctional system will be a challenge for public administration, to the extent that policy makers should select an economic instrument which allows to reach a compromised solution between the socioeconomic and environmental performance of irrigated farms [10]. There is a growing literature devoted to the analysis of economic, social and environmental effects of irrigation water pricing, among which can be highlighted the most recent works of Berbel et al. [9], Dono et al. [11], Iglesias and Blanco [12], Manos et al. [13,14], Latinopoulos [15] and Viaggi et al. [16] among others. However it should be noted that these studies have focused their analysis of the irrigation water pricing through a battery of relevant socioeconomic and environmental policy indicators separately. This has led to further research with the aim of analysing the irrigated water pricing impacts in an integrated manner. In line with this, [17,18] analyse the effects of water pricing implementation using a decision support system and a composite index respectively. The objective of this work is to apply a multi-methodological approach to support the selection of those irrigation water pricing alternatives that allow to obtain a better compromise solution between the socioeconomic and environmental criteria in conflict. To this end, a methodology based on the simulation of irrigators behaviour through mathematical programming techniques will be used, allowing to obtain a set of socioeconomic and environmental attributes, that then will be utilized in a hybrid model of the Analytic Hierarchy Process (AHP) and the modified Technique for Order Preference by Similarity to Ideal Solution (TOPSIS) to rank the water pricing alternatives in terms of their performance with respect to the socioeconomic and environmental attributes. To operationalize this objective, an empirical application has been undertaken in a real agricultural system. In particular, two irrigated areas of the province of Palencia (Spain) have been analysed. The results of this study are intended to serve as a useful tool for policy makers in order to design and implement the most appropriate tools that enable to improve the ‘‘governance’’ of irrigated agricultural systems and allow for a balance in the sustainable performance of irrigated areas: economic viability, social acceptance and eco-compatibility. The paper is structured as follows. This introductory section is followed by a description of the studied areas used for the empirical analysis. The third section offers a detailed description of the methodology employed. The fourth section is a summary of the results, while the paper finishes with a section that discusses the main conclusions. 2. Case study The empirical application of this research focuses on the Farming Districts (FD) of Cerrato and Saldaña-Valdavia, located in the centre of the Northern Spanish plateau, in the province of Palencia (Castilla y León region). These two FD are situated in the north of the Duero river basin. Their high altitude (between 800 and 900 m.a.s.l.) and long distance from the sea give them a continental climate, with an average rainfall typically not exceeding 500 mm per annum, not distributed evenly over the year (most of the rain fall in autumn, and to a lesser degree, in spring). Under such climatic conditions, irrigated agriculture is the only means of breaking the rain-fed monoculture of winter cereals typical of the area, to allow for the introduction of summer crops. The main characteristics of the selected FD are:

• Cerrato—Farming district: irrigated agriculture in this district covers 10705 ha, accounting for 9.9% of its utilized agricultural area, which is distributed among 941 farms. Water resources for irrigated agriculture come from surface water resources. The main irrigation technology is the sprinkler which occupies 70% of the irrigated surface. The most important irrigated crops are winter cereals, which occupy 63% of the total area, followed by alfalfa (16%) and sugar-beet (9%). • Saldaña-Valdavia—Farming district: some 4886 ha or 7.2% of the total agricultural area of Saldaña-Valdavia are under irrigation. The FD comprises 679 irrigated farms. As in Cerrato—Farming district, the water used by irrigated agriculture is supplied from surface water resources. The predominant irrigation technology is furrow irrigation (87% of the irrigated area). The main irrigated crops are winter cereals, which occupy 41.0% of the total area, grain maize (32%), green maize (11%) and alfalfa (10%). In order to characterize the farm diversity within these two irrigated areas, a farm typology via a cluster analysis based on the farmers’ crop-mix as a classificatory variable (see Section 3.2) was performed. This defined three homogeneous groups within each farming district, with their respective farm-types. Table 1 shows the main features of these farm-types. These areas were chosen in order to study a real case both on account of their technical characteristics, in that they are representative of Spanish inland irrigated agricultural systems, and for practical reasons, i.e. the availability of high-quality data (see Section 3.6).

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Table 1 Main features of different farm-types.

Cerrato-FD

SaldañaValdavia-FD

Cluster

% of farmers sampled

% of total area analysed

Farm size (ha)

% of irrigated land

Main irrigation technology

Main irrigated crops

Farmers with diversified production

45.8

60.9

164

22

Sprinkler (78% of the irrigated area)

Winter cereals (43%), alfalfa (30%) and sugar-beet (20%)

Sprinkler irrigation cereal-sugar-beet growers

28.9

24.5

102

31

Sprinkler (100% of the irrigated area)

Winter cereals (85%) and sugar-beet (13%)

Furrow irrigation cereal-sugar-beet growers

25.3

14.5

74

29

Furrow (88% of the irrigated area)

Winter cereals (84%) and sugar-beet (10%)

Fodder growers

29.2

28.0

73

18

Sprinkler (80% of the irrigated area)

Green-maize (30%), alfalfa (20%) and grain maize (10%)

Cereal growers

39.6

56.8

102

18

Furrow (92% of the irrigated area)

Winter cereals (80%) and grain maize (15%)

Grain maize growers

31.2

15.2

36

45

Furrow (92% of the irrigated area)

Grain maize (75%)

3. Methodology The methodological framework proposed to select the irrigation water pricing alternatives is based on five steps: (1) selection of the potential water pricing alternatives to be implemented, (2) performance of a cluster analysis to identify the farm types in the study area, (3) development of positive mathematical programming models to simulate irrigated farmers’ behaviour when facing different water pricing alternatives, (4) selection of the socioeconomic and environmental attributes and estimation of their values for different water pricing scenarios analysed and (5) identification of the best alternatives using a hybrid model that integrates the AHP and the modified TOPSIS. The methodological framework in which this research is based can be summarized through the chart-flow presented in Fig. 1. This methodological outline is based in the previous works of Gómez-Limón and Riesgo [19], Gómez-Limón et al. [20] and Gallego-Ayala and Gómez-Limón [21]. Nonetheless, it should be noted that in Fig. 1, the steps below the broken line (application of the hybrid multi-criteria decision making model to rank the alternatives integrating the AHP and the modified TOPSIS), represent the main novelty presented in this research for the analysis of water pricing policies. The five steps of the methodology are described in the next sections. 3.1. Irrigation water pricing alternatives Taking into consideration different alternative methods applicable for irrigation water pricing [22], as well as the particular characteristics of the case study (public irrigated lands and surface water resources), the following three instruments have been selected as being of greatest interest for their potential implementation in the study areas:

• Pricing per unit irrigated area. This is based on water pricing per irrigated hectare, irrespective of the crop produced. In consequence, three different scenarios are proposed for the simulation in our case study, in which the charge increases progressively from e50 to e150/ha per year. • Volumetric pricing. This considers an irrigation water pricing scheme based on the volume of water used. For this purpose, three pricing levels have been selected, ranging from e0.02 to e0.06/m3 . • Two-part tariff system. This is a combination of the two alternative pricing systems described above, which levies a fixed tariff per hectare actually irrigated and a volumetric tariff on irrigation water. Four new different tariff levels have been generated by combining two fixed tariffs per hectare (e 50, e100/ha per year) with two levels of volumetric pricing (e 0.02, e0.04/m3 ). 3.2. Decision-making heterogeneity and cluster analysis Modelling farming activity at the agricultural system level (or at any other level that deals with a set of individual farms) implies problems of aggregation bias. Indeed, modelling a set of farms in a unique programming model overestimates the mobility of resources, allowing the modelled farms to combine resources in proportions that are impossible in the real world [23]. This aggregation bias can only be avoided if the farms included in the models fulfil strict homogeneity criteria [24] such as technological homogeneity, pecuniary proportionality and institutional proportionality.

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Fig. 1. Main steps in the methodological framework. Source: Based on [19–21].

The irrigated areas under consideration as case studies are located within two different agricultural counties. Thus, taking into account climate and soil-quality homogeneity, and technological, institutional and market characteristics, the case study areas could be considered as geographical units that fulfil the above-mentioned homogeneity criteria. It therefore seems reasonable to assume similar behaviour for all farmers within the same farming district, which would mean that the operation of the water pricing instruments being considered could be analysed through a single simulation model with relatively small problems of aggregation bias. Nonetheless, such homogeneity in the producers’ behaviour rarely exists in the real world. Thus, although they have similar resource base, farmers in the same agricultural systems typically display significant differences in their production decisions. Therefore to minimize the aggregation bias in simulation, it is necessary to classify farmers in terms of homogeneous groups with regard to their crop mixes [25], which include farmers with similar cost and net revenues functions (pecuniary proportionality and technological homogeneity). In order to develop a typology of producers, a survey was carried out among the irrigators in the two FD areas, with the aim of gathering information on crop-mixes that would allow the farmers’ production schemes to be characterized (see Section 3.5). This information was used to apply a cluster analysis, which utilizes farmers’ actual crop mixes as classification criteria (crop-mixed were actually featured bearing in mind the binomial crop-irrigation_technology; further discussion about this issue is made in Section 3.3.1). This statistical technique took the Euclidean squared distance as a measure of distance among actual crop-mixes (vector crop area expressed in percentages). The Ward or minimum variance method was utilized as the aggregation criterion. This procedure has been applied to each farming district under analysis, which produced three groups of irrigators within each county as mentioned in Section 2. The corresponding farm-types, which are

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representative of the whole group of farms in each of the case study areas, were treated as the unit of analysis for building the simulation models. 3.3. The simulation model Positive mathematical programming (PMP), developed by Howitt [26], is a mathematical modelling technique based on a calibration system, which establishes either a non-linear yield or non-linear cost functions that allows to reproduce the same cop-mix distribution as the one observed in the real world, by using the information contained in the dual values of the decision variables (crops). Despite the fact that both approaches (non-linear yield and cost functions) are equally valid to calibrate mathematical models, the method based on costs calibration is more commonly applied in the existing literature than that based on yields. Within this premise, quadratic cost functions were used as the mathematical calibration method. Among the different PMP approaches, the extension of the PMP developed by Röhm and Dabbert [27] has been used for the irrigation water pricing scenarios simulation. Röhm and Dabbert [27] proposed a PMP model which allows for a higher degree of substitution between similar crops (called ‘variant activities’), rather than between other less similar crops (activities). Thus, the concept of variant activities can be applied to the same crop that is grown under different techniques (e.g. irrigated and rain-fed), as well as to crops belonging to the same family [27]. This property is suitable for identifying relevant water-pricing scenarios since farmers would presumably substitute irrigated crops for rain-fed when facing water pricing tariffs. The mathematical formulation of this extension of the PMP can be summarized as follows,1 bearing in mind the different activities (t) and the possible variants (v ) (the activities and variant activities considered for this research are described in detail in Section 3.3.1). The initial model takes the following formulation: MaxTGM =

−− t

v



pt ,v · yt ,v − ct ,v + st ,v xt ,v + SFP

(1a)

Subject to:

−− t

− v

v



xt ,v ≤

−− v

t



xt ,v ≤

− v

x0t ,v



x0t ,v (1 + ε1 )

xt ,v ≤ x0t ,v (1 + ε2 )



(1b)

∀t

(1c)

∀t , v

(1d)

ε2 > ε1 xt ,v ≥ 0 ∀t , v

(1e) (1f)

Function (1a) represents the Linear Programming (LP) model objective function, where TGM is the total gross margin. The TGM is obtained by summing the gross margins resulting from each activity. For this reason, the objective function is logically a function of the area allocated to each crop, xt ,v (hectares devoted to crop t, with variant v ). These xt ,v are regarded as the decision variables of the model. In order to calculate the TGM, it is also necessary to have the following technical coefficient data: price (pt ,v ), yield (yt ,v ), variable cost (ct ,v ) and Common Agricultural Policy (CAP) direct subsidies, coupled to the production per unit area (st ,v ). It also includes the Single Farm Payment (SFP). The SFP is a subsidy that agricultural producers receive regardless of their crop-mixes or yields achieved, and that is fixed individually on the basis of the amount of subsidies granted in the past. Nonetheless, to receive this subsidy the farmers are subjected to a series of cross-compliance obligations. The SFP can be seen as a ‘‘fixed income’’ that is independent of crop decisions taken by farmers. Thus the SFP is only added in function (1a) to calculate the farmers’ TGM. The set of constraints included in the above model can be interpreted as follows: constraint (1b) limits the total agricultural land available, where x0t ,v represents the crop-mix observed in the base year. Constraint (1c) represents the constraints for total activities, where ε1 is a small positive number. Finally, constraint (1d) represents the constraints for the variant activity, with ε2 being another small positive number that must satisfy Eq. (1e). The addition of constraints (1c) and (1d) forces an optimal solution in the LP model that reproduces the activities observed in the base year (x0t ,v ). As a result of the introduction of these two constraints, the model solution generates the dual values for the different activities. Constraint (1c) produces the dual values of activities λt and constraint (1d) the dual values of the variant activity λt ,v . Once the dual values have been obtained, they are used to calibrate the cost function of the individual activities. These parameters are also used to define the new objective function for the PMP model. Thus, function [2] introduces the objective function of the extended version of the PMP:

 MaxTGM =

−− t

v

xt ,v



 yt ,v pt ,v − ct ,v

 αt ,v + βt ,v xt ,v + γt ,v

− v

xt ,v

1 For detailed information about the mathematical development of this PMP approach, see [27].

 + st ,v

+ SFP

(2)

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Table 2 Decision variables for the study areas. Decision variables

Crop

Winter cereals group and its variants X1,1 Rain-fed wheat X1,2 Furrow-irrigation wheat X1,3 Sprinkler-irrigation wheat X1,4 Rain-fed barley X1,5 Furrow-irrigation barley X1,6 Sprinkler-irrigation barley Sunflower group and its variants X2,1 Rain-fed sunflower X2,2 Furrow-irrigation sunflower X2,3 Sprinkler-irrigation sunflower Alfalfa group and its variants X3,1 Rain-fed alfalfa X3,2 Furrow-irrigation alfalfa X3,3 Sprinkler-irrigation alfalfa Other crop activities X4 X5 X6 X7 X8 X9



Rain-fed green peas Furrow-irrigation grain maize Sprinkler-irrigation grain maize Furrow-irrigation green maize Sprinkler-irrigation green maize Sprinkler-irrigation sugar-beet

where αt ,v denotes the axis intercepted coefficient αt ,v = 1 −

 level

βt ,v =

λt ,v ct ,v x0t ,v



λt +λt ,v



, βt ,v denotes the slope coefficient of variant activity   λ ∑t 0 and γt ,v denotes the slope coefficient of total crop activity level γt ,v = . c x ct ,v

t ,v

v t ,v

Once the PMP model is calibrated, it allows the productive pattern behaviour of farmers to be simulated when they face a new economic (products and/or inputs prices, subsidies, etc.) or normative (productive constraints) context that affects the agricultural sector. Based on this calibrated model, the water pricing alternatives will be simulated.2 3.3.1. Decision variables in the simulation models The decision variables considered for building the simulation models were the surfaces devoted to each one of the most common crops in the study area (xt ,v ). Nonetheless, due to the differences in cost and existing yields, it was considered adequate to characterize these activities based on two factors: crop and irrigation technology. Thus, bearing in mind only the combinations really used by the farmers in the analysed areas, a total of 18 decision variables have been selected, as can be seen in Table 2. In this regard, it is worth pointing out that the models developed were designed with the aim of simulating the productive behaviour of the farm-types set analysed, including both their irrigated areas, whether these were used for irrigated or rainfed crops, and those which are purely rain-fed (with no possibility of irrigation). In the literature devoted to the analysis of the impacts of irrigation water pricing policies, it is frequently found that only irrigated farm plots are modelled. The approach presented in this research may prove to be more suitable for explaining the farmers’ behaviour, since their decisions are probably based on an overall assessment of their farms, rather than focusing exclusively on the irrigated part of the farm. With the aim of giving greater flexibility to the simulation models and allowing a greater level of substitution between the variant activities when faced with changes in the water pricing policy (substitution of irrigated crops for rain-fed crops), three groups of variant activities were defined following the extension of the PMP developed by Röhm and Dabbert [27]. First, activities t were established on the basis of crops (e.g. sunflower, alfalfa, etc.). Second, for each activity t, variant activities v were defined on the basis of the irrigation techniques available for each activity (irrigated_furrow, irrigated_sprinkler and rain-fed). The resulting variant activities comprise a set of ‘‘crop-irrigation_technology’’ (e.g., alfalfa-rain-fed, alfalfasprinkler_irrigation). Finally, the different variant activities of winter cereals (wheat and barley) were combined in one single group of variant activities, given the botanical similarity of these crops. This assumes that within any group of these variants, there is a higher degree of substitution (one irrigated crop for the same crop in rain-fed conditions, or one winter cereal for another crop from this botanic family) than between other activities. Following this procedure were defined the following groups: (a) winter cereals, made up of the variant activities wheat and barley, both irrigated and rain-fed, (b) sunflower, made

2 A different model was built for each group of farmers, in order to be able to simulate independently for each cluster the effects of the alternative irrigation water pricing methods. The aim was to minimize the aggregation bias discussed in Section 3.2.

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up of the variant activities irrigated sunflower and rain-fed sunflower, and (c) alfalfa, with the variant activities irrigated alfalfa and rain-fed alfalfa. Table 2 summarizes the activities and variant activities considered for this study. 3.3.2. Simulation model for irrigation water pricing alternatives The objective function of the model built to simulate the water pricing alternatives incorporates the respective fixed (ts ) and volumetric water tariff (tw ):

 Max

−− t

v

+ SFP − ts ·

 xt ,v

yt ,v pt ,v − ct ,v

−− tr





αt ,v + βt ,v xt ,v + γt ,v

− v

xt ,v

xt ,v

+ st ,v − tw ·

WRt ,v



Efic t ,v (3a)

vr

Subject to: Total area constraint:

−− t

v

xt ,v ≤ AREA

Total irrigated area constraint:

−− tr

Sprinkler irrigation area constraint:

(3b)

xt ,v ≤ AREAirrigated

(3c)

vr

−− t rs

xt ,v ≤ AREAsprinkler

(3d)

v rs

Water availability constraint: AREA · ALLOT ≥

−− tr

vr

xt ,v ·

WRt ,v Efic t ,v

(3e)

Sugar-beet CAP constraint: x9 ≤ 0.5 · x09

(3f)

Non-negativity constraint: xt ,v ≥ 0 ∀t , v

(3g)

Function (3a) represents the objective function, which is adjusted to the expression [2]. This includes the fee per irrigated area ts that would be charged for the crops and variants actually irrigated (indicated by the sub-indices t r and v r ), and tw as the volumetric irrigation water tariff. The first constraint (3b) limits the crop area to the total area (irrigated plus rain-fed) actually available on the farm (AREA). Constraint (3c) limits the irrigated area to the available irrigated area (AREAirrigated ). As this is a short and mediumterm model, the conversion of rain-fed into irrigated land is not allowed. For the same reason, the possibility of introducing innovations in irrigation technology was not included. The area using sprinkler irrigation (crops and variants indicated by indices t rs and v rs ) is therefore limited to the area currently under irrigation using that technique (AREAsprinkler ), as established in expression (3d). Constraint (3e) limits the water available for irrigation, where ALLOT is the annual water allotment assigned to each farm measured in m3 /ha, WRt ,v are the water requirements of the crop t , v and Efic t ,v is the technical efficiency associated with the irrigation technique used for that crop. Expression (3f) was included in order to allow for a suitable simulation to be made of the restructuring of the sugar-beet market following the latest reform of the Common Market Organization for sugar. This reform forces sugar-beet growers to a compulsory abandonment of 50% of this crop production from the 2008/2009 season, for which they were compensated with e 40 for each tonne that they had delivered as average during the period 2004–2008 (a quantity which is included, duly annualized, within the SFP). 3.3.3. Calibration of the models It is worth pointing out that the different PMP models built for this research were calibrated bearing in mind the crop mix followed by the producers in the 2007–2008 farming year, where the regulatory framework of the CAP referred to the mid-term review approved in 2003 (partial decoupling of support). However, faced with the subsequent change in the CAP and the implementation of the 2009 Health Check (total decoupling of production support), the change in the CAP was also taken into consideration in the simulation of the various economic instruments for irrigation water pricing. This was done in order to give greater meaning to the results obtained. 3.4. Selecting and weighting the criteria for the analysis With the aim to achieve the objective proposed in this work, it is necessary to select a set of criteria that will allow to quantify the multidimensional performance of the selected irrigated agricultural systems from a holistic perspective (economic, social and environmental), when facing the proposed water pricing alternatives. Bearing in mind the modelling

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possibilities using mathematical programming, this paper has considered 12 indicators,3 based on the proposed set of indicators developed by Gómez-Limón and Sanchez-Fernandez [28] for the same agricultural systems, which are shown in Table 3. Weighting makes it possible to differentiate the relative importance of the various socioeconomic and environmental attributes considered. The weights presented in [28], calculated by means of the Analytic Hierarchy Process have been integrated in this research to determine the weights of the criteria evaluation when developing the modified TOPSIS (see Section 3.5) to rank the water pricing alternatives. The Analytic Hierarchy Process technique was first applied to a representative sample of the population of Castilla y León region (survey of 321 individuals), with the aim of obtaining the weights of the three criteria dimensions (economic, social and environmental) considered for the study, in order to calculate the relative importance of the set of economic, social and environmental criteria. The same technique was then applied to a panel of 16 technical experts from universities and research institutes, with the aim of obtaining the weights of the socioeconomic and environmental criteria contained in each of the three criteria dimensions. The weight given to each attribute is shown in Table 3.4 3.5. The modified TOPSIS method The TOPSIS analysis developed by Hwang and Yoon [31] is a widely used multi-criteria decision making tool to support the selection of the best compromise solution between a finite set of alternatives [32], resulting in a rank of alternatives by using a distance measures framework. This procedure is based in the premise that the best alternative should have the closest distance to the positive ideal-solution and the farthest distance from the negative ideal-solution [33,34]. The original TOPSIS method has been criticized and some shortcomings of the technique have been identified [35,36]. This has led to further development of the TOPSIS with the aim of mitigating the drawbacks of the original approach. Within this context, Deng [37] presents a modified TOPSIS which allows to obtain a meaningful interpretation of the results by using weighted Euclidean distances rather than the n-dimensional Euclidean distance. This approach has been used to select the irrigation water pricing alternative that allows to obtain the best compromise solution when confronting the performance of the set of socioeconomic and environmental attributes. The modified TOPSIS is applied in six steps as listed below: Step 1. Build the decision matrix (D) for ranking the irrigation water pricing alternatives, by using the data obtained from the simulation models for each criterion analysed. The decision matrix for evaluating the alternatives implemented is as follows: F1

f11  f21



A1 A2

..   . .  .. D=  Ai  fi1 ..   .. . .

fm1

Am

F2

···

Fj

···

f12 f22

··· ···

f1j f2j

··· ···

fi2

··· ···

fij

··· ···

fm2

··· ···

fmj

··· ···

.. .

.. .

.. .

.. .

Fn

f1n f2n 



..   .   fin  ..   .

(4)

fmn

where fij denotes the performance value of alternative Ai with respect to each criteria Fj . Step 2. Calculate the normalized decision matrix (R). The normalization has been carried out by using vector normalization, following the next expression: rij = 

fij n ∑

,

j = 1, . . . , n; i = 1, . . . , m

(5)

fij2

j =1

where rij denotes the normalized value. Thus R = [rij ]mxn . Step 3. Determine the positive (V + ) and negative (V − ) ideal-solution, using the following formulation: V

+

= r1 , r2 , . . . , rn 

+

+

+



 =

   ′′ max rij |j ∈ J , min rij |j ∈ J ′

i

i

(6)

3 For a detailed description of the selected attributes and methodology employed to calculate the socioeconomic and environmental attributes the works of Gómez-Limón and Sanchez-Fernandez [28] and Bazzani et al. [29] can be consulted. 4 The agricultural activity in Castilla y León region has a strong socioeconomic role, as this sector generates 6% of the total region GDP and contributes with more than 11% to the regional employment. On the other hand, the region faces a significant problem of depopulation in rural areas, mostly due to the agricultural modernization process that took place in the past decades. However, the agricultural activity is still a key role player for the socioeconomic survival of rural communities. These circumstances explain the weights assigned to each criteria dimension at regional level. Indeed, the perception of Castilla y León society prioritizes the social role of irrigated agriculture – as a rural backbone – over the environmental and economic performance of the agricultural sector [30]. For these reasons, the weights used in this research are specific for Castilla y León agricultural sector and cannot be extrapolated to other case studies. This issue is discussed later in the Conclusions Section.

J. Gallego-Ayala / Mathematical and Computer Modelling 55 (2012) 861–883

869

Table 3 Selected criteria and weights. Criteria dimensions

Weights of criteria dimensions (%)

Economic

28.45

Social

39.87

Environmental 31.68

Criteria

Measurement units

Weights of criteria (%)

Normalized weights of criteria (%)

Polarity of criteria*

Total gross margin (TGM) Contribution to the regional GDP (CONGDP)

e/ha e/ha

70.26 29.74

19.98 8.46

+ +

Farm employment (EMPLT) Seasonal labour (SEAS) Risk of farming abandonment (ABAND)

h/ha % %

41.59 14.70 43.71

15.38 5.44 16.16

+ − −

Specialization (SPEC) Soil covering (SOILCOV) Nitrogen balance (BALN) Phosphorus balance (BALP) Pesticides risk (PESTRISK) Water consumption (WATER) Energy balance (ENBA)

% % kg N/ha kg P/ha kg/ha m3 /ha kcal/ha

6.79 13.73 15.07 8.07 18.49 16.42 21.45

2.35 4.75 5.21 2.79 6.39 5.68 7.42

− + − − − − +

Source: Based on Gómez-Limón and Sanchez-Fernandez [25]. * Criteria with polarity + means: more is better; criteria with polarity—means: less is better.

V − = r1− , r2− , . . . , rn− =







min rij |j ∈ J ′ i

   , max rij |j ∈ J ′′

(7)

i

where J ′ and J ′′ are linked to the criteria with positive polarity (more is better) and the criteria with negative polarity (less is better), respectively. Step 4. Calculate the separation distance of each alternative from the positive and negative ideal-solution, by using the weighted Euclidean distances. Eqs. (8) and (9) define the distance of each alternative from the positive ideal-solution (Si+ ) and the negative ideal-solution (Si− ), respectively:

 −  n Si+ =  wj (rij − rj+ )2 , i = 1, . . . , m

(8)

j =1

 −  n Si =  wj (rij − rj− )2 , i = 1, . . . , m −

(9)

j =1

where wj denotes the associated weight to each attribute (for this research, as stated before, using the weights obtained from the AHP method). Step 5. Calculate the relative closeness to the ideal solution for each irrigation water pricing alternative analysed. The relative closeness of the alternative Ai to the ideal solution is given as: Ci =

Si− Si+ + Si−

,

i = 1, . . . , m

(10)

where Ci is an index with values ranging between 0 and 1, where 0 corresponds to the worst possible performance of the alternative and 1 to the best. Step 6. Finally, rank the alternatives according to the descending order of Ci index values. 3.6. Data acquisition The input data needed to feed the simulation models, as well as for calculating the socioeconomic and environmental attributes, was gathered from both primary and secondary sources. The primary information was obtained from a survey of farmers in the two study areas. A questionnaire was drawn up to collect information about the socioeconomic characteristics of the owners, the structural characteristics of their farms, their crop plans and the agricultural practices and techniques they employed. The sample universe comprised farmers with irrigated land in the Cerrato and Saldaña-Valdavia districts: 1636 farmers according to the last Agricultural Census. Given the practical impossibility of performing a simple random sampling, we opted to use quota sampling based on affiliation of the producers to different Farmers’ Unions (ASAJA, UPA and COAG). This procedure produced 107 valid questionnaires (59 for Cerrato – FD and 48 for Saldaña-Valdavia – FD).

870

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The information collected enabled to characterize the diversity of farms in the study areas and to establish the farm-types in the districts. The survey was also the main source of information for building the simulation models and calculating the attributes selected for the empirical application. The sources of secondary information made it possible to collect the data needed for the models and to calculate the attributes, especially in the cases in which this information is uniform for all the producers in the analysed areas: output and input prices, coefficients of nitrogen, phosphorus or energy contents in inputs and outputs, water requirements for irrigated crops, efficiency of irrigation systems or pesticide toxicity. 4. Results 4.1. Ranking irrigation water pricing alternatives First of all, the resolution of the simulation models described above made it possible to obtain results (calculation of the selected attributes to perform the analysis) for each farm-type when faced with the irrigation water pricing alternatives proposed. The results obtained for each group of farmers were subsequently aggregated at farming district level by weighting the sum of the results for each farm-type, based on the area represented by each of them. Then, a ranking of the alternative irrigation water pricing instruments has been elaborated considering the socioeconomic and environmental attributes obtained for each alternative. Thus, in order to summarize the presentation of the results, this section focuses on the analysis of the aggregated results for Cerrato and Saldaña-Valdavia districts, as these are the most important for supporting political decision-making. Tables 4 and 5 display the crop-mix evolution of the two FD when the irrigation water pricing instruments are implemented. Tables 6 and 7 show the values of the socioeconomic and environmental attributes for the study areas as a whole, in each of the alternative water pricing instruments simulated. The decision matrix for each of the case studies analysed is generated using the data contained in those tables. On the other hand, Tables 8 and 9 show the normalized decision matrix, derived from Tables 6 and 7 by applying the vector normalization. Before commenting on the results of the irrigation water pricing instruments ranking, it is important to point out that, in general terms, different tariffs generate evolutions in the attributes analysed in the same direction in the two irrigated agricultural systems analysed: an erosion of the economic attributes (worsening of economic viability of irrigated agriculture), a decrease in the social attributes and a mix of positive (BALN, BALP, PESTRISK and WATER attributes) and negative (SPEC, SOILCOV and ENBA attributes) effects in the environmental attributes. Thus, as shown in Tables 6 and 7, when different types of water charges increase, additional falls take place in the attributes compared to the baseline scenario (see Table A.1). The explanation for this lies in the fact that the farmers introduce new changes in their productive strategies as a response to water pricing, substituting irrigated crops for rain-fed alternatives (see Tables 4 and 5). On the other hand, special attention should be given to the impact of irrigation water pricing instruments on irrigation water consumption (WATER indicator), bearing in mind that this economic instrument promoted by the WFD aims to incentivate the rational and efficient use of the water resources. An in-depth analysis of the impacts generated by the implementation of the water pricing policy in the WATER indicator, would point to significant decreases in the water consumption. In fact, the WATER indicator would register falls that range from −17.29% (50 e/ha water pricing alternative) to −63.83% (100 e/ha + 0.04 e/m3 water pricing scenario) in the case of Cerrato FD, and decreases in this indicator from −8.13% (50 e/ha water pricing alternative) to −51.50% (0.06 e/m3 ) for the Saldaña-Valdavia FD (see Appendix B). In broad terms, all the water pricing alternatives implemented produce higher positive impacts in the irrigation water consumption in CerratoFD, comparatively to Saldaña-Valdavia-FD. This circumstance can be explained by the farmers’ production behaviour (cropmix) in each farming district. Indeed, Cerrato-FD has a predominant presence of irrigated crops that are highly sensitive to water pricing policies due to their low added value, such as winter cereals. Therefore these crops are rapidly substituted by the most common rain-fed crops in the FD when the water pricing instruments are implemented. On the other hand, in Saldaña-Valdavia FD there is a significant abundance of high added value crops (cash crops) that are also intensive water demanding crops, such as grain maize; that are slowly substituted for rain-fed crops. These results are in agreement with those provided by Gómez-Limón et al. [38] and Riesgo and Gómez-Limón [39] from other irrigated areas of the Duero river basin when farmers face the implementation of an irrigation water pricing policy. Once the values of the socioeconomic and environmental attributes are obtained with respect to the water pricing alternatives under evaluation in the two irrigated agricultural systems analysed, the modified TOPSIS method has been applied to rank the alternatives. The results are shown in Table 10. It is worth to highlight that, by comparing the Ci values of the 10 alternatives for the two case studies, the results show a ranking disparity between the alternatives in the farming districts analysed. In line with this, the analysis of the ranking of alternatives obtained for Cerrato-FD points that, in a descendent order, the three water pricing alternatives (see values in bold, Table 10) that allow to obtain a better compromise solution confronting the socioeconomic and environmental attributes in conflict, are the two-part tariff system of 50 e/ha + 0.02 e/m3 (Ci performance value 0.667), the volumetric tariff of 0.04 e/m3 (Ci value of 0.657) and the two-part tariff system of 100 e/ha + 0.02 e/m3 (Ci value of 0.643). On the contrary, in Saldaña-Valdavia—FD the compromise priority ranking for the three best alternatives is the volumetric tariff of 0.02 e/m3 (Ci value of 0.559), the two-part tariff system of 50 e/ha + 0.02 e/m3 (Ci performance value 0.548) and the volumetric tariff of 0.04 e/m3 (Ci performance value 0.547).

1.28 1.20 1.13 1.27 1.18 1.09 1.20 1.11 1.12 1.03

1.62 1.52 1.43

Pricing instrument: volumetric tariff 0.02 e/m3 11.49 1.58 0.04 e/m3 11.60 1.44 0.06 e/m3 11.65 1.31

Pricing instrument: two-part tariff system 50 e/ha + 0.02 e/m3 11.57 1.48 50 e/ha + 0.04 e/m3 11.64 1.35 100 e/ha + 0.02 e/m3 11.62 1.39 100 e/ha + 0.04 e/m3 11.68 1.25

X1,3 1.38

Pricing instrument: irrigated area 50 e/ha 11.31 100 e/ha 11.40 150 e/ha 11.49

X1,2

1.73

X1 ,1

64.34 66.13 65.70 67.42

62.59 64.84 66.47

60.26 62.18 64.09

57.24

X1,4

2.91 2.35 2.52 1.96

3.29 2.74 2.18

3.46 3.08 2.69

3.94

X1,5

6.96 5.92 6.06 5.02

7.86 6.83 5.79

7.99 7.09 6.19

9.10

X1,6

Decision variables – crop-mixes – expressed in %

11.18

Baseline year

Irrigation water pricing alternatives

Table 4 Crop-mix evolution for Cerrato-FD.

3.59 3.65 3.61 3.67

3.54 3.62 3.67

3.44 3.49 3.54

3.37

X2 ,1

X2,3

0.54 0.46 0.51 0.42

0.57 0.49 0.41

0.62 0.59 0.55

0.66

0.10 0.11 0.10 0.11

0.10 0.11 0.11

0.07 0.08 0.09

0.06

X3,1

0.03 0.00 0.14 0.00

0.31 0.00 0.00

0.59 0.54 0.48

0.59

X3,2

0.22 0.00 0.00 0.00

0.67 0.00 0.00

3.50 2.57 1.64

3.59

X3,3

X4

4.78 5.04 4.96 5.19

4.44 4.89 5.09

3.57 3.98 4.39

2.87

0.27 0.25 0.26 0.24

0.27 0.25 0.23

0.29 0.28 0.27

0.30

X5

0.05 0.04 0.05 0.04

0.05 0.04 0.04

0.05 0.05 0.05

0.05

X6

1.97 1.97 1.97 1.97

1.97 1.97 1.97

1.97 1.97 1.97

3.93

X9

84.38 85.56 85.99 88.06

82.15 85.05 86.98

78.65 81.13 83.60

74.72

% of rainfed area

15.62 13.44 14.01 11.94

17.85 14.95 13.02

21.35 18.87 16.40

25.28

% of irrigated area

4.69 3.95 4.31 3.46

5.46 4.43 3.72

5.95 5.41 4.88

6.56

Irrigated area by furrow irri. (%)

10.93 9.50 9.69 8.48

12.39 10.51 9.30

15.40 13.46 11.52

18.71

Irrigated area by sprinkler irri. (%)

J. Gallego-Ayala / Mathematical and Computer Modelling 55 (2012) 861–883 871

0.55 0.52 0.49 0.55 0.51 0.47 0.52 0.48 0.48 0.44

Pricing instrument: volumetric tariff 0.02 e/m3 41.57 5.38 0.04 e/m3 42.20 4.92 0.06 e/m3 42.75 4.46

Pricing instrument: two-part tariff system 50 e/ha + 0.02 e/m3 41.85 5.06 50 e/ha + 0.04 e/m3 42.46 4.60 100 e/ha + 0.02 e/m3 42.12 4.74 100 e/ha + 0.04 e/m3 42.70 4.28

X1 ,3

Pricing instrument: irrigated area 50 e/ha 41.06 5.52 100 e/ha 41.40 5.20 150 e/ha 41.73 4.88

X1,2 0.60

X1,1

X1,5

33.27 35.05 34.07 35.73

1.84 1.48 1.59 1.24

32.47 2.08 34.28 1.73 35.83 1.38

30.94 2.19 31.98 1.95 32.96 1.70

30.18 2.52

X1,4

0.13 0.11 0.11 0.10

0.15 0.13 0.11

0.15 0.13 0.12

0.17

X1,6

1.30 1.36 1.32 1.38

1.27 1.34 1.39

1.21 1.25 1.28

1.19

X2,1

0.18 0.15 0.17 0.14

0.19 0.16 0.13

0.21 0.20 0.19

0.23

X2,2

Decision variables – crop-mixes – expressed in %

40.78 5.95

Baseline year

Irrigation water pricing alternatives

Table 5 Crop-mix evolution for Saldaña-Valdavia-FD.

0.55 0.47 0.52 0.43

0.59 0.50 0.42

0.63 0.60 0.56

0.68

X2,3

X3,1

5.55 5.63 5.59 5.65

5.52 5.61 5.66

5.15 5.36 5.51

4.52

0.63 0.49 0.58 0.49

0.68 0.49 0.41

0.96 0.91 0.87

0.95

X3,2

0.00 0.00 0.00 0.00

0.00 0.00 0.00

1.04 0.46 0.03

1.30

X3 ,3

1.41 1.66 1.52 1.73

1.30 1.55 1.74

1.03 1.20 1.36

0.99

X4

5.16 4.61 5.01 4.46

5.31 4.76 4.21

5.71 5.56 5.41

6.05

X5

X6

1.00 0.94 0.98 0.92

1.02 0.96 0.90

1.06 1.03 1.01

1.11

0.95 0.50 0.77 0.18

1.13 0.55 0.02

1.52 1.35 1.18

1.56

X7

0.49 0.01 0.30 0.00

0.67 0.19 0.00

0.95 0.78 0.60

1.00

X8

X9

0.12 0.12 0.12 0.12

0.12 0.12 0.12

0.12 0.12 0.12

0.23

83.38 86.17 84.62 87.19

82.13 84.98 87.37

79.38 81.19 82.84

77.66

% of rainfed area

16.62 13.83 15.38 12.81

17.87 15.02 12.63

20.62 18.81 17.16

22.34

% of irrigated area

13.82 11.84 12.87 10.79

14.78 12.61 10.61

16.11 15.17 14.23

17.25

Irrigated area by furrow irri. (%)

2.80 1.99 2.51 2.02

3.09 2.41 2.02

4.50 3.64 2.93

5.09

Irrigated area by sprinkler irri. (%)

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Table 6 Decision matrix for Cerrato-FD: models results for the selected attributes for each irrigation water pricing alternative. Irrigation water pricing alternatives

TGM (e/ha)

CONGDP EMPLT (e/ha) (h/ha)

SEAS (%)

106.68 102.05 97.20

10.15 9.97 9.79

79.14 29.52 80.53 32.11 81.98 34.39

Pricing instrument: volumetric tariff 0.02 e/m3 264.16 102.42 0.04 e/m3 250.95 96.26 0.06 e/m3 239.43 91.23

9.66 9.45 9.41

Pricing instrument: two-part tariff system 50 e/ha + 0.02 e/m3 255.84 97.81 50 e/ha + 0.04 e/m3 243.86 92.53 100 e/ha + 0.02 e/m3 248.44 94.08 100 e/ha + 0.04 e/m3 237.51 88.81

9.50 9.42 9.46 9.39

Pricing instrument: irrigated area 50 e/ha 273.37 100 e/ha 263.32 150 e/ha 254.50

ABAND SPEC (%) (%)

SOILCOV BALN BALP PESTRISK WATER (%) (kg N/ha) (kg P/ha) (kg/ha) (m3 /ha)

ENBA (kcal/ha)

60.26 62.18 64.09

62.12 61.73 61.35

18.14 17.33 16.52

11.56 11.05 10.53

423.48 420.59 417.70

4640.33 4003.56 3367.40

7.95 × 106 7.88 × 106 7.81 × 106

83.28 31.90 85.05 35.30 85.36 38.27

62.59 64.84 66.47

60.91 60.52 60.53

17.92 16.91 15.90

10.86 10.29 9.93

410.36 407.35 408.45

3120.58 2390.15 2145.55

8.02 × 106 7.89 × 106 7.75 × 106

84.59 85.26 84.89 85.45

64.34 66.13 65.70 67.42

60.62 60.52 60.57 60.52

17.12 16.11 16.31 15.30

10.40 9.98 10.07 9.67

408.53 408.58 409.29 409.79

2573.32 2209.73 2354.53 2029.29

7.92 × 106 7.79 × 106 7.82 × 106 7.68 × 106

34.04 37.13 35.95 38.77

Table 7 Decision matrix for Saldaña-Valdavia-FD: models results for the selected attributes for each irrigation water pricing alternative. Irrigation water pricing alternatives

TGM (e/ha)

CONGDP EMPLT (e/ha) (h/ha)

SEAS (%)

184.81 179.84 174.92

10.60 10.48 10.38

72.81 22.55 73.92 24.29 74.89 25.79

Pricing instrument: volumetric tariff 0.02 e/m3 319.15 176.70 0.04 e/m3 298.62 164.25 0.06 e/m3 281.69 152.32

10.37 10.27 10.18

Pricing instrument: two-part tariff system 50 e/ha + 0.02 e/m3 310.78 171.88 50 e/ha + 0.04 e/m3 291.65 159.80 100 e/ha + 0.02 e/m3 303.07 167.05 100 e/ha + 0.04 e/m3 285.24 154.88

10.33 10.24 10.28 10.20

Pricing instrument: irrigated area 50 e/ha 334.49 100 e/ha 324.86 150 e/ha 316.30

ABAND SPEC (%) (%)

SOILCOV BALN BALP PESTRISK WATER (%) (kg N/ha) (kg P/ha) (kg/ha) (m3 /ha)

ENBA (kcal/ha)

41.06 41.69 42.26

62.69 62.62 62.60

26.44 26.25 26.06

11.67 11.47 11.30

551.58 537.00 522.79

5571 4919 4359

1.02 × 107 9.96 × 106 9.68 × 106

74.99 24.26 76.57 26.94 77.82 29.07

42.04 43.06 43.88

62.52 62.80 63.02

26.47 26.17 25.73

11.44 11.31 11.12

519.36 477.49 443.99

4426 3588 2941

9.74 × 106 8.91 × 106 8.27 × 106

75.58 77.06 76.17 77.50

42.47 43.48 42.89 43.80

62.62 62.96 62.72 62.97

26.24 25.91 26.02 25.65

11.34 11.28 11.24 11.06

506.29 468.33 493.20 455.25

4084 3305 3741 3036

9.44 × 106 8.69 × 106 9.14 × 106 8.40 × 106

25.75 28.17 27.11 29.28

Table 8 Normalized decision matrix for Cerrato-FD. Irrigation water pricing alternatives

TGM

CONGDP EMPLT

SEAS

ABAND

SPEC

SOILCOV BALN

BALP

PESTRISK WATER

ENBA

Pricing instrument: irrigated area 50 e/ha 0.3412 100 e/ha 0.3286 150 e/ha 0.3176

0.3475 0.3324 0.3174

0.3336 0.3277 0.3218

0.2994 0.3047 0.3102

0.2679 0.2914 0.3120

0.2958 0.3052 0.3146

0.3223 0.3203 0.3183

0.3419 0.3266 0.3114

0.3499 0.3343 0.3188

0.3247 0.3225 0.3203

0.4888 0.4217 0.3547

0.3203 0.3173 0.3144

Pricing instrument: volumetric tariff 0.02 e/m3 0.3297 0.04 e/m3 0.3132 0.06 e/m3 0.2988

0.3336 0.3136 0.2972

0.3174 0.3105 0.3091

0.3151 0.3218 0.3230

0.2894 0.3203 0.3473

0.3072 0.3182 0.3262

0.3160 0.3141 0.3141

0.3378 0.3188 0.2996

0.3287 0.3115 0.3004

0.3146 0.3123 0.3132

0.3287 0.2518 0.2260

0.3230 0.3179 0.3122

Pricing instrument: two-part tariff system 50 e/ha + 0.02 e/m3 0.3193 0.3186 50 e/ha + 0.04 e/m3 0.3043 0.3014 100 e/ha + 0.02 e/m3 0.3101 0.3065 100 e/ha + 0.04 e/m3 0.2964 0.2893

0.3122 0.3095 0.3109 0.3085

0.3200 0.3226 0.3212 0.3233

0.3089 0.3369 0.3262 0.3518

0.3158 0.3245 0.3224 0.3309

0.3145 0.3141 0.3143 0.3140

0.3228 0.3036 0.3075 0.2884

0.3148 0.3021 0.3047 0.2927

0.3132 0.3133 0.3138 0.3142

0.2711 0.2328 0.2480 0.2138

0.3190 0.3136 0.3151 0.3092

Despite the different ranking of alternatives for the two irrigated farming districts, it is important to point out how those pricing instruments, which consider the current consumption of irrigation water (volumetric and two-part tariff), permit to obtain better compromise solutions confronting the tools that price water irrespective of current consumption (pricing by irrigated area).

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J. Gallego-Ayala / Mathematical and Computer Modelling 55 (2012) 861–883

Table 9 Normalized decision matrix for Saldaña-Valdavia-FD. Irrigation water pricing alternatives

TGM

CONGDP EMPLT

SEAS

ABAND

SPEC

SOILCOV BALN

BALP

PESTRISK WATER

ENBA

Pricing instrument: irrigated area 50 e/ha 0.3445 100 e/ha 0.3346 150 e/ha 0.3258

0.3459 0.3366 0.3274

0.3244 0.3207 0.3177

0.3040 0.3086 0.3127

0.2700 0.2909 0.3089

0.3043 0.3090 0.3132

0.3159 0.3156 0.3155

0.3204 0.3181 0.3158

0.3258 0.3203 0.3156

0.3498 0.3405 0.3315

0.4322 0.3817 0.3381

0.3492 0.3398 0.3301

Pricing instrument: volumetric tariff 0.02 e/m3 0.3287 0.04 e/m3 0.3076 3 0.06 e/m 0.2901

0.3307 0.3074 0.2851

0.3175 0.3142 0.3116

0.3131 0.3197 0.3249

0.2905 0.3227 0.3482

0.3115 0.3191 0.3252

0.3151 0.3165 0.3176

0.3207 0.3172 0.3118

0.3195 0.3158 0.3105

0.3293 0.3028 0.2815

0.3433 0.2783 0.2282

0.3324 0.3040 0.2822

Pricing instrument: two-part tariff system 50 e/ha + 0.02 e/m3 0.3201 0.3217 50 e/ha + 0.04 e/m3 0.3004 0.2991 3 100 e/ha + 0.02 e/m 0.3121 0.3127 3 100 e/ha + 0.04 e/m 0.2938 0.2899

0.3161 0.3134 0.3147 0.3120

0.3155 0.3217 0.3180 0.3236

0.3084 0.3374 0.3246 0.3506

0.3147 0.3222 0.3179 0.3246

0.3156 0.3173 0.3160 0.3173

0.3180 0.3140 0.3153 0.3108

0.3167 0.3149 0.3139 0.3089

0.3210 0.2970 0.3127 0.2887

0.3186 0.2564 0.2902 0.2355

0.3221 0.2966 0.3119 0.2865

Table 10 Relative closeness and rank of the alternatives. Irrigation water pricing alternatives

Cerrato-FD

Saldaña-Valdavia-FD

Si+

Si−

Ci

Rank

Si+

Si−

Ci

Rank

Pricing instrument: irrigated area 50 e/ha 100 e/ha 150 e/ha

0.0674 0.0523 0.0415

0.0446 0.0364 0.0394

0.398 0.410 0.487

9 8 7

0.0517 0.0409 0.0351

0.0484 0.0403 0.0374

0.484 0.496 0.516

10 9 7

Pricing instrument: volumetric tariff 0.02 e/m3 0.04 e/m3 0.06 e/m3

0.0330 0.0311 0.0420

0.0503 0.0595 0.0641

0.604 0.657 0.604

5 2 5

0.0328 0.0347 0.0478

0.0417 0.0419 0.0517

0.559 0.547 0.520

1 3 6

Pricing instrument: two-part tariff system 50 e/ha + 0.02 e/m3 50 e/ha + 0.04 e/m3 100 e/ha + 0.02 e/m3 100 e/ha + 0.04 e/m3

0.0284 0.0375 0.0332 0.0447

0.0570 0.0627 0.0599 0.0674

0.667 0.626 0.643 0.601

1 4 3 6

0.0321 0.0402 0.0346 0.0467

0.0390 0.0450 0.0397 0.0495

0.548 0.528 0.534 0.515

2 5 4 8

4.2. Sensitivity analysis for irrigation water pricing alternatives A sensitivity analysis concerning the weights of the socioeconomic and environmental criteria used in the modified TOPSIS model has been carried out, in order to check the consistency of the results obtained in the previous section. For this purpose, a total of 19 experiments have been undertaken to compare the impact of potential changes in the weights of socioeconomic and environmental dimensions and criteria (these experiments have been applied for the two FD). For this exercise, in the first 4 experiments the weights associated to the socioeconomic and environmental dimensions have been modified. Obviously, the weights of the three criteria dimensions would also have a different impact on the socioeconomic and environmental criteria weights analysed. However, these 4 experiments can be used to compare the different preferences of society regarding the public objectives in Castilla y León agriculture. In Experiment 1, all the criteria dimensions have equal weights; in Experiments 2–4, the weight of one criterion dimension is higher than the weight of the remaining criterion dimensions. For Experiment 5, all the socioeconomic and environmental criteria weights are the same; and for Experiments 6–17, the weight of one criterion is higher than the weight of the remaining criteria. The exercise conducted has been completed by calculating two additional experiments focusing in the criteria polarity. Thus, in Experiment 18, the criteria with polarity + have higher weights than the criteria with polarity −; on the other hand, in Experiment 19, the criteria with polarity − have the higher weights than the criteria with polarity +. Tables 11 and 12 show the results obtained for this exercise, as well as a detailed description of the experiments. The results obtained for the sensitivity analysis explained above indicate that, in the case of Cerrato-FD, the volumetric water pricing at 0.04 e/m3 level allows to obtain the best compromise solution in 11 of the 19 experiments. On the other hand, for Saldaña-Valdavia-FD, the two-part tariff system of 50 e/ha + 0.04 e/m3 performs the best compromise solution in 7 of the experiments. However, it should be noted that the results obtained for the 19 designed experiments in the two FD are heterogeneous and do not match exactly with the results obtained in the previous section regarding the best compromise solutions. In any case, the most important information provided by Tables 11 and 12 is that, for all the 19 experiments carried out in the two FD, the best compromise solution always considers the current consumption of irrigation water (volumetric and two-part tariff).

Weight of social criterion dimension 50% Weight of the other criteria dimensions 25%

Weight of environment criterion dimension 50% Weight of the other criteria dimensions 25%

All criteria same weight

Experiment 2

Experiment 3

Experiment 4

Experiment 5

Experiment 7

Experiment 6

Weight of economic criterion dimension 50% Weight of the other criteria dimensions 25%

Weight of CONGDP criterion 25% Weight of the other criteria 6.82%

Weight of TGM criterion 25% Weight of the other criteria 6.82%

All criteria dimensions same weight

Experiment 1

Experiments

0.352

0.333

0.300

0.325

0.458

0.444

0.402

0.379

0.364

0.343

0.358

0.455

0.445

0.413

0.490

0.489

0.490

0.488

0.486

0.486

0.487

0.590

0.584

0.576

0.588

0.618

0.620

0.606

0.693

0.701

0.721

0.710

0.611

0.628

0.655

0.658

0.669

0.702

0.677

0.544

0.561

0.601

0.06 e/m3

0.02 e/m3

0.04 e/m3

Pricing instrument: volumetric tariff 150 e/ha

50 e/ha

100 e/ha

Pricing instrument: irrigated area

Ci index value of the alternatives

Table 11 Results of the sensitivity analysis for Cerrato-FDa .

0.686

0.693

0.704

0.701

0.636

0.649

0.666

0.672

0.686

0.716

0.695

0.569

0.585

0.623

50 e/ha + 0.04 e/m3

0.648

0.667

0.699

0.675

0.542

0.556

0.597

100 e/ha+ 0.04 e/m3

(continued on next page)

0.680

0.695

0.719

0.703

0.593

0.607

0.640

100 e/ha + 0.02 e/m3

Pricing instrument: two-part tariff system 50 e/ha + 0.02 e/m3

J. Gallego-Ayala / Mathematical and Computer Modelling 55 (2012) 861–883 875

Weight of EMPLT criterion 25% Weight of the other criteria 6.82%

Weight of SEAS criterion 25% Weight of the other criteria 6.82%

Weight of ABAND criterion 25% Weight of the other criteria 6.82%

Weight of SPEC criterion 25% Weight of the other criteria 6.82%

Weight of SOILCOV criterion 25% Weight of the other criteria 6.82%

Weight of BALN criterion 25% Weight of the other criteria 6.82%

Weight of BALP criterion 25% Weight of the other criteria 6.82%

Experiment 8

Experiment 9

Experiment 10

Experiment 11

Experiment 12

Experiment 13

Experiment 14

Experiments

Table 11 (continued)

0.290

0.291

0.301

0.321

0.391

0.310

0.311

0.338

0.339

0.344

0.357

0.405

0.351

0.351

0.495

0.496

0.490

0.489

0.488

0.491

0.491

0.559

0.539

0.576

0.579

0.601

0.573

0.572

0.718

0.699

0.719

0.708

0.662

0.707

0.706

0.710

0.706

0.701

0.684

0.610

0.691

0.690

0.06 e/m3

0.02 e/m3

0.04 e/m3

Pricing instrument: volumetric tariff 150 e/ha

50 e/ha

100 e/ha

Pricing instrument: irrigated area

Ci index value of the alternatives

0.697

0.675

0.702

0.694

0.672

0.692

0.691

0.722

0.716

0.714

0.697

0.633

0.703

0.702

50 e/ha + 0.04 e/m3

0.723

0.714

0.717

0.701

0.650

0.706

0.705

100 e/ha + 0.02 e/m3

Pricing instrument: two-part tariff system 50 e/ha + 0.02 e/m3

0.710

0.709

0.698

0.678

0.609

0.689

0.688

100 e/ha+ 0.04 e/m3

876 J. Gallego-Ayala / Mathematical and Computer Modelling 55 (2012) 861–883

Weight of ENBA criterion 25% Weight of the other criteria 6.82%

Weight of criteria with polarity +14% Weight of criteria with polarity −4.29%

Weight of criteria with polarity +6% Weight of criteria with polarity −10%

Experiment 16

Experiment 17

Experiment 18

Experiment 19

0.281

0.374

0.302

0.187

0.300

0.331

0.394

0.344

0.281

0.343

0.491

0.489

0.490

0.488

0.490

0.573

0.592

0.578

0.580

0.577

0.732

0.672

0.721

0.802

0.722

0.04 e/m3

0.719

0.633

0.700

0.813

0.703

0.06 e/m3

0.02 e/m3

150 e/ha

Pricing instrument: volumetric tariff

100 e/ha

50 e/ha

Ci index value of the alternatives

Pricing instrument: irrigated area

First best alternative 0.000 ; second best alternative 0.000 ; third best alternative 0.000 .

Weight of WATER criterion 25% Weight of the other criteria 6.82%

Experiment 15

a

Weight of PESTRISK criterion 25% Weight of the other criteria 6.82%

Experiments

Table 11 (continued)

0.712

0.671

0.704

0.759

0.705

0.732

0.649

0.714

0.819

0.716

50 e/ha + 0.04 e/m3

0.733

0.659

0.717

0.805

0.719

100 e/ha + 0.02 e/m3

Pricing instrument: two-part tariff system 50 e/ha + 0.02 e/m3

0.718

0.625

0.696

0.812

0.700

100 e/ha+ 0.04 e/m3 J. Gallego-Ayala / Mathematical and Computer Modelling 55 (2012) 861–883 877

All criteria same weight

Weight of TGM criterion 25% Weight of the other criteria 6.82%

Experiment 6

Weight of environment criterion dimension 50% Weight of the other criteria dimensions 25%

Weight of social criterion dimension 50% Weight of the other criteria dimensions 25%

Weight of economic criterion dimension 50% Weight of the other criteria dimensions 25%

All criteria dimensions same weight

Experiment 5

Experiment 4

Experiment 3

Experiment 2

Experiment 1

Experiments

0.430

0.388

0.420

0.534

0.536

0.457

0.421

0.447

0.534

0.546

0.511

0.495

0.503

0.521

0.546

0.529

0.509

0.525

0.587

0.587

0.582

0.612

0.590

0.513

0.510

0.542

0.503

0.522

0.563

0.490

0.04 e/m3

0.571

0.615

0.582

0.471

0.466

0.513

0.06 e/m3

Pricing instrument: volumetric tariff 0.02 e/m3

150 e/ha

50 e/ha

100 e/ha

Pricing instrument: irrigated area

Ci index value of the alternatives

Table 12 Results of the sensitivity analysis for Saldaña-Valdavia-FDa .

0.552

0.552

0.551

0.544

0.553

0.550

50 e/ha + 0.02 e/m3

0.579

0.617

0.587

0.480

0.482

0.523

50 e/ha + 0.04 e/m3

0.571

0.590

0.572

0.500

0.515

0.533

100 e/ha + 0.02 e/m3

Pricing instrument: two-part tariff system

0.572

0.612

0.579

0.463

0.466

0.509

100 e/ha+ 0.04 e/m3

878 J. Gallego-Ayala / Mathematical and Computer Modelling 55 (2012) 861–883

Weight of CONGDP criterion 25% Weight of the other criteria 6.82%

Weight of EMPLT criterion 25% Weight of the other criteria 6.82%

Weight of SEAS criterion 25% Weight of the other criteria 6.82%

Weight of ABAND criterion 25% Weight of the other criteria 6.82%

Weight of SPEC criterion 25% Weight of the other criteria 6.82%

Weight of SOILCOV criterion 25% Weight of the other criteria 6.82%

Weight of BALN criterion 25% Weight of the other criteria 6.82%

Experiment 7

Experiment 8

Experiment 9

Experiment 10

Experiment 11

Experiment 12

Experiment 13

Experiments

Table 12 (continued)

0.387

0.388

0.395

0.468

0.395

0.390

0.439

0.421

0.421

0.426

0.477

0.426

0.423

0.468

0.495

0.495

0.496

0.500

0.496

0.495

0.520

0.507

0.509

0.511

0.554

0.510

0.509

0.537

0.611

0.612

0.607

0.560

0.606

0.609

0.582

0.04 e/m3

0.615

0.615

0.607

0.537

0.607

0.612

0.563

0.06 e/m3

Pricing instrument: volumetric tariff 0.02 e/m3

150 e/ha

50 e/ha

100 e/ha

Pricing instrument: irrigated area

Ci index value of the alternatives

0.551

0.552

0.551

0.546

0.550

0.550

0.558

50 e/ha + 0.02 e/m3

0.618

0.617

0.610

0.540

0.610

0.615

0.575

50 e/ha + 0.04 e/m3

0.613

0.612

0.605

0.527

0.605

0.609

0.564

100 e/ha+ 0.04 e/m3

(continued on next page)

0.590

0.590

0.586

0.536

0.586

0.588

0.573

100 e/ha + 0.02 e/m3

Pricing instrument: two-part tariff system

J. Gallego-Ayala / Mathematical and Computer Modelling 55 (2012) 861–883 879

Weight of WATER criterion 25% Weight of the other criteria 6.82%

Weight of ENBA criterion 25% Weight of the other criteria 6.82%

Experiment 15

Experiment 16

Experiment 17

a

Weight of criteria with polarity +6% Weight of criteria with polarity −10%

0.335

0.494

0.448

0.256

0.360

0.386

0.392

0.518

0.478

0.328

0.388

0.420

0.481

0.546

0.527

0.474

0.461

0.496

0.494

0.566

0.543

0.464

0.478

0.508

0.633

0.540

0.570

0.692

0.623

0.612

0.04 e/m3

0.648

0.507

0.544

0.746

0.642

0.616

0.06 e/m3

Pricing instrument: volumetric tariff 0.02 e/m3

150 e/ha

50 e/ha

100 e/ha

Pricing instrument: irrigated area

Ci index value of the alternatives

First best alternative 0.000 ; second best alternative 0.000 ; third best alternative 0.000 .

Experiment 19

Experiment 18

Weight of PESTRISK criterion 25% Weight of the other criteria 6.82%

Experiment 14

Weight of criteria with polarity +14% Weight of criteria with polarity −4.29%

Weight of BALP criterion 25% Weight of the other criteria 6.82%

Experiments

Table 12 (continued)

0.550

0.560

0.559

0.560

0.531

0.552

50 e/ha + 0.02 e/m3

0.644

0.525

0.566

0.734

0.635

0.618

50 e/ha + 0.04 e/m3

0.602

0.547

0.568

0.653

0.583

0.591

100 e/ha + 0.02 e/m3

Pricing instrument: two-part tariff system

0.642

0.511

0.555

0.744

0.636

0.614

100 e/ha+ 0.04 e/m3

880 J. Gallego-Ayala / Mathematical and Computer Modelling 55 (2012) 861–883

J. Gallego-Ayala / Mathematical and Computer Modelling 55 (2012) 861–883

881

5. Conclusions This study has presented a multi-methodological framework to select irrigation water pricing alternatives. The first conclusion refers to the practical usefulness of the approach proposed to select economic instruments, as a tool to achieve compromise solutions and balance the socioeconomic and environmental performance of irrigated areas when implementing water pricing instruments. The aim would be to select those water pricing instruments whose implementation in the irrigated areas would lead to a more balanced performance of the economic (economic viability), social (social acceptability) and environmental (eco-compatibility) attributes. This highlights the potential use of the TOPSIS method, both to support the public decision makers in the design and implementation of the irrigation water pricing policy required by the WFD and in the field of economics for irrigation water. The results indicate that the volumetric and two-part tariffs systems in general allow a better compromise solution between the instruments for potential implementation of the water pricing policy, since they generate the highest level of Ci index. Nonetheless, it is worth noting that the application of water pricing instruments which take into account the actual water consumption (volumetric or two-part tariff) to charge irrigators, would require changes in irrigated farms management and public controls for its application (use of individual water meters on the irrigated plots to measure the water consumption—technical infeasibility), which would generate additional costs (transaction and control cost) for farmers, irrigators and for the public administration responsible for its implementation. These costs have not been taken into account in this work, but its consideration could certainly modify the evaluation of the alternatives analysed. In this sense, it is recommended that, in the future, the cost-benefit analysis of the implementation of such instruments is included in the criteria that make part of the TOPSIS decision matrix, to perform a more accurate evaluation. Furthermore, considering the results achieved, it should be noted that the irrigation water pricing policy could be implemented in function of different farming districts, rather than establishing one kind of irrigation water pricing instrument and tariff level for a whole river basin, as these would not allow to achieve the same degree of compromise solution in different farming-districts. Thus, the irrigation water pricing policy could be implemented locally (farming district level) rather than at the river basin level. It is worth mentioning that this work must be considered as a starting point for future research. Regarding the methodology, alternative weighting procedures which allow taking into account the interdependence relationships between different socioeconomic and environmental criteria (e.g., the Analytic Network Process) should be implemented, as well as a comparative analysis of results using different Multicriteria Decision-Making techniques (VIKOR, ELECTRE, PROMETHEE etc.). On the other hand, further qualitative analysis could also be developed to complement the results obtained in this research, especially focusing on farmers’ willingness and/or objection to pay for irrigation water. This is a key issue for the analysis of the feasibility of the implementation of irrigation water pricing instruments in real agricultural systems. Finally, it should be noted that the results of the application performed may not easily be extrapolated to other irrigated areas outside the Castilla y León region. As mentioned before, the operability of the Ci index has been made based on the weights assigned to the Castilla y León agriculture socioeconomic and environmental criteria. Consequently, the Ci values obtained depend on particular weights of the socioeconomic and environmental criteria established on the basis of such regional assignments of the relative importance to the criteria dimensions and the set of socioeconomic and environmental criteria used for this study, where the social aspects assume a greater importance than economic and environmental aspects. In this regard, any transfer of benefits to other space–time contexts must be made with extreme caution. Acknowledgements The author would like to thank the two anonymous reviewers for their useful comments and suggestions, which have improved the quality of the manuscript. The author also wishes to thank Prof. José A. Gómez-Limón for provision of data. The research was co-financed by the Spanish Ministry of Science and Innovation (research project FUTURPAC, AGL2006-05587C04-01) and the Regional Government of Castilla y León (Consejería de Educación research project FUTURCYL, VA036A08). Appendix A. Values of the socioeconomic and environmental attributes in the baseline year

Table A.1 Values of the socioeconomic and environmental attributes in the baseline model calibration: farming year 2007/08. Farming district

TGM (e/ha)

Baseline year Cerrato 299.90 Baseline year Saldaña346.52 Valdavia

CONGDP (e/ha)

EMPLT (h/ha)

SEAS (%)

ABAND SPEC (%) (%)

SOILCOV (%)

BALN (kg N/ha)

BALP (kg P/ha)

PESTRISK (kg/ha)

WATER (m3 /ha)

ENBA (kcal/ha)

135.04

10.32

76.89

22.89

57.24

62.18

20.51

11.51

496.10

5610.32

8.87 × 106

193.17

10.67

72.24

20.55

40.82

62.49

27.04

11.72

566.01

6064.26

1.05 × 107

882

J. Gallego-Ayala / Mathematical and Computer Modelling 55 (2012) 861–883 Table B.1 Evolution of WATER indicator for the two irrigated areas. Irrigation water pricing alternatives

Cerrato-FD WATER (m3 /ha)

Saldaña-Valdavia-FD WATER (m3 /ha)

Baseline year

5610.32

6064.26

Pricing instrument: irrigated area 50 e/ha 100 e/ha 150 e/ha

−17.29% −28.64% −39.98%

−8.13% −18.89% −28.12%

Pricing instrument: volumetric tariff 0.02 e/m3 0.04 e/m3 0.06 e/m3

−44.38% −57.40% −61.76%

−27.02% −40.83% −51.50%

Pricing instrument: two-part tariff system 50 e/ha + 0.02 e/m3 50 e/ha + 0.04 e/m3 100 e/ha + 0.02 e/m3 100 e/ha + 0.04 e/m3

−54.13% −60.61% −58.03% −63.83%

−32.65% −45.50% −38.31% −49.94%

Appendix B. Methodological procedure to quantify irrigation water pricing alternatives impacts in irrigation water consumption Bearing in mind the relevance of the analysis of the evolution of the WATER indicator, it should be explained that this evolution has been calculated using the following expression: WATER consumption evolution scenario y =

WATER Xy − WATER X 0 WATER X 0

where Xy denotes the value of the WATER indicator for the water pricing alternative (y) and X 0 denotes the value of the WATER indicator in the baseline scenario. Thus, the calculation of the evolution of WATER indicator in Salrdaña-Valdavia-FD for economic instrument of volumetric water pricing at 0.04 e/m3 level, is obtained as follows: WATER consumption evolution scenario 0.04 e/m3 =

3588 − 6064.26 6064.26

= −0.4083

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