Combining the simulation crop model AquaCrop with an economic model for the optimization of irrigation management at farm level

Europ. J. Agronomy 36 (2012) 21–31

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Combining the simulation crop model AquaCrop with an economic model for the optimization of irrigation management at farm level Margarita García-Vila a,∗ , Elías Fereres a,b a b

Instituto de Agricultura Sostenible, CSIC, Apdo. 4084, 14080 Córdoba, Spain Dep. Agronomía, Universidad de Córdoba, Apdo. 3048, 14080 Córdoba, Spain

a r t i c l e

i n f o

Article history: Received 5 May 2011 Received in revised form 16 August 2011 Accepted 24 August 2011 Keywords: AquaCrop Irrigation management Crop planning Decision support system Economic optimization Deficit irrigation

a b s t r a c t Water resources used in irrigated agriculture are increasingly scarce, particularly in many countries where irrigation has undergone recent expansion. To optimize the limited resources available, optimization models provide useful tools for technical and economic analyses. One of the key inputs of these models is the yield response to water which is often simulated with empirical water production functions. At present, dynamic crop simulation models, such as AquaCrop (Steduto et al., 2009) offer alternative predictions of crop responses to different irrigation strategies as inputs to economic optimization. A model at farm scale was developed and applied to an area in South-western Spain to assist farmers in pre-season decision making on cropping patterns and on irrigation strategies. Yield predictions were obtained from the AquaCrop model which was validated for four different crops. The model simulated the impact on farm income of: (a) irrigation water constraints; (b) variations in agricultural policies; (c) changes in product and water prices; and, (d) variations in the communication to farmers of the specific level of irrigation water allocation. The applications of the models to the study area showed that currently, the changes in cropping patterns induced by the agricultural policy will encourage water savings more than an increase in water prices. Under water restrictions, the best strategy combines planting of low water use crops in part of the area to release water to grow more profitable crops with greater water needs. The model predicted a strong negative impact on farm income of delaying a decision on the level of seasonal water allocation by the water authority, reaching up to 300 D ha−1 in the case of the study area. © 2011 Elsevier B.V. All rights reserved.

1. Introduction Water resources for agriculture are heavily exploited in most countries that have an extensive irrigated agriculture, such as the countries of the Mediterranean basin. Additionally, many areas in the Mediterranean region suffer a structural water scarcity, imposed by the periodic droughts and by the expansion of water demands from agriculture and other sectors of society. Therefore, irrigated agriculture is usually the first to be subjected to water allocation cuts, making water scarcity an important issue for the future of irrigated agriculture. In this context, optimizing the use of limited resources is a priority, especially in Mediterranean regions, for better environmental and economic performance (Howell, 2001), and for meeting the dual challenge of increasing food production and saving water. The optimization process must be addressed at different spatial scales and taking into account multiple factors. Among the options explored better pre-season strategic decisions at farm level (i.e. the

∗ Corresponding author. Tel.: +34 957499231; fax: +34 957499252. E-mail address: [email protected] (M. García-Vila). 1161-0301/$ – see front matter © 2011 Elsevier B.V. All rights reserved. doi:10.1016/j.eja.2011.08.003

planning of farm production and irrigation management; Bergez et al., 2001) is important. Crop selection is considered critical (Jury and Vaux, 2007), and this agrees with the observations of GarcíaVila et al. (2008) on farmers’ adaptability to water scarcity which is primarily based on cropping pattern changes and on adjustments of irrigation scheduling. In water scarce situations, farmers face the following questions: what crops should they grow? and, how to use best a limited amount of irrigation water?. Therefore, it is necessary to develop precise methodologies or tools to answer these questions thus achieving optimal pre-season decisions. Decision support systems (DSS) are useful tools to help farmers optimize their resources, land and water, according to socio-economic and political prospects, under water constraints. The applications of DSS to irrigation and production planning have been extensively studied and reported in the literature. However, seldom DSS have been built with a balanced approach, giving adequate importance to both the agronomic and the economic aspects of the model. For instance, in most DSS, simple, empirical water-production functions are utilized (Doorenbos and Kassam, 1979; Vaux and Pruitt, 1983). However, the need for precise quantification of waterlimited yield is essential to improve the use of scarce irrigation water and to apply deficit irrigation (Fereres and Soriano, 2007).

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As an alternative to water production functions, crop simulation models can provide rapidly reasonable estimates of water-limited yield over a range of environmental conditions. Most of these models require often detailed information (difficult to obtain) about parameters which describe plant behaviour (APSIM, McCown et al., 1996; CERES, Ritchie et al., 1985), or make use of empirical functions (CROPWAT; Smith, 1992). AquaCrop (Steduto et al., 2009) is a model focused on simulating water-limited attainable yield, thought to have an optimum balance between accuracy, simplicity, and robustness. AquaCrop has already been parameterized and tested to simulate yield response to water supply for a number of crops under diverse environments; such as cotton (Farahani et al., 2009; García-Vila et al., 2009), maize (Hsiao et al., 2009; Heng et al., 2009), and sunflower (Todorovic et al., 2009). It has also been used for deficit irrigation (DI) optimization (García-Vila et al., 2009) and to design different DI strategies (Geerts and Raes, 2009; Geerts et al., 2010). Although models have not been extensively applied to the task of developing water-production functions, AquaCrop will be used in this work for this purpose. Water management decisions are based, not only on technical issues but also on an economic and socio-political context which varies among regions. Models which include both technical and economic components (e.g. Bazzani, 2005; Bergez et al., 2001) may be useful in dealing with such complex systems. In Europe, future trends in the Common Agricultural Policy (CAP) of the European Union, changes in agricultural markets, and the Water Frame Directive (EU-WFD), will affect the sustainability of irrigated farming systems (Bartolini et al., 2007). A large proportion of agricultural income depends upon CAP subsidies, affecting the marginal profitability of water use in irrigation. On the other hand, the EU-WFD establishes criteria for water management and regulations, and recommends the use of economic instruments, such as water pricing for encouraging the efficient use of water. Dealing with all these interactive factors in the face of dwindling water supplies is a challenge that can be addressed using models such as the one developed in this work. Although the ultimate objective of such models should be to help farmers in planning, few models are directly used by them, because they are complex tools lacking a user-friendly interface that permits easy access to end users. However, models may improve the understanding of problems involved in planning farm operations, thereby contributing significantly to decision making. Moreover, DSS can be used at the level of irrigation district to provide advice to end users, to explore farmer’s behaviour, and to assess the impact of new policies on farm productivity and sustainability. In this work we have developed a pre-season economic optimization model with a strong agronomic component which was designed to optimize irrigation water management and cropping patterns at farm level, under different levels of water scarcity. The application of the model is illustrated for a study area located in Southern Spain. As an alternative to water production functions, the model uses water-limited yield predictions obtained from AquaCrop, a dynamic simulation model that was specifically validated in this study. Additionally, a scenario analysis was carried out to study the effects of agricultural and water policies, markets, and water authorities’ decision making on the economic sustainability and resources management (land and water) of an irrigated farming system.

2. Materials and methods The area selected for this study was the ‘Colectividad de Santaella’ (hereafter called ‘Santaella’), which encompasses 6989 ha within the Genil–Cabra irrigation scheme (Lorite et al., 2004), located in the province of Cordoba, in Guadalquivir Valley, Southern

Spain. The climate is typically Mediterranean with an annual average precipitation of around 600 mm (mostly distributed between October and April), and an average annual reference evapotranspiration (ETo ) of around 1300 mm. The area has a modern pressurized on demand delivery irrigation system and has already been described by Lorite et al. (2004) and García-Vila et al. (2008). An ideal farm was defined as a reference, combining a maximum of four crops. Cotton, maize, and sunflower were chosen because they are major crops in the area (García-Vila et al., 2008). Potato, a horticultural crop which has low irrigation requirements under winter plantings, was selected as the fourth crop of the ideal farm. The methodology herein followed a series of four steps, as shown in Fig. 1: (1) validation of AquaCrop for each of the four crops; (2) development of crop-water production functions, that is the yield as a function of applied irrigation water (AIW) using AquaCrop; (3) development of a farm economic optimization model for decision making on resource allocation (land and irrigation water) under water scarcity; and (4) simulation of the impacts of different scenarios on cropping pattern, applied irrigation water, farm income, water productivity, and climatic risk. 2.1. Validation of AquaCrop Before using AquaCrop (v. 3.0), the model should be validated for the study area. The recommended crop parameters for each crop under a wide range of conditions in FAO (2010) were assessed using data from experiments conducted in the area, as described below. In the case of potato, lacking local experimental data AquaCrop was validated here using literature data from California and Scotland (Wolfe, 1981; Wolfe et al., 1983; Jefferies and Mackerron, 1989). 2.1.1. Experimental data The three sets of cotton data (COR85, COR86, and ST06; Table 1), obtained in field experiments conducted in or near the study area (Guadalquivir Valley) are reported in detail in García-Vila et al. (2009) and in the original experimental reports (Orgaz et al., 1992; Carmona et al., 2007). The cotton COR85 and COR86 experiments were carried out on a Typic Xerofluvent soil of sandy loam texture with a sprinkler line-source experimental design. The ST06 experiment was conducted on a Chromic Haploxererts soil of clay–loam texture with three differential irrigation treatments. To validate AquaCrop for maize, we used data reported by Aguilar (1990) and Aguilar and López-Bellido (1996) from field experiments performed in two locations of the Guadalquivir Valley, “Lora del Río” (37◦ 37 N, 5◦ 32 W, altitude 49 m) and “Palma del Río” (37◦ 38 N, 5◦ 10 W, altitude 58 m), in 1986 (LO86 and PAL86) and 1987 (LO87 and PAL87). In both years and places, water was applied to avoid water stress at all times. The soil was a Typic Xerofluvent of sandy loam texture. Detailed information on these experiments is available in Aguilar and López-Bellido (1996), and in Table 1. For the validation of AquaCrop for potato, two field experiments one in Davis (California) (CA80) (Wolfe, 1981; Wolfe et al., 1983) and another in Dundee, UK (DUN86) (Jefferies and Mackerron, 1989) were used (Table 1). A sprinkler line-source experimental design was used in the CA80 experiment conducted on a deep Yolo loam soil. In DUN86, the experiment consisted of two treatments, droughted and irrigated plots on a sandy loam soil. Both experiments are reported in detail in the corresponding papers. Data from sunflower experiments performed at the Agricultural Research Center of Cordoba (37◦ 31 N, 4◦ 51 W, altitude 110 m) in 1981 (COR81) and 1983 (COR83) (Giménez, 1985; Giménez and Fereres, 1986), in 1987 (COR87) (Prieto, 1992), and in 1996 (COR96) (Fereres et al., 1998), were used to validate AquaCrop (Table 1). The experiments were carried out on a deep, sandy loam soil (Typic

M. García-Vila, E. Fereres / Europ. J. Agronomy 36 (2012) 21–31

23

Experimental works

Data

Recommended cropparameters

Evaluation

AquaCrop Validation

Validatedcrop parameters

Data

AquaCrop

Irrigation strategies Expert knowledge

26 years of climatic information Water-production functions

FARM

Irrigation water constrains Economic optimization model

Economic data

Scenarios: Agricultural policy Water price Crop price

Optimal cropping pattern and irrigation depth + Maximum profit + Risk Fig. 1. Flow chart showing the approach followed for the economic optimization process at farm level.

Table 1 Experimental data sets used in the validation of AquaCrop with information on location, year, number of irrigation treatments (n), cultivar, sowing date, and plant density. These data were reported in Orgaz et al. (1992), Carmona et al. (2007), Aguilar and López-Bellido (1996), Wolfe (1981), Jefferies and Mackerron (1989), Prieto (1992), Fereres et al. (1998), and Giménez and Fereres (1986). Crop

Field experiments

Location and year

n

Cultivar

Sowing date

Plant density (plants ha−1 )

Cotton

COR85 COR86 ST06 LO86 LO87 PAL86 PAL87 CA80 DUN86 COR81 COR83 COR87 COR96

Cordoba (Spain), 1985 Cordoba (Spain), 1986 Santaella (Spain), 2006 Lora del Río (Spain), 1986 Lora del Río (Spain), 1987 Palma del Río (Spain),1986 Palma del Río (Spain),1987 Davis (California), 1980 Dundee (UK), 1986 Cordoba (Spain), 1981 Cordoba (Spain), 1983 Cordoba(Spain), 1987 Cordoba (Spain), 1996

4 6 2 1 1 1 1 3 2 2 2 2 2

Coker-310 Coker-310 Viky Prisma Prisma Prisma Prisma White rose Maris Piper Sungro-380 Sungro-380 Sungro-380 Don José

24 April 25 April 11 May 16 March 4 March 10 March 14 March 31 March 15 May 15 March 25 February 6 March 5 February

100 × 103 100 × 103 132 × 103 95 × 103 95 × 103 95 × 103 95 × 103 405 × 102 555 × 102 57 × 103 57 × 103 70 × 103 57 × 103

Maize

Potato Sunflower

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Xerofluvent) under two water treatments (irrigation every 5–10 days and rainfed). 2.1.2. Validation procedure AquaCrop algorithms, calculation procedures, and parameters are described in detail in the model manual (http://www.fao. org/nr/water/aquacrop.html) and a brief description of the concepts and basic development of AquaCrop can be found in Steduto et al. (2009) and Raes et al. (2009). The values of the conservative crop parameters (Raes et al., 2009) used in the validation are listed in FAO (2010). The validation process was performed by comparing the simulated with the measured results of green canopy cover (CC), final aboveground biomass (B), and harvestable yield (Y), as dry matter, in that order (a detailed description of the validation process is available on demand from the corresponding author). The input weather data required by AquaCrop are minimum and maximum air temperatures (Tmin and Tmax ), rainfall (RF), and ETo calculated by the FAO Penman–Monteith equation (Allen et al., 1998), as recommended in Raes et al. (2009). The Hargreaves method (Hargreaves and Samani, 1985) was used to estimate ETo for CA80, since only daily solar radiation and temperatures data were available. Input data on planting density, phenology, and growing period coefficients were obtained from the experiments. The CC values were calculated using CC–LAI relationships for the four crops. The relationship for cotton was derived in GarcíaVila et al. (2009), while it is reported in Hsiao et al. (2009) for maize. Fereres (1984) reported the CC–LAI relationship for sunflower. In the case of potato, a field trial was conducted at the Agricultural Research Center of Cordoba in 2008 to develop the CC–LAI relationship. Briefly, the cultivar ‘Liseta’ (short-medium season), was planted on 19 September with a plant density of 4.8 plants m−2 on a Typic Xerofluvent soil of sandy loam texture that did not restrict root penetration. Water was applied by sprinkler to ensure adequate supply. Photographs were taken above the canopy with a digital camera every 3–5 days after emergence, estimating CC through an image processing procedure (classification supervised) using ENVI 4.3 software (ITT Corporation). At the same time, LAI was estimated periodically using a planimeter. From this information, the following relationship was developed: CC = 1.005 × [1 − exp(−1.2 × LAI)]1.7

(1)

The properties of the soil used in the simulations were either obtained from the description by Coelho et al. (2000) for the Cordoba experiments or were estimated from soil texture using pedotransfer functions (Saxton and Rawls, 2006). When there was no information on the initial soil water content (SWC), the soil profile was considered to be at field capacity. AquaCrop performance was evaluated by linear regression between the observed and simulated values of CC, B, and Y. The goodness of fit was also assessed by the following statistics: root mean square error (RMSE), the index of agreement (d) (Willmott, 1982), and modeling efficiency (EF) (Loague and Green, 1991). The model fit improves as RMSE, an indicator of the absolute model uncertainty, approaches zero; while d, a stable and bounded index, and EF, an overall deviation indicator, approach unity. 2.2. Simulating the crop response to applied irrigation water Once AquaCrop was validated, the assessed crop parameter values (FAO, 2010) were used to simulate yield as a function of applied irrigation water. AquaCrop was run in growing degree day mode, which uses a base temperature (Tb ) and an upper or optimum temperature (Tup ) (the temperature above which crop development no longer increases with an increase in air temperature; Raes et al.,

2009). The cardinal temperatures for cotton and maize were those used in García-Vila et al. (2009) and in Hsiao et al. (2009), respectively. As in Villalobos et al. (1996), Tb for sunflower was 4 ◦ C, while Tup was 28 ◦ C. For the potato, Tb and Tup were 7 ◦ C and 25 ◦ C respectively (Moorby and Milthorpe, 1975). For the study area of Santaella, sowing dates were obtained from farmers’ surveys (Lorite et al., 2004; García-Vila et al., 2008) and the input soil parameters were those used in ST06 (Table 1) and reported by Carmona et al. (2007). The initial SWC was considered at field capacity in our simulations, consistent with the rainfall pattern. The simulated irrigation method was sprinkler. To account for climate variations in the crop response to irrigation, we used climatic data over a 26 years period (from 1981 to 2006) recorded at a agro-meteorological station located some 40 km from the area at the Agricultural Research Center of Cordoba. The simulated yield as a function of the level of applied water was used to generate the crop-water production functions for the 26 years analyzed. The simulations were performed starting with a rainfed crop, and increasing the seasonal applied irrigation water (AIW) in 60-mm increments until it was ensured that a level of full supply was reached (amounts up to 900 mm, depending on the crop). For every level of AIW, the specific irrigation schedule (timing and amounts) followed for each crop attempted to achieve the maximum possible yield for the given level of AIW and was based on expert knowledge of the specific responses to irrigation of each crop. Namely, for all crops, the simulated applications were aimed at avoiding significant water stress during the most sensitive periods, e.g. flowering and grain filling periods in maize. Some water deficits were allowed in periods relatively tolerant to water stress such as the vegetative a phase in maize. In sunflower, the most sensitive period to water deficits is flowering, followed by the early seed set. In the case of potato short periods of water stress during tuber initiation, and yield formation periods have the most significant effects on the marketable yield (MacKerron and Jefferies, 1986), but important yield reductions can be caused by reducing canopy growth and consequently, biomass due to water stress (Yuan et al., 2003). For cotton, DI optimization followed was already reported in García-Vila et al. (2009). Based on the method of irrigation, site characteristics, and advice from local experts, the irrigation application efficiency was considered to be 85%. The dry matter yield output of the simulations was converted to commercial yields using water content values of 12%, 14%, 80%, and 11% for cotton, maize, potato, and sunflower, respectively. The yield response function to AIW for each crop was obtained from the 26-year simulations using regression techniques, and from those, the 20th and 80th percentiles yield values for each AIW were selected to develop two crop-water production functions to simulate unfavourable and favourable climatic conditions.

2.3. On-farm economic optimization model A farm scale economic optimization model was developed and applied to an ideal farm of the Santaella irrigation area to maximize total gross margin, by searching for the optimum combinations of crop area and seasonal AIW, taking into account water allocation constraints, area restrictions, and other factors set out in various scenarios, as discussed below. Given the yield response functions to AIW, a non-linear programming model was defined. The General Algebraic Modeling System (GAMS) (Rosenthal, 2007) was used for programming. This model consists basically in the optimization of an objective function (total gross margin) by selecting the optimal crop pattern and the optimal amount of AIW for each crop, being the variables subject to a series of linear restrictions. The objective

M. García-Vila, E. Fereres / Europ. J. Agronomy 36 (2012) 21–31

function then becomes: TGM =

N 

with a certain cropping pattern selected by the optimization process is computed as the greater value of the two TGM differences, as:

[(Pci × Xi × Fi (Yi ) + Si × Xi ) − (Cai × Xi + Cpi × Xi × Fi (Yi )

i=1

+ Pwi × Yi × Xi × 10)]

(2)

where TGM is the total gross margin of the farm (D ); i represents each crop analyzed (1, 2, . . ., N); X is the area devoted to each crop (i) (ha); Y is the seasonal AIW for each crop (i) (mm); F(Y) is the crop-water production function; Pc is crop price received by the farmer (D t−1 ); S is crop subsidies from the CAP (D ha−1 ); Ca is production costs per unit area (D ha−1 ); Cp is production costs varying with crop yield (D t−1 ); and Pw is the price of irrigation water (D m−3 ). The objective function is subject to water allocation and area availability constraints within the farm: N 

Xi ≤ A

(3)

(Yi × Xi × 10) ≤ A × W

(4)

i=1 N  i=1

where A is the irrigable area of the farm (ha) (in our simulation study 100 ha); and W represents available seasonal irrigation supply for the farm (m3 ha−1 ), as given by the Basin Water Authority (BWA). Other limitations of crop area and production had to be introduced according to Common Agricultural Policy (CAP). These limitations refer to the minimum cultivated area and the minimum yield per crop required for receiving subsidies. These constraints were added to the general restrictions, using lower and upper bounds of the optimization variables (X.lo, X.up, Y.lo, and Y.up; Rosenthal, 2007). The economic data on production costs and incomes were collected by farmers surveys in 2009 (García-Vila, 2010). Ca groups the costs of: seeds, pesticides, labor, machinery, harvest, and irrigation fees; while Cp includes transport costs and fertilizers. The nonlinear objective function is optimized using an algorithm (the solver CONOPT; Drud, 1985), that is particularly well suited for non-linear models that are almost square, as is the case of the optimization model developed here. From the output of the economic optimization model, the water productivity (WP; D m−3 ) calculated as the ratio of total gross margin to AIW, as: WP =

N

TGM

(Y × Xi × 10) i=1 i

25

(5)

Decision making must take into consideration not only the classical objective of profit maximization but should also assess the risks associated with the optimal strategy. Using the crop-water production functions for the average year, we obtain the optimal cropping pattern and a corresponding optimal irrigation scheduling for each crop. This optimum strategy has an associated risk of yield reduction due to in-season weather variations, once a decision on planting patterns has been taken. Here, risk assessment was done by using the economic model to compute the TGM for the crops already planted and for two extreme years; a year with favourable weather (with the corresponding production function of the 80th percentile; Fig. 2a–d) and a year of unfavourable weather (the corresponding production function of the 20th percentile). The economic optimization model was used to obtain the optimal irrigation scheduling and the corresponding profit for the two extreme years, where only the irrigation depth is optimized while the area devoted to each crop is fixed. The TGM differences between the average and the two extreme years were computed, and the risk (R) associated





R = Max (TGM − TGMf ), (TGM − TGMu )

(6)

where f and u are the years with favourable and unfavourable weather, respectively. For scenario analyses, four scenarios were generated to analyze the impact of: agricultural policy, water policy (water price), and farm products market. The comparison of resource allocation, TGM, WP, and risk among different scenarios was made by adopting the current situation as the reference scenario. - Reference scenario: A frequency distribution of crop prices was performed from a monthly Pc data base (from January, 2007 up to August, 2009) (MARM, 2010). The 50th percentile values (median) were used for this scenario. Also, we considered the current Pw (0.05 D m−3 ) and CAP subsidies. - World agricultural markets (WAM) scenario: It describes a situation with a high degree of liberalisation, immersed in global market mechanisms and without subsidies from the CAP. In this scenario, the current Pw and the 50th percentile values of Pc were used. - High Pw scenario: The cost recovery principle of EU-WFD suggests a doubling of the current Pw to 0.10 D m−3 in a future of higher water prices. Here, the 50th percentile values of Pc and the current CAP subsidies were considered. - High Pc scenario: Only potato and cotton prices are expected to increase in the future (COTLOOK, 2010). Therefore, in this scenario we considered the 80th percentile values for these crops, while the 50th percentile values were used for maize and sunflower. The current Pw and CAP subsidies were applied. All the scenarios above were evaluated under different levels of water allocation in the district in 50-mm increments, from 0 to a total seasonal of 600 mm. 2.4. Impact assessment of the communication date of the amount of water allocation In drought years, knowing the amount of irrigation water that would be available for the season is of paramount importance for farm planning and management. The sooner the farmer knows the level of water available, the greater the number of options he will have to cope with the limited supply. By contrast, water authorities tend to delay making this decision while hoping for additional rainfall, and balancing the water demands from all sectors. This tendency of delaying allocation decisions greatly increases the level of uncertainty, making it much harder to optimize the use of the limited water by farmers. The model developed here was used to quantify the impact of the delays in communicating the water allocation level on farm income. For this purpose, we used the optimization model to simulate farmer’s behaviour in the objective of TGM maximization by determining the crop area and the AIW under different scenarios of: amount of water allocation, the date of communication, Pc , all under three different climatic scenarios. From a data base of 19 irrigation seasons (1990/1991–2008/2009) of our study area, we formulated the scenarios for water allocation level and communication date by frequency distribution analysis, using the 20th, 50th, and 80th percentiles of both distributions. For the water allocation level that corresponded to 250, 400, and 500 mm respectively, while the approximate communication dates are mid-February, mid-March and mid-May, respectively. It is known that farmers’ decisions are greatly affected by markets and by their perception of the current year climate; thus, we used three scenarios of Pc (20th, 50th, and 80th percentiles of Pc , corresponding to low, medium and high Pc scenario, respectively) and three climate scenarios

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Fig. 2. Yield simulations for 26 years in response to applied irrigation water (AIW) for: (a) cotton; (b) maize; (c) potato; and (d) sunflower; showing the water-production functions for an average, a favourable (80 percentil), and an unfavourable year (20 percentil). For explanation see text.

(favourable, average, and unfavourable), identical to those used in the assessments above. The analysis of farmer’s behaviour reported in García-Vila et al. (2008) was the basis for defining a series of optimization strategies (different ways of using the optimization model) to simulate the farmer’s behaviour under each scenario. The high risk associated with horticultural crops perceived by farmers (high variability in prices and high labor costs), coupled with the specific strategies that farmers use under water scarcity in this area (García-Vila

et al., 2008), have determined the optimization strategies used here. Table 2 summarizes these optimization strategies, which are explained in detail in García-Vila (2010). The average and the standard deviation of the sowing dates used in the simulations for cotton, maize, potato, and sunflower were: 23 March ±7 d, 15 March ±6 d, 15 February ±12 d, and 7 March ±10 d, respectively. These dates would determine what crops are being considered once the level of water allocation is known. Additionally, growers would not plant potato unless market prices are (high Pc scenario), due

Table 2 Optimization strategies which simulate farmers’ behaviour for different communication date of water allocation, and under crop prices (Pc ) scenarios and climatic year scenarios. Optimization strategies: Strategy A takes into account the known irrigation water allocation while the B, C and D, strategies are based on water allocation forecasts of 400, 250, and 100 mm respectively. Communication date

Crop price scenario

Climatic year scenario

Optimization strategy

February

Low and medium Pc

Favourable Average Unfavourable Favourable Average Unfavourable

A A A A A A

Favourable Average Unfavourable Favourable Average Unfavourable Favourable Average Unfavourable Favourable Average Unfavourable

A A A B C D B C D B C D

High Pc

March

Low and medium Pc

High Pc

May

Low and medium Pc

High Pc

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to its low profitability (García-Vila et al., 2008). If the communication date occurs in February or in March under low or medium Pc scenarios, farmers could plan their cropping patterns and their seasonal irrigation levels without additional risks. In these cases, the simulations followed the optimization strategy A (Table 2), where the optimization process is performed by the model taking into account the known irrigation water allocation, yielding the area of each crop, the AIW, and TGM. However, for the May date and for the March date under the high Pc scenario (planting potato becomes profitable), farmers would be taking more risks because they do not know the actual water supply at sowing time. In these cases, we followed the optimization strategies B, C, and D, where the optimization is carried out based on a forecast of water allocation of 400, 250, and 100 mm respectively, depending on whether the weather scenarios are favourable, average, and unfavourable, respectively. In these three strategies, the area of each crop is fixed as a result of the optimization process under the water allocation forecast. However, once the farmers know the actual water allocation, they could optimize the seasonal irrigation. Thus, a new optimization exercise is performed with the fixed area of each crop, getting the optimal irrigation strategy with the known water supply and TGM.

3. Results and discussion 3.1. Validation of AquaCrop AquaCrop validation for cotton was carried out and the results are shown in Table 3. Comparison of observed and simulated time-trends of CC for three treatments of COR86 shows that there was a very good matching, with a RMSE of 4.43%, d and EF values of 0.995 and 0.981 respectively (Table 3). A better simulation of the seasonal evolution of CC was achieved than that published in García-Vila et al. (2009) with the new crop parameters (FAO, 2010) in the deficit irrigation treatments. The satisfactory performance in the simulation of CC and ET led to a reasonably fit in biomass accumulation for COR86 and COR85, as indicated by the high values of d, and EF (Table 3). The parameters of the linear regressions between observed and simulated B (Table 3) generally show underprediction for the wet treatments. As noted in García-Vila et al. (2009), the use of a line source caused an overestimation of measured ET for the wet treatments. Hence, underestimation of simulated ET led to an underestimation of the simulated B and Y for these treatments (Table 3). By contrast, the proper values of stress parameters (FAO, 2010) enabled the accurate simulation of B and Y in the deficit irrigation treatments. The performance of AquaCrop for maize is shown in Table 3, where the results of statistical analysis of CC time trends for LO86 and LO87 are shown, with an acceptable match between simulated and measured values. However, no significant differences of maximum CC values between the two years were simulated, as shown in the observed values. This discrepancy was also reflected in the simulated B, being overestimated the final value for the year 1986, whereas it was accurate for 1987. That is the reason for the low values of EF and high RMSE for B (Table 3). The observed value of B in 1986 was very low compared to the normal B levels for irrigated maize in the area (around 30–33 t ha−1 ), and there were only small differences in the climatic conditions between the 2 years that would not explain the low B of 1986. On the other hand, the Y fit was very good in the two cases, with a low RMSE (0.25 t ha−1 ) and high d, EF, and r2 (Table 3). The validation exercise for potato reported in Table 3 shows that the model was able to simulate satisfactorily the evolution of CC throughout the season, with differences of less than 3% in maximum CC, and simulating adequately the water stress effects on canopy duration. However, the estimated canopy decline tended to

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be slower than the observed values, which was reflected by a moderate value of EF (0.845) and high value of RMSE (11.93%) (Table 3). On the other hand, closer fit for the irrigated treatment than for the droughted treatment was observed in DUN86. The excellent agreement between observed and simulated B (Table 3) suggests that the underestimation of the simulated canopy decline may be related to the estimation of CC from LAI values. The different environmental conditions of the experiments used for model validation (CA80, Mediterranean climate, vs. DUN86, humid region with lower vapour pressure deficit) allowed for the evaluation of the robustness of the WP* parameter (Steduto et al., 2007, 2009) in potato. Also, Table 3 shows good agreement between the simulated and observed values of Y with moderate RMSE and high values of d, EF, and r2 . Nevertheless, a general underestimation of Y (up to 11%) for the deficient irrigation treatments was observed. The results of model validation for sunflower are summarized in Table 3. The effects of water stress on CC were well simulated and in general, the values of statistics reported in Table 3 for CC shows good accuracy in the simulation of CC development. Good results between observed and simulated B were obtained (Table 3), although the B overestimation for the rainfed treatment of COR87 and COR83 affected the RMSE value (1.57 t ha−1 ; Table 3). Simulated yields of the rainfed treatments were also overestimated, given the dependence of Y simulation on the simulation of B (Table 3). In summary, the statistical analysis for Y (Table 3) shows good results, with moderate values of RMSE and EF, and high values of d and r2 . However, more efforts are needed to validate the recommended values of the parameters proposed in FAO (2010) for sunflower. One option would be to use a more elaborate and mechanistic model such as OilCrop-Sun (Villalobos et al., 1996) to test the validity of the current calibrated version of AquaCrop. 3.2. Crop response to applied irrigation water The validated AquaCrop model for the four crops was used to estimate a set of discrete optimal yield-irrigation points, by simulating the response to irrigation (AIW from 0 up to around 900 mm) with a climatic dataset of 26 years (Fig. 3a–d). Crop-water production functions have been reported as the relationships between yield and the seasonal ET, showing that yield was linearly related to ET (Doorenbos and Kassam, 1979; Stewart and Hagan, 1973; Vaux and Pruitt, 1983). However, the relationships between yield and AIW have been shown to be non-linear (Stewart and Hagan, 1973; Fereres and Soriano, 2007), because a portion of the applied water is not used in ET and is lost, and their convexity illustrates that these losses increase percentagewise as full ET demand is approached. Here, the yield-AIW relationships were derived for each crop and variable climatic conditions (average, favourable, and unfavourable weather year) by polynomial regression analyses, adjusting fourth degree equations, with R2 ≥ 0.91 for cotton and maize (Fig. 3a and b) and R2 = 0.88 for sunflower (Fig. 2d). The lower R2 value for potato (0.63) is due to a greater dispersion of the yield-AIW points (Fig. 2c), since this crop is more dependent on seasonal rainfall (winter sowing). The reductions in dispersion of the yield-points for high levels of AIW is observed in all crops except in potato, due to the high ETo and the effect of very low temperatures on biomass production in some years. In the case of cotton (Fig. 2a), the function is affected by the positive effects of moderate stress on HI (Orgaz et al., 1992). The maximum simulated yield for each crop (Fig. 3a–d) is in agreement with the maximum attainable yields indicated by farmers of the Santaella area in the interviews conducted by García-Vila et al. (2008). 3.3. On-farm economic optimization model for decision making Resource allocation on-farm (land and water) implies the optimization of profit under realistic simulation scenarios. Fig. 3 depicts

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M. García-Vila, E. Fereres / Europ. J. Agronomy 36 (2012) 21–31

Table 3 Statistics for the validation of AquaCrop (root mean square error -RMSE-, index of agreement -d-, and modeling efficiency -EF-) when comparing observed and simulated values of green canopy cover (CC), final aboveground biomass (B), and harvestable yield (Y), in dry matter terms. Slope, intercept, and r2 are for the linear regression of observed against simulated values. n is the number of observed data used in the validation process. Crop

Variable

n

Cotton

CC (%) B (t ha−1 ) Y (t ha−1 ) CC (%) B (t ha−1 ) Y (t ha−1 ) CC (%) B (t ha−1 ) Y (t ha−1 ) CC (%) B (t ha−1 ) Y (t ha−1 )

18 10 12 22 2 4 27 5 5 15 8 8

Maize

Potato

Sunflower

Range of observed data 4–92 3.60–12.78 1.61–4.99 10–97 25.07–30.94 12.66–16.82 10–100 5.85–12.92 4.80–10.21 1–98 6.36–17.28 1.56–4.87

Range of simulated data 4–91 3.60–11.15 1.40–4.35 7–95 28.63–30.90 12.88–17.00 5–100 5.92–12.99 4.24–10.20 2–95 7.75–17.15 1.39–5.19

the results of the simulations of the economic model in terms of the optimal area and AIW as a function of seasonal water allocation under the four different scenarios (reference, WAM, high Pw , and high Pc ). In the reference scenario, under moderate seasonal irrigation water restrictions (600–400 mm), maize occupy 100% of farm area using all water granted (Fig. 4a and b), with the optimum AIW somewhat below the full irrigation requirements (Fig. 2b). As water allocation decreases below 400 mm, the cotton area grows at the expense of that of maize, because cotton responds well to deficit irrigation (García-Vila et al., 2009) and requires much less AIW (only 99 mm) to achieve the minimum yield threshold required by CAP. These results are supported by farmers interviews in the area who indicated that they shift from maize to cotton in years of allocation constraints (García-Vila et al., 2008). The low returns from irrigating sunflower cause that the optimal solution includes rainfed sunflower when there is almost no water available for irrigation (50–0 mm) (Fig. 4a and b) because the small water allocation can be transferred to others crops of higher gross margin (i.e. cotton). That is consistent with the observations in the study area, where during the severe drought of 1992–1995, dryland sunflower and wheat occupied more than two thirds of the total area (García-Vila et al., 2008). It appears that the objective function of the model represents with high realism farmers’ behaviour in the Santaella area, where profitability and stability are the main reasons for cropping pattern selection (García-Vila et al., 2008). The results of Fig. 3 are

RMSE

d

EF

Slope

Intercept

r2

4.43 0.84 0.38 13.14 2.52 0.25 11.93 0.24 0.43 8.14 1.57 0.54

0.995 0.979 0.966 0.950 0.728 0.995 0.957 0.998 0.989 0.986 0.942 0.947

0.981 0.928 0.878 0.826 0.263 0.978 0.845 0.991 0.953 0.946 0.809 0.795

1.041 0.836 0.870 0.830 – 1.036 0.855 1.040 1.102 0.975 0.745 0.900

−1.573 1.089 0.280 17.625 – −0.325 14.713 −0.313 −1.157 6.345 3.829 0.623

0.984 0.969 0.924 0.860 – 0.993 0.860 0.994 0.998 0.967 0.891 0.862

also consistent with the scenario analysis of irrigation performance at the plot and scheme levels in the Santaella area by Lorite et al. (2007). When we compare the reference scenario with the WAM scenario (Fig. 4c and d), we can see that cotton moves out of the picture because its profitability is highly dependent on CAP subsidies and therefore it is replaced by maize, which profits from the allocation to sunflower. In the WAM scenario, the area devoted to maize declines with a decrease in water allocation (Fig. 4c), but some maize is sown even when only 50 mm are allocated to the whole farm. In this scenario, the optimal solution indicated that maize should be irrigated only slightly less (16% below full irrigation requirements) under severe constrains because of the high sensitivity of maize yields to water deficits (Figs. 4d and 3b). Doubling the price of water (high Pw scenario; Fig. 3f), only induced a 5% reduction in AIW for maize with 600 mm of water allocation and did not vary under increased supply constrains (relative to the reference scenario); additionally, the optimal cropping pattern was not affected by Pw increases (Fig. 3e). It appears that a major economic incentive suggested by EU-WFD (i.e. through water pricing) will not encourage much water savings in some farming systems such as the one of Santaella. Water authorities in many parts of the world have proposed to use water pricing as an economic incentive to conserve water in irrigation (Briscoe, 1997); but the results here show that some agricultural systems are not very responsive to increased water costs up to a limit (Molle, 2009). Finally, the high

Fig. 3. Optimal area and optimal applied irrigation water for each crop with different water allocations levels (from 0 mm up to 600 mm) in a 100 ha farm, under the following scenarios: reference, world agricultural markets (WAM), high water price (Pw ), and high crop price (Pc ).

M. García-Vila, E. Fereres / Europ. J. Agronomy 36 (2012) 21–31

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Fig. 4. (a) Total gross margin and associated climatic risk; and (b) water productivity for the optimal management strategy with different water allocations levels (from 0 to 600 mm) in a 100 ha farm, under the four scenarios: reference, world agricultural markets (WAM), high water price (Pw ), and high crop price (Pc ).

Pc scenario (Fig. 3g) shows that potato displaces cotton due to its low water requirements, although potato is only profitable when the Pc is above a threshold (around 0.09 D kg−1 ). García-Vila et al. (2008) shows a high coefficient of variation for potato planted acreage in Santaella for 15 seasons, associated with the high volatility and poor forecast of potato prices, a common problem with vegetable production in many world areas. Maize, whose area has been reduced in this scenario, receives up to 72% more irrigation water than in the reference scenario (in 300–350 mm of water allocation) as water shifts from potato to maize under the assumed potato Pc (Fig. 3h). In summary, water pricing in some EU countries may have less impact on irrigation water usage than the effects of markets and changes in agricultural policy, as suggested also by Bartolini et al. (2007). Fig. 4a compares the TGM and the estimated risk due to climatic uncertainty for the four scenarios under different levels of irrigation water allocation. In the reference scenario, profits decrease gradually with increasing water constraints, with a steeper decline as allocation decreases to 100 mm, due to the sowing of sunflower. This behaviour is also observed in high Pw scenario (Fig. 4a), since

the optimum cropping pattern is not affected (Fig. 3e). TGM for large water allocations is the lowest in high Pw scenario; here, water policy may have more impact on farm profits than on water savings (as observed in Fig. 3) (Gómez-Limón et al., 2002). In the case of high Pc scenario, profits remain high and constant from 600 to 250 mm of water allocation, due to the high returns from potato and to its low irrigation water requirements. This is the reason why WP is higher for high Pc scenario (Fig. 4b). WP for reference scenario and for high Pw scenario is almost the same (the cost recovery principle of EU-WFD does not increase WP), since profits and AIW are reduced in high Pw scenario; but it is higher than in WAM scenario (under high irrigation water constraints) due to low WP of sunflower. The quantification of the risk (R) associated with a cropping pattern for the reference and high Pw scenarios showed the same values for both, increasing with irrigation water restrictions (Fig. 4a). The highest R is reached with 100 mm of water allocation because with lower allocation levels, the difference between the TGM of average and the unfavourable year is reduced (and thus estimated R) due to the replacement of cotton by sunflower. The low climatic R of

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M. García-Vila, E. Fereres / Europ. J. Agronomy 36 (2012) 21–31

Gross margin total loss (103€)

50

40

500 400 250

30

20

10

0 Feb

Mar

May

Month of year Fig. 5. Total gross margin losses in a 100 ha farm depending on communication date and amount of water allocation, under different crop price and climatic year scenarios. Error bars represent the standard deviation of the mean loss, reflecting the variability in losses due to the different scenarios.

WAM scenario is due to the elimination of subsidies which favours planting sunflower (Fig. 3c), whose profitability is little affected by climate, unlike maize (that is why R reaches the maximum value at 300 mm of water allocation, the level at which maize occupies 100% of the farm area). In a way, the CAP has a negative impact on R (increasing the risk by 91% under some scenarios), because it favours the cultivation of crops with high water demands. In the high Pc scenario, the maximum R (Fig. 4a) occurs at the highest and lowest water allocation (unlike in the other scenarios) because the crop choice in both cases is conservative and R, as quantified here (TGM differences) is less than at intermediate allocation levels where the area of potato is high and so is R (Fig. 3g). 3.4. Impact of communication date of water allocation In drought years, the date on which farmers know the level of water restrictions is critical for their seasonal planning. Fig. 5 shows the TGM losses for the ideal farm of 100 ha that would occur when the decision is delayed until three different dates and for three different water allocation amounts. Bars reflect the variability in lost profits due to different scenarios which varied in crop prices and seasonal weather. As expected, economic losses increased as the decision on water allocation would be delayed by the Water Authority, reaching 30,000 D in May (16% of TGM). If the level of water allocation turns out to be high, the opportunities for growing crops of high profitability (e.g. maize) are greater, and the losses would increase relative to a situation where substantial water constraints materialize. As the decision is delayed, farmers tend to react to uncertainty following a conservative behaviour and planting crops with low irrigation requirements which are not very profitable (e.g. sunflower). For the most common situation in Santaella, i.e. communication in mid-March of 400 mm of water allocation (see Section 2), the model simulated a potential loss to the irrigation scheme of about 9000 D (5% of TGM), relative to knowing the same level of water allocation before February. 4. Conclusions A tool and a methodology were developed here to optimize farm-scale irrigation under water scarcity. Economic optimization models linked to crop simulation models were used for pre-season decision making on cropping patterns and on irrigation strategies, favouring farm economic sustainability and efficient use of

irrigation. Models such as the one developed here may be applied for scenario analysis and strategic planning, but is limited to areas of collective irrigation networks with well established institutional arrangements between farmers and the water authorities. Combining a crop simulation model with an economic optimization model aimed at optimizing farm income is a complex task. Here, the AquaCrop simulation model was used to generate non-linear crop-water production functions for specific conditions, improving the accuracy of the agronomic inputs for economic optimization. The satisfactory results of the yield simulations for four crops (cotton, maize, potato, and sunflower) under the specific climatic and soil conditions of southern Spain support the suitability of the crop parameters recommended by FAO (2010), and illustrate the robustness and the general applicability of AquaCrop. The developed economic optimization model has shown to be a good tool to perform scenario analyses and for assisting irrigation scheme managers, water authorities, and policy makers about making irrigation management more sustainable at farm level. After the analysis of the different scenarios under the particular conditions of the study area, it was concluded that, the CAP subsidies are essential to maintain the profitability of cotton, a crop that would phase out in a world market scenario. Also, the current CAP subsidies have a negative impact on risk due to climatic uncertainty, since it favours the cultivation of crops with high water demands (e.g. maize). A scenario of increased crop prices would lead to increased WP due to on the high profits and the introduction of potato (a crop with high production costs but low irrigation water requirements). An increase in water prices, as suggested by the EU-WFD, was found not to encourage water savings, as the model predicted that cropping patterns would not change and only modest reductions in water use would occur in years of high water allocation (and thus, years of high water availability). Even though extracting decision rules is a complex process, the optimization model developed, linked to a set of farmer’s decision criteria (such as those reported by García-Vila et al., 2008), may be a good tool to simulate farmer’s decision making process and to analyze the impact that a delay in informing farmers on the level of water allocation by the Water Authority would have on economy farm (maximum losses reached 300 D ha−1 ). These results emphasize the need to improve the decision making process by water authorities to attain the desired goals of properly managing water scarcity without compromising the sustainability of farming. Acknowledgments We thank, J. Berlanga, S. Carmona, G. Izzi, I.J. Lorite, M. Morales, C. Ruz, and M.A. Soriano for help with this work. The climatic data, comments, and support of F.J. Villalobos is gratefully acknowledged. Thanks are due to M.H. Prieto and D. Wolfe for use of their experimental data. EF acknowledges the support from the Ministry of Science and Innovation (MCI; project CONSOLIDER-RIDECO CSD2006-67). M. G-V was supported by a I3P grant of CSIC, cofinanced by the European Social Fund. References Aguilar, M., 1990. Influencia de la densidad de plantas en el crecimiento, rendimiento y calidad del grano de tres cultivares de maíz (Zea Mays L.) (Ciclos 600, 700 y 800 FAO), en el valle medio del Guadalquivir. Doctoral Thesis. University of Cordoba, Spain. Aguilar, M., López-Bellido, L., 1996. Growth and yield of irrigated maize under Mediterranean conditions: the effect of cultivar and plant density. Cereal Res. Commun. 24, 499–506. Allen, R.G., Pereira, L.S., Raes, D., Smith, M., 1998. Crop evapotranspiration. Guidelines for computing crop water requirements. FAO Irrig. Drain. Paper No. 56. FAO, Rome. Bartolini, F., Bazzani, G.M., Gallerani, V., Raggi, M., Viaggi, D., 2007. The impact of water and agriculture policy scenarios on irrigated farming systems in Italy: an

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