Bioeconomic model to optimize water use: A study case of Segarra-Garrigues channel in Catalonia
A Thesis Presented to
The School of Agricultural Engineering of Barcelona (ESAB) at Polytechnic University of Catalonia (UPC)
In Partial Fulfillment of the Requirements for the Degree of Masters of Science
by
Mariem Khalfaoui
July 2014
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© 2014 Mariem Khalfaoui ALL RIGHTS RESERVED
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Mariem Khalfaoui
______[Lluc Mercade Romeu], Thesis Advisor ______[José Maria Gil], Thesis Advisor
Credits: 30 ECTS Level: Master Course title: Master’s Thesis Course code: 390404 Program/education: European Master in Agricultural, Food and Environmental Policy Analysis (AFEPA)
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Abstract
Water resources used in irrigated agriculture are increasingly scarce, in several countries the implementation of new irrigation management seems to be an adequate answer to this critical situation. Segarra-Garrigues Channel is one of the largest water projects carried out in Catalonia-Spain and designed to become a big part of today's cultivated lands in the province of Lleida in irrigated crops. To optimize the limited resources available and use the potential of the channel in an efficient way, 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. In the present study, Yield functions where obtained from dynamic crop simulation model, AquaCrop (Steduto et al., 2009) taking into account physiological and agronomic specificities in addition to the different irrigation strategies. A model at farm scale was developed and applied to an area in Catalonia related to Segerra Garrirgues Irrigation Channel. The applications of the model to the study area showed in this particular study case that Maize is the most profitable crop, in particular the variety Maize 600, this result still sustainable even with price simulation.
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Table Of contents
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List of Figures
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List of Tables
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Acknowledgements
I am grateful to the Research Center for Economic And Agribusiness Development 'CREDA-UPC' and its staff for the enriching experience and the knowledge I acquired during my stay. I would like to thank the Institute of Food and Agriculture Research 'IRTA' and Dr. Joan Girona for their support and for providing us with the necessary information and data to accomplish this study.
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Chapter 1 - Introduction
The agricultural sector is critical to social and economic progress, particularly with regard to the creation of employment and livelihood-earning opportunities, and the generation of trade and foreign exchange earnings. It is also at the core of environmental concerns over the management of natural resources – land degradation, water scarcity, deforestation, and the threat to biodiversity. (Fischer & al. 2002, Sauer & al.2008, Tao et al. 2011)
Although it's usually low in developed countries GDP, it remains important with regard to the rural development in certain region. In Spain for example, the agriculture accounted in 2011 for 2.0% of the GDP at market prices, and employed 4.1% of the civilian working population, values close to the European averages (1.2% and 5.3% respectively in EU-27) (European Commission, 2012), the concerns about the water use in agriculture and the production efficiency are increasing, despite the fact that the agriculture is not very well presented in the GDP but it still the main source of income and employment in certain rural regions and despite its complexity, the agricultural system is facing a number of obstacles; first natural constraints (climate changes, deterioration of the soil quality, water scarcity..), second the fluctuation of the market prices worldwide. The water scarcity problem is becoming more serious and requiring intervention (Turner et al. 2006), and managing the risk of water scarcity is a challenge to optimize the production reducing the water use. As an answer to this critical situation Irrigation systems are applied to avoid water deficits that reduce crop production and to optimize the use of such scarce resource. The process of crop water use has two main components: one due to evaporation losses from the soil and the crop, usually called evapo-transpiration (ET), and the other that includes all the losses resulting from the distribution of water to the land. (Monteith, 1990; Steduto et al., 2006, Fereres 2006). In the example of Spain, Catalonia (as an Autonomous region is the main contributor to the Spanish economy with nearly 19% of Spain’s GDP), is facing a rapid increase in water demand for all consumption, Agrarian uses, including agricultural irrigation and livestock consumption, account for 72.6% from the total water consumption. The water resources available in Catalonia could become insufficient in order to satisfy the demands placed by society in terms of water quantity and quality. In order to avoid a lack of guaranteed supply, a management improvement was required; increases in water savings, realizing more effective use of the existing resources, and the introduction of new resources.
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In Catalonia, a good example of the debate generated in irrigation and the effects of implementation and management is the Segarra-Garrigues Canal, in the province of Lleida. from a historical claim which is secured in the late 1990s to the transformation of irrigated drylands, the project, with over seventy thousand new irrigated hectares affected six districts,, has been involved in the last decade of economic, environmental and social problems by social agents involved: "Regional public companies Segarra-Garrigues irrigation System"(REGSEGA) and " Waters Segarra Garrigues " (ASG), "State Segarra-Garrigues S.A." (CASEGA) and the " Water Ebro Basin S.A" (AcuaEbro); General Community Irrigation Canal Segarra-Garrigues or signatories of Vallbona Manifest (in 2007 constituted as per Compromís Lleida), three separate but parallel actions around the same concepts. Segarra- Garrigues is considered as one of the largest water projects carried out in Catalonia-Spain (initially covering 70,000ha of irrigation surface) and designed to become a big part of today's cultivated lands , Segarra-Garrigues Irrigation Channel is not yet used in an efficient way, according to IRTA responsibles. It was also a part of most recent Efficiency plans: The Water Efficiency Plan for Agricultural Irrigation, developed in 2008, aimed to draw up a map of agrarian water uses in Catalonia, and to establish a raft of recommendations intended to improve productive water efficiency, to promote the rational use of the resource and to favor savings, while also quantifying the actual potential for savings of resources, and the measures required in order to achieve this, with an emphasis on the reuse of regenerated water. The first sections was opened in July 2009, and it should be ready before 2013, but some section of the irrigation system are not yet functional.
Segarra-Garrigues Channel is a very important irrigation project in Catalonia, , given the role it will plays as a part of the water scarcity solution, and in increasing the agricultural activity profitability and the contribution in rural development. However no previous study about the profitability of the crops planted in the area was done to help farmer, improve the water allocation and increase to rural development
The question now is if the crops sowing in the new irrigates areas are the most profitable ones to the farmers? knowing that the agricultural products market prices are a very unstable, to what extend can the price variation affect the profitability of the crops? Therefore, the primary research question, Is To find which crop are the most profitable to the farmers in the study area region? and farther how sensitive is the profit when we consider the fluctuation of the market prices?
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This study is organized as follows. In chapter 1, literature is reviewed generally on Water scarcity in Spain and particularly in Catalonia, the importance of agriculture and its vulnerability to water scarcity and the public intervention to face this problem. Another will be dedicated to introduce the methodology used in the study. Chapter 2 explains the , context and the background of the present study. It covers topics like the study area giving a general overview of the economic activities in Catalonia, the agricultural activities ...
Another section in the chapter covers the project "Segarra-Garriges", the origin of the project, justification, infrastructure... Chapter 3 describes the methodology of the study and addresses the method of analysis employed in addressing the various objectives of this study. In chapter 4, the bio-economic model is specified. The model is described in details and the various equations involved in the model will be specified. In chapter 5, the results of the study are presented and explanations offered. The results of each objective will be addressed and discussed. The final chapter 6 provides some concluding remarks and recommendations. The major conclusion of the study will be stated and based on these conclusions. The limitations of the study will be the final part of this chapter.
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Chapter 2 - Literature review
The chapter is divided into three main parts. The first part covers the general literature review the water scarcity problem and its impact on the agriculture. The second part covers the new action plan developed by the Department of Agriculture, Food and Rural Action as an answer to the water scarcity problem, and mainly the Irrigation Channel project "Segarra-Garrigues" . The third and final part of the chapter reviews literature on methodology. It covers previous studies using economic model for the optimization of irrigation management at farm level.
1. Water Scarcity
Water is becoming one of the largest, and certainly the most universal of the problems facing mankind as the earth moves into the 21st century( Wipenny ,1994), It may be due to different causes, relative to different xeric regimes, nature produced and man-induced (Vlachos and James, I983; Pereira, 1990), it is usually due to one or to a combination of the following concepts: Aridity, Drought, Desertification and Water shortage.
Water scarcity is an imbalance between available water demand and existing demands; According to (Duarte , 2002) 'The problem of the availability of water can be viewed from at least three perspectives: First, that the resource is a clearly limited one. Secondly, that the demand for water caused by economic and demographic growth is increasing. Thirdly, that the fit between the time, place and quality of the requirements, on the one hand, and the availability, on the other, cannot be automatically assumed'. Over the past decade, the concerns about water scarcity have grown within the EU, especially with regard to long-term imbalances of water demand and water availability in Europe (EC,2012) European commission. In 2007 at least 11% of the EU population and 17% of its territory had experienced water scarcity and the phenomena is getting worse; currently an important share of river basins can be considered as under water stress all year round. During summer months water scarcity is more pronounced in Southern Europe but is also becoming increasingly important in Northern basins, including UK and Germany. (EC,2012)
Spain, is characterized by a mixture of the spatial and time irregularity of precipitation and a deficient hydrological planning regime have given rise to permanent imbalances between resources and requirements (Durante,2002), It has a fragile water balance, with strong contrasts, a powerful and historical agricultural sector that demands water.
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2. Water Infrastructures investments
In countries where water scarcity is a Major problem, water infrastructures investments were always observed as a solution to increase to efficiency and the productivity related to agricultural. The measures adopted to the water scarcity issue are usually directed to both; large hydraulic infrastructures (water transfers, irrigation canals), and also to the demand management (Estrela et al., 2012)
In Spain for exemple, there has been a slight increase of irrigated surfaces (e.g. from 2004 to 2012) (Ministerio de Agricultura, Alimentación y Medio Ambiente, 2013b), linked to major irrigation infrastructures of modernisation plans, which were meant to provide important water savings at a time when water scarcity increased(Vargas-Amelin et Pindado,2013). Increasing irrigation efficiency in agriculture can reduce irrigation water withdrawals to some degree but will not be sufficient to compensate for climate-induced increases in water stress. In addition the hydropower sector will be increasingly affected by lower water availability and increasing energy demand, while the tourism industry will face less favorable conditions in summer. Environmental flows, which are important for the healthy maintenance of aquatic ecosystems, are threatened by climate change impacts and socioeconomic developments.
3. On-farm economic optimization model
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 (Gracia-Vila, Ferers,2012).A farm scale economic optimization model to maximize total gross margin, taking into account water allocation constraints, area restrictions, and other factors set out in various scenarios, can be developed through a non-linear programming model. The Data used in the farm scale economic optimization model to maximize the profits is basically obtained from Yield predictions, critical for a robust result. Models like CERES (Jones and Kiniry, 1986)which has been inserted in the DSSAT (Jones et al., 2003) and APSIM(Keating et al., 2003), EPIC (Williams et al., 1989), ALMANAC (Kiniryet al., 1992), CropSyst (Stöckle et al., 2003), and the Wagenin-gen models (van Ittersum et al., 2003), based on the crop’s physiological response to environmental factors, are useful tools to help farmers optimize their resources. Most of these models require a very high number of parameters to run, and
- 14 - many of them are not easily available in the field and need to be determined experimentally. For this reason, detailed models maybe less reliable and require more advanced skills than simpler butmore robust models (Sinclair and Seligman, 1996).
In the context of water scarcity, the software AquaCrop was developed by the Food and Agri- culture Organization (FAO) in 2009 to help project managers, consultants, irrigation engineers, agronomists, and even farm managers with the formulation of guidelines to increase the crop water productivity for both rained and irrigated production systems. By linking a robust soil water model to the newly developed crop water productivity model, the expected crop development and production for specific climate and growing conditions can be estimated with AquaCrop (Raes et al.,2009) During the last past years, and since its creation, AquaCrop was applied for a set of crops described in several researchs; Farahani et al. (2009) and Garcia-Vila et al. (2009) investigated AquaCrop model for cotton under full and deficit irrigation regimes in Syria and Spain. They showed that the key parameters such as normalized water productivity, canopy cover and total biomass, for calibration must be tested under different climate, soil, cultivars, irrigation methods and field management. Geerts et al. (2009), Heng et al. (2009), Todorovic et al. (2009), and Hsiao et al. (2009) applied AquaCrop model to evaluate the effect of changes in the quantity of irrigation water for quinoa, Maize, sunflower and maize, respectively.
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Chapter 3 - Context/background
1. The geographical area
Spain is a decentralized country with 17 autonomous regions and two autonomous cities. Distinct traditional regional identities within. Spain include the Basques, Catalans (Figure III.1), Galicians and Castilians, among others. Figure III.1: Localization of Catalonia in Europe
Catalonia comprises four provinces: Barcelona, Girona, Lleida, and Tarragona (Figure III.2). The capital and largest city is Barcelona, the second largest city in Spain, and the centre of one of the largest metropolitan areas in Europe.
Figure III.2:Catalonia's provinces
Catalonia (Fig. 1) is one of the most densely populated, urbanized and industrialized regions of Spain. With a population of 7.5 million, it represents 16 % of the Spanish population (INE 2012) and it accounted for 18.6 % of total GDP (INE 2011).
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Catalonia is facing an extremely increasing rate in Water demand for all consumptions, and in 73% for agricultural uses (ACA, 2008), along with the growing impact of climate change effect on the availability of resources (a reduction in water supply and aquifer recharge of 5% by 2025, (ACA. 2008)).
2. Hydrological situation in Catalonia
The territory of Catalonia is divided into two hydrographic areas (Figure III.3):
-The Catalan river basin district (internal hydrographic basins).
This occupies an area of 16,423 km2, representing 52% of the territory of Catalonia, a region which is home to 92% of the Catalan population, and over which the Catalan Water Agency (ACA) has full authority (Legislative Decree 3/2003, of 4 November 2003).
-The interregional hydrographic basins
They cover a surface area of some 15,567 km2, representing 48% of the surface area of Catalonia, housing the remaining 8% of the Catalan population. Figure III.3: Catalan Water System
(ACA,2008)
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The total demand for water in Catalonia for all consumption uses amounts to 3,123 hm3/year, urban usage comprising household and industrial consumption, makes up 27.4% of the total (856 hm3/year). Agrarian uses, including agricultural irrigation and livestock consumption, account for the remaining 72.6% (2,267 hm3/year).
The water resources available in Catalonia could become insufficient (ACA. 2008), in order to satisfy the demands placed by society in terms of water quantity and quality. In order to avoid a lack of guaranteed supply, a management improvement is required. One hand, increases in water savings, and on the other more effective use of the existing resources, and the introduction of new resources. Catalonia accounts for 10 reservoirs in total in the internal basins (Fig.4), with a capacity of more than 5 hm3, giving the ability to regulate 695 hm3. The interregional basins have a total of 14 reservoirs with a capacity of more than 5 hm3, allowing for the regulation of 3,721 hm3.
The main functions of reservoirs are to regulate resources, to laminate inflows and to generate electrical-energy. At present, in certain cases, recreational uses are being added to these traditional uses, serving to highlight intrinsic heritage, natural and landscape values.
Figure III. 4:Catalonia's Main Reservoirs
(ACA,2008)
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The agricultural sector is the biggest consumer of water, making up some 70% of total demand for water in Catalonia, although the percentage for the internal basins is 31%. The promotion and the modernization of existent irrigation systems, in terms of both losses across the network and how they are applied to crops are necessary to increase the efficiency. Traditional irrigation requirements of 10,000 m3/ha over the course of a year can be reduced, using a modern pressure irrigation system (spray or drip) to 6,500 m3/ha per year, in other words a saving of 35%.
3. The Water Efficiency Plan for Agricultural Irrigation
The Water Efficiency Plan for Agricultural Irrigation is the most recent water efficiency plan, developed in 2008, and aimed to draw up a map of agrarian water uses in Catalonia, and to establish a raft of recommendations intended to improve productive water efficiency, to promote the rational use of the resource and to favor savings, while also quantifying the actual potential for savings of resources, and the measures required in order to achieve this, with an emphasis on the reuse of regenerated water.
This also falls within the Irrigation Plan developed by the (Department of Agriculture, Food and Rural Action) DAR, which aims to improve water management in Catalonia.
The Water Efficiency Plan for Agricultural Irrigation included two main projects:
-The modernization of traditional irrigation systems: the Urgell, Pinyana, and Aragon and Catalonia Canals and the Ebro Delta (Figure III.5).
-The introduction of new, efficient irrigation systems: L’Algerri-Balaguer, Segrià Sud, Garrigues sud and "Segarra-Garrigues" (Segerra Garrigues Channel project started long time before the Water efficiency plan, but it wasn't connected yet to the plots)
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Figure III.5:The modernization of traditional irrigation systems plan
(ACA,2008)
4. Segarra Garrigues
Segarra-Garrigues Channel(Figure III.6) is one of the largest water projects carried out in Catalonia-Spain and designed to become a big part of today's cultivated lands in the province of Lleida in irrigated crops.
From a historical claim which is secured in the late 1990s to the transformation of irrigated drylands, the project, with more than seventy thousand hectares and affecting six districts, has been involved in the last decade in economic, environmental and social issues by various stakeholders: regional public enterprises Reg System Segarra-Garrigues (REGSEGA) and Aigues Segarra Garrigues (ASG) and state Segarra-Garrigues Canal SA (CASEGA ) and Aguas de la Cuenca del Ebro SA (AcuaEbro); General Community Irrigation Canal Segarra- Garrigues or signatories of Vallbona Manifest (in 2007 constituted as per Compromís Lleida), three separate but parallel action around the same concepts. (Sandra et al.)
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Figure III.6: Segarra-Garrigues Channel
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The Segarra-Garrigues System covers 70.150 ha hectares of land in 74 municipalities in the Noguera, Segarra, Pla d’Urgell,Garrigues, Urgell and Segrià districts (Table III.1), but used for irrigation only in 24.474ha.
Table III.1: Irrigates superficies and Municipalities per Sector
REGSA,1997
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Setting off from the reservoir of Rialb, in the river Segre and drains in the reservoir of the Albagés, in the river Set, the Segarra-Garrigues channel is 85.7km long. The System integrates,besides, two situated direct collections in the Segre into Albatàrrec and Aitona-Seròs (TableIII.2)
Table III.2: Geographical Aspects of Segarra-Garrigues Channel Geographical Aspects Total Surface 70.150 ha Irrigated land surface 24.474 ha Dry land Surface (Natura2000 and Special Protection Areas for 45.676 ha Birds) Length 85,7 km Irrigated Sectors 15 Districts 6 Municipalities 74 Generalitat de Catalonia, 2007; Aldomà, 2007ab
Introducing irrigation system related to Segarra-Garrigues Channel in the regions (1) and (2) (Figure 6) where farmers are used to traditional production system depending on rainfall, is a real challenge.
Before answering the research questions, let's answer the most important question in this study, WHY? why such study is important? As it was shown upper the Irrigation Channel project is mainly an action to face the water scarcity problem and to satisfy the increasing demand, But why are we interested by the agricultural activity in Catalonia?
5. Agriculture in Catalonia
Despite the fact that the agriculture represents less than 1% in the Catalan GDP and employs less than 3% (IDESCAT ,2011) , it still a very important sector.
From one side, in 2009 the cultivated lands in Catalonia counted for around 40% from the total surface. The activities are divided into 65% animal production (56.3% pigs) and 35% crop production (EVOLUCIÓ MACROMAGNITUDS AGRÀRIES CATALONIA 2002- 2012) According to data presented by the Department of Agriculture, livestock, fisheries, food and environment in Catalonia (DAAM, 2011), the region had 27,5% of the national porcine census and 40% of the national pork production, summing 1,4 million tons in 2011.
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In Catalonia, the porcine sector is the principal agrarian subsector, it represented 31,5% of all agrarian production in 2010 and pork meat production generated 1.238 million euros to the Catalan economy during that same year (DAAM, 2011) when Cereals present 20% from the crop production, and is mainly dedicated to animal feeding (porcine sector).
From another hand, the agricultural sector is considered as fundamental in the rural development, generating several non agricultural activities; such as Tourism, Craft..(Table III.3.)
Table III.3: Other activities generated by the agricultural activities
Agriculture Tourism, Processing Production Work NON Total accomodation Transform- of of under agricultural Year number of and other Craft ation of Forestry agriculture renewable Contract to work under exploitation related Wood products Energy other contract activities Farms 2009 2318 679 31 446 94 27 567 147 184
(Idescat.,2014/)
In some regions in Catalonia, agriculture is main activity and increasing the production means increasing the farmer incomes and contributing to the rural development (Cens Agrari, 2009)
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Chapter 4 - Material and Methods
In this Chapter we will try to first present the study area briefly, then the data we have (how we got it and the data generation process) before explaining the analysis method used in this study. 1. Study area
The areas selected for this study were (1) and (2) (shown in figure III.6) located in the municipality of Norguera within the Segarra-Garrigues irrigation scheme, in Catalonia,Spain.
The area has was recently connected to the new Irrigation Channel "Segara-Garrigues.
2. Data Description
The data used in the optimization model are obtained from the IRTA research center, while the data used for the price simulations are obained from "Generalit de Catalonia-Departament d'agricultura, Ramaderia, Pesca, Alimentacio i Medi Natural" Website.
2.1. Crop Data
AquaCrop provides default or sample values for all required parameters as the starting point to use for unexplored crops in the absence of specific information (e.g., Geerts et al., 2009).
In this case IRTA provided data for a set of 9 crops: 3 different varieties of Maize (800, 600 and 500), Wheat, Durum, Oats, Barley, Potatoes and sunflower usig 2 types of irrigation systems (Drip and Sprinkles).
2.2. Costs Data
Two types of costs were considered in this study: Fixed and Variable Costs.
The fixed costs are divided into 4 categories (Table IV.1):
-Connection Fees related to the integration of the plot in the irrigation system and which are fixed to 40€/ha for all the crops
-The Amortization which is The depreciation of the irrigation system, considering that this is worth 3.500 €per ha, and is applied to a rate of 1.5% in 12 years, the amortization is fixed to 320€ per hectare and year
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-The plantation Costs were given by a service company that takes care of planting, cultivating, processing.., this cost is fixed per crop and per hectar.
-The last fixed cost is related to the irrigation Cost and is fixed to 181€/ha
Table IV.1: Fixed Costs (Euro/ha) Fixed Costs
Connection Amortization Fixed Cost Plantation fees Costs Maize800 Drip 40 320 181 1200 Maize800 Sprinklers 40 320 181 1200 Maize600 Drip 40 320 181 1200 Maize600 Sprinklers 40 320 181 1200 Maize500 Drip 40 320 181 1200 Maize500 Sprinklers 40 320 181 1200 Barley Drip 40 320 181 500 Barley Sprinklers 40 320 181 500 Durum Drip 40 320 181 500 Durum Sprinklers 40 320 181 500 Wheat Drip 40 320 181 500 Wheat Sprinklers 40 320 181 500 Sunflower Drip 40 320 181 500 Sunflower Sprinklers 40 320 181 500 Oat Drip 40 320 181 500 Oat Sprinklers 40 320 181 500 Potatoes Drip 40 320 181 5000 Potatoes Sprinklers 40 320 181 5000
The variable costs, that are exclusively the water costs calculated inside the economic model (multiplying the water quantities by Water Price (given by IRTA is 0.08€/m3 ))
3. AquaCrop model
The FAO AquaCrop model predicts crop productivity, water requirement, and water use efficiency (WUE) under water-limiting conditions (Hrng et al., 2009) It uses a relatively small number of explicit parameters and largely-intuitive input variables, either widely used or requiring simple methods for their determination. The inputs are stored in climate, crop, soil and management files and can be easily changed through the user interface.
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Multiple Figures and schematic displays in the Menus help the user to discern the consequences of input changes (Figure IV.1) Figure IV.1: Structure and Components of AquaCrop
(IRTA,2014)
The crop grows by developing a green canopy that transpires water, and a root system that deepens and takes up water. The transpired water is in exchange for biomass produced (via the assimilation of carbon dioxide, not directly simulated). At a certain phonological stage, a part of the biomass is partitioned to the yield component as determined by the harvest index (HI).
The rough out of the crop cycle the amount of water stored in the root zone is simulated by budgeting the incoming (rainfall and irrigation) and outgoing (runoff ET and deep percolation) water fluxes at its boundaries.
The root zone depletion determines the magnitude of the water stress coefficients (Ks) affecting (i) green canopy cover (CC) expansion, (ii) stomatal conductance and hence transpiration per unit CC, (iii) canopy senescence and decline, and (iv) the HI. Each of these
- 27 - effects has its own threshold depletions and response curves. Additionally, (v) the root system deepening rate is a function of Ks for stomatal conductance. If water stress occurs, the simulated CC will be less than the potential canopy cover (CCpot) for no stress conditions. The coefficient for transpiration (Kctr) is proportional to CC, and hence continuously adjusted throughout the simulation.
The Biomass (B) is derived from transpiration by means of the normalized water productivity (WP*), a conservative parameter. At the end of the crop cycle, yield is calculated as the product of the simulated B and the adjusted (HI) (Figure IV.2).
FigueIV.2: Process Description
( Raes, et al. ,2009)
Simulation results are usually recorded in output files and can be retrieved in spread sheet programs for further processing and analysis.
Physiologic and agronomic data have to be introduced to the Aqua crop Model to simulate first biomass (1) and second the yield (2) corresponding to each crop with the two types of irrigation systems. (1)
B: biomass produced cumulatively (kg / m2)
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WP : water productivity (kg of biomass / m3 of water transpired)
Tr :crop transpiration (mm or m3 / unit of surface)
(2) Y :yield (kg / m2)
HI: harvest index
Simulation results are then recorded in output files and retrieved in spread sheet programs for further processing and analysis .
In this case IRTA research center stuff runned the AquaCrop model and provided us with the yield equations corresponding to the study area with a set of 9 crops: 3 different varieties of Maize (800, 600 and 500), Wheat, Durum, Oats, Barley, Potatoes and sunflower using 2 types of irrigation systems (Drip and Sprinkles).With the equations received and the Applied irrigation water limits, the yield fuctions were drawn using continuous data on an Excel datasheet.
For each crop, random increasing amounts of water was applied to the yield equations within the limits established for each function, allowing to draw the yield functions for all the crops(Appendix1). The following Figure illustrate the example of the Maize with its 3 different varieties and the 2 types of irrigations systems (Figure IV.3)
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Figure IV.3: Yield function of the three varieties of Maize (kg/ha) Maize800/Sprinklers Maize800/Drips 16000 16000 14000 14000
12000
10000 12000 8000 10000
6000
Yield (kg/ha) Yield Yield (kg/ha) Yield 4000 8000 2000 6000 0 198 298 398 498 598 698 285 435 585 735 885 1035 Applied Irrigation Water (mm) Applied Irrigation Water (mm) Maize600/Sprinklers Maize600/Drips 16000 18000 14000 16000
12000
10000 14000 8000
6000 12000
Yield (kg/ha) Yield Yield (kg/ha) Yield 4000 10000 2000
0 8000 370 470 570 670 770 870 250 350 450 550 650 750 Applied Irrigation Water (mm) Applied Irrigation Water (mm)
Maize500/Sprinklers 14000 Maize500/Drips 14000
12000 12000
10000 10000 8000 8000
6000 6000 Yield (kg/ha) Yield Yield (kg/ha) Yield 4000 4000 2000 2000 0 0 250 350 450 550 650 750 850 950 20 120 220 320 420 520 620 720 Applied Irrigation Water (mm) Applied Irrigation Water (mm)
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4. The Economic Model
The validation and Calibration of Aquacrop model was carried by the research center IRTA.
The validated AquaCrop model for the 9 crops with 2 types of irrigation systems was used to estimate a set of discrete optimal yield-irrigation points, by simulating the response to irrigation respecting the production functions limits Table IV.1.a and Table IV.1.b)
Table IV. 1.a:Irrigation quantities limits (mm) (Maiza800, 600 and 500, Durum and Wheat) Crop Maize 800 Maize600 Maize500 Durum Wheat Irrigation Sprinkler Drip Sprinkler Drip Sprinklers Drip Sprinklers Drip Sprinklers Drip System
Max 1133 791 934 785 928 548 429 300 458 322 Min 285 198 373 262 201 108 41 30 43 30
Table IV.1.b: Irrigation quantities restrictions (mm) (Barley, Oat, Sunflower and Potatoes)
Crop Potatos Sunflower Oat Barley Irrigation Sprinklers Drip Sprinklers Drip Sprinklers Drip Sprinklers Drip System Max 1390 966 569 397 466 336 326 232 Min 340 242 55 78 19 12 35 24
The Crop-water production functions as the relationships between yield and Applied Irrigation Water (AIW) were described for each crop and irrigation system by a set of equations (Annexe1).
The Aquacrop Model gives robust output, that can be used to develop a farm scale economic optimization model using a non-linear programming model. The General Algebraic Modeling System (GAMS) (Rosenthal, 2007) was selected for this purpose.
The General Algebraic Modeling System (GAMS) is a high-level modeling system for mathematical programming and optimization
GAMS code is used to define the structure of the model, and to attach data to the model, it provides a wide range of optimization solvers for linear, non-linear, mixed integer, mixed integer non-linear optimization and mixed complimentarily problems.
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The objective of the study being to find which crop are the most profitable to the farmers in the specific study area, the first step is to calculate the maximum profit possible for each of the set of cops suggested in the study.
The economic model consists basically on the optimization of an objective function (Gross Profit). The profit is calculated by taking out the Costs (Variable and fixed) from the income realized by the production under a number of constraint related to water use, applied irrigation water have to be strictly lower than the Irrigation quantities maximum and higher than the r Irrigation quantities minimum (Table IV.1.a and Table IV.1.b)
Gross Profit ci =Yieldci*Market_pricec-Fixedcostci–Variable Costci (3)
Variable Costci=Water_quantityci*Water_Price (4) with c: Crop and i: irrigation system
Yield: is the yield corresponding to each crop productivity with the different irrigation systems and is obtained from the equations given by IRTA research center as a result of the Aquacrop Model previously described.
Market Price: is the crop price corresponding the real price taken from the " Generalit de Catalonia-Departament d'agricultura, Ramaderia, Pesca, Alimentacio i Medi Natural" and corresponding to 2012/2013 prices (Base2005). The database given on the website of the DAMM (Department of agriculture, livestock, fisheries, food and environment in Catalonia ) present the monthly weighted average depending on the quantities and prices of the actual market
The market prices used in this study are the seasonal average depending on the production and sale cycle of each crop. For Maize,for exemple, the market price used is not the annual average (January-December) but the average from September to February next year.
The Variable costs are related to the applied irrigation water, the water quantity is a result from optimization model and the Official Water Price for irrigation is 0.08€/m3 (IRTA). The following Figure is a summary of the previous explanations.
- 32 -
Figure IV.3:Summary
5. The price Simulation
The aim of this price simulation is to see how robust is the ranking and which are the most sensitive crops to the price variations.
After running the economic optimization model on GAMS, obtaining the maximum profit possible per crop and the correspondent yield and applied irrigation water, a ranking of crops is made from the higher to lower profit crop.
Following the market prices evolutions, we noticed that the prices were more or less stable (or with minor variations (+/-10%)) and that the important variations start only 9 years ago (DAMM,2008; DAMM,2014), the reason why we are using market prices for the last 9 years (2005 to 2014) in the price simulations
The database used in this study contain 7 different crops and 3 varieties of Maize (a total of 9 crops), that can be divided into 3 main groups: Cereals: Maize, Wheat, Durum, Barley and Oat Industrial Crop: Sunflower
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Tuberous Crop: Potatoes
Cereals prices in Catalonia have been oscillating between 13,16 and 25,43€/100kg during the last 9 years following an increasing movement (Durum and Wheat have the exact same prices and their curves are superimposed, the reason the Durum's curve is not noticeable on the Figure), while the industrial crop:Sunflower's prices show a higher variation (between 23,97 and 55,38€/100kg) and higher prices than cereals. Potatoes prices oscillate between 19,40 and 38,43€/100kg but still higher than cereals prices and lower than Sunflower prices (since 2007) (FigureIV.4.)
FigureIV.4: Price Variations in Catalonia from 2005 to 2014 (€/100kg) (Base 2005)
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Chapter 5 - Results and discussion
1. On-farm economic optimization model for decision making 1.1. Yield and Applied Irrigation Water obtained with the Benefits maximization function
The results of the simulations of the economic model in terms of AIW as a function of water allocation under the 2 following assumptions:1st Assumption: Climate is an intermediate Climate and same for the all the study area (section 1and 2 located in the municipality of Noguera)
2nd Assumption: the Soil is the same for the entire study area: . Based on the Yield and taking into account the previous assumptions; For the first Scenario, when we have the "Sprinklers" as irrigation system, "Potatoes" has the higher production level with 15056kg/ha followed by the "Maize600" with 14979,73 kg/ha than Maize 500 with 14351,7kg/ha than Maize500, Wheat, Durum, Oat, Barley and finally Sunflower with the lowest yield 3254,9kg/ha (Figure V.1.a.)
Figure V.1.a: Yield per Crop withSprinklers(kg/ha)
Soil: Falcons Weather: Intermediate Irrigation Systems: Sprinklers Year:2012/2013
Potatoes 15056
Oat 6008,8
Sunflower 3254,9
Wheat 7428,5
Durum 7149,2 Crops Barley 5713,412
Maize500 11508,9
Maize600 14979,73
Maize800 14351,7
0 2000 4000 6000 8000 10000 12000 14000 16000 Yield (kg/ha)
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For the second Scenario, when the irrigation system is Drip we observe a different ranking, since the higher yield is 15727,6kg/ ha obtained with the Maize 600, Followed by the Maize 800 with 15156,2kg/ha Potatoes with 15097,3kg/ha, than Maize500, Wheat, Durum, Oat, Barley and Sunflower (Figure V.1.b)
Figure V.1.b: Yield per Crop with Drip(kg/ha)
Soil: Falcons Weather: Intermediate Irrigation Systems: Drips Year: 2012/2013
Potatoes 15097,3
Oat 5973,7
Sunflower 3238,927
Wheat 7467,6
Crops Durum 7162,9
Barley 5778,336
Maize500 12026,3
Maize600 15727,6
Maize800 15156,2
0 5000 10000 15000 20000 Yield (kg/ha)
- 36 -
A quick comparison between the two scenarios shows that the Yield changes slightly when the irrigation system changes, except for the Maize with its 3 different varieties where we observe an increase in the yield with the Drip system (Figure V.2.)
Figure V.2: Yield per Crop with the two different irrigation systems (kg/ha) Soil: Falcons Weather: Intermediate Year:2012/2013
15056 Potatoes 15097,3
6008,8 Oat 5973,7
3254,9 Sunflower 3238,927
7428,5 Wheat 7467,6
Sprinklers
7149,2 Durum Drips
7162,9 Crops
5713,412 Barley 5778,336
11508,9 Maize500 12026,3
14979,73 Maize600 15727,6
14351,7 Maize800 15156,2
0 2000 4000 6000 8000 10000 12000 14000 16000 18000 Yield kg/ha
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1.2. Applied Irrigation Water
When it comes to water use, comparing the Applied Water Irrigation quantities used to obtain the maximum benefits (Figure V.3) for each crops shows the lower rate of water use with the Drip irrigation system conformed to the literature about this system efficiency (EEA, 2009; CA, 2007; World Bank, 2006)
Figure V.3: Comparison of the Applied Irrigation Water per Crop with the two different irrigation systems (mm/ha)
Soil: Falcons Weather: Intermediate Year:2012/2013
94,5 Oat 71,6
100,7 Barley 120,3 145,8 Durum 127,8 174,0 Wheat 143,3
Sprinklers 295,9 Sunflower Drips Crop 7162,9 404,4 Maize500 359,5 533,3 Maize600 429,1 575,4 Potatoes 459,9
495,9 Maize800 474,9
0 100 200 300 400 500 600 700 Applied Irrigation Water
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1.3. Benefits Maximization
Applying the benefits equations (described above) for the Two scenarios taking into account the yield functions and the respective costs for each of different crops used in the study.
The benefits results with the First scenario (Irrigation System= Sprinklers), shows that they higher benefits are obtained with the Maize 600 (1520€/ha) followed by Maize800 with 1395€/ha than Maize500, Wheat, Durum, Sunflower and Oat (Figure 4).
Contrary to the yield result that showed that Potatoes has the higher production, its benefits is not only the lowest one but with a high loss of 1796€/ha, and this is due to the very high crop cost (5000€/ha) since its price is one of the highest market prices (considering the set of crop used in this study. Figure V.4.a:The Maximum Benefits per crop with Sprinklers (€/ha)
Soil: Falcons Weather: Intermediate Irrigation Systems: Sprinkler Year: 2012/2013 2000
1 520,4 € 1500 1 395,7 €
1000 769,0 € 709,6 € 661,1 € 449,7 € 500 247,9 € 160,2 €
0
Oat
Wheat Barley Durum
-500 Potatos
Maize600 Maize800 Maize500 Sunflower
-1000
-1500
-1 796,2 € -2000 Sprinklers
- 39 -
The benefits results with the Second scenario (Irrigation System= Drip), shows that the benefits follow the same ranking as with the sprinklers but with higher benefits .
The higher benefits are also obtained with the Maize 600 (1787€/ha) followed by Maize800 with 1610€/ha than Maize500, Wheat, Durum, Sunflower and Oat (FigureV.4.b) Potatoes keep causing losses (a little bit lower but it still important).
FigureV.4.b: The Maximum Benefits per crop with Drip(€/ha)
Soil: Falcons Weather: Intermediate Irrigation Systems: Drip Year: 2012/2013
2000 1 787,9 € 1 610,5 € 1500
1000 932,3 € 744,1 € 679,0 € 480,7 € 500 247,8 € 171,1 €
0
Oat
Wheat Barley Durum
-500 Potatos
Maize600 Maize800 Maize500 Sunflower
-1000
-1500
-1 692,2 € Drips -2000
- 40 -
The benefits from the second scenario are all higher than the ones from the first scenario for the same crop and under the same conditions (Figure V.5) Figure V.5: The Maximum Benefits per crop (€/ha)
Soil: Falcons Weather: Intermediate Year: 2012/2013
2000
1500
€
1000 €
€
€
1 787,9 787,9 1
1 610,5 610,5 1
€
1 520,4 520,4 1
1 395,7 395,7 1
€
€ €
500 €
€
€
€
€ € € €
932,3 932,3
769,0 769,0
744,1 744,1
709,6 709,6
679,0 679,0
661,1 661,1
480,7 480,7
449,7 449,7
247,8 247,8 247,9 171,1 160,2
0
Oat
Wheat
Barley
Durum
Potatos
Maize600 Maize800 Maize500
-500 Sunflower
€ €
-1000 692,2 1
-
1 796,2 796,2 1 -
-1500
-2000 Drips Sprinklers
- 41 -
If the scenarios are fixed and the irrigations systems is already installed the ranking of the most profitable crop for the farmer will be the following (Table V.1), if not yet, the farmer has an incentive to install the Drip irrigation system.
Table V.1: Ranking of the most profitable crops based on the Benefits
Ranking Crop Benefits with Sprinklers Benefits with Drip Order
1 Maize600 1520,357 1787,855 2 Maize800 1395,669 1610,536 3 Maize500 768,971 932,275 4 Wheat 709,61 744,117 5 Durum 661,116 679,002 6 Sunflower 449,655 480,695 7 Barley 247,928 247,789 8 Oat 160,238 171,116 9 Potatos -1796,179 -1692,244
2. Price Simulations
After answering the first question and finding the ranking of the most profitable crop (from the considred list) with respect to the different irrigation systems.
A price simulation was applied to the different crops to check how robust is ranking we found and to see how far a change in the Crop prices may influence the benefits. A number of assumptions was considering in this task: 1. The yield is constant 2. The different costs are constant 3. The water price is constant Starting with the Maize, since the prices used are the same for the 3 varieties, the order of the higher profit remains the same, besides we observe that Maize 500 benefits went negative with the price variations, which can be explained by the fact thatit has a benefits level lower
- 42 - than the other two varieties (Maize600 and Maize800) and when the prices go down to certain point (18€/100kg), the benefits became negative, but the decreasing in the benefits is quite similar in the three varieties Another important point to be mentioned is that the benefits are more sensitive to the price variations when the irrigation system is sprinklers; for the same year 2005/2006 when the prices were the lowest, when the profits of Maize 600 and 800 were slightly positive with Drip as irrigation system, they were strictly negative with sprinklers. Figure V.6:Impact of price variations on the 3 varieties of Maize for both irrigation systems (€/100kg)
2000 2000 Sprinklers A Drip B
1500 1500
1000 1000
500 500
0 0
-500 -500 Corn800 Corn600 Corn500 Corn800 Corn600 Corn500
For the remaining Cereals (Wheat, Durum Barley and Oat), there are a slight differences between the two irrigation systems. Concerning the sensibility to the price variations, Oat and Barley seems to be highly affected with the price variations, this can be also explained by the low productivity of both those crops. Wheat and Durum are more robust face to price variations except when the prices are below 16€/100kg.
- 43 -
Figure V.7 :Impact of price variations on4 Cereals (Wheat, Durum, Barley and Oat) for both irrigation systems (€/100kg)
Despite the fact that The tuberous crop 'Potatoes' is the one with relatively high price (FigureIV.4), regardless the prices during the last 9 years and the irrigation system, it always gives negative profit, this may be explained by the very high production cost (5000€/ha) (Table IV.1).
Figure V.8:. Impact of price variations Potatoes and Sunflower for both irrigation systems (€/100kg)
Concerning the Sunflower, the negative benefits when the price is below 39€/100kg, which can be explained with the low productivity of the crop ( Figure V.2) - 44 -
To summarize, Maize 800 and 600 are the most robust to the price variations and keep being the most profitable ones. For Maize 500 for instance, can lose its ranking to the benefit of Wheat and Durum (2007/2008; from 2009/2010 to 2012/2013) and to be at the same level of Barley, Oat and Sunflower.
Figure V.9:Impact of price variations for the different Crops with Drip(€/100kg)
1500
Maize800 500 Maize600
Maize500
Barley -500 Durum
Wheat
2005/2006 2006/2007 2007/2008 2008/2009 2009/2010 2010/2011 2011/2012 2012/2013 2013/2014 -1500 Sunflower Oat Potatos -2500
-3500
Figure V.10:Impact of price variations for the different Crops with Sprinkler(€/100kg)
1400
900
Maize800 400
Maize600
-100 Maize500 Barley -600
Durum
2005/2006 2006/2007 2007/2008 2008/2009 2009/2010 2010/2011 2011/2012 2012/2013 2013/2014 -1100 Wheat Sunflower -1600 Oat -2100 Potatos
-2600
-3100
- 45 -
Chapter 6 - Conclusion
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 strategies, favoring efficient use of irrigation and profit maximization.
Models such as the one developed in this study may be applied for scenario analysis and strategic planning.
Combining a crop simulation model with an economic optimization model aimed at optimizing farm profits 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 9 crops (Maize 800,600 and 500, Barley, Wheat, Durum, Oat, Potatoes, and sunflower) under the specific climatic and soil conditions of the sector 1 and 2 of the irrigation channel Segarra_Garrigues After the analysis of the different scenarios under the particular conditions of the study area, it was concluded that, the Maize 600 is the most profitable for this specific region and under the specific climatic and soil conditions and with both irrigation systems.
A ranking of the most profitable crops was established (1.Maize600, 2.Maize800,3.Maize500, 4.Wheat, 5.Durum, 6.Sunflower, 7.Barley, 8.Oat, 9.Potatos) for farmers who have already installed one of the irrigation system. For farmers who still cultivate dry land crops and have not yet installed an irrigation system, it's recommended that they install the "Drip irrigation system", since it was proved that it is more efficient in water use and more profitable.
When checking what would happened with the prices of the last 9 years (from 2005/2006 to 2013/2014), Maize 600 still always the most profitable, but the rank of the most profitable crops changed and between 2008/2009 and 2009/2010 all the crops except Maize 600 and Maize 800 had negative or null benefits (we cannot confirm this result because we don't know the costs or the productivity during this year)
- 46 -
The model designed for this study is a first approximation to the issue, which can be modified, by adding more variables to better approximate the reality. However this model can be applied to all different sectors of Segarra_Garrigues Channel with some changes of course and can give farther results scenarios to tackle the Climate changes in the region and to insure a maximum profit to farmers.
- 47 -
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Appendix A - Yield Functions
Maize800/Sprinklers Maize800/Drips 16000 16000 14000 14000
12000
10000 12000 8000 10000
6000 (kg/ha) Yield Yield (kg/ha) Yield 4000 8000 2000 6000 0 198 298 398 498 598 698 285 435 585 735 885 1035 Applied Irrigation Water (mm) Applied Irrigation Water (mm) Maize600/Sprinklers Maize600/Drips 16000 18000 14000 16000
12000
10000 14000 8000
6000 12000
Yield (kg/ha) Yield Yield (kg/ha) Yield 4000 10000 2000
0 8000 370 470 570 670 770 870 250 350 450 550 650 750 Applied Irrigation Water (mm) Applied Irrigation Water (mm)
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Maize500/Sprinklers Maize500/Drips 14000 14000 12000 12000
10000
10000 8000 8000
6000 6000
Yield (kg/ha) Yield Yield (kg/ha) Yield 4000 4000
2000 2000
0 0 250 350 450 550 650 750 850 950 20 120 220 320 420 520 620 720 Applied Irrigation Water (mm) Applied Irrigation Water (mm)
Barley/ Sprinklers Barley/ Drips 6000 7000
6500
5700
6000 5400 5500
5100 Yield (kg/ha) Yield Yield (kg/ha) Yield 5000
4800 4500
4500 4000 0 100 200 300 400 500 600 700 0 100 200 300 400 500 Applied Irrigation Water (mm) Applied Irrigation Water (mm)
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Potatos/Sprinklers Potatos/ Drips 17000 16500 15500
15000
14000 13500 12500
12000 Yield (kg/ha) Yield Yield (kg/ha) Yield 11000
10500 9500
9000 8000 250 450 650 850 1050 1250 200 400 600 800 1000 Applied Irrigation Water (mm) Applied Irrigation Water (mm) Durum/Sprinklers Durum/Drips 8000 7500
7500
7000
7000
6500 6500 Yield (kg/ha) Yield 6000 (kg/ha) Yield 6000 5500
5000 5500 0 100 200 300 400 500 0 50 100 150 200 250 300 350 Applied Irrigation Water (mm) Applied Irrigation Water (mm) Wheat/Sprinklers Wheat/Drips 7500 7500
7000 7000
6500 6500
Yield (kg/ha) Yield Yield (kg/ha) Yield 6000 6000
5500 5500 0 100 200 300 400 500 0 50 100 150 200 250 300 350 Applied Irrigation Water (mm) Applied Irrigation Water (mm)
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Sunflower/Sprinkler Sunflower/Drips 3500 s
3400
3000 3100
2800 Yield (kg/ha) Yield 2500 (kg/ha) Yield 2500
2000 2200 0 100 200 300 400 500 600 0 100 200 300 400 Applied Irrigation Water (mm) Applied Irrigation Water (mm)
Oat/Sprinklers Oat/Drips 7000 6500
6500 6000
6000
5500 5500 5000 5000
4500
Yield (kg/ha) Yield Yield (kg/ha) Yield 4000 4500 3500
3000 4000 0 100 200 300 400 500 0 50 100 150 200 250 300 350 Applied Irrigation Water (mm) Applied Irrigation Water (mm)
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Appendix B: GAMS MODEL
$Title: The economic model for the optimization of irrigation management at farm level set v vrops/ Maize800 Maize800_Drip Maize600 Maize600_Drip Maize500 Maize500_Drip Barley Barley_Drip Durum Durum_Drip Wheat Wheat_Drip Sunflower Sunflower_Drip Oat Oat_Drip /
alpha /b1, b2, b3, b4, b5, b6/
limit /min, med, max/
;
Scalars ** Per hevtar **
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Connection_fees /40/ Irr_Syst_Amortization /320/ Fixe_per_ha /181/ Water_price /0.08/ ;
Parameter lluc_prices(v) / Maize800 0.2462 Maize800_Drip 0.2462 Maize600 0.2462 Maize600_Drip 0.2462 Maize500 0.2462 Maize500_Drip 0.2462 Barley 0.2397 Barley_Drip 0.2397 Durum 0.2544 Durum_Drip 0.2544 Wheat 0.2544 Wheat_Drip 0.2544 Sunflower 0.5307 Sunflower_Drip 0.5307 Oat 0.2125 Oat_Drip 0.2125
/ Parameter Crop_fixed_cost(v) / Maize800 1200 Maize800_Drip 1200 Maize600 1200 Maize600_Drip 1200
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Maize500 1200 Maize500_Drip 1200 Barley 500 Barley_Drip 500 Durum 500 Durum_Drip 500 Wheat 500 Wheat_Drip 500 Sunflower 500 Sunflower_Drip 500 Oat 500 Oat_Drip 500 /
Table Yield(v, alpha) b1 b2 b3 b4 b5 b6 Maize800 14351.7 111.3 495.9 0.9574 0.2214 Maize800_Drip 15156.2 13.8407 474.9 -0.6708 -0.0591 Maize600 14980 3.1664 533.4 1.8413 -0.4933 Maize600_Drip 15727.6 35.9545 429.1 -0.0154 -0.0528 Maize500 11508.9 113.2 404.4 1.0589 0.2754 Maize500_Drip 12026.3 5.6872 359.5 0.1448 -0.2871 - 0.00069 Barley 5734 -0.1155 113.5 -0.0606 -0.1351 Barley_Drip 5799.2 1.8446 128.4 -0.6903 -0.0927 Durum 7149.2 10.8994 145.8 0.0977 -0.0105 Durum_Drip 7162.9 9.4774 127.8 0.0172 -0.0371 Wheat 7428.5 9.814 174 0.2286 -0.0098 Wheat_Drip 7467.6 10.7269 143.3 0.0851 -0.0243 Sunflower 3254.9 2.5231 295.9 0.0387 -0.00612 Sunflower_Drip 3267.5 -0.7393 320.9 -0.0591 -0.0151 Oat 6008.8 48.7217 94.5398 -0.1976 0.206
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Oat_Drip 5973.7 59.1235 71.6191 -0.0855 0.3281
; Table Water_bounds(v,limit) min med max Maize800 285 495.9 1133 Maize800_Drip 198 474.9 791 Maize600 373 533.4 934 Maize600_Drip 262 429.1 785 Maize500 221 404.4 928 Maize500_Drip 108 359.5 548 Barley 35 113.5 326 Barley_Drip 24 128.4 232 Durum 41 145.8 429 Durum_Drip 30 127.8 300 Wheat 43 174 458 Wheat_Drip 30 143.3 322 Sunflower 55 295.9 569 Sunflower_Drip 78 320.9 397 Oat 19 94.5398 466 Oat_Drip 12 71.6191 336
; Variable z, z2; POSITIVE VARIABLES prodt_First(v), Water(v),cost_crop(v),cost_vF(v), market_p(v),prodt_Second(v), Water_S(v) , cost_vS(v), benef_S(v) ,benef_F(v) Equation Fo1 Fo2 limit_sup(v) limit_inf(v)
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production_first(v) Variable_Cost_F(v) Benefice_F(v) *market_price(v) Crop_cost(v)
limit_s(v) limit_in(v) production_second(v) Variable_Cost_S(v) Benefice_S(v) ; Fo1..z=e=sum(v,(prodt_First(v)*lluc_prices(v))-cost_crop(v)-cost_vF(v)); Fo2..z2=e=sum(v,(prodt_Second(v)*lluc_prices(v))-cost_crop(v)-cost_vS(v)); **with the first production function production_first(v)..prodt_First(v)=e=((Yield(v,'b1'))+(Yield(v,'b2')*(Water(v)- Yield(v,'b3')))+(Yield(v,'b5')*(Water(v)-Yield(v,'b3'))*(Water(v)- Yield(v,'b3')))+(Yield(v,'b6')*sqr(Water(v)-Yield(v,'b3'))*(Water(v)-Yield(v,'b3')))); limit_inf(v)..Water(v)=g=Water_bounds(v,'min') ; limit_sup(v)..Water(v)=l=Water_bounds(v,'med') ; Variable_Cost_F(v)..cost_vF(v)=e=Water(v)*10*Water_price; Benefice_F(v)..benef_F(v)=e=(prodt_First(v)*lluc_prices(v))-cost_crop(v)- cost_vF(v); ***********valable pour les deux Crop_cost(v)..cost_crop(v)=e=Crop_fixed_cost(v)+Connection_fees+Irr_Syst_Amorti zation+Fixe_per_ha;
production_second(v)..prodt_Second(v)=e=(Yield(v,'b1')+(Yield(v,'b4')*(Water_S(v)- Yield(v,'b3')))) ; limit_s(v)..Water_S(v)=l=Water_bounds(v,'max') ; limit_in(v)..Water_S(v)=g=Water_bounds(v,'med') ; Variable_Cost_S(v)..cost_vS(v)=e=Water_S(v)*10*Water_price; Benefice_S(v)..benef_S(v)=e=(prodt_Second(v)*lluc_prices(v))-cost_crop(v)- cost_vS(v);
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model Max_eq1 /Fo1,limit_sup,limit_inf,production_first,Variable_Cost_F,Crop_cost,Benefice_F/ solve Max_eq1 using nlp maximizing z; display Water.l; display prodt_First.l; display benef_F.l;
model Max_eq2 /Fo2,limit_s,limit_in,production_second,Variable_Cost_S,Crop_cost,Benefice_S/ solve Max_eq2 using nlp maximizing z2; display Water_S.l; display prodt_Second.l; display benef_S.l;
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