# Climate Change and Irrigation Water: Should the North/South Hierarchy of Impacts on Agricultural Systems Be Reconsidered?

Delphine Barberis, Ines Chiadmi, Pierre Humblot, Pierre-Alain Jayet, Anna Lungarska, Maxime Ollier

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## To cite this version:

Delphine Barberis, Ines Chiadmi, Pierre Humblot, Pierre-Alain Jayet, Anna Lungarska, et al., Climate Change and Irrigation Water: Should the North/South Hierarchy of Impacts on Agricultural Systems Be Reconsidered?. Environmental Modeling & Assessment, 2021, 26 (1), pp.13-36. 10.1007/s10666-020-09724-8. http://hal-03152273

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Submitted on 23 May 2024

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# Climate Change and Irrigation Water: Should the North/South Hierarchy of Impacts on Agricultural Systems Be Reconsidered?

Delphine Barberis, Ines Chiadmi, Pierre Humblot, Pierre-Alain Jayet, Anna Lungarska, Maxime Ollier

► To cite this version:

Delphine Barberis, Ines Chiadmi, Pierre Humblot, Pierre-Alain Jayet, Anna Lungarska, et al., Climate Change and Irrigation Water: Should the North/South Hierarchy of Impacts on Agricultural Systems Be Reconsidered?. Environmental Modeling & Assessment, 2021, 26 (1), pp.13-36. 10.1007/s10666-020-09724-8 . hal-03152273

HAL Id: hal-03152273

https://hal.inrae.fr/hal-03152273v1

Submitted on 23 May 2024

HAL is a multi-disciplinary open access
archive for the deposit and dissemination of sci-
entific research documents, whether they are pub-
lished or not. The documents may come from
teaching and research institutions in France or
abroad, or from public or private research centers.

L'archive ouverte pluridisciplinaire HAL, est
destinée au dépôt et à la diffusion de documents
scientifiques de niveau recherche, publiés ou non,
émanant des établissements d'enseignement et de
recherche français ou étrangers, des laboratoires
publics ou privés.

<figure><img src="image_1.png" /></figure>

Distributed under a Creative Commons Attribution 4.0 International License
Climate change and irrigation water:
should the north/south hierarchy of
impacts on agricultural systems be
reconsidered?

This is an Accepted Manuscript of the article published by Springer in
Environmental Modeling & Assessment on 27 September 2020 (online)
and in Volume 26, pages 13–36, (2021), DOI: [10.1007/s10666-020-09724-8](https://doi.org/10.1007/s10666-020-09724-8).
Climate change and irrigation water:
should the north/south hierarchy of
impacts on agricultural systems be
reconsidered?

This is an Accepted Manuscript of the article published by Springer in
Environmental Modeling & Assessment on 27 September 2020 (online)
and in Volume 26, pages 13–36, (2021), DOI: [10.1007/s10666-020-09724-8](https://doi.org/10.1007/s10666-020-09724-8).
# Climate change and irrigation water: should the north/south hierarchy of impacts on agricultural systems be reconsidered?

Delphine Barberis<fnref n="1" />, Inès Chiadmi<fnref n="1" />, Pierre Humblot<fnref n="1" />, Pierre-Alain Jayet<fnref n="1" />*, Anna Lungarska<fnref n="1" />, Maxime Ollier<fnref n="1" />

*Corresponding author: Pierre-Alain Jayet pierre-alain.jayet@inra.fr

**Acknowledgements:** Public institutions associated with the *PIREN-Seine* program, the French Ministry of Research and Ecole Normale Supérieure de Lyon are gratefully acknowledged for their financial support. This work is part of the "Investissements d'Avenir" program overseen by the French National Research Agency (ANR) (LabEx *BASC*; ANR-11-LABX-0034). The authors thank Michael Westlake for his copy-editing and Jeffrey Norville for helpful comments on the manuscript.

## Abstract

Pressures on resources and climate change are likely to strongly impact the availability of water, which directly affects agricultural systems. To estimate these impacts, we develop a prospective approach combining an agricultural supply side economic model and a crop model. We extend previous work by incorporating water resource constraints and apply our model to a large part of the French agricultural sector under three climate scenarios over 2010-2010. Results indicate that, at a given water price, potential change in irrigation water demand would differ strongly according to the region concerned and the scenario applied. In France as a whole, irrigation increases in all scenarios, by 60% under the intermediate scenario, by 40% under the least extreme scenario and by 20% under the toughest scenario. Differentiating the northern and southern regions, the relative increase is more pronounced in the north, while demand in the south significantly increases under the intermediate scenario and decreases under the toughest scenario. When considering autonomous adaptation of farming systems to climate change, agricultural income in northern regions is likely to be negatively affected to a greater extent than in southern regions.

**Key words:** irrigation water demand; climate change; water price; agro-economic supply model

<footnote n="1">¹ UMR Économie Publique, INRAE, Université Paris-Saclay, F-78850 Grignon, France</footnote>
# Climate change and irrigation water: should the north/south hierarchy of impacts on agricultural systems be reconsidered?

Delphine Barberis<fnref n="1" />, Inès Chiadmi<fnref n="1" />, Pierre Humblot<fnref n="1" />, Pierre-Alain Jayet<fnref n="1" />*, Anna Lungarska<fnref n="1" />, Maxime Ollier<fnref n="1" />

*Corresponding author: Pierre-Alain Jayet pierre-alain.jayet@inra.fr

**Acknowledgements:** Public institutions associated with the *PIREN-Seine* program, the French Ministry of Research and Ecole Normale Supérieure de Lyon are gratefully acknowledged for their financial support. This work is part of the "Investissements d'Avenir" program overseen by the French National Research Agency (ANR) (LabEx *BASC*; ANR-11-LABX-0034). The authors thank Michael Westlake for his copy-editing and Jeffrey Norville for helpful comments on the manuscript.

## Abstract

Pressures on resources and climate change are likely to strongly impact the availability of water, which directly affects agricultural systems. To estimate these impacts, we develop a prospective approach combining an agricultural supply side economic model and a crop model. We extend previous work by incorporating water resource constraints and apply our model to a large part of the French agricultural sector under three climate scenarios over 2010-2010. Results indicate that, at a given water price, potential change in irrigation water demand would differ strongly according to the region concerned and the scenario applied. In France as a whole, irrigation increases in all scenarios, by 60% under the intermediate scenario, by 40% under the least extreme scenario and by 20% under the toughest scenario. Differentiating the northern and southern regions, the relative increase is more pronounced in the north, while demand in the south significantly increases under the intermediate scenario and decreases under the toughest scenario. When considering autonomous adaptation of farming systems to climate change, agricultural income in northern regions is likely to be negatively affected to a greater extent than in southern regions.

**Key words:** irrigation water demand; climate change; water price; agro-economic supply model

<footnote n="1">¹ UMR Économie Publique, INRAE, Université Paris-Saclay, F-78850 Grignon, France</footnote>
# 1. Introduction

Agriculture is a water-intensive economic sector in France. In 2009, 3 billion cubic meters of water were extracted, among which 1 billion came from groundwater (Eau France 2012, Ministère de l'environnement 2017). Since water for agriculture is extracted without immediate return, this sector accounts for the greatest net withdrawal. Given the projected 50% increase in food demand between 2012 and 2050 (Alexandratos and Bruinsma 2012), the growing bioenergy market requiring more feedstock, the intensification of production factors and the expansion of irrigated land, water demand is expected to increase in the up-coming years. As domestic and industrial water uses sharply increase, the competition over water for agriculture can only intensify (International Water Management Institute 2007) and further aggravate water scarcity.

The vulnerability of farms to less reliable water availability could be reduced by access to multiple water resources (Mukherjee and Shwabe 2014). However, water availability for agriculture is expected to drop by 18% as a result of competition over water resources by 2050 (Strzepek and Boehlert 2010). This risk is enhanced by the potentially harmful consequences of climate change (CC). Changing precipitation patterns and inter-annual variability, rising temperatures (which increase crop water requirements and alter growing season length), and increasing frequency of extreme weather events would have strong impact on agriculture, especially on irrigation (IPCC 2013; Foster et al. 2018). Pressures on water quantity have a direct impact on water quality and on freshwater ecosystems. For instance, in aquifers, the pollutant concentration increases as water quantities dwindle. Freshwater ecosystems are sensitive to both water quantity and quality (Oberdorff et al. 2002). In France, the existence of disparate irrigation practices from one region to another, intensive in the south and less widespread in the north, complicates territorial decision-making in terms of integrated resource management. Tensions over water resource will be intensified by the threat of increasing restrictions on water withdrawals and uses.

In the global context of economic and environmental changes, especially the constant evolution of water resources both in time and geographical space, the aim of the present study is to provide economic prospective views on future irrigation demand jointly with fertilizer demand and major crop supply in France. Our work specifically focuses on the change in the economic demand for agricultural water under changing economic and physical environments. Our study differs from previous works in accounting for irrigation costs and potential land use change in terms of crops. In order to integrate the increasing pressure over water resources, we consider that irrigation cost (or water price) reflects water scarcity. From an economic perspective, when water demand
# 1. Introduction

Agriculture is a water-intensive economic sector in France. In 2009, 3 billion cubic meters of water were extracted, among which 1 billion came from groundwater (Eau France 2012, Ministère de l'environnement 2017). Since water for agriculture is extracted without immediate return, this sector accounts for the greatest net withdrawal. Given the projected 50% increase in food demand between 2012 and 2050 (Alexandratos and Bruinsma 2012), the growing bioenergy market requiring more feedstock, the intensification of production factors and the expansion of irrigated land, water demand is expected to increase in the up-coming years. As domestic and industrial water uses sharply increase, the competition over water for agriculture can only intensify (International Water Management Institute 2007) and further aggravate water scarcity.

The vulnerability of farms to less reliable water availability could be reduced by access to multiple water resources (Mukherjee and Shwabe 2014). However, water availability for agriculture is expected to drop by 18% as a result of competition over water resources by 2050 (Strzepek and Boehlert 2010). This risk is enhanced by the potentially harmful consequences of climate change (CC). Changing precipitation patterns and inter-annual variability, rising temperatures (which increase crop water requirements and alter growing season length), and increasing frequency of extreme weather events would have strong impact on agriculture, especially on irrigation (IPCC 2013; Foster et al. 2018). Pressures on water quantity have a direct impact on water quality and on freshwater ecosystems. For instance, in aquifers, the pollutant concentration increases as water quantities dwindle. Freshwater ecosystems are sensitive to both water quantity and quality (Oberdorff et al. 2002). In France, the existence of disparate irrigation practices from one region to another, intensive in the south and less widespread in the north, complicates territorial decision-making in terms of integrated resource management. Tensions over water resource will be intensified by the threat of increasing restrictions on water withdrawals and uses.

In the global context of economic and environmental changes, especially the constant evolution of water resources both in time and geographical space, the aim of the present study is to provide economic prospective views on future irrigation demand jointly with fertilizer demand and major crop supply in France. Our work specifically focuses on the change in the economic demand for agricultural water under changing economic and physical environments. Our study differs from previous works in accounting for irrigation costs and potential land use change in terms of crops. In order to integrate the increasing pressure over water resources, we consider that irrigation cost (or water price) reflects water scarcity. From an economic perspective, when water demand
exceeds the available resources, the cost is not high enough to regulate the use of water. A possible decline in water availability is consequently taken into account by conducting simulations using increasing water prices.

The analysis focuses on four aspects: (i) the direct impact of evolving CC over the “climatic years” of the period 2010-2100 in three contrasting scenarios, (ii) the impact on mean and variance of demand for irrigation water when considering climatic years as probabilistic occurrences of CC, (iii) the impact of increasing water price pressure, and (iv) geographical contrasts at an infra-national level. Our approach incorporates two levels of autonomous adaptation practices by farming systems, namely at the plot and the farm-group levels.

Various methods have been developed in order to assess the environmental and economic effects of CC, such as climatic approaches (Van der Velde et al. 2010; Supit et al. 2010), econometric models (Mendelson et al. 1994) and bio-economic models (Cortignani and Severini 2009; Kampas et al. 2012; Graveline et al. 2014). Our work can be assigned to the last category, which relates farmers’ behaviour to technical processes based on agronomic information (Janssen and van Ittersum 2007). In other words, we analyze producers’ choices in terms of crop area and the use of inputs when anticipating changes in climate affecting crop-growth processes. Moreover, in the papers that discuss the impacts of climate change on the agricultural water resource, most contributed to two different research fields, either the field of water supply and availability or that of crop irrigation requirements from an agronomic or hydrologic perspective (Döll 2002; Levis et al. 2016). In our literature review, the water demand issue is mainly raised in the urban and residential context (Yoo 2014, among others).

Among the papers dealing with the impact of CC on the irrigation water requirements, Döll suggests that the first step is to quantify how these requirements are affected. The estimated impact is then used as an input to an agro-economic model that uses crop yields, prices, costs and water availability to calculate economic water demand (Döll 2002). Our work, however, simultaneously integrates economic demand and crop water requirements via a crop model. We specify the agricultural economic variables by means of the AROPAj agro-economic model, refined through climate dependent input-yield functions estimated by the STICS crop model.

Results from Döll (2002) provide evidence that irrigation requirements are expected to increase by up to 30% in most irrigated areas located north of 40° latitude until the 2020s. Estimating irrigation water demand is of crucial importance when evaluating the sustainability of water systems and their management. Different prospective studies on irrigation demand in France under climate change have been conducted. The most recent and thorough, Explore 70¹, provides insights on water supply and demand by agriculture within the 2070 time

<footnote n="1">¹ http://www.gesteau.fr/document/bilan-du-projet-explore-2070-eau-et-changement-climatique</footnote>
exceeds the available resources, the cost is not high enough to regulate the use of water. A possible decline in water availability is consequently taken into account by conducting simulations using increasing water prices.

The analysis focuses on four aspects: (i) the direct impact of evolving CC over the “climatic years” of the period 2010-2100 in three contrasting scenarios, (ii) the impact on mean and variance of demand for irrigation water when considering climatic years as probabilistic occurrences of CC, (iii) the impact of increasing water price pressure, and (iv) geographical contrasts at an infra-national level. Our approach incorporates two levels of autonomous adaptation practices by farming systems, namely at the plot and the farm-group levels.

Various methods have been developed in order to assess the environmental and economic effects of CC, such as climatic approaches (Van der Velde et al. 2010; Supit et al. 2010), econometric models (Mendelson et al. 1994) and bio-economic models (Cortignani and Severini 2009; Kampas et al. 2012; Graveline et al. 2014). Our work can be assigned to the last category, which relates farmers’ behaviour to technical processes based on agronomic information (Janssen and van Ittersum 2007). In other words, we analyze producers’ choices in terms of crop area and the use of inputs when anticipating changes in climate affecting crop-growth processes. Moreover, in the papers that discuss the impacts of climate change on the agricultural water resource, most contributed to two different research fields, either the field of water supply and availability or that of crop irrigation requirements from an agronomic or hydrologic perspective (Döll 2002; Levis et al. 2016). In our literature review, the water demand issue is mainly raised in the urban and residential context (Yoo 2014, among others).

Among the papers dealing with the impact of CC on the irrigation water requirements, Döll suggests that the first step is to quantify how these requirements are affected. The estimated impact is then used as an input to an agro-economic model that uses crop yields, prices, costs and water availability to calculate economic water demand (Döll 2002). Our work, however, simultaneously integrates economic demand and crop water requirements via a crop model. We specify the agricultural economic variables by means of the AROPAj agro-economic model, refined through climate dependent input-yield functions estimated by the STICS crop model.

Results from Döll (2002) provide evidence that irrigation requirements are expected to increase by up to 30% in most irrigated areas located north of 40° latitude until the 2020s. Estimating irrigation water demand is of crucial importance when evaluating the sustainability of water systems and their management. Different prospective studies on irrigation demand in France under climate change have been conducted. The most recent and thorough, Explore 70¹, provides insights on water supply and demand by agriculture within the 2070 time

<footnote n="1">¹ http://www.gesteau.fr/document/bilan-du-projet-explore-2070-eau-et-changement-climatique</footnote>
horizon. The study predicts an increase in irrigation demand by 43% to 66% for climate change scenario A1B and without adaptation of agricultural practices. Adaptation options are also considered, but these are ad hoc scenarios and do not explicitly consider farmers' economic choices. Projections for the regional impacts are summarized in a report commissioned by French Ministry of Agriculture (CGAAER 2017). This study underlines the potential aridification in Mediterranean France and the “mediterraneanization” of the central parts of the country. The impact on northern agriculture is also considered but to a lesser extent. The results of our study show that climate change may impact water demand by northern agriculture more than previously supposed. This finding invites policymakers to reconsider the focus of their future or on-going actions.

Climate simulations are obtained at the regional scale on the basis of 2010-2100 climatic projections sourced from the ARPEGE-CLIMAT model and related to scenarios proposed by the IPCC, namely A2, A1B and B1, which are used in the analysis (Pagé and Terray 2010; Pagé et al. 2010). Although they have been superseded by the Representative Concentration Pathways since 2014, these scenarios are still used in recent studies, such as in the evaluation of the impacts of projected climate change on yields and irrigation requirements in Europe by Zhao et al. (2015). They therefore remain reliable for comparison of future climate projections because they can account for contrasting climate situations. Thereafter, scenarios of rising water costs are simulated to illustrate the medium-term importance of pressure on the resource in the context of CC. Although the process is developed at the European level, France has been chosen as a case study in farming system diversity and soil and climatic diversity.

Our modeling approach was initiated by Godard et al. (2008) and then developed by Leclère et al. (2013). The latter deals with farmers' autonomous adaptation to climate change and focuses on nitrogen input deriving from the building of crop yield functions. Our paper applies the methodological study by Humblot et al. (2017), which generates yield response functions that account for changing demand for nitrogen and water inputs at the plot level when climate changes. The analysis is reinforced by a downscaling module aiming at geographically distributing the model's results. Obtaining high resolution maps leads to visualization of spatial variability of irrigation practices from one region to another, as explained in Jayet et al. (2018). Tested by Humblot et al. (2017) for maize in two French regions and based on preliminary estimates of yield and of irrigation and fertilization costs, the development of yield functions has been extended to a large part of the regions of the EU and nine crops through dedicated IT applications. The use of the crop model also makes it possible to overcome the difficulty of estimating input prices. The main technical challenge faced in this study concerns the use of
horizon. The study predicts an increase in irrigation demand by 43% to 66% for climate change scenario A1B and without adaptation of agricultural practices. Adaptation options are also considered, but these are ad hoc scenarios and do not explicitly consider farmers' economic choices. Projections for the regional impacts are summarized in a report commissioned by French Ministry of Agriculture (CGAAER 2017). This study underlines the potential aridification in Mediterranean France and the “mediterraneanization” of the central parts of the country. The impact on northern agriculture is also considered but to a lesser extent. The results of our study show that climate change may impact water demand by northern agriculture more than previously supposed. This finding invites policymakers to reconsider the focus of their future or on-going actions.

Climate simulations are obtained at the regional scale on the basis of 2010-2100 climatic projections sourced from the ARPEGE-CLIMAT model and related to scenarios proposed by the IPCC, namely A2, A1B and B1, which are used in the analysis (Pagé and Terray 2010; Pagé et al. 2010). Although they have been superseded by the Representative Concentration Pathways since 2014, these scenarios are still used in recent studies, such as in the evaluation of the impacts of projected climate change on yields and irrigation requirements in Europe by Zhao et al. (2015). They therefore remain reliable for comparison of future climate projections because they can account for contrasting climate situations. Thereafter, scenarios of rising water costs are simulated to illustrate the medium-term importance of pressure on the resource in the context of CC. Although the process is developed at the European level, France has been chosen as a case study in farming system diversity and soil and climatic diversity.

Our modeling approach was initiated by Godard et al. (2008) and then developed by Leclère et al. (2013). The latter deals with farmers' autonomous adaptation to climate change and focuses on nitrogen input deriving from the building of crop yield functions. Our paper applies the methodological study by Humblot et al. (2017), which generates yield response functions that account for changing demand for nitrogen and water inputs at the plot level when climate changes. The analysis is reinforced by a downscaling module aiming at geographically distributing the model's results. Obtaining high resolution maps leads to visualization of spatial variability of irrigation practices from one region to another, as explained in Jayet et al. (2018). Tested by Humblot et al. (2017) for maize in two French regions and based on preliminary estimates of yield and of irrigation and fertilization costs, the development of yield functions has been extended to a large part of the regions of the EU and nine crops through dedicated IT applications. The use of the crop model also makes it possible to overcome the difficulty of estimating input prices. The main technical challenge faced in this study concerns the use of
computer applications to readjust crop yield functions in complete sets of climate data over a distant time horizon.

The paper is organized as follows. The methodology used, including the AROPAj optimization problem, yield function estimation, the spatial downscaling procedure and the different climatic scenarios that frame the analysis, is described in section 2. Then, section 3 details results in terms of CC impacts on water and nitrogen input demand, gross margin and land allocated to series of crops. Changes in results when water prices change are also quantified. Section 4 concludes and then suggests future research perspectives.

## 2. Models and data

To simulate the response of agriculture to economic and climate changes, we incorporate agronomic information sourced by a plant growth simulation tool into the AROPAj agro-economic model. The agricultural supply is thus linked to water and nitrogen demand. Concretely, AROPAj integrates dose-response function to these production factors that are parametrized via their exogenous prices. An overview of the modeling framework is provided in **Figure 1**.

### 2.1. *The AROPAj economic model*

AROPAj is a cluster of mathematical programming models designed to represent the economic behaviour of widely diverse European farming system sets. Each individual model refers to a farm group which maximizes its gross margin subject to technical and economic constraints. Technical constraints limit cropping and breeding activities within feasible production sets (e.g. required crop rotations, nitrogen and water intakes and crop yields, protein and energy intakes and milk or meat production). Economic constraints refer to public policies such as the Common Agricultural Policy or policies targeting environmental criteria. The model includes a wide range of animal and crop production, with the exception of horticulture, viticulture and arboriculture. Model outcomes include gross margin², input demand (fertilizers, irrigation water, and concentrated feed), crop yields (split into marketed and on-farm quantities), animal production (with a detailed representation of cattle), areas allocated to different crops, and environmental outputs (greenhouse gas emissions, nitrogen losses). Farm group outcomes can be upscaled at regional, national and European levels, and can be downscaled at a fine resolution level through the spatialization module.

The model's economic agents are farm groups that aggregate farming systems with similar technical and economic characteristics. Farm groups result from a clustering procedure applied to individuals of the European

² Gross margin is commonly defined as the difference between farmers' revenues and their variable costs.
computer applications to readjust crop yield functions in complete sets of climate data over a distant time horizon.

The paper is organized as follows. The methodology used, including the AROPAj optimization problem, yield function estimation, the spatial downscaling procedure and the different climatic scenarios that frame the analysis, is described in section 2. Then, section 3 details results in terms of CC impacts on water and nitrogen input demand, gross margin and land allocated to series of crops. Changes in results when water prices change are also quantified. Section 4 concludes and then suggests future research perspectives.

## 2. Models and data

To simulate the response of agriculture to economic and climate changes, we incorporate agronomic information sourced by a plant growth simulation tool into the AROPAj agro-economic model. The agricultural supply is thus linked to water and nitrogen demand. Concretely, AROPAj integrates dose-response function to these production factors that are parametrized via their exogenous prices. An overview of the modeling framework is provided in **Figure 1**.

### 2.1. *The AROPAj economic model*

AROPAj is a cluster of mathematical programming models designed to represent the economic behaviour of widely diverse European farming system sets. Each individual model refers to a farm group which maximizes its gross margin subject to technical and economic constraints. Technical constraints limit cropping and breeding activities within feasible production sets (e.g. required crop rotations, nitrogen and water intakes and crop yields, protein and energy intakes and milk or meat production). Economic constraints refer to public policies such as the Common Agricultural Policy or policies targeting environmental criteria. The model includes a wide range of animal and crop production, with the exception of horticulture, viticulture and arboriculture. Model outcomes include gross margin², input demand (fertilizers, irrigation water, and concentrated feed), crop yields (split into marketed and on-farm quantities), animal production (with a detailed representation of cattle), areas allocated to different crops, and environmental outputs (greenhouse gas emissions, nitrogen losses). Farm group outcomes can be upscaled at regional, national and European levels, and can be downscaled at a fine resolution level through the spatialization module.

The model's economic agents are farm groups that aggregate farming systems with similar technical and economic characteristics. Farm groups result from a clustering procedure applied to individuals of the European

² Gross margin is commonly defined as the difference between farmers' revenues and their variable costs.
Farm Accounting Data Network (FADN) and based on four criteria, i.e. (i) technical and economic orientation (referring to 14 FADN sourced “farm-types”), (ii) the proportion of irrigated areas, (iii) economic size (with nine categories) and (iv) altitude (referring to three thresholds, namely 0, 300 and 600 meters above sea level). Clustering is processed at the regional level (FADN regions corresponding to NUTS-2 in France). Farm groups thus obtained meet FADN privacy policy. The clustering procedure also improves the processing time of AROPAj because of the reduced number of agents to be simulated.

The generic envelope form of the model is a linear optimization program designed to fit all representative farming systems. It is represented here by dissociating areas, crop productions and their inputs from the other variables of the model:

$$ \max_{x,S,U,V,N,O \in A} \sum_i p_i x_i + \sum_j [p_j U_j - (a_j + b_j + c_j) S_j], $$

$$ A = \left\{ x, S, U, V, N, O \text{ subject to: } \begin{array}{l} \forall j: U_j + V_j \le y_j S_j \\ \forall j: N_j + \sum_l \alpha_{l,j} O_{l,j} \ge \beta_j y_j S_j \\ F(x, S, U, V, N, O) \le 0 \end{array} \right\}, \quad (1) $$

where j index refers to plant activities (crops) and i index refers to other activities. The components of the price vector are made up of the sale prices of the marketed outputs and the purchase prices of the inputs or variable costs depending on the type of input considered. Plant activities are characterized by the area S, the marketed part of production U, the part of production intended for animal feed V and per hectare production costs broken down into irrigation costs a, nitrogen fertilization costs b, and other costs c. Yield per hectare is denoted by y. In the model, except for the seven straw cereals taken into account, the plant production is either sold entirely ($V_j = 0$, e.g. oleo-protein crops), or used on the farm entirely ($U_j = 0$, e.g. meadows and fodder). In this formal representation, x denotes the vector of other activities p the vector of “prices” and A the set of production into which the constraints of economic policy are integrated.

In the production set, a distinction is made between the constraints subsequently reset which characterize the use of available production and the nitrogen requirements of plants, and the other constraints represented by the set of inequalities F. The first two subsets of constraints relate to relationships between plant production and animal husbandry. On the farm, plant productions participate in animal feed, and livestock manure supplies nitrogen nutrient for crops. Depending on the crop j, nitrogen is supplied by marketed mineral fertilizers, denoted by N, and or manure, denoted by O. The latter depends on the animal category and the type of effluent indexed by l. Crops nitrogen requirements are represented by β, while α stands for the equivalence factors between organic nitrogen and nitrogen of a generic fertilizer. In the absence of a dose-response function that links yield to inputs, yields and costs per hectare are used as parameters. If the price of purchased mineral
Farm Accounting Data Network (FADN) and based on four criteria, i.e. (i) technical and economic orientation (referring to 14 FADN sourced “farm-types”), (ii) the proportion of irrigated areas, (iii) economic size (with nine categories) and (iv) altitude (referring to three thresholds, namely 0, 300 and 600 meters above sea level). Clustering is processed at the regional level (FADN regions corresponding to NUTS-2 in France). Farm groups thus obtained meet FADN privacy policy. The clustering procedure also improves the processing time of AROPAj because of the reduced number of agents to be simulated.

The generic envelope form of the model is a linear optimization program designed to fit all representative farming systems. It is represented here by dissociating areas, crop productions and their inputs from the other variables of the model:

$$ \max_{x,S,U,V,N,O \in A} \sum_i p_i x_i + \sum_j [p_j U_j - (a_j + b_j + c_j) S_j], \\ A = \left\{ x, S, U, V, N, O \text{ subject to: } \begin{array}{l} \forall j: U_j + V_j \le y_j S_j \\ \forall j: N_j + \sum_l \alpha_{l,j} O_{l,j} \ge \beta_j y_j S_j \\ F(x, S, U, V, N, O) \le 0 \end{array} \right\} , \quad (1) $$

where j index refers to plant activities (crops) and i index refers to other activities. The components of the price vector are made up of the sale prices of the marketed outputs and the purchase prices of the inputs or variable costs depending on the type of input considered. Plant activities are characterized by the area S, the marketed part of production U, the part of production intended for animal feed V and per hectare production costs broken down into irrigation costs a, nitrogen fertilization costs b, and other costs c. Yield per hectare is denoted by y. In the model, except for the seven straw cereals taken into account, the plant production is either sold entirely ($V_j = 0$, e.g. oleo-protein crops), or used on the farm entirely ($U_j = 0$, e.g. meadows and fodder). In this formal representation, x denotes the vector of other activities p the vector of “prices” and A the set of production into which the constraints of economic policy are integrated.

In the production set, a distinction is made between the constraints subsequently reset which characterize the use of available production and the nitrogen requirements of plants, and the other constraints represented by the set of inequalities F. The first two subsets of constraints relate to relationships between plant production and animal husbandry. On the farm, plant productions participate in animal feed, and livestock manure supplies nitrogen nutrient for crops. Depending on the crop j, nitrogen is supplied by marketed mineral fertilizers, denoted by N, and or manure, denoted by O. The latter depends on the animal category and the type of effluent indexed by l. Crops nitrogen requirements are represented by β, while α stands for the equivalence factors between organic nitrogen and nitrogen of a generic fertilizer. In the absence of a dose-response function that links yield to inputs, yields and costs per hectare are used as parameters. If the price of purchased mineral
nitrogen, denoted by f, is available, the demand for it becomes a variable of the optimization program, with crop requirements still met according to the constraint above. In this case, $f N_j = c_j S_j$. The complete explanation of the relationships between nitrogen inputs and cultivated areas and between animal and plant activities is given by Aghajanzadzh-Darzi et al., 2017. At this stage, the elements x, S, U, V, N, O are control variables of the optimization problem.

The basic version of AROPAj does not directly use the raw data concerning the different technical and physical aspects of farming practices. For instance, per area unit crop input and yield are first parametrized using econometric calculation before being introduced into the model. Coupling AROPAj with a crop model allows us to integrate relationships between inputs and yields, consistently represented by dose-response functions as detailed below. The AROPAj-STICS coupling is carried out for V5 version of the AROPAj model applied to 2009-FADN.

## 2.2. The STICS crop model feeding the AROPAj model

The agro-economic model is improved by substituting a function associating yield and inputs at the scale of the plot. A dose-response function is specific to a given crop present on a given farm group of the model. The main reason for the coupling is to make up for the lack of micro-economic data which would have made it possible to estimate yield functions for a large number of crops in a large number of very diversified farming systems in the European Union. The generic functional form must have mathematical properties consistent with the usual assumptions of the micro-economics of production, while remaining suitable for standard representations of agronomy. This objective is achieved thanks to physical data covering the European Union, concerning land use, soil characteristics, topography, meteorology, phenology and technical routes in the production management plant.

For a given representative farm and a given crop, yield functions $y(w, n, \theta)$ are generated from a biophysical model. $w$ and $n$ denote the water and nitrogen inputs respectively and $\theta$ stands for farm group and crop dependent biophysical parameters. $y$, $w$ and $n$ are quantities per hectare. Limited to the changes induced by taking into account the yield functions, the formal presentation of the model is then:

$$ \max_{x,S,U,V,W,N,O \in B} \sum_i p_i x_i + \sum_j [p_j U_j - e_j W_j - f_j N_j - c_j S_j], $$
nitrogen, denoted by $f$, is available, the demand for it becomes a variable of the optimization program, with crop requirements still met according to the constraint above. In this case, $f N_j = c_j S_j$. The complete explanation of the relationships between nitrogen inputs and cultivated areas and between animal and plant activities is given by Aghajanzadzh-Darzi et al., 2017. At this stage, the elements $x, S, U, V, N, O$ are control variables of the optimization problem.

The basic version of AROPAj does not directly use the raw data concerning the different technical and physical aspects of farming practices. For instance, per area unit crop input and yield are first parametrized using econometric calculation before being introduced into the model. Coupling AROPAj with a crop model allows us to integrate relationships between inputs and yields, consistently represented by dose-response functions as detailed below. The AROPAj-STICS coupling is carried out for V5 version of the AROPAj model applied to 2009-FADN.

## 2.2. The STICS crop model feeding the AROPAj model

The agro-economic model is improved by substituting a function associating yield and inputs at the scale of the plot. A dose-response function is specific to a given crop present on a given farm group of the model. The main reason for the coupling is to make up for the lack of micro-economic data which would have made it possible to estimate yield functions for a large number of crops in a large number of very diversified farming systems in the European Union. The generic functional form must have mathematical properties consistent with the usual assumptions of the micro-economics of production, while remaining suitable for standard representations of agronomy. This objective is achieved thanks to physical data covering the European Union, concerning land use, soil characteristics, topography, meteorology, phenology and technical routes in the production management plant.

For a given representative farm and a given crop, yield functions $y(w, n, \theta)$ are generated from a biophysical model. $w$ and $n$ denote the water and nitrogen inputs respectively and $\theta$ stands for farm group and crop dependent biophysical parameters. $y$, $w$ and $n$ are quantities per hectare. Limited to the changes induced by taking into account the yield functions, the formal presentation of the model is then:

$$ \max_{x,S,U,V,W,N,O \in B} \sum_i p_i x_i + \sum_j [p_j U_j - e_j W_j - f_j N_j - c_j S_j], $$
$$ B = \left\{ \begin{array}{l} x, S, U, V, W, N, O \text{ subject to:} \quad \left\{ \begin{array}{l} \forall j: U_j + V_j \le y_j(w_j, n_j, \theta) S_j \\ \forall j: N_j + \sum_l \alpha_{l,j} O_{l,j} \ge n_j S_j \\ \forall j: W_j \ge w_j S_j \\ \forall j: n_j \ge \beta_j y_j(w_j, n_j, \theta) \\ \forall j: w_j \ge \gamma_j y_j(w_j, n_j, \theta) \\ F(x, S, U, V, N, O) \le 0 \end{array} \right. \\ , \end{array} \right. \quad (2) $$

where the variable costs associated with crops include irrigation costs (at the price per cubic meter e) and mineral nitrogen purchase costs (at the price per unit of nitrogen f). In comparison with program (1), program (2) integrates the satisfaction of water and nitrogen needs of crops according to the yield which becomes a variable of the problem. Crop requirements for water are denoted by $γ$. Crop-dependent irrigation water is denoted by $W$. It should be noted that these constraints are binding with the optimal solution of the program.

STICS is a dynamic, generic and robust tool for simulating the soil-atmosphere-crop system applied to a wide range of crops and pedo-climatic conditions. It operates at a daily time step, over one or two calendar years depending on the type of plant considered (Brisson et al. 2003)¹. Various elements are required as inputs:

- climatic parameters, obtained using the ARPEGE atmospheric model (Déqué et al. 1994; Pagé and Terray 2010; Pagé et al. 2010);

- soil information, extracted from the European Soil Database (ESDB) (Panagos et al. 2012);

- data on management practices, provided by the STICS library.

For a hypothetical unit of area allocated to a specific crop grown on a specific soil in specific climatic conditions, STICS provides the yield given nitrogen intake and water stress. It is able to calibrate H₂O-N-yield relationships for various crops observed in a given AROPAj farm group. The H₂O-N-yield relationships will substitute fixed input-yield points in AROPAj and thus transform the quasi-linear programming structure of AROPAj into a non-linear one.

The method, originated by Godard et al. (2008), who focused on nitrogen, was extended by Leclère et al. (2013) for exploring autonomous adaptation by farmers to CC impacts on crop systems. In this study, we further the analysis, by implementing double input-yield functions (Humblot et al., 2017) as explained below. The STICS biophysical model allows the lack of water-dependent economic and physical information to be overcome, thus greatly improving the AROPAj economic model.

## 2.3. The two levels of adaptation in the model

Using yield functions makes the model mathematically nonlinear, but it is possible and efficient to solve the optimization problem by retaining the basic linear structure of the AROPAj model (Bourgeois et al., 2014;
$$ B = \left\{ \begin{array}{l} x, S, U, V, W, N, O \text{ subject to:} \quad \left\{ \begin{array}{l} \forall j: U_j + V_j \le y_j(w_j, n_j, \theta) S_j \\ \forall j: N_j + \sum_l \alpha_{l,j} O_{l,j} \ge n_j S_j \\ \forall j: W_j \ge w_j S_j \\ \forall j: n_j \ge \beta_j y_j(w_j, n_j, \theta) \\ \forall j: w_j \ge \gamma_j y_j(w_j, n_j, \theta) \\ F(x, S, U, V, N, O) \le 0 \end{array} \right. , \end{array} \right. \quad (2) $$

where the variable costs associated with crops include irrigation costs (at the price per cubic meter e) and mineral nitrogen purchase costs (at the price per unit of nitrogen f). In comparison with program (1), program (2) integrates the satisfaction of water and nitrogen needs of crops according to the yield which becomes a variable of the problem. Crop requirements for water are denoted by $\gamma$. Crop-dependent irrigation water is denoted by $W$. It should be noted that these constraints are binding with the optimal solution of the program.

STICS is a dynamic, generic and robust tool for simulating the soil-atmosphere-crop system applied to a wide range of crops and pedo-climatic conditions. It operates at a daily time step, over one or two calendar years depending on the type of plant considered (Brisson et al. 2003)¹. Various elements are required as inputs:

- climatic parameters, obtained using the ARPEGE atmospheric model (Déqué et al. 1994; Pagé and Terray 2010; Pagé et al. 2010);

- soil information, extracted from the European Soil Database (ESDB) (Panagos et al. 2012);

- data on management practices, provided by the STICS library.

For a hypothetical unit of area allocated to a specific crop grown on a specific soil in specific climatic conditions, STICS provides the yield given nitrogen intake and water stress. It is able to calibrate H₂O-N-yield relationships for various crops observed in a given AROPAj farm group. The H₂O-N-yield relationships will substitute fixed input-yield points in AROPAj and thus transform the quasi-linear programming structure of AROPAj into a non-linear one.

The method, originated by Godard et al. (2008), who focused on nitrogen, was extended by Leclère et al. (2013) for exploring autonomous adaptation by farmers to CC impacts on crop systems. In this study, we further the analysis, by implementing double input-yield functions (Humblot et al., 2017) as explained below. The STICS biophysical model allows the lack of water-dependent economic and physical information to be overcome, thus greatly improving the AROPAj economic model.

## 2.3. The two levels of adaptation in the model

Using yield functions makes the model mathematically nonlinear, but it is possible and efficient to solve the optimization problem by retaining the basic linear structure of the AROPAj model (Bourgeois et al., 2014;
Leclère et al., 2013). The principle is here extended to the case of two inputs (water and nitrogen). The problem-solving process is in two stages. The first step is to solve the problem of maximizing the gross margin per unit area for each of the potentially existing crops and for each of the farms represented in the model. To do this, we simply need to know the ratio of input prices to the price of the crop. The second step involves replacing the yields and the variable loads thus calculated in the standard linear programs. In theory, we obtain the exact mathematical solution when there is at least partial consumption of purchased inputs and at least partial sale of the harvest. The price ratios used in the first step are market prices. Otherwise, implicit price ratios that are endogenous to the mathematical programming model should be used. The exact solution can be obtained or approximated in a few iterations, as shown by Aghajanzadzh-Darzi et al., 2017. Given the large number of simulations to be carried out as part of our analysis, we did not use the iterative process. For a fraction of the crops and farms represented, the mathematical solution is therefore an approximate solution.

Economic and climatic changes are leading farmers to adapt their decisions. For a given crop, as the ratio of input prices to crop prices changes, input demand per hectare and yield change as the gross margin is optimized. This first stage of optimization is the first step of adaptation. This intensive margin effect can be accompanied by a change in variety and technical route at the plot level (for example, sowing date), not only in the case of a price change, but especially in case of climate change. However, even in the case of an unchanged crop variety and process, the relationship between inputs and yield is modified by climate change. This phenomenon, in the context of the autonomous adaptation made by farmers facing changes in their global environment, is taken into account in the model.

When per area unit gross margins change between different crops growing in a given farming system, optimizing the overall gross margin can lead to a change in land distribution. This extensive margin effect is also taken into account as the second level of autonomous adaptation. However, the reference solution resulting from the AROPAj model translates the state of the irrigated areas as observed by the FADN in 2009. In the rotations recalculated by the model, the area of an irrigated crop can be modified (upward or downward), without modifying the “irrigable vs. non-irrigable” character of its initial status. It is possible for an initially irrigated crop to be removed from the rotation, but in the absence of information on the cost of access to water for non-irrigated crops at present (the FADN reflecting only what is observed), a non-irrigated crop at the start cannot get irrigated.

We can therefore consider that there is an underestimation of irrigable areas since the extensive margin effect taken into account is asymmetrical.
Leclère et al., 2013). The principle is here extended to the case of two inputs (water and nitrogen). The problem-solving process is in two stages. The first step is to solve the problem of maximizing the gross margin per unit area for each of the potentially existing crops and for each of the farms represented in the model. To do this, we simply need to know the ratio of input prices to the price of the crop. The second step involves replacing the yields and the variable loads thus calculated in the standard linear programs. In theory, we obtain the exact mathematical solution when there is at least partial consumption of purchased inputs and at least partial sale of the harvest. The price ratios used in the first step are market prices. Otherwise, implicit price ratios that are endogenous to the mathematical programming model should be used. The exact solution can be obtained or approximated in a few iterations, as shown by Aghajanzadzh-Darzi et al., 2017. Given the large number of simulations to be carried out as part of our analysis, we did not use the iterative process. For a fraction of the crops and farms represented, the mathematical solution is therefore an approximate solution.

Economic and climatic changes are leading farmers to adapt their decisions. For a given crop, as the ratio of input prices to crop prices changes, input demand per hectare and yield change as the gross margin is optimized. This first stage of optimization is the first step of adaptation. This intensive margin effect can be accompanied by a change in variety and technical route at the plot level (for example, sowing date), not only in the case of a price change, but especially in case of climate change. However, even in the case of an unchanged crop variety and process, the relationship between inputs and yield is modified by climate change. This phenomenon, in the context of the autonomous adaptation made by farmers facing changes in their global environment, is taken into account in the model.

When per area unit gross margins change between different crops growing in a given farming system, optimizing the overall gross margin can lead to a change in land distribution. This extensive margin effect is also taken into account as the second level of autonomous adaptation. However, the reference solution resulting from the AROPAj model translates the state of the irrigated areas as observed by the FADN in 2009. In the rotations recalculated by the model, the area of an irrigated crop can be modified (upward or downward), without modifying the “irrigable vs. non-irrigable” character of its initial status. It is possible for an initially irrigated crop to be removed from the rotation, but in the absence of information on the cost of access to water for non-irrigated crops at present (the FADN reflecting only what is observed), a non-irrigated crop at the start cannot get irrigated.

We can therefore consider that there is an underestimation of irrigable areas since the extensive margin effect taken into account is asymmetrical.
A third level of adaptation based on technical advances in plant genomics or culture processes could help in developing varieties more resistant to temperature and water stress. Doing so could improve resilience to climate change (Marshall and al. 2015), but it is not included in our modeling framework. Nevertheless, the part of the autonomous adaptation taken into account in our analysis is very important and realistic.

## 2.4. Estimating double-input yield functions in the context of CC

Given the crop and farm group, the objective is to propose a yield function relating nitrogen and water inputs to the yield. It should be noted that physical conditions are not accurately geo-referenced but averaged at the regional level.

### 2.4.1. Selecting the baseline functions in current time

The function is assumed to be monotonous and quasi concave for value intervals of interest in line with usual intake observed in the real world. The selected relationship is of the Mitscherlich-Baule form (MB) such that:

$$y(W, N \mid \varphi, \sigma, \tau, W_0, N_0) = \varphi(1 - e^{-\sigma(W+W_0)})(1 - e^{-\tau(N+N_0)}), \quad (3)$$

where W and N respectively denote the added quantities of water (irrigation) and nitrogen (fertilization), which are assumed to be as allocated by farmers. Parameters φ, σ, τ, W₀, N₀, respectively denote the agronomic potential, water-related curvature, nitrogen-related curvature, and exogenous natural availability of water and nitrogen. Note that organic fertilizers (sourced by five types of manure) are crop-inputs included in the AROPAj model, transformed into standard mineral nitrogen input through differentiated weights.

Dose-response functions result from a two-step process. The first step selects the set of information required by the STICS crop model, namely climate (averaged in terms of temperatures, rainfall and CO₂ concentration at the regional level, weighted by the farm group's altitude), soils (among the major soils present in the region) and phenotypical data related to the crop. We consider 2400 sets, combining soil, variety and sowing date. We process STICS for series of W and N quantities (7x7-grid points). We adjust each of the 2400 sets of points to a function of the MB functional form. The second step aims at selecting one among these 2400 functions. We restrict the number of functions to those for which the estimated φ potential is greater than the FADN-estimated yield. Finally, the selected function minimizes the angle between the input-price vector normalized by the crop price and the vector orthogonal to the yield-surface function, given that the yield is equal to the FADN estimate (for more details, see Humblot et al. 2017). At this point, the selection process relates each crop within each farm group to a specific triplet of soil, variety and sowing date.
A third level of adaptation based on technical advances in plant genomics or culture processes could help in developing varieties more resistant to temperature and water stress. Doing so could improve resilience to climate change (Marshall and al. 2015), but it is not included in our modeling framework. Nevertheless, the part of the autonomous adaptation taken into account in our analysis is very important and realistic.

## 2.4. Estimating double-input yield functions in the context of CC

Given the crop and farm group, the objective is to propose a yield function relating nitrogen and water inputs to the yield. It should be noted that physical conditions are not accurately geo-referenced but averaged at the regional level.

### 2.4.1. Selecting the baseline functions in current time

The function is assumed to be monotonous and quasi concave for value intervals of interest in line with usual intake observed in the real world. The selected relationship is of the Mitscherlich-Baule form (MB) such that:

$$y(W, N \mid \varphi, \sigma, \tau, W_0, N_0) = \varphi(1 - e^{-\sigma(W+W_0)})(1 - e^{-\tau(N+N_0)}), \quad (3)$$

where W and N respectively denote the added quantities of water (irrigation) and nitrogen (fertilization), which are assumed to be as allocated by farmers. Parameters φ, σ, τ, W₀, N₀, respectively denote the agronomic potential, water-related curvature, nitrogen-related curvature, and exogenous natural availability of water and nitrogen. Note that organic fertilizers (sourced by five types of manure) are crop-inputs included in the AROPAj model, transformed into standard mineral nitrogen input through differentiated weights.

Dose-response functions result from a two-step process. The first step selects the set of information required by the STICS crop model, namely climate (averaged in terms of temperatures, rainfall and CO₂ concentration at the regional level, weighted by the farm group's altitude), soils (among the major soils present in the region) and phenotypical data related to the crop. We consider 2400 sets, combining soil, variety and sowing date. We process STICS for series of W and N quantities (7x7-grid points). We adjust each of the 2400 sets of points to a function of the MB functional form. The second step aims at selecting one among these 2400 functions. We restrict the number of functions to those for which the estimated φ potential is greater than the FADN-estimated yield. Finally, the selected function minimizes the angle between the input-price vector normalized by the crop price and the vector orthogonal to the yield-surface function, given that the yield is equal to the FADN estimate (for more details, see Humblot et al. 2017). At this point, the selection process relates each crop within each farm group to a specific triplet of soil, variety and sowing date.
The process is applied to all farm groups and to nine of the most marketed crops in Europe (soft wheat, durum wheat, maize, barley, rapeseed, sunflower, beet, potato and soya). As a result, a set of one crop and one farm group refers to a set of STICS parameters, associating one soil and one crop variety under the baseline 2009 scenario. The method applies for irrigated crops as well as for non-irrigated crops, insofar as we can access additional price information, especially for water (Graveline and Mérel 2014). According to FADN data, nitrogen and water prices can fluctuate around an average value of 1.5 €/kg and 0.08 €/m3 respectively. We emphasize that the method results in water-dependent crop yield functions even in the case of no irrigation (i.e. optimal W equals zero).

### 2.4.2. Re-evaluating the yield functions over the long term and the economic rationale of farmers

Once the yield functions are selected for the baseline scenario, they are shaped to accommodate the long-term effects of climate change. At the plot level, for a given crop in a given farm group, we consider that soil previously inferred by the yield function selection for the baseline remains unchanged. We assume that the crop variety, the preceding crop and the sowing date also remain unchanged, corresponding to a weak level of autonomous adaptation. The yield function is then reshaped for each climatic year considered in the analysis.

We process the STICS crop model for all crop- and farm group-dependent yield functions as many times as there are different climatic years involved in the different scenarios. In our modeling chain, only the physical CC characteristics directly impact the farming systems by reshaping yield functions. It is thus important to consider the key role upstream of scenarios designed for CC. The other important point here is our hypothesis that the annual climate simulated by the general circulation model (GCM) is considered by farmers as the meteorological context representative of the period. In other words, each of the meteorological situations modelled by the GCM over an annual time step is supposed to reflect CC perceived by the farmers for the climate year. This leads to considering the meteorological year both as a random state of the climate and as the farmer's representation of the climate over the period. The chain of models (biophysical and economic) involved in the model therefore reproduces the “annual climatic jumps” observed from one year to the next in all the results we obtain. This leads us to combine two approaches, one based on a time perspective, the other on a statistical analysis.

We used the ARPEGE-CLIMAT model's climatic projections from 2010 to 2100, applied to three evolution scenarios taken from the IPCC's Special Report on Emissions Scenarios (SRES) (IPCC, Fourth Assessment Report). The three scenarios correspond to different levels of radiative forcing, extreme (A2), medium (B1) and intermediate (A1B). Climatic projections are regionalized on an 8x8km grid at a daily time step (Pagé and Terray 2010).
The process is applied to all farm groups and to nine of the most marketed crops in Europe (soft wheat, durum wheat, maize, barley, rapeseed, sunflower, beet, potato and soya). As a result, a set of one crop and one farm group refers to a set of STICS parameters, associating one soil and one crop variety under the baseline 2009 scenario. The method applies for irrigated crops as well as for non-irrigated crops, insofar as we can access additional price information, especially for water (Graveline and Mérel 2014). According to FADN data, nitrogen and water prices can fluctuate around an average value of 1.5 €/kg and 0.08 €/m3 respectively. We emphasize that the method results in water-dependent crop yield functions even in the case of no irrigation (i.e. optimal W equals zero).

### 2.4.2. Re-evaluating the yield functions over the long term and the economic rationale of farmers

Once the yield functions are selected for the baseline scenario, they are shaped to accommodate the long-term effects of climate change. At the plot level, for a given crop in a given farm group, we consider that soil previously inferred by the yield function selection for the baseline remains unchanged. We assume that the crop variety, the preceding crop and the sowing date also remain unchanged, corresponding to a weak level of autonomous adaptation. The yield function is then reshaped for each climatic year considered in the analysis.

We process the STICS crop model for all crop- and farm group-dependent yield functions as many times as there are different climatic years involved in the different scenarios. In our modeling chain, only the physical CC characteristics directly impact the farming systems by reshaping yield functions. It is thus important to consider the key role upstream of scenarios designed for CC. The other important point here is our hypothesis that the annual climate simulated by the general circulation model (GCM) is considered by farmers as the meteorological context representative of the period. In other words, each of the meteorological situations modelled by the GCM over an annual time step is supposed to reflect CC perceived by the farmers for the climate year. This leads to considering the meteorological year both as a random state of the climate and as the farmer's representation of the climate over the period. The chain of models (biophysical and economic) involved in the model therefore reproduces the “annual climatic jumps” observed from one year to the next in all the results we obtain. This leads us to combine two approaches, one based on a time perspective, the other on a statistical analysis.

We used the ARPEGE-CLIMAT model's climatic projections from 2010 to 2100, applied to three evolution scenarios taken from the IPCC's Special Report on Emissions Scenarios (SRES) (IPCC, Fourth Assessment Report). The three scenarios correspond to different levels of radiative forcing, extreme (A2), medium (B1) and intermediate (A1B). Climatic projections are regionalized on an 8x8km grid at a daily time step (Pagé and Terray 2010).
### 2.4.3. Re-allocating the agricultural land

At the farm level, in addition to re-evaluating the yield functions, the AROPAj model allows us to account for farmers adapting their optimal allocation of agricultural area by switching between different crops and pastures, taking account of changes in gross margin ratios. From year to year, change in optimal land allocation results from the changes in the ratios of gross margins per unit of crop area after reshaping the yield functions. In other words, even with fixed prices, the AROPAj supply side model estimations evolve when the climate changes. Apart from CC, we also consider changes in irrigation water prices over a wide range of values, increasing by 0 up to 500%. Doing so helps us to explore the cost of water scarcity for the agricultural sector, since we do not account for limitations to irrigation water supply when irrigation occurs, because in our scenario farming systems do not change their irrigation investment.

Considering the 90 years of an IPCC scenario, the results can be analyzed within two perspectives. The first puts forward a trend in climate change that would be consequently noted in general circulation model (GCM) projections (even if projections strongly vary in sign and in amplitude from one year to another). In that sense, the temporal evolution is represented by the succession of decades. According to the second perspective, climatic years related to the IPCC scenario occur within a random field, and these random events are independent of each other and are equally distributed. In both cases, our approach provides a prospective analysis, not a forecasting study.

### 2.5. Geographical downscaling of AROPAj outputs

Due to FADN's privacy policy and sample sizes, it is not possible to directly access farm groups' geographical location at an infra-regional level. In order to do so, the geographical downscaling method involves three steps. The first step combines geo-referenced physical information and agricultural activities to obtain crop location priors. The second consists of the combination of the priors and information on agricultural activities (at the regional level by aggregating FADN data), resulting in geo-referenced probabilities of activity presence. In the third step, the latter are combined with the farm groups' activity mix to estimate the probabilistic geographical distribution of farm groups within the region at a very fine resolution. For further information on the two first steps, see Chakir (2009). The whole method was developed and applied by Cantelaube et al. (2012). The finest spatial unit – the pixel – is related to physical databases in which information covers the geographical space (i.e. 100m x 100m). Aggregating pixels into homogenous polygons keeps the resolution level fine (more than 2000 polygons per million hectares). The V5 AROPAj version of the model is updated in spatial
### 2.4.3. Re-allocating the agricultural land

At the farm level, in addition to re-evaluating the yield functions, the AROPAj model allows us to account for farmers adapting their optimal allocation of agricultural area by switching between different crops and pastures, taking account of changes in gross margin ratios. From year to year, change in optimal land allocation results from the changes in the ratios of gross margins per unit of crop area after reshaping the yield functions. In other words, even with fixed prices, the AROPAj supply side model estimations evolve when the climate changes. Apart from CC, we also consider changes in irrigation water prices over a wide range of values, increasing by 0 up to 500%. Doing so helps us to explore the cost of water scarcity for the agricultural sector, since we do not account for limitations to irrigation water supply when irrigation occurs, because in our scenario farming systems do not change their irrigation investment.

Considering the 90 years of an IPCC scenario, the results can be analyzed within two perspectives. The first puts forward a trend in climate change that would be consequently noted in general circulation model (GCM) projections (even if projections strongly vary in sign and in amplitude from one year to another). In that sense, the temporal evolution is represented by the succession of decades. According to the second perspective, climatic years related to the IPCC scenario occur within a random field, and these random events are independent of each other and are equally distributed. In both cases, our approach provides a prospective analysis, not a forecasting study.

## 2.5. Geographical downscaling of AROPAj outputs

Due to FADN's privacy policy and sample sizes, it is not possible to directly access farm groups' geographical location at an infra-regional level. In order to do so, the geographical downscaling method involves three steps. The first step combines geo-referenced physical information and agricultural activities to obtain crop location priors. The second consists of the combination of the priors and information on agricultural activities (at the regional level by aggregating FADN data), resulting in geo-referenced probabilities of activity presence. In the third step, the latter are combined with the farm groups' activity mix to estimate the probabilistic geographical distribution of farm groups within the region at a very fine resolution. For further information on the two first steps, see Chakir (2009). The whole method was developed and applied by Cantelaube et al. (2012). The finest spatial unit – the pixel – is related to physical databases in which information covers the geographical space (i.e. 100m x 100m). Aggregating pixels into homogenous polygons keeps the resolution level fine (more than 2000 polygons per million hectares). The V5 AROPAj version of the model is updated in spatial
downscaling, including information on irrigation (Jayet et al. 2018). After making the three-step procedure operational, we can downscale any results provided by the AROPAj model. We used this procedure to map our results in the rest of the paper.

### 3. Results

The model draws its strength from the diversity of farming systems it represents, which is structural and geographic. The 300,000 to 350,000 farms represented by 157 representative farms cover a wide spectrum of animal and plant activities carried out under very varied soil and climatic conditions. The area covered by input-yield functions represents half of the UAA (excluding meadows and fodder in particular). Irrigation as represented by FADN is very probably underestimated, while the STICS crop model tends to overestimate the quantities of input (water and nitrogen). Both estimations face the difficulty of translating the quantity of input enabling a given level of yield to be reached (in the real world, a significant proportion of the irrigation water consumed may not be declared and paid for).

The necessarily summary presentation of the results reflects the great diversity of situations, which is likely to increase with changing climatic conditions. We show in the appendix (Figures A1 and A2) such change in terms of precipitation regime, temperature and carbon dioxide concentration, as it is determined by the climatic models of general circulation of the atmosphere. Rainfall and temperature vary considerably from one year to the next, reminding us that climate change and meteorological variability are obviously interacting but distinct phenomena. We have translated this variability by considering that a meteorological year is the result of a random climatic event. Taken into account by the culture model, the yield functions are subject to complex deformations, certain climatic variables having positive effects on the yield (CO₂ concentration), but most often contrasting effects depending on the mean (with positive effect of temperature) and on the amplitude of the variations (with negative effects in the event of extreme variations in rainfall and temperatures compared to the average).

The biophysical and economic processes that the model integrates cannot be reproduced in their complexity by necessarily reductionist geographic and temporal representations. For example, water use efficiency varies with temperature and CO₂ concentration, which also affects the capacity of soils to assimilate the nitrogen that plants need. Less frequent rainfall does not necessarily mean higher water consumption for plants, but scarcity of precipitation leads to a higher demand for irrigation water for the plants concerned. And because of the effects of these two processes, the hierarchy of crops in terms of profitability per hectare is called into question, which is all the greater when the irrigation constraint is strong. Consequently, the allocation of the UAA between the
downscaling, including information on irrigation (Jayet et al. 2018). After making the three-step procedure operational, we can downscale any results provided by the AROPAj model. We used this procedure to map our results in the rest of the paper.

### 3. Results

The model draws its strength from the diversity of farming systems it represents, which is structural and geographic. The 300,000 to 350,000 farms represented by 157 representative farms cover a wide spectrum of animal and plant activities carried out under very varied soil and climatic conditions. The area covered by input-yield functions represents half of the UAA (excluding meadows and fodder in particular). Irrigation as represented by FADN is very probably underestimated, while the STICS crop model tends to overestimate the quantities of input (water and nitrogen). Both estimations face the difficulty of translating the quantity of input enabling a given level of yield to be reached (in the real world, a significant proportion of the irrigation water consumed may not be declared and paid for).

The necessarily summary presentation of the results reflects the great diversity of situations, which is likely to increase with changing climatic conditions. We show in the appendix (Figures A1 and A2) such change in terms of precipitation regime, temperature and carbon dioxide concentration, as it is determined by the climatic models of general circulation of the atmosphere. Rainfall and temperature vary considerably from one year to the next, reminding us that climate change and meteorological variability are obviously interacting but distinct phenomena. We have translated this variability by considering that a meteorological year is the result of a random climatic event. Taken into account by the culture model, the yield functions are subject to complex deformations, certain climatic variables having positive effects on the yield (CO₂ concentration), but most often contrasting effects depending on the mean (with positive effect of temperature) and on the amplitude of the variations (with negative effects in the event of extreme variations in rainfall and temperatures compared to the average).

The biophysical and economic processes that the model integrates cannot be reproduced in their complexity by necessarily reductionist geographic and temporal representations. For example, water use efficiency varies with temperature and CO₂ concentration, which also affects the capacity of soils to assimilate the nitrogen that plants need. Less frequent rainfall does not necessarily mean higher water consumption for plants, but scarcity of precipitation leads to a higher demand for irrigation water for the plants concerned. And because of the effects of these two processes, the hierarchy of crops in terms of profitability per hectare is called into question, which is all the greater when the irrigation constraint is strong. Consequently, the allocation of the UAA between the
different productions are modified. Finally, in the model, apart from any irrigation water supply system, scarcity
is reflected in the increase in the price of irrigation water, while maintaining the hierarchy of water prices
(between crops and representative farms).

The illustrations in this section more simply reflect the great diversity of situations. After an analysis
focusing on the geography of impacts evolving over time, this diversity is illustrated in the context of a simple
statistical approach in which “climatic years” are equiprobable realizations of a meteorological situation
impacted by climate change. We will systematically keep the same north-south division of agricultural France
for the presentation of the results, even if these two remain very heterogeneous: the north covers regions of
arable crops, as well as regions of above-ground livestock farming to the west (Brittany) and mid-mountain to
the east (Burgundy, Jura, Vosges and Ardennes). Irrigation is fairly low on average, but applied to potentially
large areas. The south is even more contrasted with fluvial and Atlantic regions where irrigation is extensively
applied (southwest), mountain regions oriented towards extensive livestock farming (Pyrenees, Alps, Massif
Central) and an area along the Mediterranean coast where “AROPAj activities” are less represented.

We carried out all the simulations equally between three SRES climate change scenarios, namely B1, A1B and A2. Scenario B1 (“global environmental sustainability”) corresponds to a moderate evolution of the CO2 concentration (with a peak in 2050) and temperatures (with a world average increase in the 1.1-1.9°C range by 2100). Scenario A2 (“regionally oriented economic development”) results in a sharp and accelerated increase in CO2 concentration, with a temperature increase of around 2.0-5.4°C by 2100. Scenario A1B is an intermediate scenario with a relatively high CO2 concentration peak after 2050, reflecting a large enough climate change for part of the results to focus on it.

Simulations are performed for 91 yearly GCM projections, over the period 2010-2100. We consider here the case of no change in the economic environment, in terms of prices and policies. Regarding the Common Agricultural Policy, we keep unchanged the 2007 regulation which followed the reform of 2003 (the so-called Luxembourg agreement, which is mainly oriented toward decoupled payments in favor of agricultural lands) and includes changes to the sugar regime and the ending of compulsory set-aside.

3.1. *Analyzing CC impacts on agricultural water demand from a temporal perspective*

The temporal perspective presented here is based on the results of a climate dynamics model using a re-
analysis upstream of the meteorological data of the present climate. Even though we use the AROPAj model
solution originating from FADN in 2009 as a reference, the start of the time sequence therefore differs from the
solution obtained at the present time.
different productions are modified. Finally, in the model, apart from any irrigation water supply system, scarcity
is reflected in the increase in the price of irrigation water, while maintaining the hierarchy of water prices
(between crops and representative farms).

The illustrations in this section more simply reflect the great diversity of situations. After an analysis
focusing on the geography of impacts evolving over time, this diversity is illustrated in the context of a simple
statistical approach in which “climatic years” are equiprobable realizations of a meteorological situation
impacted by climate change. We will systematically keep the same north-south division of agricultural France
for the presentation of the results, even if these two remain very heterogeneous: the north covers regions of
arable crops, as well as regions of above-ground livestock farming to the west (Brittany) and mid-mountain to
the east (Burgundy, Jura, Vosges and Ardennes). Irrigation is fairly low on average, but applied to potentially
large areas. The south is even more contrasted with fluvial and Atlantic regions where irrigation is extensively
applied (southwest), mountain regions oriented towards extensive livestock farming (Pyrenees, Alps, Massif
Central) and an area along the Mediterranean coast where “AROPAj activities” are less represented.

We carried out all the simulations equally between three SRES climate change scenarios, namely B1, A1B and A2. Scenario B1 (“global environmental sustainability”) corresponds to a moderate evolution of the CO2 concentration (with a peak in 2050) and temperatures (with a world average increase in the 1.1-1.9°C range by 2100). Scenario A2 (“regionally oriented economic development”) results in a sharp and accelerated increase in CO2 concentration, with a temperature increase of around 2.0-5.4°C by 2100. Scenario A1B is an intermediate scenario with a relatively high CO2 concentration peak after 2050, reflecting a large enough climate change for part of the results to focus on it.

Simulations are performed for 91 yearly GCM projections, over the period 2010-2100. We consider here the case of no change in the economic environment, in terms of prices and policies. Regarding the Common Agricultural Policy, we keep unchanged the 2007 regulation which followed the reform of 2003 (the so-called Luxembourg agreement, which is mainly oriented toward decoupled payments in favor of agricultural lands) and includes changes to the sugar regime and the ending of compulsory set-aside.

3.1. *Analyzing CC impacts on agricultural water demand from a temporal perspective*

The temporal perspective presented here is based on the results of a climate dynamics model using a re-
analysis upstream of the meteorological data of the present climate. Even though we use the AROPAj model
solution originating from FADN in 2009 as a reference, the start of the time sequence therefore differs from the
solution obtained at the present time.
**Figure 2** illustrates the CC effect on AROPAj-estimated demand for irrigation water, for all of France on the one hand and differentiating northern and southern regions of France on the other. In the CC scenario, each point refers to a simulation involving all farm group models for one year. At the national scale, demand for irrigation water appears to be increasing, to the greatest extent in the A1B scenario and less so for the B1 and A2 scenarios. Potential overall irrigation demand increases by 64% for A1B against 34% for B1 and 25% for A2, between 2010 and 2100. All climate projections reveal that the amplitude of change in annual demand for irrigation water would remain high throughout and demand would increase in the long term on average, up to 4 billion cubic meters, compared to present average demand of around 3 billion cubic meters.

When the geographical distinction is considered, water demand increases in the three CC scenarios in the north, most strongly for the A1B scenario. The results show more contrasting trends in water demand change in the south, since water demand is relatively constant in B1 and is decreasing in A2. In this particular case and under constraints of available water supply, we would expect a relative decline in yields or the emergence of other cropping systems if they prove to be more beneficial for farmers.

Between regions, the response of water demand to CC appears to be heterogeneous. **Figure A3 (Appendix)** illustrates average water demand per decade separately in the northern and southern regions, from 2011-2020 to 2091-2100, for the intermediate CC A1B. Across both the northern and southern halves of the country, quantities of irrigation water required noticeably vary and strongly increase over the decades (131-Champagne-Ardenne, 134-Centre, 162-Pays de la Loire in the north; 164-Poitou-Charentes, 182-Aquitaine, 183-Midi-Pyrénées in the south). However, the greatest increase in irrigation water demand concerns three regions in the north (131, 134 and 162). Some climate decades would have a strongly pronounced impact, as in the 134-Centre region, where irrigation demand doubles as of 2071-2080 compared to 2011-2020.

**Figure 3** presents maps obtained from the spatial downscaling procedure described in section 2.3. Geographical reporting is normalized in cubic meters of irrigation per "AROPAj" hectare, given that (i) the AROPAj model represents only the part of total agriculture available through FADN data, (ii) agriculture accounts for only part of used land, and (iii) farming systems can have high demand of water for specific crops while other crops are not irrigated at all. Focusing on the regional scale leads to different average results at the national or half-national scale. Also, downscaled results within regions show to what extent certain irrigation hot-spots are affected, like the regions 134-Centre, 162-Pays de la Loire and 164-Poitou-Charentes. Interestingly, strong contrasts may occur between CC scenarios, as well as between decades. Irrigation demand could disappear in some regions of the north under the most severe CC scenario, namely A2 in the decade 2091-2100,
**Figure 2** illustrates the CC effect on AROPAj-estimated demand for irrigation water, for all of France on the one hand and differentiating northern and southern regions of France on the other. In the CC scenario, each point refers to a simulation involving all farm group models for one year. At the national scale, demand for irrigation water appears to be increasing, to the greatest extent in the A1B scenario and less so for the B1 and A2 scenarios. Potential overall irrigation demand increases by 64% for A1B against 34% for B1 and 25% for A2, between 2010 and 2100. All climate projections reveal that the amplitude of change in annual demand for irrigation water would remain high throughout and demand would increase in the long term on average, up to 4 billion cubic meters, compared to present average demand of around 3 billion cubic meters.

When the geographical distinction is considered, water demand increases in the three CC scenarios in the north, most strongly for the A1B scenario. The results show more contrasting trends in water demand change in the south, since water demand is relatively constant in B1 and is decreasing in A2. In this particular case and under constraints of available water supply, we would expect a relative decline in yields or the emergence of other cropping systems if they prove to be more beneficial for farmers.

Between regions, the response of water demand to CC appears to be heterogeneous. **Figure A3 (Appendix)** illustrates average water demand per decade separately in the northern and southern regions, from 2011-2020 to 2091-2100, for the intermediate CC A1B. Across both the northern and southern halves of the country, quantities of irrigation water required noticeably vary and strongly increase over the decades (131-Champagne-Ardenne, 134-Centre, 162-Pays de la Loire in the north; 164-Poitou-Charentes, 182-Aquitaine, 183-Midi-Pyrénées in the south). However, the greatest increase in irrigation water demand concerns three regions in the north (131, 134 and 162). Some climate decades would have a strongly pronounced impact, as in the 134-Centre region, where irrigation demand doubles as of 2071-2080 compared to 2011-2020.

**Figure 3** presents maps obtained from the spatial downscaling procedure described in section 2.3. Geographical reporting is normalized in cubic meters of irrigation per "AROPAj" hectare, given that (i) the AROPAj model represents only the part of total agriculture available through FADN data, (ii) agriculture accounts for only part of used land, and (iii) farming systems can have high demand of water for specific crops while other crops are not irrigated at all. Focusing on the regional scale leads to different average results at the national or half-national scale. Also, downscaled results within regions show to what extent certain irrigation hot-spots are affected, like the regions 134-Centre, 162-Pays de la Loire and 164-Poitou-Charentes. Interestingly, strong contrasts may occur between CC scenarios, as well as between decades. Irrigation demand could disappear in some regions of the north under the most severe CC scenario, namely A2 in the decade 2091-2100,
while it increases in the same decade for the A1B and B1 scenarios. It is clear that, when demand for water becomes very high for some crops, less water-intensive crops become more competitive. In other words, water could be abundantly present in the favorable seasons at the present time in some regions, resulting in high yields from some crops, but CC could dramatically alter the situation, either by increasing demand for water for crops that are still profitable, or by radically shifting the crop system toward crops requiring much less irrigation water.

The diversity of results at the national and regional scales is due to that the diversity of the various processes and phenomena integrated upstream in the input data of the model and in the model itself. The time perspective underlying the presentation of the above results does not clearly show a trend, but rather variance. The agro-economic model embodies the diversity of agricultural production systems, with very contrasting impacts in terms of input demand, allocation of agricultural land and gross margin due to the entanglement of the intensive and extensive margin effects. Temporal variability, supported by the climate data provided by the GCM, is itself strongly dependent on the climate scenario. We studied to what extent the north-south contrast may emerge from a time perspective. For this, we analyzed separately for northern and southern France the very chaotic evolution of the gross margin of moving average and trend. The 10-year moving averages and the full series trends are illustrated in **Figure 4**. While these trends reveal an upward trend in northern France for SRES B1 and A1B, and a downward trend for northern France in SRES A2 and for the three SRES for southern France, they are not significant (with R-squared from 0.0015 to 0.045). We show that the change in the price of water results in a significant drop in gross margins, more significantly in the north than in the south (of the order of -400 million euros versus -150 million euros), with an unfavorable trend deviation to the north. This suggests that the variability of the impacts of CC on agriculture is closely linked to inter-annual weather variations, which are themselves highly contrasted from one SRES to another.

## 3.2. Combined effects of a random approach to climate change and the change in the cost of access to water

We now change the analysis by introducing a two-tier link between time, water price and CC. First of all, given the CC scenario, we consider that any annual “climate” provided by the GCM model over the period from 2010 to 2100 is a random state of CC. In doing so, we set as background the temporal dimension of the analysis. Second, apart from the physical change represented here by CC, we introduce economic change through the cost of access to agricultural water. We run the model with eight levels of water irrigation price, in addition to the 2009 prices estimated when calibrating the model based on the 2009-FADN.

Water price change is introduced through the price increasing by 0, 25, 50, 75, 100, 150, 200, 250 and 500% respectively, applied to all farming systems, corresponding to a relative price change with nine levels being 1,
while it increases in the same decade for the A1B and B1 scenarios. It is clear that, when demand for water becomes very high for some crops, less water-intensive crops become more competitive. In other words, water could be abundantly present in the favorable seasons at the present time in some regions, resulting in high yields from some crops, but CC could dramatically alter the situation, either by increasing demand for water for crops that are still profitable, or by radically shifting the crop system toward crops requiring much less irrigation water.

The diversity of results at the national and regional scales is due to that the diversity of the various processes and phenomena integrated upstream in the input data of the model and in the model itself. The time perspective underlying the presentation of the above results does not clearly show a trend, but rather variance. The agro-economic model embodies the diversity of agricultural production systems, with very contrasting impacts in terms of input demand, allocation of agricultural land and gross margin due to the entanglement of the intensive and extensive margin effects. Temporal variability, supported by the climate data provided by the GCM, is itself strongly dependent on the climate scenario. We studied to what extent the north-south contrast may emerge from a time perspective. For this, we analyzed separately for northern and southern France the very chaotic evolution of the gross margin of moving average and trend. The 10-year moving averages and the full series trends are illustrated in **Figure 4**. While these trends reveal an upward trend in northern France for SRES B1 and A1B, and a downward trend for northern France in SRES A2 and for the three SRES for southern France, they are not significant (with R-squared from 0.0015 to 0.045). We show that the change in the price of water results in a significant drop in gross margins, more significantly in the north than in the south (of the order of -400 million euros versus -150 million euros), with an unfavorable trend deviation to the north. This suggests that the variability of the impacts of CC on agriculture is closely linked to inter-annual weather variations, which are themselves highly contrasted from one SRES to another.

## 3.2. Combined effects of a random approach to climate change and the change in the cost of access to water

We now change the analysis by introducing a two-tier link between time, water price and CC. First of all, given the CC scenario, we consider that any annual “climate” provided by the GCM model over the period from 2010 to 2100 is a random state of CC. In doing so, we set as background the temporal dimension of the analysis. Second, apart from the physical change represented here by CC, we introduce economic change through the cost of access to agricultural water. We run the model with eight levels of water irrigation price, in addition to the 2009 prices estimated when calibrating the model based on the 2009-FADN.

Water price change is introduced through the price increasing by 0, 25, 50, 75, 100, 150, 200, 250 and 500% respectively, applied to all farming systems, corresponding to a relative price change with nine levels being 1,
1.25, 1.5, 1.75, 2, 2.5, 3, 3.5 and 6 respectively. The availability of irrigation water, which depends on access to surface water and groundwater, competition between uses, and climate change, would depend on supply modeling, which is not covered in this paper. The issue of the scarcity of irrigation water is therefore addressed via the cost of access. It should be noted that the price of water taken into account by AROPAj, depending on the crops and farms, varies between 2 and 20 euro cents per cubic meter, before modification. This price is much lower than tap water paid by consumers (several euros per cubic meter). By increasing the costs of access to water by 500%, the maximum price paid by farmers in our simulations is still much lower than the price of tap water. As long as price is an indicator of scarcity, the highest price reveals what might occur in terms of agricultural production and income when demand for water collapses due to lack of resources.

With regard to gross margins the results fluctuate between 25 and 29 billion euros in all scenarios (Figure 5a). We cannot infer any general trend of CC impacts on gross margin at the national level, partially due to the marked inter-annual heterogeneity induced by climate data variability, presented below. Nevertheless, the A2 scenario appears to be the least favorable to farm income.

We present results for France at the national level, distinguishing north ("fra1" covering thirteen regions, 121-163) and south ("fra2" covering nine regions, 164-204) as elsewhere in the paper. Following this division, Figures 5a ("fra1") and 5b ("fra2") illustrate the impact of price changes on three model outputs: (i) gross margin as indicator for agricultural income; (ii) fertilizer demand; and (iii) irrigation water demand (Figure A4 for France as a whole). Both figures present the statistical distribution of the three outputs over the 91 years (2010-2100) and for each of the three CC scenarios. Each curve of every chart in Figures 5 shows the distribution of one model output referring to one of the nine water price levels, given the CC scenario.

As expected, distribution peaks, which all are of unimodal shape, clearly move towards lower values for the gross margin and demand for water when the water price increases. The variance of water demand distribution also decreases with increasing prices. As regards demand for mineral fertilizer, change is ambiguous and of lower amplitude. Considering the AROPAj baseline results for 2009 and the lowest price curve, it is confirmed that the demand for irrigation water increases with CC, but to a lesser extent as the climate scenario becomes more extreme. Compared to the 2009 baseline estimates, contrasts appear between north and south on the one hand and between CC scenarios on the other. Regarding the distributions, we use peaks or averaged values as indicators of changes, even though peaks differ from averages, especially in the case of water demand.

On average, when CC occurs for all scenarios, the demand for irrigation water significantly increases in the north and slightly decreases in the south, with water price at its reference value, whereas variance is high. Also,
1.25, 1.5, 1.75, 2, 2.5, 3, 3.5 and 6 respectively. The availability of irrigation water, which depends on access to surface water and groundwater, competition between uses, and climate change, would depend on supply modeling, which is not covered in this paper. The issue of the scarcity of irrigation water is therefore addressed via the cost of access. It should be noted that the price of water taken into account by AROPAj, depending on the crops and farms, varies between 2 and 20 euro cents per cubic meter, before modification. This price is much lower than tap water paid by consumers (several euros per cubic meter). By increasing the costs of access to water by 500%, the maximum price paid by farmers in our simulations is still much lower than the price of tap water. As long as price is an indicator of scarcity, the highest price reveals what might occur in terms of agricultural production and income when demand for water collapses due to lack of resources.

With regard to gross margins the results fluctuate between 25 and 29 billion euros in all scenarios (Figure 5a). We cannot infer any general trend of CC impacts on gross margin at the national level, partially due to the marked inter-annual heterogeneity induced by climate data variability, presented below. Nevertheless, the A2 scenario appears to be the least favorable to farm income.

We present results for France at the national level, distinguishing north ("fra1" covering thirteen regions, 121-163) and south ("fra2" covering nine regions, 164-204) as elsewhere in the paper. Following this division, Figures 5a ("fra1") and 5b ("fra2") illustrate the impact of price changes on three model outputs: (i) gross margin as indicator for agricultural income; (ii) fertilizer demand; and (iii) irrigation water demand (Figure A4 for France as a whole). Both figures present the statistical distribution of the three outputs over the 91 years (2010-2100) and for each of the three CC scenarios. Each curve of every chart in Figures 5 shows the distribution of one model output referring to one of the nine water price levels, given the CC scenario.

As expected, distribution peaks, which all are of unimodal shape, clearly move towards lower values for the gross margin and demand for water when the water price increases. The variance of water demand distribution also decreases with increasing prices. As regards demand for mineral fertilizer, change is ambiguous and of lower amplitude. Considering the AROPAj baseline results for 2009 and the lowest price curve, it is confirmed that the demand for irrigation water increases with CC, but to a lesser extent as the climate scenario becomes more extreme. Compared to the 2009 baseline estimates, contrasts appear between north and south on the one hand and between CC scenarios on the other. Regarding the distributions, we use peaks or averaged values as indicators of changes, even though peaks differ from averages, especially in the case of water demand.

On average, when CC occurs for all scenarios, the demand for irrigation water significantly increases in the north and slightly decreases in the south, with water price at its reference value, whereas variance is high. Also,
regarding water demand, the impact of the water price is greater in the north than the south, but there is no clear
difference between CC scenarios. On the other hand, the contrast between north and south is more pronounced
with regard to the demand for mineral fertilizing. Climate change would lead to nitrogen demand decreasing
greatly in the south but only slightly in the north, with a less pronounced variance in the SRES B1. Under the
moderate B1 scenario, changes in gross margins hit the northern half of France harder than the south, although
variance is higher, leading to greater economic difficulty for northern farmers under this scenario. Increasing
prices for irrigation water accentuate this difficulty, as the average gross margin decreases more in the north as
the price goes up. Finally, when access to water is more expensive or when CC influence approaches GCM
simulated values, or under the combined effect of the two, northern agriculture appears more vulnerable than
southern agriculture.

The results presented above reveal the complexity of bio-physical and economic phenomena involved in CC
and in water price change. Even though the AROPAj model leads to widely diverse results for series of crops in
each of the represented farm groups, intermediate scale analysis adequately illustrates the diversity of situations.
Since farming systems in different regions specialize in different crops (to a certain extent), it is plausible that
changes in water demand could differ greatly at the regional scale.

The A1B scenario is an intermediate scenario between B1 and A2, while remaining subject to major changes
in climate and to large inter-annual variations in climate data. The time perspective presented in **Figure 4** seems
to indicate that this scenario is more favorable to agriculture in the north of France, and more unfavorable in the
south, compared to the other two SRES. The statistical approach challenges this hierarchy. We now return to the
temporal dimension of CC by focusing on three decades, namely 2011-2020, 2051-2060 and 2090-2100, and we
consider the 22 regions facing change in water prices over time for the A1B intermediate scenario. **Figure 6**
illustrates the diversity of regional irrigation responses to the two-tier pressure of water price change and
changing climate over these decades. This diversity refers to (i) the amplitude of decline in water demand, which
is larger for the 2091-2100 decade in most northern regions, and to (ii) water-intensive crops (e.g. maize in 182-
Aquitaine, maize, sugar beet or potatoes in 134-Centre and 132-Picardie). Interestingly, some regions vary
strongly in terms of irrigation from decade to decade, with the increasing required quantity of water, as in 162-
Pays de la Loire and to a greater extent 134-Centre in the north and 164-Poitou-charentes in the south. Overall,
changes in curves (in slope and in level) are much more pronounced in northern regions than in southern regions.

Again for A1B-CC, we estimate rates of water demand reduction when the water price increases and report
the results in **Table A1** (Appendix). Some regions are less affected by increasing prices than others. In a couple
regarding water demand, the impact of the water price is greater in the north than the south, but there is no clear
difference between CC scenarios. On the other hand, the contrast between north and south is more pronounced
with regard to the demand for mineral fertilizing. Climate change would lead to nitrogen demand decreasing
greatly in the south but only slightly in the north, with a less pronounced variance in the SRES B1. Under the
moderate B1 scenario, changes in gross margins hit the northern half of France harder than the south, although
variance is higher, leading to greater economic difficulty for northern farmers under this scenario. Increasing
prices for irrigation water accentuate this difficulty, as the average gross margin decreases more in the north as
the price goes up. Finally, when access to water is more expensive or when CC influence approaches GCM
simulated values, or under the combined effect of the two, northern agriculture appears more vulnerable than
southern agriculture.

The results presented above reveal the complexity of bio-physical and economic phenomena involved in CC
and in water price change. Even though the AROPAj model leads to widely diverse results for series of crops in
each of the represented farm groups, intermediate scale analysis adequately illustrates the diversity of situations.
Since farming systems in different regions specialize in different crops (to a certain extent), it is plausible that
changes in water demand could differ greatly at the regional scale.

The A1B scenario is an intermediate scenario between B1 and A2, while remaining subject to major changes
in climate and to large inter-annual variations in climate data. The time perspective presented in **Figure 4** seems
to indicate that this scenario is more favorable to agriculture in the north of France, and more unfavorable in the
south, compared to the other two SRES. The statistical approach challenges this hierarchy. We now return to the
temporal dimension of CC by focusing on three decades, namely 2011-2020, 2051-2060 and 2090-2100, and we
consider the 22 regions facing change in water prices over time for the A1B intermediate scenario. **Figure 6**
illustrates the diversity of regional irrigation responses to the two-tier pressure of water price change and
changing climate over these decades. This diversity refers to (i) the amplitude of decline in water demand, which
is larger for the 2091-2100 decade in most northern regions, and to (ii) water-intensive crops (e.g. maize in 182-
Aquitaine, maize, sugar beet or potatoes in 134-Centre and 132-Picardie). Interestingly, some regions vary
strongly in terms of irrigation from decade to decade, with the increasing required quantity of water, as in 162-
Pays de la Loire and to a greater extent 134-Centre in the north and 164-Poitou-charentes in the south. Overall,
changes in curves (in slope and in level) are much more pronounced in northern regions than in southern regions.

Again for A1B-CC, we estimate rates of water demand reduction when the water price increases and report
the results in **Table A1** (Appendix). Some regions are less affected by increasing prices than others. In a couple
of regions, this resilience is due to the fact that their AROPAj-sourced productions are not severely water-
dependent. This is particularly the case for the 203-Provence-Alpes-Côte d'Azur region (water-dependent for
crops not included in AROPAj), and the 163-Bretagne and 184-Limousin regions (mostly oriented towards
animal production). Water demand steadily decreases when the water price increases for all regions except for
133-Haute Normandie, 136-Bourgogne, 141-Nord-Pas de Calais and to a lesser extent 162-Pays de la Loire.
Own-price elasticity roughly computed on the price change interval [0, 100%] is close to -0.40 for 7 regions in
the decades 2011-2020 and 2051-2060 and for 12 regions for the decade 2091-2100. Apart from the 3 resilient
regions, elasticity lies within the interval [-0.30,-0.20] for 7 regions in the two first decades and for 6 regions in
the final decade. In other words, demand for irrigation water would be increasingly sensitive to water prices over
the years even in the case of moderate CC.

3.3. Major crops response to CC and water price

Agricultural income and demand for water and nitrogen are key factors for estimating the impacts of CC and
change in water price on farming systems. However, it is important to extend the analysis of farming activities
with more details on land allocation, production and greenhouse gas emissions (GHGs), insofar as the model is
capable of providing new insights. In this section, we consider the 91 years of the intermediate A1B-CC scenario
as specific realizations of CC.

Soft wheat and maize are two major cereals which usually compete for land but differ greatly regarding
irrigation. **Figure 7** presents the model’s outputs for maize, in terms of acreage, marketed production, on-farm
re-used production (feed) and irrigation, for north, south and the whole of France. Maize is strongly impacted by
CC and water prices by irrigation, unlike soft wheat (see **Figure A5**). The various charts present the output
distributions over the years for the nine water price series. As expected, soft wheat is weakly affected by water
price, since this crop requires little irrigation. Declining acreage and production is due to CC, which is
proportionally more pronounced in the south than the north, but the decline in terms of quantity is much greater
in the north than the south. Concurrently, maize acreage, and to a greater extent production, increase in the north
of France under CC, while the impact is neutral on average in the south. In the north, maize depends on sharply
increasing demand for irrigation. Nevertheless, variance is high in both cases. In the case of the highest water
price, irrigation falls back far from the baseline level in the north (and falls less strongly in the south), while
changes in acreage and production are ambiguous in both the north and south, compared to the baseline.

We extend the analysis by providing some additional perspectives, illustrated in **Figure 8**. We show that CC
leads to a 3% decrease in cereal acreage, an 8% decline in marketed production and a 4% decline in on-farm
of regions, this resilience is due to the fact that their AROPAj-sourced productions are not severely water-
dependent. This is particularly the case for the 203-Provence-Alpes-Côte d'Azur region (water-dependent for
crops not included in AROPAj), and the 163-Bretagne and 184-Limousin regions (mostly oriented towards
animal production). Water demand steadily decreases when the water price increases for all regions except for
133-Haute Normandie, 136-Bourgogne, 141-Nord-Pas de Calais and to a lesser extent 162-Pays de la Loire.
Own-price elasticity roughly computed on the price change interval [0, 100%] is close to -0.40 for 7 regions in
the decades 2011-2020 and 2051-2060 and for 12 regions for the decade 2091-2100. Apart from the 3 resilient
regions, elasticity lies within the interval [-0.30,-0.20] for 7 regions in the two first decades and for 6 regions in
the final decade. In other words, demand for irrigation water would be increasingly sensitive to water prices over
the years even in the case of moderate CC.

3.3. Major crops response to CC and water price

Agricultural income and demand for water and nitrogen are key factors for estimating the impacts of CC and
change in water price on farming systems. However, it is important to extend the analysis of farming activities
with more details on land allocation, production and greenhouse gas emissions (GHGs), insofar as the model is
capable of providing new insights. In this section, we consider the 91 years of the intermediate A1B-CC scenario
as specific realizations of CC.

Soft wheat and maize are two major cereals which usually compete for land but differ greatly regarding
irrigation. **Figure 7** presents the model’s outputs for maize, in terms of acreage, marketed production, on-farm
re-used production (feed) and irrigation, for north, south and the whole of France. Maize is strongly impacted by
CC and water prices by irrigation, unlike soft wheat (see **Figure A5**). The various charts present the output
distributions over the years for the nine water price series. As expected, soft wheat is weakly affected by water
price, since this crop requires little irrigation. Declining acreage and production is due to CC, which is
proportionally more pronounced in the south than the north, but the decline in terms of quantity is much greater
in the north than the south. Concurrently, maize acreage, and to a greater extent production, increase in the north
of France under CC, while the impact is neutral on average in the south. In the north, maize depends on sharply
increasing demand for irrigation. Nevertheless, variance is high in both cases. In the case of the highest water
price, irrigation falls back far from the baseline level in the north (and falls less strongly in the south), while
changes in acreage and production are ambiguous in both the north and south, compared to the baseline.

We extend the analysis by providing some additional perspectives, illustrated in **Figure 8**. We show that CC
leads to a 3% decrease in cereal acreage, an 8% decline in marketed production and a 4% decline in on-farm
consumption on average compared to the baseline. In the case of CC combined with the highest water price, the decreases are 7%, 13% and 10% respectively. Water price change would significantly affect the demand for marketed concentrate feed, which is likely to increase by 3%. It is clear that climate change and water price change would strongly impact all farming activities, including livestock. Focusing on acreage allocation, we expect a decrease in cereals and oleaginous products, while grasslands may help to compensate feed requirements. It is interesting to consider these outcomes in relation to GHGEs. Based on a 100-year time frame equivalence in terms of global warming potential, estimated emissions of nitrous oxide and methane together appear to remain stable on average compared to the baseline. Separately, nitrous oxide emissions would decrease by 1% under CC and by 3.5% under CC combined with the highest price change, while methane would increase by 2.5% and 5% respectively. Series of complex phenomena taken into account by our model add to the complexity of the analysis when considering random change in the two GHGEs separately and together, given the fact that the two GHGEs estimates are similar in weight at the national level.

4. Conclusion

The general framework in which the analysis takes place is obviously set by the assumptions that underlie the AROPAj agro-economic model. By construction, as with any supply model, the general price system for the goods included in the model is exogenous. In our analysis, the same is true for the exogenous and immutable character of agricultural structures, including in terms of livestock, even if this can vary with limited amplitude. These elements make it possible to consider that this analysis of the CC impacts is more relevant when it is conducted from a statistical rather than a temporal angle, even though it should in any event be considered as a prospective analysis and not at all as a forecasting exercise. Still in relation to the hypothesis of exogenous and unchanged prices, the developing versions of the AROPAj model based on FADN data sets for different years show that, over a short period, the price variations of products and inputs are undoubtedly more dependent on weather variations and the international political context than on market price adjustments. According to our experience in agro-economic modeling, it is relevant to consider price changes as exogenous, like climate change or changes in public policy, and to assess the effects on the agricultural production system. Conversely, this type of modeling makes it possible to assess the impacts of agriculture on the environment, for example in terms of agricultural greenhouse gas emissions. The interactions between climate and the global economy and the readjustment of market equilibrium prices do not lie within our field of analysis, and require more than a simple link with general equilibrium models. Nevertheless, the analysis we offer deals as fully as possible with a
consumption on average compared to the baseline. In the case of CC combined with the highest water price, the decreases are 7%, 13% and 10% respectively. Water price change would significantly affect the demand for marketed concentrate feed, which is likely to increase by 3%. It is clear that climate change and water price change would strongly impact all farming activities, including livestock. Focusing on acreage allocation, we expect a decrease in cereals and oleaginous products, while grasslands may help to compensate feed requirements. It is interesting to consider these outcomes in relation to GHGEs. Based on a 100-year time frame equivalence in terms of global warming potential, estimated emissions of nitrous oxide and methane together appear to remain stable on average compared to the baseline. Separately, nitrous oxide emissions would decrease by 1% under CC and by 3.5% under CC combined with the highest price change, while methane would increase by 2.5% and 5% respectively. Series of complex phenomena taken into account by our model add to the complexity of the analysis when considering random change in the two GHGEs separately and together, given the fact that the two GHGEs estimates are similar in weight at the national level.

4. Conclusion

The general framework in which the analysis takes place is obviously set by the assumptions that underlie the AROPAj agro-economic model. By construction, as with any supply model, the general price system for the goods included in the model is exogenous. In our analysis, the same is true for the exogenous and immutable character of agricultural structures, including in terms of livestock, even if this can vary with limited amplitude. These elements make it possible to consider that this analysis of the CC impacts is more relevant when it is conducted from a statistical rather than a temporal angle, even though it should in any event be considered as a prospective analysis and not at all as a forecasting exercise. Still in relation to the hypothesis of exogenous and unchanged prices, the developing versions of the AROPAj model based on FADN data sets for different years show that, over a short period, the price variations of products and inputs are undoubtedly more dependent on weather variations and the international political context than on market price adjustments. According to our experience in agro-economic modeling, it is relevant to consider price changes as exogenous, like climate change or changes in public policy, and to assess the effects on the agricultural production system. Conversely, this type of modeling makes it possible to assess the impacts of agriculture on the environment, for example in terms of agricultural greenhouse gas emissions. The interactions between climate and the global economy and the readjustment of market equilibrium prices do not lie within our field of analysis, and require more than a simple link with general equilibrium models. Nevertheless, the analysis we offer deals as fully as possible with a
complex element, irrigation, which is at the heart of an agricultural sector of great diversity, impacted by climate change, which is itself complicated to grasp.

Given the present agricultural water usage and the potential limits CC may impose on the resource's availability, the development of appropriate modeling tools is essential for incorporating demand for irrigation water. Directly through temperature and rainfall, and indirectly through water availability for irrigation, CC may strongly impact farming systems. Accordingly, we developed a prospective approach combining the AROPAj agro-economic model and the STICS crop model, focusing on links between climate, crop yields, and nitrogen and water inputs. Simulations were carried out for three climate projections, namely B1, A1B and A2 as defined in the IPCC Fourth Assessment Report, over the period 2010-2100. We emphasize the fact that, in this paper, we estimate demand for irrigation water, given the price and climate, but not the effective irrigation use clearing demand and supply. Crop water requirements are integrated through the crop model, while availability is taken into consideration via the changes of water prices.

The biophysical elements taken into account through the impacts of climate change on the relationships between water intakes, nitrogen intakes and crop yields are likely to fuel the two powerful economic drivers, which are (i) the intensive margin effect at the scale of the crop plot and (ii) the extensive margin effect at the scale of the farming system. The first effect is directly linked to the water use efficiency, the evolution of which depends on that of the temperature and the CO2 concentration of the atmosphere. Combined with the change in rainfalls and correlatively with the demand for irrigation water, which is highly dependent on the crop, the crop-to-crop ratios of gross margins per hectare lead to an extensive margin effect that varies greatly from one region to another. In France, the land turned towards the main productions of agriculture and breeding is generally more remunerative in the north than in the south, while benefiting from a pluviometry more adapted to arable crops. If the change in the rain regime, as we have started to observe it in recent years, affects more and more the northern regions, the need for irrigation water will increase and will be more difficult to meet, so some very profitable productions today will be replaced by productions requiring less water while being less profitable. A climate that becomes drier and warmer can therefore lead to a drop in demand for irrigation water due to the change in use of agricultural land.

Our results suggest an increase in water demand from 2010 to 2100, particularly for the scenarios with more severe CC, A2 and A1B. Nevertheless, the irrigation trajectory over time is irregular due to inter-annual variability in the rainfall pattern. The realization of cartographic representations for France illustrates the great capacity of the method to grasp the regional diversity of farming systems. It is noteworthy that, in terms of
complex element, irrigation, which is at the heart of an agricultural sector of great diversity, impacted by climate change, which is itself complicated to grasp.

Given the present agricultural water usage and the potential limits CC may impose on the resource's availability, the development of appropriate modeling tools is essential for incorporating demand for irrigation water. Directly through temperature and rainfall, and indirectly through water availability for irrigation, CC may strongly impact farming systems. Accordingly, we developed a prospective approach combining the AROPAj agro-economic model and the STICS crop model, focusing on links between climate, crop yields, and nitrogen and water inputs. Simulations were carried out for three climate projections, namely B1, A1B and A2 as defined in the IPCC Fourth Assessment Report, over the period 2010-2100. We emphasize the fact that, in this paper, we estimate demand for irrigation water, given the price and climate, but not the effective irrigation use clearing demand and supply. Crop water requirements are integrated through the crop model, while availability is taken into consideration via the changes of water prices.

The biophysical elements taken into account through the impacts of climate change on the relationships between water intakes, nitrogen intakes and crop yields are likely to fuel the two powerful economic drivers, which are (i) the intensive margin effect at the scale of the crop plot and (ii) the extensive margin effect at the scale of the farming system. The first effect is directly linked to the water use efficiency, the evolution of which depends on that of the temperature and the CO2 concentration of the atmosphere. Combined with the change in rainfalls and correlatively with the demand for irrigation water, which is highly dependent on the crop, the crop-to-crop ratios of gross margins per hectare lead to an extensive margin effect that varies greatly from one region to another. In France, the land turned towards the main productions of agriculture and breeding is generally more remunerative in the north than in the south, while benefiting from a pluviometry more adapted to arable crops. If the change in the rain regime, as we have started to observe it in recent years, affects more and more the northern regions, the need for irrigation water will increase and will be more difficult to meet, so some very profitable productions today will be replaced by productions requiring less water while being less profitable. A climate that becomes drier and warmer can therefore lead to a drop in demand for irrigation water due to the change in use of agricultural land.

Our results suggest an increase in water demand from 2010 to 2100, particularly for the scenarios with more severe CC, A2 and A1B. Nevertheless, the irrigation trajectory over time is irregular due to inter-annual variability in the rainfall pattern. The realization of cartographic representations for France illustrates the great capacity of the method to grasp the regional diversity of farming systems. It is noteworthy that, in terms of
regional water withdrawals, current AROPAj outputs are in line with data recorded by the French Observation and Statistics Department (given that some water-intensive crops are excluded from the AROPAj cover), a correspondence that calls for the development of more detailed analysis at the regional scale. The spatial analysis highlights the wide range of crops requiring irrigation to a greater or lesser extent and disparate irrigation practices at the regional level, mainly concentrated in the west and southwest of France. The most irrigated regions, such as Aquitaine Midi-Pyrénées, Poitou-Charentes and Pays de la Loire, are characterized by significant increase of demand over the decades, but contrasting pathways characterized by increase or decrease also occur, especially on the north-south central axis, from Normandy to Centre and Rhone-Alps, in the A2 CC scenario.

As well as CC, economic change introduced in the analysis through water price is a powerful driver with regard to farming systems. We demonstrate this by considering the demand for irrigation, gross margin and production of major crops. Water price change resulting from water scarcity exacerbates the impact of CC by up to more than double, in some extreme cases, on the activity and profitability of farming systems. More importantly, combined climatic and economic changes might impact the agricultural economy more strongly in the north than the south.

Our analysis starts with a moderate capacity of adaptation adopted by farming systems. Adaptation stems from (i) yield functions reshaped by CC for existing crops, and (ii) land reallocation among existing crops in changing proportions in response to changing crop gross margins per hectare. Even when CC impacts are significant, farming systems show a high level of economic resilience due to the biophysical and economical adaptation captured by our model. But this resilience strongly varies with latitude and farm type. We can expect that higher capacity for autonomous adaptation, with change in practices through sowing dates and crop variety, would increase this resilience. In some cases, CC could benefit European agriculture, in both the north and the south. Our model is able to address this issue along lines developed by Leclère et al. 2013, and further work is currently in progress.

The present analysis focusing on water shows how changes in water availability can mitigate the expected benefit of the higher capacity of farming system adaptation to the extent that crops require water. Change in rainfall, evapotranspiration and consequently natural water availability would affect the demand for irrigation water, and therefore its price, to which farming systems would be increasingly sensitive. In the long term, water prices would compete with CC in terms of pressure on farming systems. In view of the regions for which
regional water withdrawals, current AROPAj outputs are in line with data recorded by the French Observation and Statistics Department (given that some water-intensive crops are excluded from the AROPAj cover), a correspondence that calls for the development of more detailed analysis at the regional scale. The spatial analysis highlights the wide range of crops requiring irrigation to a greater or lesser extent and disparate irrigation practices at the regional level, mainly concentrated in the west and southwest of France. The most irrigated regions, such as Aquitaine Midi-Pyrénées, Poitou-Charentes and Pays de la Loire, are characterized by significant increase of demand over the decades, but contrasting pathways characterized by increase or decrease also occur, especially on the north-south central axis, from Normandy to Centre and Rhone-Alps, in the A2 CC scenario.

As well as CC, economic change introduced in the analysis through water price is a powerful driver with regard to farming systems. We demonstrate this by considering the demand for irrigation, gross margin and production of major crops. Water price change resulting from water scarcity exacerbates the impact of CC by up to more than double, in some extreme cases, on the activity and profitability of farming systems. More importantly, combined climatic and economic changes might impact the agricultural economy more strongly in the north than the south.

Our analysis starts with a moderate capacity of adaptation adopted by farming systems. Adaptation stems from (i) yield functions reshaped by CC for existing crops, and (ii) land reallocation among existing crops in changing proportions in response to changing crop gross margins per hectare. Even when CC impacts are significant, farming systems show a high level of economic resilience due to the biophysical and economical adaptation captured by our model. But this resilience strongly varies with latitude and farm type. We can expect that higher capacity for autonomous adaptation, with change in practices through sowing dates and crop variety, would increase this resilience. In some cases, CC could benefit European agriculture, in both the north and the south. Our model is able to address this issue along lines developed by Leclère et al. 2013, and further work is currently in progress.

The present analysis focusing on water shows how changes in water availability can mitigate the expected benefit of the higher capacity of farming system adaptation to the extent that crops require water. Change in rainfall, evapotranspiration and consequently natural water availability would affect the demand for irrigation water, and therefore its price, to which farming systems would be increasingly sensitive. In the long term, water prices would compete with CC in terms of pressure on farming systems. In view of the regions for which
cropping systems are abundant and profitable in the present climate, mostly in the north of France, but elsewhere
in the European Union, modeling could lead to revising the latitudinal gradient of impacts.
cropping systems are abundant and profitable in the present climate, mostly in the north of France, but elsewhere
in the European Union, modeling could lead to revising the latitudinal gradient of impacts.
<figure><img src="image_3.png" /><figcaption>**Fig. 1.** Diagram of the modeling chain, combining economic and physical data, linking the AROPAj agro-economic model and the STICS crop model (—the brown color refers to the core of AROPAj, green refers to STICS, and blue refers to the spatialization module) (Jayet et al. 2018)</figcaption></figure>
<figure><img src="image_2.png" /><figcaption>**Fig. 1.** Diagram of the modeling chain, combining economic and physical data, linking the AROPAj agro-economic model and the STICS crop model

(–the brown color refers to the core of AROPAj, green refers to STICS, and blue refers to the spatialization module) (Jayet et al. 2018)</figcaption></figure>
<table><thead><tr><th></th><th>France</th><th>North / South</th></tr></thead><tbody><tr><th>B1</th><td></td><td></td></tr><tr><th>A1B</th><td></td><td></td></tr><tr><th>A2</th><td></td><td></td></tr></tbody></table>

**Fig. 2.** Estimated evolution of water demand (in million cubic meters) in France as a whole (on the left) and north and south separately (light and dark blue respectively on the right) for the agricultural sector provided by the AROPAj model for three climate projections (B1, A1B, A2) over from the period 2010 to 2100. The lines refer to the trends over time.
<table><thead><tr><th></th><th>France</th><th>North / South</th></tr></thead><tbody><tr><th>B1</th><td></td><td></td></tr><tr><th>A1B</th><td></td><td></td></tr><tr><th>A2</th><td></td><td></td></tr></tbody></table>

**Fig. 2.** Estimated evolution of water demand (in million cubic meters) in France as a whole (on the left) and north and south separately (light and dark blue respectively on the right) for the agricultural sector provided by the AROPAj model for three climate projections (B1, A1B, A2) over from the period 2010 to 2100. The lines refer to the trends over time.
<figure><img src="image_4.png" /><figcaption>**Fig. 3.** Evolution of irrigation water demand in France during the periods 2011-2020, 2051-2060 and 2091-2100 (averages per decades): mapping at a fine scale resulting from the AROPAj downscaling process.</figcaption></figure>

Legend: 121 - Île-de-France; 131 - Champagne-Ardenne; 132 - Picardie; 133 - Haute-Normandie; 134 - Centre; 135 - Basse-Normandie; 136 - Bourgogne; 141 - Nord-Pas-de-Calais; 151 - Lorraine; 152 - Alsace; 153 - Franche-Comté; 162 - Pays de la Loire; 163 - Bretagne; 164 - Poitou-Charentes; 182 - Aquitaine; 183 - Midi-Pyrénées; 184 - Limousin; 192 - Rhône-Alpes; 193 - Auvergne; 201 - Languedoc-Roussillon; 203 - Provence-Alpes-Côte d'Azur
<figure><img src="image_3.png" /><figcaption>**Fig. 3.** Evolution of irrigation water demand in France during the periods 2011-2020, 2051-2060 and 2091-2100 (averages per decades): mapping at a fine scale resulting from the AROPAj downscaling process.</figcaption></figure>

Legend: 121 - Île-de-France; 131 - Champagne-Ardenne; 132 - Picardie; 133 - Haute-Normandie; 134 - Centre; 135 - Basse-Normandie; 136 - Bourgogne; 141 - Nord-Pas-de-Calais; 151 - Lorraine; 152 - Alsace; 153 - Franche-Comté; 162 - Pays de la Loire; 163 - Bretagne; 164 - Poitou-Charentes; 182 - Aquitaine; 183 - Midi-Pyrénées; 184 - Limousin; 192 - Rhône-Alpes; 193 - Auvergne; 201 - Languedoc-Roussillon; 203 - Provence-Alpes-Côte d'Azur
<figure><img src="image_5.png" /></figure>

<figure><img src="image_6.png" /></figure>

<figure><img src="image_7.png" /></figure>

<figure><img src="image_8.png" /></figure>

<figure><img src="image_9.png" /></figure>

<figure><img src="image_10.png" /><figcaption>**Fig. 4.** Gross margin for northern France (left) and southern France (right) according to the climate year (x-axis), in terms of 10-year moving average and trend calculated on the complete annual series of values (in billions of euros) for 2 relative levels of the price of water (reference level in blue, with a factor of 6 in orange), for the 3 SRES B1 (top), A1B (middle) and A2 (below); linear adjustments on complete series are indicated in the subtitles.</figcaption></figure>
<figure><img src="image_4.png" /></figure>

<figure><img src="image_5.png" /></figure>

<figure><img src="image_6.png" /></figure>

<figure><img src="image_7.png" /></figure>

<figure><img src="image_8.png" /></figure>

<figure><img src="image_9.png" /><figcaption>**Fig. 4.** Gross margin for northern France (left) and southern France (right) according to the climate year (x-axis), in terms of 10-year moving average and trend calculated on the complete annual series of values (in billions of euros) for 2 relative levels of the price of water (reference level in blue, with a factor of 6 in orange), for the 3 SRES B1 (top), A1B (middle) and A2 (below); linear adjustments on complete series are indicated in the subtitles.</figcaption></figure>
<figure><img src="image_11.png" /><figcaption>**Fig. 5a.** Impact of changes in water price by increasing level from 1 up to 6, respectively on gross margin (top row, billion euros), demand for irrigation water (middle row, billion cubic meters) and demand for N-mineral fertilizer (bottom row, million metric tons), distributed over the period 2010-2100 for northern regions of France ("fra1") and for three climate projections (B1, A1B and A2). Vertical red lines refer to the benchmark (AROPAj baseline results for 2009).</figcaption></figure>
<figure><img src="image_10.png" /><figcaption>**Fig. 5a.** Impact of changes in water price by increasing level from 1 up to 6, respectively on gross margin (top row, billion euros), demand for irrigation water (middle row, billion cubic meters) and demand for N-mineral fertilizer (bottom row, million metric tons), distributed over the period 2010-2100 for northern regions of France ("fra1") and for three climate projections (B1, A1B and A2). Vertical red lines refer to the benchmark (AROPAj baseline results for 2009).</figcaption></figure>
<figure><img src="image_12.png" /><figcaption>**Fig. 5b.** Impact of changes in water price by increasing level from 1 up to 6, respectively on gross margin (top row, billion euros), demand for irrigation water (middle row, billion cubic meters) and demand for N-mineral fertilizer (bottom row, million metric tons), distributed over the period 2010-2100 for southern regions of France ("fra2") and for three climate projections (B1, A1B and A2). Vertical red lines refer to the benchmark (AROPAj baseline results for 2009).</figcaption></figure>
<figure><img src="image_11.png" /><figcaption>**Fig. 5b.** Impact of changes in water price by increasing level from 1 up to 6, respectively on gross margin (top row, billion euros), demand for irrigation water (middle row, billion cubic meters) and demand for N-mineral fertilizer (bottom row, million metric tons), distributed over the period 2010-2100 for southern regions of France ("fra2") and for three climate projections (B1, A1B and A2). Vertical red lines refer to the benchmark (AROPAj baseline results for 2009).</figcaption></figure>
<figure><img src="image_13.png" /><figcaption>**Fig. 6.** Regional impact of change in water price on irrigation water demand in the north (on the left) and the south (on the right) of France for three decades, 2011-2020, 2051-2060 and 2091-2100, related to the A1B-CC scenario (averages per decade in millions of cubic meters).</figcaption></figure>

Legend: 121 - Île-de-France; 131 - Champagne-Ardenne; 132 - Picardie; 133 - Haute-Normandie; 134 - Centre; 135 - Basse-Normandie; 136 - Bourgogne; 141 - Nord-Pas-de-Calais; 151 - Lorraine; 152 - Alsace; 153 - Franche-Comté; 162 - Pays de la Loire; 163 - Bretagne; 164 - Poitou-Charentes; 182 - Aquitaine; 183 - Midi-Pyrénées; 184 - Limousin; 192 - Rhône-Alpes; 193 - Auvergne; 201 - Languedoc-Roussillon; 203 - Provence-Alpes-Côte d'Azur; 204 - Corse
<figure><img src="image_12.png" /><figcaption>**Fig. 6.** Regional impact of change in water price on irrigation water demand in the north (on the left) and the south (on the right) of France for three decades, 2011-2020, 2051-2060 and 2091-2100, related to the A1B-CC scenario (averages per decade in millions of cubic meters).</figcaption></figure>

Legend: 121 - Île-de-France; 131 - Champagne-Ardenne; 132 - Picardie; 133 - Haute-Normandie; 134 - Centre; 135 - Basse-Normandie; 136 - Bourgogne; 141 - Nord-Pas-de-Calais; 151 - Lorraine; 152 - Alsace; 153 - Franche-Comté; 162 - Pays de la Loire; 163 - Bretagne; 164 - Poitou-Charentes; 182 - Aquitaine; 183 - Midi-Pyrénées; 184 - Limousin; 192 - Rhône-Alpes; 193 - Auvergne; 201 - Languedoc-Roussillon; 203 - Provence-Alpes-Côte d'Azur; 204 - Corse
<figure><img src="image_14.png" /><figcaption>**Fig.7.** Impact of changes in water price by increasing level from 1 up to 6, on maize activity, respectively with regard to area (million hectares), marketed and on-farm quantity (million tons) and demand for irrigation water (billion cubic meters), from the left column to the right column, distributed over the period 2010-2100 for southern France (top row), northern France (middle row) and the whole of France (bottom row) for the A1B climate projections. Vertical red lines refer to the benchmark (AROPAj baseline results for 2009).</figcaption></figure>
<figure><img src="image_13.png" /><figcaption>**Fig.7.** Impact of changes in water price by increasing level from 1 up to 6, on maize activity, respectively with regard to area (million hectares), marketed and on-farm quantity (million tons) and demand for irrigation water (billion cubic meters), from the left column to the right column, distributed over the period 2010-2100 for southern France (top row), northern France (middle row) and the whole of France (bottom row) for the A1B climate projections. Vertical red lines refer to the benchmark (AROPAj baseline results for 2009).</figcaption></figure>
<figure><img src="image_15.png" /><figcaption>**Fig. 8.** Impact of changes in water price by increasing level from 1 up to 6, on cereal activity (area, marketed and on-farm quantities), concentrated feed, areas of rapeseed and sunflower, grasslands, fallows, and GHG emissions (nitrous oxide, methane and sum of the two greenhouse gas), distributed over the period 2010-2100 for the whole of France (bottom row) for the A1B climate projections. Vertical red lines refer to the benchmark (AROPAj baseline results for 2009).</figcaption></figure>
<figure><img src="image_14.png" /><figcaption>**Fig. 8.** Impact of changes in water price by increasing level from 1 up to 6, on cereal activity (area, marketed and on-farm quantities), concentrated feed, areas of rapeseed and sunflower, grasslands, fallows, and GHGs (nitrous oxide, methane and sum of the two greenhouse gas), distributed over the period 2010-2100 for the whole of France (bottom row) for the A1B climate projections. Vertical red lines refer to the benchmark (AROPAj baseline results for 2009).</figcaption></figure>
References

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Graveline, N., and Mérel P. (2014). "Intensive and extensive margin adjustments to water scarcity in France's Cereal Belt." *European Review of Agricultural Economics* 41(5), 707-743.

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Marshall, E., Aillery M., Malcolm S., and Williams R. (2015). "Agricultural Production under Climate Change: The Potential Impacts of Shifting Regional Water Balances in the United States." *American Journal of Agricultural Economics* 97 (2), 568-588.
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Observation and Statistics Department. *Geography and indicators related to sustainable development*.
Retrieved from [http://geoidd.developpement-durable.gouv.fr/geoclip_stats_o3/#l=fr;v=map1](http://geoidd.developpement-durable.gouv.fr/geoclip_stats_o3/#l=fr;v=map1)

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Supit, I., Van Diepen C. A., Boogaard H. L., Ludwig F., and Baruth B. (2010). "Trend analysis of the water requirements, consumption and deficit of field crops in Europe." *Agricultural and Forest Meteorology* 150(1), 77–88.
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Appendix

<figure><img src="image_16.png" /><figcaption>**Fig. A1.** Summary indicators for precipitations derived from the ARPEGE simulations for the A1B SRES scenario of the IPCC (Pagé et Terray, 2010; Pagé et al., 2010).</figcaption></figure>

<figure><img src="image_17.png" /><figcaption>**Fig. A2.** Summary indicators for temperatures derived from the ARPEGE simulations for the A1B SRES scenario of the IPCC (Pagé et Terray, 2010; Pagé et al., 2010).</figcaption></figure>
Appendix

<figure><img src="image_15.png" /><figcaption>**Fig. A1.** Summary indicators for precipitations derived from the ARPEGE simulations for the A1B SRES scenario of the IPCC (Pagé et Terray, 2010; Pagé et al., 2010).</figcaption></figure>

<figure><img src="image_16.png" /><figcaption>**Fig. A2.** Summary indicators for temperatures derived from the ARPEGE simulations for the A1B SRES scenario of the IPCC (Pagé et Terray, 2010; Pagé et al., 2010).</figcaption></figure>
<figure><img src="image_18.png" /><figcaption>**Fig. A3.** Evolution of water demand in the north “fra1” (on the left) and south (on the right) of France “fra2” for the A1b scenario over period from 2010 to 2100 (averages per decade) by region for the A1B CC scenario.</figcaption></figure>

Legend: 121 - Île-de-France; 131 - Champagne-Ardenne; 132 - Picardie; 133 - Haute-Normandie; 134 - Centre; 135 - Basse-Normandie; 136 - Bourgogne; 141 - Nord-Pas-de-Calais; 151 - Lorraine; 152 - Alsace; 153 - Franche-Comté; 162 - Pays de la Loire; 163 - Bretagne; 164 - Poitou-Charentes; 182 - Aquitaine; 183 - Midi-Pyrénées; 184 - Limousin; 192 - Rhône-Alpes; 193 - Auvergne; 201 - Languedoc-Roussillon; 203 - Provence-Alpes-Côte d'Azur; 204 - Corse.
<figure><img src="image_17.png" /><figcaption>**Fig. A3.** Evolution of water demand in the north “fra1” (on the left) and south (on the right) of France “fra2” for the A1b scenario over period from 2010 to 2100 (averages per decade) by region for the A1B CC scenario.</figcaption></figure>

Legend: 121 - Île-de-France; 131 - Champagne-Ardenne; 132 - Picardie; 133 - Haute-Normandie; 134 - Centre; 135 - Basse-Normandie; 136 - Bourgogne; 141 - Nord-Pas-de-Calais; 151 - Lorraine; 152 - Alsace; 153 - Franche-Comté; 162 - Pays de la Loire; 163 - Bretagne; 164 - Poitou-Charentes; 182 - Aquitaine; 183 - Midi-Pyrénées; 184 - Limousin; 192 - Rhône-Alpes; 193 - Auvergne; 201 - Languedoc-Roussillon; 203 - Provence-Alpes-Côte d'Azur; 204 - Corse.
<figure><img src="image_19.png" /><figcaption>**Fig. A4.** Impact of changes in water price by increasing level from 1 up to 6, respectively on gross margin (top row, billion euros), demand for irrigation water (middle row, billion cubic meters) and demand for N-mineral fertilizer (bottom row, million metric tons), distributed over the period 2010-2100 for France as a whole and for three climate projections (B1, A1B and A2). Vertical red lines refer to the benchmark (AROPAj baseline results for 2009).</figcaption></figure>
<figure><img src="image_18.png" /><figcaption>**Fig. A4.** Impact of changes in water price by increasing level from 1 up to 6, respectively on gross margin (top row, billion euros), demand for irrigation water (middle row, billion cubic meters) and demand for N-mineral fertilizer (bottom row, million metric tons), distributed over the period 2010-2100 for France as a whole and for three climate projections (B1, A1B and A2). Vertical red lines refer to the benchmark (AROPAj baseline results for 2009).</figcaption></figure>
<table><caption>**Table A1:** Regional impact of water price change on demand for irrigation, for three decades in the A1B CC scenario, 2011-2020, 2051-2060 and 2091-2100, expressed as a % compared to demand with 0-change water prices (on grey lines: absolute value averaged per decade of required irrigation in million cubic meters). Baseline prices are from 2009.</caption><thead><tr><th rowspan="2">periods</th><th rowspan="2">increase in base price (%)</th><th colspan="16">Regions</th></tr><tr><th>121</th><th>131</th><th>132</th><th>133</th><th>134</th><th>135</th><th>136</th><th>141</th><th>151</th><th>152</th><th>153</th><th>162</th><th>163</th><th>164</th><th>182</th><th>183</th><th>184</th><th>192</th><th>193</th><th>201</th><th>203</th><th>204</th></tr></thead><tbody><tr><td rowspan="10">2011-2020</td><td>0</td><td>34,0</td><td>121,9</td><td>170,0</td><td>53,8</td><td>279,7</td><td>35,3</td><td>98,3</td><td>104,3</td><td>53,6</td><td>168,9</td><td>40,4</td><td>342,9</td><td>107,8</td><td>291,2</td><td>270,1</td><td>237,9</td><td>12,2</td><td>138,5</td><td>38,4</td><td>33,9</td><td>42,7</td><td>0,1</td></tr><tr><td>25</td><td>-16</td><td>-7</td><td>-14</td><td>-5</td><td>-15</td><td>-15</td><td>-10</td><td>-10</td><td>-10</td><td>-9</td><td>-14</td><td>-5</td><td>-5</td><td>-10</td><td>-7</td><td>-15</td><td>-2</td><td>-11</td><td>-13</td><td>-14</td><td>-3</td><td>0</td></tr><tr><td>50</td><td>-29</td><td>-16</td><td>-25</td><td>-9</td><td>-25</td><td>-27</td><td>-16</td><td>-16</td><td>-18</td><td>-17</td><td>-23</td><td>-11</td><td>-10</td><td>-20</td><td>-12</td><td>-24</td><td>-6</td><td>-20</td><td>-23</td><td>-28</td><td>-6</td><td>-1</td></tr><tr><td>75</td><td>-38</td><td>-24</td><td>-32</td><td>-13</td><td>-33</td><td>-35</td><td>-22</td><td>-21</td><td>-24</td><td>-26</td><td>-30</td><td>-16</td><td>-15</td><td>-26</td><td>-16</td><td>-32</td><td>-9</td><td>-29</td><td>-32</td><td>-36</td><td>-9</td><td>-1</td></tr><tr><td>100</td><td>-45</td><td>-31</td><td>-37</td><td>-17</td><td>-40</td><td>-41</td><td>-26</td><td>-26</td><td>-30</td><td>-34</td><td>-36</td><td>-22</td><td>-19</td><td>-31</td><td>-20</td><td>-40</td><td>-11</td><td>-35</td><td>-39</td><td>-39</td><td>-10</td><td>-1</td></tr><tr><td>150</td><td>-57</td><td>-41</td><td>-45</td><td>-24</td><td>-47</td><td>-47</td><td>-35</td><td>-33</td><td>-40</td><td>-48</td><td>-44</td><td>-33</td><td>-25</td><td>-40</td><td>-25</td><td>-50</td><td>-20</td><td>-44</td><td>-51</td><td>-42</td><td>-14</td><td>-2</td></tr><tr><td>200</td><td>-64</td><td>-23</td><td>-50</td><td>-30</td><td>-52</td><td>-53</td><td>-41</td><td>-39</td><td>-48</td><td>-61</td><td>-51</td><td>-42</td><td>-32</td><td>-44</td><td>-30</td><td>-57</td><td>-34</td><td>-50</td><td>-60</td><td>-45</td><td>-16</td><td>-2</td></tr><tr><td>250</td><td>-68</td><td>-30</td><td>-55</td><td>-34</td><td>-57</td><td>-58</td><td>-47</td><td>-44</td><td>-55</td><td>-70</td><td>-57</td><td>-54</td><td>-35</td><td>-49</td><td>-35</td><td>-62</td><td>-43</td><td>-56</td><td>-66</td><td>-48</td><td>-18</td><td>-2</td></tr><tr><td>500</td><td>-81</td><td>-52</td><td>-70</td><td>-51</td><td>-71</td><td>-73</td><td>-64</td><td>-65</td><td>-77</td><td>-88</td><td>-76</td><td>-72</td><td>-55</td><td>-64</td><td>-54</td><td>-80</td><td>-64</td><td>-72</td><td>-79</td><td>-55</td><td>-23</td><td>-6</td></tr><tr><td>1000</td><td>-88</td><td>-88</td><td>-90</td><td>-70</td><td>-80</td><td>-84</td><td>-80</td><td>-91</td><td>-93</td><td>-95</td><td>-93</td><td>-87</td><td>-73</td><td>-81</td><td>-77</td><td>-93</td><td>-81</td><td>-88</td><td>-89</td><td>-61</td><td>-33</td><td>-22</td></tr><tr><td rowspan="10">2051-2060</td><td>0</td><td>70,0</td><td>157,7</td><td>190,3</td><td>59,9</td><td>359,8</td><td>57,9</td><td>98,5</td><td>108,3</td><td>30,0</td><td>144,9</td><td>31,7</td><td>374,9</td><td>192,8</td><td>385,0</td><td>298,5</td><td>317,3</td><td>13,6</td><td>120,4</td><td>51,0</td><td>35,6</td><td>73,7</td><td>0,1</td></tr><tr><td>25</td><td>-14</td><td>-9</td><td>-11</td><td>-6</td><td>-15</td><td>-12</td><td>-7</td><td>-7</td><td>-13</td><td>-12</td><td>-14</td><td>-7</td><td>-8</td><td>-6</td><td>-9</td><td>-10</td><td>-6</td><td>-10</td><td>-13</td><td>-12</td><td>-3</td><td>0</td></tr><tr><td>50</td><td>-19</td><td>-17</td><td>-20</td><td>-12</td><td>-25</td><td>-23</td><td>-13</td><td>-12</td><td>-26</td><td>-22</td><td>-24</td><td>-13</td><td>-14</td><td>-13</td><td>-17</td><td>-16</td><td>-14</td><td>-18</td><td>-24</td><td>-17</td><td>-5</td><td>0</td></tr><tr><td>75</td><td>-32</td><td>-23</td><td>-26</td><td>-17</td><td>-33</td><td>-28</td><td>-20</td><td>-17</td><td>-34</td><td>-30</td><td>-36</td><td>-18</td><td>-20</td><td>-20</td><td>-24</td><td>-22</td><td>-19</td><td>-26</td><td>-33</td><td>-21</td><td>-8</td><td>0</td></tr><tr><td>100</td><td>-43</td><td>-29</td><td>-32</td><td>-21</td><td>-40</td><td>-33</td><td>-24</td><td>-21</td><td>-39</td><td>-38</td><td>-42</td><td>-23</td><td>-24</td><td>-25</td><td>-30</td><td>-28</td><td>-24</td><td>-31</td><td>-40</td><td>-24</td><td>-10</td><td>0</td></tr><tr><td>150</td><td>-58</td><td>-37</td><td>-44</td><td>-27</td><td>-51</td><td>-42</td><td>-30</td><td>-29</td><td>-46</td><td>-51</td><td>-52</td><td>-32</td><td>-32</td><td>-33</td><td>-40</td><td>-38</td><td>-32</td><td>-39</td><td>-50</td><td>-30</td><td>-14</td><td>0</td></tr><tr><td>200</td><td>-66</td><td>-44</td><td>-51</td><td>-32</td><td>-59</td><td>-49</td><td>-35</td><td>-35</td><td>-51</td><td>-62</td><td>-60</td><td>-41</td><td>-39</td><td>-40</td><td>-47</td><td>-46</td><td>-38</td><td>-44</td><td>-57</td><td>-34</td><td>-17</td><td>0</td></tr><tr><td>250</td><td>-71</td><td>-50</td><td>-57</td><td>-36</td><td>-64</td><td>-53</td><td>-41</td><td>-41</td><td>-55</td><td>-78</td><td>-63</td><td>-50</td><td>-45</td><td>-45</td><td>-53</td><td>-53</td><td>-43</td><td>-48</td><td>-63</td><td>-37</td><td>-20</td><td>0</td></tr><tr><td>500</td><td>-84</td><td>-70</td><td>-74</td><td>-50</td><td>-79</td><td>-68</td><td>-58</td><td>-65</td><td>-67</td><td>-89</td><td>-81</td><td>-71</td><td>-63</td><td>-61</td><td>-70</td><td>-72</td><td>-69</td><td>-63</td><td>-77</td><td>-47</td><td>-36</td><td>-1</td></tr><tr><td>1000</td><td>-93</td><td>-86</td><td>-91</td><td>-63</td><td>-90</td><td>-81</td><td>-76</td><td>-88</td><td>-82</td><td>-94</td><td>-91</td><td>-83</td><td>-81</td><td>-77</td><td>-85</td><td>-88</td><td>-82</td><td>-81</td><td>-88</td><td>-60</td><td>-75</td><td>-12</td></tr><tr><td rowspan="10">2091-2100</td><td>0</td><td>119,1</td><td>148,9</td><td>296,8</td><td>85,7</td><td>646,1</td><td>108,5</td><td>113,5</td><td>215,1</td><td>72,8</td><td>180,6</td><td>53,7</td><td>459,5</td><td>291,8</td><td>429,1</td><td>319,2</td><td>358,3</td><td>22,2</td><td>175,5</td><td>68,1</td><td>38,4</td><td>41,6</td><td>0,3</td></tr><tr><td>25</td><td>-18</td><td>-9</td><td>-18</td><td>-11</td><td>-16</td><td>-11</td><td>-10</td><td>-8</td><td>-12</td><td>-10</td><td>-8</td><td>-4</td><td>-9</td><td>-8</td><td>-13</td><td>-5</td><td>-16</td><td>-11</td><td>-8</td><td>-3</td><td>-1</td></tr><tr><td>50</td><td>-33</td><td>-24</td><td>-27</td><td>-22</td><td>-24</td><td>-24</td><td>-20</td><td>-15</td><td>-22</td><td>-20</td><td>-30</td><td>-18</td><td>-9</td><td>-16</td><td>-15</td><td>-21</td><td>-9</td><td>-27</td><td>-20</td><td>-14</td><td>-5</td><td>-2</td></tr><tr><td>75</td><td>-42</td><td>-29</td><td>-31</td><td>-28</td><td>-31</td><td>-36</td><td>-27</td><td>-21</td><td>-30</td><td>-29</td><td>-36</td><td>-26</td><td>-14</td><td>-25</td><td>-20</td><td>-30</td><td>-13</td><td>-34</td><td>-27</td><td>-27</td><td>-6</td><td>-3</td></tr><tr><td>100</td><td>-45</td><td>-33</td><td>-40</td><td>-34</td><td>-37</td><td>-42</td><td>-34</td><td>-27</td><td>-36</td><td>-37</td><td>-41</td><td>-38</td><td>-18</td><td>-31</td><td>-26</td><td>-36</td><td>-18</td><td>-40</td><td>-35</td><td>-23</td><td>-7</td><td>-4</td></tr><tr><td>150</td><td>-57</td><td>-40</td><td>-48</td><td>-41</td><td>-48</td><td>-52</td><td>-43</td><td>-35</td><td>-47</td><td>-51</td><td>-48</td><td>-49</td><td>-26</td><td>-39</td><td>-34</td><td>-45</td><td>-27</td><td>-50</td><td>-46</td><td>-32</td><td>-9</td><td>-6</td></tr><tr><td>200</td><td>-75</td><td>-45</td><td>-53</td><td>-47</td><td>-53</td><td>-58</td><td>-49</td><td>-43</td><td>-55</td><td>-63</td><td>-53</td><td>-55</td><td>-32</td><td>-46</td><td>-40</td><td>-52</td><td>-37</td><td>-55</td><td>-55</td><td>-44</td><td>-10</td><td>-7</td></tr><tr><td>250</td><td>-80</td><td>-49</td><td>-57</td><td>-54</td><td>-60</td><td>-62</td><td>-52</td><td>-48</td><td>-62</td><td>-72</td><td>-58</td><td>-59</td><td>-37</td><td>-50</td><td>-45</td><td>-59</td><td>-47</td><td>-61</td><td>-59</td><td>-46</td><td>-12</td><td>-8</td></tr><tr><td>500</td><td>-88</td><td>-62</td><td>-72</td><td>-66</td><td>-77</td><td>-73</td><td>-70</td><td>-66</td><td>-79</td><td>-87</td><td>-77</td><td>-77</td><td>-61</td><td>-69</td><td>-63</td><td>-79</td><td>-73</td><td>-69</td><td>-78</td><td>-53</td><td>-28</td><td>-15</td></tr><tr><td>1000</td><td>-94</td><td>-75</td><td>-93</td><td>-77</td><td>-91</td><td>-84</td><td>-83</td><td>-87</td><td>-90</td><td>-96</td><td>-92</td><td>-87</td><td>-82</td><td>-86</td><td>-79</td><td>-93</td><td>-90</td><td>-84</td><td>-92</td><td>-63</td><td>-56</td><td>-31</td></tr></tbody></table>

Legend:121 - Île-de-France; 131 - Champagne-Ardenne; 132 - Picardie; 133 - Haute-Normandie; 134 - Centre; 135 - Basse Normandie; 136 - Bourgogne; 141 - Nord-Pas-de-Calais; 151 - Lorraine; 152 - Alsace; 153 - Franche-Comté; 162 - Pays de la Loire; 163 - Bretagne; 164 - Poitou-Charentes; 182 - Aquitaine; 183 - Midi-Pyrénées; 184 - Limousin; 192 - Rhône-Alpes; 193 - Auvergne; 201 - Languedoc-Roussillon; 203 - Provence-Alpes-Côte d'Azur; 204 - Corse.
<table><caption>**Table A1:** Regional impact of water price change on demand for irrigation, for three decades in the A1B CC scenario, 2011-2020, 2051-2060 and 2091-2100, expressed as a % compared to demand with 0-change water prices (on grey lines: absolute value averaged per decade of required irrigation in million cubic meters). Baseline prices are from 2009.</caption><thead><tr><th rowspan="2">periods</th><th rowspan="2">increase in base price (%)</th><th colspan="15">Regions</th></tr><tr><th>121</th><th>131</th><th>132</th><th>133</th><th>134</th><th>135</th><th>136</th><th>141</th><th>151</th><th>152</th><th>153</th><th>162</th><th>163</th><th>164</th><th>182</th><th>183</th><th>184</th><th>192</th><th>193</th><th>201</th><th>203</th><th>204</th></tr></thead><tbody><tr><td rowspan="10">2011-2020</td><td>0</td><td>34,0</td><td>121,9</td><td>170,0</td><td>53,8</td><td>279,7</td><td>35,3</td><td>98,3</td><td>104,3</td><td>53,6</td><td>168,9</td><td>40,4</td><td>342,9</td><td>107,8</td><td>291,2</td><td>270,1</td><td>237,9</td><td>12,2</td><td>138,5</td><td>38,4</td><td>33,9</td><td>42,7</td><td>0,1</td></tr><tr><td>25</td><td>-16</td><td>-7</td><td>-14</td><td>-5</td><td>-15</td><td>-15</td><td>-10</td><td>-10</td><td>-10</td><td>-9</td><td>-14</td><td>-5</td><td>-5</td><td>-10</td><td>-7</td><td>-15</td><td>-2</td><td>-11</td><td>-13</td><td>-14</td><td>-3</td><td>0</td></tr><tr><td>50</td><td>-29</td><td>-16</td><td>-25</td><td>-9</td><td>-25</td><td>-27</td><td>-16</td><td>-16</td><td>-18</td><td>-17</td><td>-23</td><td>-11</td><td>-10</td><td>-20</td><td>-12</td><td>-24</td><td>-6</td><td>-20</td><td>-23</td><td>-28</td><td>-6</td><td>-1</td></tr><tr><td>75</td><td>-38</td><td>-24</td><td>-32</td><td>-13</td><td>-33</td><td>-35</td><td>-22</td><td>-21</td><td>-24</td><td>-26</td><td>-30</td><td>-16</td><td>-15</td><td>-26</td><td>-16</td><td>-32</td><td>-9</td><td>-29</td><td>-32</td><td>-36</td><td>-9</td><td>-1</td></tr><tr><td>100</td><td>-45</td><td>-31</td><td>-37</td><td>-17</td><td>-40</td><td>-41</td><td>-26</td><td>-26</td><td>-30</td><td>-34</td><td>-36</td><td>-22</td><td>-19</td><td>-31</td><td>-20</td><td>-40</td><td>-11</td><td>-35</td><td>-39</td><td>-39</td><td>-10</td><td>-1</td></tr><tr><td>150</td><td>-57</td><td>-41</td><td>-45</td><td>-24</td><td>-47</td><td>-47</td><td>-35</td><td>-33</td><td>-40</td><td>-48</td><td>-44</td><td>-33</td><td>-25</td><td>-40</td><td>-25</td><td>-50</td><td>-20</td><td>-44</td><td>-51</td><td>-42</td><td>-14</td><td>-2</td></tr><tr><td>200</td><td>-64</td><td>-23</td><td>-50</td><td>-30</td><td>-52</td><td>-53</td><td>-41</td><td>-39</td><td>-48</td><td>-61</td><td>-51</td><td>-42</td><td>-32</td><td>-44</td><td>-30</td><td>-57</td><td>-34</td><td>-50</td><td>-60</td><td>-45</td><td>-16</td><td>-2</td></tr><tr><td>250</td><td>-68</td><td>-30</td><td>-55</td><td>-34</td><td>-57</td><td>-58</td><td>-47</td><td>-44</td><td>-55</td><td>-70</td><td>-57</td><td>-54</td><td>-35</td><td>-49</td><td>-35</td><td>-62</td><td>-43</td><td>-56</td><td>-66</td><td>-48</td><td>-18</td><td>-2</td></tr><tr><td>500</td><td>-81</td><td>-52</td><td>-70</td><td>-51</td><td>-71</td><td>-73</td><td>-64</td><td>-65</td><td>-77</td><td>-88</td><td>-76</td><td>-72</td><td>-55</td><td>-64</td><td>-54</td><td>-80</td><td>-64</td><td>-72</td><td>-79</td><td>-55</td><td>-23</td><td>-6</td></tr><tr><td>1000</td><td>-88</td><td>-88</td><td>-90</td><td>-70</td><td>-80</td><td>-84</td><td>-80</td><td>-91</td><td>-93</td><td>-95</td><td>-93</td><td>-87</td><td>-73</td><td>-81</td><td>-77</td><td>-93</td><td>-81</td><td>-88</td><td>-89</td><td>-61</td><td>-33</td><td>-22</td></tr><tr><td rowspan="10">2051-2060</td><td>0</td><td>70,0</td><td>157,7</td><td>190,3</td><td>59,9</td><td>359,8</td><td>57,9</td><td>98,5</td><td>108,3</td><td>30,0</td><td>144,9</td><td>31,7</td><td>374,9</td><td>192,8</td><td>385,0</td><td>298,5</td><td>317,3</td><td>13,6</td><td>120,4</td><td>51,0</td><td>35,6</td><td>73,7</td><td>0,1</td></tr><tr><td>25</td><td>-14</td><td>-9</td><td>-11</td><td>-6</td><td>-15</td><td>-12</td><td>-7</td><td>-7</td><td>-13</td><td>-12</td><td>-14</td><td>-7</td><td>-8</td><td>-6</td><td>-9</td><td>-10</td><td>-6</td><td>-10</td><td>-13</td><td>-12</td><td>-3</td><td>0</td></tr><tr><td>50</td><td>-19</td><td>-17</td><td>-20</td><td>-12</td><td>-25</td><td>-23</td><td>-13</td><td>-12</td><td>-26</td><td>-22</td><td>-24</td><td>-13</td><td>-14</td><td>-13</td><td>-17</td><td>-16</td><td>-14</td><td>-18</td><td>-24</td><td>-17</td><td>-5</td><td>0</td></tr><tr><td>75</td><td>-32</td><td>-23</td><td>-26</td><td>-17</td><td>-33</td><td>-28</td><td>-20</td><td>-17</td><td>-34</td><td>-30</td><td>-36</td><td>-18</td><td>-20</td><td>-20</td><td>-24</td><td>-22</td><td>-19</td><td>-26</td><td>-33</td><td>-21</td><td>-8</td><td>0</td></tr><tr><td>100</td><td>-43</td><td>-29</td><td>-32</td><td>-21</td><td>-40</td><td>-33</td><td>-24</td><td>-21</td><td>-39</td><td>-38</td><td>-42</td><td>-23</td><td>-24</td><td>-25</td><td>-30</td><td>-28</td><td>-24</td><td>-31</td><td>-40</td><td>-24</td><td>-10</td><td>0</td></tr><tr><td>150</td><td>-58</td><td>-37</td><td>-44</td><td>-27</td><td>-51</td><td>-42</td><td>-30</td><td>-29</td><td>-46</td><td>-51</td><td>-52</td><td>-32</td><td>-32</td><td>-33</td><td>-40</td><td>-38</td><td>-32</td><td>-39</td><td>-50</td><td>-30</td><td>-14</td><td>0</td></tr><tr><td>200</td><td>-66</td><td>-44</td><td>-51</td><td>-32</td><td>-59</td><td>-49</td><td>-35</td><td>-35</td><td>-51</td><td>-62</td><td>-60</td><td>-41</td><td>-39</td><td>-40</td><td>-47</td><td>-46</td><td>-38</td><td>-44</td><td>-57</td><td>-34</td><td>-17</td><td>0</td></tr><tr><td>250</td><td>-71</td><td>-50</td><td>-57</td><td>-36</td><td>-64</td><td>-53</td><td>-41</td><td>-41</td><td>-55</td><td>-78</td><td>-63</td><td>-50</td><td>-45</td><td>-45</td><td>-53</td><td>-53</td><td>-43</td><td>-48</td><td>-63</td><td>-37</td><td>-20</td><td>0</td></tr><tr><td>500</td><td>-84</td><td>-70</td><td>-74</td><td>-50</td><td>-79</td><td>-68</td><td>-58</td><td>-65</td><td>-67</td><td>-89</td><td>-81</td><td>-71</td><td>-63</td><td>-61</td><td>-70</td><td>-72</td><td>-69</td><td>-63</td><td>-77</td><td>-47</td><td>-36</td><td>-1</td></tr><tr><td>1000</td><td>-93</td><td>-86</td><td>-91</td><td>-63</td><td>-90</td><td>-81</td><td>-76</td><td>-88</td><td>-82</td><td>-94</td><td>-91</td><td>-83</td><td>-81</td><td>-77</td><td>-85</td><td>-88</td><td>-82</td><td>-81</td><td>-88</td><td>-60</td><td>-75</td><td>-12</td></tr><tr><td rowspan="10">2091-2100</td><td>0</td><td>119,1</td><td>148,9</td><td>296,8</td><td>85,7</td><td>646,1</td><td>108,5</td><td>113,5</td><td>215,1</td><td>72,8</td><td>180,6</td><td>53,7</td><td>459,5</td><td>291,8</td><td>429,1</td><td>319,2</td><td>358,3</td><td>22,2</td><td>175,5</td><td>68,1</td><td>38,4</td><td>41,6</td><td>0,3</td></tr><tr><td>25</td><td>-18</td><td>-9</td><td>-18</td><td>-11</td><td>-16</td><td>-11</td><td>-10</td><td>-8</td><td>-12</td><td>-10</td><td>-8</td><td>-4</td><td>-9</td><td>-8</td><td>-13</td><td>-5</td><td>-16</td><td>-11</td><td>-8</td><td>-3</td><td>-1</td></tr><tr><td>50</td><td>-33</td><td>-24</td><td>-27</td><td>-22</td><td>-24</td><td>-24</td><td>-20</td><td>-15</td><td>-22</td><td>-20</td><td>-30</td><td>-18</td><td>-9</td><td>-16</td><td>-15</td><td>-21</td><td>-9</td><td>-27</td><td>-20</td><td>-14</td><td>-5</td><td>-2</td></tr><tr><td>75</td><td>-42</td><td>-29</td><td>-31</td><td>-28</td><td>-31</td><td>-36</td><td>-27</td><td>-21</td><td>-30</td><td>-29</td><td>-36</td><td>-26</td><td>-14</td><td>-25</td><td>-20</td><td>-30</td><td>-13</td><td>-34</td><td>-27</td><td>-27</td><td>-6</td><td>-3</td></tr><tr><td>100</td><td>-45</td><td>-33</td><td>-40</td><td>-34</td><td>-37</td><td>-42</td><td>-34</td><td>-27</td><td>-36</td><td>-37</td><td>-41</td><td>-38</td><td>-18</td><td>-31</td><td>-26</td><td>-36</td><td>-18</td><td>-40</td><td>-35</td><td>-23</td><td>-7</td><td>-4</td></tr><tr><td>150</td><td>-57</td><td>-40</td><td>-48</td><td>-41</td><td>-48</td><td>-52</td><td>-43</td><td>-35</td><td>-47</td><td>-51</td><td>-48</td><td>-49</td><td>-26</td><td>-39</td><td>-34</td><td>-45</td><td>-27</td><td>-50</td><td>-46</td><td>-32</td><td>-9</td><td>-6</td></tr><tr><td>200</td><td>-75</td><td>-45</td><td>-53</td><td>-47</td><td>-53</td><td>-58</td><td>-49</td><td>-43</td><td>-55</td><td>-63</td><td>-53</td><td>-55</td><td>-32</td><td>-46</td><td>-40</td><td>-52</td><td>-37</td><td>-55</td><td>-55</td><td>-44</td><td>-10</td><td>-7</td></tr><tr><td>250</td><td>-80</td><td>-49</td><td>-57</td><td>-54</td><td>-60</td><td>-62</td><td>-52</td><td>-48</td><td>-62</td><td>-72</td><td>-58</td><td>-59</td><td>-37</td><td>-50</td><td>-45</td><td>-59</td><td>-47</td><td>-61</td><td>-59</td><td>-46</td><td>-12</td><td>-8</td></tr><tr><td>500</td><td>-88</td><td>-62</td><td>-72</td><td>-66</td><td>-77</td><td>-73</td><td>-70</td><td>-66</td><td>-79</td><td>-87</td><td>-77</td><td>-77</td><td>-61</td><td>-69</td><td>-63</td><td>-79</td><td>-73</td><td>-69</td><td>-78</td><td>-53</td><td>-28</td><td>-15</td></tr><tr><td>1000</td><td>-94</td><td>-75</td><td>-93</td><td>-77</td><td>-91</td><td>-84</td><td>-83</td><td>-87</td><td>-90</td><td>-96</td><td>-92</td><td>-87</td><td>-82</td><td>-86</td><td>-79</td><td>-93</td><td>-90</td><td>-84</td><td>-92</td><td>-63</td><td>-56</td><td>-31</td></tr></tbody><tfoot><tr><td colspan="2">-10%;0%</td><td colspan="2">-10%;-20%</td><td colspan="2">-30%,-20%</td><td colspan="2">-30%;-50%</td><td colspan="2">-50%;-75%</td><td colspan="2">&lt;-75%</td><td colspan="2"></td><td colspan="2"></td><td colspan="2"></td><td colspan="2"></td><td colspan="2"></td><td colspan="2"></td></tr></tfoot></table>

Legend:121 - Île-de-France; 131 - Champagne-Ardenne; 132 - Picardie; 133 - Haute-Normandie; 134 - Centre; 135 - Basse Normandie; 136 - Bourgogne; 141 - Nord-Pas-de-Calais; 151 - Lorraine; 152 - Alsace; 153 - Franche-Comté; 162 - Pays de la Loire; 163 - Bretagne; 164 - Poitou-Charentes; 182 - Aquitaine; 183 - Midi-Pyrénées; 184 - Limousin; 192 - Rhône-Alpes; 193 - Auvergne; 201 - Languedoc-Roussillon; 203 - Provence-Alpes-Côte d'Azur; 204 - Corse.
<figure><img src="image_20.png" /></figure>

**Fig. A5.** Impact of changes in water price by increasing level from 1 up to 6, on wheat activity, respectively with regard to area (million hectares), marketed and on-farm quantity (million tons) and demand for irrigation water (billion cubic meters), from the left column to the right column, distributed over the period 2010-2100 for southern France (top row), northern France (middle row) and the whole of France (bottom row) for the A1B climate projections. Vertical red lines refer to the benchmark (AROPAj baseline results for 2009).
<figure><img src="image_19.png" /></figure>

**Fig. A5.** Impact of changes in water price by increasing level from 1 up to 6, on wheat activity, respectively with regard to area (million hectares), marketed and on-farm quantity (million tons) and demand for irrigation water (billion cubic meters), from the left column to the right column, distributed over the period 2010-2100 for southern France (top row), northern France (middle row) and the whole of France (bottom row) for the A1B climate projections. Vertical red lines refer to the benchmark (AROPAj baseline results for 2009).