# The European agro-economic model AROPAj

Pierre-Alain Jayet, Athanasios Petsakos, Raja Chakir, Anna Lungarska, Stéphane De Cara, Elvire Petel, Pierre Humblot, Caroline Godard, David Leclère, Pierre Cantelaube, et al.

► To cite this version:

Pierre-Alain Jayet, Athanasios Petsakos, Raja Chakir, Anna Lungarska, Stéphane De Cara, et al. The European agro-economic model AROPAj. INRAE-PSAE. 2023. [hal-04109872v3](https://hal.inrae.fr/hal-04109872v3)

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https://hal.inrae.fr/hal-04109872v3

Submitted on 28 Aug 2023

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Distributed under a Creative Commons Attribution 4.0 International License
# The European agro-economic model AROPAj

Pierre-Alain Jayet, Athanasios Petsakos, Raja Chakir, Anna Lungarska, Stéphane De Cara, Elvire Petel, Pierre Humblot, Caroline Godard, David Leclère, Pierre Cantelaube, et al.

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

## To cite this version:

Pierre-Alain Jayet, Athanasios Petsakos, Raja Chakir, Anna Lungarska, Stéphane De Cara, et al. The European agro-economic model AROPAj. INRAE-PSAE. 2025, 220 p. hal-04109872v4

HAL Id: hal-04109872

https://hal.inrae.fr/hal-04109872v4

Submitted on 4 Sep 2025

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_2.png" /></figure>

Distributed under a Creative Commons Attribution 4.0 International License
The European agro-economic model AROPAj

Pierre-Alain Jayet Athanasios Petsakos Raja Chakir
Anna Lungarska Stéphane De Cara Elvire Petel
Pierre Humblot Caroline Godard David Leclère
Pierre Cantelaube Cyril Bourgeois Mélissa Clodic
Laure Bamière Nosra Ben Fradj Parisa Aghajanzadeh-Darzi
Gaspard Dumollard Ancuţa Isbăşoiu Juliette Adrian
Gregory Pilchak Myriam Bounaffaa Delphine Barberis
Coline Assaiante Maxime Ollier Loïc Henry
Alessandro Florio Ines Chiadmi Eva Gossiaux
Erica Ramirez Maxence Gérard Julie Reineix
Olga Zuravel Lisa Baldi Mingzhu Weng

PSAE - INRAE-AgroParisTech - Université Paris-Saclay
22 place de l'agronomie, F - 91220 Palaiseau

https://doi.org/10.17180/nxw3-3537

<2023/08/28 14:46:47>
The European agro-economic model AROPAj

Pierre-Alain Jayet Athanasios Petsakos Raja Chakir
Anna Lungarska Stéphane De Cara Elvire Petel
Pierre Humblot Caroline Godard David Leclère
Pierre Cantelaube Cyril Bourgeois Mélissa Clodic
Laure Bamière Nosra Ben Fradj Parisa Aghajanzadeh-Darzi
Gaspard Dumollard Ancuţa Isbăşoiu Juliette Adrian
Gregory Pilchak Myriam Bounaffaa Delphine Barberis
Coline Assaiante Maxime Ollier Loïc Henry
Alessandro Florio Ines Chiadmi Eva Gossiaux
Erica Ramirez Maxence Gérard Julie Reineix
Olga Zuravel Lisa Baldi Mingzhu Weng
Robin Nizou Yasmine Derbal

PSAE - INRAE-AgroParisTech - Université Paris-Saclay
22 place de l'agronomie, F - 91220 Palaiseau

https://doi.org/10.17180/nxw3-3537

<2025/09/02 16:33:25>
# Contents

<table><tr><td>1</td><td>Introduction</td><td>5</td></tr><tr><td>1.1</td><td>Objectives</td><td>5</td></tr><tr><td>1.2</td><td>State of the art and early future</td><td>7</td></tr><tr><td>2</td><td>AROPAj among other agricultural economic models</td><td>12</td></tr><tr><td>2.1</td><td>MP models vs macro-econometric models</td><td>12</td></tr><tr><td>2.2</td><td>One side of the market in agricultural models</td><td>12</td></tr><tr><td>2.3</td><td>LP vs NLP models</td><td>13</td></tr><tr><td>3</td><td>Input data</td><td>17</td></tr><tr><td>3.1</td><td>The FADN at the core of the farming system representation</td><td>17</td></tr><tr><td>3.2</td><td>Other sources required by some AROPAj modules</td><td>18</td></tr><tr><td>3.2.1</td><td>Data concerning land use and land cover</td><td>19</td></tr><tr><td>3.2.2</td><td>The European Soil Database (ESDB v2.0)</td><td>19</td></tr><tr><td>3.2.3</td><td>Digital Elevation Model (DEM)</td><td>19</td></tr><tr><td>3.2.4</td><td>Climate</td><td>19</td></tr><tr><td>3.2.5</td><td>IPCC guidelines</td><td>20</td></tr><tr><td>3.3</td><td>Data related to other models</td><td>20</td></tr><tr><td>3.3.1</td><td>STICS</td><td>20</td></tr><tr><td>3.3.2</td><td>PaSim</td><td>20</td></tr><tr><td>4</td><td>Architecture of the modelling framework</td><td>22</td></tr><tr><td>4.1</td><td>Overall technical structure of the model</td><td>23</td></tr><tr><td>4.2</td><td>Model blocks in detail</td><td>24</td></tr><tr><td>4.2.1</td><td>Indices and parameters</td><td>25</td></tr><tr><td>4.2.2</td><td>Activities operating in the model</td><td>37</td></tr><tr><td>4.2.3</td><td>The objective function and constraints</td><td>40</td></tr><tr><td>4.2.4</td><td>CAP implementation</td><td>53</td></tr><tr><td>4.2.5</td><td>Greenhouse gas emissions</td><td>62</td></tr><tr><td>4.2.6</td><td>Nitrogen</td><td>74</td></tr><tr><td>4.2.7</td><td>Water</td><td>77</td></tr><tr><td>4.3</td><td>Non linearities within the LP framework</td><td>77</td></tr><tr><td>5</td><td>Typology and farming system clustering</td><td>80</td></tr><tr><td>5.1</td><td>Clustering methodology</td><td>80</td></tr><tr><td>5.2</td><td>Farm groups throughout the AROPAj versions</td><td>83</td></tr><tr><td>6</td><td>Parameter estimation</td><td>88</td></tr><tr><td>6.1</td><td>Variable costs</td><td>88</td></tr><tr><td>6.1.1</td><td>Estimation of activity variable costs</td><td>88</td></tr><tr><td>6.1.2</td><td>Implementation details for cost estimating</td><td>90</td></tr><tr><td>6.2</td><td>Parameters estimating for farm groups</td><td>94</td></tr></table>
# Contents

<table><tr><td>1</td><td>Introduction</td><td>7</td></tr><tr><td>1.1</td><td>Objectives</td><td>7</td></tr><tr><td>1.2</td><td>State of the art and early future</td><td>9</td></tr><tr><td>2</td><td>AROPAj among other agricultural economic models</td><td>14</td></tr><tr><td>2.1</td><td>MP models vs macro-econometric models</td><td>14</td></tr><tr><td>2.2</td><td>One side of the market in agricultural models</td><td>14</td></tr><tr><td>2.3</td><td>LP vs NLP models</td><td>15</td></tr><tr><td>3</td><td>Input data</td><td>19</td></tr><tr><td>3.1</td><td>The FADN at the core of the farming system representation</td><td>19</td></tr><tr><td>3.2</td><td>Other sources required by some AROPAj modules</td><td>20</td></tr><tr><td>3.2.1</td><td>Data concerning land use and land cover</td><td>21</td></tr><tr><td>3.2.2</td><td>The European Soil Database (ESDB v2.0)</td><td>21</td></tr><tr><td>3.2.3</td><td>Digital Elevation Model (DEM)</td><td>21</td></tr><tr><td>3.2.4</td><td>Climate</td><td>21</td></tr><tr><td>3.2.5</td><td>IPCC guidelines</td><td>22</td></tr><tr><td>3.3</td><td>Data related to other models</td><td>22</td></tr><tr><td>3.3.1</td><td>STICS</td><td>22</td></tr><tr><td>3.3.2</td><td>PaSim</td><td>22</td></tr><tr><td>4</td><td>Architecture of the modelling framework</td><td>24</td></tr><tr><td>4.1</td><td>Overall technical structure of the model</td><td>25</td></tr><tr><td>4.2</td><td>Model blocks in detail</td><td>26</td></tr><tr><td>4.2.1</td><td>Indices and parameters</td><td>27</td></tr><tr><td>4.2.2</td><td>Activities operating in the model</td><td>39</td></tr><tr><td>4.2.3</td><td>The objective function and constraints</td><td>43</td></tr><tr><td>4.2.4</td><td>CAP implementation</td><td>58</td></tr><tr><td>4.2.5</td><td>Greenhouse gas emissions</td><td>66</td></tr><tr><td>4.2.6</td><td>Nitrogen</td><td>78</td></tr><tr><td>4.2.7</td><td>Water</td><td>81</td></tr><tr><td>4.2.8</td><td>Biogas</td><td>81</td></tr><tr><td>4.2.9</td><td>Cover crops</td><td>82</td></tr><tr><td>4.3</td><td>Non linearities within the LP framework</td><td>82</td></tr><tr><td>5</td><td>Typology and farming system clustering</td><td>85</td></tr><tr><td>5.1</td><td>Clustering methodology</td><td>85</td></tr><tr><td>5.2</td><td>Farm groups throughout the AROPAj versions</td><td>88</td></tr></table>
<table>
  <tbody>
    <tr>
      <td>7</td>
      <td>Calibration of the AROPAj model</td>
      <td>97</td>
    </tr>
    <tr>
      <td>8</td>
      <td>Spatialization of AROPAj outputs</td>
      <td>103</td>
    </tr>
    <tr>
      <td>8.1</td>
      <td>Disaggregation approach in spatial econometrics devoted to crop location</td>
      <td>103</td>
    </tr>
    <tr>
      <td>8.1.1</td>
      <td>The land use model</td>
      <td>103</td>
    </tr>
    <tr>
      <td>8.1.2</td>
      <td>The disaggregation model: the Generalized Cross Entropy approach</td>
      <td>103</td>
    </tr>
    <tr>
      <td>8.2</td>
      <td>Method and process implementation</td>
      <td>105</td>
    </tr>
    <tr>
      <td>8.2.1</td>
      <td>Crop location estimates at a fine resolution level</td>
      <td>105</td>
    </tr>
    <tr>
      <td>8.2.2</td>
      <td>Estimation of probabilities for farm types</td>
      <td>107</td>
    </tr>
    <tr>
      <td>8.3</td>
      <td>Application</td>
      <td>110</td>
    </tr>
    <tr>
      <td>9</td>
      <td>Models linkage</td>
      <td>112</td>
    </tr>
    <tr>
      <td>9.1</td>
      <td>STICS</td>
      <td>112</td>
    </tr>
    <tr>
      <td>9.1.1</td>
      <td>N to yield functions</td>
      <td>113</td>
    </tr>
    <tr>
      <td>9.1.2</td>
      <td>N to emission functions</td>
      <td>114</td>
    </tr>
    <tr>
      <td>9.1.3</td>
      <td>ArTiX</td>
      <td>115</td>
    </tr>
    <tr>
      <td>9.2</td>
      <td>Carbo-PRO</td>
      <td>115</td>
    </tr>
    <tr>
      <td>9.2.1</td>
      <td>Organic nitrogen sources</td>
      <td>116</td>
    </tr>
    <tr>
      <td>9.2.2</td>
      <td>Carbo-PRO</td>
      <td>120</td>
    </tr>
    <tr>
      <td>9.3</td>
      <td>PaSim</td>
      <td>120</td>
    </tr>
    <tr>
      <td>9.4</td>
      <td>MODCOU</td>
      <td>121</td>
    </tr>
    <tr>
      <td>9.5</td>
      <td>GLOBIOM</td>
      <td>126</td>
    </tr>
    <tr>
      <td>9.6</td>
      <td>GeoMIRET</td>
      <td>128</td>
    </tr>
    <tr>
      <td>9.7</td>
      <td>OURSEurope</td>
      <td>129</td>
    </tr>
    <tr>
      <td>10</td>
      <td>Model evolution</td>
      <td>132</td>
    </tr>
    <tr>
      <td>10.1</td>
      <td>The model over time</td>
      <td>132</td>
    </tr>
    <tr>
      <td>10.2</td>
      <td>Version list</td>
      <td>132</td>
    </tr>
    <tr>
      <td>10.3</td>
      <td>Adding blocks, programs and tools</td>
      <td>134</td>
    </tr>
    <tr>
      <td>10.4</td>
      <td>Comparison tables and AROPAj sourced biases</td>
      <td>135</td>
    </tr>
    <tr>
      <td>11</td>
      <td>Computing tools</td>
      <td>140</td>
    </tr>
    <tr>
      <td>11.1</td>
      <td>Hardware and software</td>
      <td>140</td>
    </tr>
    <tr>
      <td>11.1.1</td>
      <td>Operating system, software and runtime</td>
      <td>140</td>
    </tr>
    <tr>
      <td>11.1.2</td>
      <td>Software and runtime</td>
      <td>140</td>
    </tr>
    <tr>
      <td>11.1.3</td>
      <td>The AROPAj files and shell</td>
      <td>141</td>
    </tr>
    <tr>
      <td>11.2</td>
      <td>Basic use and call of the model</td>
      <td>144</td>
    </tr>
    <tr>
      <td>11.2.1</td>
      <td>Parameter value transmission through AROPAj steps and files</td>
      <td>144</td>
    </tr>
    <tr>
      <td>11.2.2</td>
      <td>Reporting</td>
      <td>147</td>
    </tr>
    <tr>
      <td>11.2.3</td>
      <td>Inserting new items, linking parameters and outputs</td>
      <td>148</td>
    </tr>
    <tr>
      <td>11.2.4</td>
      <td>Starting and managing simulations</td>
      <td>150</td>
    </tr>
  </tbody>
</table>
<table>
  <tbody>
    <tr>
      <td><b>6 Parameter estimation</b></td>
      <td><b>93</b></td>
    </tr>
    <tr>
      <td>6.1 Variable costs</td>
      <td>93</td>
    </tr>
    <tr>
      <td>6.1.1 Estimation of activity variable costs</td>
      <td>93</td>
    </tr>
    <tr>
      <td>6.1.2 Implementation details for cost estimating</td>
      <td>95</td>
    </tr>
    <tr>
      <td>6.2 Parameters estimating for farm groups</td>
      <td>99</td>
    </tr>
    <tr>
      <td><b>7 Calibration of the AROPAj model</b></td>
      <td><b>102</b></td>
    </tr>
    <tr>
      <td><b>8 Spatialization of AROPAj outputs</b></td>
      <td><b>108</b></td>
    </tr>
    <tr>
      <td>8.1 Disaggregation approach in spatial econometrics devoted to crop location</td>
      <td>108</td>
    </tr>
    <tr>
      <td>8.1.1 The land use model</td>
      <td>108</td>
    </tr>
    <tr>
      <td>8.1.2 The disaggregation model: the Generalized Cross Entropy approach</td>
      <td>108</td>
    </tr>
    <tr>
      <td>8.2 Method and process implementation</td>
      <td>110</td>
    </tr>
    <tr>
      <td>8.2.1 Crop location estimates at a fine resolution level</td>
      <td>110</td>
    </tr>
    <tr>
      <td>8.2.2 Estimation of probabilities for farm types</td>
      <td>112</td>
    </tr>
    <tr>
      <td>8.3 Application</td>
      <td>115</td>
    </tr>
    <tr>
      <td><b>9 Models linkage</b></td>
      <td><b>117</b></td>
    </tr>
    <tr>
      <td>9.1 STICS</td>
      <td>117</td>
    </tr>
    <tr>
      <td>9.1.1 N to yield functions</td>
      <td>118</td>
    </tr>
    <tr>
      <td>9.1.2 N to emission functions</td>
      <td>119</td>
    </tr>
    <tr>
      <td>9.1.3 ArTiX</td>
      <td>119</td>
    </tr>
    <tr>
      <td>9.2 Carbo-PRO</td>
      <td>120</td>
    </tr>
    <tr>
      <td>9.2.1 Organic nitrogen sources</td>
      <td>121</td>
    </tr>
    <tr>
      <td>9.2.2 Carbo-PRO</td>
      <td>125</td>
    </tr>
    <tr>
      <td>9.3 PaSim</td>
      <td>125</td>
    </tr>
    <tr>
      <td>9.4 MODCOU</td>
      <td>126</td>
    </tr>
    <tr>
      <td>9.5 GLOBIOM</td>
      <td>131</td>
    </tr>
    <tr>
      <td>9.6 GeoMIRET</td>
      <td>132</td>
    </tr>
    <tr>
      <td>9.7 OURSEurope</td>
      <td>134</td>
    </tr>
    <tr>
      <td><b>10 Model evolution</b></td>
      <td><b>137</b></td>
    </tr>
    <tr>
      <td>10.1 The model over time</td>
      <td>137</td>
    </tr>
    <tr>
      <td>10.2 Version list</td>
      <td>137</td>
    </tr>
    <tr>
      <td>10.3 Adding blocks, programs and tools</td>
      <td>139</td>
    </tr>
    <tr>
      <td>10.4 Comparison tables and AROPAj sourced biases</td>
      <td>140</td>
    </tr>
    <tr>
      <td><b>11 Computing tools</b></td>
      <td><b>145</b></td>
    </tr>
    <tr>
      <td>11.1 Hardware and software</td>
      <td>145</td>
    </tr>
    <tr>
      <td>11.1.1 Operating system, software and runtime</td>
      <td>145</td>
    </tr>
    <tr>
      <td>11.1.2 Software and runtime</td>
      <td>145</td>
    </tr>
    <tr>
      <td>11.1.3 The AROPAj files and shell</td>
      <td>146</td>
    </tr>
    <tr>
      <td>11.2 Basic use and call of the model</td>
      <td>149</td>
    </tr>
    <tr>
      <td>11.2.1 Parameter value transmission through AROPAj steps and files</td>
      <td>149</td>
    </tr>
    <tr>
      <td>11.2.2 Reporting</td>
      <td>152</td>
    </tr>
  </tbody>
</table>
<table><thead><tr><th></th><th></th></tr></thead><tbody><tr><td><strong>12 Applications</strong></td><td><strong>152</strong></td></tr><tr><td>12.1 Agricultural policy analysis</td><td>152</td></tr><tr><td>12.2 GHG emissions and abatement</td><td>160</td></tr><tr><td>12.3 N-sourced pollutions</td><td>165</td></tr><tr><td>12.4 Biomass provision from perennial crops</td><td>168</td></tr><tr><td>12.5 Bio-economy oriented studies</td><td>170</td></tr><tr><td>12.6 Adaptation to climate change</td><td>173</td></tr><tr><td><strong>13 Perspectives and further developments</strong></td><td><strong>179</strong></td></tr><tr><td>13.1 Water issues</td><td>179</td></tr><tr><td>13.2 Low input agriculture</td><td>180</td></tr><tr><td>13.3 Facilitating MP solutions involving interacting agents</td><td>181</td></tr><tr><td>13.4 Anchoring the use of the STICS crop model and the calculation of probability farm group location to the core of AROPAj computing applications</td><td>182</td></tr><tr><td>13.5 Organic matter, biogas, digestates</td><td>183</td></tr><tr><td><strong>14 Glossary, communication, references</strong></td><td><strong>184</strong></td></tr><tr><td><strong>A User's call for the model</strong></td><td><strong>202</strong></td></tr><tr><td><strong>B Contributors to AROPAj and to related publications</strong></td><td><strong>205</strong></td></tr><tr><td><strong>C Funded projects and supports benefiting AROPAj</strong></td><td><strong>207</strong></td></tr></tbody></table>
<table><tr><td>11.2.3 Inserting new items, linking parameters and outputs</td><td>153</td></tr><tr><td>11.2.4 Starting and managing simulations</td><td>155</td></tr><tr><td><b>12 Applications</b></td><td><b>157</b></td></tr><tr><td>12.1 Agricultural policy analysis</td><td>157</td></tr><tr><td>12.2 GHG emissions and abatement</td><td>165</td></tr><tr><td>12.3 N-sourced pollutions</td><td>171</td></tr><tr><td>12.4 Biomass provision from perennial crops</td><td>175</td></tr><tr><td>12.5 Bio-economy oriented studies</td><td>178</td></tr><tr><td>12.6 Adaptation to climate change</td><td>181</td></tr><tr><td><b>13 Perspectives and further developments</b></td><td><b>187</b></td></tr><tr><td>13.1 Water issues</td><td>187</td></tr><tr><td>13.2 Low input agriculture</td><td>190</td></tr><tr><td>13.3 Facilitating MP solutions involving interacting agents</td><td>190</td></tr><tr><td>13.4 Anchoring the use of the STICS crop model and the calculation of probability farm group location to the core of AROPAj computing applications</td><td>191</td></tr><tr><td>13.5 Organic matter, biogas and digestates, intermediate crops</td><td>192</td></tr><tr><td>13.6 Intermediate crops</td><td>192</td></tr><tr><td><b>14 Glossary, communication, references</b></td><td><b>193</b></td></tr><tr><td><b>A User's call for the model</b></td><td><b>211</b></td></tr><tr><td><b>B Contributors to AROPAj and to related publications</b></td><td><b>214</b></td></tr><tr><td><b>C Funded projects and supports benefiting AROPAj</b></td><td><b>216</b></td></tr></table>
This publication presents the European agro-economic *AROPAj* model. Throughout recent years the model has been adapted to suit *FADN* data and the expansion of the European Union (*EU*). The revised model, which is presented here, is based on the same principles, modularity, and generic conceptions of the previous renditions. The strength of the model lies in the evolution of computing capacities and facilities, especially when new scientific problems arise.

The starting premise of the model resulted from the combination of different factors, namely new policy tools announced to be implemented by the changing Common Agricultural Policy (*CAP*), the need to account for a wide diversity of farming systems, and the changing geographical area following the *EU* enlargement. In complement of econometric approaches relying on past information, the model introduces new mathematical programming (*MP*) approaches using the most relevant data.

The Farm Accountancy Data Network (*FADN*) is considered as a permanent, robust and representative source of information, useful for *MP* models delineated at the farm level. The information in the *FADN* database consists of surveys of individual farm samples. The database provides individual information mainly accounting of accountancy and financial or economic variables. The *AROPAj* model is also capable of using data on physical variables such as livestock, production, and land. Nevertheless, a lot of *AROPAj* parameters are not directly sourced by raw *FADN* data. For example, the model makes use of other data sources, including expert reports and books, such as livestock feeding. Other sources utilized by some *AROPAj* modules are *inter alia* data concerning land use and land cover (Land Use/Cover Area frame Statistical Survey (*LUCAS*), CORINE Land Cover (*CLC*)), the European Soil Database provided by the European Joint Research Centre (*JRC*), the Digital Elevation Model (*DEM*), and the Climate information provided by the European *MARS JRC* Unit. These variables are grouped by means of a clustering method to form a group of similar farms that present similar characteristics and thus can form a unit of modeling for the *AROPAj* model: the farm type (also denominated by farm group). The overall model is based on farm-groups, designed on a regional scale, for all of the *EU*.

In large part, the *AROPAj* model originates from modeling tools aiming at *CAP* impact assessments. Mathematical programming models are effective in this way, especially when the implementation of new policy tools in economic models has to rely on non-time dependent data, unlike time-inferred econometric models. Due to the wide and complex diversity of *CAP* tools renewed throughout decades, the *CAP* block size quickly increased. The generic modeling approach embraces the wide variety of European farming systems which are subsumed by the continually-growing *EU*. It involves a multi-scale analysis from the farm type level to the *EU* level, accounting for realistic discontinuities at the farm level.

The model is also designed to assess global change impacts and analyze policy while accounting for the complexity of interactions between agriculture and the environment. In this regard, it is a tool used for the analysis of a large range of economic and environmental domains, such as greenhouse gas (*GHG*) emissions and abatement, nitrogen sourced pollutions, biomass provision from perennial crops, ozone impacts and adaptation to climate change. Other collateral outputs may exist when providing farm-based estimates and data related to physical parameters.

The interest of linking the *AROPAj* economic model with biophysical models relies on the possibility of accounting for environmental (physical impacts such as soil and climate) and technical variable impacts on the production functions, as well as on the agricultural system
This publication presents the European agro-economic *AROPAj* model. Throughout recent years the model has been adapted to suit *FADN* data and the expansion of the European Union (*EU*). The revised model, which is presented here, is based on the same principles, modularity, and generic conceptions of the previous renditions. The strength of the model lies in the evolution of computing capacities and facilities, especially when new scientific problems arise.

The starting premise of the model resulted from the combination of different factors, namely new policy tools announced to be implemented by the changing Common Agricultural Policy (*CAP*), the need to account for a wide diversity of farming systems, and the changing geographical area following the *EU* enlargement. In complement of econometric approaches relying on past information, the model introduces new mathematical programming (*MP*) approaches using the most relevant data.

The Farm Accountancy Data Network (*FADN*) is considered as a permanent, robust and representative source of information, useful for *MP* models delineated at the farm level. The information in the *FADN* database consists of surveys of individual farm samples. The database provides individual information mainly accounting of accountancy and financial or economic variables. The *AROPAj* model is also capable of using data on physical variables such as livestock, production, and land. Nevertheless, a lot of *AROPAj* parameters are not directly sourced by raw *FADN* data. For example, the model makes use of other data sources, including expert reports and books, such as livestock feeding. Other sources utilized by some *AROPAj* modules are *inter alia* data concerning land use and land cover (Land Use/Cover Area frame Statistical Survey (*LUCAS*), CORINE Land Cover (*CLC*)), the European Soil Database provided by the European Joint Research Centre (*JRC*), the Digital Elevation Model (*DEM*), and the Climate information provided by the European *MARS JRC* Unit. These variables are grouped by means of a clustering method to form a group of similar farms that present similar characteristics and thus can form a unit of modeling for the *AROPAj* model: the farm type (also denominated by farm group). The overall model is based on farm-groups, designed on a regional scale, for all of the *EU*.

In large part, the *AROPAj* model originates from modeling tools aiming at *CAP* impact assessments. Mathematical programming models are effective in this way, especially when the implementation of new policy tools in economic models has to rely on non-time dependent data, unlike time-inferred econometric models. Due to the wide and complex diversity of *CAP* tools renewed throughout decades, the *CAP* block size quickly increased. The generic modeling approach embraces the wide variety of European farming systems which are subsumed by the continually-growing *EU*. It involves a multi-scale analysis from the farm type level to the *EU* level, accounting for realistic discontinuities at the farm level.

The model is also designed to assess global change impacts and analyze policy while accounting for the complexity of interactions between agriculture and the environment. In this regard, it is a tool used for the analysis of a large range of economic and environmental domains, such as greenhouse gas (*GHG*) emissions and abatement, nitrogen sourced pollutions, biomass provision from perennial crops, ozone impacts and adaptation to climate change. Other collateral outputs may exist when providing farm-based estimates and data related to physical parameters.

The interest of linking the *AROPAj* economic model with biophysical models relies on the possibility of accounting for environmental (physical impacts such as soil and climate) and technical variable impacts on the production functions, as well as on the agricultural system
output relevant to environmental concerns. The general goal is to bring to light the relationship
between crop production inputs (e.g. fertilizer applications) and crop production outputs (e.g.
yields). The potential relation between the economic and biophysical models is to be found
in the management practices of the farmer, such as irrigation, application of pesticides, and
fertilizer.

Some refinements are required when the farm group's optimal solution is made of non-marketed crop output (or of non-marketed nitrogen input). In other words, this occurs when, at the optimum, the crop production is entirely re-used on-farm (e.g. for livestock feeding), or when no N-input comes from the market (e.g. manure sourced). In this case, market prices have to be replaced by relevant shadow prices, which are part of the optimal solution. In practice, the problem is solved by iterated AROPAj runs with shadow prices replacing the prices used at the previous iteration for the yield function derivative. This process of convergence is fast in most AROPAj LP's, except for a few cases where solutions have periodic forms over iterations, with slight amplitudes.

The model is running using the GNU software and applications, except for the marketed
optimization solving tool (GAMS). Year after year, the choice has been made to promote the
use of GNU software for AROPAj improvement, not only regarding the financial cost, but
mainly to facilitate the maintenance and the evolution of our programs and applications. The
model also produces some interesting spatially disaggregated outputs in line with multi-scale
environmental problems. The computing and algorithm facilities embedded in the modeling
process allow new improvements and new model exploitation exercises.

The European agro-economic AROPAj model is built of a set of linear programming models, aiming at a good representation of European farming systems in term of geography and farm type diversity as well. As a result, the model aims at being a tool and a reference, which benefits a significant numbers of PhDs and MSc students, and contributes to many published peer-reviewed papers (to which this document refers).
output relevant to environmental concerns. The general goal is to bring to light the relationship
between crop production inputs (e.g. fertilizer applications) and crop production outputs (e.g.
yields). The potential relation between the economic and biophysical models is to be found
in the management practices of the farmer, such as irrigation, application of pesticides, and
fertilizer.

Some refinements are required when the farm group's optimal solution is made of non-marketed crop output (or of non-marketed nitrogen input). In other words, this occurs when, at the optimum, the crop production is entirely re-used on-farm (e.g. for livestock feeding), or when no N-input comes from the market (e.g. manure sourced). In this case, market prices have to be replaced by relevant shadow prices, which are part of the optimal solution. In practice, the problem is solved by iterated AROPAj runs with shadow prices replacing the prices used at the previous iteration for the yield function derivative. This process of convergence is fast in most AROPAj LP's, except for a few cases where solutions have periodic forms over iterations, with slight amplitudes.

The model is running using the GNU software and applications, except for the marketed
optimization solving tool (GAMS). Year after year, the choice has been made to promote the
use of GNU software for AROPAj improvement, not only regarding the financial cost, but
mainly to facilitate the maintenance and the evolution of our programs and applications. The
model also produces some interesting spatially disaggregated outputs in line with multi-scale
environmental problems. The computing and algorithm facilities embedded in the modeling
process allow new improvements and new model exploitation exercises.

The European agro-economic AROPAj model is built of a set of linear programming models, aiming at a good representation of European farming systems in term of geography and farm type diversity as well. As a result, the model aims at being a tool and a reference, which benefits a significant numbers of PhDs and MSc students, and contributes to many published peer-reviewed papers (to which this document refers).
# 1 Introduction

## 1.1 Objectives

### Key-points:

- Policy analysis (agricultural and environmental policies)

- Scope (crops, geographical cover)

- Agricultural land allocation

- Linkage between agriculture and the environment

- Mitigation and adaptation of the EU agriculture (to global changes)

- New challenges agriculture could face over next years, when no past information leads usual econometric approaches to fail in feeding analysis

The basic premise of the *AROPAj* model is derived in order to suit a combination of different factors: the newly introduced policy tools of the ever-changing Common Agricultural Policy (CAP); the need to account for the heterogeneity of farming systems, and the growing geographical area of the European Union (EU). The *AROPAj* approach of the *AROPAj* model uses a combination of mathematical programming (MP) and statistical techniques. This choice is motivated by the availability of micro-economic and technical data of sufficient quality. The Farm Accountancy Data Network (FADN) -"an instrument for evaluating the income of agricultural holdings and the impacts of the Common Agricultural Policy" <fnref n="1" />- is considered to be a permanent, robust, and representative source of farm level information for MP models.

The FADN data, combined with technical information, allows one to adequately describe the "production set" of the representative economic agents. Production sets are viewed as sets of technical constraints. Furthermore, the numerous policy instruments, which are currently implemented in the CAP framework, as well as those that will be implemented in the future, are easily managed by MP modeling. Following conventional approaches, the basic structure of production sets is linear. The modeling of the farming systems by means of technical relationships between agricultural activities has to be informed by behavioural elements, which are to be selected in accordance with micro-economic standards. In our case, farming system decisions result from gross margin optimization. Stated otherwise, the rationale for the *AROPAj* modeling approach is predicated on linear programming (LP) techniques. The *AROPAj* model is composed of a set of LP models in order to correctly represent the geographical and typical diversity of European farming systems.

The *AROPAj* model is a supply-side model. The entire price system is included in the set of parameters. Of course, the "small country" assumption does not hold when the agriculture of the European Union is considered as a whole. Nevertheless, there exists already a number of well-performing general or partial equilibrium models which can supply us with the price vectors when necessary.

The *AROPAj* model is a mono-periodic short run model. Results are delivered at an annually level. Since the model is static, the estimated results can be interpreted as the long run impacts of economic policy (CAP) or physical (climate) changes under the *ceteris paribus* hypothesis:

<footnote n="1">¹http://ec.europa.eu/agriculture/rica/</footnote>
# 1 Introduction

## 1.1 Objectives

### Key-points:

- Policy analysis (agricultural and environmental policies)

- Scope (crops, geographical cover)

- Agricultural land allocation

- Linkage between agriculture and the environment

- Mitigation and adaptation of the EU agriculture (to global changes)

- New challenges agriculture could face over next years, when no past information leads usual econometric approaches to fail in feeding analysis

The basic premise of the *AROPAj* model is derived in order to suit a combination of different factors: the newly introduced policy tools of the ever-changing Common Agricultural Policy (*CAP*); the need to account for the heterogeneity of farming systems, and the growing geographical area of the European Union (*EU*). The *AROPAj* approach of the *AROPAj* model uses a combination of mathematical programming (*MP*) and statistical techniques. This choice is motivated by the availability of micro-economic and technical data of sufficient quality. The Farm Accountancy Data Network (*FADN*) -"an instrument for evaluating the income of agricultural holdings and the impacts of the Common Agricultural Policy" <fnref n="1" />- is considered to be a permanent, robust, and representative source of farm level information for *MP* models.

The *FADN* data, combined with technical information, allows one to adequately describe the "production set" of the representative economic agents. Production sets are viewed as sets of technical constraints. Furthermore, the numerous policy instruments, which are currently implemented in the *CAP* framework, as well as those that will be implemented in the future, are easily managed by *MP* modeling. Following conventional approaches, the basic structure of production sets is linear. The modeling of the farming systems by means of technical relationships between agricultural activities has to be informed by behavioural elements, which are to be selected in accordance with micro-economic standards. In our case, farming system decisions result from gross margin optimization. Stated otherwise, the rationale for the *AROPAj* modeling approach is predicated on linear programming (*LP*) techniques. The *AROPAj* model is composed of a set of *LP* models in order to correctly represent the geographical and typical diversity of European farming systems.

The *AROPAj* model is a supply-side model. The entire price system is included in the set of parameters. Of course, the "small country" assumption does not hold when the agriculture of the European Union is considered as a whole. Nevertheless, there exists already a number of well-performing general or partial equilibrium models which can supply us with the price vectors when necessary.

The *AROPAj* model is a mono-periodic short run model. Results are delivered at an annually level. Since the model is static, the estimated results can be interpreted as the long run impacts of economic policy (*CAP*) or physical (climate) changes under the *ceteris paribus* hypothesis:

<footnote n="1">¹http://ec.europa.eu/agriculture/rica/</footnote>
no change in farms structure or in land endowment except through exogenous signals via the
parameters. Included in the model, land allocation is joined to (bovine) livestock adjustment.

Because of the linear structure of the model and the necessity of implementing many *CAP* tools, there is a need for binary variables. Particular attention must be paid to the restrictions imposed by the *CAP* measures. Set-aside requirements as well as milk and sugar beet quotas fall into this category. Mandatory and voluntary set-asides are accounted for, each type of set-aside being treated as a productive activity associated with the corresponding payments. The different types of sugar beet quotas (A, B, and C) are also included. Many of the *CAP* policy instruments included in the model involve the use of binary or integer variables whenever producers have to face mutually exclusive “discrete” choices. At this stage, *AROPAj* leaves the general *LP* framework and calls upon Mixed Integer Programming solvers (*MIP*).

After the seminal period devoted to the *CAP*, strong opportunities for *AROPAj* improvement were provided by environmental issues. The first occurred in the middle of the nineties with the emerging problem of climatic change (*CC*) impacts. A greenhouse gas (*GHG*) block has been added, following the methodology developed by the International Panel for Climate Change (*IPCC*), in order to compute agricultural *GHG* emissions (De Cara & Jayet, 2000a). It makes it possible to assess the impacts of *CAP* reforms on GHG emissions as well as to assess the impact of *GHG* emission mitigation or *CC* adaptation on *CAP* sourced agricultural support.

The interest in agricultural pollution other than that of GHG emissions, and the improvement of the agronomic block of the *AROPAj* model lead to a reexamination of the linkage between nitrogen (*N*) sources and crop yields. The seminal work builds on a stylized plot analysis, based on crop modeling (i.e. the *STICS* crop model use), which has expanded to cover a serie of crops throughout the various European farming systems. This expansion of the model is made possible by the myriad of physical data at the European scale, particularly concerning soil and climate, as well was the digital elevation information (Godard et al., 2008). Mathematically, the implementation of these functions makes the *AROPAj* model non-linear, even when *LP* solvers are used as part of a two-step calculation process (Aghanjanzadeh-Darzi et al., submitted paper).

The introduction of the nitrogen block in the model creates a gap in the applications originating from the *AROPAj* model. Subtle analyses of environmental regulation are provided when dose-response functions, initially devoted to nitrogen-to-yield functions, were expanded to *N*-pollutant functions (Jayet & Petsakos, 2013; Bourgeois et al., 2014). Another field of application refers to autonomous adaptation of agricultural systems to climate change, when adaptation applies at the plot level via the *N*-yield functions which are transformed by climate change (Leclère et al., 2013).

Another gap arises when probabilistic contribution of *AROPAj* representative farming systems are geographically distributed within a region. This spatialization block is based on spatial econometric methods (developed by Chakir (2009)). The methodology and applied calculation process are explained by Cantelaube et al. (2012). By using tropospheric ozone (*O*₃) concentration yield functions as well as spatialization blocks, we are allowed to improve the assessment of *O*₃ impact on farming systems of various scales (Humblot et al., 2013). The spatialization block also allows us to couple models based on different spatial grids. An example of such a coupling of models is the concomitant uses of the *AROPAj* and hydroecological *MODCOU* models, the former dedicated to agricultural surfact activities and related pollution factors and the latter to water and pollutant transfers to aquifers (Bourgeois et al., submitted).
no change in farms structure or in land endowment except through exogenous signals via the
parameters. Included in the model, land allocation is joined to (bovine) livestock adjustment.

Because of the linear structure of the model and the necessity of implementing many *CAP* tools, there is a need for binary variables. Particular attention must be paid to the restrictions imposed by the *CAP* measures. Set-aside requirements as well as milk and sugar beet quotas fall into this category. Mandatory and voluntary set-asides are accounted for, each type of set-aside being treated as a productive activity associated with the corresponding payments. The different types of sugar beet quotas (A, B, and C) are also included. Many of the *CAP* policy instruments included in the model involve the use of binary or integer variables whenever producers have to face mutually exclusive “discrete” choices. At this stage, *AROPAj* leaves the general *LP* framework and calls upon Mixed Integer Programming solvers (*MIP*).

After the seminal period devoted to the *CAP*, strong opportunities for *AROPAj* improvement were provided by environmental issues. The first occurred in the middle of the nineties with the emerging problem of climatic change (*CC*) impacts. A greenhouse gas (*GHG*) block has been added, following the methodology developed by the International Panel for Climate Change (*IPCC*), in order to compute agricultural *GHG* emissions (De Cara & Jayet, 2000a). It makes it possible to assess the impacts of *CAP* reforms on *GHG* emissions as well as to assess the impact of *GHG* emission mitigation or *CC* adaptation on *CAP* sourced agricultural support.

The interest in agricultural pollution other than that of GHG emissions, and the improvement of the agronomic block of the *AROPAj* model lead to a reexamination of the linkage between nitrogen (*N*) sources and crop yields. The seminal work builds on a stylized plot analysis, based on crop modeling (i.e. the *STICS* crop model use), which has expanded to cover a serie of crops throughout the various European farming systems. This expansion of the model is made possible by the myriad of physical data at the European scale, particularly concerning soil and climate, as well was the digital elevation information (Godard et al., 2008). Mathematically, the implementation of these functions makes the *AROPAj* model non-linear, even when *LP* solvers are used as part of a two-step calculation process (Aghanjanzadeh-Darzi et al., submitted paper).

The introduction of the nitrogen block in the model creates a gap in the applications originating from the *AROPAj* model. Subtle analyses of environmental regulation are provided when dose-response functions, initially devoted to nitrogen-to-yield functions, were expanded to *N*-pollutant functions (Jayet & Petsakos, 2013; Bourgeois et al., 2014). Another field of application refers to autonomous adaptation of agricultural systems to climate change, when adaptation applies at the plot level via the *N*-yield functions which are transformed by climate change (Leclère et al., 2013).

Another gap arises when probabilistic contribution of *AROPAj* representative farming systems are geographically distributed within a region. This spatialization block is based on spatial econometric methods (developed by Chakir (2009)). The methodology and applied calculation process are explained by Cantelaube et al. (2012). By using tropospheric ozone (*O*₃) concentration yield functions as well as spatialization blocks, we are allowed to improve the assessment of *O*₃ impact on farming systems of various scales (Humblot et al., 2013). The spatialization block also allows us to couple models based on different spatial grids. An example of such a coupling of models is the concomitant uses of the *AROPAj* and hydroecological *MODCOU* models, the former dedicated to agricultural surfact activities and related pollution factors and the latter to water and pollutant transfers to aquifers (Bourgeois et al., submitted).
The last on-going step is to incorporate water as a major production factor, as was done with nitrogen. Academic papers are on progress and PhD students are currently working on this front.

## 1.2 State of the art and early future

### Key-points:

- What runs

- What is in progress

As the *AROPAj* model continuously evolves, some discrepancies may arise among itself various key elements: namely the model itself, its construction, extensions, and applications. These elements are clustered as follows:

1. the core of the model, including different internal blocks added over time
(see also Section 4.2),

1. the three steps of the model building, namely:

(a) typology and sample farm clustering (see also Section 5),

(b) parameter estimation (see also Section 6),

(c) farm cluster model calibration (see also Section 7),

2. the dose-response functions dedicated to nitrogen fertilizing and crop yields (see also Sections 4.3 and 9.1.1),

3. the spatialization processing tools (see also Section 8),

4. the shell and its user-friendly interface (see also Section 11.2).

An overall overview of data and processes involved in and close around the *AROPAj* model is presented in Figure 1. At the present stage, the “spatialisation” and “crop yield function” blocks are dissociated from the *AROPAj* kernel in the way that each block building is made separately. The computing limitations now being overcome, each block building is scheduled to be refined through interacting with others. More accurately, spatializing *AROPAj* farm groups will be used for improving the yield function selection (through soil characteristics), and yield functions will be included in the *AROPAj* calibrating process.

At the core of the model, we put the design of farming systems and the way crops, pastures and animals interact, as well as their relation to demand for inputs such as mineral fertilizer and feedstuff and to the export of marketed products and non marketed externalities. The basic *LP* structure of *AROPAj* has remained stable and robust for many yearswhile constantly integrating new blocks, which improve the representational quality of the production set and the assessment of agricultural externalities. The integration of new blocks is rather simple and their impact on relative computer run time is minimal. In a word, there is no difficulty in adding parameters and primal or dual variables in the model as long as relevant data exists for parameter estimates for the model.

The computing tools that enable the model to evolve are themself constantly evolving. The goal of this is to make programmers and users as less dependent as possible on the operating system and
The last on-going step is to incorporate water as a major production factor, as was done with nitrogen. Academic papers are on progress and PhD students are currently working on this front.

## 1.2 State of the art and early future

### Key-points:

* What runs

* What is in progress

As the *AROPAj* model continuously evolves, some discrepancies may arise among itself various key elements: namely the model itself, its construction, extensions, and applications. These elements are clustered as follows:

1. the core of the model, including different internal blocks added over time
(see also Section 4.2),

1. the three steps of the model building, namely:

(a) typology and sample farm clustering (see also Section 5),

(b) parameter estimation (see also Section 6),

(c) farm cluster model calibration (see also Section 7),

2. the dose-response functions dedicated to nitrogen fertilizing and crop yields (see also Sections 4.3 and 9.1.1),

3. the spatialization processing tools (see also Section 8),

4. the shell and its user-friendly interface (see also Section 11.2).

An overall overview of data and processes involved in and close around the *AROPAj* model is presented in Figure 1. At the present stage, the “spatialisation” and “crop yield function” blocks are dissociated from the *AROPAj* kernel in the way that each block building is made separately. The computing limitations now being overcome, each block building is scheduled to be refined through interacting with others. More accurately, spatializing *AROPAj* farm groups will be used for improving the yield function selection (through soil characteristics), and yield functions will be included in the *AROPAj* calibrating process.

At the core of the model, we put the design of farming systems and the way crops, pastures and animals interact, as well as their relation to demand for inputs such as mineral fertilizer and feedstuff and to the export of marketed products and non marketed externalities. The basic *LP* structure of *AROPAj* has remained stable and robust for many yearswhile constantly integrating new blocks, which improve the representational quality of the production set and the assessment of agricultural externalities. The integration of new blocks is rather simple and their impact on relative computer run time is minimal. In a word, there is no difficulty in adding parameters and primal or dual variables in the model as long as relevant data exists for parameter estimates for the model.

The computing tools that enable the model to evolve are themself constantly evolving. The goal of this is to make programmers and users as less dependent as possible on the operating system and
<figure><img src="image_2.png" /><figcaption>**Figure 1.** General overview of data and processes associated to the *AROPAj* kernel and its surrounding applications. Red arrows refer to improving the interface between the core model and other processes.</figcaption></figure>
<figure><img src="image_3.png" /><figcaption>**Figure 1.** General overview of data and processes associated to the *AROPAj* kernel and its surrounding applications. Red arrows refer to improving the interface between the core model and other processes.</figcaption></figure>
computers that hosts the model. Nevertheless tools operate in Unix or Linux environment. When it comes to software, things get a little complicated. At the beginning, linear programming tools were based on commercial software, namely MGG dedicated to matrix generating and SCICONIC as a LP solver. Currently we use the MGG structure as if it is composed of FORTRAN instructions making that now free of license costs. The AROPAj code under MGG-FORTRAN is automatically converted in GAMS; we use MP solvers proposed in the GAMS library. Other software contributed to the building of the AROPAj model and to external blocks such as SAS and ArcGIS. These blocks are now replaces by R modules (PostGIS and QGIS are also used for a series of specific tasks and works). The core of the model is designed in such a way that all past applications developed for any version of the model are still operational.

The nitrogen block refers to parameterized yields by default. When N-yield functions are available, mineral nitrogen intakes and crop yields become AROPAj endogenous variables. These functions result from the STICS - AROPAj linkage, which is based on a tremendous undertaking involving biophysical databases and database management systems. An earlier cluster of computer networks at the Laboratoire des Sciences du Climat et de l'Environnement (CEA - CNRS Saclay) was used for this purpose. This project was realized by the efforts of D. Leclère for the AROPAj-V2 version on the European scale. Our current work (2014-2016), managed at our workstation by P. Humblot, entails extending the model, facilitating database management, undertaking STICS calculation runs, and processing results.

In the early 2000's during the EC-FP5 GENEDEC period, P. Cantelaube and his colleagues at the Joint Research Center in Ispra, Italy, created a means of incorporating calculations related to Geographical Information System (GIS) and the crossing of spatial databases.

A. Lungarska and P. Humblot are managing the renewed spatialization block on our workstation with the support of open source softwares (2017-2021). Over the years, colleagues from INRA-EA teams (Orléans, Laon, Avignon) contributed to the improvement of the yield function blocks in AROPAj in relation with the development of the STICS crop model. All these factors strengthen the model's capacity to build the link between the farming system's representation and the geo-referenced soil characteristics, giving us opportunities to enlarge our analysis field in terms of agro-environmental problematics.

<table><caption>Table 1. List of AROPAj versions.</caption><thead><tr><th>version</th><th>EU cover</th><th>FADN year</th><th>yield functions<br>(MS/number in case)</th><th>spatialization<br>(FADN-region number)</th><th>OS & stat. software</th></tr></thead><tbody><tr><td>V1 (obsolete)</td><td>EU-12</td><td>1997</td><td></td><td></td><td>Unix & SAS</td></tr><tr><td>V2</td><td>EU-15</td><td>2002</td><td>(15)</td><td>(12)</td><td>Unix & SAS</td></tr><tr><td>V3</td><td>EU-24*</td><td>2004</td><td>(EU except Malta)</td><td>(specific way)</td><td>Unix & SAS</td></tr><tr><td>V4 (for test)</td><td>EU-27</td><td>2009</td><td></td><td></td><td>Unix/Linux & SAS</td></tr><tr><td>V5</td><td>EU-27**</td><td>2007</td><td></td><td>(109/136)</td><td>Linux & R</td></tr><tr><td>V5</td><td>EU-27</td><td>2008</td><td>(EU27 except Malta, Cyprus)</td><td>(110/135)</td><td>Linux & R</td></tr><tr><td>V5</td><td>EU-27</td><td>2009</td><td>(EU27 except Malta, Cyprus)</td><td>(111/135)</td><td>Linux & R</td></tr><tr><td>V5</td><td>EU-27</td><td>2010</td><td>(EU27 except Malta, Cyprus)</td><td>(110/135)</td><td>Linux & R</td></tr><tr><td>V5</td><td>EU-27</td><td>2011</td><td>(EU27 except Malta, Cyprus)</td><td>(111/135)</td><td>Linux & R</td></tr><tr><td>V5</td><td>EU-27***</td><td>2012</td><td>(EU27 except Malta, Cyprus)</td><td>(104/134)</td><td>Linux & R</td></tr><tr><td>V5</td><td>EU-28</td><td>2013</td><td>(EU28 except Malta, Cyprus)</td><td>(130/135)</td><td>Linux & R</td></tr><tr><td>V5</td><td>EU-28</td><td>2014</td><td>(EU28 except Malta, Cyprus)</td><td>(129/134)</td><td>Linux & R</td></tr><tr><td>V5</td><td>EU-28</td><td>2015</td><td>(EU28 except Malta, Cyprus)</td><td>(130/135)</td><td>Linux & R</td></tr><tr><td>V5</td><td>EU-28</td><td>2016</td><td>(EU28 except Malta, Cyprus)</td><td>(130/135)</td><td>Linux & R</td></tr><tr><td>V5</td><td>EU-28</td><td>2017</td><td>(EU28 except Malta, Cyprus)</td><td>(130/135)</td><td>Linux & R</td></tr><tr><td>V5</td><td>EU-28</td><td>2018</td><td>(EU28 except Malta, Cyprus)</td><td>(129/135)</td><td>Linux & R</td></tr></tbody></table>

<footnote>*EU-25, except Malta</footnote>

<footnote>**Some regions subdivided compared to next years in Portugal</footnote>

<footnote>***The FADN covers 3 French overseas Regions, and some Hungarian regions grouped</footnote>
computers that hosts the model. Nevertheless tools operate in Unix or Linux environment. When it comes to software, things get a little complicated. At the beginning, linear programming tools were based on commercial software, namely MGG dedicated to matrix generating and SCICONIC as a LP solver. Currently we use the MGG structure as if it is composed of FORTRAN instructions making that now free of license costs. The AROPAj code under MGG-FORTRAN is automatically converted in GAMS; we use MP solvers proposed in the GAMS library. Other software contributed to the building of the AROPAj model and to external blocks such as SAS and ArcGIS. These blocks are now replaces by R modules (PostGIS and QGIS are also used for a series of specific tasks and works). The core of the model is designed in such a way that all past applications developed for any version of the model are still operational.

The nitrogen block refers to parameterized yields by default. When N-yield functions are available, mineral nitrogen intakes and crop yields become AROPAj endogenous variables. These functions result from the STICS - AROPAj linkage, which is based on a tremendous undertaking involving biophysical databases and database management systems. An earlier cluster of computer networks at the Laboratoire des Sciences du Climat et de l'Environnement (CEA - CNRS Saclay) was used for this purpose. This project was realized by the efforts of D. Leclère for the AROPAj-V2 version on the European scale. Our current work (2014-2016), managed at our workstation by P. Humblot, entails extending the model, facilitating database management, undertaking STICS calculation runs, and processing results.

In the early 2000's during the EC-FP5 GENEDEC period, P. Cantelaube and his colleagues at the Joint Research Center in Ispra, Italy, created a means of incorporating calculations related to Geographical Information System (GIS) and the crossing of spatial databases.

A. Lungarska and P. Humblot are managing the renewed spatialization block on our workstation with the support of open source softwares (2017-2021). Over the years, colleagues from INRA-EA teams (Orléans, Laon, Avignon) contributed to the improvement of the yield function blocks in AROPAj in relation with the development of the STICS crop model. All these factors strengthen the model's capacity to build the link between the farming system's representation and the geo-referenced soil characteristics, giving us opportunities to enlarge our analysis field in terms of agro-environmental problematics.

<table><caption>Table 1. List of AROPAj versions.</caption><thead><tr><th>version</th><th>EU cover</th><th>FADN year</th><th>yield functions<br>(MS/number in case)</th><th>spatialization<br>(FADN-region number)</th><th>OS & stat. software</th></tr></thead><tbody><tr><td>V1 (obsolete)</td><td>EU-12</td><td>1997</td><td></td><td></td><td>Unix & SAS</td></tr><tr><td>V2</td><td>EU-15</td><td>2002</td><td>(15)</td><td>(12)</td><td>Unix & SAS</td></tr><tr><td>V3</td><td>EU-24*</td><td>2004</td><td>(EU except Malta)</td><td>(specific way)</td><td>Unix & SAS</td></tr><tr><td>V4 (for test)</td><td>EU-27</td><td>2009</td><td></td><td></td><td>Unix/Linux & SAS</td></tr><tr><td>V5</td><td>EU-27**</td><td>2007</td><td></td><td>(109/136)</td><td>Linux & R</td></tr><tr><td>V5</td><td>EU-27</td><td>2008</td><td>(EU27 except Malta, Cyprus)</td><td>(110/135)</td><td>Linux & R</td></tr><tr><td>V5</td><td>EU-27</td><td>2009</td><td>(EU27 except Malta, Cyprus)</td><td>(111/135)</td><td>Linux & R</td></tr><tr><td>V5</td><td>EU-27</td><td>2010</td><td>(EU27 except Malta, Cyprus)</td><td>(110/135)</td><td>Linux & R</td></tr><tr><td>V5</td><td>EU-27</td><td>2011</td><td>(EU27 except Malta, Cyprus)</td><td>(111/135)</td><td>Linux & R</td></tr><tr><td>V5</td><td>EU-27***</td><td>2012</td><td>(EU27 except Malta, Cyprus)</td><td>(104/134)</td><td>Linux & R</td></tr><tr><td>V5</td><td>EU-28</td><td>2013</td><td>(EU28 except Malta, Cyprus)</td><td>(130/135)</td><td>Linux & R</td></tr><tr><td>V5</td><td>EU-28</td><td>2014</td><td>(EU28 except Malta, Cyprus)</td><td>(129/134)</td><td>Linux & R</td></tr><tr><td>V5</td><td>EU-28</td><td>2015</td><td>(EU28 except Malta, Cyprus)</td><td>(130/135)</td><td>Linux & R</td></tr><tr><td>V5</td><td>EU-28</td><td>2016</td><td>(EU28 except Malta, Cyprus)</td><td>(130/135)</td><td>Linux & R</td></tr><tr><td>V5</td><td>EU-28</td><td>2017</td><td>(EU28 except Malta, Cyprus)</td><td>(130/135)</td><td>Linux & R</td></tr><tr><td>V5</td><td>EU-28</td><td>2018</td><td>(EU28 except Malta, Cyprus)</td><td>(129/135)</td><td>Linux & R</td></tr></tbody></table>

<footnote>*EU-25, except Malta</footnote>

<footnote>**Some regions subdivided compared to next years in Portugal</footnote>

<footnote>***The FADN covers 3 French overseas Regions, and some Hungarian regions grouped</footnote>
One version of AROPAj is animated by the annual FADN sample on which farm clustering, parameter estimating, and LP calibrating are based. Table 1 lists the various versions which have been or still are in use. The V1 version is not maintained for operational uses. All versions refer to one or more European research programs, as cited in Section 3.1.

In 2016, a “water block” is included in the model under the V5 -version. It allows to integrate irrigation water as well as nitrogen fertilizing through 2 -input yield functions. This was first operating for the V5/2009 -version of the model applied to France, for which such yield functions were estimated in 2016 (see the seminal paper by Humblot et al. (2017)). The extension is completed and operational in 2020 for the FADN years 2008-2012.

All improvements inside and around the model, including the kernel updating, the spatial downscaling of results at a fine level of resolution (within FADN region), and the implementation of crop model based yield functions, are designed and built in a generic way to run the V5 class of AROPAj for all EU countries (see the map covering FADN regions of the EU-28, Figure 2). The yield functions in ”future climate” were first built in line with the FADN-years 2009 and 2012 (IPCC RCP4.5 scenario, CC-years 2010-2100) in a situation of weak adaptation of production systems (sowing dates).

<figure><img src="image_3.png" /><figcaption>**Figure 2.** Map of FADN regions - 28 countries of the EU (2018).</figcaption></figure>

Regional delineation and map on line

https://ec.europa.eu/agriculture/rica/regioncodes_f_r.cfm?CodeCountry = EUR

In 2018, the downscaling step is implemented for the 6 FADN years 2007-2012. The coupling of AROPAj with the crop model is completed and operational for different countries and for 5 of the 6 FADN years, 2008-2012.

In 2020-2022, the AROPAj calibration is realized for the 6 FADN years 2013-2018. Downscaling
One version of AROPAj is animated by the annual FADN sample on which farm clustering, parameter estimating, and LP calibrating are based. Table 1 lists the various versions which have been or still are in use. The V1 version is not maintained for operational uses. All versions refer to one or more European research programs, as cited in Section 3.1.

In 2016, a “water block” is included in the model under the V5 -version. It allows to integrate irrigation water as well as nitrogen fertilizing through 2 -input yield functions. This was first operating for the V5/2009 -version of the model applied to France, for which such yield functions were estimated in 2016 (see the seminal paper by Humblot et al. (2017)). The extension is completed and operational in 2020 for the FADN years 2008-2012.

All improvements inside and around the model, including the kernel updating, the spatial downscaling of results at a fine level of resolution (within FADN region), and the implementation of crop model based yield functions, are designed and built in a generic way to run the V5 class of AROPAj for all EU countries (see the map covering FADN regions of the EU-28, Figure 2). The yield functions in ”future climate” were first built in line with the FADN-years 2009 and 2012 (IPCC RCP4.5 scenario, CC-years 2010-2100) in a situation of weak adaptation of production systems (sowing dates).

<figure><img src="image_4.png" /><figcaption>Figure 2. Map of FADN regions - 28 countries of the EU (2018).</figcaption></figure>

Regional delineation and map on line
https://ec.europa.eu/agriculture/rica/regioncodes_f_r.cfm?CodeCountry = EUR

In 2018, the downscaling step is implemented for the 6 FADN years 2007-2012. The coupling of AROPAj with the crop model is completed and operational for different countries and for 5 of the 6 FADN years, 2008-2012.

In 2020-2022, the AROPAj calibration is realized for the 6 FADN years 2013-2018. Downscaling
is realized for FADN years 2013-2018, including Croatia. Re-calibration of yield functions is carried
out in 2022-23 for FADN years 2012-2018. The yield functions related to "future climate" (IPCC
RCP4.5 scenario) have to be renewed, after adjustments in physical parameters and after reshaping
of yield functions in "present time". This function building is realized for 3 GCM-years (2016, 2043
and 2073 as considered of statiscally representative of three-decade periods, respectively 2011-2040,
2140-2070, 2071-2100 ) in a context of climate change threw a RCP4.5 model scenario (based on
the GCM IPSL2014-CM5A-WRF 2) with strong adaptation of crops (including changes in crop
cultivars and technical routes).

New projects involving AROPAj in a climate change context will refer to greater warming under RCP8.5 scenarios. This means building new yield-functionslp for "future climate" years.

In terms of technical modules, the AROPAj model will soon benefit from the inclusion of the
transformation of organic matter of plant and animal origin into biogas.

<footnote n="2">²http://www.drias-climat.fr/document/Doc_DRIAS_database_IPSL2014-IPSL-CM4_WRF.pdf</footnote>
is realized for FADN years 2013-2018, including Croatia. Re-calibration of yield functions is carried
out in 2022-23 for FADN years 2012-2018. The yield functions related to "future climate" (IPCC
RCP4.5 scenario) have to be renewed, after adjustments in physical parameters and after reshaping
of yield functions in "present time". This function building is realized for 3 GCM-years (2016, 2043
and 2073 as considered of statiscally representative of three-decade periods, respectively 2011-2040,
2140-2070, 2071-2100 ) in a context of climate change threw a RCP4.5 model scenario (based on
the GCM IPSL2014-CM5A-WRF 2) with strong adaptation of crops (including changes in crop
cultivars and technical routes).

New projects involving AROPAj in a climate change context will refer to greater warming under RCP8.5 scenarios. This means building new yield-functions for "future climate" years.

In terms of technical modules, the AROPAj model will soon benefit from the inclusion of the
transformation of organic matter of plant and animal origin into biogas.

<footnote n="2">²http://www.drias-climat.fr/document/Doc_DRIAS_database_IPSL2014-IPSL-CM4_WRF.pdf</footnote>
# 2 AROPAj among other agricultural economic models

## 2.1 MP models vs macro-econometric models

**Key-point:**

Completeness over competition

Compared to the econometric methods that are used for policy analyses in the agricultural sector, *MP* models offer a number of advantages. The most important difference is arguably that there are significantly fewer data requirements, allowing *MP* models to be built with just one observation (data from a single year). Econometric models, on the contrary, require large amounts of time series or panel data in order to estimate production relationships; they relate varied input to the observed output on the basis of an assumed model. Since their estimates depend on the data set that was used for estimation, they are only valid for the reference period corresponding to this data. This means that they cannot be used for economic analyses in cases of drastic policy changes, unlike *MP* models, which have the ability to examine different production methods and policy contexts as well as to analyze the interrelation between the different resources and production activities.

Econometric models are considered “descriptive” (positive) since they seek to answer the “why” and “how” questions, that is, to what extent, and how certain observable economic factors can affect a specific economic phenomenon (e.g. production). On the other hand, *MP* models are normative (determenistic) in the sense that they try to identify the optimal solution to a specific economic problem, under the assumption that economic agents behave “rationally”, i.e., they optimize their utility or welfare, under a set of constraints related to resource endowments. This framework of mathematical formulation for economic analysis presents the additional advantage that it allows the estimation of shadow prices for all scarce resources, which is important when there is no market or when their social value is not reflected in market prices.

## 2.2 One side of the market in agricultural models

**Key-points:**

Fine *LPs* aggregation regarding one side of the market

Wide opportunities for demand - supply coupling

Two inter-connected concerns are often raised by the use of *LP* one-market side models. Linearity in itself and linear programming by extension may be negatively perceived when one desires smooth functions that link prices and quantities (i.e. when there is a preference for many order differential functions). Clearly, usual *LP* corner solutions and stepwise result functions do not meet this expectation. At the same time, reality is rarely, if ever, amenable to representation by smooth functions. At the farm level, for instance, there is no doubt that discontinuous land sharing changes when prices or *CAP* tools change. This is why linearity should not be rejected *per se*. The *LP* design of farm level models is discussed hereafter (see the 2.3).
# 2 AROPAj among other agricultural economic models

## 2.1 MP models vs macro-econometric models

**Key-point:**

Completeness over competition

Compared to the econometric methods that are used for policy analyses in the agricultural sector, *MP* models offer a number of advantages. The most important difference is arguably that there are significantly fewer data requirements, allowing *MP* models to be built with just one observation (data from a single year). Econometric models, on the contrary, require large amounts of time series or panel data in order to estimate production relationships; they relate varied input to the observed output on the basis of an assumed model. Since their estimates depend on the data set that was used for estimation, they are only valid for the reference period corresponding to this data. This means that they cannot be used for economic analyses in cases of drastic policy changes, unlike *MP* models, which have the ability to examine different production methods and policy contexts as well as to analyze the interrelation between the different resources and production activities.

Econometric models are considered “descriptive” (positive) since they seek to answer the “why” and “how” questions, that is, to what extent, and how certain observable economic factors can affect a specific economic phenomenon (e.g. production). On the other hand, *MP* models are normative (determenistic) in the sense that they try to identify the optimal solution to a specific economic problem, under the assumption that economic agents behave “rationally”, i.e., they optimize their utility or welfare, under a set of constraints related to resource endowments. This framework of mathematical formulation for economic analysis presents the additional advantage that it allows the estimation of shadow prices for all scarce resources, which is important when there is no market or when their social value is not reflected in market prices.

## 2.2 One side of the market in agricultural models

**Key-points:**

Fine *LPs* aggregation regarding one side of the market

Wide opportunities for demand - supply coupling

Two inter-connected concerns are often raised by the use of *LP* one-market side models. Linearity in itself and linear programming by extension may be negatively perceived when one desires smooth functions that link prices and quantities (i.e. when there is a preference for many order differential functions). Clearly, usual *LP* corner solutions and stepwise result functions do not meet this expectation. At the same time, reality is rarely, if ever, amenable to representation by smooth functions. At the farm level, for instance, there is no doubt that discontinuous land sharing changes when prices or *CAP* tools change. This is why linearity should not be rejected *per se*. The *LP* design of farm level models is discussed hereafter (see the 2.3).
Using the *LP* option at the farm level does not preclude results with smooth curves at the sectoral level. Clearly, the aggregation of *LP* models will rarely yield a “linear” result. But, there remains the question of aggregation bias, which was raised early on by Day (1963), and subject to relaxed condition discussions that (Kennedy, 1975) dealt with among others. This is a typical problem of production sector representation when the sector is composed of numerous economic agents. Since computing tools allow us to extend the limits of modeling capabilities, the real limit is data availability and the diversity of surveyed farm systems (see Sections 3.1 related to *FADN* and Section 6 related to parameter estimation). The diversity of farm systems covered by the *AROPAj* model is addressed in Section 5.

A thorough representation of one side of the market by a model leads modelers and model users to seek information on price feedbacks. Undoubtedly, the “small country” assumption has to be rejected when the model aims at covering tje agriculture of the entire EU. Consequently, we can expect that any change in European agricultural supply would impact world and domestic prices. Scientific challenges encountered here are of different categories. First of all, adding a demand side model in the modeling framework or including the supply side model in an existing partial or general equilibrium model would be questionable in terms of modeling cost-benefit analysis. The demand system may be of high complexity comparable to the supply side, and using a simple demand elasticities matrix might not meet basic requirement of well balanced sides of the markets. More importantly, and paradoxically, possibly incorrectly calculated price feedback impacts may hide what is also of interest, namely direct impacts of environmental or economic change on the agricultural sector *ceteris paribus*. Some attempts to account for clearing market price impacts were undertaken with the linking of *AROPAj* to partial equilibrium models (e.g. *PEATSim* as illustrated in Chapter 3 of (Jayet, 2006), and *ESIM*, as illustrated by (Galko & Jayet, 2011)).

Another application of market clearing calculus is based the *MODANI* framework. The *MODANI* model incorporates the agricultural supply side model and a feed industry model developed by Olivier Lapierre (AgroParisTech) in the nineties. Raw matters supplied by *AROPAj* farmers are used by the feed industry, meanwhile concentrates produced by the latter are used by *AROPAj* breeders. More than 40 markets (raw matters and concentrates) are simultaneously taken into account (Jayet & Lapierre (1998), Jayet (2002)). An adaptive process was developed for market clearing computation, as illustrated by Figure 3.

The need for coupling supply and demand remains challenging, yet useful in many cases. This is not only a question of prices, but above all, a question of quantity limits. *AROPAj* has yet expe-rienced partial equilibrium approach with spatial and industrial capacity limits. The development of a three stage modeling chain was an attempt to assess European farmers’ capability to meet the target set by the *EC* Directive on the use of bioenergy (see Section9.7).

## 2.3 LP vs NLP models

### Key-points:

* Basic linear structure

* Linear basis does not prevent from non-linearity inclusion
Using the *LP* option at the farm level does not preclude results with smooth curves at the sectoral level. Clearly, the aggregation of *LP* models will rarely yield a “linear” result. But, there remains the question of aggregation bias, which was raised early on by Day (1963), and subject to relaxed condition discussions that (Kennedy, 1975) dealt with among others. This is a typical problem of production sector representation when the sector is composed of numerous economic agents. Since computing tools allow us to extend the limits of modeling capabilities, the real limit is data availability and the diversity of surveyed farm systems (see Sections 3.1 related to *FADN* and Section 6 related to parameter estimation). The diversity of farm systems covered by the *AROPAj* model is addressed in Section 5.

A thorough representation of one side of the market by a model leads modelers and model users to seek information on price feedbacks. Undoubtedly, the “small country” assumption has to be rejected when the model aims at covering tje agriculture of the entire EU. Consequently, we can expect that any change in European agricultural supply would impact world and domestic prices. Scientific challenges encountered here are of different categories. First of all, adding a demand side model in the modeling framework or including the supply side model in an existing partial or general equilibrium model would be questionable in terms of modeling cost-benefit analysis. The demand system may be of high complexity comparable to the supply side, and using a simple demand elasticities matrix might not meet basic requirement of well balanced sides of the markets. More importantly, and paradoxically, possibly incorrectly calculated price feedback impacts may hide what is also of interest, namely direct impacts of environmental or economic change on the agricultural sector *ceteris paribus*. Some attempts to account for clearing market price impacts were undertaken with the linking of *AROPAj* to partial equilibrium models (e.g. *PEATSim* as illustrated in Chapter 3 of (Jayet, 2006), and *ESIM*, as illustrated by (Galko & Jayet, 2011)).

Another application of market clearing calculus is based the *MODANI* framework. The *MODANI* model incorporates the agricultural supply side model and a feed industry model developed by Olivier Lapierre (AgroParisTech) in the nineties. Raw matters supplied by *AROPAj* farmers are used by the feed industry, meanwhile concentrates produced by the latter are used by *AROPAj* breeders. More than 40 markets (raw matters and concentrates) are simultaneously taken into account (Jayet & Lapierre (1998), Jayet (2002)). An adaptive process was developed for market clearing computation, as illustrated by Figure 3.

The need for coupling supply and demand remains challenging, yet useful in many cases. This is not only a question of prices, but above all, a question of quantity limits. *AROPAj* has yet expe-rienced partial equilibrium approach with spatial and industrial capacity limits. The development of a three stage modeling chain was an attempt to assess European farmers’ capability to meet the target set by the *EC* Directive on the use of bioenergy (see Section9.7).

## 2.3 LP vs NLP models

### Key-points:

* Basic linear structure

* Linear basis does not prevent from non-linearity inclusion
<figure><img src="image_4.png" /><figcaption>Figure 3. Looking for French market clearing approximated by the *MODANI* model: the case of one raw market (“mp4” refers to soft wheat) up to 40 iterations.</figcaption></figure>
<figure><img src="image_5.png" /><figcaption>Figure 3. Looking for French market clearing approximated by the *MODANI* model: the case of one raw market (“mp4” refers to soft wheat) up to 40 iterations.</figcaption></figure>
Since *LP* models have been traditionally used for farm planning, moving to aggregate geograph-
ical levels pushes the limits and renders questionable the ability to adequately simulate production
technologies. The Leontieff technology implied by *LP* is regarded as an oversimplification that
can only be justified by a lack of data necessitated by more appropriate profit functions (Howitt,
1995). Clearly, developing models that do not correctly represent the technology used, means that
model outcomes do not necessarily reflect reality and cannot be considered as valid analytical tools
(Arfini, 2001). The validation of the model is thus one of the most important steps in the process
of model building. *MP* models are commonly validated with the production test, which entails
examining how well the model is able to replicate the observed production levels (Hazell & Norton,
1986). Given that most constraints that are used for farm models cannot be formulated at the
regional level, the problem of overspecialization (or corner solutions) is of great concern for *LP*
models.

In order to overcome the limitations of the *LP* framework, the literature suggests the use of nonlinear objective functions with which interior solutions can be achieved. It should be noted that nonlinearities in optimization models were not sought initially for calibration reasons but rather for their ability to answer specific questions of economic research, such as price formation in agricultural markets and farmers’ risk considerations (such models will be presented in the next paragraphs), for which *LP* models are inadequate. Nevertheless, their ability to provide optimal solutions that are not limited to the edges of the constraint set (corner solutions) is supposed to increase the validity of the model.

Probably the most widely used type of nonlinear programming (NLP) models built for policy
analysis are those which are based on the principles of Positive Mathematical Programming (PMP).
PMP was formalized by Howitt (1995) and relies on the assumption that there is some marginal
implicit information that needs to be captured in order to calibrate the model. The traditional
PMP method uses a three-step algorithm, beginning with a model that includes calibration con-
straints, whose *shadow prices* are supposed to contain all information not observed by the analyst.
In the following steps, the PMP algorithm introduces (or re-estimates) nonlinear terms in the ob-
jective function using the previously estimated implicit information, so that the model’s first order
conditions are satisfied exactly at the observed production level. The main advantage of PMP is its
ability to exactly calibrate any type of optimization model –typically *LP* ones– by using minimal
data, such as a total land constraint. Despite criticisms (e.g. Heckelei & Wolff, 2003), PMP has
continued to be used in numerous applications, including major European research projects such
as *CAPRI* and *EUROTOOLS* with the aim to analyze the effects of the continuously changing
European *CAP* regime.

NLP models can be built using simulated partial equilibrium conditions by finding the optimal price-quantity correspondance for clearing the market of one or more activities and/or factors of production (e.g. McCarl & Sreen, 1980). Since such models (also called “price-endogenous” models) consider both the supply and the demand side of inputs and outputs, they relax the basic assumption of traditional LP models that farmers are price takers. In this sense, such a model no longer maximizes aggregate profits but instead returns the total producer and/or consumer surplus at the point of market equilibrium. Price-endogenous models are intrinsically nonlinear since the price of one or more activities is defined as a function of the aggregate quantity produced. The main difficulty with such models is that they require a large amount of information that is rather
Since *LP* models have been traditionally used for farm planning, moving to aggregate geographical levels pushes the limits and renders questionable the ability to adequately simulate production technologies. The Leontieff technology implied by *LP* is regarded as an oversimplification that can only be justified by a lack of data necessitated by more appropriate profit functions (Howitt, 1995). Clearly, developing models that do not correctly represent the technology used, means that model outcomes do not necessarily reflect reality and cannot be considered as valid analytical tools (Arfini, 2001). The validation of the model is thus one of the most important steps in the process of model building. *MP* models are commonly validated with the production test, which entails examining how well the model is able to replicate the observed production levels (Hazell & Norton, 1986). Given that most constraints that are used for farm models cannot be formulated at the regional level, the problem of overspecialization (or corner solutions) is of great concern for *LP* models.

In order to overcome the limitations of the *LP* framework, the literature suggests the use of nonlinear objective functions with which interior solutions can be achieved. It should be noted that nonlinearities in optimization models were not sought initially for calibration reasons but rather for their ability to answer specific questions of economic research, such as price formation in agricultural markets and farmers’ risk considerations (such models will be presented in the next paragraphs), for which *LP* models are inadequate. Nevertheless, their ability to provide optimal solutions that are not limited to the edges of the constraint set (corner solutions) is supposed to increase the validity of the model.

Probably the most widely used type of nonlinear programming (*NLP*) models built for policy analysis are those which are based on the principles of Positive Mathematical Programming (*PMP*). *PMP* was formalized by Howitt (1995) and relies on the assumption that there is some marginal implicit information that needs to be captured in order to calibrate the model. The traditional *PMP* method uses a three-step algorithm, beginning with a model that includes calibration constraints, whose *shadow prices* are supposed to contain all information not observed by the analyst. In the following steps, the *PMP* algorithm introduces (or re-estimates) nonlinear terms in the objective function using the previously estimated implicit information, so that the model’s first order conditions are satisfied exactly at the observed production level. The main advantage of *PMP* is its ability to exactly calibrate any type of optimization model –typically *LP* ones– by using minimal data, such as a total land constraint. Despite criticisms (e.g. Heckelei & Wolff, 2003), *PMP* has continued to be used in numerous applications, including major European research projects such as *CAPRI* and *EUROTOOLS* with the aim to analyze the effects of the continuously changing European *CAP* regime.

*NLP* models can be built using simulated partial equilibrium conditions by finding the optimal price-quantity correspondence for clearing the market of one or more activities and/or factors of production (e.g. McCarl & Sreen, 1980). Since such models (also called “price-endogenous” models) consider both the supply and the demand side of inputs and outputs, they relax the basic assumption of traditional *LP* models that farmers are price takers. In this sense, such a model no longer maximizes aggregate profits but instead returns the total producer and/or consumer surplus at the point of market equilibrium. Price-endogenous models are intrinsically nonlinear since the price of one or more activities is defined as a function of the aggregate quantity produced. The main difficulty with such models is that they require a large amount of information that is rather
difficult to find, namely pre-estimated demand and supply elasticity values. Although they can
offer important insights on how the global agri-food system works, partial equilibrium models are
usually highly aggregated representations of agricultural markets and cannot easily capture the
heterogeneity of agricultural production within a specific region. Examples of such models are the
IMPACT model from IFPRI and the GLOBIOM model from IIASA.

Mean-Variance (E-V) models are another type of nonlinear MP models used for policy analysis. E-V models, building on the pioneering work of Markowitz (1952), are able to capture the effect of uncertainty and risk on farmers’ decision making process. This is achieved with a nonlinear objective function which maximizes the expected utility (EU) of farm profit (or more generally, wealth). The most commonly used specification of an E-V model is the linear one, which was first presented by Freund (1956) and which is expressed as: EU = μ - 1/2 φσ², where μ is the mean farm profit, φ is the risk aversion coefficient, and σ² the variance of farm profit. A serious shortcoming of E-V models is that they are difficult to build when a large number of activities is considered because the variance term is typically based on time series of prices and/or yields, which are rarely available at the farm or regional level.<fnref n="3" /> This may lead to a biased representation of uncertainty faced by the farmers. Another problem with linear E-V models is that the risk aversion coefficient is not easy to estimate. Nevertheless, modelers usually solve their model for different values of φ and select the one which yields an optimal solution that best approximates the observed production plan. As a result of this practice, a level of calibration is also achieved.

<footnote n="3">³In sector models that include representations of both the output supply and demand side, the initial source of uncertainty is the variation of yields, since the final market price is endogenously calculated by the model.</footnote>
difficult to find, namely pre-estimated demand and supply elasticity values. Although they can
offer important insights on how the global agri-food system works, partial equilibrium models are
usually highly aggregated representations of agricultural markets and cannot easily capture the
heterogeneity of agricultural production within a specific region. Examples of such models are the
IMPACT model from IFPRI and the GLOBIOM model from IIASA.

Mean-Variance (E-V) models are another type of nonlinear MP models used for policy analysis. E-V models, building on the pioneering work of Markowitz (1952), are able to capture the effect of uncertainty and risk on farmers’ decision making process. This is achieved with a nonlinear objective function which maximizes the expected utility (EU) of farm profit (or more generally, wealth). The most commonly used specification of an E-V model is the linear one, which was first presented by Freund (1956) and which is expressed as: EU = μ - 1/2 φσ², where μ is the mean farm profit, φ is the risk aversion coefficient, and σ² the variance of farm profit. A serious shortcoming of E-V models is that they are difficult to build when a large number of activities is considered because the variance term is typically based on time series of prices and/or yields, which are rarely available at the farm or regional level.<fnref n="3" /> This may lead to a biased representation of uncertainty faced by the farmers. Another problem with linear E-V models is that the risk aversion coefficient is not easy to estimate. Nevertheless, modelers usually solve their model for different values of φ and select the one which yields an optimal solution that best approximates the observed production plan. As a result of this practice, a level of calibration is also achieved.

<footnote n="3">³In sector models that include representations of both the output supply and demand side, the initial source of uncertainty is the variation of yields, since the final market price is endogenously calculated by the model.</footnote>
# 3 Input data

When working with a model, it is essential to carefully choose data. For the implementation of *AROPAj*, the researching and update of data required a significant effort. Indeed, the data used are regularly changed and every year it appears new. Therefore we must constantly search for updates and ensure that our data sets remain up to date and relevant. Moreover, the model *AROPAj* model necessitates the processing of collected data into a specific format (see 4).

<figure><img src="image_5.png" /><figcaption>**Figure 4.** General illustrative scheme of data management.</figcaption></figure>

## 3.1 The FADN at the core of the farming system representation

Key-points:

- Data as major limiting factor for economic analysis

- A chance with the *FADN* to relax this constraint

- Associating micro-economic and bio-physical data

The *FADN* is the main data source of the *AROPAj* model, since it statistically represents farming system heterogeneity on the regional and covers the entire European Union. The various versions of the *AROPAj* model rely on different annual *FADN* samples with respect to restricted conditions, e.g. no *FADN* sourced estimate should be based on less than 15 sample farms. Description and characteristics of the *FADN* are of free access on-line: http://ec.europa.eu/agriculture/rica/. Researchers must sign an individual form each time they use raw data from
# 3 Input data

When working with a model, it is essential to carefully choose data. For the implementation of *AROPAj*, the researching and update of data required a significant effort. Indeed, the data used are regularly changed and every year it appears new. Therefore we must constantly search for updates and ensure that our data sets remain up to date and relevant. Moreover, the model *AROPAj* model necessitates the processing of collected data into a specific format (see 4).

<figure><img src="image_6.png" /><figcaption>**Figure 4.** General illustrative scheme of data management.</figcaption></figure>

## 3.1 The FADN at the core of the farming system representation

Key-points:

- Data as major limiting factor for economic analysis

- A chance with the *FADN* to relax this constraint

- Associating micro-economic and bio-physical data

The *FADN* is the main data source of the *AROPAj* model, since it statistically represents farming system heterogeneity on the regional and covers the entire European Union. The various versions of the *AROPAj* model rely on different annual *FADN* samples with respect to restricted conditions, e.g. no *FADN* sourced estimate should be based on less than 15 sample farms. Description and characteristics of the *FADN* are of free access on-line: http://ec.europa.eu/agriculture/rica/. Researchers must sign an individual form each time they use raw data from
the European Commission. Data access is permitted by the European framework programmes for research.

As a partner or as the cordinator (GENEDEC), the INRA-Economie Publique unit was granted access to the FADN data for the following research programmes:

* FP4-FAIR EUROTOOLS (EU-12): FADN - 1997: "Tools for evaluating EU agricultural policy at different decision levels"
http://cordis.europa.eu/project/rcn/48045_en.html

* FP6 GENEDEC (EU-15 and EU-25): FADN - 2002, 2004: "A quantitative and qualitative assessment of the socio-economic and environmental impacts of decoupling of direct payments on agricultural production, markets and land use in the EU"
http://cordis.europa.eu/result/rcn/49674_de.html

* FP7 AnimalChange (EU-27): FADN - 2007-2009: "An Integration of Mitigation and Adaptation Options for Sustainable Livestock Production under Climate Change" http://www.animalchange.eu/

* FP7 FoodSecure (EU-27): FADN - 2007-2011: "An interdisciplinary research project to explore the future of global food and nutrition security" (in progress)
http://www.foodsecure.eu/

Other European programmes referred to FADN and AROPAj, i.e. INSEA (FP6, "Integrated Sink Enhancement Assessment" http://esdac.jrc.ec.europa.eu/projects/INSEA/), CCTAME (FP7, "Climate Change - Terrestrial Adaptation & Mitigation in Europe" http://www.cctame.eu/).

The FADN database provides farm-level information mainly in terms of accountancy and financial or economic variables. The FADN database also offers information regarding physical content such as areas, livestock, and products. Nevertheless, much of the AROPAj parameters are not directly sourced by raw FADN data. For instance, the model's need for costs per crop or per animal necessitates the use of econometric calculation. In addition, the techno-economic character of the AROPAj model demands that information be gathered from other data sources, including expert reports and books (among them attention is paid to livestock feeding).

The need for external information is even more critical for the technical parts of the AROPAj modeling chain, namely the "dose-response functions" (see the section devoted to N-yield function building), and the geographical probability distribution of AROPAj representative farming systems (see the section devoted to spatial econometrics and farm group spatialization). In any case we need FADN data, either for micro-economic estimates or for economic and physical data coupling.

## 3.2 Other sources required by some AROPAj modules

**Key-points:**

- Associating micro-economic and bio-physical data

- Physical data related to CLC, LUCAS, ESB, climate, DEM

- Using the IPCC guidelines for comparison with UNFCCC data

Numerous sources have been used for the spatialization procedure.
the European Commission. Data access is permitted by the European framework programmes for research.

As a partner or as the cordinator (GENEDEC), the INRA-Economie Publique unit was granted access to the FADN data for the following research programmes:

* FP4-FAIR EUROTOOLS (EU-12): FADN - 1997: "Tools for evaluating EU agricultural policy at different decision levels"
http://cordis.europa.eu/project/rcn/48045_en.html

* FP6 GENEDEC (EU-15 and EU-25): FADN - 2002, 2004: "A quantitative and qualitative assessment of the socio-economic and environmental impacts of decoupling of direct payments on agricultural production, markets and land use in the EU"
http://cordis.europa.eu/result/rcn/49674_de.html

* FP7 AnimalChange (EU-27): FADN - 2007-2009: "An Integration of Mitigation and Adaptation Options for Sustainable Livestock Production under Climate Change" http://www.animalchange.eu/

* FP7 FoodSecure (EU-27): FADN - 2007-2011: "An interdisciplinary research project to explore the future of global food and nutrition security" (in progress)
http://www.foodsecure.eu/

Other European programmes referred to FADN and AROPAj, i.e. INSEA (FP6, "Integrated Sink Enhancement Assessment" http://esdac.jrc.ec.europa.eu/projects/INSEA/), CCTAME (FP7, "Climate Change - Terrestrial Adaptation & Mitigation in Europe" http://www.cctame.eu/).

The FADN database provides farm-level information mainly in terms of accountancy and financial or economic variables. The FADN database also offers information regarding physical content such as areas, livestock, and products. Nevertheless, much of the AROPAj parameters are not directly sourced by raw FADN data. For instance, the model's need for costs per crop or per animal necessitates the use of econometric calculation. In addition, the techno-economic character of the AROPAj model demands that information be gathered from other data sources, including expert reports and books (among them attention is paid to livestock feeding).

The need for external information is even more critical for the technical parts of the AROPAj modeling chain, namely the "dose-response functions" (see the section devoted to N-yield function building), and the geographical probability distribution of AROPAj representative farming systems (see the section devoted to spatial econometrics and farm group spatialization). In any case we need FADN data, either for micro-economic estimates or for economic and physical data coupling.

## 3.2 Other sources required by some AROPAj modules

**Key-points:**

* Associating micro-economic and bio-physical data

* Physical data related to CLC, LUCAS, ESB, climate, DEM

* Using the IPCC guidelines for comparison with UNFCCC data

Numerous sources have been used for the spatialization procedure.
### 3.2.1 Data concerning land use and land cover

1. Land Use/Cover Area frame Statistical Survey (LUCAS)

Two LUCAS data sets (2001/2003 and 2012) are used for the spatialization procedures of V2 and V5 of AROPAj. LUCAS survey provides information concerning the observation of different crops at different points in space. This information serves as a regressant in a multinomial logit model. The database accounts also for irrigating practices when observed. We aggregate this information at the scale of a 10 km grid in order to integrate it into the subsequent steps of the spatialization.

Source:

http://epp.eurostat.ec.europa.eu/portal/page/portal/lucas/introduction

2. CORINE Land Cover (CLC)

Information on land cover at a fine scale (100 m) is provided in the CLC database. Land cover is presented in 44 classes. In the first version of the spatialization procedure, we use numerous classes which are often used in the agriculture covered by the FADN. In the latest version of the spatialization, the procedure only covers activities involved in AROPAj.

Sources:

http://www.eea.europa.eu/data-and-maps/data/corine-land-cover-2000-clc2000-100-m-version-

http://www.eea.europa.eu/data-and-maps/data/corine-land-cover-2006-raster-3

### 3.2.2 The European Soil Database (ESDB v2.0)

The European Soil Database and the Pedotransfer Rules Database are provided by the European Joint Research Centre (JRC).

Source:

http://eusoils.jrc.ec.europa.eu/ESDB_Archive/ESDB_Data_Distribution/ESDB_data.html
(Registration required)

### 3.2.3 Digital Elevation Model (DEM)

Geographical information concerning altitude is obtained from the United States Geographical Survey's model GTOPO30 at the scale of approximately 1km (30 arc seconds). Slope is then evaluated.

Source:

https://lta.cr.usgs.gov/GTOPO30

### 3.2.4 Climate

Climate information is provided by the European Union Joint Research Centre MARS Unit. The AGRI4CAST Interpolated Meteorological Data is available at the scale of a 25 km grid and covers weather variables since 1975.

Source:

http://mars.jrc.ec.europa.eu/mars/About-us/AGRI4CAST/Data-distribution/AGRI4CAST-Interpolate
(Registration required)
### 3.2.1 Data concerning land use and land cover

1. Land Use/Cover Area frame Statistical Survey (LUCAS)

Two LUCAS data sets (2001/2003 and 2012) are used for the spatialization procedures of V2 and V5 of AROPAj. LUCAS survey provides information concerning the observation of different crops at different points in space. This information serves as a regressant in a multinomial logit model. The database accounts also for irrigating practices when observed. We aggregate this information at the scale of a 10 km grid in order to integrate it into the subsequent steps of the spatialization.

Source:

http://epp.eurostat.ec.europa.eu/portal/page/portal/lucas/introduction

2. CORINE Land Cover (CLC)

Information on land cover at a fine scale (100 m) is provided in the CLC database. Land cover is presented in 44 classes. In the first version of the spatialization procedure, we use numerous classes which are often used in the agriculture covered by the FADN. In the latest version of the spatialization, the procedure only covers activities involved in AROPAj.

Sources:

http://www.eea.europa.eu/data-and-maps/data/corine-land-cover-2000-clc2000-100-m-version-

http://www.eea.europa.eu/data-and-maps/data/corine-land-cover-2006-raster-3

### 3.2.2 The European Soil Database (ESDB v2.0)

The European Soil Database and the Pedotransfer Rules Database are provided by the European Joint Research Centre (JRC).

Source:

http://eusoils.jrc.ec.europa.eu/ESDB_Archive/ESDB_Data_Distribution/ESDB_data.html
(Registration required)

### 3.2.3 Digital Elevation Model (DEM)

Geographical information concerning altitude is obtained from the United States Geographical Survey's model GTOPO30 at the scale of approximately 1km (30 arc seconds). Slope is then evaluated.

Source:

https://lta.cr.usgs.gov/GTOPO30

### 3.2.4 Climate

Climate information is provided by the European Union Joint Research Centre MARS Unit. The AGRI4CAST Interpolated Meteorological Data is available at the scale of a 25 km grid and covers weather variables since 1975.

Source:

http://mars.jrc.ec.europa.eu/mars/About-us/AGRI4CAST/Data-distribution/AGRI4CAST-Interpolate
(Registration required)
### 3.2.5 IPCC guidelines

The IPCC parameters for the EU Member States can be found in their National Reports of GHG Inventories, more specifically in their Tables 4 “Sectoral Report for Agriculture”. These are submitted to the United Nations Framework Convention on Climate Change (UNFCCC), whose objective is to stabilize greenhouse gas (GHG) concentrations in the atmosphere at a level that would prevent and reduce dangerous anthropogenic interference with the climate system. Achieving this objective is dependent on an accurate knowledge of GHG emissions trends and on our collective ability to alter these trends.

The use of IPCC guidelines is detailed in 4.2.5 on page 66.

## 3.3 Data related to other models

**Key-point:**

Added external data required for model coupling and applications

Due to the wide variety of models employed with AROPAj, a wide variety of data is mobilized in the modeling chain. Consistency of data involved in the various parts has to be checked. At the same time, each of the different models is developed independently. In some cases, climate, soil and farm management data are not from the same sources nor of the same scale, time period, and horizon. The reader has to keep this in mind, not only for discussing model assumptions but also for discussing scenarios which govern AROPAj based simulations.

See Section 9 for more information.

### 3.3.1 STICS

In order to run at the farm-type level, the STICS model had to make the most of data from existing databases (see Section 3.2 above for details): European Soil Database (ESDB), Digital elevation model (DEM), Climate database from MARS JRC Unit, and FADN. To infer STICS input data, a special effort was made to incorporate agricultural practices, as they are key variables for the modeling of farmers' actions and of the link between their economic behaviour (modelled by AROPAj) and the biophysical functioning of a field (modelled by STICS). The expert statements that determine all the STICS inputs are detailed in Godard et al. (2008). Through the linkage with the STICS model, AROPAj is provided with crop N-response curves (for yield and N-losses to the environment), thereby integrating the pedoclimatic conditions of each European farm-type. Moreover, thanks to this linkage, equivalence coefficients of N fertilizer were provided for manure-sourced N.

### 3.3.2 PaSim

The PaSim model feeds AROPAj through an external way, in the sense that there is no feedback between the two models, unlike the case of the AROPAj-STICS linkage (see Section 9.3).

Running the PaSim model calls for basic settings of vegetation type settings such as intensively managed productive grassland (rye-grass/white clover mixture) as well as different input combina-
### 3.2.5 IPCC guidelines

The IPCC parameters for the EU Member States can be found in their National Reports of GHG Inventories, more specifically in their Tables 4 “Sectoral Report for Agriculture”. These are submitted to the United Nations Framework Convention on Climate Change (UNFCCC), whose objective is to stabilize greenhouse gas (GHG) concentrations in the atmosphere at a level that would prevent and reduce dangerous anthropogenic interference with the climate system. Achieving this objective is dependent on an accurate knowledge of GHG emissions trends and on our collective ability to alter these trends.

The use of IPCC guidelines is detailed in 4.2.5 on page 70.

## 3.3 Data related to other models

**Key-point:**

Added external data required for model coupling and applications

Due to the wide variety of models employed with AROPAj, a wide variety of data is mobilized in the modeling chain. Consistency of data involved in the various parts has to be checked. At the same time, each of the different models is developed independently. In some cases, climate, soil and farm management data are not from the same sources nor of the same scale, time period, and horizon. The reader has to keep this in mind, not only for discussing model assumptions but also for discussing scenarios which govern AROPAj based simulations.

See Section 9 for more information.

### 3.3.1 STICS

In order to run at the farm-type level, the STICS model had to make the most of data from existing databases (see Section 3.2 above for details): European Soil Database (ESDB), Digital elevation model (DEM), Climate database from MARS JRC Unit, and FADN. To infer STICS input data, a special effort was made to incorporate agricultural practices, as they are key variables for the modeling of farmers' actions and of the link between their economic behaviour (modelled by AROPAj) and the biophysical functioning of a field (modelled by STICS). The expert statements that determine all the STICS inputs are detailed in Godard et al. (2008). Through the linkage with the STICS model, AROPAj is provided with crop N-response curves (for yield and N-losses to the environment), thereby integrating the pedoclimatic conditions of each European farm-type. Moreover, thanks to this linkage, equivalence coefficients of N fertilizer were provided for manure-sourced N.

### 3.3.2 PaSim

The PaSim model feeds AROPAj through an external way, in the sense that there is no feedback between the two models, unlike the case of the AROPAj-STICS linkage (see Section 9.3).

Running the PaSim model calls for basic settings of vegetation type settings such as intensively managed productive grassland (rye-grass/white clover mixture) as well as different input combina-
tions including: <fnref n="4" /> (i) three climate scenarios, in line with the work of Leclère et al. (2014) (see also Leclère et al. (2013)) with a 0.5° x 0.5° spatial resolution; (ii) soil properties database, in which medium soil, with the 0.25 deg mean percent sand/silt/clay/organic/gravel, has been extracted from the Harmonized World Soil Database (source: the US Department of Agriculture); (iii) three types of nitrogen management generated by the CAPRI EU-wide agricultural sector model, which are region dependent, ranging from 0 to 0.35 t N/ha.

<footnote n="4">⁴Aghajanzadeh-Darzi, P., Laperche, S., Martin, R., Jayet, P.A., (2015), Vulnerability of grassland systems to future climate variability: Impact assessment across the European Union, submitted.</footnote>
tions including: <fnref n="4" /> (i) three climate scenarios, in line with the work of Leclère et al. (2014) (see also Leclère et al. (2013)) with a 0.5° x 0.5° spatial resolution; (ii) soil properties database, in which medium soil, with the 0.25 deg mean percent sand/silt/clay/organic/gravel, has been extracted from the Harmonized World Soil Database (source: the US Department of Agriculture); (iii) three types of nitrogen management generated by the CAPRI EU-wide agricultural sector model, which are region dependent, ranging from 0 to 0.35 t N/ha.

<footnote n="4">⁴Aghajanzadeh-Darzi, P., Laperche, S., Martin, R., Jayet, P.A., (2015), Vulnerability of grassland systems to future climate variability: Impact assessment across the European Union, submitted.</footnote>
# 4 Architecture of the modelling framework

The structure of the AROPAj model and its last developments have been briefly presented in several papers (De Cara et al., 2005; Bambière et al., 2005; De Cara & Jayet, 2000a; Galko & Jayet, 2011). We focus here on the LP model core, delineated in variables, functions or routines, and parameters. In this section, we aim at describing the production set and the objective function related to each economic unit's behavior. We provide comprehensive lists of activities and parameters covering all eligible items for all economic units. As explained below, we use "flags" when certain activities and parameters are not relevant for some units.

We consider that each economic unit refers to a farm group, implicitly viewed as a cluster of homogeneous farming systems. In doing so, the overall model is based on farm-groups, designed at the region scale, for all EU regions. An AROPAj region refers to a regional FADN unit. Any AROPAj version refers to a series of farm groups accurately defined by clustering techniques within each region.

The basic structure of the modelling framework uses linear programming (LP), popular over the years in agricultural economics. Let us consider the problem of farming systems that attempt to optimize their gross margins when their activities are subject to economic and technical constraints.

The model consists of a set of independent, mixed integer and linear-programming models. Each model describes the annual supply choice of a given 'farm-group' (denoted by $k$), representative of the behaviour of "real" farmers. The farm-group representation makes it possible to account for the wide diversity of technical constraints faced by European farmers. Each farm-group $k$ is assumed to choose the supply level and the input demand ($x_k$) that maximizes total gross margin ($\pi_k$). In its most general expression, the generic model for farm-group $k$ can be written as follows:

$$ 
\begin{array}{ll}
\max_{x_k} & \pi_k(x_k) = \max g_k \cdot x_k \\
\text{s.t.} & A_k \cdot x_k \le z_k \quad (\lambda_k) \\
& x_k \ge 0 \quad (\mu_k)
\end{array}
$$

where $x_k$ is the $n$-dimension vector of producing activities for farm-group $k$, and $g_k$ is their $n$-dimension vector of valuations in the gross margin. The matrix $A_k$ is of $m \times n$ dimensions and refers to input-output coefficients. The $z_k$ $m$-dimension vector refers to right-hand side (RHS) capacities. Together, $A_k$ and $z_k$ define $m$ constraints faced by farm-group $k$. We set $\lambda_k$ as the $m$-dimension vector of associated Lagrange multipliers. Without loss of generality, the $x_k$ vector stands for positive quantities, and the associated Lagrange vector is denoted by $\mu_k$. The $x_k$ activity vector has to be understood in a wide sense, knowing that the LP model may require additional intermediate variables for which objective valuations are usually null.

The components of $x_k$ include, among others, the area and the production devoted to each crop, animal heads related to each animal category, milk and meat production as well as the quantity of purchased animal feed. The gross margin, $g_k$, contains series of elements corresponding to each production activity, which, for crops, gives per-ton revenue (price, when the production is partly or totally sold) and, when relevant, per-hectare support received, minus per-hectare variable costs. As the emphasis is on the farm-group level, each farm-group is assumed to be a price-taker. Thirty-two crop producing activities are permitted in the model and represent most of the European
# 4 Architecture of the modelling framework

The structure of the AROPAj model and its last developments have been briefly presented in several papers (De Cara et al., 2005; Bambière et al., 2005; De Cara & Jayet, 2000a; Galko & Jayet, 2011). We focus here on the LP model core, delineated in variables, functions or routines, and parameters. In this section, we aim at describing the production set and the objective function related to each economic unit's behavior. We provide comprehensive lists of activities and parameters covering all eligible items for all economic units. As explained below, we use "flags" when certain activities and parameters are not relevant for some units.

We consider that each economic unit refers to a farm group, implicitly viewed as a cluster of homogeneous farming systems. In doing so, the overall model is based on farm-groups, designed at the region scale, for all EU regions. An AROPAj region refers to a regional FADN unit. Any AROPAj version refers to a series of farm groups accurately defined by clustering techniques within each region.

The basic structure of the modelling framework uses linear programming (LP), popular over the years in agricultural economics. Let us consider the problem of farming systems that attempt to optimize their gross margins when their activities are subject to economic and technical constraints.

The model consists of a set of independent, mixed integer and linear-programming models. Each model describes the annual supply choice of a given 'farm-group' (denoted by $k$), representative of the behaviour of "real" farmers. The farm-group representation makes it possible to account for the wide diversity of technical constraints faced by European farmers. Each farm-group $k$ is assumed to choose the supply level and the input demand ($x_k$) that maximizes total gross margin ($\pi_k$). In its most general expression, the generic model for farm-group $k$ can be written as follows:

$$ 
\begin{array}{ll}
\max_{x_k} & \pi_k(x_k) = \max g_k \cdot x_k \\
\text{s.t.} & A_k \cdot x_k \le z_k \quad (\lambda_k) \\
& x_k \ge 0 \quad (\mu_k)
\end{array}
$$

where $x_k$ is the $n$-dimension vector of producing activities for farm-group $k$, and $g_k$ is their $n$-dimension vector of valuations in the gross margin. The matrix $A_k$ is of $m \times n$ dimensions and refers to input-output coefficients. The $z_k$ $m$-dimension vector refers to right-hand side (RHS) capacities. Together, $A_k$ and $z_k$ define $m$ constraints faced by farm-group $k$. We set $\lambda_k$ as the $m$-dimension vector of associated Lagrange multipliers. Without loss of generality, the $x_k$ vector stands for positive quantities, and the associated Lagrange vector is denoted by $\mu_k$. The $x_k$ activity vector has to be understood in a wide sense, knowing that the LP model may require additional intermediate variables for which objective valuations are usually null.

The components of $x_k$ include, among others, the area and the production devoted to each crop, animal heads related to each animal category, milk and meat production as well as the quantity of purchased animal feed. The gross margin, $g_k$, contains series of elements corresponding to each production activity, which, for crops, gives per-ton revenue (price, when the production is partly or totally sold) and, when relevant, per-hectare support received, minus per-hectare variable costs. As the emphasis is on the farm-group level, each farm-group is assumed to be a price-taker. Thirty-two crop producing activities are permitted in the model and represent most of the European
agricultural land related to arable land and pasture. Crop production can be sold at the market price or used for animal feeding purposes (feed grains, forage, and pastures). As for livestock, thirty-one animal categories are represented in the model (27 for cattle plus one each for sheep, goats, swine, and poultry). Cattle categories depend on the age, the gender, the origin (on-farm or bought animals), the final output (dairy or meat), and CAP subsidies.

A comprehensive list of crops and animal categories included in the model is provided on Table 35. This table also provides related index values ($i$ for animals and $j$ for crops) used in the “matrix generator” (see the aro.mgg file to which it is refereed hereafter), and the 2-character strings relating these index values to parameters in the data file mgg.par. Among other basic elements of the model, concentrated feed are of 4 categories referring to the $n$-index and to the 2-character strings a1-a4 respectively denoting simple energy concentrate, simple protein concentrate, energy concentrated compound and protein concentrated compound. Parameter names referring to bought raw feed use the ag string.

The technically feasible production set is bounded by the constraints defined by $A_k$ and $z_k$. Basic blocks of constraints include:

1. crop rotations and crop use (split in marketed output and on-farm consumption),

2. animal feeding,

3. internal relationship between bovine categories and livestock number limits (including key livestock adjustment allowing livestock to vary in a limited range (minus and plus $\pm 15\ numbers$ in the corresponding animal categories),$^5$)

4. specific environmental balances and limits,

5. CAP instruments implementation,

6. resource endowments (land, quasi-fix livestock, quotas),

7. non previously affected constraints (denominated by “general”).

All LP coefficients, i.e. valuation terms ($g_k$), matrix elements ($A_k$), and endowments ($z_k$) depend on parameters. Some of them relate to farm groups; they are denoted by $\theta_k$. Others refer to constant items or to common economic environment, e.g. related to the CAP; they are denoted by $\phi$. Any LP coefficient may be viewed like a function, i.e. $g_k(\theta_k, \phi)$, $A_{kmn}(\theta_k, \phi)$, $z_k(\theta_k, \phi)$. These functions may be non linear, perhaps even non-analytic. A key point of the modeling chain is to construct the matrix generator, which allows for the construction of the LP and the opportunity to feed it with parameter estimates.

## 4.1 Overall technical structure of the model

### Key-points:

- Modularity, genericity

- Nested partitioning: Farm group $\subset$ region $\subset$ MS $\subset$ EU

- Key items: parameters, primal and dual variables

<footnote>$^5$The discretionary level of the range is usually adopted as close to the yearly basic period of the AROPAj model divided by the average cow lifespan.</footnote>
agricultural land related to arable land and pasture. Crop production can be sold at the market price or used for animal feeding purposes (feed grains, forage, and pastures). As for livestock, thirty-one animal categories are represented in the model (27 for cattle plus one each for sheep, goats, swine, and poultry). Cattle categories depend on the age, the gender, the origin (on-farm or bought animals), the final output (dairy or meat), and CAP subsidies.

A comprehensive list of crops and animal categories included in the model is provided on Table 35. This table also provides related index values ($i$ for animals and $j$ for crops) used in the “matrix generator” (see the aro.mgg file to which it is refereed hereafter), and the 2-character strings relating these index values to parameters in the data file mgg.par. Among other basic elements of the model, concentrated feed are of 4 categories referring to the $n$-index and to the 2-character strings a1-a4 respectively denoting simple energy concentrate, simple protein concentrate, energy concentrated compound and protein concentrated compound. Parameter names referring to bought raw feed use the ag string.

The technically feasible production set is bounded by the constraints defined by $A_k$ and $z_k$. Basic blocks of constraints include:

1. crop rotations and crop use (split in marketed output and on-farm consumption),

2. animal feeding,

3. internal relationship between bovine categories and livestock number limits (including key livestock adjustment allowing livestock to vary in a limited range (minus and plus $\pm 15\ numbers$ in the corresponding animal categories),$^5$)

4. specific environmental balances and limits,

5. CAP instruments implementation,

6. resource endowments (land, quasi-fix livestock, quotas),

7. non previously affected constraints (denominated by “general”).

All LP coefficients, i.e. valuation terms ($g_k$), matrix elements ($A_k$), and endowments ($z_k$) depend on parameters. Some of them relate to farm groups; they are denoted by $\theta_k$. Others refer to constant items or to common economic environment, e.g. related to the CAP; they are denoted by $\phi$. Any LP coefficient may be viewed like a function, i.e. $g_k(\theta_k, \phi)$, $A_{kmn}(\theta_k, \phi)$, $z_k(\theta_k, \phi)$. These functions may be non linear, perhaps even non-analytic. A key point of the modeling chain is to construct the matrix generator, which allows for the construction of the LP and the opportunity to feed it with parameter estimates.

## 4.1 Overall technical structure of the model

### Key-points:

- Modularity, genericity

- Nested partitioning: Farm group $\subset$ region $\subset$ MS $\subset$ EU

- Key items: parameters, primal and dual variables

<footnote>$^5$The discretionary level of the range is usually adopted as close to the yearly basic period of the AROPAj model divided by the average cow lifespan.</footnote>
The model is built in such a way as that it facilitates its evolution and the addition of new blocks in accordance with new research problematics. That includes changes in farm group clustering and the introduction of new farm groups (e.g. in case of the EU enlargement). Other cases of model evolution are new environmental issues (nitrogen losses and GHG emissions), and refining of the production set in terms of input-output interaction (e.g. nitrogen to yield functions for crops). This requires a comprehensive parametrization of the model, and an extensible range of indexes.

Following notations mentioned above, parameters $\theta_k$ for all farm groups 1...k...K and parameters $\phi$ represent the comprehensive set of AROPAj parameters. The objective vector ($g_k$ also denoted by OBJ), the "right hand side" vector ($z_k$ also denoted by RHS), and the matrix $A_k$ are composed of elements which all refer to these parameters.

The key items facilitating the presentation of the model structure are:

* *index*: affects parameters, variables, functions, conditions

* *parameter*: refers to data; their values are raw data used in the model through matrix elements; the way in which raw data is used by the model is described in Section 11.2

* *variable*: compound of the LP solution

- *primal*: related to an activity (e.g. a command variable of the LP); regarding the LP structure, primal variables are "columns", and RHS is viewed as one of them

- *dual*: related to a constraint and labeled by constraint name; regarding the LP structure, dual variables are "rows", and OBJ is viewed as one of them

* *element*: intersects a row and a column, is a (possibly non-linear, even non-analytic) function of parameters and indexes

* *function*: of which variables are indexes, parameters and external data

* *condition*: may enter a "flag" activating one variable or a subset of variables

* *block*: a subset of activities and constraints characterizing either a part of the modeled farming system, or a policy (agricultural or environmental), or a category of environmental impacts; LP disaggregating into blocks is arbitrary but useful for model description; formally, blocks are defined by rectangle subsets of matrix elements; variables will be delineated in such a way that they are associated with only one block, allowing us to compose a partition of the LP matrix

## 4.2 Model blocks in detail

### Key-points:

Up-to-date lists in line with the current running version

Comprehensive list built by a script applying on the kernel of the model

Below we display the comprehensive list of parameters and primal or dual variables characterizing the AROPAj model. Functions linking parameters and matrix elements, and "flag conditions" are not presented, for the sake of time and space. More importantly we display the date of list inception, which refers to the activation date of FORTRAN and Linux shell scripts which build the lists from the AROPAj core script.
The model is built in such a way as that it facilitates its evolution and the addition of new blocks in accordance with new research problematics. That includes changes in farm group clustering and the introduction of new farm groups (e.g. in case of the EU enlargement). Other cases of model evolution are new environmental issues (nitrogen losses and GHG emissions), and refining of the production set in terms of input-output interaction (e.g. nitrogen to yield functions for crops). This requires a comprehensive parametrization of the model, and an extensible range of indexes.

Following notations mentioned above, parameters $\theta_k$ for all farm groups 1...k...K and parameters $\phi$ represent the comprehensive set of AROPAj parameters. The objective vector ($g_k$ also denoted by OBJ), the "right hand side" vector ($z_k$ also denoted by RHS), and the matrix $A_k$ are composed of elements which all refer to these parameters.

The key items facilitating the presentation of the model structure are:

* *index*: affects parameters, variables, functions, conditions

* *parameter*: refers to data; their values are raw data used in the model through matrix elements; the way in which raw data is used by the model is described in Section 11.2

* *variable*: compound of the LP solution

- *primal*: related to an activity (e.g. a command variable of the LP); regarding the LP structure, primal variables are "columns", and RHS is viewed as one of them

- *dual*: related to a constraint and labeled by constraint name; regarding the LP structure, dual variables are "rows", and OBJ is viewed as one of them

* *element*: intersects a row and a column, is a (possibly non-linear, even non-analytic) function of parameters and indexes

* *function*: of which variables are indexes, parameters and external data

* *condition*: may enter a "flag" activating one variable or a subset of variables

* *block*: a subset of activities and constraints characterizing either a part of the modeled farming system, or a policy (agricultural or environmental), or a category of environmental impacts; LP disaggregating into blocks is arbitrary but useful for model description; formally, blocks are defined by rectangle subsets of matrix elements; variables will be delineated in such a way that they are associated with only one block, allowing us to compose a partition of the LP matrix

## 4.2 Model blocks in detail

### Key-points:

Up-to-date lists in line with the current running version

Comprehensive list built by a script applying on the kernel of the model

Below we display the comprehensive list of parameters and primal or dual variables characterizing the AROPAj model. Functions linking parameters and matrix elements, and "flag conditions" are not presented, for the sake of time and space. More importantly we display the date of list inception, which refers to the activation date of FORTRAN and Linux shell scripts which build the lists from the AROPAj core script.
Blocks necessarily interact, leading to overlapping activities and constraints. In the lists below, and in accordance with the *LP* matrix partitioning mentioned above, any parameter or any variable is affected to one block, even if a lot of parameters (as well as activities) act in more than one block. The scheme 2 illustrates this construction. Only non-null elements are illustrated and listed. Some blocks are more easily delineated than others, in the sense that activities or constraints may play a predominant role in more than one block. And some parameters or variables are of common use without specific characterization. In this later case, items are assigned to the general block *G*. Other blocks are "animal outputs and intermediate ratios for bovine" (A), "crop rotations and outputs" (C), "environmental impacts" (E), "animal feeding" (F), "nitrogen balance for crops and nitrogen sources" (N), and "policies" (P) including the CAP.

An additional block, *T*, refers to "trans-farm group" constraints, which is acceptable thanks to performing software and workstation. This block does not generate additional primal activities in the *LP*, as long as constraints involve farm groups' activities subject to global bounds. These bounds appear in the model parametrization. This block is presently in progress.

<table><caption>**Table 2.** The *LP* matrix structure: a block refers to sub-matrix and related labels, objective and *RHS* compounds; $X_n$ and $C_m$ are respectively labels of activities and constraints; $G_n$, $E_{mn}$, and $Z_m$ are matrix elements.</caption><thead><tr><th></th><th>X<sub>1</sub></th><th>X<sub>2</sub></th><th>...</th><th>X<sub>n</sub></th><th>...</th><th>X<sub>N</sub></th><th></th><th></th><th>RHS</th></tr></thead><tbody><tr><th>OBJ</th><th>G<sub>1</sub></th><th>G<sub>2</sub></th><th>...</th><th>G<sub>n</sub></th><th>...</th><th>G<sub>N</sub></th><th></th><th></th><th></th></tr><tr><th>C<sub>1</sub></th><td>E<sub>11</sub></td><td>E<sub>12</sub></td><td>...</td><td>E<sub>1n</sub></td><td>...</td><td>E<sub>1N</sub></td><th>&le;</th><th></th><th>Z<sub>1</sub></th></tr><tr><th>C<sub>2</sub></th><td>E<sub>21</sub></td><td>E<sub>22</sub></td><td>...</td><td>E<sub>2n</sub></td><td>...</td><td>E<sub>2N</sub></td><th>&le;</th><th></th><th>Z<sub>2</sub></th></tr><tr><th>...</th><td>...</td><td>...</td><th>...</th><td>...</td><th>...</th><td>...</td><th>...</th><th>...</th><td>...</td></tr><tr><th>C<sub>m</sub></th><td>E<sub>m1</sub></td><td></td><th>...</th><td>E<sub>mn</sub></td><td>...</td><td>E<sub>mN</sub></td><th>&le;</th><th></th><th>Z<sub>m</sub></th></tr><tr><th>...</th><td>...</td><td>...</td><th>...</th><td>...</td><th>...</th><td>...</td><th>...</th><th>...</th><td>...</td></tr><tr><th>C<sub>M</sub></th><td>E<sub>M1</sub></td><td></td><th>...</th><td>E<sub>Mn</sub></td><td>...</td><td>E<sub>MN</sub></td><th>&le;</th><th></th><th>Z<sub>M</sub></th></tr></tbody></table>

Inception date of the following item lists : Tue, 10 Jan 2023 17:28:13 +0100

### 4.2.1 Indices and parameters

A large part of parameters and primal or dual variables refers to one index or more:

k : farm group index

l : farm sub-group index

j : crop index

i : animal index

m : constraint type index

n : constraint type index

o : index for organic source (effluent & urban waste)
Blocks necessarily interact, leading to overlapping activities and constraints. In the lists below, and in accordance with the *LP* matrix partitioning mentioned above, any parameter or any variable is affected to one block, even if a lot of parameters (as well as activities) act in more than one block. The scheme 2 illustrates this construction. Only non-null elements are illustrated and listed. Some blocks are more easily delineated than others, in the sense that activities or constraints may play a predominant role in more than one block. And some parameters or variables are of common use without specific characterization. In this later case, items are assigned to the general block *G*. Other blocks are "animal outputs and intermediate ratios for bovine" (A), "crop rotations and outputs" (C), "environmental impacts" (E), "animal feeding" (F), "nitrogen balance for crops and nitrogen sources" (N), and "policies" (P) including the *CAP*.

An additional block, *T*, refers to "trans-farm group" constraints, which is acceptable thanks to performing software and workstation. This block does not generate additional primal activities in the *LP*, as long as constraints involve farm groups' activities subject to global bounds. These bounds appear in the model parametrization. This block is presently in progress.

<table><caption>**Table 2.** The *LP* matrix structure: a block refers to sub-matrix and related labels, objective and *RHS* compounds; *X*<sub>*n*</sub> and *C*<sub>*m*</sub> are respectively labels of activities and constraints; *G*<sub>*n*</sub>, *E*<sub>*mn*</sub>, and *Z*<sub>*m*</sub> are matrix elements.</caption><thead><tr><th></th><th>X<sub>1</sub></th><th>X<sub>2</sub></th><th>...</th><th>X<sub>n</sub></th><th>...</th><th>X<sub>N</sub></th><th></th><th></th><th>RHS</th></tr></thead><tbody><tr><th>OBJ</th><th>G<sub>1</sub></th><th>G<sub>2</sub></th><th>...</th><th>G<sub>n</sub></th><th>...</th><th>G<sub>N</sub></th><th></th><th></th><th></th></tr><tr><th>C<sub>1</sub></th><td>E<sub>11</sub></td><td>E<sub>12</sub></td><td>...</td><td>E<sub>1n</sub></td><td>...</td><td>E<sub>1N</sub></td><th>≤</th><td></td><td>Z<sub>1</sub></td></tr><tr><th>C<sub>2</sub></th><td>E<sub>21</sub></td><td>E<sub>22</sub></td><td>...</td><td>E<sub>2n</sub></td><td>...</td><td>E<sub>2N</sub></td><th>≤</th><td></td><td>Z<sub>2</sub></td></tr><tr><th>...</th><td>...</td><td>...</td><th>...</th><td>...</td><td>...</td><td>...</td><th>...</th><td></td><td>...</td></tr><tr><th>C<sub>m</sub></th><td>E<sub>m1</sub></td><td></td><th>...</th><td>E<sub>mn</sub></td><td>...</td><td>E<sub>mN</sub></td><th>≤</th><td></td><td>Z<sub>m</sub></td></tr><tr><th>...</th><td>...</td><td>...</td><th>...</th><td>...</td><td>...</td><td>...</td><th>...</th><td></td><td>...</td></tr><tr><th>C<sub>M</sub></th><td>E<sub>M1</sub></td><td></td><th>...</th><td>E<sub>Mn</sub></td><td>...</td><td>E<sub>MN</sub></td><th>≤</th><td></td><td>Z<sub>M</sub></td></tr></tbody></table>

Inception date of the following item lists : Tue, 02 Sep 2025 16:29:23 +0200

### 4.2.1 Indices and parameters

A large part of parameters and primal or dual variables refers to one index or more:

* k : farm group index

* l : farm sub-group index

* j : crop index

* i : animal index

* m : constr and activ type index

* n : constraint type index

* o : index for organic source (effluent & urban waste)
The comprehensive list of basic eligible parameters is split into the 7 blocks delimited above
(i.e. **G**, **A**, **C**, **E**, **F**, **N**, **P**, **T**, see this section 4.2).

• the general block G

aik(i,k) : purchase price animal (k€/head)
cact : coeff. / cost multiplier (1)
cfxkk(k) : fix cost (K€/farm)
ctdie : cont. of energy in "other variable costs"
ctine : cont. of energy in fertilizer making
ejj(j) : world price crop j (k€/t)
ejk(j,k) : world price or non guaranteed price (farm group) (k€/t)
gjk(j,k) : fertilizing costs (k€/ha)
gjk0(j,k) : preserved ferti. costs in case of recalculation (k€/ha)
igene : identifier of balances combination selected by the user
ijb(j) : identifier for BOUND LOWER introduction / variable J
itest(k) : identifier of policies combination selected by the user
penrj(j,k) : price of by-product related to crop j (k€/tDM)
pii(i) : relative change in animal price (yik et aik) (1)
pjj(j) : relative change of j-crop price (1)
pjk(j,k) : domestic price or guaranteed price / crop j (k€/t)
popkk(k) : farm group number k (1000)
popul(k,l) : sub-group farm number (by defaut l=1 popul=popkk (1000))
rojk(j,k) : shadow price of j-crop product (in case of endog.) (k€/t)
pxenr : energy relative price deviation
saukk(k) : UAA (farm group) (ha/farm)
saukl(k,l) : UAA (farm sub-group) (ha/farm)
trans : corr. transmission coeff. cereal price / feeding (1)
uii(i) : FADN sourced conversion coeff. in LU equiv. (LSU/head)
vjk(j,k) : other variable costs than fertilizers (k€/ha)
yik(i,k) : raw prod. / LS i-animal (not milk, eggs) (k€/head)
yjj(j) : price deviation / EU price (>0)
yjk(j,k) : price deviation within cereals (>0)
xjk0(j,k) : pre-calculated areas [intr. D.Leclere 22 Aug 2011] (ha)
wokok : flag for work estimation (>0) (-)
wokgv(k) : wages paid per worker (kE/AWU)
wokup(k) : unpaid work (AWU)
wokut(k) : unpaid work (yearly duration) (h/y)
wokvp(k) : paid work (AWU)
wokvt(k) : paid work (yearly duration) (h/y)
wokwg(k) : wages paid (kE)
The comprehensive list of basic eligible parameters is split into the 7 blocks delimited above
(i.e. **G**, **A**, **C**, **E**, **F**, **N**, **P**, **T**, see this section 4.2 on the previous page).

• the general block G

aik(i,k) : purchase price animal (k€/head)
cact : coeff. / cost multiplier (1)
cfxkk(k) : fix cost (K€/farm)
ctdie : cont. of energy in "other variable costs"
ctine : cont. of energy in fertilizer making
ejj(j) : world price crop j (k€/t)
ejk(j,k) : world price or non guaranteed price (farm group) (k€/t)
gjk(j,k) : fertilizing costs (k€/ha)
gjk0(j,k) : preserved ferti. costs in case of recalculation (k€/ha)
igene : identifier of balances combination selected by the user
ijb(j) : identifier for BOUND LOWER introduction / variable J
itest(k) : identifier of policies combination selected by the user
penrj(j,k) : price of by-product related to crop j (k€/tDM)
pii(i) : relative change in animal price (yik et aik) (1)
pjj(j) : relative change of j-crop price (1)
pjk(j,k) : domestic price or guaranteed price / crop j (k€/t)
popkk(k) : farm group number k (1000)
popul(k,l) : sub-group farm number (by defaut l=1 popul=popkk (1000))
rojk(j,k) : shadow price of j-crop product (in case of endog.) (k€/t)
pxenr : energy relative price deviation
saukk(k) : UAA (farm group) (ha/farm)
saukl(k,l) : UAA (farm sub-group) (ha/farm)
trans : corr. transmission coeff. cereal price / feeding (1)
uii(i) : FADN sourced conversion coeff. in LU equiv. (LU/head)
vjk(j,k) : other variable costs than fertilizers (k€/ha)
yik(i,k) : raw prod. / LS i-animal (not milk, eggs) (k€/head)
yjj(j) : price deviation / EU price (>0)
yjk(j,k) : price deviation within cereals (>0)
xjk0(j,k) : pre-calculated areas [intr. D.Leclere 22 Aug 2011] (ha)
wokok : flag for work estimation (>0) (-)
wokgv(k) : wages paid per worker (kE/AWU)
wokup(k) : unpaid work (AWU)
wokut(k) : unpaid work (yearly duration) (h/y)
wokvp(k) : paid work (AWU)
wokvt(k) : paid work (yearly duration) (h/y)
wokwg(k) : wages paid (kE)
wokwp(k) : unpaid + paid work (AWU)

wokwt(k) : total work (unpaid + paid - yearly duration) (h/y)

Let us focus on two parameters: *itest* and *igene*. The *itest* k-parameter is dedicated to policies, and the *igene* parameter is dedicated to balance calculation (e.g. animal feed category sums). They refer to the case when certain sub-blocks are activated, such as specific CAP tools (*itest*) or specific environmental balances (e.g. GHG emissions, or nitrogen pollutants). This offers a wide range of combinations, since these parameters are the sum of 2 to *i* powers, i.e. $\sum_{i \in \mathcal{I}} 2^i$ when $\mathcal{I}$ refers to the user-selected compounds. We should mention that this allows up to $2^{31}$ possibilities.

Some other parameters may be of a binary type (0/1), e.g. *endrg* which activates the calculation of nitrogen intakes and crop yields when N to yield functions are available.

### the animal block A

dik(i,k) : animal lifetime *i* (equiv years time) (yr/head)

dstkk(k) : livestock adjustment coeff. (exponen. adjust.) (0<->)

hik(i,k) : animal number (head/farm)

plaic : relative change of milk price (1)

plait(k) : milk price (€/l)

renf1(k) : renewal rate for 1-yr bovine female (head/head)

renf2(k) : renewal rate for 2-yr bovine female (head/head)

renm1(k) : renewal rate for 1-yr bovine male (head/head)

renm2(k) : renewal rate for 2-yr bovine male (head/head)

repro(k) : bovine reproduction ratio (head/head)

rlait(k) : cow milk yield (kl/VL)

xii(i) : relat. prod. coeff. milk, eggs (other than bovine) (1)

xik(i,k) : prod. milk, eggs (other than bovine) (k€/head)

### the crop block C

bcekk(k) : intercept in cereal / crops econometr. rel. (ha/farm)

bockk(k) : intercept in oils / cereals econometr. rel. (ha/farm)

bovkk(k) : intercept in oils / crops econometr. rel. (ha/farm)

ctfkk(k) : rel. fodders - pasture: econometr. intercept (ha/farm)

dmas(j,k) : variation coeff. / fodder yield (-)

fcekk(k) : number of farms producing cereals (1000)

fjk(j,k) : number of farms producing crops or crop clusters (1000)

fockk(k) : number of farms producing oilseeds and cereals (1000)

fovkk(k) : number of farms producing oilseeds (1000)

renrj(j,k) : by-product yield / crop j (tDM/ha/an)

tenrj(j,k) : correlating by-prod and prod yields / crop j (tDM/tRM)

rjk(j,k) : crop yield (FADN pre-estimated or calibrated) (t/ha)

rmas(j,k) : indicative forage yield (calibration) (t/ha)
wokwp(k) : unpaid + paid work (AWU)

wokwt(k) : total work (unpaid + paid - yearly duration) (h/y)

Let us focus on two parameters: *itest* and *igene*. The *itest* k-parameter is dedicated to policies, and the *igene* parameter is dedicated to balance calculation (e.g. animal feed category sums). They refer to the case when certain sub-blocks are activated, such as specific CAP tools (*itest*) or specific environmental balances (e.g. GHG emissions, or nitrogen pollutants). This offers a wide range of combinations, since these parameters are the sum of 2 to *i* powers, i.e. $\sum_{i \in \mathcal{I}} 2^i$ when $\mathcal{I}$ refers to the user-selected compounds. We should mention that this allows up to $2^{31}$ possibilities.

Some other parameters may be of a binary type (0/1), e.g. *endrg* which activates the calculation of nitrogen intakes and crop yields when N to yield functions are available.

### the animal block A

dik(i,k) : animal lifetime *i* (equiv years time) (yr/head)

dstkk(k) : livestock adjustment coeff. (exponen. adjust.) (0<->)

hik(i,k) : animal number (head/farm)

plaic : relative change of milk price (1)

plait(k) : milk price (€/l)

renf1(k) : renewal rate for 1-yr bovine female (head/head)

renf2(k) : renewal rate for 2-yr bovine female (head/head)

renm1(k) : renewal rate for 1-yr bovine male (head/head)

renm2(k) : renewal rate for 2-yr bovine male (head/head)

repro(k) : bovine reproduction ratio (head/head)

rlait(k) : cow milk yield (kl/VL)

xii(i) : relat. prod. coeff. milk, eggs (other than bovine) (1)

xik(i,k) : prod. milk, eggs (other than bovine) (k€/head)

### the crop block C

bcekk(k) : intercept in cereal / crops econometr. rel. (ha/farm)

bockk(k) : intercept in oils / cereals econometr. rel. (ha/farm)

bovkk(k) : intercept in oils / crops econometr. rel. (ha/farm)

ctfkk(k) : rel. fodders - pasture: econometr. intercept (ha/farm)

dmas(j,k) : variation coeff. / fodder yield (-)

fcekk(k) : number of farms producing cereals (1000)

fjk(j,k) : number of farms producing crops or crop clusters (1000)

fockk(k) : number of farms producing oilseeds and cereals (1000)

fovkk(k) : number of farms producing oilseeds (1000)

mgesg : identifier 0/1 activating Biogaz module (-)

renrj(j,k) : by-product yield / crop j (tDM/ha/an)

tenrj(j,k) : correlating by-prod and prod yields / crop j (tDM/tRM)

rjk(j,k) : crop yield (FADN estim. possibly calibrated) (t/ha)
scek(k): sharing coeff. binding cereals and UAA (1)

sffkk(k): sharing coeff. binding fodders and grasslands (1)

sjk(j,k): eligible part of crop area (ha/ha SAU)

sockk(k): sharing coeff. binding oilseeds and cereals (1)

sovkk(k): sharing coeff. binding oilseeds and UAA (1)

• the environment block E

zcc01: (<EF1_2>) EF N2O- Ag soils- Dir.em. ManAppl (kgN2O-N/kgN)

zcc02(i): (<NEX(i)>) Qty N excreted per animal (kg N excr/head/yr)

zcc03: (<FRACGASM>) Qty N excr. volat. (kgNH3-N&NOx-N / kgNexcr)

zcc04: (<FRACFUELM>) Qty N excr. utilized fuel (kgN/kgN)

zcc05: (<FRACPRP>) Qty N direct deposit on soil / anim (kgN/kgN)

zcc06: (<EF3PASTU>) EF N2O Ag soils- ani produc (kgN2O-N/kgNman)

zcc07(i): (<MSPASTU(i)>) Qty N excr dep dir on soil (kgexcr/kgexcr)

zcc08: (<EF4>) EF N2O agsol atm.redep (kgN2O-N/kgNH3-N&NOx-N)

zcc09: (<EF5>) EF N2O Ag soils-Ind em / leaching (kgN2O-N/kgN)

zcc10: (<FRACLEACH>) Qty N leaching (kg N.(kg N)-1)

zcc11: (<EF3SOLID>) EF N20 manure manag syst SOLID (kgN2O-N/kgN)

zcc12: (<EF3DRYLO>) EF N20 manure manag syst DRYLO (kgN2O-N/kgN)

zcc13: (<EF3LIQUI>) EF N20 manure manag syst LIQUI (kgN2O-N/kgN)

zcc14: (<EF3ANAER>) EF N20 manure manag syst ANAER (kgN2O-N/kgN)

zcc15: (<EF3OPENP>) EF N20 manure manag syst OPENP (kgN2O-N/kgN)

zcc16: (<EF3ANADI>) EF N20 manure manag syst ANADI (kgN2O-N/kgN)

zcc17: (<EF3BURNF>) EF N20 manure manag syst BURNF (kgN2O-N/kgN)

zcc18(i): (<MSSOLID(i)>) Frac. MS manure on syst SOLID (%)

zcc19(i): (<MSDRYLO(i)>) Frac. MS manure on syst DRYLO (%)

zcc20(i): (<MSLIQUI(i)>) Frac. MS manure on syst LIQUI (%)

zcc21(i): (<MSANAER(i)>) Frac. MS manure on syst ANAER (%)

zcc22(i): (<MSOPENP(i)>) Frac. MS manure on syst OPENP (%)

zcc23(i): (<MSANADI(i)>) Frac. MS manure on syst ANADI (%)

zcc24(i): (<MSBURNF(i)>) Frac. MS manure on syst BURNF (%)

zcc25(i): (<B0(i)>) Max CH4 produc capa manu prod anim i (m3/kg-dm)

zcc26: (<MCFPASTU>) CH4 conv fact syst PASTU(/clim)(kgCH4/kg-dm)

zcc27: (<MCFSOLID>) CH4 conv fact syst SOLID(/clim)(kgCH4/kg-dm)

zcc28: (<MCFDRYLO>) CH4 conv fact syst DRYLO(/clim)(kgCH4/kg-dm)

zcc29: (<MCFLIQUI>) CH4 conv fact syst LIQUI(/clim)(kgCH4/kg-dm)

zcc30: (<MCFANAER>) CH4 conv fact syst ANAER(/clim)(kgCH4/kg-dm)

zcc31: (<MCFOPENP>) CH4 conv fact syst OPENP(/clim)(kgCH4/kg-dm)

zcc32: (<MCFANADI>) CH4 conv fact syst ANADI(/clim)(kgCH4/kg-dm)

zcc33: (<MCFBURNF>) CH4 conv fact syst BURNF(/clim)(kgCH4/kg-dm)
rjk0(j,k) : crop yield (FADN pre-estimated) (t/ha)

rmas(j,k) : indicative forage yield (calibration) (t/ha)

scekk(k) : sharing coeff. binding cereals and UAA (1)

sffkk(k) : sharing coeff. binding fodders and grasslands (1)

sjk(j,k) : eligible part of crop area (ha/ha SAU)

sockk(k) : sharing coeff. binding oilseeds and cereals (1)

sovkk(k) : sharing coeff. binding oilseeds and UAA (1)

• the environment block E

zcc01 : (<EF1_2>) EF N2O- Ag soils- Dir.em. ManAppl (kgN2O-N/kgN)

zcc02(i) : (<NEX(i)>) Qty N excreted per animal (kg N excr/head/yr)

zcc03 : (<FRACGASM>) Qty N excr. volat. (kgNH3-N&NOx-N / kgNexcr)

zcc04 : (<FRACFUELM>) Qty N excr. utilized fuel (kgN/kgN)

zcc05 : (<FRACPRP>) Qty N direct deposit on soil / anim (kgN/kgN)

zcc06 : (<EF3PASTU>) EF N2O Ag soils- ani produc (kgN2O-N/kgNman)

zcc07(i) : (<MSPASTU(i)>) Qty N excr dep dir on soil (kgexcr/kgexcr)

zcc08 : (<EF4>) EF N2O agsol atm.redep (kgN2O-N/kgNH3-N&NOx-N)

zcc09 : (<EF5>) EF N2O Ag soils-Ind em / leaching (kgN2O-N/kgN)

zcc10 : (<FRACLEACH>) Qty N leaching (kg N.(kg N)-1)

zcc11 : (<EF3SOLID>) EF N20 manure manag syst SOLID (kgN2O-N/kgN)

zcc12 : (<EF3DRYLO>) EF N20 manure manag syst DRYLO (kgN2O-N/kgN)

zcc13 : (<EF3LIQUI>) EF N20 manure manag syst LIQUI (kgN2O-N/kgN)

zcc14 : (<EF3ANAER>) EF N20 manure manag syst ANAER (kgN2O-N/kgN)

zcc15 : (<EF3OPENP>) EF N20 manure manag syst OPENP (kgN2O-N/kgN)

zcc16 : (<EF3ANADI>) EF N20 manure manag syst ANADI (kgN2O-N/kgN)

zcc17 : (<EF3BURNF>) EF N20 manure manag syst BURNF (kgN2O-N/kgN)

zcc18(i) : (<MSSOLID(i)>) Frac. MS manure on syst SOLID (%)

zcc19(i) : (<MSDRYLO(i)>) Frac. MS manure on syst DRYLO (%)

zcc20(i) : (<MSLIQUI(i)>) Frac. MS manure on syst LIQUI (%)

zcc21(i) : (<MSANAER(i)>) Frac. MS manure on syst ANAER (%)

zcc22(i) : (<MSOPENP(i)>) Frac. MS manure on syst OPENP (%)

zcc23(i) : (<MSANADI(i)>) Frac. MS manure on syst ANADI (%)

zcc24(i) : (<MSBURNF(i)>) Frac. MS manure on syst BURNF (%)

zcc25(i) : (<B0(i)>) Max CH4 produc capa manu prod anim i (m3/kg-dm)

zcc26 : (<MCFPASTU>) CH4 conv fact syst PASTU(/clim)(kgCH4/kg-dm)

zcc27 : (<MCFSOLID>) CH4 conv fact syst SOLID(/clim)(kgCH4/kg-dm)

zcc28 : (<MCFDRYLO>) CH4 conv fact syst DRYLO(/clim)(kgCH4/kg-dm)

zcc29 : (<MCFLIQUI>) CH4 conv fact syst LIQUI(/clim)(kgCH4/kg-dm)

zcc30 : (<MCFANAER>) CH4 conv fact syst ANAER(/clim)(kgCH4/kg-dm)

zcc31 : (<MCFOPENP>) CH4 conv fact syst OPENP(/clim)(kgCH4/kg-dm)
zcc34: (<EF1_1>) EF Agr soils - dir emis synt fert (kgN2O-N/kgN)
zcc35: (<FRACGASF>) Qty of N intake volatilised (kgN/kgN)
zcc36: (<EF1_3>) EF Agr soils -dir. em N-fix crops (kgN2O-N/kgN)
zcc37(j): (<RESBF/CROPBF(j)>) Fraction resid. / yield (kg/kg)
zcc38(j): (<FRACNCRBF(j)>) Fraction N / plant (kgN/kgdm)
zcc39(j): (<FRACDM(j)>) Dry matter ration / plant (kgdm/kg)
zcc40: (<EF1_4>) EF Agr soils - dir. em crop resid (kgN2O-N/kgN)
zcc41: (<FRACBURN>) Fraction of burnt resid. (kgres/kgres)
zcc42: (<FRACFUEL>) Fract resid. util. c combust (kg_res/kg_res)
zcc43: (<FRACCNST>) Fract resid. util in cstction (kgres/kgres)
zcc44: (<FRACFOD>) Fract resid. util c fodder (kg_res/kg_res)
zcc45: (<FRACR>) Fract resid. util c product (kg_res/kg_res)
zcc46: (<EFRIZ>) EF for CH4 rice production (gCH4/m2)
zcc47: (<FLAG4Dc>) Flag variable Tier1a, Tier1b, Tier 2 (0-4)
zcc48: (<FLAG4Dd>) Flag variable Tier1a, Tier1b, Tier 2 (0-4)
zcc49(i): (<ASHCONTENT(i)>) Content ash / manure (kgash/kgmanure)
zcc50: (<FLAG4A>) Flag variable Tier1a, Tier1b, Tier 2 (0-4)
zcc51(i): (<Ym(i)>) CH4 conver (gross ener in feed conv to CH4) (1)
zcc52: (<FLAG4Da>) Flag variable Tier1a, Tier1b, Tier 2 (0-4)
zcc53: (<FLAG4De>) Flag variable Tier1a, Tier1b, Tier 2 (0-4)
zcc54: (<FLAG4Df>) Flag variable Tier1a, Tier1b, Tier 2 (0-4)
zcc55: (<FLAG4Dg>) Flag variable Tier1a, Tier1b, Tier 2 (0-4)
zcc56: (<FLAG4Bn>) Flag variable Tier1a, Tier1b, Tier 2 (0-4)
zcc59(j,k): indexing crop / zcc34
zcc60(j,k): constant emission factor N2O related to N
zcc61(i): <MCFPASTU(i)> CH4 conv. fact. / manure manag. sys. PASTU
zcc62(i): <MCFSOLID(i)> CH4 conv. fact. / manure manag. sys. SOLID
zcc63(i): <MCFDRYLO(i)> CH4 conv. fact. / manure manag. sys. DRYLO
zcc64(i): <MCFLIQUI(i)> CH4 conv. fact. / manure manag. sys. LIQUI
zcc65(i): <MCFANAER(i)> CH4 conv. fact. / manure manag. sys. ANAER
zcc67(i): <MCFANADI(i)> CH4 conv. fact. / manure manag. sys. ANADI
zcc69(i): <MCFOTHER(i)> CH4 conv. fact. / manure manag. sys. OTHER
zcc70(i): <MCFDAILY(i)> CH4 conv. fact. / manure manag. sys. DAILY
zcc71(j): modulation of zcc01 (Bouwman) by crop (-)
zcc72: <EF3SOLIDDRYLOT> Em. Fact. solid storage + dry lot (0-4)
zcc73: <EF3OTHER> EF N20 manure manag syst OTHER (kgN2O-N/kgN)
zcc74: <EF3COMPOST> Emission factor for composting (kgN2O-N/kgN)
zcc75: <EF3DAILY> Emission factor for daily spread (kgN2O-N/kgN)
zcc76(i): <MCFCOMPOST> CH4 conv. fact. / manure manag. sys. COMPOST
zcc77(i): <MCFSOLIDDRY> CH4 conv. fac. / man.manag. sys. SOLID.DRY.
zcc78(i): <MSSOLIDDRYLOT> Frac. MS manure sys. SOLID STORAGE DRYLOT
zcc32 : (<MCFANADI>) CH4 conv fact syst ANADI(/clim)(kgCH4/kg-dm)
zcc33 : (<MCFBURNF>) CH4 conv fact syst BURNF(/clim)(kgCH4/kg-dm)
zcc34 : (<EF1_1>) EF Agr soils - dir emis synt fert (kgN2O-N/kgN)
zcc35 : (<FRACGASF>) Qty of N intake volatilised (kgN/kgN)
zcc36 : (<EF1_3>) EF Agr soils -dir. em N-fix crops (kgN2O-N/kgN)
zcc37(j) : (<RESBF/CROPBF(j)> ) Fraction resid. / yield (kg/kg)
zcc38(j) : (<FRACNCRBF(j)> ) Fraction N / plant (kgN/kgdm)
zcc39(j) : (<FRACDM(j)> ) Dry matter ration / plant (kgdm/kg)
zcc40 : (<EF1_4>) EF Agr soils - dir. em crop resid (kgN2O-N/kgN)
zcc41 : (<FRACBURN>) Fraction of burnt resid. (kgres/kgres)
zcc42 : (<FRACFUEL>) Fract resid. util. c combust (kg_res/kg_res)
zcc43 : (<FRACCNST>) Fract resid. util in cstction (kgres/kgres)
zcc44 : (<FRACFOD>) Fract resid. util c fodder (kg_res/kg_res)
zcc45 : (<FRACR>) Fract resid. util c product (kg_res/kg_res)
zcc46 : (<EFRIZ>) EF for CH4 rice production (gCH4/m2)
zcc47 : (<FLAG4Dc>) Flag variable Tier1a, Tier1b, Tier 2 (0-4)
zcc48 : (<FLAG4Dd>) Flag variable Tier1a, Tier1b, Tier 2 (0-4)
zcc49(i) : (<ASHCONTENT(i)> ) Content ash / manure (kgash/kgmanure)
zcc50 : (<FLAG4A>) Flag variable Tier1a, Tier1b, Tier 2 (0-4)
zcc51(i) : (<Ym(i)> ) CH4 conver (gross ener in feed conv to CH4) (1)
zcc52 : (<FLAG4Da>) Flag variable Tier1a, Tier1b, Tier 2 (0-4)
zcc53 : (<FLAG4De>) Flag variable Tier1a, Tier1b, Tier 2 (0-4)
zcc54 : (<FLAG4Df>) Flag variable Tier1a, Tier1b, Tier 2 (0-4)
zcc55 : (<FLAG4Dg>) Flag variable Tier1a, Tier1b, Tier 2 (0-4)
zcc56 : (<FLAG4Bn>) Flag variable Tier1a, Tier1b, Tier 2 (0-4)
zcc59(j,k) : indexing crop / zcc34
hseip : preserve IPCC Bouwmann calculus zcc34
zcc60(j,k) : constant emission factor N2O related to N
zcc61(i) : <MCPPASTU(i)> CH4 conv. fact. / manure manag. sys. PASTU
zcc62(i) : <MCFSOLID(i)> CH4 conv. fact. / manure manag. sys. SOLID
zcc63(i) : <MCFDRYLO(i)> CH4 conv. fact. / manure manag. sys. DRYLO
zcc64(i) : <MCFLIQUI(i)> CH4 conv. fact. / manure manag. sys. LIQUI
zcc65(i) : <MCFANAER(i)> CH4 conv. fact. / manure manag. sys. ANAER
zcc67(i) : <MCFANADI(i)> CH4 conv. fact. / manure manag. sys. ANADI
zcc69(i) : <MCFOTHER(i)> CH4 conv. fact. / manure manag. sys. OTHER
zcc70(i) : <MCFDAILY(i)> CH4 conv. fact. / manure manag. sys. DAILY
zcc71(j) : modulation of zcc01 (Bouwman) by crop (-)
zcc72 : <EF3SOLIDDRYLOT> Em. Fact. solid storage + dry lot (0-4)
zcc73 : <EF3OTHER> EF N20 manure manag syst OTHER (kgN2O-N/kgN)
zcc74 : <EF3COMPOST> Emission factor for composting (kgN2O-N/kgN)
zcc75 : <EF3DAILY> Emission factor for daily spread (kgN2O-N/kgN)
zcc79(i): <MSCOMPOST> Frac. MS manure sys. COMPOSTING
zcc80(i): <MSDAILY> fraction manure sys. DAILY SPREAD
zcc81(i): <MSOTHER> fraction manure sys. OTHER
zcc82(i): <MCFBURNF> CH4 conv. fact. / manure manag. sys. BURNFuel
zcc83: <MCFSOLIDDRYLOT> CH4 con fact syst SOLIDDRY (kgCH4/kg-dm)
zcc84: <MCFCOMPOST> CH4 conv fact syst COMPOSTING (kgCH4/kg-dm)
zcc85: <MCFDAILY> CH4 conv fact syst DAILY SPREAD (kgCH4/kg-dm)
zcc86(i): <FRACgasANAER(i)> anaerobic lagoon / fraction manure sys.
zcc87(i): <FRACgasLIQUI(i)> system Liquid / fraction manure sys.
zcc88(i): <FRACgasSOLIDDRYLOT(i)> Solid stor/ fraction manure sys.
zcc89(i): <FRACgasPASTU(i)> system Pasture / fraction manure sys.
zcc90(i): <FRACgasOTHER(i)> Other system / fraction manure sys.
zcc91(i): <FRACgasANADI(i)> Digesters / fraction manure sys.
zcc92(i): <FRACgasDAILY(i)> Daily Spread / fraction manure sys.
zcc93(i): <FRACgasCOMPOST(i)> syst. Compost. / fraction manure sys.
zcc94(i): <FRACgasBURNF(i)> Burned fuel-waste / fraction manure sys.
zcc95(i): <FRACleachANAER(i)> N loss / runoff manag. manure / zcc86
zcc96(i): <FRACleachLIQUI(i)> N loss / runoff manag. manure / zcc87
zcc97(i): <FRACleachSOLIDDRYLOT(i)> N loss / runoff man. m. / zcc88
zcc98(i): <FRACleachPASTU(i)> N loss / runoff manag. manure / zcc89
zcc99(i): <FRACleachOTHER(i)> N loss / runoff manag. manure / zcc90
zcc100(i): <FRACleachANADI(i)> N loss / runoff manag. manure / zcc91
zcc101(i): <FRACleachDAILY(i)> N loss / runoff manag. manure / zcc92
zcc102(i): <FRACleachCOMPOST(i)> N loss / runoff manag. man. / zcc93
zcc103(i): <FRACleachBURNF(i)> N loss / runoff manag. manure / zcc94
a1no3(k): coeff subsoil NO3 / geographical area unit in the region
a2no3(k): coeff livestock / geographical unit in the NO3 conc.
a3no3(k): estim IDPR in the regression related to NO3 concentr.
a4no3(k): coeff IDPR in the NO3 level regression
b1no3(k): intercept regression linking aver. NO3 conc. / explic.
b2no3(k): crops / geographical area (related to hydrological zone)
b3no3(k): UAA / geographical area (related to hydrological zone)
c1no3(k): NO3 conc. threshold (related to hydrological zone) (mg/l)
ano3(j,k): corr / emission factor NO3
bno3(j,k): constant emission factor NO3
cno3(j,k): corr / emission factor NO3 related to irrig
anh3(j,k): corr emission factor NH3
bnh3(j,k): constant emission factor NH3 j k
cnh3(j,k): corr / emission factor NH3 related to irrig
cn2o(j,k): corr / emission factor N2O related to irrig
bouw1: intercept in the Bouwman relation (N_N2O / N)
zcc76(i) : <MCFCOMPOST> CH4 conv. fact. / manure manag. sys. COMPOST
zcc77(i) : <MCFSOLIDDRY> CH4 conv. fac. / man.manag. sys. SOLID.DRY.
zcc78(i) : <MSSOLIDDRYLOT> Frac. MS manure sys. SOLID STORAGE DRYLOT
zcc79(i) : <MSCOMPOST> Frac. MS manure sys. COMPOSTING
zcc80(i) : <MSDAILY> fraction manure sys. DAILY SPREAD
zcc81(i) : <MSOTHER> fraction manure sys. OTHER
zcc82(i) : <MCFBURNF> CH4 conv. fact. / manure manag. sys. BURNFuel
zcc83 : <MCFSOLIDDRYLOT> CH4 conv fact syst SOLIDDRY (kgCH4/kg-dm)
zcc84 : <MCFCOMPOST> CH4 conv fact syst COMPOSTING (kgCH4/kg-dm)
zcc85 : <MCFDAILY> CH4 conv fact syst DAILY SPREAD (kgCH4/kg-dm)
zcc86(i) : <FRACgasANAER(i)> anaerobic lagoon / fraction manure sys.
zcc87(i) : <FRACgasLIQUI(i)> system Liquid / fraction manure sys.
zcc88(i) : <FRACgasSOLIDDRYLOT(i)> Solid stor/ fraction manure sys.
zcc89(i) : <FRACgasPASTU(i)> system Pasture / fraction manure sys.
zcc90(i) : <FRACgasOTHER(i)> Other system / fraction manure sys.
zcc91(i) : <FRACgasANADI(i)> Digesters / fraction manure sys.
zcc92(i) : <FRACgasDAILY(i)> Daily Spread / fraction manure sys.
zcc93(i) : <FRACgasCOMPOST(i)> syst. Compost. / fraction manure sys.
zcc94(i) : <FRACgasBURNF(i)> Burned fuel-waste / fraction manure sys.
zcc95(i) : <FRACleachANAER(i)> N loss / runoff manag. manure / zcc86
zcc96(i) : <FRACleachLIQUI(i)> N loss / runoff manag. manure / zcc87
zcc97(i) : <FRACleachSOLIDDRYLOT(i)> N loss / runoff man. m. / zcc88
zcc98(i) : <FRACleachPASTU(i)> N loss / runoff manag. manure / zcc89
zcc99(i) : <FRACleachOTHER(i)> N loss / runoff manag. manure / zcc90
zcc100(i) : <FRACleachANADI(i)> N loss / runoff manag. manure / zcc91
zcc101(i) : <FRACleachDAILY(i)> N loss / runoff manag. manure / zcc92
zcc102(i) : <FRACleachCOMPOST(i)> N loss / runoff manag. man. / zcc93
zcc103(i) : <FRACleachBURNF(i)> N loss / runoff manag. manure / zcc94
a1no3(k) : coeff subsoil NO3 / geographical area unit in the region
a2no3(k) : coeff livestock / geographical unit in the NO3 conc.
a3no3(k) : estim IDPR in the regression related to NO3 concentr.
a4no3(k) : coeff IDPR in the NO3 level regression
b1no3(k) : intercept regression linking aver. NO3 conc. / explic.
b2no3(k) : crops / geographical area (related to hydrological zone)
b3no3(k) : UAA / geographical area (related to hydrological zone)
c1no3(k) : NO3 conc. threshold (related to hydrological zone) (mg/l)
ano3(j,k) : corr / emission factor NO3
bno3(j,k) : constant emission factor NO3
cno3(j,k) : corr / emission factor NO3 related to irrig
anh3(j,k) : corr emission factor NH3
bnh3(j,k) : constant emission factor NH3 j k
bouw2: corr. fact. in the Bouwman relation (N\_N2O / N)
cesjk(j,k): yearly C stock qty per crop (t C /ha)
cfme(i): conversion ratio methane animal manure (%)
fch41: intercept related to methane em. / simple feed
fch42: correlation effect related to methane em. / raw feed
fch43: intercept related to methane em. / mix feed
fch44: correlation effect related to methane em. / mix feed
fech(i): yearly CH4 emission factor related to manure (kg)
fedf(i): enteric CH4 emission factor by defaut, IPCC (kg/head)
fen2o: direct N2O emission factor, IPCC
gesjk(j,k): yearly C stock qty / additionnal pasture (t C /ha)
pcch4: CH4 calorific power (kcal/kg CH4)
txcch: GHG emissions: tax / CH4 (k€/tCO2)
txcno: GHG emissions: tax / N2O (k€/tCO2)
prgch: GWP CH4 (kgCO2 / kgCH4)
prgn: GWP N2O (kgCO2 / kgN2O)
zjk(j,k): variable costs specific to pestici. (part of vjk) (k€/ha)
zsttt: factor multiplying pesticide cost accounts when >0 (-)

It must be noticed that the *i*-indexed parameters, zcc61(*i*) up to zcc70(*i*), were added in 2015, and used for estimating the GHG emissions related to the V5 versions of AROPAj (EU - 27, 2007 - 2009). These parameters replace, respectively, zcc26 up to zcc33.

• the feed block *F*

brac(n,i,k): raw energy / concentrated feed intakes (kcal/kgDM)
brag(i,k): raw energy / raw feed intakes (kcal/kgDM)
clpdc: PD needs for milk / intercept for dairy cows (kg/hd)
clpdp(k): PD needs per ton of milk / coef for dairy cows (kg/t)
clufc: PD needs for milk / intercept for dairy cows (kg/hd)
clufp(k): PD needs per ton of milk / coef for dairy cows (kg/t)
digm(i): average digestibility intake, IPCC, anim. i (%)
ebac(n,i,k): ingestion coeff. / energy content / concentrates (ce/t)
ebag(i,k): ingestion coeff. / raw matter deed (ce/t)
ebes(j): raw energy content of crop (kcal/kg DM)
ebi(i,k): ingestion capacity by animal i (ce/head)
ebj(j,k): ingestion coeff. / crop j (ce/t)
ed(j): j-crop digestibility (1)
eda1: feed concentrate digestibility (type 1 simpl energy) (1)
eda2: feed concentrate digestibility (type 2 simpl protein) (1)
eda3: feed concentrate digestibility (type 3 compound ener) (1)
eda4: feed concentrate digestibility (type 4 compound prot) (1)
cnh3(j,k) : corr / emission factor NH3 related to irrig
cn2o(j,k) : corr / emission factor N2O related to irrig
anigz(i,o) : bioch4 per animal for o-manure (m3ch4/tVS)
txmso(j,k) : fraction of j crop OM in DM (tOM/tDM)
crogz(j) : bioch4 per crop biom (m3ch4/tVS)
frxom(i,o) : volatil solid per i-animal o-manure (tVS/t)
bouw1 : intercept in the Bouwman relation (N_N2O / N)
bouw2 : corr. fact. in the Bouwman relation (N_N2O / N)
cach4(k) : max capacity of prod biogaz (m3)
kpah4(n,k) : max capacity of prod biogaz per n unit k farm (m3)
apah4(n,k) : depreciation cost n CH4 unit k farm (k€/y)
cesjk(j,k) : yearly C stock qty per crop (t C /ha)
cfme(i) : conversion ratio methane animal manure (%)
fch41 : intercept related to methane em. / simple feed
fch42 : correlation effect related to methane em. / raw feed
fch43 : intercept related to methane em. / mix feed
fch44 : correlation effect related to methane em. / mix feed
fech(i) : yearly CH4 emission factor related to manure (kg)
fedf(i) : enteric CH4 emission factor by defaut, IPCC (kg/head)
fen2o : direct N2O emission factor, IPCC
gesjk(j,k) : yearly C stock qty / additionnal pasture (t C /ha)
pcch4 : CH4 calorific power (kcal/kg CH4)
txcch : GHG emissions : tax / CH4 (k€/tCO2)
txcno : GHG emissions : tax / N2O (k€/tCO2)
tauab : ratio animal vs crop-sourced matter for bioCH4 (-)
prgch : GWP CH4 (kgCO2 / kgCH4)
prgn : GWP N2O (kgCO2 / kgN2O)
prs(m,n,j) : m intermed crop n preced or follow j crop
zcive(m) : activ flag for m intermediate crop (-)
zjk(j,k) : variable costs specific to pestici. (part of vjk) (k€/ha)
zsttt : factor multiplying pesticide cost accounts when >0 (-)
xmch4 : market price ch4 (kE/m3)
zii(i) : flag / o-org.mat. - i-animal market ()

It must be noticed that the *i*-indexed parameters, zcc61(i) up to zcc70(i), were added in 2015, and used for estimating the GHG emissions related to the V5 versions of AROPAj (EU - 27, 2007 - 2009). These parameters replace, respectively, zcc26 up to zcc33.

• the feed block *F*

brac(n,i,k) : raw energy / concentrated feed intakes (kcal/kgDM)
brag(i,k) : raw energy / raw feed intakes (kcal/kgDM)
edag : raw feed digestibility (1)
emac(n,i,k) : metabolisable energy in concentrated feed graniv (Mcal/t)
emag(i,k) : metabolisable energy in raw feed for granivore (Mcal/t)
enac(n,i,k) : digestibility of concentrated feed per animal (1)
enag(i,k) : digestibility of raw feed per animal (1)
emi(i,k) : yearly requirement of metabolisable energy (Mcal/head)
emj(j,k) : metabolisable energy in crop j farm k (Mcal/t)
eni(i,k) : yearly proteins requirement per animal i farm k (t/head)
fglai : flag for adjusted feeding parameters
pac(n,i,k) : bought conc. feed price (incl. proteins) (k€/t)
pag(i,k) : bought raw feed price (k€/t)
palac : relative change in bought conc. feed price (1)
palag : relative change in raw feed price (1)
pdib(i,k) : digest. protein requirement of i ruminant (kg/head)
pdie(j,k) : N equiv. by j crop in PDIE (kg/t)
pdin(j,k) : N equiv. by j crop in PDIN (kg/t)
peac(n,i,k) : N equiv. by n concentr. feed in PDIE / anim. i (kg/t)
peag(i,k) : N equiv. by raw feed in PDIE / anim. i (kg/t)
pnac(n,i,k) : PDIN N-equivalent / concentr. feed (kg/t)
pnag(i,k) : PDIN N-equivalent / raw feed (kg/t)
smi(i,k) : dry matter requirement / animal i (tDM/head)
smj(j,k) : dry matter ratio in j-crop (1)
smac(n,i,k) : dry matter ratio in concentr. feed / i-animal (1)
smsg(i,k) : dry matter ration in raw feed / i-animal (1)
tconv : conversion ratio of i-animal digestibility in CH4
trp(j,k) : ratio of j-cereal content proteins / energy
ufac(n,i,k) : UF content in concentr. feed / i-animal (UFL_eq/t)
ufag(i,k) : UF content in raw feed / i-animal (UFL_eq/t)
uflj(j,k) : UFL content in j-crop (UFL/t)
uflv(i,k) : UFL requirement / UFV for i-animal (UFL_V/t)
ufvj(j,k) : UFV content in j-crop (UFV/t)

• the nitrogen block N

apolt(o,k) : input N org LT / N mineral equiv
aqolt(o,k) : LT effect N org equivalent N mineral
benjk(j,k) : N need of crop (yield) (tN /(t.ha))
casti : test for benjk parameter use (0/1)
coo(o,i,j,k) : mineralisation fact. dejection o animal i / j
cpro(o,j,k) : mineralisation fact. UOR o / crop j
endrg : indicator for yield calculation activation (0/1/2) (-)
enj(j,k) : fraction of nitrogen matter in crops (feed) (t/t)
clpdc: PD needs for milk / intercept for dairy cows (kg/hd)
clpdp(k): PD needs per ton of milk / coef for dairy cows (kg/t)
clufc: PD needs for milk / intercept for dairy cows (kg/hd)
clufp(k): PD needs per ton of milk / coef for dairy cows (kg/t)
digm(i): average digestibility intake, IPCC, anim. i (%)
ebac(n,i,k): ingestion coeff. / energy content / concentrates (ce/t)
ebag(i,k): ingestion coeff. / raw matter deed (ce/t)
ebes(j): raw energy content of crop (kcal/kg DM)
ebi(i,k): ingestion capacity by animal i (ce/head)
ebj(j,k): ingestion coeff. / crop j (ce/t)
ed(j): j-crop digestibility (1)
eda1: feed concentrate digestibility (type 1 simpl energy) (1)
eda2: feed concentrate digestibility (type 2 simpl protein) (1)
eda3: feed concentrate digestibility (type 3 compound ener) (1)
eda4: feed concentrate digestibility (type 4 compound prot) (1)
edag: raw feed digestibility (1)
emac(n,i,k): metabolisable energy in concentrated feed graniv (Mcal/t)
emag(i,k): metabolisable energy in raw feed for granivore (Mcal/t)
enac(n,i,k): digestibility of concentrated feed per animal (1)
enag(i,k): digestibility of raw feed per animal (1)
emi(i,k): yearly requirement of metabolisable energy (Mcal/head)
emj(j,k): metabolisable energy in crop j farm k (Mcal/t)
eni(i,k): yearly proteins requirement per animal i farm k (t/head)
fglai: flag for adjusted feeding parameters
pac(n,i,k): bought conc. feed price (incl. proteins) (k€/t)
pag(i,k): bought raw feed price (k€/t)
palac: relative change in bought conc. feed price (1)
palag: relative change in raw feed price (1)
pdib(i,k): digest. protein requirement of i ruminant (kg/head)
pdie(j,k): N equiv. by j crop in PDIE (kg/t)
pdin(j,k): N equiv. by j crop in PDIN (kg/t)
peac(n,i,k): N equiv. by n concentr. feed in PDIE / anim. i (kg/t)
peag(i,k): N equiv. by raw feed in PDIE / anim. i (kg/t)
pnac(n,i,k): PDIN N-equivalent / concentr. feed (kg/t)
pnag(i,k): PDIN N-equivalent / raw feed (kg/t)
smi(i,k): dry matter requirement / animal i (tDM/head)
smj(j,k): dry matter ratio in j-crop (1)
smac(n,i,k): dry matter ratio in concentr. feed / i-animal (1)
smsg(i,k): dry matter ration in raw feed / i-animal (1)
tconv: conversion ratio of i-animal digestibility in CH4
trp(j,k): ratio of j-cereal content proteins / energy
epd(o,i,k) : spreadable proportion of manure type o / animal i
flf(o,i,k) : part solid/liquid/droppings / effluent (t/t)
fmfu(i) : average mineral fraction in manure, IPCC (%)
fned(o,i,k) : fraction N in effluent o from animal i (kgN/kg)
fnedo(o,k) : fraction N in UOR type o
fnes(j,k) : fraction N / fertilizers for crop j (kgN/kg fert)
fnesc(j,k) : fraction N / ferti. regul. for crop j (kgN/kg fert)
fnesf(j,k) : fraction N / ferti. starter for crop j (kgN/kg fert)
mgesd : identifier 0/1 activating manure spreading block (-)
yexjk(j,k) : calculated N input requirement (crop model) (tN/ha)
pexne : price of exceeding N / spreadable limit
proo(o,k) : UOR type o available for Farm Group k (t RawMat)
prixn : relative change in price of fertilizer N-content (-)
prxn(j,k) : j-crop fertilizer price / farm group k (k€/t)
prxnc(j,k) : regular fertilizer price / crop j / farm group k (k€/t)
prxnf(j,k) : starter fertilizer price / crop j / farm group k (k€/t)
qengf(j,k) : starter fertilizer quantity brought to j-crop (t/ha)
qidej(o,i,k) : o-manure quantity excret. by i-animal (t ou m3/head)
volat(o,k) : N-volatil. coeff. reletd to o-manure/UOR storage (tN/tN)
wjk(j,k) : irrigation costs (k€/ha)

## the policy block P

aidkk(k) : lump-sum farm payment (k€/farm)
cerjk(j) : caloric content per 100g of j-crop (kcal/hg)
cerik(i) : caloric content per 100g of i-animal (meat) (kcal/hg)
calai : caloric content per 100g of milk (kcal/hg)
calorac(n) : caloric content per 100g of concentrated feed (kcal/hg)
calorag : caloric content per 100g of (hay) raw feed (kcal/hg)
capro : protein / calorie ratio requested for diet (adefinir)
proteac(n) : caloric yield from protein per 100g of feed (kcal/hg)
proteag : caloric yield from protein per 100g of raw feed (kcal/hg)
berjk(j) : caloric yield from protein per 100g of j-crop (kcal/hg)
berik(i) : caloric yield from protein per 100g of i-animal (kcal/hg)
cplai : caloric yield from protein per 100g of milk (kcal/hg)
derik(i) : food content per i-animal (t/head)
acerj : ACE energy crop subsidy non set-aside / CAP
aenrj(j) : ACE energy crop subsidy non set-aside / CAP per crop j
aidkk(k) : lump-sum farm payment (k€/farm)
aii(i) : subsidy per animal ("small" herd) (k€/head)
ajj(j) : subsidy per crop (k€/t)
amah : threshold defining small herbivore producer (LU/farm)
ufac(n,i,k) : UF content in concentr. feed / i-animal (UFL_eq/t)

ufag(i,k) : UF content in raw feed / i-animal (UFL_eq/t)

uflj(j,k) : AFL content in j-crop (UFL/t)

uflv(i,k) : AFL requirement / UFV for i-animal (UFL_V/t)

ufvj(j,k) : UFV content in j-crop (UFV/t)

### the nitrogen block N

apolt(o,k) : input N org LT / N mineral equiv

aqolt(o,k) : LT effect N org equivalent N mineral

benjk(j,k) : N need of crop (yield) (tN /(t.ha))

casti : test for benjk parameter use (0/1)

coo(o,i,j,k) : mineralisation fact. dejection o animal i / j

cpro(o,j,k) : mineralisation fact. UOR o / crop j

endrg : indicator for yield calculation activation (0/1/2) (-)

enj(j,k) : fraction of nitrogen matter in crops (feed) (t/t)

epd(o,i,k) : spreadable proportion of manure type o / animal i

flf(o,i,k) : share solid/liquid/droppings / manure (sum_o = 1) (t/t)

fmfu(i) : average mineral fraction in manure, IPCC (%)

fnec(j,k) : fraction N prod byprod from crop j (tN/tVS)

fned(o,i,k) : fraction N in effluent o from animal i (tN/tVS)

fnedo(o,k) : fraction N in UOR type o

fnes(j,k) : fraction N / fertilizers for crop j (kgN /kg fert)

fnesc(j,k) : fraction N / ferti. regul. for crop j (kgN /kg fert)

fnesf(j,k) : fraction N / ferti. starter for crop j (kgN /kg fert)

mgesd : identifier 0/1 activating manure spreading block (-)

mgeso : identifier 0/1 activating Org.Mat. purchase - sale (-)

yexjk(j,k) : calculated N input requirement (crop model) (tN/ha)

pexne : price of exceeding N / spreadable limit

proo(o,k) : UOR type o available for Farm Group k (t RawMat)

prixn : relative change in price of fertilizer N-content (-)

prxn(j,k) : j-crop fertilizer price / farm group k (k€/t)

prxnc(j,k) : regular fertilizer price / crop j / farm group k (k€/t)

prxnf(j,k) : starter fertilizer price / crop j / farm group k (k€/t)

qengf(j,k) : starter fertilizer quantity brought to j-crop (t/ha)

qidej(o,i,k) : o-manure quantity excret. by i-animal (t ou m3/LU)

volat(o,k) : N-volatil. coeff. reletd to o-manure/UOR storage (tN/tN)

wjk(j,k) : irrigation costs (k€/ha)

xoxox : price excess Norg (tmanure)

### the policy block P

aidkk(k) : lump-sum farm payment (k€/farm)
amaj : threshold small prod. (young bovine premium) (LU/farm)

angel : min. area ratio set-aside allowing subsidy (1988) (0<->1)

ave : subsidy / calves (k€/head)

bii(i) : animal premium (McSh - extensif. animal) (k€/head)

bjj(j) : per crop area premium (McSh hard wheat) (k€/ha)

bjk(j,k) : net "subsidy" / area (type XD wood fallow) (k€/ha)

cerea : threshold McSh CAP cereal yield (4.6 t/Ha) (t/ha)

chgpa : Livestock limit 1 (grass premium) (LU/ha)

chgpb : Livestock limit 2 (grass premium) (LU/ha)

chgpc : Livestock limit 3 (grass premium) (LU/ha)

chgpd : Livestock limit 4 (grass premium) (LU/ha)

chgpe : Livestock limit 5 (grass premium) (LU/ha)

chgpf : Livestock limit 6 (grass premium) (LU/ha)

chgpg : Livestock limit 7 (grass premium) (LU/ha)

chgph : Livestock limit 8 (grass premium) (LU/ha)

chgpi : Livestock limit 9 (grass premium) (LU/ha)

chgtj : Livestock limit young bovine premium (LU/ha)

chgtk : Livestock limit superpremium young bovine (LU/ha)

chgui : Livestock limit herbivores / non subsid. prem. (LU/ha)

chgus : Livestock limit grass super-premium (LU/ha)

cii(i) : subsid top up / national complement / animal (k€/head)

cjj(j) : subsid top up / national complement / vegetal (k€/ha)

cjk(j,k) : revenue / ha out of FEOGA (type XD wood fallow) (k€/ha)

cqlai : reduct. (>0) milk quota without prem. red. (1-cqlai) (-)

crlai : top up milk (k€/t)

cupp : coeff. min. set-aside part to get set-as prem Msh (0<->1)

cupq : coeff. fix set-aside part (0<->1)

cvpp : coeff. maximal set-aside to get premium Msh (0<->1)

djj(j) : floor price McSharry reform / SCOP (k€/t)

faxou : max cumulative premimum for grass production (k€)

ienrj(j) : energy use identifier (val. 1 in case)

yxdej(j,k) : upper limit of epandable org. N / crop area unit (tN/ha)

nhpgp : option number for piecewise linear. subs. for grass (1)

ojj(j) : add. subsid. per hectare*yield of crop j (k€/t)

olea : ref. oilseeds yield (2.36 t/ha) (t/ha)

penrr(j) : relative price change of by-product / crop j (-)

pesac : tax/subsid. (tax if >0 ) on concentr. feed (GHG) (k€/t)

pesag : tax/subsid. (tax if >0 ) on raw feed (GHG) (k€/t)

pgms : McSh set-aside subsid. (block / CAP cereal yield) (k€/t)

piac(n,i) : tax/subsid. on n-concentr. feed / anim. i (k€/t)

piag(i) : tax/subsid. on raw feed / animal i (k€/t)
cerjk(j) : caloric content per 100g of j-crop (kcal/hg)

cerik(i) : caloric content per 100g of i-animal (meat) (kcal/hg)

calai : caloric content per 100g of milk (kcal/hg)

calorac(n) : caloric content per 100g of concentrated feed (kcal/hg)

calorag : caloric content per 100g of (hay) raw feed (kcal/hg)

capro : protein / calorie ratio requested for diet (adefinir)

proteac(n) : caloric yield from protein per 100g of feed (kcal/hg)

proteag : caloric yield from protein per 100g of raw feed (kcal/hg)

berjk(j) : caloric yield from protein per 100g of j-crop (kcal/hg)

berik(i) : caloric yield from protein per 100g of i-animal (kcal/hg)

cplai : caloric yield from protein per 100g of milk (kcal/hg)

derik(i) : food content per i-animal (t/head)

acerj : ACE energy crop subsidy non set-aside / CAP

aenrj(j) : ACE energy crop subsidy non set-aside / CAP per crop j

aidkk(k) : lump-sum farm payment (k€/farm)

aii(i) : subsidy per animal ("small" herd) (k€/head)

ajj(j) : subsidy per crop (k€/t)

amah : threshold defining small herbivore producer (LU/farm)

amaj : threshold small prod. (young bovine premium) (LU/farm)

angel : min. area ratio set-aside allowing subsidy (1988) (0<->1)

ave : subsidy / calves (k€/head)

bii(i) : animal premium (McSh - extensif. animal) (k€/head)

bjj(j) : per crop area premium (McSh hard wheat) (k€/ha)

bjk(j,k) : net "subsidy" / area (type XD wood fallow) (k€/ha)

cerea : threshold McSh CAP cereal yield (4.6 t/Ha) (t/ha)

chgpa : Livestock limit 1 (grass premium) (LU/ha)

chgpb : Livestock limit 2 (grass premium) (LU/ha)

chgpc : Livestock limit 3 (grass premium) (LU/ha)

chgpd : Livestock limit 4 (grass premium) (LU/ha)

chgpe : Livestock limit 5 (grass premium) (LU/ha)

chgpf : Livestock limit 6 (grass premium) (LU/ha)

chgpg : Livestock limit 7 (grass premium) (LU/ha)

chgph : Livestock limit 8 (grass premium) (LU/ha)

chgpi : Livestock limit 9 (grass premium) (LU/ha)

chgtj : Livestock limit young bovine premium (LU/ha)

chgtk : Livestock limit superpremium young bovine (LU/ha)

chgui : Livestock limit herbivores / non subsid. prem. (LU/ha)

chgus : Livestock limit grass super-premium (LU/ha)

cii(i) : subsidy top up / national complement / animal (k€/head)

cjj(j) : subsidy top up / national complement / vegetal (k€/ha)

cjk(j,k) : revenue / ha out of FEOGA (type XD wood fallow) (k€/ha)
pges(j): subsidy(<0) / tax(>0) ferti. crop j (k€/tN)
pgsn: subsidy(<0) / tax(>0) fertilizers (k€/tN)
pgeso: subsidy(<0) / tax(>0) organic Nitrogen intakes (k€/tN)
pies(i): subsidy(<0) / tax(>0) animal i (GHG) (k€/head)
pjes(j): subsidy(<0) / tax(>0) crop j (GHG) (k€/ha)
pjr(j): reference price before CAP reform basing djj(j) (k€/t)
plaid: relative change of milk price on 2nd market (1)
plaiw(k): milk price on 2nd market (€/l)
prges: GHG em. tax/subsidy on CO2 equiv. (k€/tCO2)
qenrj(j,k): quota holding crop j final energy use (t/F)
prgpa: premium 1 livestock limit 1 (grass subsidy) (k€/ha)
prgb: premium 2 livestock limit 2 (grass subsidy) (k€/ha)
prgpc: premium 3 livestock limit 3 (grass subsidy) (k€/ha)
prgpd: premium 4 livestock limit 4 (grass subsidy) (k€/ha)
prgpe: premium 5 livestock limit 5 (grass subsidy) (k€/ha)
prgpf: premium 6 livestock limit 6 (grass subsidy) (k€/ha)
prgpg: premium 7 livestock limit 7 (grass subsidy) (k€/ha)
prgph: premium 8 livestock limit 8 (grass subsidy) (k€/ha)
prgpi: premium 9 livestock limit 9 (grass subsidy) (k€/ha)
prgte: superpremium young bov. limit 1 (young bov subs.) (k€/ha)
prgtj: young bov subs. LS limit 1 (young bov. subs.) (k€/ha)
prgtl: milk cow subs. LS limit 1 (milk cow subsidy) (k€/ha)
prgtn: suckler cow subs. LS limit 1 (suckler cow subs.) (k€/ha)
prjml: male calve subsidy 8 days / milk herd (k€/head)
qplai: milk quota price in case of quota market (k€/t)
prlai: milk premium / Agenda 2000 / under initial quota (k€/t)
psgel(k): set-aside premium / Luxembourg decoupling (k€/ha)
psngl(k): non set-aside premium L Luxembourg decoupling (k€/ha)
psrpa(k): grassland premium / Luxembourg decoupling (k€/ha)
psrta(k): arable land premium Luxembourg decoupling (k€/ha)
pssap(k): single farm-dependent area payment (k€/ha)
psuni: single area payment (k€/ha)
puges: premium(<0) / tax(>0) LU (GHG) (k€/LU)
qdfau(k): sugarbeet frac. A+B/TOT in case of missing estim. quota
qpcab(k): min frac. of C sugarbeet related to A and B
qfo(n,k): upper limit per support category (Lux. CAP reform) (k€)
qgelu(k): set-aside quota / Luxembourg decoupling (ha)
qjk(j,k): vegetal quota (kt)
qlait(k): milk quota (kl)
qlaiw(k): milk quota 2nd market (kl)
qopes(k,l): GHG emission quota (sub-group k,l)
cqlai: reduct. (>0) milk quota without prem. red. (1-cqlai) (-)
crlai: top up milk (k€/t)
cupp: coeff. min. set-aside part to get set-as prem Msh (0<->1)
cupq: coeff. fix set-aside part (0<->1)
cvpp: coeff. maximal set-aside to get premium Msh (0<->1)
djj(j): floor price McSharry reform / SCOP (k€/t)
faxou: max cumulative premimum for grass production (k€)
ienrj(j): energy use identifier (val. 1 in case)
yxdej(j,k): upper limit of epandable org. N / crop area unit (tN/ha)
nhpgp: option number for piecewise linear. subs. for grass (1)
ojj(j): add. subsid. per hectare*yield of crop j (k€/t)
olea: ref. oilseeds yield (2.36 t/ha) (t/ha)
penrr(j): relative price change of by-product / crop j (-)
pesac: tax/subsid. (tax if >0) on concentr. feed (GHG) (k€/t)
pesag: tax/subsid. (tax if >0) on raw feed (GHG) (k€/t)
pgms: McSh set-aside subsid. (block / CAP cereal yield) (k€/t)
piac(n,i): tax/subsid. on n-concentr. feed / anim. i (k€/t)
piag(i): tax/subsid. on raw feed / animal i (k€/t)
prac(n,i): relative price. on n-concentr. feed / anim. i (-)
prag(i): relative price on raw feed / animal i (-)
pges(j): subsidy(<0) / tax(>0) ferti. crop j (k€/tN)
pgesn: subsidy(<0) / tax(>0) fertilizers (k€/tN)
pgeso: subsidy(<0) / tax(>0) organic Nitrogen intakes (k€/tN)
pies(i): subsidy(<0) / tax(>0) animal i (GHG) (k€/head)
pjes(j): subsidy(<0) / tax(>0) crop j (GHG) (k€/ha)
pjr(j): reference price before CAP reform basing djj(j) (k€/t)
plaid: relative change of milk price on 2nd market (1)
plaiw(k): milk price on 2nd market (€/l)
prges: GHG em. tax/subsidy on CO2 equiv. (k€/tCO2)
qenrj(j,k): quota holding crop j final energy use (t/F)
prgpa: premium 1 livestock limit 1 (grass subsidy) (k€/ha)
prgpb: premium 2 livestock limit 2 (grass subsidy) (k€/ha)
prgpc: premium 3 livestock limit 3 (grass subsidy) (k€/ha)
prgpd: premium 4 livestock limit 4 (grass subsidy) (k€/ha)
prgpe: premium 5 livestock limit 5 (grass subsidy) (k€/ha)
prgpf: premium 6 livestock limit 6 (grass subsidy) (k€/ha)
prgpg: premium 7 livestock limit 7 (grass subsidy) (k€/ha)
prgph: premium 8 livestock limit 8 (grass subsidy) (k€/ha)
prgpi: premium 9 livestock limit 9 (grass subsidy) (k€/ha)
prgte: superpremium young bov. limit 1 (young bov subs.) (k€/ha)
prgtj: young bov subs. LS limit 1 (young bov. subs.) (k€/ha)
qorkk(k) : barley quota (kt)
qpsth(k) : lower bound / grasslands (INSEA / C storage)
qtalk(k) : reference milk yield / young bovine premium (t/VL/an)
qtete : young bov. number limit / young bov. premium (heads)
qtola : milk quota limit / young bov. premium (t/an)
rafou : ratio grassland / UAA required for grass subsidy (1)
rcehm(k) : region ref. yield of cereal but maize (ir. or not) (t/ha)
rceja(k) : reference yield / fallow (t/ha)
rcemg(k) : region reference yield maize (irrig or not) (t/ha)
redes : single reduction coef. on quota C/GHG
rqlai : exceeding milk quota / initial quota Agenda 2000 (1)
rwlai : variation / milk quota 2nd market / quota B (1)
quank(k) : financial quantum (k€/farm)
sbett(k) : average sugarbeet area (under quota) (ha/farm)
scop(k,l) : reference COP area limiting set-aside subsidy (ha/farm)
senrj(k) : upper bound of total area in energy crops (ha/farm)
rii(i) : slaughter premium (Agenda 2000 = option 14) (k€/head)
sii(i) : threshold "small" herd (national) (head/farm)
sjc(j,k) : reference crop area accounting for C storage (ha)
spre : additional premium if LS load < chgus / amateur (k€/LU)
ndivb : min number of crops for 1st diversification threshold
ndivc : min number of crops for 2nd diversification threshold
sdmax(k) : max limit for crop diversification (ha)
sdmin(k) : min limit for crop diversification (ha)
sudiv(k) : subsidy for crop diversification
thrss(k) : crop area limit accounting for crop diversification
tabkk(k) : ratio binding sugarbeet quotas A and B (1)
tan : equiv. cereal "230t" in COP (non-subs. set-aside) (t)
tegkk(k) : fertilizer tax (cox, cozy()) (1)
timou : UAA threshold for grass subsidy (ha)
tjj(j) : j-crop tax (see tjk(j,k)) (1)
tjk(j,k) : marketed prod. j-crop tax (price * (1+t)) (1)
tlaid : "superlevy" / milk price 2nd market (1)
ton : equiv. cereal "92t" in COP (threshold "amateur") (t)
txn2o : direct N2O loss tax (k€/tN)
txnh3 : direct NH3 loss tax (k€/tN)
txno3 : direct N03 loss tax (k€/tN)
u(i,j,k) : LS load i-animal / j-fodder area (head/ha)
ugbou : lower bound of herd for grass subsidy (LSU)

• the water block W
prgtl: milk cow subs. LS limit 1 (milk cow subsidy) (k€/ha)
prgtn: suckler cow subs. LS limit 1 (suckler cow subs.) (k€/ha)
prjml: male calve subsidy 8 days / milk herd (k€/head)
pqlai: milk quota price in case of quota market (k€/t)
prlai: milk premium / Agenda 2000 / under initial quota (k€/t)
psgel(k): set-aside premium / Luxembourg decoupling (k€/ha)
psngl(k): non set-aside premium L Luxembourg decoupling (k€/ha)
psrpa(k): grassland premium / Luxembourg decoupling (k€/ha)
psrta(k): arable land premium Luxembourg decoupling (k€/ha)
pssap(k): single farm-dependent area payment (k€/ha)
psuni: single area payment (k€/ha)
puges: premium(<0) / tax(>0) LU (GHG) (k€/LU)
qdfau(k): sugarbeet frac. A+B/TOT in case of missing estim. quota
qpcab(k): min frac. of C sugarbeet related to A and B
qfo(n,k): upper limit per support category (Lux. CAP reform) (k€)
qgelu(k): set-aside quota / Luxembourg decoupling (ha)
qjk(j,k): vegetal quota (kt)
qlait(k): milk quota (kl)
qlaiw(k): milk quota 2nd market (kl)
qopes(k,l): GHG emission quota (sub-group k,l)
qorkk(k): barley quota (kt)
qpsth(k): lower bound / grasslands (INSEA / C storage)
qtalk(k): reference milk yield / young bovine premium (t/VL/an)
qtete: young bov. number limit / young bov. premium (heads)
qtola: milk quota limit / young bov. premium (t/an)
rafou: ratio grassland / UAA required for grass subsidy (1)
rcehm(k): region ref. yield of cereal but maize (ir. or not) (t/ha)
rceja(k): reference yield / fallow (t/ha)
rcemg(k): region reference yield maize (irrig or not) (t/ha)
redes: single reduction coef. on quota C/GHG
rqlai: exceeding milk quota / initial quota Agenda 2000 (1)
rwlai: variation / milk quota 2nd market / quota B (1)
quank(k): financial quantum (k€/farm)
sbett(k): average sugarbeet area (under quota) (ha/farm)
scop(k,l): reference COP area limiting set-aside subsidy (ha/farm)
senrj(k): upper bound of total area in energy crops (ha/farm)
rii(i): slaughter premium (Agenda 2000 = option 14) (k€/head)
sii(i): threshold "small" herd (national) (head/farm)
sjc(j,k): reference crop area accounting for C storage (ha)
spre: additional premium if LS load < chgus / amateur (k€/LU)
ndivb: min number of crops for 1st diversification threshold
ywajk(j,k) : calculated water input requirement (crop model) (m3/ha)

pxeau(j,k) : water price / crop j / farm group k (k€/m3)

wjk0(j,k) : preserved water costs in case of recalculation (k€/ha)

xsikk(k) : shadow price of k-irrig water limit case endog. (k€/m3)

xsitt : common shadow price of water limit in case endog (k€/m3)

wirig(k) : water irrigation limit k-scale (m3)

wirtt : water irrigation limit for the whole set of k-GT (m3)

### the "trans-farm group" block T

qymin(j) : Min j-crop Qty to be marketed at domestic price (t)

qycal : Min calories Qty to be exported from agr.sys. (teqcere)

qene(n) : Min bio-energy typ1 provided 1+2G from ag.sys. (tgazoleq)

qymce : Min cereal Qty to be marketed at domestic price (t)

qmxnm : Max Qty of mineral nitrogen (t)

qmxge : Max Qty of GHG emissions (soil-C exclud.) (tCO2eq)

eenrj(n,j,k) : biomass transformed into energy / crop j farm k (tbd)

## 4.2.2 Activities operating in the model

Activities designate the command variables (also named by primal variables) against which the optimization problem is solved.

The comprehensive list of activities also includes those activities which were incorporated in past AROPAj versions but are now possibly obsolete. We provide units in which variables are expressed. At the farm level, main units are metric tons (t), livestock units (LU), animal head numbers (head), hectares (ha), 1000 liters (kl), metric tons of CO2eq (tCO2eq), 1000 € (k€). At the farm group level, numerical figures have to be multiplied by f, which is implicitly equal to 1000 and relates to the representativity of the farm group. In other words, when the number of farms represented by a farm group is 954, the population enters in the model with the value 0.954, f = 1000.

The animal and plant activities on which the model is based are listed in Table 35 with the labels used in the files. It should be added that the links between these two groups of activities exist in different forms, in particular through animal feed (by distinguishing the cereals and fodder produced and consumed on the farm on the one hand, raw feed or concentrates purchased on the other hand) and by nitrogen inputs (distinguishing between fertilizers of industrial origin and organic amendments sourced from manure).

### the general block G

aokeu(k) : not if CONDITION work paid - wages per farm (kE)

aokwu(k) : not if CONDITION work unpaid - working units per farm (AWU)

aoket : not if CONDITION work paid (kE)

aokut : not if CONDITION work unpaid (AWU)

efo(n,k,l) : generic variable of "deficit or excedent" (CAP) (var)
<table>
   <tr>
    <td>ndivc</td>
    <td>min number of crops for 2nd diversification threshold</td>
   </tr>
   <tr>
    <td>sdmax(k)</td>
    <td>max limit for crop diversification (ha)</td>
   </tr>
   <tr>
    <td>sdmin(k)</td>
    <td>min limit for crop diversification (ha)</td>
   </tr>
   <tr>
    <td>sudiv(k)</td>
    <td>subsidy for crop diversification</td>
   </tr>
   <tr>
    <td>thrss(k)</td>
    <td>crop area limit accounting for crop diversification</td>
   </tr>
   <tr>
    <td>tabkk(k)</td>
    <td>ratio binding sugarbeet quotas A and B (1)</td>
   </tr>
   <tr>
    <td>tan</td>
    <td>equiv. cereal "230t" in COP (non-subs. set-aside) (t)</td>
   </tr>
   <tr>
    <td>tegkk(k)</td>
    <td>fertilizer tax (cox, cozy()) (1)</td>
   </tr>
   <tr>
    <td>timou</td>
    <td>UAA threshold for grass subsidy (ha)</td>
   </tr>
   <tr>
    <td>tjj(j)</td>
    <td>j-crop tax (see tjk(j,k)) (1)</td>
   </tr>
   <tr>
    <td>tjk(j,k)</td>
    <td>marketed prod. j-crop tax (price * (1+t)) (1)</td>
   </tr>
   <tr>
    <td>tlaid</td>
    <td>"superlevy" / milk price 2nd market (1)</td>
   </tr>
   <tr>
    <td>ton</td>
    <td>equiv. cereal "92t" in COP (threshold "amateur") (t)</td>
   </tr>
   <tr>
    <td>txn2o</td>
    <td>direct N2O loss tax (k€/tN)</td>
   </tr>
   <tr>
    <td>txnh3</td>
    <td>direct NH3 loss tax (k€/tN)</td>
   </tr>
   <tr>
    <td>txno3</td>
    <td>direct N03 loss tax (k€/tN)</td>
   </tr>
   <tr>
    <td>u(i,j,k)</td>
    <td>LS load i-animal / j-fodder area (head/ha)</td>
   </tr>
   <tr>
    <td>ugbou</td>
    <td>lower bound of herd for grass subsidy (LSU)</td>
   </tr>
  </table>

### the water block W

<table>
   <tr>
    <td>ywajk(j,k)</td>
    <td>calculated water input requirement (crop model) (m3/ha)</td>
   </tr>
   <tr>
    <td>pxeau(j,k)</td>
    <td>water price / crop j / farm group k (k€/m3)</td>
   </tr>
   <tr>
    <td>wjk0(j,k)</td>
    <td>preserved water costs in case of recalculation (k€/ha)</td>
   </tr>
   <tr>
    <td>xsikk(k)</td>
    <td>shadow price of k- irrig water limit case endog. (k€/m3)</td>
   </tr>
   <tr>
    <td>xsitt</td>
    <td>common shadow price of water limit in case endog (k€/m3)</td>
   </tr>
   <tr>
    <td>wirig(k)</td>
    <td>water irrigation limit k-scale (m3)</td>
   </tr>
   <tr>
    <td>wirtt</td>
    <td>water irrigation limit for the whole set of k-GT (m3)</td>
   </tr>
  </table>

### the "trans-farm group" block T

<table>
   <tr>
    <td>qymin(j)</td>
    <td>Min j-crop Qty to be marketed at domestic price (t)</td>
   </tr>
   <tr>
    <td>qycal</td>
    <td>Min calories Qty to be exported from agr.sys. (teqcere)</td>
   </tr>
   <tr>
    <td>qene(n)</td>
    <td>Min bio-energy typ1 provided 1+2G from ag.sys. (tgazoleq)</td>
   </tr>
   <tr>
    <td>qymce</td>
    <td>Min cereal Qty to be marketed at domestic price (t)</td>
   </tr>
   <tr>
    <td>qmxnm</td>
    <td>Max Qty of mineral nitrogen (t)</td>
   </tr>
   <tr>
    <td>qmxge</td>
    <td>Max Qty of GHG emissions (soil-C exclud.) (tCO2eq)</td>
   </tr>
   <tr>
    <td>eenrj(n,j,k)</td>
    <td>biomass transformed into energy / crop j farm k (tbd))</td>
   </tr>
  </table>
excdt(n) : generic variable "deficit or excedent or total" (var)

ief(n,k,l) : not if CONDITION generic binary variable

zf(k,l) : not if CONDITION farm number k l (f)

• the animal block A

ani(i,k,l) : animal number cat. i (total) (heads)

ant(i) : not if CONDITION aggregated i-herd (heads)

xolai(k,l) : not if CONDITION dairy milk production (f*kl)

xolat : total dairy milk production (f*kl)

xugb(k,l) : not if CONDITION livestock (per sub-group) (f*LU)

xugbk(k) : livestock (per group) (f*LU)

xugbt : total livestock (f*LU)

yolai(k,l) : not if CONDITION dairy milk product. entitling premium Agenda2000 (f*kl)

• the crop block C

aut(j) : aggregated on-farm use of j-crop prod. (f*t)

c(i,j,k,l) : not if CONDITION on-farm j-prod. to feed i-animal (f*t)

dctr : trade balance defic. / sugarbe (if demand info.) (f*k€)

excr : trade balance excess / sugarbe (if demand info.) (f*k€)

x(j,k,l) : not if CONDITION standard j-crop area (out of CAP) (f*ha)

xtk(j,k) : aggregated j-crop area (per k) (f*ha)

xtt(j) : aggregated j-crop area (f*ha)

y(j,k,l) : not if CONDITION marketed j-crop prodution (farm) (f*t)

y0(j,k) : not if CONDITION marketed j-crop prodution (farm) exluding energy (f*t)

ye(o,j,k) : not if CONDITION marketed j-crop prodution (farm) for energy type O (f*t)

yc(j,k) : not if CONDITION marketed j-crop by-product (f*t)

yb0(j,k) : not if CONDITION marketed j-crop by-product excluding bioenergy (f*t)

yb(o,j,k) : not if CONDITION marketed j-crop by-product for energy type O (f*t)

ycj(j) : aggregated j-crop by-product

yi(j) : marketed j-crop production (domestic price) (f*t)

ym(j) : marketed j-crop prod. (out of quota / worldprice) (f*t)

• the environment block E

emcdt(n) : generic counterpart of GHG balance (tCO2)

epcdt(n) : balance N-pollutant emission (3 cat.: N2O NO3 NH3)

qzz(j,k) : not if CONDITION utilized amount of pesticide on area j (k EUR)

• the feed block F

acgta(m) : not if CONDITION aggregated feed (conc. bought / cat.) (f*t)

b(n,i,k,l) : concentrate feed cat. n bought for i-herd (f*t)

agt(i,k,l) : not if CONDITION raw feed bought for i-herd (f*t)
### 4.2.2 Activities operating in the model

Activities designate the command variables (also named by primal variables) against which the optimization problem is solved.

The comprehensive list of activities also includes those activities which were incorporated in past AROPAj versions but are now possibly obsolete. We provide units in which variables are expressed. At the farm level, main units are metric tons (t), livestock units (LU), animal head numbers (head), hectares (ha), 1000 liters (kl), metric tons of CO₂eq (tCO₂eq), 1000 € (k€). At the farm group level, numerical figures have to be multiplied by f, which is implicitly equal to 1000 and relates to the representativity of the farm group. In other words, when the number of farms represented by a farm group is 954, the population enters in the model with the value 0.954, $f = 1000$.

The animal and plant activities on which the model is based are listed in Table 35 with the labels used in the files. It should be added that the links between these two groups of activities exist in different forms, in particular through animal feed (by distinguishing the cereals and fodder produced and consumed on the farm on the one hand, raw feed or concentrates purchased on the other hand) and by nitrogen inputs (distinguishing between fertilizers of industrial origin and organic amendments sourced from manure).

#### ● the general block G

aokeu(k) : not if CONDITION work paid - wages per farm (kE)

aokwu(k) : not if CONDITION work unpaid - working units per farm (AWU)

aoket : not if CONDITION work paid (kE)

aokut : not if CONDITION work unpaid (AWU)

efo(n,k,l) : generic variable of "deficit or excedent" (CAP) (var)

excdt(n) : generic variable "deficit or excedent or total" (var)

ief(n,k,l) : not if CONDITION generic binary variable

zf(k,l) : not if CONDITION farm number k l (f)

#### ● the animal block A

ani(i,k,l) : animal number cat. i (total) (heads)

ant(i) : not if CONDITION aggregated i-herd (heads)

xolai(k,l) : not if CONDITION dairy milk production (f*kl)

xolat : total dairy milk production (f*kl)

xugb(k,l) : not if CONDITION livestock (per sub-group) (f*LU)

xugbk(k) : livestock (per group) (f*LU)

xugbt : total livestock (f*LU)

yolai(k,l) : not if CONDITION dairy milk product. entitling premium Agenda2000 (f*kl)

#### ● the crop block C

aut(j) : aggregated on-farm use of j-crop prod. (f*t)