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scenario_simulation [2022/11/07 10:23] – external edit 127.0.0.1scenario_simulation [2023/08/25 09:51] – [Annual transitions if SUPREMA is active] massfeller
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 A number of recent developments are not covered in the previous exposition of supply model equations A number of recent developments are not covered in the previous exposition of supply model equations
  
-  -A series of projects have added a distinction of rainfed and irrigated varieties of most crop activities which is the core of the so-called “CAPRI-water” version of the system((A more complete presentation is given in [[https://ec.europa.eu/jrc/en/publication/eur-scientific-and-technical-research-reports/extension-capri-model-irrigation-sub-module]].)). +   - A series of projects have added a distinction of rainfed and irrigated varieties of most crop activities which is the core of the so-called “CAPRI-water” version of the system 
-  -Several projects have added endogenous GHG mitigation options((These are most completely included in the “trunk” version of the CAPRI system. For details, see, for example, [[http://publications.jrc.ec.europa.eu/repository/bitstream/JRC101396/jrc101396_ecampa2_final_report.pdf]].))  +  - Several projects have added endogenous GHG mitigation options 
-  -Several new equations serve to explicitly represent environmental constraints deriving from the Nitrates Directive and the NEC directive((These are most completely included in the “trunk” version of the CAPRI system but developments are still ongoing.)).  +  - Several new equations serve to explicitly represent environmental constraints deriving from the Nitrates Directive and the NEC directive
-  -A complete area balance monitoring the land use changes according to the six UNFCCC land use types (cropland, grassland, forest land, wetland, settlements, residual land) has been introduced for carbon accounting+
  
 ====Calibration of the regional programming models====   ====Calibration of the regional programming models====  
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-====Annex: Land supply and land transitions in the supply part of CAPRI====+====== LULUCF in the supply model of CAPRI ======
  
-**Introduction**+===== Introduction =====
  
-This technical paper explains how the most aggregate level of the CAPRI area allocation in the context of the supply models has been re-specified in the TRUSTEE project((https://www.trustee-project.eu/ +This technical paper explains how the most aggregate level of the CAPRI area allocation in the context of the supply models has been re-specified in the TRUSTEE ((https://www.trustee-project.eu/ 
-)) and subsequently adopted in the CAPRI trunk. The former specification for land supply and transformation functions focused on agricultural land use and the transformation of agricultural land between arable land and grass land((See https://svn1.agp.uni-bonn.de/svn/capri/trunk/doc/landSupplyCAPRI_v5.pdf (Torbjörn Jansson, Wolfgang Britz, Alan Renwick and Peter Verburg (2010) Modelling CAP reform and land abandonment in the European Union with a focus on Germany.) +)) and SUPREMA ((https://www.suprema-project.eu/)) projects and subsequently adopted in the CAPRI trunk. The former specification for land supply and transformation functions focused on agricultural land use and the transformation of agricultural land between arable land and grass land.
-)).+
  
 During the subsequent period, CAPRI was increasingly adapted to analyses of greenhouse gas (GHG) emission studies. Examples include CAPRI-ECC, GGELS, ECAMPA-X, AgCLim50-X, (European Commission, Joint Research Centre), ClipByFood (Swedish Energy Board), SUPREMA (H2020). This vein of research is very likely to gain in importance in the future. During the subsequent period, CAPRI was increasingly adapted to analyses of greenhouse gas (GHG) emission studies. Examples include CAPRI-ECC, GGELS, ECAMPA-X, AgCLim50-X, (European Commission, Joint Research Centre), ClipByFood (Swedish Energy Board), SUPREMA (H2020). This vein of research is very likely to gain in importance in the future.
  
 In order to improve land related climate gas modelling within CAPRI, it was deemed appropriate to (1) extend the land use modelled to //all// available land in the EU (i.e. not only agriculture), and (2) to explicitly model //transitions// between land use classes. The pioneering work was carried out within the TRUSTEE project((https://www.trustee-project.eu/ In order to improve land related climate gas modelling within CAPRI, it was deemed appropriate to (1) extend the land use modelled to //all// available land in the EU (i.e. not only agriculture), and (2) to explicitly model //transitions// between land use classes. The pioneering work was carried out within the TRUSTEE project((https://www.trustee-project.eu/
-)), but as always, an operational version emerged only after integrating efforts by researchers in several projects working at various institutions.+)), but as always, an operational version emerged only after integrating efforts by researchers in several projects working at various institutions. Within the SUPREMA project another important change in the depiction of land use change was made: the Markov chain approach was replaced by prespecifying the total land transitions as average transitions per year times the projection. This paper focusses on the theory applied while data and technical implementation are only briefly covered.
  
-This paper focusses on the theory applied while data and technical implementation are only briefly covered. 
  
-**A simple theory of land supply**+===== A simple theory of land supply =====
  
 Recall the dual methodological changes attempted in this paper: Recall the dual methodological changes attempted in this paper:
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 The model is somewhat complicated by the fact that land use classes in CAPRI are defined somewhat differently compared to the UNFCCC accounting and also in the land transition data set. Therefore, some of the land classes used in the land transitions are different from the ones used in the land supply model. In particular, “Other land”, “Wetlands” and “Pasture” are differently defined. To reconcile the differences, we assumed constant shares of the intersections of the different sets, as explained below. The model is somewhat complicated by the fact that land use classes in CAPRI are defined somewhat differently compared to the UNFCCC accounting and also in the land transition data set. Therefore, some of the land classes used in the land transitions are different from the ones used in the land supply model. In particular, “Other land”, “Wetlands” and “Pasture” are differently defined. To reconcile the differences, we assumed constant shares of the intersections of the different sets, as explained below.
  
-**Inner model – land transitions**+===== Inner model – transitions =====
  
 A vector of supply of land of various types could result from a wide range of different transitions. The inner model determines the matrix of land transitions that is “most likely”. The concept of “most likely” is formalized by assuming a joint density function for the land transitions, based on the historically observed transitions. The model then is to find the transition matrix that maximizes the joint density function. A vector of supply of land of various types could result from a wide range of different transitions. The inner model determines the matrix of land transitions that is “most likely”. The concept of “most likely” is formalized by assuming a joint density function for the land transitions, based on the historically observed transitions. The model then is to find the transition matrix that maximizes the joint density function.
 +
 +==== Gamma density ====
  
 Since each transition is non-negative, but in principle unlimited upwards, we opted for a gamma density function, that has the support $\lbrack 0,\infty\rbrack$. For those that cannot immediately recall what the gamma density function looks like, and as entertainment for those that can, Figure 1 shows the graph of the density function for different parameters, all derived from an assumed mode of “1” and different assumed ratios “mode/standard deviations” (that we called “acc” for “accuracy” in the figure). Since each transition is non-negative, but in principle unlimited upwards, we opted for a gamma density function, that has the support $\lbrack 0,\infty\rbrack$. For those that cannot immediately recall what the gamma density function looks like, and as entertainment for those that can, Figure 1 shows the graph of the density function for different parameters, all derived from an assumed mode of “1” and different assumed ratios “mode/standard deviations” (that we called “acc” for “accuracy” in the figure).
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 $$\text{variance} = \frac{\alpha}{\beta^{2}}$$ $$\text{variance} = \frac{\alpha}{\beta^{2}}$$
  
-**Land use transitions as implemented in CAPRI**+==== Annual transitions via Marcov chain in basic model ====
  
 The implementation in CAPRI differs from the above general framework in that it explicitly identifies the //annual// transitions in year t $T_{\text{lk}}^{t}$ from the initial $\text{LU}_{l}^{\text{initial}}$ land use to the final land use $\text{LU}_{k}$. This is necessary to identify the annual carbon effects occurring only in the final year in order to add them to the current GHG emissions, say from mineral fertiliser application in the final simulation year. If the initial year is the base year = 2008 and projection is for 2030, then the carbon effects related to the change from the 2008 $\text{LU}_{l}^{\text{initial}}$ to the final land use $\text{LU}_{k}$ (=$T_{\text{lk}}$in the above notation, without time index) refer to a period of 22 years that cannot reasonably be aggregated with the “running” non-CO2 effects from the final year 2030. Furthermore the historical time series used to determine the mode of the gamma density for the transitions also refer to annual transitions. The implementation in CAPRI differs from the above general framework in that it explicitly identifies the //annual// transitions in year t $T_{\text{lk}}^{t}$ from the initial $\text{LU}_{l}^{\text{initial}}$ land use to the final land use $\text{LU}_{k}$. This is necessary to identify the annual carbon effects occurring only in the final year in order to add them to the current GHG emissions, say from mineral fertiliser application in the final simulation year. If the initial year is the base year = 2008 and projection is for 2030, then the carbon effects related to the change from the 2008 $\text{LU}_{l}^{\text{initial}}$ to the final land use $\text{LU}_{k}$ (=$T_{\text{lk}}$in the above notation, without time index) refer to a period of 22 years that cannot reasonably be aggregated with the “running” non-CO2 effects from the final year 2030. Furthermore the historical time series used to determine the mode of the gamma density for the transitions also refer to annual transitions.
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 $$\Leftrightarrow 1 = \sum_{k}^{}P_{\text{lk}}$$ $$\Leftrightarrow 1 = \sum_{k}^{}P_{\text{lk}}$$
  
-So the simple condition is that probabilities have to add up to one (e_addUpTransMatrix in supply_model.gms). In this form the model is currently implemented in CAPRI.+So the simple condition is that probabilities have to add up to one (e_addUpTransMatrix in supply_model.gms). 
  
-**Outer model – land supply**+==== Annual transitions if SUPREMA is active ====
  
 +As the use of the Marcov-chain approach allows the annual transitions to be explicit model variables that could be used to compute annual carbon effects but leads to computational limitations especially in the market model a new approach was developed under SUPREMA (i.e. if %supremaSup% == on) by re-specifying the total land transitions as average transitions per year times the projection horizon and by considering for the remaining class without land use change (on the diagonal of the land transition matrix) only the annual carbon effects per ha, relevant for the case of gains via forest management.
 +
 +The new accounting in the CAPRI global supply model may be explained as follows, starting from a calculation of the total GHG effects G over horizon h = t-s from total land transitions L<sub>lk</sub> and carbon effects per ha for the whole period e<sub>lk</sub>:
 +
 +$$G = Γ*h = \sum_{i,l}^{}{e_{\text{il}}^{}\text{L}}_{il}^{}$$
 +
 +Where Γ collects the annual GHG effects that correspond to the total GHG effects divided by the time horizon G / h. These annual effects may be calculated as based on average annual transitions and annual effects for the remaining class as follows:
 +
 +$$Γ= \sum_{i,l}^{}{e_{\text{il}}^{}\text{L}}_{il}^{}/h = \sum_{i≠l}^{}{e_{\text{il}}^{}\text{Λ}}_{il}^{}
 ++ \sum_{i}^{}{ε_{\text{ii}}^{}\text{L}}_{ii}^{} $$
 +
 +Where Λ<sub>il</sub> = L<sub>il</sub> / h is the average land use change per year and ε<sub>ii</sub> is the annual carbon effect on a remaining class (relevant might be an annual increase due to growing forests while this will be zero for most effects based on IPCC default assumptions).
 +
 +Using these average annual transitions for true (off-diagonal) LUC we may compute the final classes as follows:
 +
 +$$ = \sum_{i,l}^{}{e_{\text{il}}^{}\text{L}}_{il}^{}/h$$
 +
 +While adding up of shares (or probabilities) of LUC from class I to k over all receiving classes k continues to hold as stated above. It should be highlighted that the land use accounting implemented under SUPREMA avoids the need to explicitly trace the annual transitions in the form of a Markov chain and thereby economised on equations and variables.
 +
 +
 +
 +===== Outer model – land supply =====
 The outer problem is defined as a maximization of the sum of land rents minus a quadratic cost term, subject to the first order optimality conditions of the inner problem: The outer problem is defined as a maximization of the sum of land rents minus a quadratic cost term, subject to the first order optimality conditions of the inner problem:
  
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 The key equations corresponding to the approach explained above are collected in file supply_model.gms or the included files supply/declare_calibration_models_for_luc.gms and supply/declare_calibration_models_for_land_supply.gms. The declarations of parameters, variables, equations, models and even some sets only used in the calibration given in these files are included by the “supply_model.gms” only if “BASELINE==ON” or if it was a CAPREG base year task that was carried out. Loading of priors, initialisation of parameters and variables for the calibration as well as the organisation of solve attempts are handled in new sections of file “cal_land_nests.gms”, in turn called by the gams file “prep_cal.gms”. This implies that the land supply and land use change calibrations were inserted before the ordinary calibration of the supply models. The key equations corresponding to the approach explained above are collected in file supply_model.gms or the included files supply/declare_calibration_models_for_luc.gms and supply/declare_calibration_models_for_land_supply.gms. The declarations of parameters, variables, equations, models and even some sets only used in the calibration given in these files are included by the “supply_model.gms” only if “BASELINE==ON” or if it was a CAPREG base year task that was carried out. Loading of priors, initialisation of parameters and variables for the calibration as well as the organisation of solve attempts are handled in new sections of file “cal_land_nests.gms”, in turn called by the gams file “prep_cal.gms”. This implies that the land supply and land use change calibrations were inserted before the ordinary calibration of the supply models.
  
-The new land supply specification is only activated if the global variable %trustee_land%==on which may be set via the CAPRI GUI. In order to store the results of the calibration in a compact way that is compatible with the existing code, the existing parameter files “pmppar_XX.gdx” was used. The parameters of the land supply functions, called “c” and “D” above, were stored on two parameters “p_pmpCnstLandTypes” and “p_pmpQuadLandTypes”. As a new symbol (p_pmpCnstLandTypes) is introduced in an existing file, the first run of CAPRI after setting %trustee_land%==on may give errors if the file exists already but has been used with the previous land supply specification before. In this case it helps to delete or rename the old pmppar files.+//SupremaSup// should be active together with //trustee_land// to have smoother adjustments which may be set via the CAPRI GUI. In order to store the results of the calibration in a compact way that is compatible with the existing code, the existing parameter files “pmppar_XX.gdx” was used. The parameters of the land supply functions, called “c” and “D” above, were stored on two parameters “p_pmpCnstLandTypes” and “p_pmpQuadLandTypes”. As a new symbol (p_pmpCnstLandTypes) is introduced in an existing file, the first run of CAPRI after setting %trustee_land%==on may give errors if the file exists already but has been used with the previous land supply specification before. In this case it helps to delete or rename the old pmppar files.
  
 At this point, it should also be explained that rents for non-agricultural land types were entirely based on assumptions (a certain ratio to agricultural rents). As there were no plans to run scenarios with modified non-agricultural rents, these land rents //r// used in calibration for those land types were subtracted from the “c-paramter”, so that it is implicitly stored in p_pmpCnstLandTypes and enters the objective function through the PMP terms. This requires changes if the rents shall be modified or if non-agricultural production shall be included in some simplified form. At this point, it should also be explained that rents for non-agricultural land types were entirely based on assumptions (a certain ratio to agricultural rents). As there were no plans to run scenarios with modified non-agricultural rents, these land rents //r// used in calibration for those land types were subtracted from the “c-paramter”, so that it is implicitly stored in p_pmpCnstLandTypes and enters the objective function through the PMP terms. This requires changes if the rents shall be modified or if non-agricultural production shall be included in some simplified form.
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 More detailed explanations on the technical implementation are covered elsewhere, for example in the “Training material” included in the EcAMPA-4 deliverable D5. More detailed explanations on the technical implementation are covered elsewhere, for example in the “Training material” included in the EcAMPA-4 deliverable D5.
 +
 +Concerning the improvements made under SUPREMA from a technical perspective, the changes are merged to the trunk. The approach is controlled by globals in capmod\set_global_variables.gms. If the global variable %supremaSup% == on, the yearly transition rate p_lucAnnualFac_sup is calculated. If it is %supremaSup% == off, the old approach using the Marcov chain is used with the respective variable v_luYearly. The FOC-approach to calculate LUC as described above is standard and independent from if the global variable supremaSup is on or off.
 +
 +===== Emission Equations =====
 +
 +Under EcAMPA 3 and partly in earlier projects (inter alia EcAMPA 2) new modelling outputs have been developed for indicators without matching reporting infrastructure helping users to organise the additional information. This applied for example to
 +
 +1) Additional CAPRI results on land use results related to the complete area coverage, mappings to UNFCCC area categories and their transitions;
 +
 +2) The carbon effects linked to these land transitions.
 +
 +Furthermore, additional non-CO2 and CO2 related mitigation measures had been included under EcAMPA 3.
 +
 +The scenarios including the emission equations are only run if %ghgabatement% == on, otherwise emissions are only calculated and not simulated.
 +
 +The following emission equations have been implemented:
 +
 +^**Code**          ^**Description**                                                                                                ^
 +|GWPA              |Agricultural emissions                                                                                         |
 +|CH4ENT            |Methane emissions from enteric fermentation                                                                    |
 +|CH4MAN            |Methane emissions from manure management                                                                       |
 +|CH4RIC            |Methane emissions from rice production                                                                         |
 +|N2OMAN            |Direct nitrous oxide emissions stemming from manure management (only housing and storage)                      |
 +|N2OAPP            |Direct nitrous oxide emissions stemming from manure application on soils except grazings per animal activity   |
 +|N2OGRA            |Direct nitrous oxide emissions stemming from manure managment on grazings                                      |
 +|N2OSYN            |Direct nitrous oxide emissions from anorganic fertilizer application                                           |
 +|N2OCRO            |Direct nitrous oxide emissions from crop residues                                                              |
 +|N2OAMM            |Indirect nitrous oxide emissions from ammonia volatilisation                                                   |
 +|N2OLEA            |Indirect nitrous oxide emissions from leaching                                                                 |
 +|N2OHIS            |Direct nitrous oxide emissions from cultivation of histosols                                                   |
 +|GLUC              |Emissions related to indirect land use changes                                                                 |
 +|CO2BIO            |Carbon dioxide emissions from land use change due to losses of carbon in biomass and litter                    |
 +|CO2SOI            |Carbon dioxide emissions from land use change due to soil carbon losses                                        |
 +|CO2HIS\\ \\ CH4HIS|Carbon dioxide emissions from the cultivation of histosols\\ \\ Methane emissions from cultivation of histosols|
 +|CO2LIM\\ \\ CO2BUR|Carbon dioxide emissions from limestone and dolomit\\ \\ Carbon dioxide emissions from burning                 |
 +|CH4BUR            |Methane emissions from burning                                                                                 |
 +|N2OBUR            |Nitrous oxide emissions from burning                                                                           |
 +|N2OSOI            |N2O emissions from land use change due to soil carbon losses                                                   |
 +|GPRD              |Emissions related to the production of non-agricultural inputs to agriculture                                  |
 +|N2OPRD            |Nitrous oxide emissions during fertilizer production                                                           |
 +|O2PRD             |Carbon Dioxide emissions during fertilizer production                                                          |
  
 =====Premium module===== =====Premium module=====
scenario_simulation.txt · Last modified: 2023/09/08 12:07 by massfeller
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