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--- scenario_simulation [2022/01/04 10:27] – [Annex: Land use modelling] himics
+++ scenario_simulation [2022/01/17 09:28] – [Annex: Land supply and land transitions in the supply part of CAPRI] matsz
@@ Line 434: / Line 434: @@
 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).
-[CHART]
+{{:wiki:gamma_dens_land.png?nolink|}}
 Figure 1: Gamma density graph for mode=1 and various standard deviations. “acc”="mode/standard deviation".
@@ Line 446: / Line 446: @@
 subject to
-$$\text{LU}_{k} - \sum_{l}^{}T_{\text{lk}} = 0\text{~~~~~~~~~}\left\lbrack \tau_{k} \right\rbrack$$
+$$\text{LU}_{k} - \sum_{l}^{}T_{\text{lk}} = 0 \; \left\lbrack \tau_{k} \right\rbrack$$
-$$\text{LU}_{l}^{\text{initial}} - \sum_{k}^{}T_{\text{lk}} = 0\text{~~~~~~~~~}\left\lbrack \tau_{l}^{\text{initial}} \right\rbrack$$
+$$\text{LU}_{l}^{\text{initial}} - \sum_{k}^{}T_{\text{lk}} = 0\;\left\lbrack \tau_{l}^{\text{initial}} \right\rbrack$$
 $$\text{LU}_{k} - \sum_{i}^{}{\text{shar}e_{\text{ki}}\text{LEV}L_{i}} = 0$$
@@ Line 480: / Line 480: @@
 When using the transition probabilities in the consistency condition for initial land use we obtain
-$$\text{LU}_{l}^{\text{initial}} - \sum_{k}^{}T_{\text{lk}}^{1} = 0\text{~~~~~~~~}$$
+$$\text{LU}_{l}^{\text{initial}} - \sum_{k}^{}T_{\text{lk}}^{1} = 0$$
-$$\Longleftrightarrow \text{LU}_{l}^{\text{initial}} = \sum_{k}^{}{P_{\text{lk}}^{}\text{LU}}_{l}^{\text{iniital}}\text{~~~~~~~~}$$
+$$\Longleftrightarrow \text{LU}_{l}^{\text{initial}} = \sum_{k}^{}{P_{\text{lk}}^{}\text{LU}}_{l}^{\text{iniital}}$$
 $$\Leftrightarrow 1 = \sum_{k}^{}P_{\text{lk}}$$
@@ Line 498: / Line 498: @@
 $$\text{LU}_{k} - \sum_{i}^{}{\text{shar}e_{\text{ki}}\text{LEV}L_{i}} = 0$$
-$$\text{LU}_{k} - \sum_{l}^{}T_{\text{lk}} = 0\text{~~~~~~~~~}\left\lbrack \tau_{k} \right\rbrack$$
+$$\text{LU}_{k} - \sum_{l}^{}T_{\text{lk}} = 0\;\left\lbrack \tau_{k} \right\rbrack$$
-$$\text{LU}_{l}^{\text{initial}} - \sum_{k}^{}T_{\text{lk}} = 0\text{~~~~~~~~~}\left\lbrack \tau_{l}^{\text{initial}} \right\rbrack$$
+$$\text{LU}_{l}^{\text{initial}} - \sum_{k}^{}T_{\text{lk}} = 0\;\left\lbrack \tau_{l}^{\text{initial}} \right\rbrack$$
 $$\ \left( \alpha_{\text{lk}} - 1 \right)T_{\text{lk}}^{- 1} - \beta_{\text{lk}} + \tau_{k}^{} + \tau_{l}^{\text{initial}} = 0$$
@@ Line 637: / Line 637: @@
 **Technical implementation**
-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.