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--- scenario_simulation [2022/01/04 10:27] – [Annex: Land use modelling] himics
+++ scenario_simulation [2022/01/04 10:48] – [Annex: Land supply and land transitions in the supply part of CAPRI] himics
@@ 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: @@
 $$\text{LU}_{k} - \sum_{i}^{}{\text{shar}e_{\text{ki}}\text{LEV}L_{i}} = 0$$
-$$\text{LU}_{k} - \sum_{l}^{}T_{\text{lk}} = 0\text{~~~~~~~~~}\left\lbrack \tau_{k} \right\rbrack$$
+$$\text{LU}_{k} - \sum_{l}^{}T_{\text{lk}} = 0\;\left\lbrack \tau_{k} \right\rbrack$$
-$$\text{LU}_{l}^{\text{initial}} - \sum_{k}^{}T_{\text{lk}} = 0\text{~~~~~~~~~}\left\lbrack \tau_{l}^{\text{initial}} \right\rbrack$$
+$$\text{LU}_{l}^{\text{initial}} - \sum_{k}^{}T_{\text{lk}} = 0\;\left\lbrack \tau_{l}^{\text{initial}} \right\rbrack$$
 $$\ \left( \alpha_{\text{lk}} - 1 \right)T_{\text{lk}}^{- 1} - \beta_{\text{lk}} + \tau_{k}^{} + \tau_{l}^{\text{initial}} = 0$$