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--- disaggregation_of_yield_and_irrigation [2020/03/29 07:54] – [Downscaling of other CAPRI regional data] matsz
+++ disaggregation_of_yield_and_irrigation [2020/03/29 08:22] – [Data preparation (disyield.gms)] matsz
@@ Line 126: / Line 126: @@
 \begin{equation}
+f_r^{irri,FAO}=\frac{\sum_h \left( \sum_c [a_{h,c}] \cdot f_h^{irri,FAO}\right)} {\sum_{h,c} [a_{h,c}] }
+\end{equation}
+\begin{equation}
+f_r^{irri,SAPM}=\sum_c \frac{ \left[ A_{r,c} \cdot f_{r,c}^{irri,SAPM} \right] } {\sum_{c} [A_{r,c}] }
 \end{equation}
+\begin{equation}
+\hat{f_h^{irri}}= f_h^{irri,FAO} \cdot \frac{f_r^{irri,SAPM} } {f_r^{irri,FAO}}
 \end{equation}
+===Calculation of relative irrigation shares===
+Priors for the relative irrigation shares per crop are obtained from the weighted average of crop-specific irrigation shares
+\begin{equation}
+\hat{r_{r,c}^{irri}}= \frac{f_{r,c}^{irri,SAPM} } {\sum_{c^\prime} \left[A_{c^\prime} \cdot f_{r,c^\prime}^{irri,SAPM}\right] / \sum_{c^\prime} \left[A_{c^\prime} \right] }
+\end{equation}
+===Relative water limited yields and relative potential to water limited yields===
+The calculation of relative yields is done with various steps:
+(i) Ensuring complete data set covering all PESETA grids in the region and all PESETA crops by filling eventual data ‘gaps’ with the average water limited and potential yield for all PESETA crops available in the region
+(ii) Calculation of the relative potential – to – water limited yield
+\begin{equation}
+y_{g,p}^{reply}= \frac{y_{g,p}^{py}} {y_{g,p}^{wly}}
+\end{equation}
+\(y_{g,p}^{relpy}\)	= Relative yield increase [parameter, dimensionless] for PESETA crop //p// in PESETA grid //g//  if removing water limitation by full irrigation as from PESETA simulations. \\
+\(y_{g,p}^{py}\)	= Potential yield [parameter, kg/ha] for PESETA crop //p// in PESETA grid //g//  \\
+\(y_{g,p}^{wy}\)	= Water limited yield [parameter, kg/ha] for PESETA crop //p// in PESETA grid //g//
+(iii) Mapping from PESETA grids to spatial units.
+\begin{equation}
+y_{h,p,y}= \sum_g \{ f_{h,g} \cdot y_{g,p,y} \} \sum_g \{ f_{h,g} \}
+\end{equation}
+\(y_{h,p,y}\)	= Yields simulated with PESETA [parameter, kg/ha] on PESETA grid //g// and for PESETA crop //p// under water limited and potential conditions \(y \in \{wyl,relpy\}\). \\
+\(f_{h,g}\)	= Fraction of spatial unit //h// in PESETA grid //g// [parameter, dimensionless]. The sum of \(f_{h,g}\) = over all spatial units //h// gives 1 unless a few occasions where spatial inaccuracies leave small shares of a spatial unit outside the land area covered by the PESETA grid.
+(iv) Calculation of relative water limited yield per spatial unit
+\begin{equation}
+r_{h,p}^{wly}= y_{h,p}^{wly} / \overline{y_{h,p}^{wly}}
+\end{equation}
+\(r_{h,c}^{wly}\) =	Relative water limited yield [parameter, dimensionless] of PESETA crop //p// in spatial unit //h//. \\
+\(y_{h,p}^{wly}\) =	Water limited yield [parameter, kg/ha] of PESETA crop //p// in spatial unit //h// \\
+\(\overline{y_{h,p}^{wly}}\)	 =Averge water limited yield [parameter, kg/ha] of PESETA crop //p// over all spatial units //h// in region //r//
+If the water limited yield for a PESETA crop is missing for a spatial unit, but available in other spatial units in the same region, the area-weighted water limited yield for the PESETA crop over the region is assigned to the spatial unit.
+(v) Mapping from PESETA crop //p// to CAPRI crop //c//
+In a final step, PESETA crops are mapped to CAPRI crops.
+Data for CAPRI crops without corresponding PESETA crop are assigned the values of the crop which is assumed to be most similar as defined in the set mmarsyieldgroups(*,*)