disaggregation_of_yield_and_irrigation
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disaggregation_of_yield_and_irrigation [2020/03/29 07:21] – created matsz | disaggregation_of_yield_and_irrigation [2022/11/07 10:23] (current) – external edit 127.0.0.1 | ||
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\end{equation} | \end{equation} | ||
- | \(y_{h, | + | \(y_{h, |
- | \(Y_{r, | + | \(Y_{r, |
- | \(s_{r, | + | \(s_{r, |
- | \(r_{h, | + | \(r_{h, |
In practice, the product of the observed regional yield and the scaling factor \(Y_{r,c} \cdot s_{r,c}^Y\) represents the regional average water limited yield that is consistent with observed (or simulated) irrigation shares and regional observed yields. | In practice, the product of the observed regional yield and the scaling factor \(Y_{r,c} \cdot s_{r,c}^Y\) represents the regional average water limited yield that is consistent with observed (or simulated) irrigation shares and regional observed yields. | ||
Line 44: | Line 44: | ||
\end{equation} | \end{equation} | ||
- | \(y_{h,c}, Y_{r,c}\) as defined above \\ | + | \(y_{h,c}, Y_{r, |
- | \(a_{h, | + | \(a_{h, |
- | \(A_{r, | + | \(A_{r, |
===Equation 5 MCACTYIELD_=== | ===Equation 5 MCACTYIELD_=== | ||
Line 54: | Line 54: | ||
\end{equation} | \end{equation} | ||
- | \(y_{h,c}, Y_{r,c}, s_{r, | + | \(y_{h,c}, Y_{r,c}, s_{r, |
- | \(y_{h, | + | \(y_{h, |
In principle, there are endless possibilities to adjust the irrigation shares to satisfy the equations TOTYIELD_ an MCACTYIELD_ so constraints in the irrigation shares itself are required. Those are found in statistical data on the irrigation shares by crop from the Survey on Agricultural Production Methods (SAPM, 2010) and the FAO irrigation map. | In principle, there are endless possibilities to adjust the irrigation shares to satisfy the equations TOTYIELD_ an MCACTYIELD_ so constraints in the irrigation shares itself are required. Those are found in statistical data on the irrigation shares by crop from the Survey on Agricultural Production Methods (SAPM, 2010) and the FAO irrigation map. | ||
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\begin{align} | \begin{align} | ||
\begin{split} | \begin{split} | ||
- | hdp_{irri} \cdot \left( \sum_c A_{r,c} \right)^2 | + | hdp_{irri} \cdot \left( \sum_c A_{r,c} \right)^2 = \left\{ \sum_h \left( \sum_c (a_{h,c}) \cdot \frac{f_h^{irri} -\hat{f_h^{irri}}} {s_{f_h^{irri}}} \right)^2 + \sum_{h,c} \left( A_{r,c} \cdot \frac{r_{r, |
- | & + \sum_{h,c} \left( a_{h,c} \cdot \frac {y_{h, | + | + \sum_{h,c} \left( a_{h,c} \cdot \frac {y_{h, |
\end{split} | \end{split} | ||
\end{align} | \end{align} | ||
+ | |||
+ | \(a_{h,c}, y_{h,c}, Y_{r,c}\) = as defined above \\ | ||
+ | \(f_h^{irri}\) = Irrigation share [variable, dimensionless] over crops in spatial unit //h//. This is calculated as weighted average of irrigation shares of individual crops, using the cultivated area as weights | ||
+ | |||
+ | ===Equation 7 UAARIRRI_=== | ||
+ | |||
+ | \begin{equation} | ||
+ | f_h^{irri} \cdot \sum_c \{a_{h,c} \} =\sum_c \{a_{h,c} \cdot f_{h, | ||
+ | \end{equation} | ||
+ | |||
+ | \(r_{r, | ||
+ | \cdot f_{h, | ||
+ | |||
+ | ===Equation 8 IRRISHARE_=== | ||
+ | |||
+ | \begin{equation} | ||
+ | r_{r, | ||
+ | \end{equation} | ||
+ | |||
+ | \(s_{f_h^{irri}}\), | ||
+ | \(s_{r_{r, | ||
+ | \(s_{y_{h, | ||
+ | |||
+ | The ‘hats’ \(\hat{x} in Equation YIELDHPD_ indicate //prior values// of the variables, determined as explained below. | ||
+ | |||
+ | This completes the set of equations required to set up the model minimizing the objective function under the given constraints: | ||
+ | |||
+ | ===Equation 9 MODEL m_hpdYieldIrri=== | ||
+ | |||
+ | \begin{equation} | ||
+ | m_{hpdYiedIrri} : min [ hdp_{irri} ] cf. TOTYIELD\_ , | ||
+ | \end{equation} | ||
+ | |||
+ | |||
+ | ====Downscaling of other CAPRI regional data==== | ||
+ | |||
+ | No information on time series of irrigation shares and currently no time series of PESETA yields for irrigated and rainfed situation are available. Therefore, we apply the principle of the primacy of stable yield spatial distributions. | ||
+ | |||
+ | Yield data are simply scaled to match the regional average yield in CAPRI. | ||
+ | |||
+ | Before doing so, the data are checked if any crop is grown in a region where it is not available in the prior data set. | ||
+ | |||
+ | ====Data sets==== | ||
+ | |||
+ | Update pending | ||
+ | |||
+ | SAPM 2010 – Irrigation shares by crop and region \\ | ||
+ | FAO irrigation map \\ | ||
+ | PESETA water limited and potential yields | ||
+ | |||
+ | ====Data preparation (disyield.gms)==== | ||
+ | |||
+ | ===Consistency between SAPM (2010) and FAO irrigation map=== | ||
+ | |||
+ | Irrigation shares from SAPM (2010) are obtained from farmers’ surveys, while the FAO irrigation map is obtained from remote sensing data. We consider therefore the data from SAPM (2010) more reliable and scale FAO data, so that the average irrigation share of all crops and spatial units in a region matches the data from SAPM (2010) to obtain the priors for the irrigation share per spatial unit: | ||
+ | |||
+ | \begin{equation} | ||
+ | f_r^{irri, | ||
+ | \end{equation} | ||
+ | |||
+ | \begin{equation} | ||
+ | f_r^{irri, | ||
+ | \end{equation} | ||
+ | |||
+ | \begin{equation} | ||
+ | \hat{f_h^{irri}}= f_h^{irri, | ||
+ | \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, | ||
+ | \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, | ||
+ | \end{equation} | ||
+ | |||
+ | \(y_{g, | ||
+ | \(y_{g, | ||
+ | \(y_{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, | ||
+ | \(f_{h, | ||
+ | |||
+ | (iv) Calculation of relative water limited yield per spatial unit | ||
+ | |||
+ | \begin{equation} | ||
+ | r_{h, | ||
+ | \end{equation} | ||
+ | |||
+ | \(r_{h, | ||
+ | \(y_{h, | ||
+ | \(\overline{y_{h, | ||
+ | |||
+ | 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(*, | ||
+ |
disaggregation_of_yield_and_irrigation.1585466470.txt.gz · Last modified: 2022/11/07 10:23 (external edit)