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--- disaggregation_of_nitrogen_input [2020/03/29 08:59] – [Crop response curve] matsz
+++ disaggregation_of_nitrogen_input [2020/04/10 09:07] – [Data preparation] matsz
@@ Line 74: / Line 74: @@
 \begin{align}
 \begin{split}
-&\text{Crop growth model (Godard et al., 2008) without ‘minimum yield’} \\
+y_{h,c}^{mx} = y_{man,r,c}^{mx}+y_{man,h,c} \cdot (y_{min,r,c}^{mx}-y_{man,r,c}^{mx}) \\
-&Y_{r,c} = Y_{r,c}^{mx}-(1 - exp\{-f^{cropcurve}\cdot Q_{r,c}\}) \cdot @ Y_{r,c}^{mn} = 0
+χ_{man,h,c} = \frac {q_{man,h,c}} {q_{man,h,c}+ q_{min,h,c}}
 \end{split}
 \end{align}
+\(y_{h,c}^{mx}\)	= Maximum yield [variable, kg N ha<sup>-1</sup> yr<sup>-1</sup>] according to the crop response curve (Godard et al., 2008) for crop //c// in the spatial unit //h//. \\
+\(y_{man,r,c}^{mx}\)	= Maximum yield for manure [parameter, kg N ha<sup>-1</sup> yr<sup>-1</sup>] according to the crop response curve (Godard et al., 2008) for crop //c// in spatial unit //h//. \\
+\(y_{min,r,c}^{mx}\) =	Maximum yield for mineral fertilizer [parameter, kg N ha<sup>-1</sup> yr<sup>-1</sup>] according to the crop response curve (Godard et al., 2008) for crop //c// in spatial unit //h//. \\
+\(χ_{man,h,c}\)	= Share of manure [variable, dimensionless] in the application of nitrogen from manure and mineral fertilizer.
+===Manure availability===
+Manure can be traded between individual spatial units. Manure trade between regions (or even countries) is covered by the regional model of CAPRI and does not need to be considered here.
+The availability of manure is obtained therefore from each spatial unit plus neighboring spatial units within the same region. The range of spatial units from which manure can be used is assumed to a region-specific variable and
+\begin{align}
+\begin{split}
+\sum_{c} \{ q_{man,h,c}\cdot a_{h,c} \} & \le \sum_{h^\prime,l} \{ e_{man,h,l}\cdot n_{h,l} \} \\
+d_{h,h^\prime} & \le D_r^{mx}
+\end{split}
+\end{align}
+\(q_{man,h,c}\)	= Manure application rate [variable, kg N/ha] to crop //c// in spatial unit //h// \\
+\(a_{h,c}\)	= Area [parameter, 1000 ha] cultivated with crop //c// \\
+\(e_{man,h,l}\)	= Manure excretion [parameter, kg N/head] by animal species //l// in spatial unit //h//– net of losses in livestock housing and manure storage and management systems. No heterogeneity is assumed for nitrogen excretion rate within one NUTS2 region. \\
+\(n_{h,l}\)	= Livestock number [parameter, 1000 heads] \\
+\(d_{h,h^\prime}\)	= Distance [parameter, km] between spatial unit //h// and spatial unit //h<sup>´</sup>// \\
+\(D_r^{mx}\)	= Maximum distance [variable, km] for which transport of manure is allowed in region //r//. \\
+Obviously, the total manure available for application must be exhausted:
+\begin{equation}
+\sum_{h,c}\{q_{man,h,c}\cdot a_{h,c}\} = \sum_l \{ E_{man,r,l}\cdot N_{h,l} \}
+\end{equation}
+====Fertilization distribution model====
+===Recover regional N flows===
+For each flow of nitrogen and crop, the sum of flows over all spatial units must recover the total flow at regional level for each crop.
+This holds both for input flows and output flows (i.e. harvest, surplus).
+===Potential yield===
+The maximum (potential) yield is proportional to the relative potential yield (without water limitation).
+\begin{equation}
+y_{h,c}^{mx} = F_{r,c}^{ymx}\cdot r_{h,c}^{py}
+\end{equation}
+\(y_{h,c}^{mx}\) =	Maximum yield [variable, kg/ha] determining the shape of the crop growth curve in each spatial unit for each crop. \\
+\(r_{h,c}^{py}\) =	Relative potential yield [parameter, dimensionless] of crop //c// in spatial unit //h//.  \\
+\(F_{r,c}^{ymx}\) =	Scaling factor [variable, kg/ha] adjusting the relative potential yield so that it gives the maximum yield in the crop growth curve for each spatial unit //h// and crop //c//.  \\
+===Crop growth curve===
+Total input of nitrogen is obtained from the observed yield for the crop in the spatial unit (parameter, calculated in the yield and irrigation module) and the maximum yield obtainable in the crop in the spatial unit (variable).
+\begin{equation}
+q_{h,c} = -\frac{1}{x}\cdot ln \left\{ \frac{y_{h,c}}{y_{h,c}^{mx}} \right\}
+\end{equation}
+===Nitrogen source===
+Once the total N input per crop and spatial unit is determined, the individual N sources need to be calculated. We have:
+  * Biological N fixation: this is directly calculated from the crop type and yield and is ‘fixed’
+  * Atmospheric deposition: this is obtained from external data and cannot be modified
+  * Mineralization of soil organic matter. We have no data yet for calculating mineralization of soil organic matter at the regional level, thus it is not possible to include this term in the disaggregation. If there were data on soil organic mineralization, the following assumptions would need be taken:
+    * Mineralization of soil organic matter occurs in extensive fields, thus at low application rates of mineral fertilizer and irrigation rates
+    * Manure is able to replenish soil organic matter. It is thus unlikely that mineralization of soil organic matter occurs where manure is applied or deposited by grazing animals.
+====Data preparation====
+===Collecting information===
+At Nuts2 level, //y// and //f// are known and y<sub>m</sub> can be calculated
+\begin{equation}
+y_{r,c}^{mx} = \frac{y_{r,c}}{1-exp\{-f^{cropcurve}\cdot Q_{r,c}\}}
+\end{equation}
+For each spatial unit, the yield is given from the distribution of irrigation shares and yield.
+We can assume that the potential yield y<sub>m</sub> follows the pattern of the irrigated yield obtained from PESETA.
+\begin{equation}
+y_{h,c}^{mx} \propto r_{h,c}^{py}
+\end{equation}
+\(r_{h,c}^{py}\) =	Relative potential yield [parameter, dimensionless] of crop //c// in spatial unit //h//.
+=== Calculation of relative potential yield per spatial unit ===
+\begin{equation}
+r_{h,p}^{py} = y_{h,p}^{py}/\overline{y_{h,p}^{py}}
+\end{equation}
+\(r_{h,c}^{py}\)	FIXME= Relative potential yield [parameter, dimensionless] of crop //c// in spatial unit //h//. \\
+\(\overline{y_{h,p}^{py}}\) = Average potential yield [parameter, kg/ha] of crop //c// in region //r//.
+\begin{equation}
+\overline{y_{h,c}^{py}} = \frac{\sum_h\{y_{h,c}^{py}\cdot a_{h,c}\}}{\sum_h\{a_{h,c}\}}
+\end{equation}
+===Calculation of distances between HSUs===
+Update pending
+===Calculation of manure availability===
+Excretion net of all volatilization must be back-calculated so that emissions from applications are not subtracted.
+Update pending
+===Consideration of mitigation options===
+Update pending