Differences

This shows you the differences between two versions of the page.

--- disaggregation_of_nitrogen_input [2020/03/29 08:26] – created matsz
+++ disaggregation_of_nitrogen_input [2020/03/29 08:59] – [Crop response curve] matsz
@@ Line 17: / Line 17: @@
 ====Crop response curve====
+Different crop response curves are proposed (Bodirsky and Müller, 2014; Godard et al., 2008). We base our response curve on the proposal of (Godard et al., 2008) in particular for the ‘saturation’ velocity((  The model proposed by Bodirsky and Mueller (2014) ‘saturates’ only at very high N input levels > 1000 kg N ha<sup>-1</sup> yr<sup>-1</sup> )).
+\begin{align}
+\begin{split}
+&\text{Crop growth model (Godard et al., 2008)} \\
+&Y_{r,c} = Y_{r,c}^{mx}-(Y_{r,c}^{mx}-Y_{r,c}^{mn}) \cdot exp\{-f^{cropcurve}\cdot Q_{r,c}\}
+\end{split}
+\end{align}
+\begin{align}
+\begin{split}
+&\text{Crop growth model (Godard et al., 2008) without ‘minimum yield’} \\
+&Y_{r,c} = Y_{r,c}^{mx}-(1 - exp\{-f^{cropcurve}\cdot Q_{r,c}\}) \cdot @ Y_{r,c}^{mn} = 0
+\end{split}
+\end{align}
+\(Y_{r,c}\)	= Yield [parameter, kg N ha<sup>-1</sup> yr<sup>-1</sup>] for crop __c__ in region //r//. \\
+\(Y_{r,c}^{mx}\)	= Maximum yield [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 region //r//. \\
+\(Y_{r,c}^{mn}\)	= Minimum yield [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 region //r//. This parameter is set to zero in our model. \\
+\(f^{cropcurve}\)	= Scaling factor [parameter, dimensionless] used in the crop response curve (Godard et al., 2008). We use a uniform value of \(f^{cropcurve}=0.008\). \\
+\(Q_{r,c}\)	= Total N input [parameter, kg N ha<sup>-1</sup> yr<sup>-1</sup>] for region r and crop c.
+====Crop growth scaling factor====
+We use a constant factor \(f^{cropcurve}\) for all regions/spatial units and crops in order to not leave too many degrees of freedom. However, if infeasibilities occur, ‘opening’ this factor to differ between crop types could be a first test. However, the range of possible values for the crop growth scaling factor is narrow:
+  * For \(f^{cropcurve}>0.010\) a N uptake is larger than N input until an application rate of more than 100 kg N ha<sup>-1</sup> yr<sup>-1</sup>. For a value of 0.010 this is the case for an application rate of about 100 kg N ha<sup>-1</sup> yr<sup>-1</sup>
+  * For \(f^{cropcurve}<0.008\) the N input rate at which a yield of 80% of the maximum yield is attained is very high. For a value of 0.0064 this happens at Q=250 kg N ha<sup>-1</sup> yr<sup>-1</sup>; and for a value of 0.0054 at Q=300 kg N ha<sup>-1</sup> yr<sup>-1</sup>.
+Therefore, only a narrow range around a value of 0.008 seems plausible.
+**Figure 44: Crop growth curves according to Godard et al. (2008) for different crop growth scaling factors.**
+{{::figure_44.png?600|}} \\ Parameters from light blue to dark blue curves: \(0.004\le f^{cropcurve}\le 0.020\). The curves with \(f^{cropcurve} \in {0.006,0.008,0.010} \) are plotted in bold. Other parameter: Y<sup>mx</sup>=150; Y<sup>mn</sup>=0.
+**Figure 45: N input rates that give a yield of 80% of the maximum yield for different crop growth scaling factors according to Godard et al. (2008)**
+{{:figure_45.png?600|}}
+**Lower efficiency for manure application**
+We assume that manure is applied with less efficiency than mineral fertilizer. First, because we take into account lower nutrient availability in manure with respect to mineral fertilizer (due to reduced opportunity to target release of nutrients to crop demand, thus increasing the chance of nutrient releases in periods with enhanced risks of losses to the environment). Second, due to the fact that higher availability of manure often goes ahead with increased lack of surface where the manure can be applied in a reasonable manner.
+Therefore, we assume a decrease of the NUE the higher the share of manure in the fertilizer mix.
+We account for this fact by using a different crop response curve for mineral fertilizer and manure. This is realized by varying the theoretical crop curve’s maximum yield.
+This is shown in figure below.
+**Figure 46: Examples of crop response curves according to Godard et al. (2008).**
+{{:figure_46.png?600|}} \\ Parameters used: f=0.008. Light blue curve for manure: y<sup>mx</sup>=130; dark blue curve for mineral fertilizer: y<sup>mx</sup>=150.
+We introduce a dependency of y<sup>mx</sup> on the share of mineral fertilizer and manure in the mix of the nitrogen source.
+\begin{align}
+\begin{split}
+&\text{Crop growth model (Godard et al., 2008) without ‘minimum yield’} \\
+&Y_{r,c} = Y_{r,c}^{mx}-(1 - exp\{-f^{cropcurve}\cdot Q_{r,c}\}) \cdot @ Y_{r,c}^{mn} = 0
+\end{split}
+\end{align}