## 3 Methodology  
### Postprocessing Methods  
A generator-based method, the GPP, and a distribution-based method, the BMA, which have been widely used and proven to be beneficial [9; 23; 32], were used to postprocess  
\begin{table}
\begin{tabular}{l c c c c c} \hline \hline \multirow{2}{*}{**Center**} & \multirow{2}{*}{**Country/Region**} & \multirow{2}{*}{**Ensemble Members**} & **Base** & **Spatial** & **Forecast** \\  & & **(Perturbed)** & **Time** & **Resolution** & **Length** \\ \hline ECMWF & Europe & 50 & 00 UTC & 0.5\({}^{\circ}\)\(\times\) 0.5\({}^{\circ}\) & 360 h at 6 h \\ NCEP & America & 20 & 00 UTC & 0.5\({}^{\circ}\)\(\times\) 0.5\({}^{\circ}\) & 384 h at 6 h \\ \hline \hline \end{tabular}
\end{table}
Table 1: The ensemble precipitation forecasts.  
Figure 1: The study area.  
ensemble precipitation forecasts in this study. The parametric probability distribution function (PDF) denoted by g for the precipitation is as follows [32]:  
\[y|x_{1},\dots,x_{M}\sim g(y|x_{1},\dots,x_{k}) \tag{1}\]  
where \(y\) and \(x_{1}\),..., \(x_{k}\) represent the variable of precipitation and the ensemble precipitation forecasts with K members, respectively. The PDF of precipitation is characterized by a mixed discrete/continuous distribution: a positive probability of being exactly zero, and a continuous skewed distribution for positive precipitation amounts. A mixed distribution model for precipitation proposed by [PERSON], [PERSON] [33] is as follows:  
\[g(y|f_{k})=P(y=0|f_{k})\cdot I(y=0)+P(y>0|f_{k})\cdot g_{k}(y|f_{k})\cdot I(y>0) \tag{2}\]  
where given the member forecast \(f_{k}g(y|f_{k})\) represents the probability distribution, and \(I(\dots)\) represents unity if the condition in brackets holds, and zero otherwise; \(P(y=0|f_{k})\) and \(g(y>0|f_{k})\) represent the probabilities of non-precipitation and precipitation above zero, respectively. \(g_{k}(y|f_{k})\) represents a two-parameter gamma distribution. Different postprocessing methods differ in the ways of calibrating the PDF for precipitation and generating the postprocessed ensemble precipitation forecasts.  
For GPP [19], the PDF of the precipitation in different seasons or magnitudes is calibrated independently to fit the observations. Then, the postprocessed EFFs are accordingly resampled from the calibrated PDF based on the forecast information within raw EFFs. For BMA [17], the PDF of the precipitation at different days or periods is calibrated to fit the ensemble forecasts according to a historical training set, including both EFFs and observations, as follows:  
\[P(y|f_{1},\dots,f_{k})=\frac{1}{K_{\sigma}}\sum_{k=1}^{K}N(\frac{y-z_{k}}{ \sigma}) \tag{3}\]  
where \(N(\dots)\) represents the normal distribution with the mean \(z_{k}\) and difference \(\sigma\) of the ensemble forecasts.  
In this study, given the 4-year (2014-2017) available EPFs and observations, the postprocessing was conducted by using the cross-validation method. Specifically, when generating forecasts for a particular year, the remaining 3-year forecasts were used as the training data to calibrate the postprocessing method. The ensemble size of the postprocessed EFFs was set to 1000 to better represent the calibrated PDF. The postprocessing was conducted by using the MATLAB software.