*2.2. Statistical Methods Applied for Comparison*

In this study, the root mean square error (RMSE) for the comparison between the SPPs and the CWB data is calculated based on Equation (1):

$$\text{RMSE} = \sqrt{\sum \text{(SPPs} - \text{CWB data})^2 / (N - 1)},\tag{1}$$

where *N* is the sample size [35]. The temporal correlation (Tcorr) [35] and the spatial correlation (Scorr) [35] between the SPPs and the CWB data are also calculated to evaluate the performance of SPPs.

Additionally, following the procedures in earlier literature [36–39], the frequently used threat score (TS) and bias score (BS) are adopted for quantitative evaluation of the precipitation estimations in Taiwan. The values of TS and BS are calculated based on Equations (2) and (3), respectively [36]:

$$\text{TTS} = \text{H} / (\text{O} + \text{F} - \text{H}),\tag{2}$$

$$\text{BS} = \text{F/O}\_2\tag{3}$$

where O is the area (i.e., number of grid points) of precipitation depicted by the CWB data that exceeds a given precipitation threshold, F is the area of precipitation depicted by the selected SPP that exceeds the given precipitation threshold, and H is the intersection of O and F over a period of accumulation. The worst and best possible values for TS are 0 and 1, respectively. BS can be described by any value from 0 to infinity. As stated in Levizzani et al. [40], BS gives the ratio of the estimated rain area (frequency) to the observed rain area (frequency), regardless of how well the rain patterns correspond with each other. TS measures the fraction of all events estimated and/or observed that were correctly diagnosed. For other details of TS and BS, please refer to Levizzani [40].

Moreover, to clarify the spatial-temporal characteristics of diurnal precipitation over Taiwan, we applied the widely used empirical orthogonal function (EOF) analysis [41] on the variation of diurnal precipitation. For more details of EOF analysis, please refer to Hannachi et al. [41].
