## 2 Methods
### Verification Methods  
The forecasts of precipitation at the surface were verified against the observations of the 134 AWSs in southern Taiwan (Figure 1) over the model domain. Forecast performance of precipitation was evaluated using root-mean-square error (RMSE), Pearson product-moment correlation coefficient (PPMCC; Ref. [49]), and Spearman rank correlation coefficient (SRCC; Ref. [50]). Verification scores used were the threat score (TS; Ref. [51]) and bias score (BS; Ref. [49]). The calculation methods for the aforementioned coefficients and scores are defined as follows.  
\[\text{RMSE}=\sqrt{\frac{\sum_{i=1}^{n}\left(\text{P}_{i}-\text{O}_{i}\right)^{ 2}}{n}} \tag{3}\]  
\[\text{PPMCC}=\frac{\sum_{i=1}^{n}\left(\text{P}_{i}-\overline{\text{P}}\right) \left(\text{O}_{i}-\overline{\text{O}}\right)}{\sqrt{\sum_{i=1}^{n}\left( \text{P}_{i}-\overline{\text{P}}\right)^{2}}\sqrt{\sum_{i=1}^{n}\left(\text{O }_{i}-\overline{\text{O}}\right)^{2}}} \tag{4}\]  
where \(\text{P}_{i}\), \(\text{O}_{i}\) and \(\text{n}\) refer to the predicted value, observed value and the number of observations, respectively. \(\overline{\text{P}}\), and \(\overline{\text{O}}\), refer to the sample mean for predicted value, and the sample mean for observed value, respectively.  
\[\text{SRCC}=1-\frac{6\sum_{i=1}^{n}\text{d}_{i}^{2}}{n(n^{2}-1)} \tag{5}\]  
\begin{table}
\begin{tabular}{c c c c} \hline \hline
**Group** & **Experiments** & **Assimilation Time** & **Forecast Time** \\ \hline \multirow{4}{*}{C1} & NDA01 & Without assimilation & 0100–1300 UTC \\  & NDA02 & Without assimilation & 0200–1400 UTC \\  & NDA03 & Without assimilation & 0300–1500 UTC \\  & NDA04 & Without assimilation & 0400–1600 UTC \\ \hline \multirow{4}{*}{C2} & DA01 & 0100 UTC & 0100–1300 UTC \\  & DA02 & 0200 UTC & 0200–1400 UTC \\  & DA03 & 0300 UTC & 0300–1500 UTC \\  & DA04 & 0400 UTC & 0400–1600 UTC \\ \hline \multirow{4}{*}{C3} & CDA01 & 0100–0400 UTC (hourly) & 0400–1300 UTC \\  & CDA02 & 0200–0400 UTC (hourly) & 0400–1400 UTC \\  & CDA03 & 0300–0400 UTC (hourly) & 0400–1500 UTC \\ \hline \hline \end{tabular}
\end{table}
Table 1: Design of experiments.  
where \(\rm d_{i}\) refers to the difference between the two ranks of prediction and observation.  
\[\rm TS= C/(F+O-C) \tag{6}\] \[\rm BS= F/O \tag{7}\]  
where F, O, and C refer to the numbers of forecast points, observed points, and correctly forecast points with precipitation occurrence (hits; binary value is one), respectively.  
The TS ranges from zero (no skill) to one (perfect skill). The BS ranges from positive infinity (over-forecasting) to negative infinity(under-forecasting), with a score of one representing the best performance of the model. The RMSE ranges from zero to positive infinity. The smaller the RMSE is, the better the model performance is. The PPMCC ranges from \(-1\) to \(1\), with \(1\) representing the best performance of the model. The SRCC ranges from \(-1\) to \(1\), with \(1\) representing the perfect monotonic relationship (a direct association) between observed and simulated data.  
To verify forecast performance in comparison with the observations of 134 the AWSs, the 6-h accumulated precipitations from 0500 UTC to 1100 UTC (the black box of Figure 2), the major impact period of the AT event, were adopted from the 12-h precipitation operational forecasts of the WRF model. The quantitative precipitation forecast (QPF) skills such as TS and BS under data assimilation simulations for 6-h accumulated precipitation with thresholds of 5, 15, 10, and 20 mm were also calculated. Similar to the calculations of the RMSE, PPMCC, and SRCC, the TS and BS calculations were first performed by interpolation from the model grid data to station locations.