## 3 Results  
### Spatial Patterns of IMERG Precipitation Data and Gauge Observations  
As shown in Figure 2(a1-d1, a2-d2), the annual precipitation total records obtained from IMERG and meteorological stations exhibited a very similar spatial pattern, although IMERG generally overestimated this parameter. The relative bias of IMERG data with respect to gauge observation was also calculated, and the regional mean RB statistics are reported in Table 2. The IMERG precipitation data obtained for China largely reflected the spatial patterns of gauge observations, and specifically the spatial distribution divided by the Qinling-Huaihe Line. The southeastern coastal region of China was characterized by abundant precipitation, with annual totals exceeding 800 mm/y, and even reaching up to 2000 mm/y in some areas. Precipitation decreased progressively from the southeast to the northwest. Specifically, the northwestern inland regions experienced sparse precipitation \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Metric** & **Formula** & **Optimal Value** & **Reference** \\ \hline Correlation & \(CC=\frac{\frac{1}{N}\sum_{m=1}^{N}\big{(}S_{n}-\overline{S}\big{)}\big{(}G_{n} -\overline{G}\big{)}}{\sigma_{S}\sigma_{G}}\) & 1 & [PERSON] et al., 2010 [57] \\ \hline Mean Absolute Error & \(MAE=\frac{1}{N}\sum_{n=1}^{N}|S_{n}-G_{n}|\) & 0 & [PERSON] et al., 2010 [57] \\ \hline Root Mean Square & \(RMSE=\sqrt{\frac{1}{N}\sum_{n=1}^{N}(S_{n}-G_{n})^{2}}\) & 0 & [PERSON] et al., 2010 [57] \\ \hline Relative Bias & \(RB=\frac{\frac{1}{N}\sum_{n=1}^{N}(S_{n}-G_{n})}{\frac{1}{N}\sum_{n=1}^{N}G_{n} }\times 100\%\) & 0 & [PERSON] et al., 2010 [57] \\ \hline Probability of & \(POD=\frac{n_{11}}{n_{11}+n_{01}}\) & 1 & [PERSON] et al., 2007 [60] \\ \hline False Alarm Ratio & \(FAR=\frac{n_{10}}{n_{11}+n_{10}}\) & 0 & [PERSON] et al., 2007 [60] \\ \hline Critical Success Index & \(CSI=\frac{n_{11}}{n_{11}+n_{01}+n_{10}}\) & 1 & Gerapetritis and Pelissier, 2004 [61] \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Equations used to calculate the metrics for the evaluation of IMERG precipitation data and their optimal values. In these formulas, \(N\) represents the number of samples, \(S_{n}\) and \(\sigma_{S}\) represent satellite-derived precipitation data and standard deviation, respectively, while \(G_{n}\) and \(\sigma_{G}\) represent gauge observations and standard deviation, respectively. Additionally, \(n_{11}\) denotes the number of hours for which both gauge observations and IMERG precipitation data were obtained, \(n_{10}\) represents the hours for which IMERG data were obtained but gauge observations were not, \(n_{01}\) denotes the opposite of \(n_{10}\), and \(n_{00}\) represents the hours for which neither records were obtained. with annual totals below 800 mm/y, while in most of the other areas total precipitation reached less than 400 mm/y annually. In North America, the special distributions of both IMERG data and gauge observations were also quite similar. To the west of 100\({}^{\circ}\)W, both methods recorded annual precipitation totals below 800 mm/y, with most areas reaching around 400 mm/y. In the Pacific Northwest, due to the influence of atmospheric rivers, precipitation is more abundant, which was reflected in both IMERG data and gauge observations. Past studies have shown that the precipitable water and integrated water vapor fluxes over this area were largely enhanced by the negative anomalies in sea level pressure and upper-level height in the central Pacific [62]. The variability in atmospheric river frequency can drive hydrometeorological extremes with broad societal impacts over the Pacific Northwest of North America [63]. To the east of 100\({}^{\circ}\)W, the frequent tropical cyclones and cold fronts result in higher precipitation, as revealed by values exceeding 800 mm/y annually in most areas and reaching up to 1400 mm/y in the southeastern regions.