## 3 Results
### Spatial Patterns of IMERG Precipitation Data and Gauge Observations
In Europe, despite the few selected grid points, the annual precipitation total estimates derived from IMERG were still quite consistent with gauge observations. On average, the average RB in the annual precipitation total records from 2001 to 2020 at almost all stations was larger than zero, indicating that IMERG generally overestimated this parameter. Spatially, the RB between IMERG data and gauge observations was larger in regions with lower annual precipitation totals, such as the northwestern regions of China and parts of \begin{table}
\begin{tabular}{c c c c c} \hline \hline  & **North America** & **Europe** & **North Asia** & **South Asia** \\ \hline CC & 0.367 \({}^{\star}\) & 0.308 \({}^{\star}\) & 0.373 \({}^{\star}\) & 0.350 \({}^{\star}\) \\ MAE (mm/h) & 0.131 & 0.155 & 0.115 & 0.223 \\ RMSE (mm/h) & 0.880 & 0.761 & 0.842 & 1.291 \\ RB & 22.7\% & 27.7\% & 28.0\% & 12.7\% \\ POD & 49.2\% & 41.9\% & 51.0\% & 49.3\% \\ FAR & 69.6\% & 54.8\% & 62.6\% & 55.1\% \\ CSI & 22.7\% & 27.4\% & 27.2\% & 30.1\% \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Variability of hourly precipitation in different regions as revealed by the Pearson Correlation Coefficient (CC), Mean Absolute Error (MAE), Root Mean Square Error (RMSE), Relative Bias (RB), Probability of Detection (POD), False Alarm Ratio (FAR), and Critical Success Index (CSI). \({}^{\star\star}\) denotes statistical significance at the 0.05 level. Figure 2: Average annual precipitation total from 2001 to 2020 obtained from gauge observations (**a1–d1**) and IMERG data (**a2–d2**), and the bias of IMERG data relative to gauge observations (**a3–d3**), for North America, Europe, North Asia, and South Asia, respectively. the western United States, where it exceeded 30%, and even reached 50% in some grids. In other regions, the RB of most grids was less than 10%. Figure 3 shows that the precipitation frequency estimated by IMERG was significantly higher than that obtained from meteorological stations, especially in northern China and western America. This discrepancy may be attributed to the fact that GPM products are capable of detecting light rainfall and solid precipitation events. Previous assessments have also demonstrated the clear improvement achieved in the IMERG precipitation product in comparison with its predecessor, especially in reducing missed precipitation and hit bias in winter, revealing the general superiority of GPM IMERG [44; 64]. However, due to differences in data sources, observation methods, and spatial scales, a certain bias was detected between IMERG data and gauge observations. Specifically, in China, IMERG data overestimated the precipitation frequency in the northern region by approximately 4% compared to gauge observations, with RB values reaching up to 100% in some areas. This could be due to the complex atmospheric circulation and convective precipitation in northern China [65; 66], leading to errors in the GPM inversion of these complex processes. Similarly, in western America, IMERG overestimated the precipitation frequency overall, with the RB values in most grids exceeding 40% and reaching up to 100% in some cases. This may be related to the complexity of the terrain and the influence of atmospheric circulation near the Pacific Ocean. The precipitable water and integrated water vapor fluxes over this area derived from the atmospheric river and were blocked by the Rocky Mountains, resulting in plentiful precipitation [62]. It was found that the IMERG precipitation records in this area were related to the documented low detection rate of satellites and to over arid/semiarid areas with hot background surfaces [19; 67]. Significant overestimation biases were also identified between IMERG data and gauge observations in terms of the spatial distribution of high-frequency rainfall events. In China, IMERG estimated high-frequency rainfall in the Yangtze-Huaihe River basin, with annual precipitation frequencies as high as 20%.