*3.3. Diurnal Variation*

The summer precipitation over Taiwan also exhibits a clear diurnal feature in which the maximum precipitation generally occurs in the afternoon [24,30]. To illustrate this feature, we apply an EOF analysis on the variation of diurnal precipitation, averaged during the summers of 2014–2017. This analysis method is frequently adopted by earlier studies in examining the characteristics of diurnal variation of precipitation over East Asia [44–46]. Here, only the first mode of the EOF analysis is presented in Figure 5, and several features noted from Figure 5 are summarized below:


two maximum centers in Figure 5a. However, the locations of the maximum centers in GSMaP7 are apparently shifted to the west compared to the CWB data.

3. Temporally (Figure 5b), the first EOF mode of the CWB data shows the timing of diurnal precipitation maximum occurred between 15–18 h. For the SPPs, all of them are able to capture similar feature in Figure 5b, even though their amplitudes of diurnal variation are weaker than the CWB data. Among the four SPPs, GSMaP7 underestimates the most in the amplitude of diurnal variation of precipitation.

**Figure 5.** The first empirical orthogonal function (EOF) mode of diurnal precipitation, averaged during the summers of 2014–2017: (**a**) the normalized spatial patterns (i.e., eigen-vectors normalized to the maximum precipitation), and (**b**) the temporal patterns (i.e., eigen-coefficients). The percentages (%) of the total variability in hourly precipitation explained by the first EOF mode are added in (**b**).

Based on Figure 5, it seems that GSMaP7 performs worse than the other SPPs in illustrating the diurnal variation of precipitation. Indeed, by calculating the Scorr (RMSE) between the SPPs and the CWB data from Figure 5a, we note from Table 2 that GSMaP7 has the lowest (highest) value of Scorr (RMSE), suggesting its spatial pattern is less similar to the CWB data. In addition, by calculating the Tcorr (RMSE) between the SPPs and the CWB data from Figure 5b, we note from Table 2 that GSMaP7 has the lowest (highest) value of Tcorr (RMSE), suggesting its temporal pattern is also less similar to the CWB data.

It is also apparent from Table 2 that IMERG6 has the smallest bias in capturing the spatial-temporal characteristics of the diurnal precipitation over Taiwan. Tan et al. [47] examined the performance of IMERG6 in capturing the diurnal cycle of precipitation over the southeastern United States also noted that IMERG6 tends to underestimate the diurnal amplitude, but is capable of depicting the phase of diurnal precipitation. However, why IMERG6 (GSMaP7) performs the best (worst) with regards to the diurnal precipitation over Taiwan is unclear and requires further study.



The performance of IMERG6 and TRMM7 in illustrating the variation of diurnal precipitation area-averaged over Taiwan during the summers of 2000–2017 was further evaluated based on Figure 6. The CWB data (Figure 6a) shows that all examined periods have maximum diurnal precipitation occurred between 15-18 h. By comparing Figure 6a with Figure 6b,c, we note that both TRMM7 and IMERG6 are able to show the temporal phase evolution similar to the CWB data, with the value of Scorr between Figures 6a and 6b (Figure 6c) is about 0.91 (0.92). However, it is also apparent in Figure 6 that both TRMM7 and IMERG6 tend to underestimate the amplitude of diurnal precipitation for all examined time periods, but TRMM7 (IMERG6) is less (more) close to the CWB data. All above features revealed in Figure 6 are consistent with those suggested by Figure 5 and Table 2, suggesting again that IMERG6 is better than TRMM7 in depicting the variation of diurnal precipitation over Taiwan.

**Figure 6.** Temporal evolution of the hourly precipitation area-averaged over Taiwan extracted from the selected data for each specific summer during 2000–2017: (**a**) the CWB data, (**b**) TRMM7, and (**c**) IMERG6.
