(1) Temporal Variation

Table 6 compares the mean values of the four continuous (CC, RMSE, RB, and MAD) over the seven months from April to October and seasonally (spring, summer, fall) among the SPPs at the hourly scale. With their seven-month CC values all staying close to 0.5, SPPs have performed less satisfactorily in estimating hourly rainfall in the SRB.


**Table 6.** Mean continuous evaluation metrics of the SPPs at hourly scale.

<sup>a</sup> Spring extends from April to May; Summer extends from June to August; Fall extends from September to October.

All IMERG products tend to underestimate hourly rainfall throughout the three seasons. The absolute RBs of IMERG\_F are all below 13%, while those of the near-real-time products remain above 20%. With the smallest absolute RB among the SPPs, 3B42 tends to slightly overestimate daily rainfall in spring, but underestimate in summer and fall. Different from the other SPPs, 3B42RT shows a strong tendency of overestimation in summer.

Except for RB, the five SPPs all exhibit similar season patterns of change. Seasonally, the CCs of the SPPs all peak in spring followed by a continuous decline in summer and fall. Both the RMSEs and MADs of the SPPs are the highest in summer, followed by spring and then fall. The observed seasonal patterns at the hourly scale are quite similar to those observed at the daily scale.

Figure 7a to Figure 7l further examine the changes in mean continuous metrics over a diurnal cycle in three seasons. Meanwhile, Figure 7m to Figure 7o compare the observed amount of average hourly rainfall with the corresponding SPP estimates in the three seasons. The CCs of all five SPPs have shown considerable diurnal variations in the three seasons. Despite the differences in amount, the overall diurnal patterns of change in CCs are somewhat similar among the SPPs. In summer, for example, the CCs of all SPPs tend to reach a high plateau between 3:00 a.m. and 12:00 p.m., followed by a steady fall to the bottom at around 4:00 p.m. and a rebound afterwards. As shown in Figure 7n, mean hourly summer ground measurement peaks at 3:00 p.m. All SPPs, however, have exhibited a lag of one or more hours in reaching the peak value, which may have caused their CCs all drop to the lowest in the afternoon. The diurnal patterns of change in RMSE/MAD are even more similar among the SPPs in all three seasons. Diurnal variations in both metrics are the highest in summer, followed by spring and then fall, which are consistent with the three seasons' relative magnitude of diurnal changes in hourly precipitation (Figure 7m–o). In addition, the RMSEs and MADs of all five SPPs peak at 5:00 a.m., 5:00 p.m., and 10:00–11:00 p.m. in spring, and at 3:00–4:00 p.m. in summer. As seen from Figure 7m,n, hourly ground measurements also peak at these times.

**Figure 7.** Changes in mean continuous metrics over a diurnal cycle in three seasons: (**a**) *CC* in spring; (**b**) *CC* in summer; (**c**) *CC* in fall; (**d**) *RMSE* in spring; (**e**) *RMSE* in summer; (**f**) *RMSE* in fall; (**g**) *RB* in spring; (**h**) *RB* in summer; (**i**) *RB* in fall; (**j**) *MAD* in spring; (**k**) *MAD* in summer; (**l**) *MAD* in fall; (**m**) average observed and estimated hourly rainfall in spring; (**n**) average observed and estimated hourly rainfall in summer; and (**o**) average observed and estimated hourly rainfall in fall.

The diurnal patterns of change in RB are more complex. Although differing much in their actual amount, the RBs of the five SPPs seem to follow a somewhat similar trend of change throughout the diurnal cycle, especially in summer. This is probably because rainfall estimates by the SPPs all exhibit a largely similar hourly trend in each season, in spite of the differences in their actual amount. Nevertheless, precisely because of the difference in their actual RB amount, the five SPPs give quite different estimation performance across the diurnal cycle. For example, 3B42RT tend to overestimate hourly rainfall most seriously at night (6:00 p.m. and 9:00–10:00 p.m.), while giving the estimates with the least bias in the morning. In contrast, IMERG products tend to underestimate rainfall mostly seriously in the morning (8:00–11:00 a.m.), but give the estimates with the least bias at night (7:00–10:00 p.m.) (Figure 7).

In addition, the relative performance of the SPPs at the hourly scale is somewhat different from that at the monthly and daily scales. In general, there is much less variability in the performance of the SPPs at the hourly scale compared to that at the monthly and daily scales. Except for RB, only two IMERG products (IMERG\_F and IMERG\_L) have slightly outperformed the TMPA products for most of the time.

To date, only limited studies have evaluated the quality of the hourly rainfall estimates of the SPPs. Similar to our study, they have mostly found that the performance of SPPs in estimating hourly rainfall was less satisfactory. For example, Caracciolo et al. [53] calculated the CCs to be respectively 0.32 and 0.26 when using the IMERG\_F V4 for estimating hourly rainfall in Sardinia and Sicily of Italy. Li et al. [54] evaluated the performance of IMERG\_F in estimating hourly rainfall in the Ganjiang River Basin of China, and calculated its CC, RMSE, and RB to be 0.33, 1.72 mm/h, and 0.12%, respectively. Yuan et al. [55] evaluated the 3-hour rainfall estimates by the three IMERG and two TMPA products in the Chindwin River basin, Myanmar, and they found that IMERG\_F performed best with a CC of 0.33 and RB of −6.8%. Meanwhile, the RMSEs of the SPPs were similar, ranging from 2.9 to 3.1 mm/h.
