3.1. Seasonal Mean
Figure 2a shows the horizontal distribution of the seasonal mean total rainfall over Taiwan, averaged during 2000–2018 JASO and estimated from the CWB and selected SPPs. Focusing on the CWB of
Figure 2a, there are two maximum rainfall centers, one each in southern and northeastern Taiwan. The formation of these two maximum centers is caused mainly by the interactions between the topography and monsoonal flows [
38,
39]. By separating the total rainfall (
Figure 2a) into non-TC (
Figure 2b) and TC (
Figure 2c) rainfall, we note from CWB that both also consist of two maximum centers, similar to those for total rainfall. However, relative to non-TC rainfall, TC rainfall distribution shows a more evident east–west contrast, with greater rainfall over eastern than western Taiwan. This feature, which was also noted in previous studies [
40], might arise because TCs tend to make landfall more frequently over eastern Taiwan than over western Taiwan [
4,
41].
By comparing the features documented in
Figure 2a–c, we note that all IMERG products tend to underestimate the total, non-TC, and TC rainfall. The use of IMERG products to estimate rainfall distribution over Taiwan seems minimizing the topographic effect (i.e., too smooth compared to CWB). Among IMERG products, IMERG-F has an area-averaged rainfall value much closer to that of CWB, whereas the value of IMERG-E is much less than that of CWB (see
Table 3). Despite the magnitude difference, all IMERG products can depict the southern (but not northern) maximum center, for the total and non-TC rainfall. As inferred from [
30], two possible reasons might explain why IMERG has bias in underestimating precipitation over northern Taiwan: (1) the brightness temperature of warm orographic clouds is generally too warm for infrared thresholds, and (2) the ice content within warm orographic clouds is generally too low to be detected by passive microwave sensors. For the TC rainfall, IMERG-E and IMERG-L have depicted two maximum rainfall centers similar to CWB, while IMERG-F shows only one maximum center and a more distinct east–west contrast, with greater rainfall over eastern Taiwan than western Taiwan. Overall, the rainfall distribution suggested by the two NRT products (i.e., IMERG-E and IMERG-L) is similar, but the rainfall magnitude in IMERG-L is slightly greater than that in IMERG-E and closer to CWB. Relative to IMERG-E and IMERG-L, it seems that IMERG-F reduces the bias in underestimating the rainfall magnitude but increases the bias in illustrating the spatial distribution.
To further clarify the performance difference among IMERG products, we calculated RB and Scorr between CWB and SPPs for those patterns shown in
Figure 2a–c; the results are shown in
Figure 2d–f. All SPPs were found to have negative RB values, suggesting that all SPPs have a bias toward underestimating typhoon season rainfall (
Table 3). Among SPPs, IMERG-F has the value of RB closest to 0 (−0.15 for total rainfall, −0.18 for non-TC rainfall, and −0.12 for TC rainfall), suggesting that its performance in the quantitative estimation of examined rainfall is better than that of other SPPs. After IMERG-F, IMERG-L has a slightly better overall performance for RB (−0.23 for total rainfall, −0.27 for non-TC rainfall, and −0.21 for TC rainfall) than IMERG-E (−0.25 for total rainfall, −0.29 for non-TC rainfall, and −0.22 for TC rainfall). Overall, IMERG-L had the highest Scorr values for total rainfall (~0.62), non-TC rainfall (~0.60), and TC rainfall (~0.68), while IMERG-E has higher Scorr values than IMERG-F for all assessed rainfall. This confirms the earlier suggestion that IMERG NRT products are more skilled than IMERG-F in illustrating the spatial distribution of examined rainfall, especially for TC rainfall.
It is noteworthy that [
33] recently demonstrated that IMERG-F is better than TRMM7 in capturing the summer rainfall variations over Taiwan. Based on the findings of [
33], we conducted the horizontal distribution of seasonal mean rainfall for total, non-TC, and TC days estimated from TRMM7 (
Figure 2a–c) and compared these with the IMERG products. As seen from
Figure 2d–f, IMERG-F performs better than TRMM7 in terms of RB and Scorr for all examined rainfall. Furthermore, IMERG-E and IMERG-L tended to perform better than TRMM7, especially for TC rainfall. To clarify whether the findings revealed in
Section 3.1 are also true for the daily variations, we conducted related evaluations as discussed below.
3.2. Daily Variation
Figure 3 shows the comparison of daily rainfall area-averaged over Taiwan between CWB and selected SPPs for non-TC days (
Figure 3a) and TC days (
Figure 3b). The evaluations are based on the Tcorr and RRMSE. It is understood that when the values of Tcorr and RRMSE closer to the perfect score (i.e., 1 and 0, respectively), it implies that the SPP has better performance skill. Therefore, for non-TC rainfall in
Figure 3a, we concluded that IMERG-F had the best performance (Tcorr = 0.88, RRMSE = 0.79), followed by IMERG-L (Tcorr = 0.84, RRMSE = 0.89), TRMM7 (Tcorr = 0.84, RRMSE = 0.91), and IMERG-E (Tcorr = 0.82, RRMSE = 0.95), in that order. With regard to TC rainfall (
Figure 3b), IMERG-F (Tcorr = 0.95, RRMSE = 0.34) also performed best, followed by IMERG-L (Tcorr = 0.89, RRMSE = 0.54), IMERG-E (Tcorr = 0.89, RRMSE = 0.56), and TRMM7 (Tcorr = 0.88, RRMSE = 0.60).
To assess the ability of SPPs to illustrate the spatial distribution of daily rainfall over Taiwan, we calculated the values of Scorr between CWB and selected SPPs for each of the non-TC and TC days. The Scorr-related occurrence frequency is shown in
Figure 4a (non-TC) and
Figure 4c (TC) with the probability density function given in
Figure 4b (non-TC) and
Figure 4d (TC). As noted in
Figure 4a,b, the non-TC days have the top three Scorr occurrence frequencies with values of <0.1, (0.6–0.7), and (0.7–0.8). In contrast,
Figure 4c,d show that the TC days have the top three Scorr occurrence frequencies at (0.5–0.6), (0.6–0.7), and (0.7–0.8). All SPPs appear to perform better in representing the Scorr for TC days than for non-TC days. Indeed, by accumulating the percentage with Scorr values ≥ 0.5 in
Figure 4b,d, we note from
Table 4 that about 67.7% to 74.5% of TC days have Scorr values ≥ 0.5, whereas only about 47.2% to 52.2% of non-TC days have Scorr values ≥ 0.5. This implies that, overall, all SPPs are more capable of illustrating the spatial distribution of daily rainfall for TC days than for non-TC days. This is consistent with the results shown in
Figure 2e,f.
Figure 4 and
Table 4 also demonstrate that all IMERG products showed increases within 3.9–6.8% in the accumulated percentage of Scorr ≥ 0.5 for non-TC days as well as TC days, relative to TRMM7. Among the IMERG products, IMERG-L has the best Scorr performance, and IMERG-F has the poorest, although the difference among IMERG products shown in
Table 4 is only <2.9% and <1.1% for TC and non-TC days, respectively. The possible reasons why IMERG NRT products are better than IMERG-F in terms of Scorr values will be discussed in
Section 4.
It is noted that the results shown in
Figure 3 and
Figure 4 do not provide information on the ability of SPPs to capture the rainfall occurrence frequency at different intensity thresholds. This information is important for constructing
Table 1, which provides the necessary elements for calculating POD, CSI, and FAR. Therefore, we examined the ability of SPPs to capture the occurrence frequency of non-TC and TC rainfall at various intensity thresholds (
Figure 5). In total, 761,264 grids counted from 1942 non-TC days, and 110,544 grids from 282 TC days were used to construct
Figure 5a,b. The method for the calculation of the number of grids is explained in the caption of
Figure 5.
Overall, as shown in
Figure 5a,b, IMERG-F (TRMM7) performs better (poor) than other SPPs for capturing the occurrence frequency of rainfall events at most rainfall thresholds; this finding is true for both non-TC days and TC-days. To better compare the difference among SPPs and the difference between non-TC and TC days, we further utilized the information provided in
Figure 5a,b to calculate the related probability density function for five different ranges of rainfall intensity: 0–0.1 mm⋅d
−1 as non-rainy, 0.1–5 mm⋅d
−1 as light rainfall, 5–20 mm⋅d
−1 as moderate rainfall, 20–80 mm⋅d
−1 as heavy rainfall, and >80 mm mm⋅d
−1 as extreme rainfall. The selection of criteria for non-rainy to heavy rainfall followed the method of [
33], while the definition of extreme rainfall was defined according to [
42].
As shown in
Figure 5c,d, all SPPs overestimate the non-rainy percentage, and the related bias (i.e., the difference between CWB and SPPs) is much greater in
Figure 5c than in
Figure 5d. For light rainfall, all SPPs tend to underestimate the percentage of its occurrence frequency, and the related bias is also greater in
Figure 5c than in
Figure 5d. Among SPPs, IMERG products perform better than TRMM7 in capturing the non-rainy and light rainfall occurrence frequencies, not only for non-TC days (
Figure 5c) but also for TC days (
Figure 5d). Other features that were observed during the comparison between
Figure 5c,d are as follows: (1) the capabilities of all SPPs in depicting the percentage of moderate to extreme rainfall for non-TC days are similar; (2) overall, TRMM7 has poor performance than all IMERG products in depicting the percentage of heavy to extreme rainfall for TC days; (3) IMERG-F is better than others for extreme TC rainfall, while IMERG-L is better for light to heavy TC rainfall. Using all the rainy grids identified in
Figure 5, we calculated POD, CSI, and FAR based on Equations (4)–(6) to evaluate the capabilities of SPPs for quantitative rainfall estimation at different thresholds (
Figure 6).
It is known that the higher the POD value, the higher the CSI value, and the lower the FAR value, the better the performance in quantitative rainfall estimation [
43]. As shown in
Figure 6, IMERG-F has the highest POD and CSI values among other SPPs at most rainfall thresholds; this is not only the case for non-TC days (
Figure 6a,b) but also for TC days (
Figure 6d,e). Conversely, the value of FAR in IMERG-L is the lowest among SPPs at most rainfall thresholds; this is also true for both non-TC (
Figure 6c) and TC days (
Figure 6f). Relative to IMERG-E and TRMM7, IMERG-L also had higher POD and CSI values for TC days at rainfall thresholds > 80 mm⋅d
−1, suggesting that its performance in quantitative estimation for extreme rainfall on TC days is better than IMERG-E and TRMM7. However, for non-TC days, IMERG-L has POD and CSI values closer to IMERG-E and TRMM7 at most rainfall thresholds.
It is worthy of note that TRMM7 has a poor performance than all IMERG products in terms of illustrating POD, CSI, and FAR for TC days, especially at rainfall thresholds > 80 mm⋅d
−1 (
Figure 6d–f). This suggests that, relative to TRMM7, IMERG products can provide more accurate rainfall estimations for studying and monitoring TC rainfall in Taiwan. Furthermore, it can be inferred from
Figure 6d–f that areas with more intense rainfall would likely have larger errors in quantitative rainfall estimation for TC days. Indeed, by calculating the point-to-point RMSE between CWB and SPPs for TC days during the 2000–2018 JASO (
Figure 7b), we note that all SPPs tend to have more bias over southern mountainous regions and northeastern Taiwan—areas of more intense rainfall—as demonstrated in the CWB of
Figure 2c. For the non-TC days, we noted that there are also two maximum RMSE centers (
Figure 7a), the locations of which are consistent with the two maximum centers revealed in the CWB (
Figure 2b). Overall, relative to
Figure 7a which shows no significant difference among SPPs,
Figure 7b clearly demonstrates that all IMERG products outperform TRMM7 in the quantitative rainfall estimation of TC days. This is consistent with the results shown in
Figure 3,
Figure 4,
Figure 5 and
Figure 6.
3.3. Interannual Variation
In addition to the seasonal mean and daily variation, the interannual variation of TC rainfall in Taiwan is also an issue that has attracted research attention [
2,
9,
10]. Here, we examined the ability of SPPs to depict the temporal evolution of interannual variations in non-TC (
Figure 8a) and TC rainfall (
Figure 8b), area-averaged in Taiwan during the period 2000–2018 JASO. By focusing on the CWB in
Figure 8a,b, it is noted that TC rainfall has a greater interannual variability than non-TC rainfall; this is consistent with the results of previous studies [
10]. Despite the bias in underestimating the rainfall intensity, all SPPs seem to be able to capture the phase evolution of the interannual variation of non-TC and TC rainfall, similar to those estimated by the CWB. To clarify this hypothesis, we further calculated the related Tcorr between the CWB and selected SPPs using the time series in
Figure 8a,b, and the results are given in
Table 5.
As shown in
Table 5, all SPPs had a Tcorr of ≥0.88 (passing a 99% significance
t-test), confirming that all SPPs are highly capable of capturing the phase evolution for the interannual variation in rainfall for both non-TC and TC days. Spatially, the point-to-point Tcorr shown in
Figure 8c suggests that all SPPs tend to better illustrate the interannual variation of non-TC rainfall over southwestern Taiwan. In the case of TC rainfall, all SPPs tend to better illustrate its interannual variation not only over southwestern Taiwan but also in northeastern Taiwan. The differences shown in
Figure 8c,d are consistent with those in
Figure 2c,d, which show that all SPPs tend to capture the northeastern maximum rainfall center better for TC days than for non-TC days.
It is also noted from
Figure 8 that IMERG-F is much better than the other SPPs at illustrating the temporal evolution of TC rainfall and slightly better for non-TC rainfall on the interannual timescale. Consistent with this result, we note from
Table 5 that IMERG-F also has a much smaller RRMSE value than the others when comparing the time series of TC rainfall (
Figure 8b) and a slightly smaller value for non-TC rainfall (
Figure 8a). After IMERG-F, IMERG-L ranks second in
Table 5, with higher Tcorr values and smaller RRMSE values than those of IMERG-E and TRMM7. This is true for both TC and non-TC rainfall.