*3.2. Evaluation Using Correlation Coe*ffi*cient Metric*

The CCs of LTs for the products and the observed values are depicted in Figure 3(a1–a5). For annual LTs, the corresponding CCs for TRMM3B42RT, TRMM3B42, PERSIANN, PERSIANN-CCS, and MERRA-2 were generally >0.40, suggesting that spatial distributions of annual LTs across MC can be derived from these products (Figure 3(a1)), especially for TRMM3B42 and MERRA-2 with CCs around 0.80. Besides, ERA-Interim, with an annual CC < 0.40, exhibited limited capacity in detecting annual LTs in space. However, annual CCs for the remaining six products were all below 0.10 and some were even negative, which indicates that these products are not able to capture the spatial distribution of LTs across MC. Comparing CCs of annual LTd and LTn, CC-based performance for each precipitation product differed over daytime and nighttime, especially PERSIANN-CCS and ERA-Interim, followed by TRMM3B42RT and PERSIANN. In spring (Figure 3(a2)), GSMaP-RNL, GSMaP-RNLG, JRA-55, ERA-55, NCEP1, and NCEP2 had negative CCs and therefore no ability to reflect the spatial distribution of LTs; however, the other products, with CCs > 0.40, had good performances, of which TRMM3B42 showed the best performances (CCs around 0.80) and the next was in TRMM3B42RT, PERSIANN, and MERRA-2 (CCs around 0.70). Furthermore, the spring CC-based performance of PERSIANN-CCS exhibited differences > 0.10 between daytime and nighttime. During summer (Figure 3a3), TRMM3B42 with CCs around 0.80 showed the best performance, followed by TRMM3B42RT and MERRA-2 (CCs around 0.70), ERA-Interim (CCs around 0.60), and PERSIANN and PERSIANN-CCS (CCs around 0.50). JRA-55, EAR-55, NCEP1, and NCEP2 with CCs < 0 indicated poor performance. Relative to spring, the capacity of GSMaP-RNL and GSMaP-RNLG to reproduce LTs in space increased in summer but was still limited, with CCs < 0.20. PERSIANN-CCS, GSMaP-RNL, and GSMaP-RNLG showed the greatest differences (>0.10) in summer CCs between daytime and nighttime. In autumn (Figure 3a4), the largest CCs (>0.80) were detected by TRMM3B42 and MERRA-2, while TRMM3B42RT, PERSIANN, and ERA-Interim had CCs ranging from 0.60 to 0.80. PERSIANN-CCS, JRA-55, and ERA-4 had CCs around 0.40 and could capture summer LTs spatially, while the remaining four products showed limited CC-based performance (CCs generally < 0.10). Comparisons of CCs for autumn LTd and LTn indicated that larger differences (>0.10) existed in PERSIANN, PERSIAN-CCS, JRA-55, and ERA-5, especially for the former three products with differences exceeding 0.20. Regarding winter CCs (Figure 3(a5)), eight of the products had values below 0.20 or 0, indicating that they had limited or no ability to capture winter LTs in space. Of the remaining products, the best product based on CC in winter was MERRA-2 (CCs around 0.90), followed by TRMM3B42 (CCs around 0.70), TRMM3B42RT (CCs around 0.50), and ERA-Interim (CCs < 0.40); no significant differences in CCs for LTd and LTn existed among these products.

To identify the CC-based optimal products (OPs) of LTwd, LTd, and LTn, we compared CCs from the 12 examined products. The results are depicted in Figure 3(b1–b5). For MC, the annual, spring, summer, and autumn (excluding LTd) CC-based OP for the three LTs was TRMM3B42, and the winter OP was MERRA-2. For annual cases (including the three LTs and ten WRRs), the CC-based OP for 17 of the 30 cases was MERRA-2, generally in northern WRRs, while 11 cases, including LTs for southern WRRs (excluding YZRB) and LTd for LRB, HaRB, and YRB had an OP of TRMM3B42. In spring, the OP for more than ten cases was TRMM3B42, generally in southern WRRs, while 15 cases with the OP of MERRA-2 were in northern WRRs. With several exceptions (e.g., SHRB, HuRB, and NWRB) showing the summer OP of MERRA-2, TRMM3B42 was the OP in 16 cases. In winter, the OP for the overwhelming majority (27) of cases was MERRA-2, followed by three cases with ERA-Interim in SERB. Notably, some cases had CCs below 0.40 for the identified OPs, e.g., for LTwd, LTd, and LTn in LRB and NWRB; this indicates that using the so-called CC-based OPs to represent spatial distribution of precipitation trends needs more caution in certain regions.

**Figure 3.** Correlation coefficients (CCs) for LTs from the selected 12 precipitation products (**a1**–**a5**), CC-based optimal products (OPs) for MC and ten WRRs (**b1**–**b5**), and number of cases corresponding to OPs for an annual or seasonal scale in ten WRRs (**c1**–**c5**). In figures (**b1**–**b5**), the number of each box represents the CC of the identified OP, which has been labelled with different colors. The number of figures (**c1**–**c5**) indicates the amount of a certain OP.
