*3.3. Evaluation Using Bias Metric*

Figure 4(a1–a5,b1–b5) depict the percentage of grids with negative and positive Bs of annual and seasonal LTs across MC, respectively. For simplicity, we focused on analyses regarding negative Bs in this paragraph. More than 50% of grids had negative annual Bs for PERSIANN, PERSIANN-CCS, GSMaP-RNL, and GSMaP-RNLG products (Figure 4(a1)). In particular, PERSIANN LTwd and LTd had negative Bs in >65% of grids. With several exceptions (i.e., TRMM3B42, JRA-55, and MERRA-2 for LTd; and NCEP1 for LTn), annual Bs for the remaining products were negative in <50% of grids, and even TRMM3B42RT, ERA-Interim, and NCEP2 showed negative Bs in <35% of grids. As shown in Figure 4(a2), most products had negative spring Bs for LTwd and LTd in >50% of grids, especially for PERSIANN, ERA-Interim, and MERRA-2 with >65% of grids. However, six of the 12 products underestimated LTn in around 50% of grids in spring, followed by the other six products with overestimations in >50% of grids. Similar to spring, >50% of grids with negative Bs for summer LTwd and LTd were detected by most of the products, of which PERSIANN, GSMaP-RNL, ERA-Interim, and NCEP2 corresponded to >65% of grids (Figure 4(a3)). Except for PERSIANN, summer LTn was underestimated in <50% of grids by the products, particularly for JRA-55, ERA-Interim, and ERA-5 with a grid percentage < 25%. In autumn (Figure 4(a4)), despite several exceptions, >50% of grids had negative Bs for the three LTs, and the PERSIANN product had negative Bs in >70% of grids. Relative to autumn cases, the opposite happened during winter (Figure 4(a5)), i.e., percentages of grids with

negative Bs for LTwd, LTd, and LTn being generally <50%, in particular for JRA-55 and ERA-Interim. In addition, based on percentages of grids with negative Bs for LTd and LTn (Figure 4(a1–a5)), differences generally exceeding 10% were identified on both annual and seasonal scales for most of products, particularly MERRA-2 and ERA-Interim with annual and summer differences around 40%, respectively. This suggests that, in terms of grid percentages corresponding to underestimated and overestimated precipitation LTs, the products' performance varies at daytime and nighttime.

**Figure 4.** Grid percentages with negative (**a1**–**a5**) and positive biases (Bs; **b1**–**b5**) for annual and seasonal LTs across MC.

Taking MC as a whole, regional mean Bs for LTwd, LTd and LTn derived from each product were calculated and are shown in Figure 5(a1–a5). At the annual scale, five products exhibited positive Bs for LTwd, with a range from 0.39 mm/yr for TRMM3B42 to 10.10 mm/yr for NCEP2, while four products exhibited positive Bs for LTd, ranging from 1.44 mm/yr for TRMM3B42RT to 5.01 mm/yr for NCEP2. Negative Bs were found for the remaining products, of which the lowest values of –7.88 mm/yr and –4.98mm/yr for LTwd and LTd, respectively, were recorded for PERSIANN (Figure 5(a1)). In contrast, seven products overestimated annual LTn, particularly ERA-Interim, NCEP2, and MERR-2 with Bs > 5 mm/yr, while the other products' Bs were all negative and generally <−3 mm/yr. Regarding the spring LTs (Figure 5(a2)), TRMM3B42RT, TRMM3B42, and MERRA-2 had positive Bs < 1.40 mm/yr, except for LTd. However, negative spring Bs were found in the remaining products, ranging from −2.60 mm/yr (−1.61 mm/yr) for JRA-55 to −0.88 mm/yr (−0.51 mm/yr) for ERA-Interim for LTwd (LTd), and from −1.52 mm/yr for NCEP1 to −0.31 mm/yr for PERSIANN-CCS for LTn. For summer LTwd and LTn (Figure 5(a3)), most of the products exhibited positive Bs, while LTd was generally underestimated by the products (excluding TRMM3B42RT and NCEP1). Despite that, summer Bs for LTs were generally from −2 mm/yr to 2 mm/yr, except for TRMM3B42RT LTwd and LTn, and MERRA-2 LTn with Bs >

2 mm/yr, and PERSIANN-CCS LTwd and LTd with Bs < −2 mm/yr. In autumn (Figure 5(a4)), absolute values of Bs for LTs from TRMM3B42, TRMM3B42RT, and MERRA-2 were all < 0.60 mm/yr, but Bs were generally < −1 mm/yr for the remaining products, and even some were lower than −4 mm/yr (i.e., PERSIANN, and NCEP2 for LTwd). In contrast, the majority of products overestimated winter LTwd, LTd, and LTn, and Bs were generally < 3 mm/yr, with exceptions of JRA-55, ERA-Interim, and ERA-5 having Bs > 3 mm/yr (Figure 5(a5)). In terms of Bs for annual LTd and LTn (Figure 5(a1)), there were differences for some products, i.e., TRMM3B42RT, PERSIANN-CCS, and ERA-Interim with large differences > 2 mm/yr, and TRMM3B42, JRA-55, ERA-5, NCEP1, and MERRA-2 showing different sign (positive/negative). Evident differences in Bs existed for some products in each season (Figure 3(a2–a5)); in summer there were eight products with different signs of Bs and four products with large differences (around ±1 mm/yr) but the same sign.

**Figure 5.** MC Bs derived from the selected 12 precipitation products (**a1**–**a5**), B-based optimal products (OPs) for MC and ten WRRs (**b1**–**b5**), and number of cases corresponding to B-based OPs on an annual or seasonal scale for ten WRRs (**c1**–**c5**). In figures (**b1**–**b5**), the number of each box represents grid percentage (%) of OP, which has been labelled with different colors. The number of figures (**c1**–**c5**) indicates the amount of a certain OP.

Considering offset effects of positive and negative Bs within MC and each WRR, we calculated the percentage of grids with the minimum absolute B for each product, and B-based OPs were identified as the product with the largest grid percentage (Figure 5(b1–b5,c1–c5)). Except for annual LTd and LTn and summer LTwd and LTd, for which the OP was TRMM3B42, the OP for all other LTs was MERRA-2 for MC (Figure 5(b1–b5)). For annual cases of the ten WRRs (Figure 5(c1)), the OPs were TRMM3B42 and MERRA-2 in 14 and 12 cases, respectively. Furthermore, the OP for most WRRs was MERRA-2 for annual LTwd, and TRMM3B42 for both annual LTd and LTn (Figure 5(b1)). For B-based OPs of spring and autumn LTwd (Figure 5(b2,b4)), the OP was MERRA-2 in most WRRs, while the OPs for LTd and LTn in southern and northern WRRs differed and were mainly TRMM3B42RT and MERRA-2, respectively. In summer (Figure 5(b3)), there were differences in OP for the three LTs, i.e., most WRRs with OPs of TRMM3B42 and MERRA-2 for LTwd, TRMM3B42, MERRA-2, and ERA-Interim for LTd, and ERA-Interim and TRMM3B42RT for LTn. During winter (Figure 5(b5)), with four exceptions, all cases had an OP of MERRA-2. Overall, more than 20 cases had MERRA-2 as their OP for spring, autumn, and winter, while TRMM3B42 had fewer than six cases. For summer, the OP was TRMM3B42 for nine cases, ERA-Interim for eight cases, and MERRA-2 for seven cases (Figure 5(c2–c5)).
