*3.5. Evaluation Using Metric of Sign Accuracy*

To examine the degree of agreement between the positive or negative sign of LTs from the products and the observed values, metrics of AS and JAS were computed over MC and are illustrated in Figure 7(a1–a5) and Figure 8(a1–a5), respectively. At the annual scale, MC AS values for LTwd, LTd, and LTn from all products were > 50%. This suggests that the observed signs of LTs can be captured by the products, among which TRMM3B42RT, TRMM3B42, and MERRA-2 showed AS values > 70% for the three LTs, followed by PERSIANN, PERSIANN-CCS, ERA-Interim, and NCEP2 with values > 60% (Figure 7(a1)). During each season (Figure 7(a2–a5)), TRMM3B42RT, TRMM3B42, PERSIANN, PERSIANN-CCS, ERA-Interim, and MERRA-2 showed MC AS values > 60% for the three LTs, and the largest percentage (>70%) was found for TRMM3B42RT (except in winter), TRMM3B42 (except in winter), and MERRA-2. For the remaining six products, their AS-based performances differed among seasons. For example, all of them corresponded to autumn AS values > 50% for the three LTs; however, the values in the other seasons were generally < 50%. As shown in Figure 7(b1–b5), MC annual and summer AS-based OPs were MERRA-2 for LTwd, but TRMM3B42 for LTd and LTn. For MC LTs in the remaining three seasons, the AS-based OP was MERRA-2, except for spring LTd. Of the 30 annual cases in ten WRRs, AS-based OPs were MERRA-2 in 13 cases, TRMM3B42 in six cases and TRMM3B42RT in three cases, and there was more than one OP in five cases (Figure 7(b1–c1)). Among the ten WRRs, there were five or more OPs for each of the three LTs, indicating obvious regional differences for the products in detecting the same signs of LTs. In spring (Figure 7(b2–c2)), the AS-based OPs were MERRA-2 (15 cases), TRMM3B42 (five cases), TRMM3B42RT (four cases), ERA-Interim (four cases), and PERSIANN (two cases). Southern WRRs generally had OPs of TRMM3B42, TRMM3B42RT, and PERSIANN, while the OPs for northern WRRs were MERRA-2 and ERA-Interim. During summer (Figure 7(b3–c3)), AS-based OP was TRMM3B42 in 14 cases, mainly in southern WRRs, HaRB, YRB, and HuRB; and the OP was MERRA-2 in nine cases primarily in SHRB, LRB and NWRB. Of the 30 cases in autumn (Figure 7(b4–c4)), MERRA-2 was identified as the AS-based OP in 14 cases mainly in northern WRRs (excluding YRB), however, in eight cases the OP was TRMM3B42 generally in YRB, YZRB, and SWRB. Each of the six autumn cases in SERB and PRB had more than one OP. Regarding the 30 cases in winter (Figure 7(b5–c5)), 26 cases had AS-based OPs of MERRA-2 (22 cases) and TRMM3B42RT (four cases).

**Figure 7.** MC accurate sign (AS) values derived from the selected 12 precipitation products (**a1**–**a5**), AS-based optimal products (OPs) for MC and ten WRRs (**b1**–**b5**), and the number of cases corresponding to AS-based OPs (**c1**–**c5**) for the annual or seasonal scales in ten WRRs. For figures (**a1**–**a5**), AS is computed with Equation (5), indicating the degree of agreement between the positive or negative sign of precipitation trends from the products and the observed data. In figures (**b1**–**b5**), the number in each box represents AS values (%) of the OP, which have been labelled with different colors. The number of figures (**c1**–**c5**) indicates the amount of a certain OP.

Except for TRMM3B42RT, TRMM3B42, and MERRA-2 with annual JAS values > 55% (Figure 8(a1)), values of this metric were all below 50%, suggesting that these products have limited capacity to detect the co-variations of daytime and nighttime precipitation, in spite of relatively large AS for LTs (Figure 7(a1)). In spring (Figure 8(a2)), the best JAS-based performance was found in TRMM3B42 and MERRA-2 (with JAS around 60%), followed by TRMM3B42RT and ERA-Interim. Excluding PERSIANN and PERSIANN-CCS, the other six products had spring JAS values < 25%. JRA-55 and ERA-5 had JAS < 20%, which indicated that those six products could not capture the co-variations of spring precipitation changes at daytime and nighttime. During summer (Figure 8(a3)), TRMM3B42RT, TRMM3B42, and MERRA-2 performed the best (with JAS values > 53%), followed by PERSIANN, PERSIANN-CCS, and ERA-Interim with the next best performance (with JAS around 45%), and the remaining products (with JAS around 30%). For autumn (Figure 8(a4)), seven of the products correctly detected the co-variations of daytime and nighttime precipitation changes in >50% grids (i.e., JAS > 50%), particularly for TRMM3B42RT, TRMM3B42, ERA-Interim, and MERRA-2, which had JAS values > 64%. GSMaP-RNL and NCEP1 had JAS values near to 40% and performed the worst. Regarding winter JAS (Figure 8(a5)), values > 50% only appeared for MERRA-2, and the minima (around 25%) were found in GSMaP-RNL, GSMaP-RNLG, and NCEP2. As depicted in Figure 8b, MC annual and summer JAS-based OP was TRMM3B42, but for the other seasons the OP was MERRA-2. Except for SHRB and NWRB, with MERRA-2 as their annual JAS-based OP, the remaining WRRs generally had TRMM3B42 as the OP (Figure 8b). In southern WRRs, most had OPs of TRMM3B42 and

PERSIANN in spring and summer but MERRA-2 and PERSIANN in autumn and winter. By contrast, summer JAS-based OPs were MERRA-2 and TRMM3B42 in northern WRRs, while MERRA-2 was the OP in most northern WRRs.

**Figure 8.** MC joint AS (JAS) values derived from the selected 12 precipitation products (**a1**–**a5**), and JAS-based optimal products (OPs) for MC and ten WRRs (**b**). For figures (**a1**–**a5**), JAS is computed with Equation (6), indicating the capacity of a given product to rightly detect the signs of both Pd and Pn changes relative to the observed data. In (**b**), the number in each box represents JAS values (%) of the OP, which has been labelled with different colors.
