*2.2. Methodolody*

The precipitation trends were calculated using

$$y = at + b \tag{1}$$

where *y* is annual or seasonal accumulative precipitation; *t* refers to time; *a* represents the slope coefficient, namely, linear trend; and *b* is the constant. Pearson's correlation and the two-tailed Student's *t* test (i.e., *p* < 0.05) were applied to check for statistically significant relationships.

Satellite-based and reanalysis precipitation trends were quantitatively assessed with the metrics of bias (B), which measured the trend differences between the products and the gauge observations; root mean square error (RMSE), which represented the overall accuracy of the trends derived from the products; the correlation coefficient (CC), which quantified the spatial consistency of the trends derived from the products; and accuracy of sign (AS), which examined the degree of agreement between the positive or negative sign of precipitation trends from the products and the observed data. These metrics were calculated using the following equations:

$$\mathcal{B} = \overline{a\_P} - \overline{a\_O} \tag{2}$$

$$\text{RMSE} = \sqrt{\frac{1}{N} \sum\_{i=1}^{N} \left( a\_{O,i} - a\_{P,i} \right)^2} \tag{3}$$

$$\text{CC} = \frac{\sum\_{i=1}^{N} (a\_{O,i} - \overline{a\_O})(a\_{P,i} - \overline{a\_P})}{\sqrt{\sum\_{i=1}^{N} (a\_{O,i} - \overline{a\_O})^2 \sum\_{i=1}^{N} (a\_{P,i} - \overline{a\_P})^2}} \tag{4}$$

$$\text{AS} = \frac{nP}{nG} \tag{5}$$

where *aP,i* and *aO,i* represent the linear trends from a certain precipitation product and the gauge observation at the *i*th grid, respectively; *N* is the number of the used grids for evaluation across MC or each WRR; *aP* and *aO* represent the products and the observed trends averaged at the grids within MC or a certain WRR, respectively; and *nP* is the number of the grids, where the examined products shows the same sign of precipitation (e.g., Pwd, Pd or Pn) changes as the observed within a given region, but *nG* indicates the total number of grids in the region.

Considering the co-variation of Pd and Pn, we defined a joint AS (JAS), which represented the capacity of a given product to rightly detect the signs of both Pd and Pn changes relative to the observed data. JAS can be calculated by

$$\text{JAS} = \frac{nP\_{co}}{nG} \tag{6}$$

where *nPco* is the number of the grids in which the signs of both Pd and Pn changes derived from the products are the same as those observed in a given region.
