**Appendix A**

The effectiveness of precipitation estimations was measured via the following metrics: the root mean square error (RMSE), bias, the mean absolute error (MAE), and the correlation coefficient (CC):

$$Bias = \frac{\sum\_{i=1}^{n} (P\_{S\_i} - P\_{O\_i})}{N} \qquad (mm), \tag{A1}$$

$$\text{CC} = \frac{\sum\_{i=1}^{N} \left( P\_{S\_i} - \overline{P}\_S \right) \left( P\_{O\_i} - \overline{P}\_O \right)}{\sqrt{\sum\_{i=1}^{N} \left( P\_{S\_i} - \overline{P}\_S \right)^2} \sqrt{\sum\_{i=1}^{N} \left( P\_{O\_i} - \overline{P}\_O \right)^2}} \tag{A2}$$

$$RMSE = \sqrt{\frac{1}{N} \sum\_{i=1}^{n} \left(P\_{S\_i} - P\_{O\_i}\right)^2} \text{ (mm)},\tag{A3}$$

$$MAE = \frac{\sum\_{i=1}^{N} \left| P\_{S\_i} - P\_{O\_i} \right|}{N} \text{ (mm)},\tag{A4}$$

where *PSi* and *POi* are the value of satellite/reanalysis precipitation estimates and the value of rain-gauge observations, respectively; *i* is the index of the station number and N the total number of stations; *PS* and *PO* are the average value of satellite precipitation estimates and rain-gauge observations for *N* stations over the study area.

Another assessment technique of satellite/reanalysis precipitation estimation is using a contingency table that reflects the frequency of "Yes" and "No" of the precipitation estimation products


**Table A1.** Contingency table.

A dichotomous estimate says, "Yes, an event will happen", or "No, the event will not happen". By using this table for daily precipitation, a set of statistical indices are shown as follows:

Probability of detection (POD) responds to the question of what fraction of the observed "Yes" events were correctly estimated/forecasted. The perfect score is 1:

$$POD = \frac{\text{hits}}{\text{hits} + \text{misses}'} \tag{A5}$$

False alarm ratio (FAR) deals with the question of what fraction of the estimated/forecasted "Yes" events did not occur. The ideal score is 0:

$$FAR = \frac{false\,\,alarms}{hits + false\,\,alarms'} \tag{A6}$$
