**3. Methods**

#### *3.1. Contingency Statistical Indices*

Four indices are used to assess the contingency of satellite precipitation estimates. The probability of detection (POD) represents the proportion of correctly detected precipitation occurrences to the total number of events detected by satellites. The false alarm ratio (FAR) indicates the ratio of rainfall events that are falsely alarmed among the total number of satellite-detected precipitation occurrences. The frequency bias index (FBI) shows the degree of precipitation occurrence estimates from satellites. In other words, it indicates the overestimated or underestimated tendency in satellite-detected precipitation occurrences. The critical success index (CSI) denotes the fraction of rainfall events detected by satellites correctly to the total number of observed or detected rainfall events [30]. The indices mentioned above have no consideration of random assignments [31]. The equations of these indicators are given in Table 1. To discriminate between wet and dry samples, the thresholds of 1 mm day-1 for daily rain events and 0.1 mm hour-1 for hourly ones were used. [6].


**Table 1.** Equations and the best values of four contingency statistical indices.

1 H(Hit) means that the precipitation occurrence is observed by a ground station as well as a satellite; M(Miss) denotes that the ground station observes the occurrence, while the satellite dose not detect it; F(False) indicates that the unobserved precipitation event is falsely detected by the satellite.

#### *3.2. Statistical Indices*

Four commonly used diagnostic statistics, including the correlation coe fficient (CC), root mean square error (RMSE), relative bias (bias), and mean absolute error (MAE), were applied in this study to quantify the consistency between satellite precipitation products and rain gauge measurements. The four indices were also used to cross-evaluate satellite precipitation products without rain gauge measurements. The equations of these four statistical indices are shown in Table 2.


**Table 2.** Equations and the best values of four statistical indices.

1 *n* means the number of precipitation pairs in the analysis; *Gi* means ground-based precipitation measurements; *G* means the average ground-based precipitation measurements; *Pi* and *P* represent satellite precipitation products and their average, respectively.
