2.3.2. Statistical Analysis

Several statistical metrics were calculated to quantify the accuracy or differences between observation and estimated precipitation from SBP products based on monthly scale data. The correlation coefficient (R, Equation (1)) was used to measure the strength and direction of the linear association between datasets. The Relative Root Mean square Error (RRMSE, Equation (2)) which reflects the average magnitude of the deviation that a dataset will have from the gauge observed data; and mean bias (MB, Equation (3)) and absolute relative error (RE, Equation (4)) which measure any persistent tendency of a dataset to either overestimate or underestimate and the discrepancies between the magnitude of the estimated precipitation and the gauge observed dataset. Graphical

plots and different statistical measures were used to facilitate the inter-comparison between the SBP and gauge observed datasets. The formulae for the statistical metrics are:

$$R = \frac{\sum\_{i=1}^{n} \left(\mathbf{O\_i} - \overline{O}\right) \left(\mathbf{E\_i} - \overline{E}\right)}{\sqrt{\sum\_{i=1}^{n} \left(\mathbf{O\_i} - \overline{O}\right)^2} \sqrt{\sum\_{i=1}^{n} \left(\mathbf{E\_i} - \overline{E}\right)^2}}\tag{1}$$

$$RRMSE = \frac{\sqrt{\frac{\sum\_{i=1}^{n} (E\_i - \mathbf{O}\_i)^2}{n}}}{\overline{O}} \tag{2}$$

$$MB = \frac{\left(\overline{E} - \overline{O}\right)}{\mathbf{n}}\tag{3}$$

$$RE = \left| \frac{\text{MB}}{\overline{\text{O}}} \right| \tag{4}$$

where O is the gauge observation data, E is the estimated precipitation data using SBP products, O and E denotes the average value of their respective datasets, and n is the sample size. The perfect score for RRMSE, MB, and RE is ~0, while for R is 1.

**Figure 2.** The flowchart of the overall processes followed in the study.

Additionally, a daily performance assessment was calculated for all SBP data based on categorical statistics. These statistics were computed for the individual stations to quantify the capacity to detect daily precipitation events. The statistics are based on a contingency table (Table 2) with two possible cases: a day with or without precipitation. In Table 2, a and d indicate the total events above 1 mm/day recorded by both datasets (gauge observed and SPB), while c and d indicate the total events recorded by both datasets below this threshold. This threshold value was selected to avoid the measurement error from the manual gauge system for the light precipitation amount (less than 1 mm/day).


No-precipitation

**Table 2.** Contingency table to define daily precipitation based categorical scores for the evaluation of SBP with gauge observation.

In this study, three categorical indices were used for the assessment: the probability of detection (POD, Equation (5))—SBP's capacity to forecast the precipitation events accurately, and ranges from 0 to 1 (with 1 being an accurate score); False Alarm Ratio (FAR, Equation (6)), which represents how often the SBP's falsely detect a gauge observed precipitation event and ranges from 0 to 1 (with 0 being a perfect score); and Accuracy (ACC, Equation (7)), which is the fraction of all SBP product-based events that were correct, this has values ranging from 0 to 1, with 1 being a perfect score. All these metrics were computed for individual stations using respective daily precipitation series for the study period, with a threshold value of 1 mm/day to separate precipitation and no-precipitation events. The formulas for these statistical metrics are as follows:

$$POD = \frac{a}{(a+c)}\tag{5}$$

a b c d

$$FAR = \frac{b}{(a+b)}\tag{6}$$

$$\text{ACC} = \frac{a+d}{(a+b+c+d)}\tag{7}$$
