# Evaluation of Global Precipitation Products over Wabi Shebelle River Basin, Ethiopia
## 3 Methodology
### Evaluation Performance Indices  
The quantitative and categorical evaluation indicator methods were carefully selected according to robustness, common usage, and recommendation in previous studies [39]. These performance indicators are described at [[https://www.cawc.gov.au/projects/verification/](https://www.cawc.gov.au/projects/verification/)]([https://www.cawc.gov.au/projects/verification/](https://www.cawc.gov.au/projects/verification/)) (accessed on 12 May 2017), implemented within the Climate Data Tool (CDT). Performance was assessed through quantitative evaluation indicators such as the coefficient of determination (\(R^{2}\)) (Equation (1)), percentage bias (Pbias) (Equation (3)), bias (Equation (4)), Pearson's correlation coefficient (CC) (Equation (2)), and root-mean-square error (RMSE) (Equation (5)). CC justifies the relationship between the exact values of two variables (independent and dependent). Values range between zero (no correlation) and one (perfect correlation). \(R^{2}\) measures how well the independent variables explain the dependent variable in a regression. Values range between zero (no correlation) and one (perfect correlation). Bias describes the extent to which the observed value is underestimated or overestimated. The RMSE represents how closely the satellite observation predicts the measured value.  
\[R^{2} =1-\frac{\sum_{i=1}^{n}\left(\text{S}_{i}-\text{G}_{i}\right)^{2}}{ \sum_{i=1}^{n}\left(\text{S}_{i}-\overline{\text{S}}\right)^{2}}, \tag{1}\] \[\text{CC} =\frac{\sum_{i=1}^{n}\left(\text{S}_{i}-\overline{\text{S}} \right)\left(\text{G}_{i}-\overline{\text{G}}\right)}{\sqrt{\sum_{i=1}^{n} \left(\text{S}_{i}-\overline{\text{S}}\right)^{2}\cdot\left(\text{G}_{i}- \overline{\text{S}}\right)^{2}}},\] (2) \[\text{Pbias} =\frac{\sum_{i=1}^{n}\left(\text{S}_{i}-\text{G}_{i}\right)}{ \sum_{i=1}^{n}\text{G}_{i}}\times 100\%,\] (3) \[\text{Bias} =\frac{\sum_{i=1}^{n}\left(\text{S}_{i}-\text{G}_{i}\right)}{ \sum_{i=1}^{n}\text{G}_{i}},\] (4) \[\text{RMSE} =\sqrt{\frac{\sum_{i=1}^{n}\left(\text{S}_{i}-\text{G}_{i}\right) ^{2}}{n}}, \tag{5}\]  
where \(\text{G}_{i}\) and \(\text{S}_{i}\) represent the gauge and global precipitation data on the i-th day, i is the index, and \(\overline{\text{S}}\) & \(\overline{\text{G}}\) are the average values of \(\text{S}_{i}\) and \(\text{G}_{i}\), respectively.  
The ability of global precipitation estimates to determine the existence of precipitation rates was tested using the probability of detection (POD) (Equation (6)). POD was employed to evaluate the likelihood of the observed precipitation event being correctly detected by the satellite estimate. A dichotomous estimate that says \"yes, an event will happen\" or \"no, an event will not happen\" was used to quantify the metrics, as shown in Table 2. For this application, a rainfall threshold value of 1 mm was applied to decide the occurrence of a rainy or non-rainy day [25; 33].  
\[P\mathrm{OD}=\frac{\mathrm{hits}}{\mathrm{hits}+\mathrm{misses}}, \tag{6}\]  
where the absolute score of \(P\mathrm{OD}\) varies from 0-1.