# Evaluation of IMERG Precipitation Products in the Southeast Costal Urban Region of China
## 3 Methods
### Evaluation Metrics  
This work provides a comprehensive evaluation of the three IMERG products in terms of their ability to estimate precipitation magnitude and capture precipitation events based on six metrics, including the mean bias error (\(MBE\)), correlation coefficient (\(Corr\)), root mean square error (\(RMSE\)), the probability of detection (\(POD\)), the false alarm ratio (\(FAR\)) and the equitable threat score (\(ETS\)). The former three are accuracy metrics to indicate the accuracy of the SPP estimates; while the latter three are detection metrics to measure the agreement of precipitation occurrence observed by the SPPs and the gauges. The six selected metrics are recommended by the World Meteorological Organization (WMO) for the evaluation of quantitative precipitation estimates [63], and have been widely used in many studies [13; 64; 65; 66; 67].  
For the accuracy metrics, \(MBE\) indicates the direction of bias. Positive and negative values of this metric suggest wetter or drier estimates of SPPs, respectively. \(Corr\) is used to describe the linear correlation between the SPP and the gauge data. The closer the value is to 1, the better the linear agreement between the SPP and the gauge records. \(RMSE\) measures the degree of overall error for the SPPs, and a smaller value denotes more accurate SPP estimates. It is worth noting that \(RMSE\) is sensitive to precipitation magnitude, i.e.,\(RMSE\) is likely to be larger for higher-value estimates. The equations of these metrics are as follows:  
\[MBE=\frac{\sum_{i=1}^{n}(x_{i}-y_{i})}{n} \tag{1}\]  
\[Corr=\frac{\sum_{i=1}^{n}(x_{i}-\overline{x})(y_{i}-\overline{y})}{\sqrt{\sum_{i =1}^{n}(x_{i}-\overline{x})^{2}\sum_{i=1}^{n}(y_{i}-\overline{y})^{2}}} \tag{2}\]  
\[RMSE=\sqrt{\sum_{i=1}^{n}\frac{(x_{i}-y_{i})^{2}}{n}} \tag{3}\]  
where \(x\) represents SPP grid estimates, \(y\) denotes the grid-average values of gauge observations, and \(n\) is the total number of SPP estimates. Considering the error magnitude, which is sensitive to precipitation amount, the \(RMSE\) divided by the corresponding real precipitation (\(rRMSE\)) is adopted in the evaluation for urban and non-urban areas.  
For the detection metrics, \(POD\) refers to the proportion of real precipitation events that can be detected by the SPPs (equivalent to the hit rate), and its optimal value is 1. \(FAR\) indicates the proportion of false events captured by the SPPs (implying a misdetection rate), with an optimal value of 0. \(ETS\) measures the overall ability of the SPPs to detect precipitation events after exclusion of hit randomness. When a SPP does not miss or misidentify any precipitation events, it will get the best \(ETS\) score of 1. The metrics are calculated as follows:  
\[POD=\frac{H}{H+M} \tag{4}\]  
\[FAR=\frac{F}{H+F} \tag{5}\]  
\[ETS=\frac{H-H_{e}}{H+M+F-H_{e}},\ H_{e}=\frac{(H+M)(H+F)}{H+M+F+C} \tag{6}\]  
where \(H\) is the number of events observed by both gauge averages and SPPs, \(M\) is the number of events observed by gauge averages but not by SPPs, \(F\) is the opposite of \(M\), \(C\) and is the events not observed by both gauge averages and SPPs, \(H_{e}\) represents the number of events correctly detected by SPPs due to randomness. To determine the presence or absence of a precipitation event, 0.1 mm/h and 1 mm/d are used instead of 0 as the threshold at hourly and daily timescales, respectively, considering the tendency for gauges and satellites to produce large uncertainties for light \"drizzle\".