# Performance Evaluation of IMERG GPM Products during Tropical Storm Imelda
## 3 Results and Discussion
### Exploratory Data Analysis and Visualization
\begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Category** & **Index** & **Formula** & **Range** & **Perfect Value** \\ \hline \multirow{6}{*}{Basic Statistical Indices 1} & Correlation & \(\frac{1}{N}\sum_{n=1}^{N}\left(S\mu_{n}-S\overline{S}\right)\left(Rad_{n}- \overline{Rad}\right)\) & \(\left(-1\right)-\left(+1\right)\) & 1 \\  & Coefficient (CC) 2 & \(\frac{\sum_{n=1}^{N}\left(S\mu_{n}-Rad_{n}\right)}{\sum_{n=1}^{N}\left(S\mu_{n }\right)\left(S\mu_{n}\right)}\) & \(-\infty/+\infty\) & 0 \\  & Relative Bias (RBIAS) & \(\frac{\sum_{n=1}^{N}\left(S\mu_{n}-Rad_{n}\right)}{\sum_{n=1}^{N}\left(S\mu_{n }\right)\left(S\mu_{n}\right)}\) & \(0-\infty\) & 0 \\  & Root Mean Square & \(\sqrt{\frac{1}{N}\sum_{n=1}^{N}\left(S\mu_{n}-Rad_{n}\right)^{2}}\) & \(0-+\infty\) & 0 \\  & Error (RMSE) & \(1-\sqrt{\left[S\mu_{n}\times\left(r-1\right)\right]^{2}+\left[S\mu_{n}\times \left(\beta-1\right)\right]^{2}+\left[S\mu_{n}\times\left(\gamma-1\right)\right] ^{2}}\) & \(\left(-\infty\right)-\left(+1\right)\) & 1 \\  & (KCE) & \(1-\sqrt{\left[S\mu_{n}\times\left(r-1\right)\right]^{2}+\left[S\mu_{n}\times \left(\beta-1\right)\right]^{2}+\left[S\mu_{n}\times\left(\gamma-1\right)\right] ^{2}}\) & \(\left(-\infty\right)-\left(+1\right)\) & 1 \\ \hline \multirow{6}{*}{Probabilistic Statistical Indices 1} & Probability of detection (POD) & \(\frac{C_{\mathrm{S}R}}{C_{\mathrm{S}R}+C_{\mathrm{S}R}S_{\mathrm{c}}}\) & \(0-1\) & 1 \\  & False Alarm Ratio & \(\frac{C_{\mathrm{S}R}}{C_{\mathrm{S}R}+C_{\mathrm{S}R}S_{\mathrm{c}}}\) & \(0-1\) & 0 \\  & (FAR) & & & \\  & & & & \\  & & & \\  & & & \\  & & & \\ \hline \hline \end{tabular} \({}^{1}\) _n_: Sample size; \(S\mu_{n}\): IMERG rainfall estimate; \(Rad_{n}\): Radar rainfall estimate; \(S\mu\): IMERG average rainfall estimate; \(\overline{Rad}\): Radar average rainfall estimate; \(SD_{Sat}\): Standard deviation of IMERG rainfall estimates; \(SD_{Sat}\): Standard deviation of radar rainfall estimates; \(C_{\mathrm{S}R}\): Number of detected rainfall hours recorded by GPM satellite and radar; \(C_{\mathrm{S}R}M_{\mathrm{S}}\): Number of detected rainfall hours recorded by radar but absent in GPM satellite estimates; \(C_{\mathrm{S}R}\): Number of detected rainfall hours recorded by GPM satellite and absent in radar estimates; \(M_{\mathrm{S}R}\): Number of rainfall hours missed by both IMERG and radar products (no estimate). 2 In this study, the negative correlation coefficients were also examined to better understand the discrepancies.  
\end{table} 
Table 1: Statistical performance indicators used for evaluation of the satellite products. When it comes to the maximum recorded grid totals by the products, all three IMERG products reported close enough totals, ranging from 740 mm to 775 mm. However, the maximum precipitation from the radar product was about 1.5 times the IMERG product at the peak grid reported value of 1150 mm. The maps shown in Figure 2 show that the IMERG satellite product generally overestimated the precipitation in the places which received lower precipitation, but underestimated the storm in places where there was very high precipitation. The satellite also did not detect precipitation in some coastal areas where radar products recorded values. All products successfully recoded the center of the storm near the southeast side of the Houston area. Overall, the radar product estimates were more concentrated over the storm center and satellite products covered a larger spatial extent of the southeast Texas region (Houston, Galveston, and Beaumont areas).