## 3 Results and Discussion  
### Spatial Distributions of Continuous Error Metrics  
As India receives about three-fourths of its annual precipitation from the southwest monsoon rainfall and it exhibits substantial spatial and temporal variability [49], this study is restricted to the monsoon rainfall spanning from June to September. Figure 2 shows the spatial distributions of 4-year mean monsoon rainfall from the IMD rain-gauge-based data and IMERG estimates. In order to compare the error characteristics in IMERG-F V6 during pre-GPM and GPM periods, monsoon precipitation from the rain-gauge-based dataset and IMERG-F V6 product for 2010-2013 has also been shown in the lower panel of the figure. The well-known large-scale features of the southwest monsoon rainfall such as higher rainfall over the west coast and northeast India, moderate rainfall over central India and foothills of the Himalayas, and low or negligible rainfall over the southeast peninsula and western parts of India are captured reasonably well by the IMERG estimates qualitatively. However, the magnitude of monsoon rainfall in IMERG estimates differs from the rain-gauge-based data. Near-real-time IMERG products (e.g., IMERG-E and IMERG-L) generally show higher mean rainfall than the research product (e.g., IMERG-F). A 20-year comparison of Early and Final Runs of IMERG V6 showed that IMERG-E provides about 12% higher annual rainfall than IMERG-F product at a global scale [50]. The differences \begin{table}
\begin{tabular}{c c c} \hline \hline
**Error Metrics** & **Formulae** & \\ \hline Bias (mm day\({}^{-1}\)) & \(\begin{array}{c}Bias=S-G\\ \text{where, }S=\sum_{i=1}^{N}S_{i}/N\text{ and }G=\sum_{i=1}^{N}G_{i}/N \\ r=\frac{\sum_{i=1}^{N}\left(G_{i}-G\right)\left(S_{i}-S\right)}{\left[\sum_{i=1 }^{N}\left(G_{i}-G\right)^{2}\times\sum_{i=1}^{N}\left(S_{i}-S\right)^{2}\right] ^{1/2}}\\ \text{Coefficient of variation (\%)}\\ \end{array}\) & \(\begin{array}{c}\left(CV\right)_{S}=\frac{\left[\sum_{i=1}^{N}\left(S_{i}-S \right)^{2}\right]^{1/2}}{\text{G}}\times 100\%\\ \left(CV\right)_{G}=\frac{\left[\sum_{i=1}^{N}\left(G_{i}-G\right)^{2}\right] ^{1/2}}{\text{G}}\times 100\%\\ \text{Root mean square error (mm day${}^{-1}$)}\\ \end{array}\) & \(\begin{array}{c}RMSE=\left[\frac{\sum_{i=1}^{N}\left(S_{i}-G\right)^{2}}{N} \right]^{\frac{1}{2}}\\ \end{array}\) \\ Modified Kling–Gupta efficiency & \(\begin{array}{c}KGE=1-\left[\left(r-1\right)^{2}+\left(\frac{\xi}{\xi}-1 \right)^{2}+\left(\frac{\left(CV\right)_{\xi}}{\left(CV\right)_{\xi}}-1\right) ^{2}\right]^{\frac{1}{2}}\end{array}\) \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Formulae for the computation of continuous error metrics used in this study. \(S_{i}\) and \(G_{i}\) denote precipitation estimates from the IMERG and rain-gauge-based products, respectively, and \(N\) is the total number of colocated points. \begin{table}
\begin{tabular}{c c c c} \hline \hline  & **Formulae** & **Range** & **Perfect Score** \\ \hline Probability of Detection & \(\begin{array}{c}POD=\frac{H}{H+M}\end{array}\) & 0 to 1 & 1 \\ False Alarm Ratio & \(\begin{array}{c}FAR=\frac{H}{H+FA}\end{array}\) & 0 to 1 & 0 \\ Frequency Bias Index & \(\begin{array}{c}FBI=\frac{H+FA}{H+M}\end{array}\) & 0 to \(\infty\) & 1 \\ Peirce\({}^{\prime}\)s Skill Score & \(\begin{array}{c}PSS=\frac{H}{H+M}-\frac{FA}{FA+CN}\end{array}\) & \(\begin{array}{c}-1\text{ to }1\end{array}\) & 1 \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Formulae, range, and perfect score of four categorical skill metrics used in this study. \(H\) (Hits) is the number of events when both IMERG and rain-gauge-based products detect rainy days, \(FA\) (False Alarms) is the number of events when only IMERG detects rainy days, \(M\) (Misses) is the events when only rain-gauge-based product detect rainy days, and \(CN\) (Correct Negatives) is the number of events when both IMERG and rain-gauge-based products detect non-rainy days. between both products were found to be small in cold regions and large in arid regions.