## 4 Results and Discussion
### Statistical Performance of Satellite Precipitation Estimates
Figure 8 displays the error characteristics of satellite precipitation estimates with rain rate. Obviously, all precipitation products showed a similar variation of error, with overestimations for light rain and underestimations for heavy rain (Figure 8a), which is a common error feature of satellite-based retrievals, as documented in previous studies [73; 74; 75]. This error feature of rain-rate dependency is important for meteorological and hydrological applications, especially for typhoon monitoring and flood forecast, which are sensitive to higher rain rates [76; 77]. In terms of RRMSE, higher values were found at low rain rates compared to at moderate-high rain rates (Figure 8b), indicating that current satellite precipitation products need to continue improving the performance at low rain rates. On the other hand, from the results of Figure 8, we can see how the calibration scheme works in precipitation estimates. It is seen that the IMERG-C elevated the precipitation estimates and GSMaP-Gauge decreased the precipitation values compared to their corresponding uncalibrated precipitation products. This gauge-calibration effectively reduced total bias while making things worse in some cases. For example, IMERG-UC overestimated gauge observations at lower rain rates; however, the bias calibration using GPCC gauge data elevated the precipitation estimates further augmenting the overestimation at lower rain rates. Another case involved the GSMaP-Gauge showing large negative hit bias than GSMaP-MVK in the winter season (Table 4). Thus, it seems important to calibrate satellite-based precipitation estimates at difference rain rates or seasons in the future. \begin{table}
\begin{tabular}{c c c c c c} \hline \hline
**Season** & **Product** & **H (\%)** & \(\mathbf{-M\ (\%)}\) & **F (\%)** & **N (\%)** & **E = H \(\mathbf{-M\ +F\ N\ (\%)}\)** \\ \hline Spring & IMERG-UC & \(-27.84\) & \(-28.62\) & \(8.07\) & \(2.04\) & \(-46.35\) \\  & IMERG-C & \(-13.73\) & \(-19.75\) & \(16.66\) & \(3.24\) & \(-13.58\) \\  & GSMaP-MVK & \(18.94\) & \(-22.63\) & \(33.22\) & \(2.41\) & \(31.94\) \\  & GSMaP-Gauge & \(-21.52\) & \(-8.31\) & \(11.14\) & \(3.16\) & \(-15.53\) \\ Summer & IMERG-UC & \(-28.70\) & \(-12.31\) & \(6.36\) & \(0.62\) & \(-34.03\) \\  & IMERG-C & \(-5.89\) & \(-8.20\) & \(10.59\) & \(0.74\) & \(-2.76\) \\  & GSMaP-MVK & \(18.45\) & \(-10.12\) & \(13.99\) & \(0.85\) & \(23.17\) \\  & GSMaP-Gauge & \(-9.47\) & \(-3.26\) & \(9.49\) & \(1.20\) & \(-2.04\) \\ Autumn & IMERG-UC & \(-26.67\) & \(-20.41\) & \(6.69\) & \(1.30\) & \(-39.09\) \\  & IMERG-C & \(-6.72\) & \(-14.80\) & \(12.22\) & \(1.88\) & \(-7.42\) \\  & GSMaP-MVK & \(19.75\) & \(-15.31\) & \(28.57\) & \(2.57\) & \(35.58\) \\  & GSMaP-Gauge & \(-11.85\) & \(-5.85\) & \(11.28\) & \(2.00\) & \(-4.42\) \\ Winter & IMERG-UC & \(-12.94\) & \(-67.39\) & \(4.42\) & \(-0.65\) & \(-76.56\) \\  & IMERG-C & \(-13.16\) & \(-60.48\) & \(9.31\) & \(2.19\) & \(-62.14\) \\  & GSMaP-MVK & \(-6.04\) & \(-55.34\) & \(37.97\) & \(5.07\) & \(-18.34\) \\  & GSMaP-Gauge & \(-32.33\) & \(-28.44\) & \(11.40\) & \(4.31\) & \(-45.06\) \\ All Season & IMERG-UC & \(-27.46\) & \(-19.59\) & \(6.71\) & \(1.01\) & \(-39.33\) \\  & IMERG-C & \(-7.96\) & \(-14.06\) & \(12.14\) & \(1.56\) & \(-8.32\) \\  & GSMaP-MVK & \(17.89\) & \(-15.59\) & \(22.09\) & \(1.72\) & \(26.11\) \\  & GSMaP-Gauge & \(-13.35\) & \(-5.84\) & \(10.30\) & \(1.90\) & \(-6.99\) \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Seasonally averaged error components as percentages of total observed precipitation. Figure 8: The relationship between the validation indices and precipitation rate: (**a**) RB, and (**b**) RRMSE.