## 3 Application of Uncertainty Quantification Methods and Results
### Results and Discussion of Uncertainty Quantification  
#### 3.3.1 Analysis of Quantified Uncertainty  
In this study, the uncertainty quantification methods were applied to generate a radar-based precipitation estimate, and the results of the uncertainty quantification are shown in Table 3 and Figure 5. In Table 3 and Figure 5, the results at each stage were obtained by averaging the data from the 18 precipitation events. During installation, radar hardware is adjusted and internally calibrated. In addition, when a weather radar receives signals, it stores data in its internal hardware, which is referred to as level zero. However, it is difficult to access the level zero data through the hardware process. Thus, this study employed the level one data which are produced by applying threshold variable and speckle filter to level zero data. In brief, because of data limitations in the radar-based precipitation estimation process, the signal processing stage was not considered; therefore, the initial uncertainty was assumed to begin with the quality control stage. In the results of applying the MEM, Table 3a and Figure 5a show that the ME values (MEV) of the ORPG and fuzzy algorithms in quality control were 4.28 and 4.15, respectively, the MEVs of the WPMM and M-P relations in precipitation estimation were 3.90 and 4.53, respectively, and the MEVs of the LGC and G/R ratio methods in post-processing were estimated at 3.77 and 3.81, respectively. From these results, it can be determined that the initial uncertainty was 4.28 (same as the MEVs of quality control) and the final uncertainty was estimated at 3.81 (same as the MEVs of the post-processing). Assuming that the final uncertainty was 100%, the MEVs of the quality control stage and the radar-based precipitation estimation stage were 112% and 119%, respectively, which implies that the uncertainty in the radar-based precipitation estimation increased in comparison with the initial uncertainty of the quality control stage. However, the uncertainty then decreased in the post-processing stage, and the final uncertainty was reduced in comparison with the initial uncertainty. The reason is that, although the MEV of the WPMM was 3.90, the MEV of the M-P relation was 4.53, which shows that the M-P relation was the major contributor to the increasing uncertainty in the precipitation estimation stage. This implies that radar-based precipitation estimates and their corresponding uncertainty are dependent on the applied methodology. \begin{table}
\begin{tabular}{c c c c c c} \hline \hline  & & \multicolumn{3}{c}{(a) MEM.} \\ \hline \multirow{2}{*}{**Procedure**} & \multirow{2}{*}{**MEV \({}^{**}\)**} & **Maximum** & \multirow{2}{*}{**Incremental**} & \multirow{2}{*}{**Ratio (\%)**} \\  & & & **of ME** & & **to the Final Uncertainty** \\ \hline \multirow{2}{*}{\begin{tabular}{c} Initial uncertainty \\ \end{tabular} } & \multirow{2}{*}{4.28} & \multirow{2}{*}{4.28} & \multirow{2}{*}{-} & \multirow{2}{*}{112} \\  & ORPG & 4.28 & & & \\ \cline{2-2} \cline{5-5}  & Fuzzy & 4.15 & & & \\ \hline \multirow{2}{*}{\begin{tabular}{c} RPE \({}^{*}\) \\ \end{tabular} } & \multirow{2}{*}{WPMM} & \multirow{2}{*}{3.90} & \multirow{2}{*}{4.53} & \multirow{2}{*}{0.25} & \multirow{2}{*}{119} \\  & M–P & 4.53 & & & \\ \hline \multirow{2}{*}{\
\begin{tabular}{c} PBC \({}^{*}\) \\ \end{tabular} } & \multirow{2}{*}{LGC} & \multirow{2}{*}{3.77} & \multirow{2}{*}{3.81} & \multirow{2}{*}{\(-\)0.72} & \multirow{2}{*}{
\begin{tabular}{c} 100 \\ (\(-\)19) \\ \end{tabular} } \\  & G/R ratio & 3.81 & & & \\ \hline \multicolumn{2}{c}{Final uncertainty} & \multirow{2}{*}{3.81} & \multirow{2}{*}{3.81} & \multirow{2}{*}{-} & \multirow{2}{*}{100} \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Comparison of uncertainty quantification results for each stage in the radar-based precipitation estimation process using the MEM, UDM, and M-FUM.