## 4 Summary and Conclusions  
In quantitative precipitation estimation based on weather radars, uncertainty propagates at each stage of quality control, precipitation estimation, and post-processing precipitation bias correction. However, existing methods have only improved the understanding and accuracy of the uncertainty at specific stages, and they have not clarified the proportion of uncertainty at each stage related to the total uncertainty. Thus, such methods have been unable to reveal the increase (or decrease) in uncertainty at each stage. Accordingly, this study proposed novel application of three methods for the  
Figure 6: Uncertainty quantification and propagation in the radar-based precipitation estimation process in case of selected superior methods for each stage using (**a**) the MEM, (**b**) the UDM, and (**c**) the M-FUM.  
quantification of uncertainty (i.e., the MEM, UDM, and M-FUM). The MEM was selected to assess uncertainty quantitatively using the ME, which has been used widely for uncertainty quantification. The UDM was developed to analyze the uncertainty at each stage using the ratio of variances of each method based on a Taylor series expansion. Then, the M-FUM modified three uncertainty sources of the FUM to estimate uncertainty in the radar-based precipitation estimation process.  
To test the applicability of the three methods, this study implemented a radar-based precipitation estimation process for the Korean Peninsula, which consisted of two quality control algorithms, two precipitation estimation methods, and two post-processing precipitation bias correction methods in relation to 18 precipitation events that occurred during 2012 to 2016. It was shown that the radar-based precipitation estimates and their corresponding uncertainty could vary depending on the precipitation estimation method applied. In addition, it was revealed that the uncertainty propagation of the MEM, together with the fuzzy algorithm in the quality control stage, WPMM in the precipitation estimation stage, and the LGC method in the post-processing stage could reduce the uncertainty. However, the UDM and M-FUM were responsible for the uncertainty propagation in the same manner as the quantitative uncertainty. Consequently, selecting a method with superior accuracy at each stage will result in the lowest uncertainty.  
Through the novel use of the three uncertainty quantification methods proposed herein, the following advancements could be expected for radar-based precipitation estimation. First, uncertainty could be quantified for the entire process and for each stage. Second, the ratios of uncertainty at each stage to the total uncertainty could be identified. Finally, the uncertainty propagation process could be demonstrated at each stage of the process. With these benefits, the major contributor to uncertainty in radar-based precipitation estimation will be better understood and its impact reduced more effectively.  
Conceptualization, J.-K.L.; methodology, J.-K.L.; investigation, J.-K.L.; writing--original draft preparation, J.-K.L.; writing--review and editing, C.G.S.; supervision, C.G.S.; project administration, C.G.S.; funding acquisition, C.G.S. All authors have read and agreed to the published version of the manuscript. This research received no external funding. This work is supported by the Korea Agency for Infrastructure Technology Advancement (KALA) grant funded by the Ministry of Land, Infrastructure and Transport (Grant 20 DPIPW-C153746-02). The authors declare no conflict of interest.