###### Abstract  
Several sources of bias are involved at each stage of a quantitative precipitation estimation process because weather radars measure precipitation amounts indirectly. Conventional methods compare the relative uncertainties between different stages of the process but seldom present the total uncertainty. Therefore, the objectives of this study were as follows: (1) to quantify the uncertainty at each stage of the process and in total; (2) to elucidate the ratio of the uncertainty at each stage in terms of the total uncertainty; and (3) to explain the uncertainty propagation process at each stage. This study proposed novel application of three methods (maximum entropy method, uncertainty Delta method, and modified-fractional uncertainty method) to determine the total uncertainty, level of uncertainty increase, and percentage of uncertainty at each stage. Based on data from 18 precipitation events that occurred over the Korean Peninsula, the applicability of the three methods was tested using a radar precipitation estimation process that comprised two quality control algorithms, two precipitation estimation methods, and two post-processing precipitation bias correction methods. Results indicated that the final uncertainty of each method was reduced in comparison with the initial uncertainty, and that the uncertainty was different at each stage depending on the method applied.  
Keywords: radar-based precipitation; uncertainty quantification; uncertainty propagation; maximum entropy; delta method; fractional uncertainty method +
Footnote †: journal: Medical  
quality control of radar variables [15], how to handle the relations between observed precipitation and radar variables [16; 17; 18; 19], how to merge radar-based precipitation related to gauge stations, and various other issues (e.g., automatic hardware/software calibration for radar variables and the quantification of reflectivity bias). As mentioned before, previous studies on radar uncertainty have focused primarily on the correction of bias in estimating precipitation notwithstanding various radar uncertainties [15; 16; 17; 18; 19; 20; 21].  
The methods generally considered in previous studies have a number of limitations. (1) The methods have difficulties in demonstrating the total uncertainty in a quantifiable way; instead, they quantify uncertainty only at specific stages. (2) As the total uncertainty cannot be quantified, the difficulty in comparing the uncertainty between previous or subsequent stages makes identification of the stage that is the major (or minor) contributor to the total uncertainty complicated. (3) It is difficult to determine how the uncertainty is propagated at each stage. For example, previous studies have failed to analyze comprehensively both the total uncertainty and the uncertainty at each stage of the radar-based estimation process.  
This study proposed novel application of three methods to improve upon the previous approaches by quantifying the uncertainty of radar-based precipitation estimation throughout the entire process (i.e., from quality control to radar precipitation estimation), and by assessing the magnitude of the uncertainty propagated at each stage. The findings of this study will be beneficial to the implementation of quality control, precipitation estimation, and post-processing stages for bias correction in radar-based precipitation estimates.