Calibration of the reflectivity-rainfall rate (Z-R) relationship using long-term radar reflectivity factor over the entire South Korea region in a Bayesian perspective

Abstract

A fixed Z-R relationship approach, such as the Marshall-Palmer relationship, for an entire year and for different seasons can be problematic in cases where the relationship varies spatially and temporally throughout a region. From this perspective, this study explores the use of a long-term radar reflectivity factor for South Korea to obtain a nationwide calibrated power law relationship, Z=α∙Rβ, where R is the rainfall intensity and Z is the reflectivity factor, in the context of bias-correction and the associated uncertainties within a Bayesian regression framework. This study also investigates seasonal differences in the bias-correction parameters (i.e., additive and multiplicative bias-correction factors) and their roles in reducing systematic error. Distinct differences in the calibrated parameters over stations are identified, and more importantly, an inverse relationship between the two reflectivity parameters α and β (i.e., decreasing trend in β with increasing α) is clearly identified with different parameter space based on the seasons. A spatially structured pattern in the parameters exists, particularly parameter α, for the wet season and parameter β for the dry season. A pronounced region of high values in the power law parameters (i.e., α and β) during the wet and dry seasons may be partially due to the overestimation of the radar reflectivity factor associated with enhancement of moisture transport directly over the coastal region. Finally, the radar rainfall estimates through the calibrated Z-R relationship are compared with the currently used Z-R relationships for estimating stratiform rainfall and convective rainfall. Overall, the radar rainfall fields based on the proposed modeling procedure are similar to the observed rainfall fields, whereas the radar rainfall fields obtained from the currently used Marshall-Palmer Z-R relationship show a systematic underestimation. The calibrated Z-R relationships are further validated by testing the predictions of unseen radar-gauge pairs in the year 2018, in the context of cross-validation. The cross-validation results are largely similar to those in the calibration process, suggesting that the derived Z-R relationships fit the radar-gauge pairs reasonably well.