A Bayesian partial pooling approach to mean field bias correction of weather radar rainfall estimates: Application to Osungsan weather radar in South Korea

The use of radar rainfall estimates has been limited by the lack of a reliable method of obtaining operationally accurate radar-based rainfall estimates and the associated potential errors embedded in the retrieval process. Moreover, the existing approaches have difficulty merging ground- and radar-based measurements due to spatial and temporal variations in bias as well as the uncertainties in model parameters that also can affect the overall bias. This study proposes a novel approach for radar rainfall estimates using a hierarchical Bayesian model (HBM) in the context of bias correction. In particular, three different variations (i.e. the partial-pooling model (PPM), complete-pooling model (CPM), no-pooling model (NPM)) of the HBM are explored to better characterize the bias correction factor and the associated uncertainty. In the case of the CPM, rain gauges are assumed to have a constant bias level over the spatial domain, which results in a significant increase in RMSE. Conversely, in the NPM approach, the parameters are independently estimated for each station, resulting in an increase in the uncertainty of the parameters caused by compensating for the estimates of other parameters; this approach also leads to a substantial increase in the RMSE. Here, we introduce the PPM approach, which aims to jointly estimate correction factors across all gauging stations, while considering the covariance structure of both parameters and model errors. The results obtained for the PPM show a noticeable reduction in the uncertainty of the parameters when compared to that of the NPM. We also note a decline in the bias of radar rainfall estimates. Finally, we further utilize the proposed PPM-based bias correction approach as an ensemble generator for simulation of radar rainfall estimates. The simulated rainfall ensembles can satisfactorily reproduce key statistical properties retrieved from ground reference measurements.