Representing Radar Rainfall Uncertainties in Complex Terrain Using A Bayesian Modelling Approach

Substantial biases exist in the operational radar-derived precipitation products and it is difficult to characterize and quantify such biases, especially in complex terrain such as the San Francisco Bay Area. The parameterization errors in radar rainfall algorithms induced by the complex precipitation microphysics along with the uncertainties in radar measurements caused by the sampling geometry pose great challenges in developing the optimized rainfall products. This paper presents a Bayesian framework which is capable of identifying radar-based precipitation estimates in terms of various probabilistic distributions conditional on surface rain gauge (i.e., targeted) measurements. In particular, the probability distribution of the targeted measurements conditional on the radar rainfall products is determined by the Bayes’ theorem. Subsequently, the associated uncertainties in radar estimates are characterized and quantified in terms of probability distributions conditional on the targeted data. The regional distribution of the model parameters is investigated, which links radar-based retrievals and ground references. In addition, the proposed Bayesian model takes into account the wind and terrain topology information aiming to quantify the impact of orographic enhancement on the variability of radar rainfall performance. Case studies using the operational radar hourly rainfall products at 1-km grids are performed during the winter storm seasons in Northern California in 2016-2017 and 2017-2018. Results show that the proposed methodology enhances the rainfall accuracy and reduces its associated uncertainties in terms of a sharper probabilistic distribution curve as more potentially useful information is added under various rainfall regimes. It is also expected that the proposed Bayesian framework can be further enhanced and applied for multi-source precipitation data fusion over this mountainous terrain.