A Bayesian Kriging model applied for spatial downscaling of daily rainfall from GCMs

Daily rainfall simulated by General Circulation Models (GCMs) are usually provided on coarse grids and need some adjustment (i.e., bias correction) to meet historical statistics observed in gauged-based data. Moreover, for hydrological applications, the simulated rainfall is needed at fine, user-specified grids to be used as input into hydrological models. Simulated rainfall also must preserve the spatial variability observed in gauged data. Here we explore an alternative approach to downscale daily GCM rainfall simulation at any desired grid resolution using a Bayesian Kriging (BK) model, that better addresses parameter uncertainties compared with traditional approaches. The BK model also attempts to reproduce, using downscaled rainfall, the spatial variability observed in gauged rainfall data. The proposed model is tested using historical data from 59 rainfall gauges located in South Korea, and from retrospective simulations and projected climate change scenarios simulated by the Met Office Hadley Centre HadGEM2-AO model. In the first step, a Bernoulli-Gamma Bayesian model is fit to the observed daily rainfall. The resulting parameters are interpolated into a fine-resolution grid through the BK model, where the uncertainties are considered and a set of parameters for downscaling and bias-correction through quantile mapping (QM) is generated for the fine-resolution grid. In the second step, a Bernoulli-Gamma model is fit to the gridded daily rainfall simulated by the HadGEM2-AO model, and a QM (or parametric distribution mapping) is employed to simultaneously downscale and correct the bias from the retrospective daily rainfall simulated by the GCM. The results show the adequacy of the proposed model to downscale GCM-determined daily rainfall at any specified grid-scale, accounting for bias-correction and parameter uncertainties. The spatial variability observed in the gauged data was reasonably well reproduced in retrospective GCM rainfall. For future rainfall, the proposed model allowed identification of an increase in spatial variability in the HadGEM2-AO simulations of scenario RCP6. The BK model can easily be extended to other applications, including downscaling of temperature or future rainfall simulated from other models and approaches.