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Spatio-temporal Bayes Regression with INLA in Statistical Downscaling Modeling for Estimating West Java Rainfall

Statistical downscaling (SD) is one of the techniques used in climate modeling by utilizing global scale data using general circulation models (GCM) output data, to obtain conclusions on a local scale such as rainfall. Currently, the inference of Bayes spatio-temporal regression in SD modeling is still used MCMC method, with convergence issue problem and very high demands for computational resources. When the spatio-temporal model is complex and designed hierarchically, MCMC computing becomes inefficient. Therefore, this paper aims to predict observed and unobserved locations, using Bayes spatio-temporal model with efficient, fast, accurate and developed inference method, INLA. The response variable is monthly rainfall at 57 locations in West Java, Indonesia, observed from 1981-2017 and assumed to have normal distribution. The explanatory variables consist of spatial and temporal random effects and fixed effects of monthly precipitation GCM with 8x5 dimensions (40 variables) and the dimension is reduced with PCA. Our model successfully predicts monthly rainfall for observed and unobserved locations using spatial characteristics from nearly locations, and primely capture the monthly rainfall trends in annually cyclic behavior. The correlations between predict and real rainfall data is about 0.8 (for 0.65, 0.8 quantile) and 0.7 (for 0.95, 0.975 high quantile) with RMSEP is 151 for low (0.65) quantile. At the end of the research results, we present the regional rainfall for the entire West Java region. The eastern part near the central Java border has higher rainfall, as well as the west, while the north and south have lower rainfall.