Statistical downscaling of precipitation using quantile regression

Statistical downscaling of precipitation is required as part of many climate change studies. Statistical downscaling based on regression models requires one to sample from the conditional distribution to preserve the variance of observed precipitation. In this paper, we present a new technique for downscaling precipitation. The proposed method employs quantile regression rather than traditional linear regression models to determine the conditional distribution for a given day. This eliminates the need for some of the assumptions required in standard linear regression, including the assumption of normally-distributed errors with constant variance. The quantile regression model also allows considerable flexibility in selecting predictor variables in that different subsets of predictors can be used for different parts of the conditional distribution. A Bayesian method adapted to quantile regression is used to select predictor variables. The method is illustrated through an application to five weather stations in Canada. It is found that the proposed method has distinct advantages over the conventional regression model for predicting summer precipitation, while for winter precipitation there is not much difference between the two methods.