Probabilistic Multisite Statistical Downscaling for Daily Precipitation Using a Bernoulli–Generalized Pareto Multivariate Autoregressive Model

Abstract

Bernoulli?generalized Pareto multivariate autoregressive (BMAR) model is proposed in this paper for multisite statistical downscaling of daily precipitation. The proposed model relies on a probabilistic framework to describe the conditional probability density function of precipitation at each station for a given day and handles multivariate dependence in both time and space using a multivariate autoregressive model. Within a probabilistic framework, BMAR employs a regression model whose outputs are parameters of the mixed Bernoulli?generalized Pareto distribution. As a stochastic component, the BMAR employs a latent multivariate autoregressive Gaussian field to preserve lag-0 and lag-1 cross correlations of precipitation at multiple sites. The proposed model is applied for the downscaling of AOGCM data to daily precipitation in the southern part of Québec, Canada. Reanalysis products are used in this study to assess the potential of the proposed method. Based on the mean errors (MEs), the root-mean-square errors (RMSEs), precipitation indices, and the ability to preserve lag-0 and lag-1 cross correlation, results of the study indicate the superiority of the proposed model over a multivariate multiple linear regression (MMLR) model and a multisite hybrid statistical downscaling procedure that combines MMLR and stochastic generator schemes.