A Bayesian processor of uncertainty for precipitation forecasting using multiple predictors and censoring

Abstract

A Bayesian processor of uncertainty for numerical precipitation forecasts is presented. The predictive density is estimated on the basis of normalized variates, the use of censored distributions, and the implementation of a parameter-parsimonious and computationally efficient processor that is applicable in operational settings. The structure of the processor is sufficiently generic to handle mixed binary-continuous random processes such as intermittent rainfall (and similarly ephemeral river flows), and an arbitrary number of predictors. First, predictors and observations, the parent data sample, are mapped into standard Gaussian variates, obtaining a nonparametric approximately multivariate normal distribution (MVND) that is considered censored for days with no precipitation. To convert the Gaussian binary-continuous multivariate precipitation process into a continuous one, the parent sample is augmented into the negative range through Bayesian imputation by Gibbs sampling, recovering the true, a priori unknown variance-covariance structure of the full uncensored sample. The dependency among marginal distributions of observations and predictions is hereby assumed multivariate normal, for which closed-form expressions of conditional densities exist. These are then mapped back into the variable space of provenience to yield the predictive density. The processor is applied to a well-monitored study area in Switzerland. Standard forecast performance evaluation and verification metrics are employed to set the approach into perspective against Bayesian model averaging (BMA).