Double zero-inflated spatio-temporal modeling of daily precipitation under detection thresholds

Abstract

Explaining precipitation behavior at daily scale is important for fine scale understanding of the mechanisms driving precipitation. However, this effort is challenging because of the frequent incidence of zeros. The challenge is amplified by the acknowledged incidence of two types of zeros -- absence of precipitation as a dry event and absence of measured precipitation due to detection limits. In this work, we propose a multilevel spatio-temporal model which allows us to distinguish and explain the two types of zeros, as well as to model positive precipitation above the detection limit. The methodology combines a point mass at zero with probability modeled through a probit regression, a Gamma regression for latent positive precipitation amounts, and an observation mechanism subject to threshold-induced censoring. To capture spatial dependencies, Gaussian processes are employed in each regression model. Working within a Bayesian framework, we can obtain a rich range of inference with exact uncertainty. In particular, we provide model-based inference tools to compare and quantify differences between the true precipitation process and its observed counterpart across relevant characteristics. We apply our model to the analysis of daily spring observations at 70 sites over 15 years from the Ebro River Basin in northeastern Spain. Our findings indicate that the threshold strongly affects the occurrence of observed precipitation, especially in humid regions. While its impact on total accumulated amounts is small, it can exert a relevant effect on upper quantiles.