Abstract
Annals of Applied Statistics 2015, Vol. 9, No. 4, 2110-2132 Modeling a precipitation field is challenging due to its intermittent and
highly scale-dependent nature. Motivated by the features of high-frequency
precipitation data from a network of rain gauges, we propose a threshold
space-time $t$ random field (tRF) model for 15-minute precipitation
occurrences. This model is constructed through a space-time Gaussian random
field (GRF) with random scaling varying along time or space and time. It can be
viewed as a generalization of the purely spatial tRF, and has a hierarchical
representation that allows for Bayesian interpretation. Developing appropriate
tools for evaluating precipitation models is a crucial part of the
model-building process, and we focus on evaluating whether models can produce
the observed conditional dry and rain probabilities given that some set of
neighboring sites all have rain or all have no rain. These conditional
probabilities show that the proposed space-time model has noticeable
improvements in some characteristics of joint rainfall occurrences for the data
we have considered.