A max-stable process model for rainfall extremes at different accumulation durations

Abstract

A common existing approach to modeling rainfall extremes employs a spatial Bayesian hierarchical model, where latent Gaussian processes are specified on distributional parameters in order to pool spatial information. The data are taken to be conditionally independent given the latent processes, and so spatial dependence arises only through this conditional structure. This methodology can be extended by incorporating an explicit max-stable dependence structure, which therefore produces more realistic spatial surfaces, and removes the assumption of conditional independence. We further extend the max-stable methodology to incorporate the joint modeling of rainfall data at different accumulation durations. We therefore pool information across both space and accumulation duration within a broad framework which includes an explicit specification of spatial dependence. Our model can be used to derive inferences at ungauged sites, and easily incorporates missing values. Our methodology is applied to a dataset of pluviometer records recorded at 182 meteorological stations located on the Central Coast of New South Wales, Australia. For each station, rainfall data are accumulated over 16 different durations ranging from 5 min to 7 days. The model is fitted using Markov chain Monte Carlo simulation, employing auxiliary variables so that exact Bayesian inference can be performed. We present estimated parameters and posterior inferences for isohyetal maps and intensity-duration-frequency curves at selected sites of interest, and compare our inferences with those derived from the standard latent variable model.

Keywords

• Bayesian hierarchical model
• Extreme value theory
• Max-stable process
• Markov chain Monte Carlo
• Intensity-duration-frequency curve
• Spatial modeling