Spatial-temporal multivariate semi-Bayesian hierarchical framework for extreme precipitation frequency analysis

We present a semi-Bayesian hierarchical modeling framework for conducting space-time frequency analysis of precipitation extremes over a large domain. In this framework, the data layer, the precipitation extreme - i.e., seasonal maximum precipitation, at each station in each year is modeled using a generalized extreme value (GEV) distribution with temporally varying parameters, which are decomposed as linear functions of covariates. The coefficients of the covariates are estimated via maximum likelihood (ML). In the process layer, the estimated ML coefficients of each of the covariates across the stations are spatially modeled with a Gaussian multivariate process which enables capturing the spatial structure and correlation between the spatial model parameters. Suitable priors are used for the spatial model hyperparameters to complete the Bayesian formulation. Since the Bayesian formulation is only at the second level, our model is semi-Bayesian and thus, the posteriors are conditional posterior distributions. With the conditional posterior distribution of spatial fields of the GEV parameters for each time, conditional posterior distribution of the nonstationary space-time return levels of the precipitation extremes are obtained. We demonstrate this framework by application to summer precipitation extreme at 73 stations covering a large domain of Southwest US consisting of Arizona, New Mexico, Colorado, and Utah. The results from fitting and cross-validation indicate that our model captures the historical variability at the stations very well. Conditional posterior distributions of return levels are simulated on a grid over the domain, which will be of immense utility in management of natural resources and infrastructure.