Over a seven day period in August 2017 Hurricane Harvey brought extreme rainfall to the Houston area, resulting loss of human life and catastrophic damage to personal property and public infrastructure. In the wake of this event, there is growing interest in understanding the degree to which this event was unusual and estimating the probability of experiencing a similar event in other locations.
We assume that the annual maximum precipitation values at Gulf Coast locations approximately follow the Generalized Extreme Value (GEV) distribution and model these GEV parameters via a multivariate spatial hierarchical model; for inference, a two-stage approach is used. Interpolation is used to estimate GEV parameters at unobserved locations, allowing us to characterize precipitation extremes throughout the region. Nearby locations may see extreme precipitation from the same event, causing dependence between annual maxima. Similar models have not captured dependence of this type; our model estimates its effect via the nonparametric bootstrap. We also investigate the degree to which sea surface temperature in the Gulf of Mexico is associated with extreme precipitation in the region.