Estimating Joint Extremes of Significant Wave Height and Wind Speed for Tropical Cyclones

We provide a computationally-efficient scheme for the estimation of joint extremes of significant wave height (Hs) and wind speed (U) for tropical cyclones. The method incorporates the simple spatial extremes method (STM-E) of Wada et al., 2019 (for spatial extremes of each of Hs and U) and the conditional extremes model of Heffernan and Tawn, 2004 (for conditional modeling of Hs given extreme U and U given extreme Hs). We demonstrate the methodology in application to data generated from hindcast simulations and track shifting of past tropical cyclones in the neighborhood of Réunion island in the Indian Ocean. Following the STM-E approach, spatio-temporal maxima (STM) and exposures (E) of both Hs and U are extracted for each tropical cyclone event. Marginal extreme value distributions are then estimated independently for the STM samples of Hs and U, providing a means for marginal extrapolation to long return periods. Exposure data are used to estimate densities for the spatial distribution of Hs and U. The conditional extremes model is then used to characterize the joint structure of STM for Hs and U, conditional on one of those variables being extreme. The estimated joint return values for Hs and U are validated by comparison with the original data.