Multivariate spatial and spatio-temporal models for extreme tropical cyclone seas

Estimates of extreme environments and responses of offshore structures for tropical cyclone conditions are typically made using time-series of ocean environmental data, hence helping to ensure safe structural design. However, estimates are often subject to large uncertainties because of the short length of available time-series. We propose a methodology to characterise extreme multivariate time-series for tropical cyclones, by extending the STM-E spatial extreme value model of Wada et al. (2018) to incorporate (a) storm peaks of multiple metocean variables, using the conditional extremes model of Heffernan and Tawn (2004) (leading to MSTM-E methodology), and additionally (b) time-series evolution around the storm peak, using a history-matching approach (leading to MSTM-TE). We use both MSTM-E and MSTM-TE to estimate the return values of multivariate extremes from synthetic cyclone data for a spatial neighbourhood of locations offshore Guadeloupe (in the Lesser Antilles). The comparison of storm peak analysis using MSTM-E against single location conditional model shows the benefit of MSTM-E in reducing return value variance without sacrificing bias, in both marginal and joint extremes. Moreover, characteristics of multivariate time-series realisations generated under fitted MSTM-TE models (with 200 years of data) are shown to be in good agreement with those of the original time-series data used to fit the model (with 1000 years of data). •Estimation method for extremes of multivariate time-series under tropical cyclone.•Reduced variance of joint extremes than single location conditional extreme models.•Generated multivariate time-series show good agreement with original data.