Spatial oceanographic extremes Adam Butler (Lancaster University), talk at RSC2003 Coworkers: Janet Heffernan, Jonathan Tawn, Roger Flather Data supplied by Proudman Oceanographic Laboratory (POL)

l SSTO data - Synthetic Spatio-Temporal Oceanographic data. Generated from deterministic models. Lattice-based spatio-temporal data. Large, high resolution datasets. Variables: surge height, wave height, surge direction,… Possibly multivariate. l Extremal properties of SSTO data Extremes are linked to risk. Key: estimating extreme return levels of a single variable at a single site. Fundamentally about extrapolation. Extremes of derived variables. Spatial aggregation: regional risk assessment. Temporal evolution of extremal properties. Introduction: SSTO data

Variable: surge level Region: NE Atlantic Period: Spatial resolution: 35km Temporal resolution: 1hr Generating model: NEAC Met input data: DNMI Data provided by: POL Data example: the dataset

l Why use EVT for modelling ? EVT = Extreme Value Theory... Modelling choice between EVT approach and process approach EVT-based models rely upon very weak assumptions The price of this is inefficiency For SSTO data, the choice is pathological. l Which EVT model to use ? Classical: univariate models for extremes, assuming independence. Asymptotically motivated models Main approaches: blockwise maxima, threshold exceedance Methodology: classical EVT models

Data example: classical EVT models Need to add indications as to how extremes get extracted etc. etc.

Data example: nonstationarity & dependence

l Nonstationarity Nonstationarities of known form: straightforward Nonstationarities of unknown form: harder ! SSTO: nature of nonstationarity usually unknown SSTO: spatial nonstationarity is dominant SSTO: temporal nonstationarities are subtle l Dependence Very strong spatial and temporal dependence Avoiding temporal dependence via aggregation e.g. Peaks over Threshold (POT) model Modelling spatial dependence via multivariate extremes e.g. Multivariate threshold exceedance models... Chapter 2 of my thesis - simulation studies. Methodology: nonstationarity & dependence

l Heffernan and Tawn (2003) A semi-parametric model for multivariate extremes No strong a priori assumptions about the form of extremal dependence Relatively parsimonious Extremal dependence parameters l Spatial extension Reduce number of dependence parameters Adjust for temporal dependence Add spatial nonstationarity via local likelihood Chapters 3-5 of my thesis. Methodology: the Heffernan-Tawn model