CMG: Multivariate Nonstationary Spatial Extremes in Climate and Atmospherics

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This project will develop methods to estimate the likelihood of extreme weather and climate events, both in observations and in climate model simulations. Extremes, expressed as the magnitude of an event that is only expected to occur once in a given time period, such as the size of the 100-year flood, are central to planning for infrastructural projects like dams and levees. But return times for extreme events are difficult to estimate from the relatively short time period available from the instrumented record. The calculation of expected extreme values for a given return time is further complicated by long-term trends in the data due to climate change, which contradict the stationarity assumption on which traditional statistics is predicated. Beyond these temporal issues, long-term data for extreme event studies is only available at specific locations, while estimates of extreme value likelihood are desired over the large intervening regions. The work conducted under this project will develop statistical techniques to overcome the difficulties presented by nonstationarity in time and sparseness in space. Three new frameworks will be introduced to characterize extremes: (1) Nonparametric multivariate spatial Dirichlet-type mixture models for the observations, (2) Bayesian nonparametric functional data analysis to estimate multivariate spatial extremes, and (3) Mixture models, with marginals that have generalized extreme value (GEV) distributions with spatially varying parameters and the observations are spatially-correlated even after accounting for the spatially varying parameters. The research will produce spatial maps of extreme values for temperature, both from observations and climate model simulations of the recent past (1970-2000).The research will be of interest to a large audience including statisticians, climatologists, and resource managers. One motivation for the work is the problem of determining how the frequency of extreme events will change in a changing climate. Climate change is usually expressed in terms of changes in long-term means averaged over large regions, but the adverse impacts associated with changes in extremes, such as increases in the occurrence of heat waves, can pose greater challenges than changes in means. In addition, planning for extreme events is usually conducted based on past occurrences of extremes, but new techniques such as the ones developed here will be required to anticipate the likelihood of extremes in a changing climate.