Mathematical Sciences: Chaotic Time Series and Environmental Extremes

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Previous research on threshold methods and extreme values is in the process of being extended from the case of univariate time series, to multivariate or spatial data. This is particularly relevant in climatological research because of the need to combine data from many measuring stations. The climatological objective is to come up with measures of trend among the crossings by a temperature series of a very high or very low threshold. A second objective is to look at alternatives to the standard models for time series. In particular the concept of long-range dependence appears to be important in climatology, and the research will explore methods of measuring this from the low- frequency behavior of the periodogram. An important theme of current climate research is the need for reliable statistical measures of greenhouse-gas-induced climate change. Global warming would cause an increase in extreme temperatures. This research will study the statistical aspects of these extreme values, paying particular attention to the problem of efficiently combining information from a number of measuring stations.