Space–time extreme value statistics of a Gaussian random field

This paper describes a new method for estimating the extreme values of a Gaussian random field in both space and time. The method relies on the use of data provided by measurement or Monte Carlo simulation combined with a technique for estimating the extreme value distribution of a recorded time series. The time series in question represents the spatial extremes of the random field at each point in time. The time series is constructed by sampling the available realization of the random field over a suitable grid defining the domain in question and extracting the extreme value. This is done for each time point of a suitable time grid. Thus, the time series of spatial extremes is produced. This time series provides the basis for estimating the extreme value distribution using available techniques for time series, which results in an accurate practical procedure for solving a very difficult problem. This is demonstrated by comparison with the results obtained from analytically derived expressions for the extreme values of a Gaussian random field. Properties of these analytical formulas are also discussed.