Extreme Value Statistics of the Total Energy in an Intermediate Complexity Model of the Mid-latitude Atmospheric Jet. Part I: Stationary case

摘要

A baroclinic model of intermediate complexity for the atmospheric jet at middle latitudes is used as astochastic generator of atmosphere-like time series. In this case, time series of the total energy of the systemare considered. Statistical inference of extreme values is applied to sequences of yearly maxima extractedfrom the time series in the rigorous setting provided by extreme value theory. The generalized extremevalue (GEV) family of distributions is used here as a basic model, both for its qualities of simplicity and itsgenerality. Several physically plausible values of the parameter TE, which represents the forced equatorto-pole temperature gradient and is responsible for setting the average baroclinicity in the atmosphericmodel, are used to generate stationary time series of the total energy. Estimates of the three GEV parameters—location, scale, and shape—are inferred by maximum likelihood methods. Standard statistical diagnostics,such as return level and quantile–quantile plots, are systematically applied to assess goodness-of-fit.The GEV parameters of location and scale are found to have a piecewise smooth, monotonically increasingdependence on TE. The shape parameter also increases with TE but is always negative, as is required a prioriby the boundedness of the total energy. The sensitivity of the statistical inferences is studied with respectto the selection procedure of the maxima: the roles occupied by the length of the sequences of maxima andby the length of data blocks over which the maxima are computed are critically analyzed. Issues related tomodel sensitivity are also explored by varying the resolution of the system. The method used in this paperis put forward as a rigorous framework for the statistical analysis of extremes of observed data, to study thepast and present climate and to characterize its variations.