Mara Felici, Valerio Lucarini, Antonio Speranza, Renato Vitolo
Extreme Value Statistics of the Total Energy in an Intermediate
Complexity Model of the Mid-latitude Atmospheric Jet.
Part I: Stationary case.
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ABSTRACT. An intermediate complexity baroclinic model for the atmospheric jet at middle-latitudes is used
as a stochastic generator of earth-like time series: in the present case the total energy of the system.
Statistical inference of extreme values is applied to yearly maxima sequences of the time series,
in the rigorous setting provided by extreme value theory. In particular, the Generalized Extreme
Value (GEV) family of distributions is used here as a fundamental model for its simplicity and
generality. Several physically realistic values of the parameter TE , descriptive of the forced equator-
to-pole temperature gradient and responsible for setting the average baroclinicity in the atmospheric
model, are examined. Stationary time series of the total energy are generated and the 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 asses goodness-of-fit. The location and scale GEV parameters are found
to have a piecewise smooth, monotonically increasing dependence on TE . This is in agreement with
the similar dependence on TE observed in the same system when other dynamically and physically
relevant observables are considered. The shape parameter also increases with TE but is always
negative, as a priori required by the boundedness of the total energy of the system. The sensitivity
of the statistical inference process is studied with respect to the selection procedure of the maxima:
the roles of both the length of maxima sequences and of the length of data blocks over which the
maxima are computed are critically analyzed. Issues related to model sensitivity are also explored
by varying the resolution of the system.