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

Abstract

A baroclinic model for the atmospheric jet at middle-latitudes is used as a stochastic generator of time series of 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. Several physically realistic values of the parameter $T_E$, descriptive of the forced equator-to-pole temperature gradient and responsible for setting the average baroclinicity in the atmospheric model, are examined. The location and scale GEV parameters are found to have a piecewise smooth, monotonically increasing dependence on $T_E$. This is in agreement with the similar dependence on $T_E$ observed in the same system when other dynamically and physically relevant observables are considered. The GEV shape parameter also increases with $T_E$ but is always negative, as \textit{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.

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• Dynamical ensembles in stationary states
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• Note on Two Theorems in Nonequilibrium Statistical Mechanics
• Extreme Value Statistics of the Total Energy in an Intermediate Complexity Model of the Mid-latitude Atmospheric Jet. Part II: trend detection and assessment
• Physical and Mathematical Properties of a Quasi-Geostrophic Model of Intermediate Complexity of the Mid-Latitudes Atmospheric Circulation

Cited by in corpus (9)

• Extremes and Recurrence in Dynamical Systems
• Universal behavior of extreme value statistics for selected observables of dynamical systems
• Numerical convergence of the block-maxima approach to the Generalized Extreme Value distribution
• Extreme value laws in dynamical systems under physical observables
• Towards a General Theory of Extremes for Observables of Chaotic Dynamical Systems
• Applications of large deviation theory in geophysical fluid dynamics and climate science
• Extreme Value Statistics of the Total Energy in an Intermediate Complexity Model of the Mid-latitude Atmospheric Jet. Part II: trend detection and assessment
• Convergence of extreme value statistics in a two-layer quasi-geostrophic atmospheric model
• Symmetry-break, mixing, instability, and low frequency variability in a minimal Lorenz-like system