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Regimes of self-organized criticality in the atmospheric convection
Large scale organization in ensembles of events of atmospheric convection can
be generated by the combined effect of forcing and of the interaction between
the raising plumes and the environment. Here the "large scale" refers to the
space extension that is larger or comparable with the basic resolved cell of a
numerical weather prediction system. Under the action of external forcing like
heating individual events of convection respond to the slow accumulation of
vapor by a threshold-type dynamics. This is due to the a time-scale separation,
between the slow drive and the fast convective response, expressed as the
"quasi-equilibrium". When there is interaction between the convection plumes,
the effect is a correlated response. We show that the correlated response have
many of the characteristics of the self-organized criticality (SOC). It is
suggested that from the SOC perspective, a description of the specific dynamics
induced by "quasi-equilibrium" can be provided by models of "punctuated
equilibrium". Indeed the Bak-Sneppen model is able to reproduce (within
reasonable approximation) two of the statistical results that have been
obtained in observations on the organized convection.
We also give detailed derivation of the equations connecting the
probabilities of the states in the update sequence of the Bak-Sneppen model
with random neighbors. This analytical framework allows the derivation of
scaling laws for the size of avalanches, a result that gives support to the SOC
interpretation of the observational data.Comment: Text prepared for the Report of COST ES0905 collaboration (2014).
Latex 45 page
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