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A maximum entropy approach to the problem of parametrization
Author(s) -
Verkley W. T. M.
Publication year - 2011
Publication title -
quarterly journal of the royal meteorological society
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.744
H-Index - 143
eISSN - 1477-870X
pISSN - 0035-9009
DOI - 10.1002/qj.860
Subject(s) - principle of maximum entropy , probability density function , state variable , parametrization (atmospheric modeling) , mathematics , maximum entropy probability distribution , laplace transform , statistical physics , maximum entropy thermodynamics , entropy (arrow of time) , binary entropy function , statistics , physics , mathematical analysis , thermodynamics , quantum mechanics , radiative transfer
It is shown that the principle of maximum entropy, as formulated by Jaynes, can be applied to parametrize the effect of unresolved variables on resolved variables in a dynamical system proposed by Lorenz. The starting point is the assumption that the unresolved variables are in a state of statistical equilibrium on the time‐scale of the resolved variables. The probability density function that describes the statistics of the unresolved variables is then determined by requiring that its information entropy is maximal under the constraint that the average time rate of change of the unresolved variables' energy is zero. By using this probability density function to determine the average effect of the unresolved variables on the resolved variables, a linear damping of the resolved variables is found. After incorporating the linear damping in the equations of the resolved system, the principle of maximum entropy is applied a second time to shed light on the statistics of the resolved system. The consequences are studied of using a priori probability density functions that go beyond Laplace's principle of indifference. Copyright © 2011 Royal Meteorological Society