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Can error source terms in forecasting models be represented as Gaussian Markov noises?
Author(s) -
Nicolis C.
Publication year - 2005
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 - 10.1256/qj.04.98
Subject(s) - universality (dynamical systems) , mathematics , markov chain , chaotic , statistical physics , representation (politics) , gaussian , phase space , computer science , statistics , physics , artificial intelligence , quantum mechanics , politics , political science , law , thermodynamics
The repercussions of model error on the long term climatological means and on the variability around them are analysed. The extent to which a stochastic representation of error source terms provides a universal correcting mechanism is addressed. General relations are derived linking the model error to the climatological means and the variability properties of a forecasting model subjected to a correcting Gaussian Markov noise on the basis of moment equations associated with Fokker–Planck and Liouville type equations. These relations are implemented in a variety of models giving rise to regular and to chaotic solutions. As it turns out, forecasting models fall into distinct universality classes differing in their response to the effect of noise according to the structure of the Jacobian and the Hessian matrices of the model phase‐space velocity. It is concluded that different trends may exist in which the ‘correcting’ noise tends to depress or, on the contrary, amplify the model error. Copyright © 2005 Royal Meteorological Society.