Dynamics of Model Error: Some Generic Features

A systematic formulation of model error is developed accounting for both its dynamical and probabilistic aspects. Some generic features, largely independent of the particular model under consideration, are brought out in connection with power-law behavior in the short time regime. The lifetime of this regime is shown to be related to the spectrum of the Lyapunov exponents and the decay characteristics of the time correlation functions involved. The results are illustrated and tested on representative low-order models of atmospheric dynamics exhibiting oscillations, bistability, and chaotic behavior.