Predictability With and Without the Influence of Random External Forces

Abstract

The practical limit of atmospheric predictability is a function of the uncertainties in the initial conditions, the uncertainties in the parameterization of the external forces, and the uncertainties involved with discretizing the continuous atmospheric variables. The stochastic dynamic method of treating time-dependent differential equations, when applied to the relevant meteorological equations, is capable of treating the above sources of error and the atmospheric predictability problem in an explicit manner. New calculations emphasizing the effects of random forcing on predictability are presented. While it has been convenient to express predictability as a function of wavenumber in rather general energy terms, it is shown how this expression of predictability is related to a new definition based upon the degree of belief one has in the phase-position of atmospheric waves. Finally, an attempt is made to isolate the uncertainties associated with the computational cutoff in physical space by the incorporation of an artificial viscosity which is considered as a nonlinear stochastic external force.