Gravitational Adjustment in Phase Space

Abstract

It is suggested that when one more properly views meteorological prediction as an initial value problem couched in random or stochastic terms, there is an additional way for the wind and the mass fields to adjust to a state of balance. A simplified spectral model is used to isolate the gravity wave energy and to show how it becomes dispersed through phase space. Calculations show that this non-Gaussian adjustment cannot be described without the inclusion of third moments. Monte Carlo and stochastic dynamic calculations show that the entire ensemble of points which describe a system in phase space tend to a state of balance which is consistent with a solution to the stochastic balance equation. Based upon the results, the implications of stochastic models in dealing with gravity waves in meteorological predictions is assessed.