The Use of the Primitive Equations of Motion in Numerical Prediction

An obstacle to the use of the primitive hydrodynamical equations for numerical prediction is that the initial wind and pressure fields determined by conventional means give rise to spurious large-amplitude inertio-gravitational oscillations which obscure the meteorologically significant large-scale motions. It is shown how this difficulty may be overcome by the use of a relationship between wind and pressure which enables one to determine these fields in such a manner that the noise motions do not arise. The method is illustrated by a numerically computed example. The wind-pressure relationship is in a sense a generalization of the geostrophic approximation and may be used where the latter approximation is inapplicable, either to determine initial conditions or to derive a set of filtering equations for numerical prediction analogous to the quasi-geostrophic equations.