Spectral model with a regional focus

Abstract

A global spectral model with selective high resolution region Is appropriate for the study of a sharp local weather system if it is not very sensitive to the atmospheric state outside a limited active region. If the linear dimension of the resolution required is 1 and the area of active region is A then one finds that an adequate spectral model has the following features: (a) the model pole is moved away from the geographical north and re-located In the Vicinity of the weather system under study, (b) the set of new spherical harmonics _ymn as basis functions should have the parallelogrammic truncated range | m | <=n <=N, 0<= | m | <=M, where N~, 2pi a|l.

M|N = 4f(1~f),j=AI(4" a2), where a is the radius of the earth.

Since the decomposition of a vector field, in a spherical coordinate system, into the radial and horizontal parts is rotationally invariant, the form of the equations of motion do not change under the re-location of the model pole except for the Coriolis force term. Mathematics of the modelling including truncation and management of non-linear terms do not change.