A nonlinear balance equation with orographic effects included applied to the whole globe
Abstract
The nonlinear surface pressure weighted balance equation was applied to the whole globe. The finite difference analog to the original equation expressed in spherical coordinates was applied to a latitude longitude grid with sigma = P/Ps as the vertical coordinate. The equation was solved over the whole globe for nondivergent piweighted wind when the mass field is given. In order to get a solution near or at the equator, where the original second order partial differential equation degenerates, three different methods were investigated. Only one gives a solution for all the different mass fields given. This method prescribes the equator to be a streamline, thus excluding crossequatorial flow, and uses this streamline as boundary values for the Northern and Southern hemispheres. This method yields a clear and correctly posed mathematical problem, with the two other proposed methods being ambiguous. The resulting wind field when a mountain is introduced seems to be in agreement with theoretical solutions for the same scale of the mountain for flow on an fplane. A limited area version of the spherical model was also developed, where the stream function at the boundaries is given instead.
 Publication:

Unknown
 Pub Date:
 December 1980
 Bibcode:
 1980nbeo.rept.....J
 Keywords:

 Atmospheric Pressure;
 Earth (Planet);
 Nonlinear Systems;
 Orography;
 Partial Differential Equations;
 Atmospheric Models;
 Boundary Value Problems;
 Divergence;
 Equators;
 Meteorology;
 Partial Differential Equations;
 Spherical Coordinates;
 Geophysics