On vertical interpolation and truncation in connexion with use of sigma system models

Abstract

The effect of vertical truncation in connexion with interpolation of geo‐potential from standard pressure to sigma levels is examined. It is shown that the hydrostatically related temperature and geopotential fields in the sigma system become inconsistently related with regard to calculation of the pressure force in this system. This inconsistency occurs as a result of vertical truncation around temperature inversions (e.g., the tropopause) above a sloping ground. Numerical examples show that erroneous pressure gradients are introduced which, expressed in equivalent gradient wind, have a magnitude of several ms⁻¹ in the tropopause region over the Himalayas and the Rocky Mountains.

To avoid those errors, a procedure is developed in which the pressure force, calculated from analyzed geo‐potentials in the p system, is interpolated to sigma levels.

For consistency, a reversed procedure of the kind just described has to be applied at the end of a forecast when results are to be displayed on pressure surfaces.

The present method has been tested in a few 36‐hour forecasts using real data. The results exhibit a noticeable improvement as compared to those obtained when the commonly adopted interpolation scheme is used.

When the pressure force is interpolated, the geopotential fields on the sigma surfaces are obtained by solving a set of vertically coupled elliptic partial differential equations. The problems involved in solving this set by successive over‐relaxation (sor) are analyzed.

Notes

Contribution no 319.

Present address: Department of Meteorology, University of Stockholm, Arrhenius Laboratory, Fack, S‐104 05 Stockholm, Sweden.