On Computing the Horizontal Pressure Gradient Force in Sigma Coordinates

Abstract

Corby et al. present a finite-difference expression for the horizontal pressure gradient force in sigma coordinates that, in a barotropic atmosphere where the temperature varies linearly with logarithm of pressure, has the same net truncation error as the centered finite-difference approximation for the isobaric geopotential gradient. The requirement that the temperature vary linearly with logarithm of pressure is imposed on analyzed isobaric heights and temperatures using a variational procedure. This reduces the errors in geostrophic winds computed using sigma coordinates. Initial surface pressures and temperatures are calculated in a mesoscale model, assuming the temperature varies linearly with logarithm of pressure and linearly with height. The first method (linear variation with logarithm of pressure) results in smaller errors in computed initial surface geostrophic winds. The structure of a sigma coordinate model is described in which temperature varies linearly with logarithms of pressure. Analytical expressions are derived for the truncation error in the case of temperature varying linearly with height. It is concluded that if a linear variation of temperature with logarithm of pressure is imposed and Corby et al.'s finite difference is employed, then truncation error in the horizontal pressure gradient force will be reduced.