On the Pressure Gradient Force Error in σ-Coordinate Spectral Models

Abstract

The pressure gradient force error of the spectral technique used in combination with the σ vertical coordinate was examined in an idealized case of an atmosphere at rest and in hydrostatic equilibrium. Small-scale (one-point and three-point) mountains were used in the tests. With such definitions of topography, difficulties could be expected with the spectral method due to slow convergence of the Fourier series. For reference, the finite-difference pressure gradient force errors were also computed. In the examples considered, it. was found that the errors of the spectral method can be large. In the rms sense, the spectral pressure gradient force errors were larger than those of the finite-difference method.