Impact of semi-Lagrangian trajectories on the discrete normal modes of a non-hydrostatic vertical-column model

Abstract

The impact of one- and two-term extrapolated-trajectory schemes on the stability properties of centred semi-implicit semi-Lagrangian schemes is analysed by examining the behaviour of the discrete (acoustic) normal modes of a prototypical column model. It is found that, in the absence of any controlling mechanism, both extrapolated-trajectory schemes are unstable. Additionally, they can significantly distort the vertical structure of the modes. Though not studied herein, the analogous distortion of Rossby and gravity waves could be expected to be deleterious to a forecast model. © Crown copyright, 2005.