Elimination of spectral blocking by ensuring rotation-free property of discretised pressure gradient within a spectral semi-implicit semi-Lagrangian global atmospheric model

TL;DR

This paper addresses spectral blocking issues in spectral semi-Lagrangian atmospheric models caused by discretisation of the pressure gradient and proposes a mimetic discretisation method to eliminate aliasing errors and improve model accuracy.

Contribution

It introduces a novel discretisation approach that preserves the rotation-free property of the pressure gradient, reducing spectral blocking in semi-Lagrangian models.

Findings

Removes aliasing errors at high wavenumbers.

Ensures the rotation-free property in discretised pressure gradient.

Improves spectral model accuracy and stability.

Abstract

The widely-adopted discretisation of the horizontal pressure gradient term formulated by Simmons and Burridge (1981) for atmospheric models on $\sigma$-$p$ hybrid vertical coordinate is found to incur spectral blocking for rotational wind components at high vertical levels when used in a spectral semi-Lagrangian model run on a linear grid. A remedy to this issue is proposed and tested using a spectral semi-implicit semi-Lagrangian hydrostatic primitive equations model. The proposed method removes aliasing errors at high wavenumbers by ensuring that the rotation-free property of the pressure gradient term on isobaric surface, a feature possessed by the continuous system, is preserved in the discretised system, which highlights the significance of mimetic discretisation within the context of numerical weather prediction models.