Numerical effects on vertical wave propagation in deep-atmosphere models

Abstract

Ray-tracing techniques have been used to investigate numerical effects on the propagation of acoustic and gravity waves in a non-hydrostatic dynamical core discretized using an Arakawa C-grid horizontal staggering of variables and a Charney–Phillips vertical staggering of variables with a semi-implicit timestepping scheme. The space discretization places limits on resolvable wavenumbers, and redirects the group velocity and the propagation of wave energy towards the vertical. The time discretization slows the wave propagation while maintaining the group velocity direction. Wave amplitudes grow exponentially with height due to the decrease in the background density, which can cause instabilities in whole-atmosphere models. Although molecular viscosity effectively damps the exponential growth of waves above about 150 km, additional numerical damping might be needed to prevent instabilities in the lowermost thermosphere. These results are relevant to the Met Office Unified Model, and provide insight into how the stability of the model may be improved as the model's upper boundary is raised into the thermosphere.