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.
Highlights
It is well-known that numerical methods can affect waves in various ways
An important application of this study is to the development of a whole-atmosphere extension of the Met Office Unified Model (UM)
The UM is based on the ENDGame dynamical core (Wood et al, 2014), which solves the non-hydrostatic compressible Euler equations, and commonly runs with an upper boundary at around 80 km
Summary
It is well-known that numerical methods can affect waves in various ways. In this article, ray-tracing techniques are used to compare the vertical propagation of acoustic and gravity waves for the discrete governing equations in an atmospheric model with that for the corresponding continuous governing equations. We have carried out a standard baroclinic instability test case (Jablonowski and Williamson, 2006) with a semi-implicit semi-Lagrangian dynamical core that uses almost identical numerical methods to ENDGame, and found that unbalanced density and divergence perturbations, i.e. acoustic waves, are generated near the surface with relative amplitude ρ /ρ0 of order 10−4 to 10−3, where ρ is the density perturbation and ρ0 is the background density. Very weak, these are significantly stronger than is realistic.
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