Kinetic Energy Spectra and Model Filters

We wish to maximize efficiency (accuracy/cost) in the design of atmospheric fluid-flow solvers. An important measure of accuracy for weather and climate applications is a model’s ability to resolve meteorologically important features at scales approaching the grid-scale. Simulated kinetic energy spectra provide a useful diagnostic for quantifying a model’s resolving capability. Using kinetic energy spectra we illustrate some of the issues affecting the resolution capabilities of models arising from the choice of spatial grid staggering, integration schemes and their implicit filters, and explicit filters. In both Eulerian and semi-Lagrangian formulations, C-grid staggering provides the best resolution of divergent modes that are an important part the KE spectrum in the mesoscale which the global models are now beginning to resolve. Other grid staggerings require special filtering that compromise resolution capabilities. The popular semi-Lagrangian semi-implicit formulations are shown to significantly damp resolvable high-frequency modes and adversely affect their resolving capabilities. While less costly at a given grid density, the SLSI models may well be significantly less efficient than Eulerian models.