Coarse Graining the Vorticity Equation in the ECMWF Integrated Forecasting System: The Search for Kinetic Energy Backscatter

Abstract

Abstract Stochastic kinetic energy backscatter parameterization schemes are now widely used in ensemble prediction systems to account for random error associated with excessive dissipation and unrepresented energy backscatter in numerical weather prediction models. This dissipation arises from numerical advection schemes and explicit diffusion terms and is also implicit in some parameterization schemes. In the absence of a backscatter theory applicable to the convective scale and mesoscale, current parameterization methods are based on simple heuristic models designed to scale the energy input in proportion to a suitable measure of net energy dissipation rate. Free parameters in the formulation of backscatter tend to be tuned for the optimal performance of ensemble prediction systems, yet other forms of uncertainty represented in these forecasting systems make that task harder. Results are presented here from a study that aims to characterize the form and magnitude of kinetic energy backscatter within a global spectral framework. This is achieved by comparing a high-resolution “truth” model with a spectrally truncated version of the model for which the effect of the missing scales of motion is to be gauged. Energy exchange between these omitted scales and the resolved scales of the truncated representation is computed for the dominant terms in the vorticity equation. It is found that although there is a nonlocal spectral energy flux to low wavenumbers due to the purely rotational part of the flow, it is much smaller than the dissipative effect associated with terms involving the divergent part of the flow. Biharmonic horizontal diffusion is found to contribute significantly as an energy sink across the entire wavenumber spectrum.