Using tendency errors to tune the parameterisation of unresolved dynamical scale interactions in atmospheric general circulation models

Abstract

A parameterisation of non-linear dynamical interactions with unresolved scales is needed inmost atmospheric models to ensure realistic fluxes of energy and enstrophy near and at thetruncation limit. In this paper, a minimisation of tendency errors in low to medium resolutionversions of the ARPEGE/IFS and the ECHAM4 spectral general circulation models is soughtin order to obtain spectral empirical interaction functions (EIFs) to be used in the formulationof horizontal diffusion. The tendency errors are calculated relative to high resolution adiabaticversions of the models themselves, meaning that the EIFs reflect all non-linear adiabatic processes.Different EIFs are obtained for vorticity, divergence and temperature. The most strikingfeature is that the vorticity and temperature EIFs have non-negligible negative values for lowwave numbers in large parts of the troposphere. This implies that these waves are enhanced inamplitude due to non-linear interactions with unresolved scales. For low resolution models thegeneration/dissipation of kinetic energy due to the interactions is not well parameterised byeither the standard horizontal diffusion in the models, or the EIFs computed here. When theEIFs are used in the formulation of horizontal diffusion it is seen that the kinetic energyspectrum is closer to observations than in the original model versions. Furthermore, the largescale systematic model errors are reduced in a medium resolution simulation, while less clearimprovement is seen in a simulation at low resolution. It is argued that the technique used inthis paper is quite general and may be used to develop a more realistic parameterisation ofunresolved dynamical scale interactions. The method should, with some modifications, also beapplicable in semi-Lagrangian spectral models and in grid point models.