Systematic Energy Errors and the Tendency toward Canonical Equilibrium in Atmospheric Circulation Models

Abstract

Systematic kinetic energy errors are examined in barotropic and multilevel general circulation models. The dependence of energy spectra on resolution and dissipation and, in addition for the barotropic model, on topography and the beta effect, is studied. We propose explanations for the behavior of simulated kinetic energy spectra by relating them to canonical equilibrium spectra characterized by entropy maximization. Equilibrium spectra at increased resolution tend to have increased large-scale kinetic energy and a drop in amplitude at intermediate and small scales. This qualitative behavior may also be found in forced and/or dissipative simulations if the forcing and dissipation operators acting on the common scales are very similar at different resolutions. An explanation for the tail ?wagging the dog? effect is presented. This effect, where scale-selective dissipation operators cause a drop in the tail of the energy spectra and, surprisingly, also an increase in the large-scale energy, is found to occur in both barotropic and multilevel general circulation models. It is shown to rely on the dissipation operators dissipating enstrophy while leaving the total kinetic energy approximately conserved. A new (short time) canonical equilibrium model and explanation of zonalization due to the beta-effect is presented; the meridionally elongated large-scale waves are regarded as adiabatic invariants, while the zonal flow and other eddies interact and equilibrate on a short timescale.