Frictional heating in global climate models

A new finite-difference formulation of the frictional heating associated with atmospheric vertical momentum diffusion is proposed. It is derived from the requirement that, according to the no-slip condition, the sum of internal and kinetic energy of a fluid column is not changed by surface friction. The present form is designed to be implemented along with the hybrid-coordinate differencing scheme of Simmons and Burridge. The effects of incorporating frictional heating in general circulation models (GCMs) of the atmosphere are assessed by analyzing representative long-term January simulations performed with an idealized GCM. The model employs the proposed discretization of vertical terms as well as recently derived horizontal diffusion and dissipation forms. For the conventional definition of a GCM with no frictional heating, the climatological global energy budget yields a spurious thermal forcing of about 2 W m(-2). In the equivalent new model definition, this shortcoming is reduced by two orders of magnitude. Moreover, the long-term global mean of the simulated frictional heating yields approximately 1.9 W m(-2). This value is in agreement with both the residuum in the conventional case as well as with existing estimates of the net dissipation owing to synoptic and planetary waves.