Nonlinear horizontal diffusion for GCMs

The mixing-length-based parameterization of horizontal diffusion, which was originally proposed by Smagorinsky, is revisited. The complete tendencies of horizontal momentum diffusion, the associated frictional heating, and horizontal diffusion of sensible heat in spherical geometry are derived. The formulations are modified for the terrain-following vertical-hybrid-coordinate system in a way that ensures energy and angular momentum conservation at each layer. Test simulations with a simple general circulation model, run at T42 horizontal resolution and for permanent January conditions, confirm the conservation properties and highlight the enhancement of nonlinear horizontal diffusion in areas of high baroclinic activity. The simulated internal variability is dependent on the nature of the horizontal diffusion, with high-frequency variability being enhanced over the northern continents and low-frequency variability being increased (decreased) over the Pacific (Atlantic) Ocean when using nonlinear rather than linear diffusion. Locally reduced horizontal dissipation over Europe is compensated by increased dissipation owing to vertical diffusion, indicating the potential importance of nonlinear horizontal diffusion for gravity wave-resolving simulations. Inspection of the spectral energy reveals that the scheme needs to be modified in order to damp unbalanced ageostrophic motions at the smallest resolved scales more efficiently. A corresponding empirical modification is proposed and proves to work properly.