The Pros and Cons of Diffusion, Filters and Fixers in Atmospheric General Circulation Models

Abstract

All atmospheric General Circulation Models (GCMs) need some form of dissipation, either explicitly specified or inherent in the chosen numerical schemes for the spatial and temporal discretizations. This dissipation may serve many purposes, including cleaning up numerical noise generated by dispersion errors or computational modes, and the Gibbs ringing in spectral models. Damping processes might also be used to crudely represent subgrid Reynolds stresses, eliminate undesirable noise due to poor initialization or grid-scale forcing from the physics parameterizations, cover up weak computational stability, damp tracer variance, and prevent the accumulation of potential enstrophy or energy at the smallest grid scales. This chapter critically reviews the wide selection of dissipative processes in GCMs. They are the explicitly added diffusion and hyper-diffusion mechanisms, divergence damping, vorticity damping, external mode damping, sponge layers, spatial and temporal filters, inherent diffusion properties of the numerical schemes, and a posteriori fixers used to restore lost conservation properties. All theoretical considerations are supported by many practical examples from a wide selection of GCMs. The examples utilize idealized test cases to isolate causes and effects, and thereby highlight the pros and cons of the diffusion, filters and fixers in GCMs.