Abstract
Stability of numerical solutions in the presence of the Asselin time filter is studied with the spectral one-dimensional linearized shallow-water wave equations. Emphasis is placed on solutions close to the stability limit. When the physical parameterizations include implicitly discretized diffusion and both implicitly and explicitly discretized damping terms, the effect of a weak time filter is to destabilize such solutions. A similar behavior is obtained when advection is computed with a semi-implicit scheme. The results of this simplified model are confirmed by stability experiments carried out with two versions of a spectral General Circulation Model.
