A Simple Comparison of Four Physics–Dynamics Coupling Schemes

Abstract

Four schemes (referred to here as explicit, implicit, split-implicit, and symmetrized split-implicit) for coupling physics parameterizations to the dynamical core of numerical weather and climate prediction models have been studied in the context of a simplified, canonical model problem. This problem models the dynamics by a representation of the terms responsible for gravitational oscillations and models the physics by both a constant forcing term and a linear damping term, representative of horizontal or vertical diffusion. The schemes have been analyzed in terms of their numerical stability and accuracy. Two of the schemes (the explicit and split-implicit) have been studied previously in the context of a three-time-level discretization. Those results are confirmed here for a two-time-level discretization. The two other schemes (the implicit and the novel symmetrized split-implicit) are both found to be second-order accurate and unconditionally stable, and both represent improvements over the explicit and split-implicit schemes. The symmetrized split-implicit has the additional advantage over the implicit scheme, for simplicity and computational efficiency, of separating the physics and dynamics steps from each other. The canonical problem considered here is a considerable simplification of any real physics?dynamics coupling, which limits the generality of the conclusions drawn. However, such simplification allows detailed analysis of some important aspects and motivates further work on both broadening and deepening understanding of physics?dynamics coupling issues.