Analysis of the numerics of physics–dynamics coupling

A methodology for analysing the numerical properties of schemes for coupling physics parametrizations to a dynamical core is presented. As an example of its application, the methodology is used to study four coupling schemes (‘explicit’, ‘implicit’, ‘split‐implicit’ and ‘symmetrized split‐implicit’) in the context of a semi‐implicit semi‐Lagrangian dynamical core. Each coupling scheme is assessed in terms of its numerical stability and of the accuracy of both its transient and steady‐state responses. Additionally, the occurrence of spurious, computational resonance is analysed and discussed. It is found that in this respect all four schemes behave similarly. In particular, in the absence of any damping mechanism to control resonance, the time‐step restriction needed to avoid spurious resonance is twice as restrictive for time‐dependent forcing as for stationary forcing.