The tendencies due to the physical parametrization schemes need to be coupled to those of the dynamical core, while ensuring that the accuracy of each constituent tendency, overall model stability and computational efficiency are preserved.
In weather and climate models a number of significant processes (such as convection and boundary layer turbulence) are not resolved by the discrete implementation of the fluid dynamical equations governing the evolution of the atmosphere.
Other processes (such as radiation and microphysics) are not governed by the same equations. These physical processes are incorporated into the model by means of parametrizations. They need to be coupled with the solution procedure for the resolved scales of atmospheric flow (the dynamics).
The way in which the physics and the dynamics are coupled to each other can determine the overall accuracy of the model. For example, it would be undesirable to use second-order accurate parameterization and have a second-order accurate dynamical core yet to then couple these together using a first-order accurate scheme. However, the analysis of the coupling schemes is not straightforward and this is perhaps why this aspect of modelling has traditionally received relatively little attention despite its potential importance.
To design and analyse the coupling scheme, each of the physical processes is classified as either slow or fast. Slow processes have timescales that are significantly longer than the model's time step. Fast processes have timescales at or below the order of the time step. As a result slow processes can be coupled using an explicit time scheme but, in order to retain stability and accuracy, fast processes require some form of implicit scheme.
A fully implicit approach, while desirable, is too expensive to be feasible. Therefore, split schemes have been developed which use predictors and iterative correctors. Such schemes need to be analysed with regard to their impact on the overall solution. A number of simplifications to the system under investigation has to be made in order to keep the analysis tractable. Normal mode analysis of the linearized equation set is one of the tools available. Simplified parametrization can also be used, and numerical experimentation performed, to extract information on the accuracy, stability and cost of alternative coupling schemes.