Local stochastic subgrid-scale modeling in efficient simulations of geophysical fluid dynamics

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Efficient models of the atmosphere are already interesting for conceptual reasons, as they can yield deepened insight into dynamic mechanisms, e.g. with regard to climate variability. They can, however, also be a helpful tool in climate-sensitivity studies, or in investigations of paleoclimate, where many or long integrations are needed, and thus computational efficiency is a matter of importance. Especially in such applications care has to be taken that as much of the inevitable subgrid-scale parameterizations of unresolved scales are based on first principles as possible. Stochastic mode reduction (SMR) offers a corresponding strategy, where most of the parameterization is derived on paper, once the nonlinear self-interactions between the unresolved modes have been fitted to a simple stochastic process. In applications so far, however, the constructed reduced model has been given a spectral formulation, where in the global subgrid-scale (SGS) parameterization all resolved modes interact with each other. This limits the applicability of this approach to very low-dimensional systems. To circumvent this problem, recently an implementation of the SMR to grid-point-based spatial discretizations has been developed which results in a local stochastic SGS parameterization. This strategy has so far been tested within the framework of the Burgers equation. In the proposed project significant steps will be taken towards the application of the local SMR strategy to realistic models of atmospheric dynamics. SGS parameterizations should be constructed for the barotropic vorticity equation and for the shallow water equations on an f-plane. Both models exhibit essential features to be taken into account in the application of the local SMR to the general equations of atmospheric dynamics.The new SGS parameterizations should fulfill the following criteria: i) they should be derived from the model equations in a systematic way under a relatively small number of basic assumptions ii) they should be as consistent as possible with the conservation properties of the model equations and iii) they should require minimal (if possible none at all) regression fitting of the resolved scales. Currently, there is a need in climate modeling for physics constrained and resolution independent formulations of stochastic parameterizations. The development of parameterizations using SMR, as proposed here, will contribute to such methods. Besides climate modeling, turbulence modeling in large eddy simulation is another field, which can benefit from such developments.