Numerical Methods for Climate Modeling

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The numerical simulations of the global climate will be feasible only with a combined effort in developing appropriate parameterizations and filtering techniques for the physical equations and in developing scalable parallel algorithms suitable for future high performance computers. Parameterizations, which simplify the model, and filtering, which allows larger explicit time steps, have reduced the computational requirements by orders of magnitudes. However, even a crude three dimensional global resolution of the atmosphere and ocean requires a number of grid points which swamps all existing computer architectures, even with these simplifications. A brute force approach of using larger machines to solve higher resolution problems is not sufficient. The models need further simplification before state- of-the-art computing will be sufficient to allow reasonable predictions of the climate. This research will focus on the simultaneous development process of both the models and solution methods. The first goal is to identify the computational bottlenecks of existing general circulation model implementations on parallel architectures. By analyzing the computation and communication complexities of the various components of the models, it will be possible to identify the areas in which there is the greatest need for simplifications in the model and/or more efficient parallel numerical algorithms. Next, appropriate data structures must be designed which allow for the evolution of the model equations. Finally, it is anticipated that many of the modern numerical methods, such as multigrid, GMRES with various parallel preconditioners and domain decomposition will prove particularly useful.