Numerical Methods for Climate Modeling

只有在为物理方程开发适当的参数化和过滤技术以及开发适用于未来高性能计算机的可扩展并行算法的共同努力下，全球气候的数值模拟才是可行的。参数化简化了模型，过滤允许更大的显式时间步长，从而将计算要求降低了数量级。然而，即使是粗略的大气和海洋三维全球分辨率也需要大量的网格点，这些网格点淹没了所有现有的计算机体系结构，即使有了这些简化。使用更大的机器来解决更高分辨率的问题的蛮力方法是不够的。在最先进的计算足以对气候进行合理预测之前，这些模型需要进一步简化。本研究将侧重于模型和求解方法的同步开发过程。第一个目标是确定现有通用环流模型在并行体系结构上实现的计算瓶颈。通过分析模型各组成部分的计算和通信复杂性，将有可能确定模型中最需要简化和/或更高效的并行数值算法的领域。接下来，必须设计适当的数据结构，以允许模型方程的演变。最后，预计许多现代数值方法，如多重网格、具有各种并行预条件的GMRES和区域分解将被证明特别有用。

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.