The evolution of global atmospheric model dynamical cores from the first developments in the early 1960s to present day is reviewed. Numerical methods for atmospheric models are not straightforward because of the so-called pole problem. The early approaches include methods based on composite meshes, on quasi-homogeneous grids such as spherical geodesic and cubed sphere, on reduced grids, and on a latitude-longitude grid with short time steps near the pole, none of which were entirely successful. This resulted in the dominance of the spectral transform method after it was introduced. Semi-Lagrangian semi-implicit methods were developed which yielded significant computational savings and became dominant in Numerical Weather Prediction. The need for improved physical propenies in climate modeling led to developments in shape preserving and conservative methods. Today the numerical methods development community is extremely active with emphasis placed on methods with desirable physical properties, especially conservation and shape preservation, while retaining the accuracy and efficiency gained in the past. Much of the development is based on quasi-uniform grids. Although the need for better physical properties is emphasized in this paper, another driving force is the need to develop schemes which are capable of running efficiently on computers with thousands of processors and distributed memory.
Test cases for dynamical core evaluation are also briefly reviewed. These range from well defined deterministic tests to longer term statistical tests with both idealized forcing and complete parameterization packages but simple geometries. Finally some aspects of coupling dynamical cores to parameterization suites are discussed.
2007 by Meteorological Society of Japan