The spatial computational grid of PCM has its pole over Hudson Bay, a relatively new feature resulting from the introduction of generalized coordinates to improve resolution near the equator and to better track El Ni o, which is an equatorial feature. The atmospheric model uses spherical harmonics, FFTs, and semi-implicit time stepping. The ocean model solves a Helmholtz-type equation with finite differences. The sea ice computations are similar, but with the elastic viscoplastic behavior of the material also incorporated. It is slow because there is lots of communication and little computation.
Resolution is a challenge if regional climates are to be modeled correctly.
Accurate modeling of evaporation over lakes, for example, requires incorporating the Great Salt Lake and, for evaporation over land, more than the twenty types of vegetation now included. Pointing to the complexity of the systems involved, Washington made clear the need for an ensemble of computational experiments that can correctly replicate natural variability of the climate system, for example, temperature anomalies. Future models must also incorporate more detailed interactions between the atmosphere and the land, as in dust storms in the Sahara desert. Next-generation climate modeling will be performed on large clusters of parallel computers via distant collaborations. Specific contributions that can be made by computational mathematicians include remapping from various grids, efficiently solving the Laplace equation on clustered machines, performing global FFTs, recoding algorithms designed for vector machines for use on distributed clusters, designing algorithms that make better use of caching, and improving numerical methods for all the constituent model components.