Parallel implementation issues: global versus local methods

Climate modeling differs from weather forecasting primarily in terms of the spatial resolution and timescales involved. For example, weather models run at high resolution for short periods (from two to 10 days), whereas climate models run for decades or centuries of simulated time at much lower resolution to make the computations tractable. There are on the order of 100,000 to 1 million grid points in a climate model as opposed to 10 million or more in a global weather model. This implies that there is far less inherent parallelism available in climate models and hiding the latency inherent in vendor memory systems and communication networks is considerably more difficult. The atmospheric 3D primitive equations are employed as the dynamical core of most existing climate models and are derived from the incompressible Navier-Stokes equations by scaling arguments applied to planetary flow on a rotating sphere. Numerical methods for solving these partial differential equations can be broadly characterized as having either global or local data dependencies, both of which have specific drawbacks on highly parallel distributed-memory microprocessor-based architectures. Network bisection bandwidth usually limits highly efficient but less scalable global methods, whereas network latency tends to hinder less efficient but more scalable local methods. Despite the lack of exploitable parallelism at relatively low climate resolutions, global spectral models have exhibited high performance on modestly parallel vector architectures. This is due to the higher efficiency and greater per-processor performance of vector systems compared to microprocessors. As a result, the spectral transform method is widely used in current climate models. It is a global method based on a representation of atmospheric flow variables by spherical harmonics. The spectral element method, in contrast, is a relatively new approach that combines the local finite-element method with high-order orthogonal polynomial expansions. Global communication might still be required for such local methods when the timestepping scheme involves an implicit solver, such as the iterative conjugate gradient (CG) algorithm. PARALLEL IMPLEMENTATION ISSUES: GLOBAL VERSUS LOCAL METHODS