Current Mathematical Research Directions for Climate Modeling

Projects

• Focused Grid Spectral Transforms and a Shallow Water Model, Using the Schmidt transformation (a conformal mapping of the sphere to itself) high resolution of a "Gaussian grid" is focused on a geographical area of interest. This technology can be added to the spectral dynamical cores of climate and weather models to provide more accurate, regionally specific forecasts. (Guo, Drake)
• Scalable F90 Module libraries for Spherical Harmonic Transforms, is continuing research on novel methods that are well suited for parallel computation and climate model development. (Worley, Drake, Putman)
• Discrete Hamiltonian Formulations of Fluid Flows, Among other geophysical flows, the shallow water equations can be cast in a Hamiltonian formulation. New developments in numerical simulation of Hamiltonian systems employing symplectic maps, high order accurate and stable time integration methods seem to be promising alternatives to the standard numerical methods. This project investigates the application of theory to practical solution algorithms. (Huang, Drake)
• Statistical Methods for Downscaling Regional Climate Predictions, As part of an LDRD in 1999, we developed a rhobust statistical downscaling method for climate predictions. This is follow on application of the method, with some further refinement for climate diagnostics and analysis.