Collaborative Research: CMG--Freedom from Coordinate Systems, and Spectral Accuracy with Local Refinement: Radial Basis Functions for Climate and Space-Weather Prediction

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Radial basis functions (RBF) represent powerful mathematical techniques for interpolation and smoothing in multidimensional data space. Their use in solving time-dependent partial differential equations (PDEs) for modeling is to be explored by a multidisciplinary group of mathematicians and geoscientists from Arizona State, University of Colorado Boulder, University of Michigan, and NCAR. Attractive attributes of this new methodology for use in problems ranging from climate science, to shallow water equations in spherical geometry to solar corona dynamics include: i) the ability to achieve spectral accuracy and local mesh refinement at arbitrary node locations including resolution in steep-gradient events, ii) grid geometry independence allowing application to irregular geometries, iii) algorithmic simplicity, and iv) higher accuracy than competing spectral methods. Of interest to many geoscientists, applications of RBFs in spherical coordinate systems will be investigated, with initial applications to climate and solar modeling. Educational outreach will feature an interactive web-site with instructional and applications modules.