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

径向基函数（RBF）代表了多维数据空间中插值和平滑的强大数学技术。他们在求解时间相关偏微分方程（PDE）建模的使用是由来自亚利桑那州立大学，科罗拉多大学博尔德分校，密歇根大学和NCAR的数学家和地球科学家的多学科小组进行探索。这种新方法的吸引人的属性用于从气候科学到球面几何浅水方程到日冕动力学的问题，包括：i）在任意节点位置处实现谱精度和局部网格细化的能力，包括陡梯度事件中的分辨率，ii）网格几何形状独立性，允许应用于不规则几何形状，iii）算法简单，和iv）比竞争的光谱方法更高的精度。许多地球科学家感兴趣的是，将研究径向基函数在球坐标系中的应用，并初步应用于气候和太阳建模。教育推广活动的特点是建立一个互动网站，提供教学和应用模块。

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.