A General Filter for Stretched-Grid Models: Application in Cartesian Geometry

Abstract

lobal climate models with variable resolution are effective means to represent regional scales over an area of interest while avoiding the nesting issues of limited-area models. The stretched-grid approach provides a dynamical downscaling approach that naturally allows two-way interactions between the regional and global scales of motion. Concentrating the resolution over a subset of the earth?s surface increases computational efficiency and reduces the computational costs compared to global uniform high-resolution models; however, it does not come free of some problems related to the variation of resolution.To address the issues associated with the stretching and anisotropy of the computational grid, a general convolution filter with a flexible response function is developed. The main feature of this filter is to locally remove scales shorter than a user-prescribed spatially varying length scale. The filtering effectiveness and computational efficiency of the filter can be custom tailored by an appropriate compromise between the filtering response and the width of the convolution stencil. This approach has been tested in one- and two-dimensional Cartesian geometry. It is shown that an effective filter can be obtained using a limited spatial stencil for the convolution to reduce computational cost, and that an adjustable spatially variable and nearly isotropic response can be obtained for application on variable grids.