Isotropic High-Order Filter for a Local Domain on the Sphere

Abstract

High-order filtering with isotropy of a local-domain data defined at an arbitrary location on the sphere, with an application to scale-decomposition of mean sea level pressure field, was investigated. The equation of high-order filter was based on the implicit hyper-diffusion of 8th-order, which was discretized by the Fourier-finite element method (FFEM). In order to apply the FFEM high-order filter to a local-domain data which is not represented with two-dimensional array, a rotation of coordinates was performed. The geometry of the rotated local domain was made to be either a polar cap (polar cap domain) or a symmetric window with respect to the Equator (Equatorial symmetric domain) to reduce the anisotropy of the local domains caused by the metric effect of spherical coordinates. The rotated local domains are extended by padding artificial data to match the boundary condition of vanishing gradient. The performance of the filters for the symmetric- or asymmetric- domain, was compared for both initial fields defined with an analytic function and the observed meteorological data. It turned out that the filters on the local domains with symmetry, i.e., the polar cap domain and the Equatorial symmetric domain, produced improved results over the local domains with asymmetry: Asymmetric error pattern between the northern and southern boundary, which is typical of the window domain defined on the middle latitude (or between the pole and the Equator), is reduced appreciably and the improvement is shown to become more significant for the window-domain closer to the pole. Through tests with wind fields, the performance of the filters on the polar cap domain and the Equatorial symmetric domain was found comparable to each other. The advantage of polar cap filter, being not available for the Equatorial symmetric domain filter, was illustrated by conducting a scale decomposition and composite analysis of the mean sea level pressure that requires the data manipulations such as a zonal averaging as well as azimuthal-phase shifting.