High-Order Spectral Filter for the Spherical-Surface Limited Area

Abstract

Abstract A high-order spectral filter for the spherical-surface limited-area domain, either window or sector type, is presented, where the window domain is finite both in longitude and latitude and the sector domain is finite in longitude, but is ranged from Pole to Pole in latitude. The data given in the physical domain are extended to either extended window or sector domain by padding artificial data that are appropriate for spectral decomposition with half-ranged Fourier series. The high-order filter equation of Laplacian operator type was split into first- or second-order spherical elliptic equations as in the global domain high-order spectral filter. Each low-order elliptic equation is discretized using half-ranged Fourier series both in longitudinal and latitudinal direction. Since the domain is of the spherical geometry, the window domain spectral filter consists of full matrices for each zonal wavenumber and thus performs filtering with O(N3) operation for N × N grids. On the other hand, the sector domain filter performs with efficient O(N2 logN) operation for the same grids, because the matrices can be constructed in tridiagonal form. The error of the filter was analyzed using the eigenfunctions of the filter equation to get insights on data-extension parameters. The limited-area domain filters were tested with localized analytic function and the midlatitude observed data of meteorological variables, and the results were compared to those of the global domain filter. Accuracies of window and sector domain filters were found almost the same, and they turned out to vary with the filter parameters and the location and size of the domain. Application of the limited domain filters to the tropical cyclone initialization scheme showed very close performances to each other for the track and intensity forecasts.