Spectral analysis method for a limited area using the eigenmodes of the spherical Laplacian operator

Abstract

We propose a spectral analysis method using the eigenmodes of the spherical Laplacian operator on the limited area domain. Two numerical methods are considered for the horizontal discretization: One uses the half-ranged Fourier series for both longitudinal and latitudinal directions, and the other uses the Fourier finite-element method with piecewise linear basis functions for the latitudinal direction. The field variable for the two numerical algorithms is represented as linear combinations of the eigenvectors of the Laplacian operator on the limited area domain; we define the one-dimensional spectrum with the eigenvector coefficients as a function of the indices equivalent to the total wavenumbers of the Laplacian operator on the global domain. The spatial robustness of this method was verified through the self-consistency test comparing the spectra of isotropic Gaussian bells on the sphere. We used the method in the kinetic energy spectral analysis for a limited area with global atmospheric data, and compared the results for different seasons. The kinetic energy spectra represented the well-known characteristics with scale and different powers with season.