SCALE-DEPENDENT ACCURACY IN REGIONAL SPECTRAL METHODS

The accuracy of a numerical model is often scale dependent. Large spat ial-scale phenomena are expected to be numerically solved with better accuracy, regardless of whether the discretization is spectral, finite difference, or finite element. The purpose of this article is to disc uss the scale-dependent accuracy associated with the regional spectral model variables expanded by sine-cosine series. In particular, the sc ale-dependent accuracy in the Chebyshev-tau, finite difference, and si nusoidal- or polynomial-subtracted sine-cosine expansion methods is co nsidered. With the simplest examples, it is demonstrated that regional spectral models may possess an unusual scale-dependent accuracy. Name ly, the numerical accuracy associated with large-spatial-scale phenome na may be worse than the numerical accuracy associated with small-spat ial-scale phenomena. This unusual scale-dependent accuracy stems from the higher derivatives of basic-state subtraction functions, which are not periodic. The discontinuity is felt mostly by phenomena with larg e spatial scale. The derivative discontinuity not only causes the slow convergence of the expanded Fourier series (Gibbs phenomenon) but als o results in the unusual scale-dependent numerical accuracy. The unusu al scale-dependent accuracy allows large-spatial-scale phenomena in th e model perturbation fields to be solved less accurately.