A spectral limited-area model formulation with time-dependent boundary conditions applied to the shallow-water equations

Abstract

The spectral technique is frequently used for the horizontal discretization in global atmospheric models. This paper presents a method where double Fourier series are used in a limited-area model (LAM). The method uses fast Fourier transforms (FFT) in both horizontal directions and take into account time-dependent boundary conditions. The basic idea is to extend the time-dependent boundary fields into a zone outside the integration area in such a way that periodic fields are obtained. These fields in the extension zone and the forecasted fields inside the integration area are connected by use of a narrow relaxation zone along the boundaries of the limited area. The extension technique is applied to the shallow-water equations. An efficient semi-Lagrangian scheme without any interpolations is introduced and shown to be unconditionally stable and nondamping for advection by a constant wind field. This scheme is tested and compared with the usual semi-Lagrangian schemes where interpolations are involved. The overall efficiency and accuracy of the proposed spectral formulation applied to the shallow-water model encouraged the development of a baroclinic spectral LAM, now in progress. -from Authors