A Spectral Limited-Area Model Formulation with Time-dependent Boundary Conditions Applied to the Shallow-Water Equations

Abstract

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 takes 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. A simple explicit (leapfrog) integration is shown to give results that are almost identical to the hemispherical forecast used as boundary fields. A nonlinear normal-mode initialization scheme developed in the framework of the spectral formulation is shown to work satisfac...