The Aliased and the Dealiased Spectral Models of the Shallow-Water Equations

Abstract

The most widely used spectral models with the transform method are the dealiased spectral models in which the dealiased technique is used in the discrete Fourier transform according to the 3/2 rule. From the viewpoint of the Walsh-Hadamard transform, the multiplications of the values of the variables on the grid points do not yield the aliasing terms. The aliased spectral model is compared with the dealiased spectral model in the shallow-water equations, using the initial conditions of the Rossby-Haurwitz wave and the First GARP (Global Atmospheric Research Program) Global Experiment (FGGE) data. For the same grid points the solutions of the aliased spectral models are more accurate than that of the dealiased spectral models. For the same wavenumber truncation, the computational amount of the aliased spectral model is only 60% of the dealiased spectral model. The phenomenon of the nonlinear computational instability induced by the aliasing terms in the long time integration of the aliased spectral models has not yet been discovered. Thus, in the spectral models with the transform method, the necessity of using the 3/2 rule in the discrete Fourier transform may be viewed with suspicion.