Bicubic Interpolation with Spectral Derivatives

A simple and accurate interpolation method applicable to semi-Lagrangian advection in a spectral global atmospheric model and downscaling is presented. The derivatives required for bicubic interpolation are usually represented by finite differences. Accuracy of bicubic interpolation is found to be improved by using derivatives calculated by the spectral method. Thus, the zonal and meridional derivatives are obtained by the Fourier and Legendre transforms, respectively. The proposed method is validated with the Gaussian hill rotation tests. The semi-Lagrangian advection model with this method produces a minimal error, comparable to that of the non-interpolating semi-Lagrangian model. In order to avoid the computationally expensive Legendre transforms, semi-spectral interpolation methods using only zonal spectral derivatives are also tested. Semi-spectral interpolation is found to be as accurate as full-spectral bicubic interpolation when quintic interpolation is used in the meridional direction.