Numerical solutions of the vertical structure equation and associated energetics

The vertical structure equation (VSE) is solved by a Galerkin method as use d by Kasahara. The sensitivity of the vertical decomposition to the truncat ion order of the Legendre polynomials series is studied, with the aim of fi nding an adequate truncation order for a given data set. Obtained results s how that: (1) the vertical scale decomposition presents little sensitivity to the truncation order; (2) the order of truncation may be greater than th e number of discrete levels in the data set. It is finally shown that the p roposed choice of truncation order may overcame the problem of aliasing in the higher internal modes.