Further Studies on a Spectral Model of the Global Barotropic Primitive Equations with Hough Harmonic Expansions

Abstract

This paper describes further improvement in a new spectral model of the global barotropic primitive equations (Kasahara, 1977) which utilizes Hough harmonies as basis functions. A review is presented on a method of constructing Hough harmonics (normal modes of Laplace's tidal equations) with new results of the eigensolutions for the logitudinal wavenumber zero case. Applying this complete set of orthonormal Hough harmonics, we formulate a spectral model of the nonlinear, barotropic primitive equations (shallow-water equations) over a sphere which eliminates separate treatment of the zonally averaged component equations in the previously proposed model by the author. An example of the model calculation with Haurwitz wavenumber 6 initial conditions is presented.