Evaluation of Spectral Versus Grid Methods of Hemispheric Numerical Weather Prediction

Abstract

Using observed hemispheric meteorological data as initial conditions, typical barotropic (one-level) filtered-equation numerical weather prediction models were integrated both by the conventional grid-point method and by the spectral method proposed by Silberman in 1954. For integrations spanning a hemisphere and for comparable space truncation measured in terms of phase speeds, the spectral method was found to be about twice as efficient in terms of computation time on the IBM 7094. It also preserves the quadratic integral invariants of the differential equations and it eliminates the cascade of energy into the smallest resolvable scales. To provide initial data for these comparative integrations, I B M 7094 machine-language programs were developed to interpolate objective analyses (prepared by the National Meteorological Center at Suitland, Maryland) to a latitude-longitude grid and to compute surface spherical harmonic expansion coefficients from the interpolated data. The latter were evaluated by the method proposed by Neumann in 1838, in which all coefficients are mutually independent. Using an intermediate latitude-longitude grid of 2592 data points spanning the northern hemisphere, 333 odd-parity expansion coefficients were evaluated from the National Meteorological Center 1977-point grid on an IBM 7094 computer in 10 seconds.