Expansion of Hemispheric Meteorological Data in Antisymmetric Surface Spherical Harmonic (Laplace) Series

Abstract

A brief review of methods of expanding scalar functions in surface spherical harmonic or Laplace series reveals that the method proposed by Neumann in 1838 has distinct advantages. Since it allows exploitation of the orthogonality of the basis in both directions, Laplace expansions are no more laborious than double Fourier expansions (except for the chore of evaluating associated Legendre functions) and the coefficients are mutually independent. Using the 1977 data points of the NWPG octagon grid as input, data were interpolated and extrapolated to a 2.5 degree latitude by 5 degree longitude grid (2592 points) and the 333 Laplace coefficients corresponding to the odd series truncated at V3518 were evaluated in 10 seconds on an IBM 7094.