Spherical harmonic
From Glossary of Meteorology
spherical harmonic
An analytic basis function on the sphere that is commonly used in a spectral model.
A spherical harmonic is defined for each total wavenumber n and zonal wavenumber m as the following function of sine of latitude μ and longitude λ: where Pm,n is the associated Legendre function defined as The spherical harmonic basis functions satisfy the orthogonal relationship and they satisfy the elliptic equation on the sphere:
