Spherical harmonic

From Glossary of Meteorology
Revision as of 16:57, 25 April 2012 by imported>Perlwikibot
(diff) ← Older revision | Latest revision (diff) | Newer revision → (diff)



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:
ams2001glos-Se46
where Pm,n is the associated Legendre function defined as
ams2001glos-Se47
The spherical harmonic basis functions satisfy the orthogonal relationship
ams2001glos-Se48
and they satisfy the elliptic equation on the sphere:
ams2001glos-Se49


Copyright 2022 American Meteorological Society (AMS). For permission to reuse any portion of this work, please contact permissions@ametsoc.org. Any use of material in this work that is determined to be “fair use” under Section 107 of the U.S. Copyright Act (17 U.S. Code § 107) or that satisfies the conditions specified in Section 108 of the U.S.Copyright Act (17 USC § 108) does not require AMS’s permission. Republication, systematic reproduction, posting in electronic form, such as on a website or in a searchable database, or other uses of this material, except as exempted by the above statement, require written permission or a license from AMS. Additional details are provided in the AMS Copyright Policy statement.