Articles | Volume 9, issue 4
https://doi.org/10.5194/gmd-9-1477-2016
https://doi.org/10.5194/gmd-9-1477-2016
Development and technical paper
 | 
20 Apr 2016
Development and technical paper |  | 20 Apr 2016

On computation of Hough functions

Houjun Wang, John P. Boyd, and Rashid A. Akmaev

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Cited articles

Andrews, D., Holton, J., and Leovy, C.: Middle Atmosphere Dynamics, Academic Press, Inc., New York, 1987.
Bailey, P., Everitt, W., and Zettl, A.: Computing eigenvalues of singular Sturm-Liouville problems, Results Math., 20, 391–423, https://doi.org/10.1007/BF03323182, 1991.
Boyd, J. P.: Planetary waves and the semiannual wind oscillation in the tropical upper stratosphere, PhD thesis, Harvard University, 1976.
Boyd, J. P.: The choice of spectral functions on a sphere for boundary and eigenvalue problems: A comparison of Chebyshev, Fourier and Associated Legendre expansions, Mon. Weather Rev., 106, 1184–1191, 1978.
Boyd, J. P.: Chebyshev and Fourier Spectral Methods, Dover Publications, Inc., 2nd Edn., 2001.
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We briefly survey numerical methods for computing eigenvalues and eigenfunctions for the Laplace tidal equation. In particular we compare two methods that have numerical or conceptual advantages over the most commonly used methods. MATLAB codes are provided to facilitate their use. Researchers interested in atmospheric tidal analysis or in numerical methods for accurately computing eigenvalues of differential operators may find the paper helpful.