Articles | Volume 15, issue 6
Development and technical paper
28 Mar 2022
Development and technical paper |  | 28 Mar 2022

Improved double Fourier series on a sphere and its application to a semi-implicit semi-Lagrangian shallow-water model

Hiromasa Yoshimura

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Cited articles

Akahori, K., Ishiguro, T., Hattori, K., Suda, R., and Sugihara, M.: A global model based on a double Fourier series, Extended abstract of the 3rd International Workshop on Next Generation Climate Models for Advanced High Performance Computing Facilities, Japan, March 2001. 
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Bihar: Netlib BIHAR library, Netlib Repository [code],, last access: 20 March 2022. 
Boer, G. J. and Steinberg, L.: Fourier series on spheres, Atmosphere, 13, 180–191,, 1975. 
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,<1184:TCOSFO>2.0.CO;2, 1978. 
Short summary
This paper proposes a new double Fourier series (DFS) method on a sphere that improves the numerical stability of a model compared with conventional DFS methods. The shallow-water model and the advection model using the new DFS method give stable results without the appearance of high-wavenumber noise near the poles. The model using the new DFS method is faster than the model using spherical harmonics (especially at high resolutions) and gives almost the same results.