[M-GI29] Computational sciences on the universe, galaxies, stars, planets and their environments

[MGI29-06] On the development of a spherical harmonic transform library and its application to the study of atmospheric dynamics

*Keiichi Ishioka¹ (1.Graduate School of Science, Kyoto University)

Keywords:spherical harmonic transform, mechanistic general circulation model, spectral method, optimization

The spherical harmonic transform is an indispensable tool for the calculation of fluid motion using the spectral method and for data analysis in spherical coordinates. The speaker has developed and released a numerical library (ISPACK), which is mainly focused on the spherical harmonic transform. To compute the spherical harmonic transform as quickly as possible, ISPACK uses an approach where the associated Legendre function, which is the latitudinal functional form of the spherical harmonics, is computed simultaneously with the transform to make the best use of the cache memory. This approach itself is not new, but during the development of ISPACK, a new recurrence formula to compute the associated Legendre function was discovered, which reduces the required number of fused multiply and add operations to 1/3 compared to the usual recurrence formula. This recurrence formula has already been adopted by other well-known libraries such as SHTns and Libsharp. ISPACK also makes the best use of SIMD instructions by writing assembly code directly. In this talk, I will outline the aforementioned speed-up know-how included in ISPACK, and as an application example, I will present a formulation of a 3D spectral mechanistic atmospheric general circulation model recently developed by the speaker's group, which also uses the spectral method in the vertical direction. In addition, as another research derived from this 3D spectral model, a research to estimate the equivalent depth of the Pekeris wave observed during the 2022 Hunga Tonga-Hunga Haʻapai eruption will also be presented.