[M-GI30] Computational sciences on the universe, galaxies, stars, planets and their environments

[MGI30-P10] A formulation of a three-dimensional spectral atmospheric dynamical core using new vertical basis functions.

*Shun Fujita¹, Keiichi Ishioka¹ (1.Graduate School of Science, Kyoto University)

Keywords:Three-dimensional spectral model , Atmospheric general circulation model, Atmospheric dynamical core

In the discretization of the dynamical core of atmospheric general circulation models, spectral methods are commonly used for horizontal discretization, while few attempts have been made to use spectral methods for vertical discretization. One such attempt is Ishioka, et al, 2022, which used the Legendre polynomials as vertical basis functions and showed that the method could achieve the same or better accuracy with fewer degrees of freedom than the finite difference method. However, this method is not suitable for simulating phenomena in the upper atmosphere because the corresponding grid point spacing increases rapidly with altitude. In addition, near the lower boundary, the grid point spacing becomes too dense which requires a smaller time step to satisfy the CFL condition, resulting in computational inefficiency. To overcome these problems, we propose two new vertical discretization methods based on spectral methods: one is to use the rational Chebyshev functions and the other is to use the Laguerre functions as vertical basis functions. These vertical discretization methods are used for time integration of the linearized two-dimensional primitive equations and their computational accuracies are checked. Numerical experiments show that both proposed methods are stable and give more accurate results than the method proposed in the previous study. The application of the proposed new methods to the three-dimensional atmospheric dynamical core is also discussed in the presentation.

References
Ishioka, K., Yamamoto, N., & Fujita, M. (2022). A Formulation of a Three-Dimensional Spectral Model for the Primitive Equations. Journal of the Meteorological Society of Japan. Ser. II, 100(2), 445–469. https://doi.org/10.2151/jmsj.2022-022