Development of a Three-dimensional Spectral Atmospheric Dynamical Core using Scaled Laguerre Functions

We propose a new formulation of a three-dimensional spectral model for the primitive equations, in which the spectral method is applied not only in the horizontal but also in the vertical direction. In this model, we utilize scaled Laguerre functions as the vertical basis and spherical harmonics as the horizontal basis. This formulation introduces a tunable scaling parameter, enabling the model top to be placed at high altitudes while maintaining adequate vertical resolution in the upper atmosphere. This formulation is implemented as a numerical model, and its performance is validated through a series of benchmark experiments. The results demonstrate that the numerical error of the present model decreases much faster than that of a corresponding vertical finite-difference model as the vertical degrees of freedom are increased. Furthermore, using linearized two-dimensional primitive equations, the properties of gravity waves under the proposed discretization are examined and compared with those of conventional vertical finite-difference discretizations. The results confirm that the proposed method can accurately represent upward-propagating waves.