Publication Date:
2014-02-13
Description:
Among the dynamical cores of the NWP communities many different discretization methods can be distinguished to solve numerically the equations governing the motions in the atmosphere. One of them, the Z-grid approach, is based on solving the equations formulated in terms of divergence and vorticity on an Arakawa A-grid, a grid where all the variables are defined at the same gridpoints. To permit an efficient semi-implicit (SI) treatment, Z-grid schemes were proposed in literature which first perform the SI time discretization on the momentum equations formulated in terms of velocity components to construct from this a discretized divergence equation. This publication shows that a careful formulation of such SI Z-grid schemes is required to conserve appropriate dispersion relations for the inertia-gravity, inertia-Lamb and Rossby waves. It is proven analytically for a two time-level (2TL) SI Z-grid scheme of the 1D shallow water equations that the spatial discretization must respect temporal symmetry, meaning that the spatial discretization must be identical in the implicit and explicit part of the scheme. If not, the discretized waves are damped or amplified and their phase and group velocity may be seriously distorted. These findings are discussed in detail and both 1D and 2D numerical tests are carried out to demonstrate that a symmetric formulation is an important modelling constraint in order to obtain an appropriate geostrophic adjustment.
Print ISSN:
0035-9009
Electronic ISSN:
1477-870X
Topics:
Geography
,
Physics
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