Abstract
The importance of the consistency between the vertical and horizontal resolution of numerical models has been suggested in recent studies. In this context, consistency means that the vertical scales that are physically related to the resolvable horizontal scales are also resolved. In this study, gravity waves produced in a hydrostatic primitive-equation numerical simulation of conditional symmetric instability (CSI) are shown to be produced by the inconsistency of the model resolution, where the physical relationship between the vertical and horizontal scales is determined by the slope of the narrow thermal structures (loosely termed “fronts”) produced by the CSI.
The detailed examination of the spurious gravity waves in the numerical simulation and height perturbations in diagnostic experiments quantify the effects of this inconsistency in the resolution. It is shown that 1) spurious height perturbations of ∼1 m or less are produced, though these may be sufficient to cause significant gravity waves detectable in the fields of certain variables, 2) the amplitudes of the height perturbations increase with increasing AS ratio (defined as the grid aspect ratio Δp/Δy, divided by the slope s of the front), 3) the amplitudes of the height perturbations increase with increasing horizontal temperature difference across the front, 4) the amplitudes of the height perturbations increase with decreasing horizontal grid-space width of the front, and 5) the wavelengths of the height perturbations, when measured in grid spaces, are numerically equal to the AS ratio for AS ⩾ 2 and can otherwise be determined for AS < 2. Only horizontal frontal widths ⩽7Δy and cross-frontal temperature differences ⩽2 K are examined. If sufficiently narrow and sufficiently strong sloping fronts exist initially or develop in a numerical simulation, AS ⩽ 1 will ensure that the amplitudes of spurious height perturbations and gravity waves caused by the resolution inconsistency will be small. The horizontal wavelengths of the gravity waves will be especially large if AS−1 is approximately an integer. Decreasing the vertical grid spacing is the most effective means of reducing the height-perturbation amplitudes, though increasing the horizontal grid spacing may reduce the perturbation amplitudes if the grid-space width of the front remains constant as the grid spacing is increased.
It is strongly recommended that the selection of a vertical grid spacing for a numerical simulation should not be done without considering the horizontal grid spacing, the likely occurrence of narrow sloping frontlike structures, and the AS ratio.
