Dependence of Model Energy Spectra on Vertical Resolution

作者：Waite Michael L^*

来源：Monthly Weather Review, 2016, 144(4): 1407-1421.

DOI：10.1175/MWR-D-15-0316.1

• Model errors
• Turbulence
• Mesoscale models
• Circulation/ Dynamics
• Models and modeling
• Mesoscale processes

Many high-resolution atmospheric models can reproduce the qualitative shape of the atmospheric kinetic energy spectrum, which has a power-law slope of -3 at large horizontal scales that shallows to approximately -5/3 in the mesoscale. This paper investigates the possible dependence of model energy spectra on the vertical grid resolution. Idealized simulations forced by relaxation to a baroclinically unstable jet are performed for a wide range of vertical grid spacings Delta z. Energy spectra are converged for Delta z
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200 m but are very sensitive to resolution with 500 m <= Delta z <= 2 km. The nature of this sensitivity depends on the vertical mixing scheme. With no vertical mixing or with weak, stability-dependent mixing, the mesoscale spectra are artificially amplified by low resolution: they are shallower and extend to larger scales than in the converged simulations. By contrast, vertical hyperviscosity with fixed grid-scale damping rate has the opposite effect: underresolved spectra are spuriously steepened. High-resolution spectra are converged except for the stability-dependent mixing case, which are damped by excessive mixing due to enhanced shear over a wide range of horizontal scales. It is shown that converged spectra require resolution of all vertical scales associated with the resolved horizontal structures: these include quasigeostrophic scales for large-scale motions with small Rossby number and the buoyancy scale for small-scale motions at large Rossby number. It is speculated that some model energy spectra may be contaminated by low vertical resolution, and it is recommended that vertical-resolution sensitivity tests always be performed.

• 出版日期2016-4