Some Problems in Reproducing Planetary Waves by Numerical Models of the Atmosphere

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Abstract
The effects of vertical resolution and the upper boundary on the structure of the planetary waves in numerical models are investigated with a simplified one dimensional model, using the quasi-geostrophic, mid-latitude β-plane approximation. The results obtained by models with different vertical resolution and different height of the upper boundary are compared with the control solution which is obtained by using a small grid increment of 0.25km and by including large dissipative effects near the upper boundary located at 90km.The influence of lowering the upper boundary is not fatal to the structure of the waves in the troposphere if the upper boundary is placed at the middle stratosphere and a model has several layers in the stratosphere, because Newtonian cooling or other damping effects of realistic magnitudes well attenuate the wave reflected at the top.Stationary planetary waves obtained by low resolution models (5 or 6 layers) show apparent similarity to the true (control) solution in a qualitative sense. But to obtain quantitatively correct solutions, vertical grid increments should be taken as small as Δz=1-2km in the troposphere andΔz=2-3km in the stratosphere and the top should be placed in the middle stratosphere. When the time integration is performed with the use of a low resolution model, using the true data (control solution) as the initial, the waves can no longer be stationary but tend to transform into the model's own stationary state. For resolving this problem we must use higher resolution models as mentioned in the stationary case.Analogous results are obtained for the simulation of the waves in the stratosphere.