The Validity of the Geostrophic Approximation in the Winter Stratosphere and Troposphere

Abstract

The validity of the geostrophic approximation is examined for the Northern Hemisphere from the lower troposphere to the stratopause in January, using a general circulation model. Substantial errors are found when the geostrophic winds are compared to the true winds in the stratosphere. The errors in the winter stratosphere are, in fact, much larger than the errors in the troposphere. The relative errors in quantities derived from the wind field, such as eddy momentum and heat fluxes are found to be even larger than the errors in the zonal wind field. The Eliasen–Palm (EP) flux divergence is now commonly used to diagnose the interactions of the eddies with the mean flow. The errors in the quasi-geostrophic EP flux divergence am found to be as large (or larger) than the true divergence in the winter stratosphere. The true EP flux from the model is convergent almost everywhere in the stratosphere although observational studies have shown a region of divergence at high latitudes, indicating an apparent source of wave activity. A divergent region is also found in the quasi-geostrophic EP flux from the model and is shown to result primarily from the use of geostrophic winds although the terms omitted in the quasi-geostrophic equations are not negligible. The rotational winds are calculated for the model and the errors associated with their use are shown to be much smaller than the errors associated with the geostrophic winds. Geostrophic winds are extremely easy to calculate from the height field but it is likely that higher order approximations to the rotational winds would produce much more accurate results in diagnostic studies of the stratosphere. The instantaneous and short-term mean errors associated with a quasi-geostrophic analysis during a minor stratospheric warming are similar in character to the long-term mean errors.