The invertibility of potential vorticity is used to investigate how flows in the middle atmosphere are determined. The distribution of potential vorticity associated with an observed flow is computed. The inversion problem, calculating the flow from the potential vorticity, is solved repeatedly, including and excluding different portions of the potential vorticity. This procedure reveals which bits of potential vorticity are important in determining the flow at a time and location of interest. We consider the minor warming of January 1979, using data obtained by the Limb Infrared Monitor of the Stratosphere (LIMS). The results indicate that the middle stratospheric flow is dominated by potential vorticity that is local both in height and latitude during this period, while flows in both the lower stratosphere and mesosphere are less locally dominated. That portion of the flow responsible for wave-mean flow interactions in the middle stratosphere is also induced by potential vorticity that is nearly local in height. Calculations of the downward influence of the rapid rearrangement of stratospheric potential vorticity during sudden warming episodes show induced tropospheric geopotential tendencies implying pressure increases over the pole of meteorologically significant magnitudes.
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Walter A. Robinson (1988) studied this question.