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Piecewise Potential Vorticity Inversion: Elementary Tests

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  • 1 Meteorologisches Institut der Universität München, Munich, Germany
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Abstract

Piecewise potential vorticity inversion (PPVI) is widely accepted as a useful tool in atmospheric diagnostics. This method is thought to quantify the instantaneous interaction at a distance of anomalies of potential vorticity (PV) separated horizontally and/or vertically. Doubts with respect to the dynamical justification of PPVI are formulated. In particular, it is argued that the tendency of the inverted streamfunction must be determined in order to quantify far-field effects. Elementary tests of PPVI are conducted to clarify these points. First, PPVI is performed for the textbook case of linear Rossby waves in a one-dimensional barotropic fluid. Analytic solutions are presented for PPVI and the related tendency problem. It is found that PPVI does not contribute to an understanding of Rossby wave dynamics. On the other hand, PPVI turns out to be more useful when applied to confined PV extrema. Neither the application of PPVI to linear baroclinic waves in zonal shear flow nor the inversions of the related temperature anomalies at the boundaries help to better understand the wave development.

It is concluded that PPVI with additional tendency calculations poses and solves a specific problem by retaining observed PV anomalies in one subdomain and removing them in others. The usefulness of the results with regard to the diagnosis of the observed state depends strongly on the flows considered and on the partitions chosen, which must comply with a simple rule.

Corresponding author address: Joseph Egger, Meteorologisches Institut der Universität München, Theresienstr. 37, 80333 Munich, Germany. Email: j.egger@lrz.uni-muenchen.de

Abstract

Piecewise potential vorticity inversion (PPVI) is widely accepted as a useful tool in atmospheric diagnostics. This method is thought to quantify the instantaneous interaction at a distance of anomalies of potential vorticity (PV) separated horizontally and/or vertically. Doubts with respect to the dynamical justification of PPVI are formulated. In particular, it is argued that the tendency of the inverted streamfunction must be determined in order to quantify far-field effects. Elementary tests of PPVI are conducted to clarify these points. First, PPVI is performed for the textbook case of linear Rossby waves in a one-dimensional barotropic fluid. Analytic solutions are presented for PPVI and the related tendency problem. It is found that PPVI does not contribute to an understanding of Rossby wave dynamics. On the other hand, PPVI turns out to be more useful when applied to confined PV extrema. Neither the application of PPVI to linear baroclinic waves in zonal shear flow nor the inversions of the related temperature anomalies at the boundaries help to better understand the wave development.

It is concluded that PPVI with additional tendency calculations poses and solves a specific problem by retaining observed PV anomalies in one subdomain and removing them in others. The usefulness of the results with regard to the diagnosis of the observed state depends strongly on the flows considered and on the partitions chosen, which must comply with a simple rule.

Corresponding author address: Joseph Egger, Meteorologisches Institut der Universität München, Theresienstr. 37, 80333 Munich, Germany. Email: j.egger@lrz.uni-muenchen.de

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