The Usefulness of Piecewise Potential Vorticity Inversion

It is today widely accepted that potential vorticity (PV) thinking is a highly useful approach for understanding important aspects of dynamic meteorology and for validation of output from state-of-the-art numerical weather prediction (NWP) models. Egger recently presented a critical view on piecewise potential vorticity inversion (PPVI). This was done by defining a PV anomaly by retaining the observed PV field in a specific region, while changing the observed PV fields to zero elsewhere. Inversion of such a modified PV field yields a flow vastly different from the observed. On the basis of this result it was argued that PPVI is useless for understanding the dynamics of the flow. The present paper argues that the results presented by Egger are incomplete in the context of PPVI, since the complementary cases were not considered and that the results also depend on the idealized model formulations. The complementary case is defined by changing the observed PV to zero in the specific region, while retaining the observed PV field elsewhere. By including the complementary cases, it can be demonstrated that the streamfunction fields associated with the PV and boundary temperature anomalies presented by Egger add up to yield the observed streamfunction field, as expected if PPVI is to be valid. It follows that PPVI is indeed valid and useful in these cases.