Piecewise potential vorticity inversion

The treatment of the potential vorticity (PV) distribution as a composite of individual perturbations is central to the diagnostic and conceptual utility of PV. Nonlinearity in the inversion operator for Ertel's potential vorticity renders quantitative piecewise inversion (inversion of individual portions of the potential vorticity field) ambiguous. Several methods of piecewise inversion are compared for idealized and observed potential vorticity anomalies of varying strengths. Even as the Rossby number of the balanced solutions increases well past unity, relative differences among the more plausible methods do not increase significantly near the anomaly. These relative differences are also found to be smaller than those obtained by comparing any of the methods to quasigeostrophic inversion. However, differences above and below anomalies increase with increasing Rossby number, suggesting that one cannot uniquely diagnose the interaction of large amplitude PV anomalies. -Author