The theory of potential vorticity (PV) allows us to describe the life cycle of mid-latitude baroclinic systems in terms of the individual impacts and interactions of distinct PV anomalies embedded in the background flow. PV anomalies associated with the undulating tropopause, the low-level thermal field, and key diabatic processes such as the latent-heat release within the cloudy systems of the cyclone, are often considered as evolving features regulated by their lateral and vertical mutual interactions and their interaction with the stratospheric high-latitude PV reservoir. Under some balance-flow assumptions, PV inversion can be used to quantify the contribution of the PV anomalies to the cyclone depth (or other attributes) at various stages of its life cycle (a static approach); but it is less clear how to diagnose with similar quantitative detail the various types of time-dependent interactions among the anomalies and mean flow that govern the processes of cyclogenesis and cyclolysis (a dynamic approach).
This paper presents a method that implements the concepts of ‘PV thinking’ quantitatively. The method first applies a piecewise PV-inversion scheme formulated according to the Charney nonlinear mass–wind-balance approximation. Then it combines a prognostic system of balance equations that are consistent with the applied inversion scheme with a factor-separation technique. By switching on and off the PV anomalies of interest, various flow configurations are generated, and the corresponding solutions to the prognostic equations can be algebraically combined to isolate the magnitude of both the individual and the synergistic effects of the PV anomalies on the spatial pattern of geopotential-height tendency (and vertical motion) around the cyclone, with low computational cost.
The potential of the method to elucidate the relative importance of physically-meaningful PV anomalies for the growth or decay of baroclinic systems is illustrated for the intense Mediterranean cyclone of 10–12 November 2001, using the NCEP meteorological grid analyses at 12 h intervals.
The upper-level PV anomalies contributed very significantly during the whole life cycle of this Mediterranean cyclone. Surface thermal anomalies were fundamental during the development period, and induced the general northeastward movement of the system during the later stages. During the mature stage of the cyclone, the interaction between the two types of anomalies became the dominant effect. All other contributions, including the individual and synergistic effects of diabatically-generated PV, were generally most relevant during this mature stage. Copyright © 2008 Royal Meteorological Society