Potential Vorticity Diagnostics of Cyclogenesis

The assumption of dynamically balanced flow allows one to completely encase the dynamics of extratropical cyclones in a potential vorticity (PV) framework. This approach offers a conceptually simple interpretation of dynamics because PV is a conserved quantity (in the absence of heating and friction) from which the flow itself can be deduced (the property of invertibility). The conservation law allows one to identify developments significantly influenced by heating and friction, and the invertibility property can be used to quantitatively measure such effects. We develop a diagnostic system based on the relative smallness of the irrotational part of the horizontal wind, which allows us to calculate the balanced flow given the three-dimensional distribution of Ertel's PV. The close agreement between the observed and balanced flows, even for intense cyclones, illustrates the practical utility of the PV approach. Furthermore, we present a technique for determining the flow associated with individual perturbations of PV. Insight gained from these diagnostics is demonstrated by examining a particular case of cyclogenesis. In the early stages of growth, the low-level perturbation winds are mostly associated with variations of potential temperature along the lower boundary and act to propagate the system as a surface Rossby wave. Amplification of this wave occurs through advection, first by the winds associated with a low-level PV feature, then later by the low-level circulation signature of an amplifying upper-level wavelike PV anomaly. In turn, development of the upper-level perturbation appears strongly influenced by the presence of the low-level anomalies. The low-level PV anomaly seems to result from the condensation of water vapor rather than from advection. This feature grows rapidly, eventually contributing about 40% of the cyclonic circulation in the mature storm. We do not identify any significant PV anomalies arising from advection on a systematic tropospheric PV gradient, implying that the integrated effect of β is dominated by the gradient of PV at the tropopause. Viewing the upper-level wave as a perturbation of potential temperature on the tropopause (a surface of constant PV), part of this development is conceptualized as interacting upper and lower boundary Rossby waves, as in the Eady model.