The threshold values were based on the strain-free angular displacement that air parcels experienced over a 72 hour period. The structure of tropical storms, relative to that of tropical depressions, has a distinct signature in the Lagrangian OW field. In addition to having maximum Lagrangian OW near the core, the composite profiles in the effective radius coordinate show that at tropical storm strength the Lagrangian OW has a steeper radial gradient, higher magnitude of Lagrangian OW values, and greater enclosure of the ring of negative Lagrangian OW values outside the vortex core than systems that have not reached tropical storm strength.
The methods proposed here are geometric; the development criteria include the shape and curvature of the Lagrangian OW field. Tropical cyclone formation is characterized by a sufficient region of Lagrangian OW with positive Gaussian curvature, and the intensity is determined by the magnitude of the intrinsic strain-free rotation rate. Though convection and vertical alignment are accepted as important factors in development, their coupling to the divergence field makes them become absorbed into the Lagrangian OW field, and the criterion for development remains exceptionally simple.
Since these criteria are frame-independent, the methods developed here can be automated very easily. The parameters used in the automated detection of Lagrangian OW=13, 15, and 30 radians, and Lagrangian vorticity=30, 40, and 70 radians for tropical depression, tropical storm, and hurricane formation, respectively, are also robust, as a change in parameters does not lead to a significant change in the number of vortices detected. While the thresholds for development require Lagrangian OW to exceed a certain value for development, the topology of the Lagrangian OW and Lagrangian vorticity fields are the same even well before formation as after formation. This allows the algorithm to locate pre-genesis systems that may develop during a forecast by finding those systems that exceed the thresholds at later times in the forecasts, and then by following those back to earlier times. Surprisingly, given the minimum thresholds for development, the automated detection produced very few false alarms although there were several early detections. Those systems found by an automated algorithm to exceed threshold values over consecutive 6 hour analyses always developed within 24 hours.