We are grateful for the support of VORTEX2 by the National Science Foundation (NSF) and the National Oceanic and Atmospheric Administration. The authors were supported by awards AGS-0801035, AGS-0801041, and AGS-1036237 made to PSU, CSWR, and Rasmussen Systems, respectively. We also thank the countless number of VORTEX2 PIs, students, and other participants, without which the project would not have been possible. We also have benefited from discussions with George Bryan, Johannes Dahl, Matt Parker, Rich Rotunno, and Jerry Straka. Radar data were edited using the SOLOII software provided by the Earth Observing Laboratory at the National Center for Atmospheric Research (NCAR). Chris Nowotarski supplied code to plot material circuits in MATLAB. The DOW radars are NSF Lower Atmospheric Observing Facilities supported by AGS-0734001. Lastly, we appreciate the selfless donation of time and constructive comments provided by the reviewers (Chris Weiss and two anonymous reviewers) and editor (George Bryan).
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Vertical vorticity can be produced close to the ground if vortex lines near the surface are turned abruptly upward by intense gradients of upward velocity, but this is highly improbable without a strong vortex being present already at low levels (Adlerman et al. 1999, p. 2045).
This unfortunate reality can be inferred from Part I’s Fig. 16, which shows forward trajectories originating within and around the low-level vorticity maximum. It is evident that most trajectories originating within roughly a kilometer of the circulation center, even as high as a few kilometers above the surface, would quickly drop below the data horizon if integrated backward.
By “captured” we are referring to backward trajectories near ζmax that sometimes (unrealistically) cannot escape the vortex when integrated backward (e.g., Kosiba et al. 2012, manuscript submitted to Mon. Wea. Rev.). The issue probably stems from the radar scans inadequately resolving or overshooting the low-level horizontal convergence. The depth of the horizontal convergence at the base of a vortex interacting with the surface thins as the vortex intensifies.
The numerical studies of Walko (1993) and Trapp and Fiedler (1995) investigated the processes that generate rotation at the surface using heat sources and sinks in a dry model, rather than simulating actual supercells.
Mashiko et al. (2009) simulated a supercell within the outer rainbands of a landfalling tropical cyclone. This simulation is probably not the best to compare to the Goshen County storm because the environment of the simulated supercell possessed considerable background vertical vorticity. Moreover, the material circuits were only tracked backward for 2 min. In that short period, the circulation was relatively constant (see their Fig. 20).
Nowotarski et al. (2011) investigated the generation of circulation in supercells that were initiated above a stable boundary layer.
The log wind profile for a neutrally stratified surface layer is
In the course of their tests with synthetic data, Majcen et al. (2008) found that retrieved horizontal pressure fields were much more credible than retrieved horizontal buoyancy fields.
The retrieved horizontal pressure-gradient force has zero curl because the density in the pressure-gradient force is replaced with the environmental density that is a function of z only.
By “far field,” we are referring to when the circuit is well upstream of the low-level mesocyclone and much larger in size than at the start of the backward integration. Much of the circuit, however, is still within the outer reaches of the forward-flank precipitation shield where light rain is falling.
To determine which portions of the circuits are responsible for the circulation differences, the best we can do is compare v ⋅ dl for two identically shaped circuits having constant |dl|, as is done in Fig. 7. Although it is tempting to compare, at different times, D(v ⋅ dl)/Dt as a function of location along the circuits, such an analysis is unenlightening because of the variation in |dl| in time, following a circuit (the distance between parcels within the circuits generally decreases as the circuits approach the low-level mesocyclone, given that the circuits experience mean convergence). Although dl is just an infinitesimal element of a circuit, the circuits are discretized, with Δl being obtained from the relative positions of adjacent parcels within the circuits.