We are grateful for the support of VORTEX2 by the National Science Foundation (NSF) and 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. Radar data were edited using the SOLOII software provided by the Earth Observing Laboratory at the National Center for Atmospheric Research (NCAR). Jim LaDue provided the photograph in Fig. 9b. The video frames in Figs. 9c,d are courtesy of Nolan Atkins, Roger Wakimoto, and the Lyndon State University–NCAR photogrammetry group. 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, Morris Weisman, and one anonymous reviewer) and editor (George Bryan).
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The Goshen County storm also has been referred to as the “LaGrange storm” (e.g., Wakimoto et al. 2011).
Circulation centers were identified at the location of the minimum in the field of Okubo–Weiss number (W; Okubo 1970; Weiss 1991) following Markowski et al. (2011). The W field was further smoothed in order to filter submesocyclone-scale features. Scales smaller than 2 km were filtered using a three-step Leise (1982) filter, which suppresses wavelengths ≤8Δ, where Δ is the grid spacing.
Although the mean motion was faster and less rightward in the 2100–2130 UTC period, the grid to which raw radar observations from this period were interpolated was translated at the same constant velocity as in the 2130–2148 UTC period. Given that the main reason for using a translating grid was to reduce time interpolation errors in the trajectory calculations, we were not concerned with a grid-relative drift of the storm during the single-Doppler observation period.
The azimuthal wind shear is defined as r−1∂υR/∂ϕ, where r is the range from the radar, υR is the radial velocity, and ϕ is the radar azimuth (not to be confused with the mathematical coordinate).
The time series of maximum azimuthal shear at low levels also is much noisier than at midlevels. One possibility is that the smaller scale of the low-level mesocyclone, relative to the midlevel mesocyclone, makes its intensity more dependent on the location of the radar beams relative to the axis of rotation. The relatively noisy time series of maximum low-level azimuthal shear also could be attributable to the influence of the gust front. Azimuthal shear can be associated with deformation or rotation. Given that gust fronts can be associated with significant deformation and rotation, whereas mesocyclones are dominated by rotation, one might expect low-level azimuthal shear to be intrinsically more variable in time than midlevel shear.
Vortex lines were computed using a fourth-order Runge–Kutta algorithm. Velocity derivatives were computed using fourth-order, centered differences, except near data boundaries where second-order, uncentered differences were used. The qualitative characteristics of the vortex lines are robust for reasonable ranges of smoothing [e.g., see the appendix in Markowski et al. (2008)]. Vortex-line calculations originating within the midlevel mesocyclone (e.g., the blue lines in Fig. 10) are qualitatively insensitive to the observed variations in the magnitude of the horizontal gradient of vertical velocity, |∇hw|, within the midlevel mesocyclone [vortex lines were computed from additional locations within the midlevel mesocyclone (not shown) spanning a wide range of |∇hw|], which suggests that the vortex lines computed from the fixed lattices of points in the midlevel mesocyclone also are qualitatively insensitive to the |∇hw| errors (errors in the retrieved w, which can be large at midlevels, potentially could be accompanied by significant errors in |∇hw|).
Even at times when the data horizon is low, the errors in the vertical velocity field accumulate with altitude (e.g., Doviak et al. 1976); thus, all retrieved midlevel vertical velocities in this study should be interpreted only qualitatively (e.g., the maximum vertical velocities evident in Fig. 13 are not credible).
Even if the mobile mesonet could have reached the storm earlier, it is unlikely that they would have been able to sample this region given the paucity of roads in the area; what few roads existed were generally unpaved and unfriendly to data collection in heavy precipitation.
The trajectories were integrated using a fourth-order Runge–Kutta algorithm (as was done for the vortex lines). A time step of 15 s was used, and the 3D wind fields were assumed to vary linearly in time between dual-Doppler analyses. The spatial interpolation was trilinear.
Bolton’s (1980) formula for pseudoequivalent potential temperature was used. When referring to θe throughout the article, we technically are referring to pseudoequivalent potential temperature, which is conserved for dry adiabatic and pseudoadiabatic processes.
This would require a hydrometeor mixing ratio of roughly 7 g kg−1.
To put this gradient into perspective, a parcel of air residing in a 1 K km−1 horizontal θρ gradient would acquire a horizontal vorticity of 0.01 s−1 in 5 min.