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at the RMW, east of the eyewall over the area of a bow-shaped echo. The updraft inside the echo drew in significant air from the surrounding area, including air from the eye, to sustain the convection. Another major convergence area associated with high reflectivity was located in the northwest of the eye. Vertical structure portrayed on an east-west cross-section through the eye is shown in Fig. 18(b). The wind vectors are composed of the density-weighted divergent E-W component and the vertical velocity. The prominent feature is the narrow band of updraft located 20 km east of the eye, where flow converges from the east and west of the line. The outward tilt of the updraft matches the reflectivity pattern well. The strength of the updraft increases with height and peaks at about a 6-7 km altitude, above which the flow diverges away from the eyewall. Also shown is a secondary circulation induced by the eyewall updraft including low-level convergence, upper-level divergence, and weak downward motion inside the eye (x = 0 km).

The initial success of this approach not only provides an avenue for retrieving asymmetric radial winds from the VTD analysis, but also opens the door to use the GBVTD-MVM-derived, dynamically consistent vortex structures as initial conditions for simulating atmospheric vortices. The update rate of 6 minutes will enable the use of these dynamically consistent wind fields in data assimilation. This is an area that still needs to be explored in future research.

7. The Generalized VTD (GVTD)

Technique — A New Paradigm

Since the invention of weather Doppler radar, the kinematic structures of weather phenomena have been displayed exclusively in radial velocity (Vd) in a spherical coordinate system. The characteristics and limitations of atmospheric vortices displayed in Vd have been discussed in detail in this article. A new paradigm was proposed by Jou et al. (1996) to display the atmospheric vortex in VdD/RT space rather than in the convectional Vd space. Its potential impact on atmospheric vortex research was not realized until recently. Displaying the atmospheric vortex in Vd D/RT space eliminates the geometric distortion of a vortex inherent in the traditional Vd space. In this framework, the dipole structure of an axisymmetric vortex is a function of the linear azimuth angle and is not distorted by a varying aspect ratio. Therefore, the center will always be the half point on the line connecting the peak inbound and outbound VdD/RT (Jou and Deng, 1997). Jou et al. (1996) named this center-finding algorithm the velocity distance azimuth display (VDAD) method.

The mathematic foundation of representing atmospheric vortices in VdD/RT space and the characteristics of the VDAD method have been documented and examined by Jou et al. (2008), who demonstrated that the GBVTD formulation when representing in Vd D/RT space becomes exact mathematically without the need to approximate cos a as required in GBVTD. This new approach is named the generalized VTD (GVTD) technique. Hence, the geometric distortion of the dipole inherent in Vd space

Figure 17. Axisymmetric structure (radius—height) of the Mulhall tornado at 4 May 1999 0310:03 UTC. The return power is shown in gray shades and contours represent (a) tangential wind, (b) radial wind, (c) advection pressure deficit, (d) divergence, (e) cyclostrophic pressure deficit, (f) vorticity, (g) total pressure deficit, and (h) angular momentum. The vectors in (b) illustrate the secondary circulation of the Mulhall tornado. Solid (dashed) lines represent positive (negative) values. (From Lee and Wurman, 2005.)

Figure 17. Axisymmetric structure (radius—height) of the Mulhall tornado at 4 May 1999 0310:03 UTC. The return power is shown in gray shades and contours represent (a) tangential wind, (b) radial wind, (c) advection pressure deficit, (d) divergence, (e) cyclostrophic pressure deficit, (f) vorticity, (g) total pressure deficit, and (h) angular momentum. The vectors in (b) illustrate the secondary circulation of the Mulhall tornado. Solid (dashed) lines represent positive (negative) values. (From Lee and Wurman, 2005.)

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