Maximum Vector

Figure 18. Radial flows superimposed on the radar echoes over the area surrounding the bow-shaped and sausage-shaped echoes. (b) Vertical structure of the secondary circulation wind vectors composed of the east—west divergent and the vertical velocities. (From Lee et al., 2005.)

Figure 18. Radial flows superimposed on the radar echoes over the area surrounding the bow-shaped and sausage-shaped echoes. (b) Vertical structure of the secondary circulation wind vectors composed of the east—west divergent and the vertical velocities. (From Lee et al., 2005.)

and the aliasing at higher wave numbers in the GBVTD-retrieved vortex circulation are effectively removed in the GVTD technique. More importantly, the constant mean wind appears as a set of parallel lines in VdD/RT space, a much simpler signature to identify than the diverging lines in Vd space. Jou et al. (2008) also showed that VTD and GBVTD are special cases of GVTD. A comparison of the differences between the GBVTD- and GVTD-derived vortex structures from wave number 0 to 3 is illustrated in Fig. 19. Clear advantages of the GVTD technique can be seen in the retrieved vortex structure, especially in wave numbers 2 and 3.

Figure 19. Comparison of GBVTD- and GVTD-retrieved vortex structure. (a1) The simulated axis-symmetry wind field, (a2) the GBVTD-retrieved wind field, and (a3) the GVTD-retrieved wind field. (b1—b3) The same as (a1—a3) but for the wave number 1 case, (c1—c3) the same as (a1—a3) but for the wave number 2 case; and (d1—d3) the same as (a1—a3) but for the wave number 3 case. (From Jou et al. 2008.)

Figure 19. Comparison of GBVTD- and GVTD-retrieved vortex structure. (a1) The simulated axis-symmetry wind field, (a2) the GBVTD-retrieved wind field, and (a3) the GVTD-retrieved wind field. (b1—b3) The same as (a1—a3) but for the wave number 1 case, (c1—c3) the same as (a1—a3) but for the wave number 2 case; and (d1—d3) the same as (a1—a3) but for the wave number 3 case. (From Jou et al. 2008.)

GVTD also expands the analysis domain to the point where it is no longer limited by R/Rt < 1 as in GBVTD. The dramatic improvement occurs when R/RT > 1, i.e. the radar is located inside the RMW where it does not observe the full component of the maximum tangential wind of a vortex. While the GBVTD technique cannot retrieve the full circulation in this situation, the GVTD technique can still retrieve the full tangential wind component (Fig. 20). Therefore, the GVTD technique can significantly expand the analysis domain. However, it still suffers from the VTD closure assumption, where the asymmetric tangential and radial winds cannot be separated in its current framework.

8. Outlook

SDWR algorithms remain the only practical avenue for deducing 3D atmospheric vortex structures for research and operation forecasts in the foreseeable future. While there are obvious limitations associated with the VTD family of techniques discussed in this article, it is evident that the VTD family of SDWR algorithms can provide a more complete picture of atmospheric vortices than other SDWR techniques. While this review article focuses on research results that have already appeared in refereed journals, research efforts to address these challenges are presented in this section.

8.1. Improve mean wind estimates

The GBVTD primary circulation can be biased by the cross-beam component of the environmental wind. This bias ultimately affects estimates of the central pressure (Lee et al., 2000; Lee and Bell, 2004). Initial attempts indicated that this component of the environmental wind could be estimated by the hurricane volume velocity processing (HVVP) method (Harasti, 2003, 2004; Harasti and List, 1995; Harasti and List, 2001) and the GVTD technique. Harasti et al. (2005) included the mean wind derived from HVVP and produced 3-8 hPa corrections to the GBVTD pressure values in Hurricane Charley (2004). The special signature of the mean wind in the Vd D/RT space provides a promising way to accurately estimate the mean wind (Jou et al., 2008). An objective method to estimate the mean wind vector is under development. Future research will need to address the quality of the mean winds derived from these techniques and to validate the pressure retrieval results for other TCs with dropsonde data and for tornados with in situ measurements.

8.2. Improving the VTD closure assumptions

The VTD closure assumptions, based on the level of understanding of TC structures and dynamics in the early 1990s, can certainly be improved. It has been shown that vor-ticity waves [so-called vortex Rossby waves (VRWs); Montgomery and Kallenbach, (1997)] live and propagate along vorticity gradients near the inner core of a TC. Their associated potential vorticity mixing processes have been widely accepted as the mechanism for forming polygonal eyewalls, mesovortices, and spiral rainbands (e.g. Guinn and Schubert, 1993; Montgomery and Kallenbach, 1997; Schubert et al., 1999; Kossin et al., 2000). The existence of the VRW in hurricane-like vortices has been simulated in numerical models of varying complexity, ranging from a barotropic, nondivergent, three-region vortex model (e.g. Terwey and Montgomery, 2002) to full-physics, nonhy-drostatic models (e.g. Wang, 2002a, b; Chen and Yau, 2001).

The VRW dynamics provides phase and amplitude relationships between asymmetric tangential wind and radial wind that may be used as closure assumptions for the VTD formulation. A simple form of the VRW is an idealized, small-amplitude, vortex edge wave traveled on the vorticity gradient of a Rankine vortex (Lamb, 1932) where a wave number 2

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