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HEh9ll4 i>TTlj

HEh9ll4 i>TTlj

Figure 16. Averaged axisymmetric tangential and radial winds obtained by averaging across all radii. (From Bluestein et al., 2003.)

is 81hPa lower than the pressure at R = 3 km, which is dominated by the cyclostrophic pressure [Fig. 17(e)] with adjustment from the advection pressure [Fig. 17(c)]. These pressure deficits are comparable with rare in situ observations (Winn et al., 1999; Lee et al., 2004; Wurman and Samaras, 2004; Lee et al., 2004) in strong tornadoes. This magnitude is also consistent with analytical pressure analysis from a similar wind profile of a Rankine combined vortex (see Appendix in Lee and Wurman, 2005).

The vorticity pattern in Fig. 17(f) shows an annular (or so-called "ring") vorticity profile where the peak vorticity of 0.28 is concentrated in an annulus between 300 and 500 m in radii. The radial vorticity gradient of a ring vorticity profile changes sign and satisfies the necessary condition for barotropic instability, usually accompanying mature TCs (Mallen et al., 2005). The angular momentum contours [Fig. 17(h)] nearly upright inside the RMW and their value increase with the radius while the angular momentum outside the RMW increased at a slower rate. This pattern is quite similar to those resolved within a mature TC and suggests that the low-level inflow brings in higher angular momentum and the secondary circulation maintains the vortex (e.g. Lee et al., 2000; Marks et al., 1992; Rotunno and Emanuel, 1987).

6. Assimilating VTD-Derived

Winds into the Numerical Model

The strength of the VTD family of SDWR techniques is in providing good axisymmetric and asymmetric tangential winds but lacking asymmetric radial winds. One of the outstanding issues is whether the asymmetric divergent component can be extracted from the VTD-derived incomplete wind fields in order to initialize numerical simulations or data assimilation.

Lee et al. (2003) proposed an innovative concept using the mesoscale vorticity method (MVM) to retrieve inner core divergence and vertical velocity from the frequently available vertical vorticity field from MM5 simulations. The MVM derives vertical velocity from vor-ticity variation in space and time based on the mesoscale vorticity equation, obtained by neglecting the solenoidal term in the full equations. When the mesoscale vorticity equation is formulated in Lagrangian coordinates composed of three nonlinear ordinary differential equations, the vertical velocity can be solved numerically along each characteristic with proper boundary conditions. In their study, observing system simulation experiments were undertaken to demonstrate that the vertical velocities derived from the MVM were less susceptible to errors in horizontal winds than the kinematic method for TCs.

Lee et al. (2006) applied the MVM to derive the inner core vertical velocity and divergent component of the horizontal wind from single Doppler radar observations of Hurricane Danny (1997) using three consecutive volumes of GBVTD analysis. The MVM-retrieved divergent component of the wind vectors superimposed on radar reflectivity of the inner core region of Danny is illustrated in Fig. 18(a). A major convergence zone was found

Table 1. Swirl ratio (S) of the Mulhall tornado from 0310:03 to 0323:12 and the key parameters used in the calculation. See details in Lee and Wurman (2005).
0 0

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