Figure 2. Trajectories (units of 500 km) of the lower-layer vortex encountering weaker (shown as +); fair (shown as *); and stronger (shown as o) vertical wind shear. (From Wu and Emanuel, 1993).

Figure 3. The relation between the maximum induced vortex speed and the magnitude of the vertical shears. (From Wu and Emanuel, 1993.)

distinct northward vortex drifts associated with different magnitudes of the mean westerly shears are found, as expected. Also, the drift in the zonal direction is a function of the background shear, i.e. more eastward drift is associated with weaker shear. Figure 3 shows the maximum total drift speed as a function of the ambient shear. The vortex drift increases initially as the shear increases, and there exists an optimal shear that maximizes the vortex drift. Above that optimal shear, the drift speed decreases with increasing shear, and approaches a constant, since the impact to the lower-layer vortex drift by the upper-layer plumed advected far downstream would be very limited.

2.4. Summary

Observations show that TCs have broad anticyclones aloft, and that the distribution of potential vorticity gradients in the tropical atmosphere is highly inhomogeneous. There are indications that the potential vorticity gradients in the subtropical troposphere are very weak (see Fig. 2 in Wu and Emanuel, 1993), perhaps having been rendered so by the action of synoptic scale disturbances.

It is found that the direct effect of ambient vertical shear is to displace the upper-level plume of anticyclonic relative potential vorticity downshear from the lower layer cyclonic point potential vortex, thus inducing a mutual interaction between the circulations associated with each other. This results in a drift of the point vortex broadly to the left of the vertical shear vector (in the Northern Hemisphere).

3. Potential Vorticity Perspective of TC Motion (Wu and Emanuel, 1995a,b; Wu and Kurihara, 1996; Wu et al., 2003, 2004)

The above papers are some pioneering works in adopting the potential vorticity (PV) diagnostics to evaluate the control by the large-scale environment of hurricane movement and, more importantly, to assess the storm's influence on its own track. By using the PV framework, the exploration of the dynamics of hurricanes is feasible with the validity of balanced dynamics in the tropics. In this section, the use of PV diagnostics is to understand the hurricane steering flow, and to demonstrate the interaction between the cyclone and its environment, including the investigation of the binary TC interaction and the major factors affecting the analyses and forecast bias of the TC track forecasts.

3.1. Background

PV methods have proven useful in understanding synoptic- and large-scale midlatitude dynamics (Hoskins et al., 1985), and are widely applied to tropical systems (e.g. Molinari, 1993; Montgomery and Farrell, 1993). A hurricane is a localized yet robust vortex, and can possibly change the surrounding environmental flow field substantially by its strong circulation, which in turn affects the evolution of the track, intensity, and structure of the hurricane. This interaction between the TC and its environment is nonlinear. Previous studies have investigated how the large-scale flow fields affect the track, intensity (e.g. Molinari et al., 1995), and structure of the hurricane, and how the storm circulation changes the environmental flow field (e.g. Ross and Kurihara, 1995). However, these studies consider only a one-way interaction between the storm and its environment. In this work, the two-way hurricane-environment interaction is studied, i.e. how the change of the environment due to the storm feeds back to affect the storm's track.

The concept of binary interaction has been well described by tank experiments (Fujiwhara, 1921, 1923, 1931), observations (Brand, 1970; Dong and Neumann, 1983; Lander and Holland, 1993; Carr et al., 1997; Carr and Elsberry, 1998), and modeling studies (Chang, 1983, 1984; DeMaria and Chan, 1984; Ritchie and Holland, 1993; Holland and Dietachmayer, 1993; Wang and Holland, 1995). All of these studies indicate that two TCs can interact and subsequently develop mutual orbiting and possible approaching, merging, and escaping processes (Lander and Holland, 1993).

The observational evidences Brand (1970) has provided suggest that there is a correlation between the separation distance and the angular rotation rate of two TCs. Brand also showed that the effect of such binary interaction depends not only on differences in storm size and intensity, but also on variations of the currents in which the tropical storm systems are imbedded.

Work from Carr et al. (1997) and Carr and Elsberry (1998) has proposed detailed conceptual models to categorize the binary interaction processes, namely: (1) the direct TC interaction with one-way influence, mutual interaction or merger of the two TCs; (2) the semidirect TC interaction involving another TC and an adjacent subtropical anticyclone; and (3) the indirect TC interaction involving the anticyclone between the two TCs. In spite of a success rate of 80% in distinguishing the modes of the binary interactions from analyses of eight-year samples of western North Pacific TCs, the ways to quantify the binary interaction of TCs are still arguable.

This section has attempted to demonstrate the quantitative use of PV diagnostics in understanding the hurricane steering flow, in addition to the interaction between the cyclone and its environment, along with the binary TC interaction and the evaluation of the forecast bias.

3.2. Methodology

(1) Defining the hurricane advection flow This is an original work to define the hurricane advection (steering) flow based on the PV diagnostics. One conventional problem in estimating the steering flow based on the azimuthal average is that the resulting wind is highly sensitive to the exact choice of the hurricane center (if the storm center is misrepresented, the averaged flow would be contaminated by the asymmetric high wind near and off the storm center). To avoid such a problem, the hurricane advection flow is defined as the balanced flow (at the storm center) associated with the entire PV field in the troposphere, except for the PV anomaly of the hurricane itself.

(2) PV inversion

The PV inversion is that given a distribution of PV, a prescribed balances condition, and boundary conditions, the balanced mass and wind fields can be recovered. Formulated on the n [n = Cp(p/p0)K] coordinate and spherical coordinates, the two equations to be solved are q =

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