PDF《H. E. WILLOUGHBY》

1102 M O N T H L Y W E A T H E R R E V I E W VOLUME

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2006 American Meteorological Society can be tracked objectively. Thus, the center position and intensity, measured in terms of maximum wind or minimum sea level pressure, provide a first-order char- acterization of tropical cyclones. Indeed, the HURDAT file (Jarvinen et al. 1984), which constitutes the authori- tative long-term hurricane climatology, contains exactly that information. The role of parametric profiles is to convert position and intensity into a geographical dis- tribution of winds. The Holland profile employs three parameters: maximum wind, radius of maximum wind, and B, an exponent that sets the sharpness of the eye- wall wind maximum. A key result of Part I was that, even for an optimally chosen B, the magnitude of the second derivative of the wind with respect to radius is too small near the radius of maximum wind where the profile is concave downward and too large away from the maximum where the profile is concave upward. Here we propose a new family of parametric profiles that do not suffer from these limitations. The profile wind is proportional to a power of radius inside the eye and decays exponentially outside the eye with a smooth transition across the eyewall. Least squares fits of these profiles to the same sample of aircraft observations used in Part I validate them and provide statistical es- timates of their parameters. Section

2 of this paper for- mulates the new family of profiles and describes the least squares fitting procedure. Subsequent sections present profiles with a single outer exponential decay length, and with a superposition of two outer exponen- tials. Section

5 considers alternative profile formula- tions and addresses hydrodynamic stability of the fitted vortices. Section

6 summarizes results and draws con- clusions. 2. Analysis a. Profile formulation Piecewise continuous wind profiles (e.g., Willoughby 1995) show promise as an alternative to the Holland model. They are composed of analytical segments patched smoothly together (Fig. 1). Inside the eye the wind increases in proportion to a power of radius. Out- side the eye, the wind decays exponentially with a ra- dial e-folding distance that changes from storm to storm. The transition across the radius of maximum wind from the inner to outer profiles is accomplished with a smooth, radially varying polynomial ramp function: V?r? ? Vi ? Vmax? r Rmax ?n , ?0 ? r ? R1?, ?1a? V?r? ? Vi?1 ? w? ? Vow, ?R1 ? r ? R2?, ?1b? V?r? ? Vo ? Vmax exp?? r ? Rmax X1 ?, ?R2 ? r?, ?1c? where Vi and Vo are the tangential wind component in the eye and beyond the transition zone, which lies be- tween r ? R1 and r ? R2;

Vmax and Rmax are the maxi- mum wind and radius at which the maximum wind oc- curs;

X1 is the exponential decay length in the outer vortex;

and n is the exponent for the power law inside the eye. Note that both Vi and Vo are defined through- out the transition zone and that both are equal to Vmax at r ? Rmax. The weighting function, w, is expressed in terms of a nondimensional argument ? ? (r ? R1)/(R2 ? R1). When ? ? 0, w ? 0;

when ? ? 1, w ? 1. In the subdo- main

0 ? ? ? 1, the weighting is defined as the poly- nomial w??? ? 126?5 ? 420?6 ? 540?7 ? 315?8 ? 70?9 , ?2? which ramps up smoothly from zero to one between R1 and R2. As described in the appendix, the weighting function is derived by integration of a bell-shaped poly- nomial curve given by C[?(1 ? ?)]k when (0 ? ? ? 1) FIG. 1. (a) Schematic illustration of a sectionally continuousù hurricane wind profile (shading) constructed by joining an inner profile with swirling wind proportional to a power of radius and an outer profile with swirling wind decaying exponentially with distance outside the radius of maximum wind (darker curves). (b) In a zone spanning the radius of maximum wind, a polynomial ramp weighting function is used to create a smooth transition between the inner and outer profiles. APRIL