PDF《H. E. WILLOUGHBY》

Parametric Representation of the Primary Hurricane Vortex.

Part II: A New Family of Sectionally Continuous Profiles H. E. WILLOUGHBY International Hurricane Research Center, Florida International University, Miami, Florida R. W. R. DARLING National Security Agency, Fort George G. Meade, Maryland M. E. RAHN* NOAA/AOML/Hurricane Research Division, Miami, Florida (Manuscript received

5 January 2005, in final form

20 July 2005) ABSTRACT For applications such as windstorm underwriting or storm-surge forecasting, hurricane wind profiles are often approximated by continuous functions that are zero at the vortex center, increase to a maximum in the eyewall, and then decrease asymptotically to zero far from the center. Comparisons between the most commonly used functions and aircraft observations reveal systematic errors. Although winds near the peak are too strong, they decrease too rapidly with distance away from the peak. PressureCwind relations for these profiles typically overestimate maximum winds. A promising alternative is a family of sectionally continuous profiles in which the wind increases as a power of radius inside the eye and decays exponentially outside the eye after a smooth polynomial tran- sition across the eyewall. Based upon a sample of

493 observed profiles, the mean exponent for the power law is 0.79 and the mean decay length is

243 km. The database actually contains

606 aircraft sorties, but

113 of these failed quality-control screening. Hurricanes stronger than SaffirCSimpson category

2 often require two exponentials to match the observed rapid decrease of wind with radius just outside the eye and slower decrease farther away. Experimentation showed that a fixed value of

25 km was satisfactory for the faster decay length. The mean value of the slower decay length was

295 km. The mean contribution of the faster exponential to the outer profile was 0.10, but for the most intense hurricanes it sometimes exceeded 0.5. The power-law exponent and proportion of the faster decay length increased with maximum wind speed and decreased with latitude, whereas the slower decay length decreased with intensity and increased with latitude, consistent with the qualitative observation that more intense hurricanes in lower latitudes usually have more sharply peaked wind profiles. 1. Introduction In the first paper of this series (Willoughby and Rahn 2004, hereafter Part I), we showed that the most com- monly used analytical representation of hurricane winds'

radial structure (Holland 1980) suffers from sys- tematic errors. Comparisons between statistically fitted profiles and nearly

500 tropical cyclones observed by aircraft demonstrated that, although the analytical pro- files overestimate the width of the eyewall wind maxi- mum, the wind decreases too rapidly with distance from the maximum both inside and outside the eye. Since variants of Holland'

s profile are fundamental to appli- cations such as modeling storm surge (Jelesnianski 1967) or windstorm risk (e.g., Vickery and Twisdale 1995), these shortcomings highlight the need for a more realistic alternative. Tropical cyclones are nearly circular vortices with damaging winds concentrated in and around the eye- wall. The geometric center of the clear eye or the stag- nation point inside the eye defines a vortex center that * Deceased. Corresponding author address: H. E. Willoughby, International Hurricane Research Center, Florida International University,

360 MARC Building, University Park Campus, Miami, FL 33199. E-mail: [email protected]