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. Pressure–wind 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 transition 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 Saffir–Simpson 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.
MEAN VALUE TYPE INEQUALITIES FOR QUASINEARLY SUBHARMONIC FUNCTIONS