14A.5
A New Parametric Model of Hurricane Wind Profiles
Hugh E. Willoughby, NOAA/AOML/HRD, Maimi, FL; and M. E. Rahn
Although predictions from full-physics numerical models are essential for hurricane forecasting, many other applications require only a realistic statistical depiction of the wind. Holland (1980, MWR) formulated the most widely used "parametric" model in which the radial structure of the symmetric vortex is a function of radius of maximum wind, Rm, maximum wind, Vm, and a measure of the width of the profile, B. The Holland profile forms the basis of "catastrophe" models used to evaluate insurance underwriting risk. A simpler version (that sets B to unity) provides wind input to the SLOSH storm surge model. Since these models guide real-world financial and emergency response decisions, it is reasonable to examine their realism closely.
The Hurricane Research Division’s online archive of flight-level data contains >4200 radial profiles observed in hurricanes by NOAA and Air Force Reserve aircraft since 1977. It represents ~450 statistically independent characterizations of Atlantic and Eastern Pacific hurricanes Least squares fits to these data present a rigorous test of parametric wind profiles' realism. Vm and Rm completely specify the SLOSH profile, but determination of the B parameter is required to specify the Holland profile. In "constrained" fits, Vm and Rm are set to the observed value, and B is determined statistically. In "unconstrained" fits, all parameters are determined with a nonlinear least-squares algorithm. These calculations show that currently used parametric hurricane wind profiles fail to capture the sharpness of the transition at the eyewall where the wind stops increasing with radius and starts decreasing. In a constrained fit, the band of strongest winds is too wide, leading to overestimated extent of extreme winds. When the observed Vm and Rm are used, the average bias toward strong wind is 3 m s-1, about 1/3 of a Saffir-Simpson category, for the best choice of B. On the other hand, if Vm is determined from the minimum observed pressure and gradient balance, the estimated Vm is less than the actual. In unconstrained fits, Vm is underestimated by 2% on average, but Rm is overestimated by 30%. Root-mean-square errors are 5.1 m s-1 for the constrained fit and 1.2 m s-1 for the unconstrained. The pattern of slightly too-weak wind spread over too much real estate generally leads to an overestimate of the actual risk.
An analytical wind profile used in theoretical studies is a promising alternative. It is composed of analytical segments patched smoothly together. Inside the eye the wind increases in proportion to a power of radius, generally between linear and quadratic. Outside the eye, the wind decays exponentially with an e-folding distance of 80-300 km. The transition at Rm is accomplished with a smooth polynomial. It is much sharper than that in the currently used profiles, but the entire profile is still smoothly differentiable through second order. Validation against the data by the procedure outlined above and determination of the statistical distributions of the parameters suggest that this profile may become standard for hurricane impacts modeling.
Session 14A, Tropical Cyclone Observations and Structure III (Parallel with Sessions 14B, 14C, and 14D)
Thursday, 2 May 2002, 2:00 PM-3:30 PM
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