Parametric Representation of the Primary Hurricane Vortex. Part I: Observations and Evaluation of the Holland (1980) Model

H. E. Willoughby International Hurricane Research Center, Florida International University, Miami, Florida

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M. E. Rahn Hurricane Research Division/AOML/NOAA, Miami, Florida

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Abstract

Although numerical models are essential to hurricane forecasting, many other applications require only statistical depiction of the wind distribution. In Holland's 1980 parametric profile, radius of maximum wind, maximum wind, and a measure of the profile width describe the radial variation of the axisymmetric wind. Variants of the Holland profile are used to predict insurance underwriting risk, ocean response, and storm-surge inundation. Since these calculations guide high-stakes financial and emergency managment decisions, it is logical to test them against observations.

The Hurricane Research Division's flight-level database archives observations were obtained by NOAA and U.S. Air Force Reserve aircraft. The data considered here are winds and geopotential heights observed during 606 lower- and midtropospheric flights into Atlantic and eastern Pacific tropical cyclones during 1977–2000. The 493 profiles that meet quality control criteria are seasonally geographically representative.

Least squares fits of the Holland model to these data provide evaluation of the parameters' distributions and critical examination of the profile's realism. Individual fitted profiles differ from the observations in a consistent pattern. The areas of strong winds in the eyewall and of nearly calm winds at the vortex center are too wide. Beyond 2 or 3 times the eye radius, the wind decreases too rapidly with distance from the center. Although the average bias in fitted profiles is <1 m s−1, the root-mean-square error is 4.2 m s−1 (5.2 m s−1 for independent data). Maximum winds estimated from the fitted Holland-profile height–wind relation average 2.5 m s−1 too strong with an rms error of 6.5 m s−1. The pattern of too strong wind spread over too much real estate exaggerates the occurrence of winds stronger than 50 m s−1 by ∼50%.

Corresponding author address and current affiliation: H. E. Willoughby, International Hurricane Research Center, 360 MARC Building, University Park Campus, Florida International University, Miami, FL 33199. Email: hugh.willoughby@fiu.edu

Abstract

Although numerical models are essential to hurricane forecasting, many other applications require only statistical depiction of the wind distribution. In Holland's 1980 parametric profile, radius of maximum wind, maximum wind, and a measure of the profile width describe the radial variation of the axisymmetric wind. Variants of the Holland profile are used to predict insurance underwriting risk, ocean response, and storm-surge inundation. Since these calculations guide high-stakes financial and emergency managment decisions, it is logical to test them against observations.

The Hurricane Research Division's flight-level database archives observations were obtained by NOAA and U.S. Air Force Reserve aircraft. The data considered here are winds and geopotential heights observed during 606 lower- and midtropospheric flights into Atlantic and eastern Pacific tropical cyclones during 1977–2000. The 493 profiles that meet quality control criteria are seasonally geographically representative.

Least squares fits of the Holland model to these data provide evaluation of the parameters' distributions and critical examination of the profile's realism. Individual fitted profiles differ from the observations in a consistent pattern. The areas of strong winds in the eyewall and of nearly calm winds at the vortex center are too wide. Beyond 2 or 3 times the eye radius, the wind decreases too rapidly with distance from the center. Although the average bias in fitted profiles is <1 m s−1, the root-mean-square error is 4.2 m s−1 (5.2 m s−1 for independent data). Maximum winds estimated from the fitted Holland-profile height–wind relation average 2.5 m s−1 too strong with an rms error of 6.5 m s−1. The pattern of too strong wind spread over too much real estate exaggerates the occurrence of winds stronger than 50 m s−1 by ∼50%.

Corresponding author address and current affiliation: H. E. Willoughby, International Hurricane Research Center, 360 MARC Building, University Park Campus, Florida International University, Miami, FL 33199. Email: hugh.willoughby@fiu.edu

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  • Atkinson, G. D., and C. R. Holliday, 1977: Tropical cyclone minimum sea-level pressure/maximum sustained wind relationship for the western North Pacific. Mon. Wea. Rev, 105 , 421427.

    • Search Google Scholar
    • Export Citation
  • Black, M. L., J. F. Gamache, F. D. Marks Jr., C. E. Samsury, and H. E. Willoughby, 2002: Eastern Pacific Hurricanes Jimena of 1991 and Olivia of 1994: The effect of vertical shear on structure and intensity. Mon. Wea. Rev, 130 , 22912312.

    • Search Google Scholar
    • Export Citation
  • Burpee, R. W., and Coauthors, 1994: Real-time guidance provided by NOAA's Hurricane Research Division to forecasters during Emily of 1993. Bull. Amer. Meteor. Soc, 75 , 17651783.

    • Search Google Scholar
    • Export Citation
  • Callaghan, J., and R. K. Smith, 1998: The relationship between maximum surface wind speeds and the central pressure in tropical cyclones. J. Aust. Meteor. Soc, 47 , 191202.

    • Search Google Scholar
    • Export Citation
  • Franklin, J. L., M. L. Black, and K. Valde, 2003: GPS dropwindsonde wind profiles in hurricanes and their operational implications. Wea Forecasting, 18 , 3244.

    • Search Google Scholar
    • Export Citation
  • Gray, W. M., 1984: Atlantic seasonal hurricane frequency. Part I: EI Niño and 30 mb quasi-biennial oscillation influences. Mon. Wea. Rev, 112 , 16491668.

    • Search Google Scholar
    • Export Citation
  • Gray, W. M., and D. J. Shea, 1973: The Hurricane's inner core region. II. Thermal stability and dynamic characteristics. J. Atmos. Sci, 30 , 15651576.

    • Search Google Scholar
    • Export Citation
  • Ho, F. P., J. C. Su, K. L. Hanevich, R. J. Smith, and F. P. Richards, 1987: Hurricane climatology for the Atlantic and Gulf Coasts of the United States. NOAA Tech. Memo. NWS-38, National Weather Service, Silver Spring, MD, 195 pp.

    • Search Google Scholar
    • Export Citation
  • Holland, G. J., 1980: An analytic model of the wind and pressure profiles in hurricanes. Mon. Wea. Rev, 108 , 12121218.

  • Jarvinen, B. R., and M. B. Lawrence, 1985: An evaluation of the SLOSH storm-surge model. Bull. Amer. Meteor. Soc, 66 , 14081411.

  • Jarvinen, B. R., C. J. Neumann, and M. A. S. Davis, 1984: A tropical cyclone data type for the North Atlantic Basin, 1886–1983: Contents, limitations, and uses. NOAA Tech. Memo. NWS NHC 22, Coral Gables, FL, 21 pp.

    • Search Google Scholar
    • Export Citation
  • Jelesnianski, C. P., 1967: Numerical computation of storm surges with bottom stress. Mon. Wea Rev, 95 , 740756.

  • Jordan, C. L., 1958: Mean soundings for the West Indies area. J. Meteor, 15 , 9197.

  • Jorgensen, D. P., 1984a: Mesoscale and convective-scale characteristics of mature hurricanes. Part I: General observations by research aircraft. J. Atmos. Sci, 41 , 12681285.

    • Search Google Scholar
    • Export Citation
  • Jorgensen, D. P., 1984b: Mesoscale and convective-scale characteristics of mature hurricanes. Part II: Inner core structure of Hurricane Allen (1980). J. Atmos. Sci, 41 , 12871311.

    • Search Google Scholar
    • Export Citation
  • Myers, V. A., 1957: Maximum hurricane winds. Bull. Amer. Meteor. Soc, 38 , 227228.

  • Neumann, C. J., B. R. Jarvinen, C. J. McAdie, and G. R. Hammer, 1999: Tropical Cyclones of the North Atlantic Ocean, 1871– 1998. Historical Climatology Series, Vol. 6-2, NOAA, 206 pp.

    • Search Google Scholar
    • Export Citation
  • Pielke Jr., R. A., and C. W. Landsea, 1998: Normalized hurricane damages in the United States: 1925–95. Wea. Forecasting, 13 , 621631.

    • Search Google Scholar
    • Export Citation
  • Pielke Jr., R. A., J. Rubiera, C. Landsea, M. L. Fernandez, and R. Klein, 2003: Hurricane vulnerability in Latin America and the Caribbean: Normalized damage and loss potentials. Nat. Hazards Rev, 4 , 101114.

    • Search Google Scholar
    • Export Citation
  • Press, W. H., B. P. Flannery, S. A. Teukolsky, and W. T. Vettering, 1986: 10.1 Golden section search in one dimension. Numerical Recipes: The Art of Scientific Computing, Cambridge University Press, 277–282.

    • Search Google Scholar
    • Export Citation
  • Rappaport, E. N., 2000: Loss of life in the United States associated with recent Atlantic tropical cyclones. Bull. Amer. Meteor. Soc, 81 , 20652074.

    • Search Google Scholar
    • Export Citation
  • Riehl, H., 1963: Some relationships between wind and thermal structure of steady state hurricanes. J. Atmos. Sci, 20 , 276287.

  • Schloemer, R. W., 1954: Analysis and synthesis of hurricane winds over Lake Okechobee, Florida. Hydrometeorological Rep. 31, U.S. Weather Bureau, Department of Commerce, and Army Corps of Engineers, 39 pp.

    • Search Google Scholar
    • Export Citation
  • Schubert, W. H., and J. J. Hack, 1982: Inertial stability and tropical cyclone development. J. Atmos. Sci, 39 , 16871697.

  • Shapiro, L. J., and H. E. Willoughby, 1982: The response of balanced hurricanes to local sources of heat and momentum. J. Atmos. Sci, 39 , 378394.

    • Search Google Scholar
    • Export Citation
  • Shea, D. J., and W. M. Gray, 1973: The hurricane's inner core region. I. Symmetric and asymmetric structure. J. Atmos. Sci, 30 , 15441564.

    • Search Google Scholar
    • Export Citation
  • Sheets, R. C., 1969: Some mean hurricane soundings. J. Appl. Meteor, 8 , 134146.

  • Smith, R. K., 1981: The cyclostrophic adjustment of vortices with application to tropical cyclone modification. J. Atmos. Sci, 38 , 20212030.

    • Search Google Scholar
    • Export Citation
  • Thompson, E. F., and V. J. Cardone, 1996: Practical modeling of hurricane surface wind fields. J. Waterw. Port Coastal Ocean Eng, 122 , 195205.

    • Search Google Scholar
    • Export Citation
  • Vickery, P. J., and L. A. Twisdale, 1995: Prediction of hurricane wind speeds in the United States. J. Struct. Eng, 121 , 16911699.

  • Willoughby, H. E., 1990a: Temporal changes of the primary circulation in tropical cyclones. J. Atmos. Sci, 47 , 242264.

  • Willoughby, H. E., 1990b: Gradient balance in tropical cyclones. J. Atmos. Sci, 47 , 265274.

  • Willoughby, H. E., and M. B. Chelmow, 1982: Objective determination of hurrincane tracks from aircraft observations. Mon. Wea. Rev, 110 , 12981305.

    • Search Google Scholar
    • Export Citation
  • Willoughby, H. E., J. A. Clos, and M. B. Shoreibah, 1982: Concentric eyewalls, secondary wind maxima, and the evolution of the hurricane vortex. J. Atmos. Sci, 39 , 395411.

    • Search Google Scholar
    • Export Citation
  • Willoughby, H. E., D. P. Jorgensen, R. A. Black, and S. L. Rosenthal, 1985: Project STORMFURY: A scientific chronicle 1962–1983. Bull. Amer. Meteor. Soc, 66 , 505514.

    • Search Google Scholar
    • Export Citation
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