Editorial Type:
Article
Article Type:
Research Article

The Probability Distribution of Sea Surface Wind Speeds. Part I: Theory and SeaWinds Observations

Adam Hugh Monahan School of Earth and Ocean Sciences, University of Victoria, Victoria, British Columbia, and Earth System Evolution Program, Canadian Institute for Advanced Research, Toronto, Ontario, Canada

Search for other papers by Adam Hugh Monahan in
Current site
Google Scholar
PubMed Close
Print Publication:
15 Feb 2006
DOI:
https://doi.org/10.1175/JCLI3640.1
Page(s):
497–520
Restricted access

We are aware of a technical issue preventing figures and tables from showing in some newly published articles in the full-text HTML view.
While we are resolving the problem, please use the online PDF version of these articles to view figures and tables.

Abstract

The probability distribution of sea surface wind speeds, w, is considered. Daily SeaWinds scatterometer observations are used for the characterization of the moments of sea surface winds on a global scale. These observations confirm the results of earlier studies, which found that the two-parameter Weibull distribution provides a good (but not perfect) approximation to the probability density function of w. In particular, the observed and Weibull probability distributions share the feature that the skewness of w is a concave upward function of the ratio of the mean of w to its standard deviation. The skewness of w is positive where the ratio is relatively small (such as over the extratropical Northern Hemisphere), the skewness is close to zero where the ratio is intermediate (such as the Southern Ocean), and the skewness is negative where the ratio is relatively large (such as the equatorward flank of the subtropical highs). An analytic expression for the probability density function of w, derived from a simple stochastic model of the atmospheric boundary layer, is shown to be in good qualitative agreement with the observed relationships between the moments of w. Empirical expressions for the probability distribution of w in terms of the mean and standard deviation of the vector wind are derived using Gram–Charlier expansions of the joint distribution of the sea surface wind vector components. The significance of these distributions for improvements to calculations of averaged air–sea fluxes in diagnostic and modeling studies is discussed.

Corresponding author address: Dr. Adam Hugh Monahan, School of Earth and Ocean Sciences, University of Victoria, P.O. Box 3055 STN CSC, Victoria, BC V8P 5C2, Canada. Email: monahana@uvic.ca

Abstract

The probability distribution of sea surface wind speeds, w, is considered. Daily SeaWinds scatterometer observations are used for the characterization of the moments of sea surface winds on a global scale. These observations confirm the results of earlier studies, which found that the two-parameter Weibull distribution provides a good (but not perfect) approximation to the probability density function of w. In particular, the observed and Weibull probability distributions share the feature that the skewness of w is a concave upward function of the ratio of the mean of w to its standard deviation. The skewness of w is positive where the ratio is relatively small (such as over the extratropical Northern Hemisphere), the skewness is close to zero where the ratio is intermediate (such as the Southern Ocean), and the skewness is negative where the ratio is relatively large (such as the equatorward flank of the subtropical highs). An analytic expression for the probability density function of w, derived from a simple stochastic model of the atmospheric boundary layer, is shown to be in good qualitative agreement with the observed relationships between the moments of w. Empirical expressions for the probability distribution of w in terms of the mean and standard deviation of the vector wind are derived using Gram–Charlier expansions of the joint distribution of the sea surface wind vector components. The significance of these distributions for improvements to calculations of averaged air–sea fluxes in diagnostic and modeling studies is discussed.

Corresponding author address: Dr. Adam Hugh Monahan, School of Earth and Ocean Sciences, University of Victoria, P.O. Box 3055 STN CSC, Victoria, BC V8P 5C2, Canada. Email: monahana@uvic.ca

Save
Cover Journal of Climate
Journal of Climate

  • Abramowitz, M., and I. A. Stegun, 1972: Handbook of Mathematical Functions. Dover, 1046 pp.

  • Atlas, R., R. Hoffman, S. Bloom, J. Jusem, and J. Ardizzone, 1996: A multiyear global surface wind velocity dataset using SSM/I wind observations. Bull. Amer. Meteor. Soc, 77 , 869–882.

    • Search Google Scholar
    • Export Citation

  • Bauer, E., 1996: Characteristic frequency distributions of remotely sensed in situ and modelled wind speeds. Int. J. Climatol, 16 , 1087–1102.

    • Search Google Scholar
    • Export Citation

  • Bentamy, A., P. Queffeulou, Y. Quilfen, and K. Katsaros, 1999: Ocean surface wind fields estimated from satellite active and passive microwave instruments. IEEE Trans. Geosci. Remote Sens, 37 , 2469–2486.

    • Search Google Scholar
    • Export Citation

  • Bourassa, M. A., D. M. Legler, J. J. O'Brien, and S. R. Smith, 2003: SeaWinds validation with research vessels. J. Geophys. Res, 108 .3019, doi:10.1029/2001JC001028.

    • Search Google Scholar
    • Export Citation

  • Cakmur, R., R. Miller, and O. Torres, 2004: Incorporating the effect of small-scale circulations upon dust emission in an atmospheric general circulation model. J. Geophys. Res, 109 .D07201, doi:10.1029/2003JD004067.

    • Search Google Scholar
    • Export Citation

  • Chelton, D. B., and M. H. Freilich, 2005: Scatterometer-based assessment of 10-m wind analyses from the operational ECMWF and NCEP numerical weather prediction models. Mon. Wea. Rev, 133 , 409–429.

    • Search Google Scholar
    • Export Citation

  • Chelton, D. B., M. G. Schlax, M. H. Freilich, and R. F. Milliff, 2004: Satellite measurements reveal persistent small-scale features in ocean winds. Science, 303 , 978–983.

    • Search Google Scholar
    • Export Citation

  • Conradsen, K., L. Nielsen, and L. Prahm, 1984: Review of Weibull statistics for estimation of wind speed distributions. J. Climate Appl. Meteor, 23 , 1173–1183.

    • Search Google Scholar
    • Export Citation

  • Curry, J., and Coauthors, 2004: SEAFLUX. Bull. Amer. Meteor. Soc, 85 , 409–424.

  • Deaves, D., and I. Lines, 1997: On the fitting of low mean windspeed data to the Weibull distribution. J. Wind Eng. Ind. Aerodyn, 66 , 169–178.

    • Search Google Scholar
    • Export Citation

  • Dixon, J., and R. Swift, 1984: The dependence of wind speed and Weibull characteristics on height for offshore winds. Wind Eng, 8 , 87–98.

    • Search Google Scholar
    • Export Citation

  • Donelan, M., W. Drennan, E. Saltzman, and R. Wanninkhof, 2002: Gas Transfer at Water Surfaces. Amer. Geophys. Union, 383 pp.

  • Ebuchi, N., 1999: Statistical distribution of wind speeds and directions globally observed by NSCAT. J. Geophys. Res, 104 , 11393–11403.

    • Search Google Scholar
    • Export Citation

  • Ebuchi, N., H. C. Graber, and M. J. Caruso, 2002: Evaluation of wind vectors observed by QuikSCAT/SeaWinds using ocean buoy data. J. Atmos. Oceanic Technol, 19 , 2049–2062.

    • Search Google Scholar
    • Export Citation

  • Einstein, A., 1956: Investigations on the Theory of Brownian Movement. Dover, 122 pp.

  • Erickson, D. J., and J. A. Taylor, 1989: Non-Weibull behavior observed in a model-generated global surface wind field frequency distribution. J. Geophys. Res, 94 , 12693–12698.

    • Search Google Scholar
    • Export Citation

  • Fairall, C. W., E. F. Bradley, J. E. Hare, A. A. Grachev, and J. B. Edson, 2003: Bulk parameterization of air–sea fluxes: Updates and verification for the COARE algorithm. J. Climate, 16 , 571–591.

    • Search Google Scholar
    • Export Citation

  • Gardiner, C. W., 1997: Handbook of Stochastic Methods for Physics, Chemistry, and the Natural Sciences. Springer, 442 pp.

  • Gradshteyn, I., and I. Ryzhik, 2000: Table of Integrals, Series, and Products. 6th ed. Academic Press, 1163 pp.

  • Hennessey, J. P., 1977: Some aspects of wind power statistics. J. Appl. Meteor, 16 , 119–128.

  • Hsieh, W. W., and B. Tang, 1998: Applying neural network models to prediction and data analysis in meteorology and oceanography. Bull. Amer. Meteor. Soc, 79 , 1855–1870.

    • Search Google Scholar
    • Export Citation

  • Isemer, H., and L. Hasse, 1991: The scientific Beaufort equivalent scale: Effects on wind statistics and climatological air–sea flux estimates in the North Atlantic Ocean. J. Climate, 4 , 819–836.

    • Search Google Scholar
    • Export Citation

  • Jet Propulsion Laboratory, cited. 2001: SeaWinds on QuikSCAT Level 3: Daily, gridded ocean wind vectors. Tech. Rep. JPL PO.DAAC Product 109, California Institute of Technology. [Available online at http://podaac.jpl.nasa.gov:2031/DATASET_DOCS/Qscat_L3.html.].

  • Johnson, N., S. Kotz, and N. Balakrishnan, 1994: Continuous Univariate Distributions. Vol. 1. Wiley, 756 pp.

  • Jondeau, E., and M. Rockinger, 2001: Gram-Charlier densities. J. Econ. Dyn. Control, 25 , 1457–1483.

  • Jones, I. S., and Y. Toba, 2001: Wind Stress over the Ocean. Cambridge University Press, 307 pp.

  • Justus, C., W. Hargraves, A. Mikhail, and D. Graber, 1978: Methods for estimating wind speed frequency distributions. J. Appl. Meteor, 17 , 350–353.

    • Search Google Scholar
    • Export Citation

  • Kelly, K. A., 2004: Wind data: A promise in peril. Science, 303 , 962–963.

  • Kelly, K. A., S. Dickinson, M. J. McPhaden, and G. C. Johnson, 2001: Ocean currents evident in ocean wind data. Geophys. Res. Lett, 28 , 2469–2472.

    • Search Google Scholar
    • Export Citation

  • Kelly, K. A., S. Dickinson, and G. C. Johnson, 2005: Comparisons of scatterometer and TAO winds reveal time-varying surface currents for the tropical Pacific Ocean. J. Atmos. Oceanic Technol, 22 , 735–745.

    • Search Google Scholar
    • Export Citation

  • Kestens, E., and J. L. Teugels, 2002: Challenges in modelling stochasticity in wind. Environmetrics, 13 , 821–830.

  • Levy, G., and D. Vickers, 1999: Surface fluxes from satellite winds: Modeling air-sea flux enhancement from spatial and temporal observations. J. Geophys. Res, 104 , 20639–20650.

    • Search Google Scholar
    • Export Citation

  • Mahrt, L., and J. Sun, 1995: The subgrid velocity scale in the bulk aerodynamic relationship for spatially averaged scalar fluxes. Mon. Wea. Rev, 123 , 3032–3041.

    • Search Google Scholar
    • Export Citation

  • Meissner, T., D. Smith, and F. Wentz, 2001: A 10 year intercomparison between collocated Special Sensor Microwave Imager oceanic surface wind speed retrievals and global analyses. J. Geophys. Res, 106 , 11731–11742.

    • Search Google Scholar
    • Export Citation

  • Monahan, A. H., 2004a: Low-frequency variability of the statistical moments of sea-surface winds. Geophys. Res. Lett, 31 .L10302, doi:10.1029/2004GL019599.

    • Search Google Scholar
    • Export Citation

  • Monahan, A. H., 2004b: A simple model for the skewness of global sea surface winds. J. Atmos. Sci, 61 , 2037–2049.

  • Monahan, A. H., 2006: The probability distribution of sea surface wind speeds. Part II: Dataset intercomparison and seasonal variability. J. Climate, 19 , 521–534.

    • Search Google Scholar
    • Export Citation

  • Pang, W-K., J. J. Forster, and M. D. Troutt, 2001: Estimation of wind speed distribution using Markov chain Monte Carlo techniques. J. Appl. Meteor, 40 , 1476–1484.

    • Search Google Scholar
    • Export Citation

  • Pavia, E. G., and J. J. O'Brien, 1986: Weibull statistics of wind speed over the ocean. J. Climate Appl. Meteor, 25 , 1324–1332.

  • Penland, C., 2003a: Noise out of chaos and why it won't go away. Bull. Amer. Meteor. Soc, 84 , 921–925.

  • Penland, C., 2003b: A stochastic approach to nonlinear dynamics: A review. Bull. Amer. Meteor. Soc, 84 , ES43–ES52.

  • Petersen, E. L., N. G. Mortensen, L. Landberg, J. Højstrup, and H. P. Frank, 1998a: Wind power meteorology. Part I: Climate and turbulence. Wind Energy, 1 , 25–45.

    • Search Google Scholar
    • Export Citation

  • Petersen, E. L., N. G. Mortensen, L. Landberg, J. Højstrup, and H. P. Frank, 1998b: Wind power meteorology. Part II: Siting and models. Wind Energy, 1 , 55–72.

    • Search Google Scholar
    • Export Citation

  • Pryor, S., and R. Barthelmie, 2002: Statistical analysis of flow characteristics in the coastal zone. J. Wind Eng. Ind. Aerodyn, 90 , 201–221.

    • Search Google Scholar
    • Export Citation

  • Rodwell, M., and B. Hoskins, 2001: Subtropical anticyclones and summer monsoons. J. Climate, 14 , 3192–3211.

  • Stewart, D. A., and O. M. Essenwanger, 1978: Frequency distribution of wind speed near the surface. J. Appl. Meteor, 17 , 1633–1642.

  • Sura, P., 2003: Stochastic analysis of Southern and Pacific Ocean sea surface winds. J. Atmos. Sci, 60 , 654–666.

  • Takle, E., and J. Brown, 1978: Note on the use of Weibull statistics to characterize wind-speed data. J. Appl. Meteor, 17 , 556–559.

  • Taylor, P. K., Ed. 2000: Intercomparison and validation of ocean-atmosphere energy flux fields. Joint WCRP/SCOR Working Group on Air-Sea Fluxes Final Rep. WMO/TD-1036, 306 pp.

  • Taylor, P. K., and M. J. Yelland, 2001: The dependence of sea surface roughness on the height and steepness of the waves. J. Phys. Oceanogr, 31 , 572–590.

    • Search Google Scholar
    • Export Citation

  • Thompson, K., R. Marsden, and D. Wright, 1983: Estimation of low-frequency wind stress fluctuations over the open ocean. J. Phys. Oceanogr, 13 , 1003–1011.

    • Search Google Scholar
    • Export Citation

  • Tuller, S. E., and A. C. Brett, 1984: The characteristics of wind velocity that favor the fitting of a Weibull distribution in wind speed analysis. J. Climate Appl. Meteor, 23 , 124–134.

    • Search Google Scholar
    • Export Citation

  • Wanninkhof, R., 1992: Relationship between wind speed and gas exchange over the ocean. J. Geophys. Res, 97 , 7373–7382.

  • Wanninkhof, R., and W. R. McGillis, 1999: A cubic relationship between air-sea CO2 exchange and wind speed. Geophys. Res. Lett, 26 , 1889–1892.

    • Search Google Scholar
    • Export Citation

  • Wanninkhof, R., S. C. Doney, T. Takahashi, and W. R. McGillis, 2002: The effect of using time-averaged winds on regional air-sea CO2 fluxes. Gas Transfer at Water Surfaces, M. A. Donelan et al., Eds., Amer. Geophys. Union, 351–356.

    • Search Google Scholar
    • Export Citation

  • Wentz, F., S. Peteherych, and L. Thomas, 1984: A model function for ocean radar cross sections at 14.6 GHz. J. Geophys. Res, 89 , 3689–3704.

    • Search Google Scholar
    • Export Citation

  • Wright, D. G., and K. R. Thompson, 1983: Time-averaged forms of the nonlinear stress law. J. Phys. Oceanogr, 13 , 341–345.

  • Yuan, X., 2004: High-wind-speed evaluation in the Southern Ocean. J. Geophys. Res, 109 .D13101, doi:10.1029/2003JD004179.

All Time Past Year Past 30 Days
Abstract Views 0 0 0
Full Text Views 1646 441 62
PDF Downloads 1229 244 15