Can Satellite Sampling of Offshore Wind Speeds Realistically Represent Wind Speed Distributions? Part II: Quantifying Uncertainties Associated with Distribution Fitting Methods

S. C. Pryor Atmospheric Science Program, Department of Geography, Indiana University at Bloomington, Bloomington, Indiana, and Department of Wind Energy and Atmospheric Physics, Risø National Laboratory, Roskilde, Denmark

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M. Nielsen Department of Wind Energy and Atmospheric Physics, Risø National Laboratory, Roskilde, Denmark

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R. J. Barthelmie Department of Wind Energy and Atmospheric Physics, Risø National Laboratory, Roskilde, Denmark, and Atmospheric Science Program, Department of Geography, Indiana University at Bloomington, Bloomington, Indiana

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J. Mann Department of Wind Energy and Atmospheric Physics, Risø National Laboratory, Roskilde, Denmark

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Abstract

Remote sensing tools represent an attractive proposition for measuring wind speeds over the oceans because, in principle, they also offer a mechanism for determining the spatial variability of flow. Presented here is the continuation of research focused on the uncertainties and biases currently present in these data and quantification of the number of independent observations (scenes) required to characterize various parameters of the probability distribution of wind speeds. Theoretical and empirical estimates are derived of the critical number of independent observations (wind speeds derived from analysis of remotely sensed scenes) required to obtain probability distribution parameters with an uncertainty of ±10% and a confidence level of 90% under the assumption of independent samples, and it is found that approximately 250 independent observations are required to fit the Weibull distribution parameters. Also presented is an evaluation of Weibull fitting methods and determination of the fitting method based on the first and third moments to exhibit the “best” performance for pure Weibull distributions. Further examined is the ability to generalize parameter uncertainty bounds presented previously by Barthelmie and Pryor for distribution parameter estimates from sparse datasets; these were found to be robust and hence generally applicable to remotely sensed wind speed data series.

Corresponding author address: Prof. S. C. Pryor, Atmospheric Science Program, Department of Geography, Indiana University, 701 E. Kirkwood Ave., Bloomington, IN 47405. spryor@indiana.edu

Abstract

Remote sensing tools represent an attractive proposition for measuring wind speeds over the oceans because, in principle, they also offer a mechanism for determining the spatial variability of flow. Presented here is the continuation of research focused on the uncertainties and biases currently present in these data and quantification of the number of independent observations (scenes) required to characterize various parameters of the probability distribution of wind speeds. Theoretical and empirical estimates are derived of the critical number of independent observations (wind speeds derived from analysis of remotely sensed scenes) required to obtain probability distribution parameters with an uncertainty of ±10% and a confidence level of 90% under the assumption of independent samples, and it is found that approximately 250 independent observations are required to fit the Weibull distribution parameters. Also presented is an evaluation of Weibull fitting methods and determination of the fitting method based on the first and third moments to exhibit the “best” performance for pure Weibull distributions. Further examined is the ability to generalize parameter uncertainty bounds presented previously by Barthelmie and Pryor for distribution parameter estimates from sparse datasets; these were found to be robust and hence generally applicable to remotely sensed wind speed data series.

Corresponding author address: Prof. S. C. Pryor, Atmospheric Science Program, Department of Geography, Indiana University, 701 E. Kirkwood Ave., Bloomington, IN 47405. spryor@indiana.edu

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  • Barthelmie, R. J. and S. C. Pryor. 2003. Can satellite sampling of offshore wind speeds realistically represent wind speed distributions? J. Appl. Meteor 42:8394.

    • Search Google Scholar
    • Export Citation
  • Barthelmie, R. J., I. Bryden, J. Coelingh, and S. C. Pryor. 2000. Energy from the oceans: Wind, wave and tidal. Seas at the Millennium, C. Sheppard, Ed., Elsevier, 303–321.

    • Search Google Scholar
    • Export Citation
  • Conradsen, K., L. B. Nielsen, and L. P. Prahm. 1984. Review of Weibull statistics for estimation of wind speed distributions. J. Climate Appl. Meteor 23:11731183.

    • Search Google Scholar
    • Export Citation
  • Davis, P. 1964. Gamma function and related functions. Handbook of Mathematical Functions, M. Abramowitz and I. Stegun, Eds., U.S. Bureau of Standards, 253–294.

    • Search Google Scholar
    • Export Citation
  • Garcia, A., J. Torres, E. Prieto, and A. De Francisco. 1998. Fitting wind speed distributions: A case study. Sol. Energy 62:139144.

  • Ghosh, A. 1999. A FORTRAN program for fitting Weibull distribution and generating samples. Comput. Geosci 25:729738.

  • Gilhousen, D. B. 1987. A field evaluation of NBDC moored buoy winds. J. Atmos. Oceanic Technol 4:94104.

  • Gong, S., L. Barrie, J. Prospero, D. Savoie, G. Ayers, J. Blancher, and L. Spacek. 1997. Modeling sea-salt aerosols in the atmosphere. 2. Atmospheric concentrations and fluxes. J. Geophys. Res 102:38053818.

    • Search Google Scholar
    • Export Citation
  • Iesemer, H. J. 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 4:819836.

    • Search Google Scholar
    • Export Citation
  • Jamil, M., S. Parsa, and M. Majidi. 1995. Wind power statistics and an evaluation of wind energy density. Renewable Energy 6:623628.

  • Johannessen, O. M. and E. Bjørgo. 2000. Wind energy mapping of coastal zones by synthetic aperture radar (SAR) for siting potential windmill locations. Int. J. Remote Sens 21:17811786.

    • Search Google Scholar
    • Export Citation
  • Justus, C. G., W. R. Hargraves, A. Mikhail, and D. Graber. 1978. Methods for estimating wind speed frequency distributions. J. Appl. Meteor 17:350353.

    • Search Google Scholar
    • Export Citation
  • Kerbaol, V., B. Chapron, and P. W. Vachon. 1998. Analysis of ERS-1/2 synthetic aperture radar wave mode imagettes. J. Geophys. Res 103:78337846.

    • Search Google Scholar
    • Export Citation
  • Korsbakken, E., J. A. Johannessen, and O. M. Johannessen. 1998. Coastal wind field retrievals from ERS synthetic aperture radar images. J. Geophys. Res 103:78577874.

    • Search Google Scholar
    • Export Citation
  • Lehner, S., J. Horstmann, W. Koch, and W. Rosenthal. 1998. Mesoscale wind measurements using recalibrated ERS SAR images. J. Geophys. Res 103:78477856.

    • Search Google Scholar
    • Export Citation
  • Lehner, S., D. Hoja, and J. Schulz-Stellenfleth. 2002. Marine parameters from synergy of optical and radar satellite data. Adv. Space Res 29:2332.

    • Search Google Scholar
    • Export Citation
  • Liu, W. T. 2002. Progress in scatterometer application. J. Oceanogr 58:121136.

  • Malthus, T. and P. Mumby. 2003. Remote sensing of the coastal zone: An overview and priorities for future research. Int. J. Remote Sens 24:935951.

    • Search Google Scholar
    • Export Citation
  • Mann, J., D. H. Lanschow, and L. Kristensen. 1995. Comments on “A definitive approach to turbulence statistical studies in planetary boundary layers.”. J. Atmos. Sci 52:31943196.

    • 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 40:14761484.

    • 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 25:13241332.

  • Press, W. H., B. P. Flannery, S. A. Teukolsky, and W. T. Vetterling. 1992. Numerical Recipes in C. Cambridge University Press, 994 pp.

  • Seguro, J. V. and T. W. Lambert. 2000. Modern estimation of the parameters of the Weibull wind speed distribution for wind energy analysis. J. Wind Eng. Ind. Aerodyn 85:7584.

    • Search Google Scholar
    • Export Citation
  • Stoffelen, A. 1998. Toward the true near-surface wind speed: Error modeling and calibration using triple collocation. J. Geophys. Res 103:77557766.

    • Search Google Scholar
    • Export Citation
  • Troen, I. and E. L. Petersen. 1989. European Wind Atlas. Risø National Laboratory, Roskilde, Denmark, 656 pp.

  • Wilks, D. S. 1990. Maximum likelihood estimation for the gamma distribution using data containing zeros. J. Climate 3:14951501.

  • Wu, J. 1995. Sea surface winds—A critical input to oceanic models but are they accurately measured? Bull. Amer. Meteor. Soc 76:1319.

    • Search Google Scholar
    • Export Citation
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