For use in various wind engineering applications (e.g. wind energy conversion, wind loads on structures, air pollution transport) it is desirable to have a consistent relationship by which to project height variations of both "instantaneous" (e.g. few minute average) winds and parameters of the wind speed probability distribution. The power law V2/V1 = (Z2/Z1)n is often used for height projection of wind profiles, with the exponent n sometimes taken as depending on surface conditions or on atmospheric stability. The power law profile for wind speed is shown here to be consistent with observed height variation of Weibull wind speed probability distribution functions which have been found to fit observed wind speed distributions (at least above relevant threshold wind speeds). For consistency between the wind speed profiles and the height variation of the Weibull wind speed probability distributions, it is necessary only that the exponent n vary as n = a + b ℓn V1, where a and b are constants whose values depend on the reference height at which wind speed V1 is measured. For a reference height of 10 m, it is found that a = 0.37 and b = −0.0881 (with V1 in m/s) adequately describes both the observed height variation of wind speed and wind speed probability distributions.
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Various models that are used for height extrapolation of short and long-term averaged wind speeds are discussed. Hourly averaged data from three tall meteorological towers (the NOAA Erie Tower in Colorado, the Battelle Goodnoe Hills Tower in Washington, and the WKY-TV Tower in Oklahoma), together with data from 17 candidate sites (selected for possible installation of large WECS), were used to analyze the variability of short-term average wind shear with atmospheric and surface parameters and the variability of the long-term Weibull distribution parameter with height. The exponents of a power-law model, fit to the wind speed profiles at the three meteorological towers, showed the same variability with anemometer level wind speed, stability, and surface roughness as the similarity law model. Of the four models representing short-term wind data extrapolation with height (1/7 power law, logarithmic law, power law, and modified power law), the modified power law gives the minimum rms for all candidate sites for short-term average wind speeds and the mean cube of the speed. The modified power-law model was also able to predict the upper-level scale factor for the WKY-TV and Goodnoe Hills Tower data with greater accuracy. All models were not successful in extrapolation of the Weibull shape factors.
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