Height variation of wind speed and wind distributions statistics

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.