Generalized wind speed probability distribution

The magnitude of the vector sum of two orthogonal, horizontal, wind velocity components is often modelled by the Rayleigh distribution. In the derivation, it is assumed that the components are independent, identically distributed, zero-mean, Gaussian random variables. The effect of unequal variance components with both zero and nonzero means is investigated and the resulting distribution is found to be closely fitted by the Rayleigh distribution calibrated to the derived mean wind speed. The more general case in which the unequal variance components are correlated, again with both zero and nonzero means, is studied. The Rayleigh distribution again provides a good approximation when calibrated to the mean wind speed. Data collected by the National Weather Service are used to illustrate the approach. Comparison of the derived distribution with the observed histogram and the Rayleigh distribution shows that the Rayleigh provides a good approximation.