Vertical extrapolation of Weibull parameters using PDF scaling and wind shear exponent

This study presents a concise yet effective approach for vertically extrapolating Weibull parameters, using the power law approximation of the wind velocity profile, which describes the exponential increase in mean wind speed with height, as specified in IEC 61400-1. A robust method is necessary to extrapolate wind data collected at lower mast heights to higher locations. Current extrapolation methods are typically constrained in their applicable height range, requiring the development of a new model to accommodate the trend toward larger wind turbines. The proposed formulation is based on extrapolating the Weibull shape and scale parameters from a reference height and assuming a power law velocity profile controlled by the wind shear exponent. The extrapolation function was derived by stretching the Weibull distribution to align with a power law relating average wind speed to height, followed by normalization of the result. Also, a revised empirical formula for the vertical extrapolation of Weibull parameters to heights exceeding 100 m is proposed and validated for accuracy. The Weibull parameter extrapolation method introduced in this study is particularly useful for wind farm development and estimating conditions relevant to the flight testing of unmanned aerial vehicles.