Improving Hub-Height Wind Speed Estimation by Accounting for Height-Dependent Power-Law Exponents

Accurate estimation of wind speed at turbine hub height is a critical prerequisite for reliable wind energy resource assessment and project development. In recent years, the hub heights of modern wind turbines have steadily increased and now commonly exceed 100 m. However, direct wind measurements at these elevations remain scarce due to the high-cost constraints associated with tall meteorological masts. This observational gap introduces substantial uncertainty in pre-construction wind resource assessments, while relying solely on near-surface wind measurements often leads to significant biased estimates.

A widely adopted solution is the power-law extrapolation derived from Monin–Obukhov similarity theory, which assumes a power-law relationship between wind speed and height. Owing to its simplicity and flexibility, the power-law method has become the most extensively used approach in both engineering practice and scientific studies, as the power-law exponent can be readily derived from wind measurements at two different heights. Nevertheless, existing applications typically treat the exponent as height-invariant, overlooking its potential dependence on altitude. In reality, the power-law exponent varies with height, and directly applying the power-law exponent estimated from low-level measurements to increasingly taller hub heights results in great uncertainty.

To address this limitation, five years (2020–2024) of radiosonde observations over China were analyzed to characterize the vertical variations of the power-law exponent. Statistical results indicate a clear increasing trend with height: the mean exponents at 50 m, 100 m, 150 m, 200 m, 250 m, and 300 m are 0.130 ± 0.192, 0.162 ± 0.207, 0.179 ± 0.221, 0.188 ± 0.212, 0.194 ± 0.199, and 0.197 ± 0.194, respectively. And we found that the relationship between power-law exponents at different heights can be significantly represented by a cubic polynomial model. The fitted models between adjacent height levels exhibit high consistency, with coefficients of determination (R²) generally exceeding 0.96. For height separations of 200 m, the fitting performance remains robust (R² > 0.80), whereas larger vertical gaps lead to a noticeable decline in reliability.

Based on these findings, power-law exponents derived at lower heights—such as those obtained from short meteorological masts—can be reliably extrapolated to turbine hub heights using the proposed polynomial framework. Comparative experiments demonstrate that, relative to using a fixed exponent of 0.14 or directly adopting low-level exponents, the cubic polynomial extrapolation approach consistently achieves the highest accuracy across all combinations of height extrapolation. On average, mean absolute error and root mean square error are reduced by 74.6% and 68.0%, and by 27.9% and 25.7%, respectively. These results highlight the importance of explicitly accounting for the height dependence of the power-law exponent and demonstrate that the proposed framework offers a practical and effective solution for improving hub-height wind speed estimation, particularly in regions lacking direct wind observations at turbine hub height.