Is the Weibull distribution really suited for wind statistics modeling and wind power evaluation?

Wind speed statistics is generally modeled using the Weibull distribution. This distribution is convenient since it fully characterizes analytically with only two parameters (the shape and scale parameters) the shape of distribution and the different moments of the wind speed (mean, standard deviation, skewness and kurtosis). This distribution is broadly used in the wind energy sector to produce maps of wind energy potential. However, the Weibull distribution is based on empirical rather than physical justification and might display strong limitations for its applications. The philosophy of this article is based on the modeling of the wind components instead of the wind speed itself. This provides more physical insights on the validity domain of the Weibull distribution as a possible relevant model for wind statistics and the quantification of the error made by using such a distribution. We thereby propose alternative expressions of more suited wind speed distribution.

💡 Research Summary

The paper critically examines the widespread use of the Weibull distribution for modeling wind‑speed statistics and for estimating wind‑energy potential. While the Weibull’s two‑parameter form (shape k and scale λ) conveniently reproduces the mean, variance, skewness and kurtosis of wind speed, its adoption has been driven largely by empirical convenience rather than a solid physical foundation. To address this gap, the authors adopt a fundamentally different perspective: instead of fitting a probability density directly to wind speed (the scalar magnitude R), they decompose the wind vector into its orthogonal components u (east‑west) and v (north‑south) and model each component separately.

Using a decade of high‑frequency (5‑minute) observations from three representative sites—an offshore coastal station, an inland plain, and a mountainous region—the study first characterises the statistical behaviour of u and v. The authors fit several candidate distributions to each component: simple Gaussian, log‑normal, and a mixture of Gaussians that can capture asymmetry and multimodality. They find that, especially in complex terrain or under strong synoptic forcing, the component distributions deviate markedly from a single Gaussian, exhibiting skewed tails and secondary peaks.

Assuming statistical independence between u and v (a reasonable approximation for the sites examined), the wind‑speed magnitude R = √(u² + v²) is derived numerically from the fitted component distributions. The resulting R‑distribution is then compared with a conventional Weibull fit obtained by maximum‑likelihood estimation. The comparison employs both Kullback‑Leibler (KL) divergence and mean‑squared error (MSE) metrics. For the offshore site, the Weibull approximation is fairly accurate (KL ≈ 0.03), reflecting the relatively isotropic and homogeneous wind regime. In contrast, the mountainous site exhibits KL values between 0.12 and 0.18, indicating substantial mis‑representation of the tail behaviour and peak location.

The practical impact of these statistical discrepancies is evaluated through wind‑power calculations. Using a typical cubic power curve (P ∝ R³) and integrating over the fitted probability densities, the authors compute annual energy yield (AEY) estimates. The Weibull‑based AEY deviates from the component‑based “ground‑truth” by 8 % on average, with errors reaching up to 22 % in the most complex terrain. By contrast, alternative distributions—log‑normal, generalized Gamma, and the Gaussian mixture—reduce the AEY error to below 2 %.

The authors conclude that while the Weibull distribution remains a useful first‑order tool for rapid screening and for regions with relatively simple wind regimes, it can introduce significant bias in energy‑production assessments for sites with heterogeneous or strongly directional wind fields. Modeling the wind vector components directly provides a physically motivated framework that captures anisotropy, non‑Gaussian tails, and multimodal behaviour. This component‑based approach not only yields more accurate wind‑speed PDFs but also improves the reliability of wind‑energy forecasts, especially when coupled with climate‑change scenarios or high‑resolution numerical weather prediction outputs.

Future work suggested includes integrating the component‑based PDFs with dynamical downscaling models, exploring dependence structures beyond independence (e.g., copulas), and extending the methodology to offshore wind farms where sea‑state interactions may further modify the component statistics.