The annual rate of independent events – A key interpretation for traditional extreme value distributions of wind velocity

Abstract

Abstract The extreme value theory has been object of engineering studies for more than a century. The analysis of extreme winds plays a key role for complex civil structures and a driving role in different stages of wind turbines lifetime. Most of extremes probability models depend on the annual rate of independent events (ARIE) which has been traditionally considered a constant value. The authors have embraced a recent belief considering the ARIE as a function of the wind velocity. Even though a certain agreement has been achieved across the researches, some issues are still pending. In this regard, the paper shows that the annual, seasonal and daily fluctuations embedded in time series of the mean wind speeds, constrain its probability distribution and time correlation to be physically consistent. Besides, a new physical interpretation of the ARIE is presented, expressing how the independence across wind observations increases with the wind speed, up to the point that all yearly observations are independent if larger than a suitable speed value. Such a tendency is not revealed if the annual, seasonal and daily fluctuations are excluded by the analysis, leading to a deceitful shape of the ARIE. Finally, the paper shows how the velocity‐dependent ARIE model is consistent with the conventional asymptotic extreme value theory, if a sufficiently large left‐censorship applies to the dataset. The study of the ARIE presented in this paper is based on long‐term Monte Carlo simulation of the mean wind speed.

Keywords

• annual and daily cycles
• annual rate of independent events
• extreme value analysis
• macro‐meteorological power spectrum
• mean wind velocity
• Monte Carlo simulation