Distributions and correlation properties of offshore wind speeds and wind speed increments

TL;DR

This study analyzes offshore wind speed data to understand their distribution and correlation properties, revealing insights into turbulence and scaling behaviors relevant for wind energy applications.

Contribution

It provides a detailed statistical analysis of offshore wind speeds and increments, highlighting their distributional forms, correlation structures, and turbulence characteristics.

Findings

Wind speeds follow Weibull distributions with weak height dependence.

Correlation functions exhibit long-term anticorrelations and sum rules.

Increment distributions transition from tent-like to Gaussian with lag.

Abstract

We determine distributions and correlation properties of offshore wind speeds and wind speed increments by analyzing wind data sampled with a resolution of one second for 20 months at different heights above sea level in the North Sea. Distributions of horizontal wind speeds can be fitted to Weibull distributions with shape and scale parameters varying weakly with the vertical height separation. Kullback-Leibler divergences between distributions at different heights change with the squared logarithm of the height ratio. Cross-correlations between time derivatives of wind speeds are long-term anticorrelated, and the even parts of their correlation functions satisfy sum rules. Distributions of horizontal wind speed increments change from a tent-like shape to a Gaussian with rising increment lag. A surprising peak occurs in the left tail of the increment distributions for lags in a range $10-200\,{\rm km}$ after applying the Taylor's hypothesis locally to transform time lags into distances. The peak is decisive in order to obtain an expected and observed linear scaling of third-order structure functions with distance. This suggests that it is an intrinsic feature of atmospheric turbulence.