Figure 1

Extracting wind persistence statistics from trajectory data. (a) The downscaled ERA-Interim data at Alpha Ventus⁴⁶ provide a trajectory of wind velocities with a 3-hour resolution. (b) The aggregated wind velocities approximately follow a Weibull distribution. The blue curve reports the recorded data and the red curve depicts the most-likely Weibull distribution, with shape parameter \(\alpha \approx 2.36\) and scale parameter \(\beta \approx 9.66\). (c) If the wind velocity drops below a threshold of \(v=4\,{\rm{m}}/{\rm{s}}\) (dashed red line in panel (a)), we count the full period until it crosses the threshold again as low-wind duration and gather these events for our persistence statistics. For high-wind speeds, we analogously employ an upper threshold of \(v=12\,{\rm{m}}/{\rm{s}}\) (not shown). Note that the plots and thresholds use the velocity scaled up from 10 m to a typical hub height of 100 m, using a power law, see Methods for details. While the mean velocity in panel (b) is close to the upper threshold, we note that here we are using data from an offshore wind farm location, with typically high wind velocities. Most wind turbines reach their rated power at \(v=12\,m/s\)⁵⁰ so that higher velocities still lead to the maximum power output.