Figure 4

Persistence statistics approximately follows exponentials for homogeneous pressure. High-wind velocity statistics \(v > 12\,{\rm{m}}/{\rm{s}}\) are analyzed for Alpha Ventus, based on the downscaled ERA-Interim data⁴⁶, conditioning the statistics on small bins of homogeneous f-parameters (in units of hPa per 1000 km). (a–c) Plotting both the most-likely exponential and q-exponential distributions for small, conditioned subsets, we notice that the q-exponential distributions are very close to the exponential ones. The q-value is determined by using the kurtosis of the data, see Eq. (3). Note that the maximum q-value derived this way is \({q}_{{\rm{\max }}}=1.2\). On average, the q-value is closer to 1 than in the unconditioned Fig. 3. (d) Combining the independent exponential distributions into one super-exponential approximates the q-exponential distribution. (e) The histogram of the individual λ_e parameters is approximated by a log-normal distribution, a typical distribution often seen in superstatistics. We report the uncertainty of q as a single standard deviation, determined via bootstrapping, see Methods. See also Supplementary Note 4 for detailed discussion and analysis of Harthaeuser Wald.