Level-crossing statistics of the horizontal wind speed in the planetary surface boundary layer

The probability density of the times for which the horizontal wind remains above or below a given threshold speed is of some interest in the fields of renewable energy generation and pollutant dispersal. However there appear to be no analytic or conceptual models which account for the observed power law form of the distribution of these episode lengths over a range of over three decades, from a few tens of seconds to a day or more. We reanalyze high resolution wind data and demonstrate the fractal character of the point process generated by the wind speed level crossings. We simulate the fluctuating wind speed by a Markov process which approximates the characteristics of the real (non-Markovian) wind and successfully generates a power law distribution of episode lengths. However, fundamental questions concerning the physical basis for this behavior and the connection between the properties of a continuous-time stochastic process and the fractal statistics of the point process generated by its level crossings remain unanswered. (c) 2001 American Institute of Physics.