Statistical characteristics and complexity of stochastic wind speeds in near-surface flow fields

Statistical characteristics of meteorological elements play an important role in climate assessment. The statistical study of wind speeds in near-surface flow fields is mainly concerned by wind energy. Determinacy and stochasticity of wind speeds are important for wind power generation system. Probability density function (PDF) is the main approach to describe wind speed distribution. Here we show a theoretical evolution pattern of statistical characteristics of stochastic wind speed system was constructed. This is simple and applicable worldwide. Poisson, gamma (or Weibull), and negative binomial distribution corresponds to the timescale of 10 min, less than one year, and many years, respectively. Downscaling functions eliminating a parameter are the distributions of the shape parameter, and statistically are the emergence of each level of system. Variations of the scale parameter characterizing thermal convection are reflected in wind speed distributions through variations of the shape parameter representing forced convection. The emergence of Poisson, gamma, and negative binomial distribution is the result of spatial interaction, spatial interaction that varies with time, and space, time and inheritable instructions, separately. Stochasticity of wind speed system is intrinsic. Static PDFs describe the deterministic statistical characteristics of stochastic wind speeds, which emphasizes that determinacy contains stochasticity. Dynamic relationships among levels of system reflect the evolution of system, which embodies constructivism. From the view of the discontinuous statistical characteristics, stochastic wind speed system is catastrophic. These results provide a new path for cross-level research of complexity science.