Probability Density Functions of Velocity Increments in the Atmospheric Boundary Layer

摘要

The probability density functions (pdf’s) of the wind increments are measured under different weather conditions in the atmospheric boundary layer, including the extreme weather of a typhoon and sand storm. It is found that in each case the measured pdf’s with respect to different time lags coincide by suitable scaling transformation. This property is similar to that of the stable distributions. However, fitting results show that the tails of the stable distributions are generally heavier than that of the measured ones. Beside, the stable distributions (except for the Gaussian distribution) have infinite variance, which implies infinite average kinetic energy. In fact, it can be proved that if the tails of the pdf’s are heavy enough, the variance will be infinite. Therefore, the tail-truncated stable distributions with finite variances are introduced to fit the data and the fitting results are excellent. Keywords Atmospheric turbulence - Probability density functions - Stable distribution - Truncated stable distribution - Velocity increments