Probability density functions of turbulent velocity and temperature fluctuations in the unstable atmospheric surface layer

The behavior of probability density functions (pdfs) of the velocity and temperature fluctuations in the unstable surface layer is systematically studied within the framework of similarity theory. The pdfs of horizontal velocity fluctuations are nearly Gaussian for a wide range of atmospheric stability conditions. Thus, the standard deviations of horizontal velocity fluctuations are sufficient to predict the pdfs. Using mixed-layer similarity, these standard deviations can be estimated from mean meteorological conditions. The pdfs of vertical velocity fluctuations are non-Gaussian. We introduce the truncated stable distributions and find that they can be better for fitting the tails of measured pdfs than other non-Gaussian pdfs commonly used in the airborne dispersion models. This implies that the truncated stable distributions can be better for describing the small probability but high-impact events. Similar to the pdfs of the horizontal velocity fluctuations, the standard deviations of vertical velocity fluctuations are also sufficient to predict the pdfs. Using Monin-Obukhov similarity, their standard deviations can also be estimated from mean meteorological conditions. The pdfs of temperature fluctuations are much more complicated than those of velocity fluctuations. We show that the left tails of the temperature pdfs are likely to be power law and the right tails of temperature pdfs are Gaussian. Although complicated for pdfs, the Monin-Obukhov similarity is also valid to the standard deviations of temperature fluctuations.