Some considerations on skewness and kurtosis of vertical velocity in the convective boundary layer

Data of skewness $S$ and kurtosis $K$ of vertical velocity in the convective boundary layer from different datasets have been analysed. Vertical profiles of $S$ were found to be grouped into two classes that display different slopes with height: one is nearly constant and the other is increasing. This behaviour can be explained using a simple model for the PDF of vertical velocity and assuming two distinct vertical profiles of updraft area fraction from literature. The possibility of describing the explicit dependence of $K$ on $S$ was revised critically, also considering the neutral limit as well as the limit for very small non-dimensional height. It was found that the coefficients of the relationship depends on both the Obukhov length scale $L$ and inversion height $z_i$.