Extreme fluctuations of vertical velocity in the unstable atmospheric surface layer

In this paper, we propose a new method to extract the extreme fluctuations of vertical velocity in the unstable atmospheric surface layer. Unlike the commonly used conditional sampling analysis, this method defines a threshold by using a systematical method and tries to reduce the artificiality in this process. It defines threshold as the position where the types of probability density functions (PDFs) of vertical velocity fluctuations begin to change character from stable distributions to truncated stable distributions. Absolute values of fluctuations greater than the threshold are considered to be extreme fluctuations. We then analyze the statistical characteristics of extracted extreme fluctuations of vertical velocity. Our results show that the amplitudes of extreme fluctuations are exponentially distributed, and the waiting times between extreme fluctuations have stretched exponential distributions. It suggests that there are statistical correlations in the time series of vertical velocity because independent time series can only have exponentially distributed waiting times. The durations of extreme fluctuations are also found to be stretched exponential distributed, while for the independent time series the distributions of durations are delta-like. Finally, the PDFs of amplitudes, waiting times and durations are all well parameterized in the context of Monin-Obukhov theory.