COMPARISON AMONG EMPIRICAL PROBABILITY DENSITY-FUNCTIONS OF THE VERTICAL VELOCITY IN THE SURFACE-LAYER BASED ON HIGHER-ORDER CORRELATIONS

Vertical velocity fluctuations were measured in the atmospheric surfac e layer by means of an ultrasonic anemometer and higher order correlat ions were calculated on two time series, recorded in unstable and neut ral conditions, and selected for the whole measurement period on the b asis of the inversion test (stationarity test). Comparisons have been made between observed and predicted correlations by considering Gaussi an joint-PDF and Gram-Charlier series expansions truncated to the four th and sixth order as done earlier by Frenkiel and Klebanoff. A bi-Gau ssian PDF, given by a mixture of two Gaussian PDFs, has also been cons idered. This last has been constructed assuming that either the first three or the first four moments are given, and the relationships betwe en correlation functions of different order are derived. The departure from Gaussian behaviour in both stability conditions is derived. Thou gh Gram-Charlier series expansions show a good correspondence to exper imental reality, their use as non-Gaussian probability distributions c annot be suggested in theoretical approaches and should be considered with care in practical applications, due to possible occurrences of sm all negative probabilities. The results shown in this paper support th e applicability of the bi-Gaussian PDF created using up to the fourth moment.