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 theatmospheric surface layer by means of an ultrasonic anemometer andhigher order correlations were calculated on two time series, recordedin unstable and neutral conditions, and selected for the wholemeasurement period on the basis of the inversion test (stationaritytest). Comparisons have been made between observed and predictedcorrelations by considering Gaussian joint-PDF and Gram-Charlierseries expansions truncated to the fourth and sixth order as doneearlier by Frenkiel and Klebanoff. A bi-Gaussian PDF, given by amixture of two Gaussian PDFs, has also been considered. This lasthas been constructed assuming that either the first three or the firstfour moments are given, and the relationships between correlationfunctions of different order are derived. The departure from Gaussianbehaviour in both stability conditions is derived. Though Gram-Charlier series expansions show a good correspondence toexperimental reality, their use as non-Gaussian probabilitydistributions cannot be suggested in theoretical approaches andshould be considered with care in practical applications, due topossible occurrences of small negative probabilities. The resultsshown in this paper support the applicability of the bi-Gaussian PDFcreated using up to the fourth moment.