PROBABILITY DENSITY-FUNCTIONS FOR VELOCITY IN THE CONVECTIVE BOUNDARY-LAYER, AND IMPLIED TRAJECTORY MODELS

When a probability density function (pdf) is to be formed on the basis of incomplete information, the ''maximum missing information'' (mmi) pdf (Jaynes, Phys. Rev. 106, 620-630, 1957) is theoretically preferable. We compare the performance of Lagrangian stochastic (LS) models of vertical dispersion in the convective boundary layer, satisfying Thomson's (J. Fluid Mech. 180, 529-556, 1987) well-mixed condition, that derive from the often-used bi-Gaussian pdf (eg. Weil, J. atmos. Sci. 47, 501-515, 1990) and from the mmi pdf. The bi-Gaussian based LS model, which we tailor to reproduce velocity moments to fourth order, is less complex than the corresponding mmi based model, and gives similar (good) predictions, which are arguably slightly superior (as regards agreement with convection tank data) to those stemming from the original bi-Gaussian based model (Luhar and Britter, Atmospheric Environment 23, 1911-1924, 1989), wherein knowledge of the kurtosis was forsaken.