Comparison of PDFs, closure schemes and turbulence parameterizations in Lagrangian stochastic models

Six one-dimensional models, based on the Ito-type stochastic equation, are presented and compared. Four of these take into account up to the fourth order moment of vertical velocity fluctuations, and two up to the third order moment. Four models make use of a bi-Gaussian probability density function (PDF) and the other two are based on a Gram-Charlier series expansion truncated to the third or fourth order. All the models were run with a parameterization of input turbulence (i.e. w²,w³, and τ profiles). Concerning the fourth order moment w⁴, two different parameterizations were considered. Comparisons are made between ground-level concentrations, plume height and plume width observed in the Willis and Deardorff water tank experiments and those predicted by the different models here considered. The goal of this study was to find the models that give greater confidence in their applicability in dispersion studies and to verify the importance of considering the fourth order moment. The main conclusions are: simulation results largely depend on the turbulence parameterization chosen; the Gram-Charlier PDF gives the best agreement with observations; some combinations of models and turbulence parameterizations perform well in simulating the shape of the ground-level concentration (g.l.c.) trend but fail in correctly simulating the form of the plume (plume height and vertical width); in the case of the Gram-Charlier PDF, the fourth order model reproduced the vertical plume width better than the third order one, whereas the two schemes yielded similar g.l.c. distributions.