Comparison of closure schemes used to specify the velocity PDF in Lagrangian stochastic dispersion models for convective conditions

Lagrangian stochastic dispersion models make use of the probability density function (PDF) of the Eulerian vertical turbulent velocities. For convective conditions, the PDF is often assumed to have a bi-Gaussian form. Using new laboratory measurements of velocity PDFs in the convective boundary layer (CBL), we propose a new closure for constructing this bi-Gaussian PDF and compare results with three other closure schemes in current use. Of the three existing closures, two utilize the second and third moments of the vertical velocity as inputs, while the third one also incorporates the fourth moment. The new closure is defined with the desirable property that it collapses to a simple Gaussian in the limit of zero skewness. The value of an adjustable parameter in this closure scheme is selected using laboratory data for the third and fourth velocity moments. We determine the parameters in the PDF expression obtained using the four closures, and compare them with those derived by fitting velocity PDF data from the convection tank experiments. Significant differences are found between the values of the PDF parameters from the various closures and the water tank data. The performance of the closure schemes is compared by using a Lagrangian stochastic model to compute ground-level crosswind-integrated concentrations from particles released at four source heights. It is shown that the differences between the concentration estimates obtained using various closures increase as the source height increases. Using, as the benchmark, the dispersion results calculated from the Lagrangian stochastic model incorporating the laboratory velocity data without any closure, we recommend our new closure scheme. The results highlight the importance of turbulence observations in the CBL for accurate dispersion modelling.