A Semi-Analytical Model for Short Range Dispersion From Ground Sources

Thursday, 18 December 2014
Ehud Gavze, Eyal Fattal and Rivka Reichman, Hebrew University of Jerusalem, Jerusalem, Israel
A semi-analytical model for dispersion of passive scalars from ground sources up to distances of a few hundred meters is presented. Most widely used analytical models are Gaussian models which assume both a uniform wind field and homogeneous turbulence. These assumptions are not valid when ground sources are involved since both the wind and the turbulence depend on height. The model presented here is free of these two assumptions. The formulation of the vertical dispersion is based on approximating the vertical profiles of the wind and the the vertical diffusion coefficient, based on Monin Obukhov Similarity Theory, as power laws. One advantage of this approach is that it allows for non Gaussian vertical profiles of the concentration which better fit the experimental data. For the lateral dispersion the model still assumes a Gaussian form. A system of equations was developed to compute the cloud width. This system of equations is based on an analytical solution of a Langevin equation which takes into account the non-homogeneity of the wind and the turbulence in the vertical direction. The model was tested against two field experiments. Comparison with a Gaussian model showed that it performed much better in predicting both the integrated cross wind ground concentration and the cloud width. Analytical, or semi-analytical models are useful as they are simple to use and require only a short computation time, compared, for example, to Lagrangian Stochastic Models. The presented model is very efficient from the computational point of view. As such it is suitable for cases in which repeated computations of the concentration field are required, as for example in risk assessments and in the inverse problem of source determination.