We present a semi-analytical model for the dispersion of passive scalars from continuous ground sources up to distances of a few hundred metres. We attempt to cope with problems typical of analytical models, such as the correct representation of the near-ground concentration and lateral dispersion, while avoiding the use of any empirical parameters. A previous analysis of Prairie Grass Project (PGP) data has shown that the near-ground, cross-wind integrated concentration decreases as some power of the distance from the source that is, itself, distance dependent. As the conventional power-law model is incapable of reproducing this behaviour, we propose a model in which the vertical diffusivity depends on both the height as a power law, and on the distance from the source. For this equation, we construct an infinite-series formal solution, with the first term used as an approximation. A set of equations based on this approximation and on Monin–Obukhov similarity theory is proposed for the the vertical diffusivity, from which the cross-wind integrated concentration is derived analytically. We further construct a simple empirical model for the distance-dependent vertical diffusivity. For the plume lateral width, a Langevin stochastic model depending on the plume height is proposed, whose formal analytical solution is used to derive a set of equations for the cloud width, which are easily solved numerically, with the results validated against PGP data. We apply four statistical measures to evaluate the performance of the model, including the computation of the 95% confidence intervals, for which we find very good agreement. Implementation of this model is extremely simple and computationally efficient.
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- Ground source
- Orthogonal regression
- Semi-analytical model
- Short-range dispersion