Dispersion modelling over the outer-scale

For dispersion in flows with significant variation in direction and speed at different heights and different times, the only reliable modelling method is to track individual fluid particles or track many clouds of particles from the source. The former method is now used for regional and synoptic scale dispersion prediction from localised sources, such as nuclear accidents and volcanoes, e.g. Maryon and Buckland, 1995 [396], Assumptions have to be made about how atmospheric turbulence on scales less than 3Ax diffuses particles as they are advected by the resolved flow field on scale Ax. This method requires large computer resources and then can be computed in minutes. For studying critical events in UK urban areas this method should be considered. 

In terms of FAM, the most basic method for estimating dispersion on the mesoscale (where crz becomes equal to or greater than h) is to assume that the concentration profile is approximately constant below the top of the boundary layer, so that for a continuous source Qs, and for steady meteorological conditions, 

This box-model approach has been used for comparison with urban dispersion experiments by Middleton, 1998 [431], This has proved satisfactory on neighbourhood scale ( 1 km from source). 

To model the transition of the plume between the neighbourhood and mesoscale regions, it is usual (as with other Gaussian plume models, e.g. Pasquill and Smith, 1983 [484] Hunt et al., 1988 [286, 287]) to estimate approximately the plume profile by one (or more) reflection terms when rzh/2, i.e. 

With such a model it is also necessary to estimate the effects on the cloud/plume dimensions of undulating terrain and any significant changes in stratification over the urban terrain. When, as is usual, the depth of the mixed layer, h, and Uh change over the diurnal period these expressions can be extended by using a FAM for the flow field and turbulence (as discussed in Section 2.2) and thence correcting the values of crx, ry, (rz(x). Also, the time dependence should be considered especially when considering 

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