On the validity of grid and trajectory models of urban air pollution

Abstract

Of the two types of dynamic urban air pollution models commonly used, grid models emply a coordinate system fixed with respect to the ground, whereas trajectory models have a coordinate system centered on a fictitious vertical air column which moves horizontally with the advective wind. Both models are based on the atmospheric diffusion equation as the essential description of turbulent advection and diffusion. The primary errors committed in the grid model are those attributed to finite-difference approximations, whereas the errors in the trajectory model are mainly a result of the assumptions inherent in the model formulation, such as neglect of horizontal turbulent diffusion across the parcel boundaries and neglect of wind shear. Quantitative conditions based on comparison of exact solutions of the atmospheric diffusion equation with those of the grid and trajectory models are derived to indicate when these two classes of models may be accurately employed for various regimes of stability, wind shear and source configuration.

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