The specified horizontal diffusion term in Eulerian

dispersion models, when combined with the effects of the

input wind fields, the numerical diffusion of the advection


scheme and the instantaneous dilution in the grid cell should

accurately simulate the diffusion that is observed in the

atmosphere. The eddy diffusivity must take into account the

genuinely advective characteristics of wind flows. For

example, Smagorinsky’s [57] horizontal diffusivity

algorithm accounts for the transport (stretching and shearing

deformation) characteristics of wind flows:

Because Eq. (23) relies on the grid-scale wind components,

it is not suitable for estimating the sub-grid scale diffusion

not resolved by the modeled wind fields. Furthermore, for a

coarse resolution where numerical diffusion is already large,

use of this formula seems inadequate. For simulations with

a larger grid size, eddy diffusivity may be parameterized to

counteract the numerical diffusion (e.g., Byun et al. [56]):


where KHf (Δx f ) stands for a uniform eddy diffusivity at a

fixed resolution Δ x f . In CMAQ KHf Δx f =4km

= 2000

(m2s-1) is used. The formula, however, is inadequate for a

very fine grid size where the physical dispersion dominates

over the numerical diffusion.

The difference in the grid size dependency between Eq. (23)

and Eq. (25) is striking. A heuristic method combining the

two formulae is suggested here as an analogy to the

resistance law concept used for the estimation of deposition



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