The last term in Eq. (27) represents the coordinate

divergence term. The importance of the vertical gradient

of γˆ ρ on the turbulence flux depends on the type of

vertical coordinates: the term vanishes for a massconserving

hydrostatic pressure coordinate, while it does not

for a fixed height coordinate. In any case, this effect is

neglected in the CMAQ. This formulation in the Reynolds

flux term can be represented with either local- or nonlocalmixing

parameterization schemes. Local closure assumes

that turbulence is analogous to molecular diffusion, i.e., the

flux at any point in space is parameterized by known mean

values at the same point (Stull [58]).

The current CMAQ system includes vertical diffusion

modules with the K-theory and a simple non-local closure

scheme. Because of its simplicity, the K-theory is widely

used in both meteorological and air quality models. The

resulting diffusion equation is discretized to form a

tridiagonal system, which is solved with a semi-implicit

method based on a Thomas algorithm [59](Gaussian

elimination without pivoting, followed by back substitution).

In atmospheric models, a nonlocal scheme is suggested to be

used in the presence of convective conditions where eddies

are larger than the grid size and the K-theory fails to

represent vertical mixing adequately. Therefore, the

Asymmetric Convective Model (ACM) (Pleim and Chang

[60]), a non-local closure model for the convective boundary

layer, is also available. The ACM was originally developed

for use in RADM and has also been applied to SAQM

(Chang et al. [61]) and MM5.



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