Given dynamically and thermodynamically consistent

meteorological data, we can maintain conservation of both

the trace species mixing ratio and mass at the model

synchronization time step. When a CTM is coupled with a

meteorology model that does not satisfy the necessary

characteristics for mass conservation (described earlier) and

the meteorological data and the numerical advection

algorithms are not exactly mass consistent, only

conservation of mixing ratio, not the tracer mass, should be

expected. In such a case, we need to solve a modified

advection equation in CTMs (Byun [29]):

where Qρ is the mass consistency error term. Eq. (19)

shows that the correction term has the same form as a firstorder

chemical reaction whose reaction rate is determined by

the mass consistency error (normalized with air density) in

the meteorology data. In CMAQ the advection process is

divided into horizontal (HADV) and vertical (VADV)

components. This distinction is possible because the mean

atmospheric motion is mostly in horizontal planes while the

vertical motion is related with the interaction of dynamics

and thermodynamics. Horizontal advection is further

decomposed into x- and y-direction processes, where the

solution alternates between (x, then y) and (y, then x)

directions to maintain a symmetric form of the advection

process calls.

The current CCTM codes include two flux-based advection

algorithms, the piecewise parabolic method (PPM) (Colella

and Woodward [53]) and the Bott scheme (Bott [54]). A

detailed test result of these schemes in comparison with

other advection algorithms is reported in Odman [55]. In

the PPM, the concentration distribution is assumed to be

parabolic in any given grid cell. The PPM is absolutely

positive definite and monotonic, while the Bott scheme is

non-monotonic and could generate unwanted local extreme

values for trace species, such as aerosol number density, that

have large concentration gradients. PPM is somewhat more



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