Refinement of Horizontal Diffusion in Photochemical Grid Models

The last decade has witnessed significant improvements in the quality of advection schemes in terms of reduced amounts of numerical dispersion and diffusion. The levels of numerical diffusion are now down to the point where one has to be concerned about adding back amounts of diffusion that are appropriate to the atmospheric conditions being modeled. In addition, there are other transport errors which begin to become evident with these higher quality transport schemes; specifically, operator splitting errors and shear flow errors, which were heretofore buried by the numerical diffusion. The characterization of these various diffusivity and error terms must be modeled so that the "needed" horizontal diffusivity term can be added back into the modeling system as a "total" desired diffusivity minus the "numerical" diffusivity already accompanying the advection scheme. Even the numerical diffusivity, known to vanish at Courant (CFL) numbers of 0, -1, and +1 in flux formulation algorithms and peak at CFL of +1/2 and -1/2, was first modeled for several of the more popular current advection schemes.

The "total" diffusivity involves a number of diffusive processes, such as temporal wind field variations that are 'lost' by the wind field model, as well as processes, such as wind shear effects, that are genuinely transportive rather than diffusive, but may be lumped into off-diagonal diffusivity terms for expediency.

The mathematical characterization of a number of diffusivity and error terms are detailed in the paper, including:

· along-wind gradient transport corrections;

· cross-wind gradient transport corrections; and

· relative versus absolute diffusion in directionally sheared and unsheared flows.

As directional shear of the wind is already partially represented in the winds output by meteorological models, it became critical to model realistic atmospheric diffusivities in the absence of wind direction shear. This was accomplished using literature estimates and runs of the synthetic turbulence model, KSP.

As a final step in this California Air Resources Board sponsored effort, the resulting diffusivity modules were added to the SAQM model and sensitivity tests performed on a multi-day SCAQS episode.