Parameterization of linear wave chemical transport in planetary atmospheres by eddy diffusion

Two-dimensional transport by linear waves is parameterized by wave velocity and temperature correlations and nonconservative properties of the atmosphere in a residual Eulerian framework. Explicit expressions derived for the eddy tracer flux vector are written in eddy diffusion tensor form, but it is demonstrated that strong coupling of chemistry and temperature through the rate constants, as is the case for ozone, requires additional terms proportional to the mixing ratio and not to its gradient. A variety of limiting cases are discussed. In the residual Eulerian framework the K(yz), K(zy) components are nonzero for a nonconservative atmosphere and/or a reactive tracer. Tracers have common transport coefficients in the limit where their chemistry is negligible in comparison to transience. It is shown that the usual one-dimensional vertical eddy diffusion continuity equation is rigorously valid only when the temperature dependence of the rate constants is negligible and the tracer has strong vertical stratification relative to its horizontal variability.