NUMERICAL ADVECTION SCHEMES, CROSS-ISENTROPIC RANDOM-WALKS, AND CORRELATIONS BETWEEN CHEMICAL-SPECIES

The advection schemes used in numerical models of chemistry and transp ort at fixed resolution must unavoidably cause the models to misrepres ent the transport in some way. This can include failure to establish o r preserve the functional relations between long-lived chemical tracer s that are often observed in the atmosphere. We show that linear funct ional relations will be preserved exactly by purely linear advection s chemes and also, less obviously, by certain ''semi-linear'' flux-limit ed schemes despite the unavoidable nonlinearity introduced by the flux limiter. In practice, semi-linear flux-limited schemes will also pres erve nonlinear functional relations better than linear centered differ ence or spectral schemes that suffer from dispersion errors. The reaso n is that the dispersion errors lead to spurious oscillations of the m ixing ratio field in physical space; artificially expanding the range of mixing ratios in any neighborhood, and hence to a spurious scatter in the relation between any two mixing ratio fields that are nonlinear ly related to begin with. Examples of correlations not only preserved, but established, by real and model transport are discussed in this li ght, including the case of stratospheric transport on timescales of ye ars, for which we discuss and extend earlier results on the ways in wh ich tracer functional relations can arise, for sufficiently long-lived tracers, purely from transport. The stratospheric results are shown n ot to depend on the quasi-horizontal Fickian eddy diffusivity assumpti on used in the earlier work. The reason is that, whenever the quasi-ho rizontal (isentropic) mixing is fast enough-even if it is non-Fickian as expected in real stratospheric surf zones-the chaotic part of the q uasi-vertical, cross-isentropic transport has the nature of a random w alk with small vertical steps.