Numerical Advection Schemes, Cross-Isentropic Random Walks, and Correlations between Chemical Species - Abstract

J.Thuburn
Centre for Global Atmospheric Modelling
Department of Meteorology
University of Reading
England
M.E.McIntyre
Centre for Atmospheric Science
Department of Applied Mathematics and Theoretical Physics
Cambridge University
England

Abstract.

The advection schemes used in numerical models of chemistry and transport at fixed resolution must, unavoidably, cause the models to misrepresent the transport in some way; this can include failure to establish or preserve the functional relations between long-lived chemical tracers that are often observed in the atmosphere. We show that linear functional relations will be preserved exactly by purely linear advection schemes and also, less obviously, by certain "well behaved" flux-limited schemes, despite the unavoidable nonlinearity introduced by the flux limiter. In practice, well behaved flux-limited schemes will also preserve nonlinear functional relations better than schemes like centered difference or pseudospectral schemes that suffer from dispersion errors; the reason is that the dispersion errors lead to spurious oscillations of the mixing ratio field in physical space, artificially extending 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 nonlinearly related to begin with. Examples of correlations established by real and model transport are discussed in this light, including the case of stratospheric transport on time scales of years, where we discuss and extend earlier results on the way in which tracer functional relations can arise, for sufficiently long-lived tracers, purely from transport in the midlatitude lower stratosphere. The results are shown not to depend on the quasi-horizontal Fickian eddy-diffusivity assumption used in the earlier work. The reason is that, whenever the quasi-horizontal (isentropic) mixing is fast enough - even if non-Fickian as in real stratospheric surf zones - the chaotic part of the quasi-vertical (cross-isentropic) transport has the nature of a random walk with small steps.

Back to my home page ---- back to Atmospheric Dynamics home page
Michael McIntyre (mem at damtp.cam.ac.uk), DAMTP, University of Cambridge, Silver Street, Cambridge CB3 9EW
Last updated March 1997