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In the context of advection of trace species by 3D atmospheric flows, a comparative test of a hierarchy of finite volume transport schemes initially derived by B. Van Leer is presented. Those schemes are conservative by construction and Van Leer proposed a simple way of ensuring monotonicity. One of the schemes, introduced independently in the atmospheric community by M. J. Prather, is now considered as a reference in the GCM community. An important aspect of the present work is to perform test simulations with various spatial resolutions in order to compare the various schemes at a comparable numerical cost. The result is that higher-order schemes are much more accurate than lower order at a given spatial resolution but much more comparable when the lower-order schemes are run on a finer grid to make the numerical costs equivalent. Moreover, the higher moments of the tracer distribution introduced in the more sophisticated schemes become an issue when other processes such as chemistry or turbulent mixing are accounted for. Finally, it is suggested that Van Leer scheme I is well suited for transport of trace species by 3D atmospheric winds. The results are shown of applications to the transport of radon in the GCM of Laboratoire de Météorologie Dynamique. The GCM implementation of Van Leer scheme I is conservative, positive, and monotonic, and it does not modify a uniform tracer distribution.
Hourdin et al. (Sat,) studied this question.