The use of finite-volume methods for atmospheric advection of trace species. Part I: Test of various formulations in a general circulation model

In the context of advection of trace species by 3D atmospheric flows, a com parative test of a hierarchy of finite volume transport schemes initially d erived by B. Van Leer is presented. Those schemes are conservative by const ruction 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 import ant 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 accu rate than lower order at a given spatial resolution but much more comparabl e when the lower-order schemes are run on a finer grid to make the numerica l costs equivalent. Moreover, the higher moments of the tracer distribution introduced in the more sophisticated schemes become an issue when other pr ocesses such as chemistry or turbulent mixing are accounted for. Finally, i t 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 Meteorologie Dynamique. The GCM implementation of Van Leer scheme I is conservative, positive, and monotonic, and it does not modify a uniform tracer distribution.