Inert Trace Constituent Transport in Sigma and Hybrid Isentropic–Sigma Models. Part I: Nine Advection Algorithms

Abstract

The University of Wisconsin hybrid isentropic?sigma (??σ) coordinate channel model and the nominally identical sigma (σ) model are used to test the relative capabilities of nine trace constituent transport algorithms. The nine are ?standard? second-order finite differencing, the standard with two local ?borrow and fill? fixers, the standard with a global fixer, four conservative flux-integrated approaches, and the conservation of second-order moments (CSOM). Transport of two analytically specified initial trace constituent distributions is simulated within a common initial atmosphere, which includes a baroclinically amplifying synoptic-scale wave. Two different vertical resolution ??σ models and four vertical resolution σ models provide excellent test beds for comparison of the transport algorithms because their 48-h predictions of standard synoptic fields are virtually identical. Although no analytic solution exists against which detailed comparisons can be made, the constraint of adiabatic conditions for a continuum provides that the maximum of a trace constituent within explicit or implicit isentropic layers of a model should be conserved throughout the simulations, and that the area between any two trace constituent contours on an isentropic surface should remain constant. With these conditions as bases of comparison, several results are unambiguous. First, in the σ models the standard with fixers is better than the other schemes except for the CSOM at the highest resolution. Second, in the ??σ models, the piecewise parabolic and CSOM schemes produce results approximately as accurate as the standard with fixers. Third, when comparing all algorithms, models, resolutions, and distributions, the CSOM scheme produces the most consistent results. Finally, for a large majority of the cases, the ??σ models perform more accurately than the σ models with respect to the conservation of constituent extrema.