Inert Trace Constituent Transport in Sigma and Hybrid Isentropic–Sigma Models. Part II: Twelve Semi-Lagrangian Algorithms

Abstract

Part I of this paper examined nine trace constituent advection algorithms as applied in channel versions of the University of Wisconsin hybrid isentropic?sigma (??σ) and sigma (σ) models. This paper examines the performance of 12 semi-Lagrangian transport (SLT) algorithms in the same models. The interpolants of trace constituent include second- through twelfth-order Lagrangian, an overlapping polynomial, a quasi-monotonic scheme, and two sixth-order schemes that employ derivative estimates. Additional experiments are performed that emulate the SLT algorithm in the NCAR Community Climate Model 2. As in Part I, these three-dimensional simulations are under adiabatic conditions so that conservation of the initial trace constituent maximum on an isentropic surface, and conservation of the areas between any two constituent contours, can be used as objective measures of SLT algorithm accuracy. Further, the experiments provide comparisons not only between the different SLT formulations but also between their performance in models using ? and σ coordinates. Similar to Part I, an important result of the experiments is that comparison of algorithms is most revealing under three-dimensional transport within a baroclinic wave in which vertical transport is important. The experiments also show 1) that the ?cascade? interpolation scheme is a reasonable method of greatly reducing computation time in SLT without affecting accuracy; 2) that ?shape-preserving? interpolation schemes reduce accuracy in both the ??σ and σ models; and 3) that Lagrangian interpolants of tenth and twelfth order do not significantly improve results. Comparisons to results in Part I suggest that the conservation of second-order moments advection scheme is the most consistent of all options tested.