An incremental remapping transport scheme on a spherical geodesic grid

Weather and climate models contain equations for transporting conserved quantities such as the mass of air, water, ice, and associated tracers. Ideally, the numerical schemes used to solve these equations should be conservative, spatially accurate, and monotonicity-preserving. One such scheme is incremental remapping, previously developed for transport on quadrilateral grids. Here the incremental remapping scheme is reformulated for a spherical geodesic grid whose cells are hexagons and pentagons. The scheme is tested in a shallow-water model with both uniform and varying velocity fields. Solutions for standard shallow-water test cases 1, 2, and 5 are obtained with a centered scheme, a flux-corrected transport (FCT) scheme, and the remapping scheme. The three schemes are about equally accurate for transport of the height field. For tracer transport, remapping is far superior to the centered scheme, which produces large overshoots, and is generally smoother and more accurate than FCT. Remapping has a high startup cost associated with geometry calculations but is nearly twice as fast as FCT for each added tracer. As a result, remapping is cheaper than FCT for transport of more than about seven tracers.