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William H. Lipscomb
and
Todd D. Ringler

Abstract

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.

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William H. Lipscomb
and
Elizabeth C. Hunke

Abstract

Sea ice models contain transport equations for the area, volume, and energy of ice and snow in various thickness categories. These equations typically are solved with first-order-accurate upwind schemes, which are very diffusive; with second-order-accurate centered schemes, which are highly oscillatory; or with more sophisticated second-order schemes that are computationally costly if many quantities must be transported [e.g., multidimensional positive-definite advection transport algorithm (MPDATA)]. Here an incremental remapping scheme, originally designed for horizontal transport in ocean models, is adapted for sea ice transport. This scheme has several desirable features: it preserves the monotonicity of both conserved quantities and tracers; it is second-order accurate except where the accuracy is reduced locally to preserve monotonicity; and it efficiently solves the large number of equations in sea ice models with multiple thickness categories and tracers. Remapping outperforms the first-order upwind scheme and basic MPDATA scheme in several simple test problems. In realistic model runs, remapping is less diffusive than the upwind scheme and about twice as fast as MPDATA.

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