edu.ucar.opensky::articles:15188 UCAR/NCAR - Library OpenSky Support PO Box 3000 Boulder CO 80307-3000 opensky@ucar.edu http://opensky.ucar.edu/ homepage pointOfContact 2025-12-26T14:58:59.087349 ISO 19115-2 Geographic Information - Metadata - Part 2: Extensions for Imagery and Gridded Data ISO 19115-2:2009(E) https://n2t.org/ark:/85065/d73x87p8 Voronoi, Delaunay, and block-structured mesh refinement for solution of the shallow-water equations on the sphere 2009-12-01T00:00:00Z publication https://n2t.org/ark:/85065/d73x87p8 https://doi.org/10.1175/2009MWR2917.1 Weller, H. author Weller, H. author Fournier, Aimé author UCAR/NCAR - Library publisher Alternative meshes of the sphere and adaptive mesh refinement could be immensely beneficial for weather and climate forecasts, but it is not clear how mesh refinement should be achieved. A finite-volume model that solves the shallow-water equations on any mesh of the surface of the sphere is presented. The accuracy and cost effectiveness of four quasi-uniform meshes of the sphere are compared: a cubed sphere, reduced latitude–longitude, hexagonal–icosahedral, and triangular–icosahedral. On some standard shallow-water tests, the hexagonal–icosahedral mesh performs best and the reduced latitude–longitude mesh performs well only when the flow is aligned with the mesh. The inclusion of a refined mesh over a disc-shaped region is achieved using either gradual Delaunay, gradual Voronoi, or abrupt 2:1 block-structured refinement. These refined regions can actually degrade global accuracy, presumably because of changes in wave dispersion where the mesh is highly nonuniform. However, using gradual refinement to resolve a mountain in an otherwise coarse mesh can improve accuracy for the same cost. The model prognostic variables are height and momentum collocated at cell centers, and (to remove grid-scale oscillations of the A grid) the mass flux between cells is advanced from the old momentum using the momentum equation. Quadratic and upwind biased cubic differencing methods are used as explicit corrections to a fast implicit solution that uses linear differencing. UCAR/NCAR - Library OpenSky Support PO Box 3000 Boulder CO 80307-3000 opensky@ucar.edu http://opensky.ucar.edu/ homepage pointOfContact PDF Text theme Resource Type 2016-01-01T00:00:00Z publication Copyright 2009 American Meteorological Society (AMS). Permission to use figures, tables, and brief excerpts from this work in scientific and educational works is hereby granted provided that the source is acknowledged. Any use of material in this work that is determined to be "fair use" under Section 107 or that satisfies the conditions specified in Section 108 of the U.S. Copyright Law (17 USC, as revised by P.L. 94-553) does not require the Society's permission. Republication, systematic reproduction, posting in electronic form on servers, or other uses of this material, except as exempted by the above statements, requires written permission or license from the AMS. Additional details are provided in the AMS Copyright Policies, available from the AMS at 617-227-2425 or amspubs@ametsoc.org. Permission to place a copy of this work on this server has been provided by the AMS. The AMS does not guarantee that the copy provided here is an accurate copy of the published work. None eng geoscientificInformation