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Comparing Numerical Accuracy of Icosahedral A-GRID and C-GRID Schemes In Solving The Shallow-water Model


A single software framework is introduced to evaluate numerical accuracy of the A-grid (NICAM) versus C-grid (MPAS) shallow-water model solvers on icosahedral grids. The C-grid staggering scheme excels in numerical noise control and total energy conservation, which results in exceptional stability for long time integration. Its weakness lies in the lack of model error reduction with increasing resolution in specific test cases (especially the root-mean-square error). The A-grid method conserves well potential enstrophy and shows a linear reduction of error with increasing resolution. The gridpoint noise manifests itself clearly on A-grid, but much less on C-grid. We show that the Coriolis force term on C-grid has a larger error than on A-grid. To treat the Coriolis term and kinetic energy gradient on an equal footing on C-grid, we propose combining these two quantities into a single tendency term and computing its value by a linear combination operation. This modification alone reduces numerical errors but still fails to converge the maximum error with resolution. The method of Peixoto can solve the maximum-error nonconvergence problem on C-grid but degrades the numerical stability. For the steady-state thin-layer test (0.01 m in depth), the A-grid method is less susceptible than C-grid methods, which are presumably disrupted by the Hollingsworth instability. The effect of horizontal diffusion on model accuracy and energy conservation is shown in detail. Programming experience shows that software implementation and optimization can strongly influence computational performance for models, although memory requirement and computational load of the two schemes are comparable.

Article / Publication Data
Available Metadata
Accepted On
June 11, 2020
Fiscal Year
Peer Reviewed
Publication Name
Monthly Weather Review
Published On
September 23, 2020
Publisher Name
American Meteorological Society
Print Volume
Print Number
Page Range
Submitted On
January 28, 2020
Project Type


Not available


Authors who have authored or contributed to this publication.

  • Yonggang Yu - lead Gsl
    Cooperative Institute for Research in Environmental Sciences, University of Colorado Boulder
    NOAA/Global Systems Laboratory
  • Ning Wang - second Gsl
    Cooperative Institute for Research in the Atmosphere, Colorado State University
    NOAA/Global Systems Laboratory
  • Jacques Middlecoff - third Gsl
    Cooperative Institute for Research in the Atmosphere, Colorado State University
    NOAA/Global Systems Laboratory
  • Mark W. Govett - fifth Gsl