Integration of the barotropic vorticity equation on a spherical geodesic grid

Article English OPEN
Williamson, David L. (2011)

A quasi-homogeneous net of points over a sphere for numerical integration is defined. The grid consists of almost equal-area, equilateral spherical triangles covering the sphere. Finite difference approximations for a nondivergent, barotropic model expressed in terms of a streamfunction are proposed for an arbitrary triangular grid. These differences are applied to the spherical geodesic grid. The model is integrated for 12-day periods using analytic initial conditions of wave number six and four. The numerical solution with these special initial conditions follows the analytic solution quite closely, the only difference being a small phase error. Small truncation errors are noticeable in the square of the streamfunction averaged over latitude bands.DOI: 10.1111/j.2153-3490.1968.tb00406.x
  • References (12)
    12 references, page 1 of 2

    Arakawa, A. 1966. Computational design for longterm numerical integration of the equations of atmospheric motion. Journal of Computational Physics 1, 119-143.

    Gates, W. L. t Riegel, C. A. 1962. A study of numerical errors in the integration of barotropic flow on a spherical grid. Journal of Cfeophyaical Research 67, 773-784.

    Grimmer, M. t Shaw, D. B. 1967. Energy-preserving integrations of the primitive equations on the sphere. Quarterly Journal of the Royal Meteorological Society 93, 337-349.

    Kurihara, Y. 1965. Numerical integration of the primitive equations on a spherical grid. Monthly Weather Review 93, 399-415.

    Kurihara, Y. & Holloway, J. L., Jr. 1967. Numerical integration of a nine-level global primitive equations model formulated by the box method. Monthly Wedher Review 95, 609-630.

    MacNeal, R. H. 1953. An asymmetrical finite difference network. Quarterly of Applied M a h . 11, 296-310.

    McHale, J. 1962. R . Buckminster Fuller. New York, George Brazeller, 127 pp.

    Neamtan, S. M. 1946. The motion of harmonic waves in the atmosphere. Journal of Meteorology 3, 63-66.

    Phillips, N. A. 1969. Numerical integration of the primitive equations on the hemisphere. Monthly Weather Review 87,333-345.

    Thompson, P. D. 1961. Numerical Weother Anoly& and Prediction. New York, The Macmillan Company, 170 PP.

  • Metrics
    No metrics available
Share - Bookmark