Circumventing the pole problem of reduced lat-lon grids with local schemes. Part I: Analysis and model formulation

Bénard, Pierre ; Glinton, Michael R.

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<p align=justify>This paper describes a possible strategy for numerically integrating global meteorological equations cast in spherical coordinates with local/scalable algorithms on a reduced latitude-longitude grid. This approach is designed to address a major obstacle known as the "pole problem" in the literature. The nature of the problem is carefully examined in order to determine the conditions for its appearance (or disappearance). A class of discretization schemes avoiding the problem while being based on local algorithms of various accuracy orders is then proposed for non-staggered grids. A numerical model for solving shallow-water equations on the sphere with these discrete schemes (GRASS) has been developed and its ability to circumvent the pole problem is demonstrated through basic validations. Further validations on standard test-cases are presented in Part II.</p>
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