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A Baroclinic Finite-Element Model for Regional Forecasting with the Primitive Equations

Andrew N. StaniforthRecherche en Prévision Numérique, Atmospheric Environment Service, Dorval, Québec, H9P 1J3, Canada

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Roger W. DaleyRecherche en Prévision Numérique, Atmospheric Environment Service, Dorval, Québec, H9P 1J3, Canada

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Abstract

A baroclinic primitive equations model is formulated using a variable resolution finite-element discretization in all three space dimensions. The horizontal domain over which the model is integrated is a rectangle on a polar stereographic projection which approximately covers the Northern Hemisphere. A wall boundary condition is imposed at this rectangular boundary giving rise to a well-posed initial boundary value problem. The mesh is specified to be of Cartesian product form with arbitrary non-uniform spacing. By choosing the mesh to be uniformly high over an area of interest and degrading smoothly away from this area, it is possible to use the model to produce a high-resolution local forecast for a limited time period. This choice of mesh avoids the noise problems of a so-called nested grid. A semi-implicit time discretization is used for efficiency. Some results for forecast periods of 24 and 48 h are also given to demonstrate its viability in an operational context.

Abstract

A baroclinic primitive equations model is formulated using a variable resolution finite-element discretization in all three space dimensions. The horizontal domain over which the model is integrated is a rectangle on a polar stereographic projection which approximately covers the Northern Hemisphere. A wall boundary condition is imposed at this rectangular boundary giving rise to a well-posed initial boundary value problem. The mesh is specified to be of Cartesian product form with arbitrary non-uniform spacing. By choosing the mesh to be uniformly high over an area of interest and degrading smoothly away from this area, it is possible to use the model to produce a high-resolution local forecast for a limited time period. This choice of mesh avoids the noise problems of a so-called nested grid. A semi-implicit time discretization is used for efficiency. Some results for forecast periods of 24 and 48 h are also given to demonstrate its viability in an operational context.

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