Staggered Vertical Discretization of the Canadian Environmental Multiscale (GEM) Model Using a Coordinate of the Log-Hydrostatic-Pressure Type

Claude Girard Recherche en Prévision Numérique Atmosphérique, Environment Canada, Dorval, Quebec, Canada

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André Plante Canadian Meteorological Centre, Environment Canada, Dorval, Quebec, Canada

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Michel Desgagné Recherche en Prévision Numérique Atmosphérique, Environment Canada, Dorval, Quebec, Canada

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Ron McTaggart-Cowan Recherche en Prévision Numérique Atmosphérique, Environment Canada, Dorval, Quebec, Canada

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Jean Côté Recherche en Prévision Numérique Atmosphérique, Environment Canada, Dorval, Quebec, Canada

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Martin Charron Recherche en Prévision Numérique Atmosphérique, Environment Canada, Dorval, Quebec, Canada

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Paul A. Vaillancourt Recherche en Prévision Numérique Atmosphérique, Environment Canada, Dorval, Quebec, Canada

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Ayrton Zadra Recherche en Prévision Numérique Atmosphérique, Environment Canada, Dorval, Quebec, Canada

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Abstract

The Global Environmental Multiscale (GEM) model is the Canadian atmospheric model used for meteorological forecasting at all scales. A limited-area version now also exists. It is a gridpoint model with an implicit semi-Lagrangian iterative space–time integration scheme. In the “horizontal,” the equations are written in spherical coordinates with the traditional shallow atmosphere approximations and are discretized on an Arakawa C grid. In the “vertical,” the equations were originally defined using a hydrostatic-pressure coordinate and discretized on a regular (unstaggered) grid, a configuration found to be particularly susceptible to noise. Among the possible alternatives, the Charney–Phillips grid, with its unique characteristics, and, as the vertical coordinate, log-hydrostatic pressure are adopted. In this paper, an attempt is made to justify these two choices on theoretical grounds. The resulting equations and their vertical discretization are described and the solution method of what is forming the new dynamical core of GEM is presented, focusing on these two aspects.

Corresponding author address: Claude Girard, 2121 TransCanada Highway, Ste. 500, Dorval, QC H9P 1J3, Canada. E-mail: claude.girard@ec.gc.ca

Abstract

The Global Environmental Multiscale (GEM) model is the Canadian atmospheric model used for meteorological forecasting at all scales. A limited-area version now also exists. It is a gridpoint model with an implicit semi-Lagrangian iterative space–time integration scheme. In the “horizontal,” the equations are written in spherical coordinates with the traditional shallow atmosphere approximations and are discretized on an Arakawa C grid. In the “vertical,” the equations were originally defined using a hydrostatic-pressure coordinate and discretized on a regular (unstaggered) grid, a configuration found to be particularly susceptible to noise. Among the possible alternatives, the Charney–Phillips grid, with its unique characteristics, and, as the vertical coordinate, log-hydrostatic pressure are adopted. In this paper, an attempt is made to justify these two choices on theoretical grounds. The resulting equations and their vertical discretization are described and the solution method of what is forming the new dynamical core of GEM is presented, focusing on these two aspects.

Corresponding author address: Claude Girard, 2121 TransCanada Highway, Ste. 500, Dorval, QC H9P 1J3, Canada. E-mail: claude.girard@ec.gc.ca
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