A Comparison of Methods for Computing the Sigma-Coordinate Pressure Gradient Force for Flow over Sloped Terrain in a Hybrid Theta-Sigma Model

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  • 1 University of Wisconsin, Department of Meteorology and Space Science and Engineering Center, Madison, WI 53706
  • | 2 Goddard Laboratory for Atmospheric Sciences, NASA/Goddard Space Flight Center, Greenbelt, MD 20771
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Abstract

Five methods for computing the pressure gradient force within a sigma domain of a hybrid model are compared for flow over a steeply sloped terrain. The comparison includes pressure gradient calculations determined from a direct transformation to sigma coordinates, an application of an atmospheric deviation state to the direct transformation (Phillips, 1974), an evaluation within isobaric coordinates (Janjić, 1977), a flux form (Johnson, 1980), and a flux prime form that applies the Phillips' deviation state to the flux form. The results from a numerical simulation establish that the Janjić, Phillips and flux prime methods reduce truncation errors substantially, and successfully predict the surface anticyclonic circulation that develops within vertically and horizontally sheared baroclinic flow over elevated terrain. A discussion of the generation of kinetic energy and elimination of a spurious kinetic energy source through reduction of the truncation error by the flux prime method is presented.

Abstract

Five methods for computing the pressure gradient force within a sigma domain of a hybrid model are compared for flow over a steeply sloped terrain. The comparison includes pressure gradient calculations determined from a direct transformation to sigma coordinates, an application of an atmospheric deviation state to the direct transformation (Phillips, 1974), an evaluation within isobaric coordinates (Janjić, 1977), a flux form (Johnson, 1980), and a flux prime form that applies the Phillips' deviation state to the flux form. The results from a numerical simulation establish that the Janjić, Phillips and flux prime methods reduce truncation errors substantially, and successfully predict the surface anticyclonic circulation that develops within vertically and horizontally sheared baroclinic flow over elevated terrain. A discussion of the generation of kinetic energy and elimination of a spurious kinetic energy source through reduction of the truncation error by the flux prime method is presented.

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