A Vertical Coordinate Mapping Technique for Semispectral Primitive Equation Models of Oceanic Circulation

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  • 1 Department of Physical Oceanography, Woods Hole Oceanographic Institution, Woods Hole, Massachusetts
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Abstract

A stretched coordinate technique for semispectral hydrodynamic models is described that allows for greater flexibility in the placement of model grid points. Stretching is implemented here for the vertical coordinate of an oceanic model that employs Chebyshey polynomials to represent the vertical structure. A three-dimensional test demonstrates how, for a fixed number of vertical levels, the technique may permit greater accuracy in the simulation of linear internal waves, by allowing the placement of grid points closer to the regions of maximum curvature in the represented velocity fields. A one-dimensional test demonstrates enhanced resolution of mixed-layer dynamics by allowing the placement of more of the available grid points, evenly spaced, near the ocean surface, with broader spacing below. These improvements are achieved with negligible computational overhead. While the method cannot yield improved accuracy for all situations, in appropriate cases it permits reduced computation for an accurate result by reducing the number of basis functions necessary for adequate resolution of the modeled fields. Some guidelines are presented for its application, along with cautions as to where the technique is disadvantageous.

Abstract

A stretched coordinate technique for semispectral hydrodynamic models is described that allows for greater flexibility in the placement of model grid points. Stretching is implemented here for the vertical coordinate of an oceanic model that employs Chebyshey polynomials to represent the vertical structure. A three-dimensional test demonstrates how, for a fixed number of vertical levels, the technique may permit greater accuracy in the simulation of linear internal waves, by allowing the placement of grid points closer to the regions of maximum curvature in the represented velocity fields. A one-dimensional test demonstrates enhanced resolution of mixed-layer dynamics by allowing the placement of more of the available grid points, evenly spaced, near the ocean surface, with broader spacing below. These improvements are achieved with negligible computational overhead. While the method cannot yield improved accuracy for all situations, in appropriate cases it permits reduced computation for an accurate result by reducing the number of basis functions necessary for adequate resolution of the modeled fields. Some guidelines are presented for its application, along with cautions as to where the technique is disadvantageous.

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