A Solution for Boundary Problems in Isentropic Coordinate Models

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  • 1 National Center for Atmospheric Research, Boulder, Colo. 80303
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Abstract

A numerical model is designed to integrate the primitive equations in two dimensions to evaluate a new vertical coordinate scheme for hydrostatic flow. Because potential temperature is nearly conserved for large-scale atmospheric flow, potential temperature is utilized as the vertical coordinate in the layer bounded by the lower troposphere and the top of the model atmosphere which is near the middle stratosphere. The vertical coordinate scheme circumvents some of the problems that have appeared in previous isentropic coordinate models by utilizing a variable depth layer near the earth's surface in which a function of pressure is the vertical coordinate. For this reason, no coordinate surface intersects the surface of the earth and complicated topographic features can easily he constructed. In addition, adiabatic and superadiabatic lapse rates can develop near the surface of the earth because the vertical coordinate in this region is a quasi-horizontal function of pressure.

Two experiments are performed to test the proposed vertical coordinate scheme. The formation of waves that appear in the atmosphere when the flow is normal to a mountain ridge is simulated by the first experiment. A temperature excess is introduced at the earth's surface for the second experiment to simulate conditions analogous to a large industrial power park.

The results of the experiments illustrate that the layer developed here can be used as the interface between an isentropic coordinate layer and the earth's surface in numerical prediction models.

Abstract

A numerical model is designed to integrate the primitive equations in two dimensions to evaluate a new vertical coordinate scheme for hydrostatic flow. Because potential temperature is nearly conserved for large-scale atmospheric flow, potential temperature is utilized as the vertical coordinate in the layer bounded by the lower troposphere and the top of the model atmosphere which is near the middle stratosphere. The vertical coordinate scheme circumvents some of the problems that have appeared in previous isentropic coordinate models by utilizing a variable depth layer near the earth's surface in which a function of pressure is the vertical coordinate. For this reason, no coordinate surface intersects the surface of the earth and complicated topographic features can easily he constructed. In addition, adiabatic and superadiabatic lapse rates can develop near the surface of the earth because the vertical coordinate in this region is a quasi-horizontal function of pressure.

Two experiments are performed to test the proposed vertical coordinate scheme. The formation of waves that appear in the atmosphere when the flow is normal to a mountain ridge is simulated by the first experiment. A temperature excess is introduced at the earth's surface for the second experiment to simulate conditions analogous to a large industrial power park.

The results of the experiments illustrate that the layer developed here can be used as the interface between an isentropic coordinate layer and the earth's surface in numerical prediction models.

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