| Hybrid coordinate employing a generalization of the Montgomery potential - :11404 | National Weather Service (NWS)
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Hybrid coordinate employing a generalization of the Montgomery potential
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  • Description:
    We describe a procedure by which a hybrid vertical coordinate, together with an associated generalized Montgomery potential, are defined in such a way that, as in a pure isentropic coordinate, the horizontal pressure gradient force for a hydrostatic atmosphere is given by the horizontal gradient of a single potential. however, the new definition allows greater generality by allowing the definition of the coordinate function to become an intermediate mixture of the potential temperature and the pressure variable while, at the same time, the generalized Montgomery potential is specially prescribed as a particular mixture of the true Montgomery potential and the ordinary geopotential. The advantage of this construction is that it overcomes the unduly restrictive constraint of the pure isentropic coordinate model, in which the existence of vertically neutral or slightly unstable layers is forbidden. Except at levels close to the ground, the new coordinate accommodates such mixed layers without sacrificing the property of having the horizontal pressure gradient force defined as the gradient of a single potential. Thus, numerical problems, common in sigma coordinates, that stem from the difficulty of accounting accurately for the near cancellation of two large opposing terms over steep terrain are avoided except near the ground where further modifications to the coordinate definition are required to retain the terrain-following condition. The new formulation allows the vertical coordinate to revert towards a pure pressure definition at the model's finite top, facilitating the implementation of sophisticated wave non-reflecting conditions here.

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