A General Formulation of Normal Modes for Limited-Area Models: Application to Initialization

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Abstract
A formulation of normal modes for a limited-area model is proposed. The case of shallow water equations on a conformal projection is considered. This formulation is a generalization of Brière's proposal. It can handle the full variation of the Coriolis parameter and of the map scale factor; it is written in physical-space variables and does not need a rectangular domain to be applied as in Brière's scheme. It gives rise to stationary Rossby modes and gravity modes fully identified and easily separated on the basis of their frequency. By applying Machenhauer's initialization scheme, we rigorously deduce the vertical mode initialization proposed and demonstrated by Bourke and McGregor for a limited-area model.

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