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On objective formulation of hybrid coordinate gridding
T. Mike Chin
RSMAS, University of Miami
(Abstract received 07/15/2007 for session X)
ABSTRACT
In layered ocean models that use hybrid coordinate systems, the variables that serve as the vertical coordinate, such as the depth (layer thickness) and density, are not necessarily held constants in time. In fact, they are usually allowed to evolve along with the other prognostic variables as governed by the model dynamics. At each model time-step, therefore, these coordinate variables need to be re-sampled to some prescribed target values that define the coordinate system. This work is motivated by desires to incorporate such a re-sampling (or \"hybrid-coordinate grid-generation\") scheme into assimilation methods. For example, assimilation of altimeter data would change the vertical profile of layer thickness and hence require a re-sampling/gridding similar to (or same as) the one described previously. Since assimilation schemes are usually based on an objective formulation such as statistical optimization, a similar formulation of the coordinate re-sampling is thus desirable. In this presentation, two issues are addressed: (1) to determine the transition point from one coordinate variable to another, and (2) to simultaneously impose both global constraints such as conservation of mass and volume and local constraints such as minimum/positive layer thickness. For the former, a \"target transition curve\" is used to mark the boundary between two vertical coordinates. For the latter, a formulation based on statistical moments is able to address all types of constraints considered. At present, determination of the target transition point appears to be more critical for well-posedness of the formulation.
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2007 LOM Workshop, Bergen, Norway, August 20-22, 2007