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Bottom Topography as a Control Parameter in an |
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Ocean Circulation Model |
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Martin Losch and Carl Wunsch |
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Bottom topography is a major factor in determining the general |
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circulation of the ocean. It is, however, inaccurately known in many |
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regions, and even where accurately known, the best way to represent |
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(parameterize) it in models is obscure. To begin to understand the |
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influence of errors in topography and of misrepresentations of both |
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resolved and sub-grid scale structures, a linear barotropic shallow |
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water model and its adjoint are developed in which depth is used as |
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a control variable. Simple basin geometries are employed to explore |
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the extent to which topographic structure determines the sea-surface |
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elevation in a steady flow and, more directly, the information |
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content about the bottom contained in elevation measurements. |
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Experiments show that even perfect measurements of sea-surface |
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elevation in a steady state cannot, by themselves, uniquely |
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determine the full structure of the bottom topography. (There is a |
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null space.) As in most control problems, a priori knowledge of its |
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structure is useful in the best topographic determination. |
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Resolution of the bottom topography as a function of position is |
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greatest where the flow velocities are greatest. Spatial correlation |
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between the resolution of the bottom topography and the flow field |
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is weaker (as expected) when noise with realistically large variance |
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is introduced into the data. Ultimately, bottom topography will |
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likely be included generally as a control variable in GCMs of |
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arbitrary complexity along with other controls such as friction and |
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lateral boundary conditions. |
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