Assimilation of Altimeter Data into Ocean Models

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Abstract
The problem of assimilating satellite altimeter data into an ocean model is considered for the case in which the ocean currents are weak, so that they can be represented by a superposition of linear Rossby waves, and the altimeter measurements are exact and available everywhere. The state of the model at each instant is represented by a state vector, and the process of assimilating data is represented by the projection of this vector onto the surface made up of all the model states consistent with the observations. The projection and the evolution of the model between assimilating each batch of data may be represented by a matrix operator, whose eigenvalues characterize the convergence properties of the scheme. The possibility of using altimeter observations of the ocean surface to determine the deeper structure of the ocean is investigated. It is found to be limited by the phase separation that develops over each assimilation cycle between modes of the ocean with the same horizontal wavenumber b... Abstract The problem of assimilating satellite altimeter data into an ocean model is considered for the case in which the ocean currents are weak, so that they can be represented by a superposition of linear Rossby waves, and the altimeter measurements are exact and available everywhere. The state of the model at each instant is represented by a state vector, and the process of assimilating data is represented by the projection of this vector onto the surface made up of all the model states consistent with the observations. The projection and the evolution of the model between assimilating each batch of data may be represented by a matrix operator, whose eigenvalues characterize the convergence properties of the scheme. The possibility of using altimeter observations of the ocean surface to determine the deeper structure of the ocean is investigated. It is found to be limited by the phase separation that develops over each assimilation cycle between modes of the ocean with the same horizontal wavenumber b...

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