Assimilation of Altimeter Data into Ocean Models

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 but differing vertical structure. If the phase separation is small, as occurs with baroclinic Rossby waves when the assimilation period is 20 days, then the convergence rate may be improved by increasing the assimilation period. Detailed calculations are made for a midlatitude ocean using a model with a barotropic and two baroclinic modes. Using a period of 100 days between assimilating new data, good phase separation between the vertical modes is achieved when the horizontal wide of the modes is on the order of the Rossby radius (?30 km). The altimeter data is inefficient at separating modes with shorter horizontal scales, modes with a predominant north-south wavenumber, and baroclinic modes with a large horizontal scale. If the assimilation period is reduced to 20 days, the altimeter is better at separating the barotropic mode from the baroclinic modes at large scales. However, in all other respects, the use of a short assimilation period is less effective.