Dimensionality reduction on ocean model´s outputs: Application to motion estimation on satellite images

Motion fields describing the ocean surface dynamics live in vectorial spaces of high dimension. Consequently, their estimation from satellite images requires huge computational resources. The issue of dimensionality reduction, that is the determination of representative low dimensional structures in these high dimensional spaces, is of major importance for any application that demands real-time or short-term results. Proper Order Decomposition allows to determine such sub-space of motion fields on which estimation may be assessed with reduced complexity. A reduced model is obtained by Galerkin projection of evolution equations on this subspace. Motion is estimated by assimilating the observed image sequence with the reduced model. The paper describes how to derive the reduced space from a database of ocean model´s outputs and explains how to estimate surface circulation from satellite sequences. Results are given on images acquired on the Black Sea basin by NOAA-AVHRR sensors.