Coupling Dynamic Equations and Satellite Images for Modelling Ocean Surface Circulation

  • Dominique Béréziat
  • Isabelle Herlin
Conference paper
Part of the Communications in Computer and Information Science book series (CCIS, volume 550)


Satellite image sequences visualise the ocean surface and allow assessing its dynamics. Processing these data is then of major interest to get a better understanding of the observed processes. As demonstrated by state-of-the-art, image assimilation permits to retrieve surface motion, based on assumptions on the dynamics. In this paper, we demonstrate that a simple heuristics, such as the Lagrangian constancy of velocity, can be used and successfully replaces the complex physical properties described by the Navier-Stokes equations for assessing surface circulation from satellite images. A data assimilation method is proposed that adds an acceleration term \(\mathbf {a}(t)\) to this Lagrangian constancy equation, which summarises all physical processes other than advection. A cost function is designed that quantifies discrepancy between satellite data and model values. This cost function is minimised by the BFGS solver with a dual method of data assimilation. The result is the initial motion field and the acceleration terms \(\mathbf {a}(t)\) on the whole temporal interval. These values \(\mathbf {a}(t)\) model the forces, other than advection, that contribute to surface circulation. Our approach was tested on synthetic data and with Sea Surface Temperature images acquired on Black Sea. Results are quantified and compared to those of state-of-the-art methods.


Dynamic model Optical flow Data assimilation Satellite image Ocean circulation 



Data have been provided by E. Plotnikov and G. Korotaev from the Marine Hydrophysical Institute of Sevastopol, Ukraine.


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© Springer International Publishing Switzerland 2015

Open Access This chapter is distributed under the terms of the Creative Commons Attribution Noncommercial License, which permits any noncommercial use, distribution, and reproduction in any medium, provided the original author(s) and source are credited.

Authors and Affiliations

  1. 1.Sorbonne Universités, UPMC Univ Paris 06, UMR 7606, LIP6ParisFrance
  2. 2.CNRS, UMR 7606, LIP6ParisFrance
  3. 3.InriaLe ChesnayFrance
  4. 4.CEREA, Joint Laboratory ENPC - EDF R&DUniversité Paris-EstMarne la Vallée Cedex 2France

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