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Geometry & Statistics in acquisition data
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Sunday, 24 July 2011 15:49


High-resolution ocean dynamics from microcanonical formulations in non linear complex signal analysis

Hussein Yahia1, Joel Sudre2, Véronique Garçon2, Claire Pottier3

(1) INRIA, GeoStat
351 Cours de la Libération, 33405 Talence Cedex, France
hussein.yahia [at] inria.fr
(2) CNRS LEGOS, DynBio team
14 avenue Edouard Belin
F-31400 Toulouse, France
joel.sudre [at] legos.obs-mip.fr
veronique.garcon [at] legos.obs-mip.fr
(3) CNES
DCT/PS/TVI, 18 Avenue E. Belin, 31401 Toulouse Cedex 9, France
claire.pottier [at] cnes.fr


This article develops on a microcanonical formulation [1,2] for the analysis of the dynamics in acquisitions of remotely sensed oceanographic images using non-linear methods. In new approaches to complexity [3,4], fundamental quantities such as singularity exponents (SEs) are computed without any stationary hypothesis, i.e. in situations far from statistical equilibrium, as it is the case in Oceanography. SEs characterize rigorously complex oceanographic coherent structures and their relations. These  quantities can be computed from the acquired data using advanced signal processing tools [5]. Computational precision is pivotal and we first give some details on techniques available in non-linear signal processing for computing SEs. SEs relate to the geometric structures linked with the cascading properties of indefinitely divisible variables in turbulent flows. In a second step, we show how cascading properties can be represented by optimal wavelets (OWs)  [6]; this opens new and fascinating directions of research for the determination of ocean motion field at high spatial resolution. OWs in a microcanonical sense pave the way for the determination of the energy injection mechanisms between the scales.  We describe a new method for the complete evaluation of oceanic motion field which consists in propagating along the scales the norm and the orientation of ocean dynamics deduced at low spatial resolution (geostrophic from altimetry [7] and a  part of ageostrophic from wind stress products). Using this approach, there is no need to use several temporal occurences as in Optical Flow, Maximum Cross Correlation or FSLE techniques. Instead, the proper determination of the turbulent cascading and energy injection mechanisms in oceanographic signals allows the determination of oceanic motion field at the SST or Ocean colour spatial resolution (pixel size: 4 kms) which often surpasses the results obtained with SQG models. We use the Regional Ocean Modelling System (ROMS) [8]  to validate the results on simulated data and compare the motion fields obtained with other techniques.


Figure 1a: monthly level-3b acquisition MODIS SST, South-east of African coast and Madagascar area comprising
the Mozambique channel and the retroflexion of Algulas current. Spatial resolution: 4kms.

Figure 1b: high-precision SEs computed on the data displayed
in figure 1a. Coherent structures associated to the Algulas current are clearly visible.

Figure 2: detail of motion field computed at high spatial resolution (pixel size: 4kms) on Ocean Colour data,
in a turbulent area, by propagating along the scales dynamic information obtained from altimetry
(spatial resolution of altimetry data: 22 kms) acquired at the same period than the Ocean Colour data.


[1] H. Yahia, J. Sudre, C. Pottier, V. Garçon
Motion analysis in oceanographic satellite images using multiscale methods and the energy cascade
Pattern Recognition, 2010,
direct access.
[2] A. Turiel ,H. Yahia, C. Perez-Vicente
Microcanonical multifractal formalism: a geometrical approach to multifractal systems. Part I: singularity analysis
in "Journal of Physics A: Math. Theor", 2008, vol. 41,
direct access.
[3] K. Christensen ,N.R. Moloney
Complexity and criticality
Imperial College Adv. Physics texts, 2005, isbn:978-1-86094-517-5(pbk).
[4] G.Boffetta, M.Cencini, M.Falcioni, A.Vulpiani
Predictability: a way to characterize complexity
Phys. rep. pp. 356-367, 2002.
[5] O. Pont, A. Turiel, H. Yahia
An optimized algorithm for the evaluation of local singularity exponents in digital signals
14th International Workshop on Combinatorial Image Analysis (IWCIA 2011), May 23-25, Madrid, Spain
in J. K. Aggarwal, R. P. Barneva, V. E. Brimkov, K. N. Koroutchev, E. R. Korutcheva Eds, Combinatorial Image Analysis, Springer Verlag, LNCS 6636, 2011.
direct access
HAL open archive.
[6] O. Pont, A. Turiel, Perez-Vicente
On optimal wavelet bases for the realization of microcanonical cascade processes
International Journal of Wavelets, Multiresolution and Information Processing 9, pp. 35-61 2011,
direct access.
[7] J. Sudre, R. Morrow
Global surface currents: a high-resolution product for investigating ocean dynamics
Ocean Dynamics 58 (2), 2008, pp. 101–118 doi: 10.1007/s10236-008-0134-9,
direct access.
[8] A.F. Shchepetkin, J.C. McWilliams
The Region Ocean Model System (ROMS): A split-explicit, free-surface, topography-following-coordinate oceanic model
Ocean Modelling, vol. 9, pp. 347–404.

Last Updated on Tuesday, 26 July 2011 08:09