Approccio ai sistemi dinamici e al telerilevamento in oceano: un'analisi Lagrangiana con l'utilizzo di esponenti di Lyapunov

This Master degree thesis has been carried in the context of Master 2 in Paris at LOCEAN (Laboratoire d'Océanographie et du Climat) in UPMC (Université Pierre et Marie Curie). The aim of the work was to analyse satellite altimetry data for studying the ocean surface transport and its evolution in time, in order to make a prediction of tracer positions in the ocean and to support a concomitant Nasa/Cnes oceanographic campaign (AirSWOT, April 2015, off California coast). At the oceanic length-scale, currents can be formally treated as a two dimensional dynamical system. By identifying the physical space ¿ the surface of the ocean - with the phase space, one can detect unstable manifolds of hyperbolic points corresponding to oceanic frontal regions where tracers field (phytoplankton, chlorophyll) is transported and stretched and where particles (water masses) are separated (maximum Lyapunov exponent). The goal is to detect eddies (position, size, water retention parameter) and Lagrangian Coherent Structures (i.e., spatial features whose lifetime last for a prescribed length) such like Lyapunov fronts or stable/unstable manifolds of hyperbolic points. This allows one to track dynamical physical structures that can be sampled by airplane/boats instruments. The campaign AirSWOT (Air Surface Water and Ocean Topography) is actually part of a broader satellite mission, SWOT, that will start in 2020 when the satellite will be launched to survey the Earth's waters, using synthetic aperture radar technologies in order to map the flow of the oceans and to improve the knowledge of freshwaters. The SWOT's goal is to join land hydrology and oceanography communities under a single satellite, in order to: (i) investigate the global dynamics of terrestrial surface waters and their interactions with coastal oceans in estuaries (Hydrology) and (ii) to have more information about heat and carbon transport from the upper ocean to the deep ocean (Oceanography). Finally, I contributed to an ongoing study at LOCEAN where Lyapunov vectors and Sea Surface Temperature are compared in global ocean for the period 2000-2012. I found that Lyapunov vectors predicts better than streamlines the direction of sea surface temperature gradient in intermediate energetic regions, like the borders of subtropical gyres.