Optimal decomposition for the evaluation of ocean dynamics
Résumé
The dynamics of the ocean flow are governed by the cascade process where the energy is injected in the system at the largest scale and dissipated at viscous scale. In between, the energy crosses all the intermediary scales and is responsible for the creation of oceanographic structures at different scales. To obtain the motion field of ocean dynamics [1] at the high resolution of Sea Surface Temperature (SST) Modis data (spatial resolution : 4 km) using one single image, we associate the Microcanonical Multiscale Formalism (MMF) [2] and the Microcanonical Cascade (MC) which represent these processes where the energy is transferred from scale to scale [3]. To link two different scales (or, in a remote sensing context, the same image at two different resolutions), the MC requires the exact determination of an optimal wavelet which separates completely the Multiscale Operator and the wavelet transform at the highest resolution. This exact determination of the optimal wavelet for a given dataset is difficult and there is no systematic algorithm to find it. Our goal is to best approximate the optimal wavelet for SST data by using Q-test [4]. References [1] H. Yahia, J. Sudre, C. Pottier and V. Garçon, 2010, Motion analysis in oceanographic satellite images using multiscale methods and the energy cascade, Pattern Recognition, DOI: 10.1016/J.patcog.2010.04.011 [2] A. Turiel, H. Yahia and C. Perez-Vicente, 2008 Microcanonical Multifractal Formalism: a geometrical approach to multifractal systems. Part I: Singularity Analysis, Journal of Physics A 41:015501. [3] C. Pottier, A. Turiel, V. Garçon, 2008, Inferring missing data in satellite chlorophyll maps using turbulent cascading, Remote Sensing of Environment, 112,4242-4260, 10.1016/j.rse.2008.07.010 [4] O. Pont, A Microcanonical cascade formalism for multifractal systems ans its application to data inference and forecasting. PhD thesis, Dept. of Fundamental Physics, University of Barcelona, 2009