Mechanical and Civil Engineering Seminar

Predicting the evolution of a geophysical fluid is obtained by the integration of a numerical model but it requires to provide an initial condition at a given time. Another source of information on the fluid is the network of observation and also satellites. Combining mathematical, physical and statistical information is the problem of Data Assimilation. Most of the main operational centers are presently using methods based on Optimal Control. Nevertheless we have to ill with a ill posed problem : the number of daily observation is around ten million and the dimension of the initial condition is near to one billion. The observation of the Earth by stellites provides two types of observations. Eulerian information obtained by the measuring radiative fluxes, in some cases we can link these quantities to the state variables of the models and use them in a classical scheme of data assimilation. Lagrangian information issued from the observation of discontinuities in the images : fronts, vortex, filaments, at the present time this information is used more in a qualitative way rather than in a quantitative one. Assimilation of images is the problem of coupling the dynamics of images and numerical models. To remain in a classical framework we will need to define the images in an adequate mathematical space. We will propose several choices : pixels, curvelets, Lyapunov exponents. The method will be applied to turbulence and flow in a rotating tank and in oceanography. The assimilation of images is a generic problem found in many scientific domains.