Section: New Results

Assimilation of Image Data

Direct assimilation of sequences of images

Participants : François-Xavier Le Dimet, Maëlle Nodet, Nicolas Papadakis, Arthur Vidard, Vincent Chabot.

At the present time the observation of Earth from space is done by more than thirty satellites. These platforms provide two kinds of observational information:

• Eulerian information as radiance measurements: the radiative properties of the earth and its fluid envelops. These data can be plugged into numerical models by solving some inverse problems.

• Lagrangian information: the movement of fronts and vortices give information on the dynamics of the fluid. Presently this information is scarcely used in meteorology by following small cumulus clouds and using them as Lagrangian tracers, but the selection of these clouds must be done by hand and the altitude of the selected clouds must be known. This is done by using the temperature of the top of the cloud.

MOISE was the leader of the ANR ADDISA project dedicated to the assimilation of images, and is a member of its current follow-up GeoFluids (along with EPI FLUMINANCE and CLIME, and LMD, IFREMER and Météo-France)

During the ADDISA project we developed Direct Image Sequences Assimilation (DISA) and proposed a new scheme for the regularization of optical flow problems [86] , [90] . Thanks to the nonlinear brightness assumption, we proposed an algorithm to estimate the motion between two images, based on the minimization of a nonlinear cost function [45] . We proved its efficiency and robustness on simulated and experimental geophysical flows [64] . As part of GeoFluids, we are investigating new ways to define distance between a couple of images. One idea was to define this distance as the norm of the apparent motion between two images. This has been done thanks to optical flow methods which turned out to need a specific parametrization for each couple of images. Another idea, currently under investigation, consists in comparing mains structures within each image. This can be done using, for example, a wavelet representation of images. We are also part of TOMMI, another ANR project started mid 2011, where we are investigating the possibility to use optimal transportation based distances for images assimilation.

Assimilation of ocean images

Participants : Vincent Chabot, Maëlle Nodet, Nicolas Papadakis, Arthur Vidard.

In addition with the direct assimilation approach previously described, a particular attention has been given to the cloud occlusion and the representation of the observation errors in the context of ocean image data. Such works will be intensified with the post-doctorate Alexandros Makris that will start his activities in December. The assimilation of images (SST and chlorophyll) provided by geostationary satellites is also studied with the oceanographers of the Laboratoire des Écoulements Géophysiques et Industriels. The objective is here to take benefit from the correlation that exists between image gradients and ocean flow discontinuities that can be exhibited through the computation of Lyapunov coefficients and vectors from numerical ocean models [70] .