On the inversion of submesoscale tracer fields to estimate the surface ocean circulation

In this paper, we demonstrate the feasibility of inverting the information contained in oceanic submesoscales, such as the ones evidenced in tracer observations of sea surface temperature (SST), to improve the description of mesoscale dynamics provided by altimetric observations. A small region of the Western Mediterranean Sea is chosen as a test case. From a SST snapshot of the region in July 2004, information is extracted to improve the velocity field as computed by geostrophy from the AVISO altimetric data at the same location and time. Image information is extracted from SST using a binarization of the SST gradients. Similarly, image information is extracted from the dynamic topography using finite size Lyapunov exponents (FSLE). The inverse problem is formulated in a Bayesian framework and expressed in terms of a cost function measuring the misfits between the two images. The large amount of information which is already available from ocean color satellites or which will be available from high-resolution altimetric satellites such as SWOT, is a strong motivation for this work. Moreover, the image data assimilation approach which is explored here, is a possible strategy for handling the huge amount of satellite data imprinted by small scale information.