Microcanonical multifractal formalism: Application to the estimation of ocean surface velocities

In this paper we investigate the validity of the multifractal formalism to study sea surface temperature (SST). It is shown that SST patterns observed in moderate resolution SST images have anomalous scaling properties characteristic of a multifractal structure. The most probable origin of the observed structures is the turbulent character of the oceanic flow as they evolve slowly and are very persistent in times compatible with ocean mesoscale dynamics (several days). The spectrum of singularity exponents indicates that the dynamics of the processes leading to the geometrical arrangement of the SST patterns is quite general over the available range of scales. As a consequence, multifractal techniques can be used to extract properties of the underlying flow. In particular, the geometry of the SST multifractal components is closely linked with the ocean flow, which allows to build a reasonable guess of the streamfunction (defined as the maximum singular streamfunction (MSS)) from a single SST image. Thus the ocean surface velocity field can be easily inferred, with some limitations. As multifractal analysis is in essence a geometrical approach, the method is able to retrieve a high resolution velocity field, well localized in space, but with some indetermination on the modulus and sense of velocity vectors. To solve this, a general framework for the integration of extra information is proposed, what is illustrated with an example merging MSS with altimetric data.