## Section: New Results

Keywords : microcanonical multifractal formalism, turbulence, sea surface temperature, altimetry, chlorophyl concentration, geostrophic velocity, ocean dynamics.

### Geometric structures in the microcanonical formalism associated to bio/geochimical datasets

Participants : Hussein Yahia, Véronique Garçon [ CNRS-LEGOS ] .

The subtropical convergence zone is one of the major frontal systems in oceans, and it is the place where specific complex ocean dynamics, algae blooms and upwelling occur. The phenomena are visible on Sea Surface Temperature (SST), cholorophyl alpha (ocean colour) and altmimetry satellite datasets. We begin the study of the ocean dynamics in the subtropical convergence zone using the microcanonical multifractal formalism (MMF), i.e. from the geometric structures associated to singularity exponents derived within the MMF on satellite acquisition datasets. The MMF provides a unified framework for analyzing the dynamics of related events acquired in different oceanographic acquisition datasets. The first phase of the study associated to these data is an experimental phase. We compute the singularity exponents in the different datasets and begin the analysis by studying the Most Singular Manifolds (MSMs) and other geometric structures derived from the singularity exponents. The datasets have different spatial and temporal resolutions. In figure 4 we show the singularity exponents and the MSM associated to a particular altimetric acquisition. In figure 5 we show the singularity exponents associated to the chlorophyl concentration and the SST (Sea Surface Temperature), these oceanographic datasets being available at a finer spatial resolution. The observed similarity between the geometric structures associated to exponents of different datasets show that a similar dynamic is under way in the specified zone. We are now exploiting these results to obtain finer characterizations of the ocean dynamics in the subtropical convergence zone.