**Turbulence and Synergy of Ocean Variables: Application to the Extrapolation of Chlorophyll Maps with SST Templates**
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Umbert, Marta; Guimbard, Sebastien; Martinez, Justino; Turiel, Antonio; Ballabrera-Poy, Joaquim
CSIC, SPAIN
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Due to their relatively rapid motion and low dynamic viscosity, geophysical fluids such as the atmosphere and the oceans are turbulent, although the particular regime of turbulence depends on the scale at which the fluid is studied. In the case of oceans, at scales of meters and below turbulence is mainly 3D with strong vertical displacements across the mixed layer, while at scales of kilometers and above turbulence is mainly 2D - except at some specific areas such as upwelling zones- and shows up as a complicated pattern of filaments, meanders and eddies. The fingerprint of those structures can be recognized in remote sensing images of different types, such as chlorophyll concentration (CC), sea surface temperature (SST), sea surface salinity (SSS) or sea surface height (SSH). The observed spatial redundancy among the different scalars suggests that a synergistic approach could be used to study and analyze ocean variables. In particular, synergy could be used to improve the signal-to-noise ratio of corrupted variables by using information from other variables or to infer missing values. However, it is very complicated to give a mathematical formalism leading to practical algorithms.

In the last years a new formalism has arisen to systematize the concept of scalar synergy: that of Microcanonical Multifractal Formalism (MMF). According to MMF, any scalar variable submitted to the action of a turbulent flow develops a structure of singular fronts, reminiscent of the streamlines of the flow, that can be extracted from any ocean scalar as a field of dimensionless variables, the singularity exponents. The validity of MMF has been verified on remote sensing images of different types, included ocean leaving radiances, SST, CC or SSH. As singularity exponents have no dimensions, singularity exponents coming from variables of different type can be directly compared, and in fact must coincide for the reasons exposed above. Not only that: an algorithm for merging the information of variables of different type has been devised using this common information. With this algorithm, a noisy variable can be improved by merging it with a higher-quality variable of a different type.

In this work we show the application of this algorithm for a different goal: the extrapolation of chlorophyll maps to missing areas by using SST as a template. This extrapolation provides significant results in open ocean without assuming any parametrization and warrants that the extrapolated field is consistent with the observed ocean structures.