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An accurate quantification of the role of the ocean as source/sink of greenhouse gases (GHGs) requires to access the high-resolution of the GHG air-sea flux at the interface. In this paper we present a novel method to reconstruct maps of surface ocean partial pressure of CO2 (pCO2) and air-sea CO2 fluxes at super resolution (4 km, i.e., 1/32° at these latitudes) using sea surface temperature (SST) and ocean color (OC) data at this resolution, and CarbonTracker CO2 fluxes data at low resolution (110 km). Inference of super-resolution pCO2 and air-sea CO2 fluxes is performed using novel nonlinear signal processing methodologies that prove efficient in the context of oceanography. The theoretical background comes from the microcanonical multi-fractal formalism which unlocks the geometrical determination of cascading properties of physical intensive variables. As a consequence, a multi-resolution analysis performed on the signal of the so-called singularity exponents allows for the correct and near optimal cross-scale inference of GHG fluxes, as the inference suits the geometric realization of the cascade. We apply such a methodology to the study offshore of the Benguela area. The inferred representation of oceanic partial pressure of CO2 improves and enhances the description provided by CarbonTracker, capturing the small-scale variability. We examine different combinations of ocean color and sea surface temperature products in order to increase the number of valid points and the quality of the inferred pCO2 field. The methodology is validated using in situ measurements by means of statistical errors. We find that mean absolute and relative errors in the inferred values of pCO2 with respect to in situ measurements are smaller than for CarbonTracker. [ABSTRACT FROM AUTHOR]