An accurate quantification of the role of the ocean as source/sink of Green House 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 CO 2 (pCO 2) and 5 air-sea CO 2 fluxes at super resolution (4 km) using Sea Surface Temperature (SST) and Ocean Colour (OC) data at this resolution, and CarbonTracker CO 2 fluxes data at low resolution (110 km). Inference of super-resolution of pCO 2 , and air-sea CO 2 fluxes is performed using novel nonlinear signal 10 processing methodologies that prove efficient in the context of oceanography. The theoretical background comes from the Microcanonical Multifractal Formalism which unlocks the geometrical determination of cascading properties of physical intensive variables. As a consequence, a multiresolution 15 analysis performed on the signal of the so-called singularity exponents allows the correct and near optimal cross-scale inference of GHGs 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 rep-20 resentation of oceanic partial pressure of CO 2 improves and enhances the description provided by CarbonTracker, capturing the small scale variability. We examine different combinations of Ocean Colour and Sea Surface Temperature products in order to increase the number of valid points and the 25 quality of the inferred pCO 2 field. The methodology is validated using in-situ measurements by means of statistical errors. We obtain that mean absolute and relative errors in the inferred values of pCO 2 with respect to in-situ measurements are smaller than for CarbonTracker.