# Ocean Currents Reconstruction from a Combination of
## 1 Introduction  
Global-scale, synoptic, high-resolution and accurate estimates of sea surface variables are necessary for a better understanding and prediction of a variety of processes occurring in the Earth system. Observations from individual sensor/platform types, however, generally provide incomplete information, either due to their non-homogeneous space-time sampling, to limited spatial-temporal resolution and coverage, and/or to measurement representativeness issues. The combination of observations of a single (or multiple) environmental variable collected by different instruments and platforms is a common technique in Earth Observation (EO) disciplines to overcome at least some of these limitations. Since the 1960s, sensors mounted on board satellite platforms were revealed to be useful for this purpose. Though providing lower-accuracy measurements compared to the in situ platforms, satellites enable the observation of large portions of the Earth surface and atmosphere over daily to sub-daily time scales, depending on the study area and satellite platform [1]. Nowadays, physical and bio-optical oceanic variables such as, e.g., sea surface temperature (SST), salinity (SSS), ocean wind stress, significant wave height, sea surface height (SSH), sea surface roughness, surface chlorophyll concentration (Chl) and total suspended matter can be obtained from satellite measurements at global scale with weekly to daily frequency. However, achieving global coverage at high spatial-temporal resolution still remains a challenge and requires advanced techniques to produce gap-free, high-resolution analyses based on multiple observations. To this scope, several approaches have been developed. Some examples are provided below. Optimal Interpolation (OI) is systematically applied within operational monitoring services.OI algorithms allow for combining several observations weighting them by their correlations to the interpolation point and penalizing them through their uncertainties and cross-correlations. They proved useful in creating gap-free estimates of physical and biogeochemical ocean variables at the operational level [2; 3; 4; 5; 6; 7; 8; 9]. Based on a different statistical analysis tool with respect to OI, DINEOF (Data INterpolating Empirical Orthogonal Functions) builds an iterative decomposition into empirical orthogonal functions (the EOF) allowing for filling in missing values in an EO data timeseries by estimating the dominant patterns of variability from available valid data. This technique can also be applied to pre-determined, multi-sensor/platform estimates of oceanographic variables [10; 11]. More recently, Artificial Intelligence (AI)-based methods are also emerging as potentially useful techniques for reconstructing physical and biogeochemical oceanic properties, also combining different observations of the ocean surface [12; 13; 14]. Here, we present an EO data fusion technique combining SSH and Chl data, testing its potential in the satellite-based marine surface currents retrieval. Since the early 1990s, the space-based monitoring of the sea surface currents has been guaranteed by constellations of radar altimeters. Such instruments are mounted on board polar-orbiting satellites and enable deriving the geostrophic component of the global sea surface circulation by observing the ocean surface topography. The altimeter-derived currents are indeed widely used for large scale ocean circulation studies (e.g., [15]), and the altimetry products are found to have better performance than data assimilative ocean circulation model outputs in simulating surface drifter trajectories [16]. However, this observing system has some intrinsic limitations due to its sampling capabilities and to the assumption of geostrophic balance needed to estimate surface velocities from sea surface level displacements. Indeed, the altimeters only provide nadir, along-track measurements, which thus need to be interpolated on 2D maps to estimate gradients.