# Ocean Currents Reconstruction from a Combination of
## Data and Methods
### Data
Based on optimal interpolation (OI), the mapping of SLA follows the DUACS DT2018 configuration for the Mediterranean Sea, described in [20]. In particular, the correlation spatial scales range from 75 to 200 km, depending on the location, while temporal scales are set to a constant value of 10 days. It means that, for a given space-time grid point, only along-track observations that lie within 75 to 200 km and 10 days with respect to the grid point are selected. The modelled large-scale SLA patterns (filtered out before the mapping) and the reconstructed small-scale maps are finally recombinedin order to compute the daily surface currents via the geostrophic approximation. Such data are provided on a regular 1/8\({}^{\circ}\) grid, as for the present-day version of the CMES Altimeter-derived gridded regional products for the Mediterranean Sea. 4. **The Synthetic Satellite-Derived Chl** Space-based bio-optical oceanic variables such as the surface Chl concentration are derived from passive observations by sensors mounted on board polar satellites through algorithms calibrated with in situ observations. The Chl remote sensing principle is based on measurements of the visible radiation that, after penetrating the first meters of the surface oceanic layer, is scattered back towards the atmosphere in the direction of a satellite sensor. Therefore, the satellite-derived Chl is an integrated quantity over the first meters of the oceanic water column. Since our study constitutes a testbed for applying the optimal reconstruction to satellite-derived data, we evaluated a satellite-derived equivalent surface Chl \"C\({}_{\text{sat}}\)\" from the CMES BIO model for the entire year 2017. We relied on the \"C\({}_{\text{sat}}\)\" expression provided by [PERSON] 1989 [45]: \[\text{C}_{\text{sat}}=\frac{\int_{0}^{\text{z_{P}}}\text{C}(z)\text{e}^{-2 \text{k}x}\text{d}z}{\int_{0}^{\text{z_{P}}}\text{e}^{-2\text{k}x}\text{d}z}\] (2) where \"C\" is the marine Chl value at the depth \"z\", \"k\" is the light attenuation coefficient, and \"Z\({}_{\text{p}}\)\" is the light penetration depth along the water column. In our study, the quantities appearing in (2) were computed from the CMES BIO model and Z\({}_{\text{P}}\) ranged from 5 to 30 m, depending on the location and season. Using C\({}_{\text{sat}}\) is more rigorous than approximating the satellite equivalent Chl via the first layer output of the MedBFM model (\(\simeq\)1 m depth). A comparison between the Chl-1m and the C\({}_{\text{sat}}\) is carried out in two distinct periods of 2017: the high biological production (20 February to 20 March 2017) and the low biological production periods (15 July to 15 August 2017) also accounting for past studies on the Mediterranean Sea trophic regimes [37]. The normalized scatter density plots of the C\({}_{\text{sat}}\) and Chl-1m are obtained computing the time-averaged Chl maps in the two aforementioned periods for the entire Mediterranean basin. The results proved that the Chl-1m mostly underestimates the C\({}_{\text{sat}}\) (Figure 1). This is more evident during the low production period, when the Z\({}_{\text{P}}\) values appearing in (2) are larger due to a decreased near surface water turbidity and the larger Chl concentrations (the Deep Chl Maximum) are found at larger depths [46], increasing the discrepancies between Chl-1m and C\({}_{\text{sat}}\). Figure 1: (**Left**) Normalized scatter density plots between Chl-1m and C\({}_{\text{sat}}\). (**Left**) high biological production period, 20 February to 20 March 2017. (**Right**) low biological production period, 15 July to 15 August 2017. In both panels, the identity line is given in blue.