# Ocean Currents Reconstruction from a Combination of
## 3 Results
### Quantitative Assessment  
Following Equation (6), we present some quantitative performances of the optimal reconstruction, sketched in Figure 6. Based on the 2017 daily data, we compute the RMSD of the Synthetic Altimeter (SAC) and OPTimal Currents (OPC), using the CMEMS PHY surface outputs as a validation benchmark. This operation is repeated for both the zonal and meridional surface flows. When the SAC are analysed, we find RMSDs always equal to or larger than 5 cm\(\cdot\)s\({}^{-1}\), with maximum values reaching 30 cm\(\cdot\)s\({}^{-1}\) in the Western Mediterranean, in the Atlantic Ionian Stream across the Sicily Channel and in many areas of the Levantine Basin (roughly from 18 to 30\({}^{\circ}\)E), including the area south of Ierapetra. Figure 4: Surface Chl from the CMEMS MedBFM BIO model in: (**A**) the Northwestern Mediterranean, (**C**) the Sicily Channel, (**E**) the Western Mediterranean. (**B,D,F**) Chl spatial gradients magnitude \(\mid\)VChl\(\mid\), same areas as (**A**,C,E**), respectively. Figure 5: Correction factors for the zonal SACs in: (**A**) the Northwestern Mediterranean; (**C**) the Sicily Channel; (**E**) the Western Mediterranean; (**B**,**D**,**F**) the same as (**A**,**C**,**E**) for the meridional SACs. Figure 6: (**Left**) column: RMSDs of the Synthetic Altimeter Currents (SAC) against the CMEMS PHY outputs, top and bottom panels show results for the zonal and the meridional currents. (**Right**) column: same as the left column, for the OPtimal Currents (OPC). When the information from the surface Chl is introduced within the Altimeter currents, large improvements are observed at the basin-scale. Patches of RMSD \(\simeq\)20 cm\(\cdot\)s\({}^{-1}\) only cover 2 to 3% of the basin and are mostly limited to coastal areas in the Western Alboran sea. Overall, the RMSD of the OPC is mostly around 7 to 8 cm\(\cdot\)s\({}^{-1}\) for both components of the motion, against the \(\simeq\)13 cm\(\cdot\)s\({}^{-1}\) found in the SAC case. This is clearly summarised by the distributions of RMSD values reported in Figure 7: the improvements of the OPC with respect to the altimeter currents result in narrower OPC RMSD distributions, with a significantly larger number of cases shifted left towards the zero value. The RMSD values enable building additional indexes that quantify the skill of the optimal reconstruction, e.g., through the percentage of improvement, PI, described by Equation (5). This analysis was performed accounting for the entire time series of the SAC and OPC datasets (i.e., relying on more than \(5\cdot 10^{7}\) data for both datasets) considering observations lying in \(\mid\
abla Chl\mid\) areas ranging from \(10^{-5}\) to \(10^{-4}\) mg\(\cdot\)m\({}^{-3}\cdot\)m\({}^{-1}\) for both the zonal and the meridional currents. Figure 8 shows that the zonal and meridional OPC improve the altimeter estimates by about 20 to 50% and that the PI is generally larger for the meridional component of the motion. This is easily explained considering the north-south orientation of the nadir-looking altimeter ground tracks, allowing for deriving more accurate zonal surface currents via the geostrophic approximation [28; 31; 51]. More in detail, the overall behaviour of the PI is summarised by the left panel of Figure 8, which considers all the 2017 data except for the mid-February to mid-March period (far from the main Chl blooming events, [36; 37]). The meridional PI is fairly constant, exhibiting values oscillating between 45% and 52%, while the zonal PI increases from 27% to 38% when the local Chl spatial gradients are intensified. As a result, the PIT09 method reproduces higher quality optimal currents for increasing local \(\mid\
abla Chl\mid\), in a good agreement with past studies based on the use of SST data [28; 29; 31]. On the other hand, Figure 8-right shows that the PIs tend to decrease towards highest \(\mid\
abla Chl\mid\) areas between mid-February to mid-March 2017 (i.e., during the main Chl blooming events found in the MedBFM simulations).