# Ocean Currents Reconstruction from a Combination of
## 3 Results
### Quantitative Assessment
Though the zonal and meridional PIs are still positive, the result suggests that, during the blooming events, the highest \(\mid\
abla Chl\mid\) may not fully optimise the altimeter derived horizontal currents, as Chl evolution is strongly dominated by biological and environmental factors favouring significant phytoplankton growth and complex interactions within the trophic network. Figure 7: Distributions of the RMSD values for the SAC (light green) and OPC (blue). Left and right panels show the results for the zonal and meridional currents, respectively. The benefits of the optimal reconstruction are also given by enhancements of the spatial and temporal variability of the OPC dataset compared to the SAC. Such benefits are quantified by means of Equation (7) and via the spatial spectral analysis illustrated in Section 2.4. To investigate the SAC and OPC temporal variabilities, we first derive the 2017 time-averaged surface currents (zonal and meridional) for the SAC, OPC, and PHY datasets. Then, we compute the SAC, OPC, and PHY currents' temporal standard deviations (STDs) using the 2017 daily data. The results are reported in Figure 9. The CMEMS PHY data show STDs around 10 to 25 cm\(\cdot\)s\({}^{-1}\) throughout the Mediterranean, with only a few areas characterised by 5 cm\(\cdot\)s\({}^{-1}\) values for both the zonal and the meridional flow. An ideal optimal reconstruction should reproduce the same PHY STD values. This is not the case for the two components of the optimal currents, which exhibit STD values mostly centered around 7 cm\(\cdot\)s\({}^{-1}\) and reaching 20 cm\(\cdot\)s\({}^{-1}\) in a few areas of the western Mediterranean. However, an interesting result is shown in the bottom panels of Figure 9, showing maps of zonal and meridional STD differences (\(\Delta\)STD) between the optimal and synthetic altimeter currents. The \(\Delta\)STDs are larger than zero in 80% of the Mediterranean Sea, confirming that the optimal currents are characterised by an enhanced temporal variability compared to the Altimeter estimates. We repeated this analysis on timescales of 10 days, which is the temporal search radius used in the SAC optimal interpolation scheme (as for the DUACS system, discussed in Section 2) and can be thought of as our lower limit for the SACs' effective temporal resolution. In this case, we also obtained \(\Delta\)STDs \(>\) 0 in more than 80% of our study area, suggesting that the OPC has larger effective temporal variability than the synthetic altimeter estimates, as shown by Figure 10.  
The optimal currents effective spatial resolution is also quantified using the 2017 daily data involved in our study. After computing daily maps of surface Kinetic Energy (KE), we derive the KE power spectral density (PSD) in two land-free areas of the Mediterranean Sea: the \"WEST\" and \"EAST\" areas, with respective horizontal extents from 37.5-38.5\({}^{\circ}\)N/0-11\({}^{\circ}\)E and 33-34\({}^{\circ}\)N/16-34\({}^{\circ}\)E, depicted in Figure 11. As discussed in Section 2, the PSDs are obtained from spatial Fast Fourier Transform analysis and enable checking simultaneously the properties of the SAC, OPC and CMEMS PHY currents (Figure 11). The OPC (blue) and the SAC (red) spectra behave similarly in the WEST and EAST areas. For low wavenumbers (scales up to 100 km), the spectra are fully superimposed, indicating that the two fields are describing the same surface dynamics. Going towards smaller spatial scales, the two spectra begin to separate, the OPC one always exhibiting larger values, closer to the theoretical predictions on surface 2D turbulence (K\({}^{-5/3}\) slope, with K the wavenumber, [51]). As a result, the optimal reconstruction is describing more accurately the finer circulation structures  
Figure 8: (**Left**) improvement of the zonal (blue) and meridional (red) optimal currents with respect to the Synthetic Altimeter estimates (January to Mid-February and Mid-March to December 2017). (**Right**) same as left, in the period mid-February to mid-March 2017.  
compared to the SAC.