# Ocean Currents Reconstruction from a Combination of
## 4 Discussion and Conclusions
More in particular, this idealized framework allows for determining perfectly the source and sink terms that modulate the Chl variations at the sea surface, i.e., the F term of Equation (3), which is clearly much more complicated to account for in a realistic observational setup, due to complex biological responses and interactions within the surface layer. Indeed, the application of the PIT09 method to satellite-derived data will require approximating the forcing term from satellite information. Specific studies coveringthose aspects are already underway and will be the subject of future papers. Preliminary analyses on this topic seem to indicate that, at scales larger than 30 to 50 km, the F term is sufficiently well approximated by the temporal derivatives of the surface Chl field (F \(\simeq\partial_{t}\)Chl). An example is provided in Figure 15. During the main blooming events (mid-to-late February in our numerical study), the agreement between F and \(\partial_{t}\)Chl is only found at a large scale, while the smaller features \(\mathcal{O}\) (20 km) cannot be retrieved exploiting the surface Chl temporal variations (Figure 15-left). Far from the blooming period, F and \(\partial_{t}\)Chl are mostly \(\mathcal{O}\) (10\({}^{-7}\) to 10\({}^{-8}\) mg\(\cdot\)m\({}^{-3}\cdot\)s\({}^{-1}\)), i.e., one to two orders of magnitude lower than in the blooming period. The variability found in the F term is still given by the superposition of a large scale signal, the \(\partial_{t}\)Chl, and a small scale component (Figure 15-right). Figure 14: Temporal evolution of the spatial Chl gradient magnitude (\(|\
abla\)Chl\(|\), normalized). Figure 15: (**Left**) Top panel represents the F term computed by means of Equation (3). The bottom panel shows the surface Chl temporal derivative on 16 February 2017. (**Right**) same analyses reproduced on 25 July 2017. Approximating the F term as \(\partial_{t}\)Chl means that the correction factors for the synthetic altimeter currents in Equation (4) are reduced to the case E = 0: the correction of the geostrophic current is only built accounting for the spatial derivatives of the surface Chl. As a result, we force the flow to follow the Chl concentration isolines. We check that this approximation (E = 0) still leads to satisfying statistical performances of the OPC (Figure 16). The percentage of improvement of the SAC is computed throughout 2017 by means of Equation (5). Figure 16 depicts the zonal and meridional PI in \(2^{\circ}\times 2^{\circ}\) boxes. Given the approximation used here, the extent of the improvement is reduced compared to the idealized case, where the basin-scale PI could also exceed 50% in large Chl gradient areas (Figure 8). Here, the local improvements mostly range from 10 to 20% and, occasionally, degradations may occur in highly active dynamical areas such as the Alboran Sea or in correspondence with the Algerian Current. This additional and preliminary analysis still encourages future applications of the PIT09 method with satellite-derived data, i.e., using only surface Chl and geostrophic currents fields, without the perfect knowledge of the daily forcing term. In such future analyses, the optimal reconstruction should also be implemented accounting for the uncertainties on the Forcing term, thus relying on the PIT09 set of equations used by [28, 29, 31]. In these studies, the uncertainties on the daily approximated forcing were computed by exploiting the high frequency (six-hourly to hourly) measurements of in situ SST by Lagrangian drifters [52, 53]. This approach is not applicable for Chl, as the temporal sampling of in situ measurements of Chl is much lower than one day [54]. This could be addressed in the future by empowering the deployment of Lagrangian drifters designed for the measurements of high frequency sea surface bio-optical parameters (as presently achieved using Saildrones [55]). In the meantime, other approaches need to be explored, for instance relying on dedicated biogeochemical numerical simulations or exploiting machine learning techniques.