# Ocean Currents Reconstruction from a Combination of
## Data and Methods  
### Data  
The following datasets were used in our study, all covering the year 2017:  
1. **The CMEMS Mediterranean Sea Physics Analysis and Forecast (PHY) Model** The Mediterranean Forecasting System is a hydrodynamic primitive equations model for the Mediterranean Basin and the Atlantic Ocean off Gibraltar-Straight [39]. It is available via the CMEMS web portal (CMEMS Product ID: MEDSEA-ANALYSIS-FORECAST-PHY-006-013). The model provides daily and hourly fields of horizontal currents, 3D temperature, salinity and free-surface elevation for the Mediterranean Area as well as a small region of the Atlantic Ocean in proximity of the Gibraltar Strait. We collected the daily outputs within the boundaries of the Mediterranean Basin (30 to 46\({}^{\circ}\)N and \(-6\) to 37\({}^{\circ}\)E), which are provided on a \(1/24^{\circ}\) regular grid and 125 unequally spaced vertical levels. The core of the hydrodynamical model is the Nucleus for European Modelling of the Ocean (NEMO, version v3.6), and the wave component is provided by Wave Watch-III. The numerical simulations take advantage of data-assimilation of temperature and salinity vertical profiles as well as along-track sea-level anomaly observations. * **CMEMS Mediterranean Biogeochemical Flux, MedBFM (BIO) Model** MedBFM BIO is a biogeochemical model for the Mediterranean Sea distributed via CMEMS [CMEMS Product ID MEDSEA-ANALYSIS-FORECAST-BIO-006-014] [40; 41; 42]. This model provides daily 3D outputs of ocean biogeochemical variables (Chl, nutrients, oxygen, etc.) on the same horizontal and vertical grids as the PHY model (1/24\({}^{\circ}\) regular horizontal grid and 125 vertical levels), which also provides the physical forcing that contributes to the biogeochemical systems evolution. MedBFM BIO also includes assimilation of satellite-derived surface Chl concentration, oxygen, nitrates and phosphates' vertical profiles. * **The Synthetic Altimeter-Derived Currents** The Synthetic Altimeter-derived Currents (SAC) are simulated using SSH data from the CMEMS PHY model. First, the Sea Level Anomaly (SLA) information is obtained from the model outputs using the following formula: \[\text{SLA}=\text{SSH}-(\text{MDT}-0.344)\] (1) with the Mean Dynamic Topography (MDT) provided by the CMEMS product. The 0.344 constant (given in m) allows to center the SLA values on the Mediterranean region during 2017, so that the spatio-temporal mean of SLA equals zero. The obtained simulated SLA exhibits rapid sea level changes across the whole basin occurring over 2-3 days. Indeed, recent progress in ocean modelling now allow for simulating rapidly moving atmospheric pressure disturbances causing storm surges and inverse barometer effects. This raw SLA cannot be handled by the mapping method based on Optimal Interpolation. With real altimetry data, this large-scale high-frequency variability is removed using the Dynamic Atmospheric Correction (DAC) derived from atmospheric forcing [43]. However, the application of this correction to our simulation is not satisfactory as some residual effects are still noticeable. The alternative consists of filtering out the large-scale patterns to focus on the reconstruction of the small-scales and therefore local gradients. A Loess filter with a cut-off frequency of 600 km is applied to SLA maps in order to preserve small-scale features, such as eddies. The small-scale SLA is finally sampled along the actual tracks of Jason-3, Sentinel-3A, SARAL/Altika, and Cryosat-2 missions, using the SWOT simulator software [44]. Measurement errors and noise representative of each mission are added to the SLA value to simulate the altimeter data (see Table 1 or Quality Information Document for CMEMS product ID SEALEVEL-GLO-PHY-L3-NRT-OBSERVATIONS-008-044). This 4-satellite constellation is representative of the CMEMS near-real-time constellation during 2017. These along-track synthetic measurements are then used in input of DUACS (Data Unification and Altimeter Combination System) to produce gap-free SLA maps.