# Ocean Currents Reconstruction from a Combination of Altimeter and Ocean Colour Data: A Feasibility Study

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## Abstract

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## 1. Introduction

## 2. Data and Methods

#### 2.1. Data

**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:$$\mathrm{SLA}=\mathrm{SSH}-(\mathrm{MDT}-0.344)$$These along-track synthetic measurements are then used in input of DUACS (Data Unification and Altimeter Combination System) to produce gap-free SLA maps. 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 recombined in 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 CMEMS Altimeter-derived gridded regional products for the Mediterranean Sea.**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${}_{\mathrm{sat}}$” from the CMEMS BIO model for the entire year 2017. We relied on the “C${}_{\mathrm{sat}}$” expression provided by Morel and Berthon 1989 [45]:$${\mathrm{C}}_{\mathrm{sat}}=\frac{{\int}_{0}^{{\mathrm{z}}_{\mathrm{p}}}\mathrm{C}\left(\mathrm{z}\right){\mathrm{e}}^{-2\mathrm{kz}}\mathrm{dz}}{{\int}_{0}^{{\mathrm{z}}_{\mathrm{p}}}{\mathrm{e}}^{-2\mathrm{kz}}\mathrm{dz}}$$

#### 2.2. The Work Logic

#### 2.3. Methods: Rationale of the Optimal Reconstruction

- (x,y) are the zonal and the meridional directions;
- ($\mathrm{u}$,$\mathrm{v}$) are respectively the zonal and meridional components of the ocean surface flow;
- F is the forcing term, representing the Chl source and sinks which, in the present case, include both biological and environmental factors. In particular, F includes contributions from the marine currents’ vertical advection, horizontal and vertical diffusion as well as the biogeochemical reactions involved in the phytoplankton dynamics [47]. The contributors to the source/sink terms can have different relative magnitudes according to space and time. For example, we expect vertical advection to be dominant under high wind stress conditions that may trigger upwelling currents or in the presence of mesoscale/submesoscale features generating strong vertical motions [48,49]. In addition, biogeochemical reactions become dominant during the so-called “Chl-blooming periods”, i.e., when the near-surface Chl production increases due to an abundance of light and nutrients (e.g., inorganic carbon dioxide, silica, nitrates and phosphorus) involved in the phytoplankton photosynthetic activity [37,38].

#### 2.4. Methods: Optimal Reconstruction Quality Assessment

- the superscripts SAC, OPC, PHY, respectively, stand for synthetic altimeter currents, optimal currents, and CMEMS PHY modelled surface currents;
- U,V respectively indicate the zonal and meridional flow;
- the i index goes from 1 to N = 365, i.e., the number of the daily surface currents data during 2017;
- the ${\langle \rangle}_{\mathrm{t}}$ operator in (7) indicates a time average over the year 2017;

## 3. Results

#### 3.1. Qualitative Assessment

- Figure 3A: the anticyclonic meander found at 43${}^{\circ}$N–7${}^{\circ}$E, the two eddy system located at 41.3${}^{\circ}$N–4${}^{\circ}$E and the meandering tongue flowing from 40${}^{\circ}$N–5${}^{\circ}$E towards the northeastern section of area A;
- Figure 3B: the current system flowing off the western tip of Sicily, perpendicular to the coastline (at the approximate location of 37.5${}^{\circ}$N–12.5${}^{\circ}$E), the eddy located at 38.5${}^{\circ}$N–12${}^{\circ}$E and the western boundary of the the Messina Rise Vortex (37${}^{\circ}$N–15.5${}^{\circ}$E);
- Figure 3C: the Alboran gyre and multiple eddies system found north of the 36.5${}^{\circ}$N parallel, particularly the one circulating at 37${}^{\circ}$N–1.5${}^{\circ}$W.

#### 3.2. Quantitative Assessment

#### 3.3. Effective Depth of the Optimal Currents

## 4. Discussion and Conclusions

- the effective temporal resolution of the optimal currents is enhanced compared to the altimeter estimates. This was obtained computing the temporal standard deviations (STD) of the Synthetic Altimeter-derived and OPtimal surface Currents (SAC and OPC, respectively). The difference between the OPC and SAC STDs, computed on both annual and weekly timescales, is positive in 80% of the Mediterranean, demonstrating an enhanced temporal variability;
- the spectral analyses of the SAC, OPC and CMEMS PHY Kinetic Energy fields suggest that the OPC fully recovers the surface dynamics until scales of 30 km that we defined as the OPC effective spatial resolution. Following the same spectral analysis, the SAC dataset fully describes larger mesoscale features around 100 km;
- the optimal currents improve the surface circulation estimates provided by satellite altimetry by about 30 to 50% at the basin scale for both the zonal and meridional currents. This was determined checking simultaneously the RMSD values of the SAC and OPC with respect to the total surface currents estimates provided by the CMEMS PHY model. Such improvements can be found throughout the year. However, the enhanced biological activity during late winter/early spring [36,37] may give rise to significant changes in surface Chl gradients. Such gradients are not strictly related to the horizontal advection and can thus slightly reduce the OPC maximum improvements with respect to the altimeter system. The summer period (mostly late June/early July) can also give rise to issues in the optimal reconstruction: in this period, the Mediterranean sea surface Chl gradients reach their minimum value (evaluated via the CMEMS BIO model and shown in Figure 14 as a basin-scale average), preventing the optimal reconstruction (PIT09 method) to extract dynamical information from the surface tracer patterns;
- the OPC built from Chl concentrations, despite Chl being obtained integrating contributions in the first tenths of meters of the water column, instead represent the surface circulation in the Mediterranean area.

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

## References

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**Figure 1.**(

**Left**) Normalized scatter density plots between Chl-1m and C${}_{\mathrm{sat}}$. (

**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.

**Figure 3.**(

**A**) Northwestern Mediterranean: left, middle and right panels, respectively, indicate the Synthetic Altimeter Currents (SAC), Optimal Currents (OPC) and CMEMS PHY modelled currents. (

**B**) same as (

**A**), with focus on the Sicily Channel. (

**C**) same as (

**A**), with focus on the Western Mediterranean.

**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 |$\nabla \mathrm{Chl}$|, 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).

**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.

**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.

**Figure 9.**Temporal standard deviation (STD) of the CMEMS PHY and optimal surface currents for the year 2017. (

**Top**) CMEMS PHY STD; (

**Middle**) STD of the optimal currents (OPC); (

**Bottom**) $\mathsf{\Delta}$STD: differences between the OPC and the Synthetic Altimeter Currents (SAC) STDs. (

**Left**) and (

**right**) columns stand for zonal and meridional currents, respectively.

**Figure 10.**Differences between the OPC and the SAC temporal standard deviations ($\mathsf{\Delta}$STD) computed on a 10-day temporal window. (

**Left**) and (

**right**) panels stand for zonal and meridional currents, respectively.

**Figure 11.**Kinetic energy power spectral density of the Synthetic Altimeter Currents (SAC, red), OPtimal currents (OPC, blue) and CMEMS PHY modelled currents (light blue). The spectra are computed in the WEST and EAST areas of the Mediterranean, depicted by the yellow and green borders, respectively.

**Figure 13.**Depth of maximum OPC PI over the year 2017, represented in ${1}^{\circ}\times {1}^{\circ}$ boxes.

**Figure 14.**Temporal evolution of the spatial Chl gradient magnitude ($|\nabla \mathrm{Chl}|$, 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.

**Figure 16.**PI of the Optimal Currents given in 2${}^{\circ}\times {2}^{\circ}$ boxes: (

**top**) zonal currents; (

**bottom**) meridional currents.

**Table 1.**Mean 1 Hz noise measurement observed for the different altimeters on along-track (L3) DUACS products in the Mediterranean Sea. Noise for raw SLA is indicated in cm rms.

Mission | Noise Measurement Error |
---|---|

Jason-3 | 2.4 |

Sentinel-3A | 2.1 |

SARAL/AltiKa | 1.75 |

Cryosat-2 | 2.1 |

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**MDPI and ACS Style**

Ciani, D.; Charles, E.; Buongiorno Nardelli, B.; Rio, M.-H.; Santoleri, R.
Ocean Currents Reconstruction from a Combination of Altimeter and Ocean Colour Data: A Feasibility Study. *Remote Sens.* **2021**, *13*, 2389.
https://doi.org/10.3390/rs13122389

**AMA Style**

Ciani D, Charles E, Buongiorno Nardelli B, Rio M-H, Santoleri R.
Ocean Currents Reconstruction from a Combination of Altimeter and Ocean Colour Data: A Feasibility Study. *Remote Sensing*. 2021; 13(12):2389.
https://doi.org/10.3390/rs13122389

**Chicago/Turabian Style**

Ciani, Daniele, Elodie Charles, Bruno Buongiorno Nardelli, Marie-Hélène Rio, and Rosalia Santoleri.
2021. "Ocean Currents Reconstruction from a Combination of Altimeter and Ocean Colour Data: A Feasibility Study" *Remote Sensing* 13, no. 12: 2389.
https://doi.org/10.3390/rs13122389