**1. Introduction**

The Strait of Gibraltar is the natural connection of the Mediterranean Sea with the world ocean, being a hot spot area in many senses. There, diverse and separated hydrodynamic phenomena occur over a wide range of spatial and temporal scales (from the small scales and submesoscale phenomena to inter-annual and climate variability). The complex hydrodynamic conditions influence the rich marine ecosystem in the adjacent coastal areas, e.g., [1–3]. Furthermore, the region is of great socioeconomic relevance as a key passage for marine trade. Almost 1/6 of global sea traffic and 1/5 of global oil traffic transits through the Mediterranean basin, still being the shortest route between Europe and Asia [4]. Then, it is not surprising that the Strait of Gibraltar and the adjacent Alboran Sea have been traditionally a focus area for many research and monitoring efforts since a long time ago, e.g., [5–7]. Although the main characteristics of the prominent processes are reasonably known and modeling efforts capture most of them, an adequate operational forecast of the hydrodynamics

conditions in this region remains a challenging task [8]. Roughly, the water mass structure is close to a two-layer system characterized by an upper surface layer of Atlantic waters entering into the basin and denser Mediterranean waters outflowing below [9]. The inflow of Atlantic water and the outflow of Mediterranean water are constrained by hydraulic control in the channel where the bottom relief, stratification, tidal, and wind regimes determine the variability of water exchanges through the strait, which are therefore linked to basin scale variability, e.g., [10,11].

The jet of Atlantic water forms and configures a quasi-permanent vortex or gyre in the western part (western Alboran vortex, WAG) of the Alboran Sea, which progresses further into the second half after Cape Tres Forcas (around 3◦W) where it forms a second gyre (eastern Alboran gyre, EAG) and continues further to the east attached to the African coast as the Algerian current, e.g., [12,13] (see Figure 1). This is the dominant general pattern of the surface circulation in the Alboran Sea, particularly in summer, emerging from the analysis of time series of sea level maps and model reanalysis [14,15] and often observed by in situ cruises, e.g., [13]. Besides, the gyres may collapse or migrate until they are restored in the spring and early summer. These events appear to be induced by high frequency processes (tides and atmospheric fluctuations) requiring high resolution in space and time to be adequately analyzed and studied [8].

**Figure 1.** Scheme of the surface circulation in the Alboran Sea showing the western and eastern Alboran gyres (WAG and EAG) as well as the jet of Atlantic waters (AJ), from Sánchez-Garrido et al. [8].

Attempts to forecast the oceanographic conditions during a recent oceanographic experiment, the MEDESS-GIB experiment [16], have shown that models reasonably reproduce the main pattern but fail to reproduce the variability of short scales and the details of the evolution of the Atlantic inflow around WAG, e.g., [17]. Once models have the necessary spatial resolution and are able to reproduce the observed physical processes, as was the case of the MEDESS-GIB experiment, a way to improve the subsequent forecast is to have initial conditions and analyzed fields as close as possible to the truth. Furthermore, in the worst case, when and where operational systems are not working well and depending on the involved scales, an empirical approach using only real time field observations and assuming some kind of persistence may provide a reasonable first guess. Sea surface temperature (SST) is quite satisfactorily retrieved in real time and with enough resolution to reach fields at submesoscale. For the ocean velocity, altimetry offers the possibility to build maps of velocity fields interpolating along-track information. In this case, the resolution attained can reach the ocean mesoscale, although with limitations in terms of accuracy and reliability, e.g., [18] and real time is not possible.

The operational estimation of ocean velocities from satellite observations remains a major problem in satellite oceanography. At present, multiple methods to estimate ocean currents from SST have been proposed with a wide range of performances, see [19] for a review on this subject. In this study, we analyzed the possibility to retrieve real time high resolution fields making use of the surface quasi-geostrophic theory (SQG) [20,21]. SQG offers the theoretical body to derive high resolution

surface velocity fields from a single infrared SST image [21–26]. This capability is of key importance for operational applications because it extends its usability in comparison with other techniques such as maximum cross correlation or optical flow that need a sequence of cloud-free images [19]. Two conditions are necessary to apply the SQG framework to SST images: surface density fluctuations have to be strong enough to capture a significant amount of the near-surface dynamics [22,27] and SST has to be a proxy of density anomalies at the base of the mixed layer [28]. In a pioneering work, LaCasce and Mahadevan [29] demonstrated the applicability of the SQG framework in the Alboran Sea and showed that it was possible to retrieve the full 3D structure of ocean density and velocity fields from SST fields. Their reconstructed fields were quite similar to those observed in a CTD cruise; however, the work was flawed by the assumption that three-day cruises could be considered synoptic. Consequently, they had errors in both horizontal and vertical velocities.

In the present study, we went further by validating the reliability of using a time series of ocean velocity fields from SST covering the full area between the Strait of Gibraltar and the Alboran Sea. In particular, we analyzed the performance of the SQG approach when applied to infrared satellite measurements and compared to velocities derived from surface drifters. Moreover, we explored new approaches to overcome the limitations imposed by the lack of observations of ocean salinity.

This paper is organized as follows. We first briefly present the dataset used in Section 2. We develop in detail the methodology to derive velocity fields applying a SQG-based methodology in Section 3. In Section 4, we present and validate the results comparing with field data from the MEDESS-GIB experiment. We finally discuss and conclude the major outcomes.

#### **2. Data**

On the frame of the MEDESS-4MS project (EU MED Program), an intensive Lagrangian experiment was organized in the Strait of Gibraltar to validate and test the operational systems running in this area [16]. The experiment consisted od a quasi-synoptic deployment network of surface drifters distributed along the Strait of Gibraltar (Figure 2). The experiment started on 9 September and lasted around three months from September to December 2014. The drifters used in the experiment were mostly of CODE type [30] dragged at 1.5 m from the surface and a few units of oil-spills tracking drifters not used in this study, all set up with a sampling rate of 30 min. The dataset is available at PANGAEA (Data Publisher for Earth and Environmental Science) repository and all the quality control procedures and first view of the trajectories were described by Sotillo et al. [17].

**Figure 2.** Trajectories of surface drifters for the MEDGIB-GIB experiment. Color scale corresponds to time with respect to 9 September 2014.

Geostrophic velocities used were derived from Near Real Time Absolute Dynamic Topography Maps (NRT-MADT) for the Mediterranean Sea generated by AVISO altimetry and distributed by the GlobCurrent project. Velocities were estimated from NRT-MADT using a nine-point stencil length, as described by Arbic et al. [31]. During the period, most drifters remained in the Alboran Sea (from 9 September to 29 September, Figure 2), but only 10 images with favorable cloud coverage were

available. These images correspond to the AVHRR instrument from NOAA 19 platform for the period from 9 September at 03:08 GMT to 14 September at 02:12 GMT. Consequently, only the WAG could be simultaneously sampled by infrared instruments and drifters.

The used SSS corresponds to the Mediterranean and North Atlantic SMOS SSS maps V2.0 product from the Barcelona Expert Centre in Remote Sensing (BEC). These maps were derived from L1B Microwave Brightness Temperatures (MBT) products measured by SMOS and provided by ESA. Then, SMOS SSS daily L3 maps at 1/4◦ × 1/4◦ resolution were produced by means of a successive corrections analysis applied over time periods of nine days using influence radii adapted to the Mediterranean Sea, see [32] and reference therein.

#### **3. Reconstruction of Velocities from Thermal Images**
