The Mercator Global Ocean forecasting system is produced by Mercator Océan (France) e.g.,. The simulation has a horizontal resolution of 1/12∘ and 50 vertical z levels. The model includes multivariate data assimilation, which consists of a singular extended evolutive Kalman (SEEK) filter analysis of along-track satellite sea level anomaly (SLA) and SST together with in situ profiles of temperature and salinity. The altimeter reference period for the assimilated SLA is 20 years . The assimilated SST is taken from the CMEMS Thematic Assembly Centre (TAC) daily level-4 Operational Sea Surface Temperature and Ice Analysis (OSTIA) composite product . In the Strait of Gibraltar, there is relaxation of temperature and salinity towards Levitus 2013 values . The bathymetry used in the system is a combination of the ETOPO1 and GEBCO08 topography databases: ETOPO1 (GEBCO08) is used in regions deeper (shallower) than 300 (200) m with linear interpolation over the 200–300 m layer.

MFS is a product of the Italian Mediterranean Forecasting System. Its horizontal resolution is 1/16∘, with 72 unevenly spaced vertical z levels. MFS includes data assimilation (based on an OceanVAR scheme) of temperature and salinity vertical profiles, satellite SST and along-track satellite SLA observations . The 20-year mean dynamic topography of is used for the assimilation of along-track SLA.

IBI is developed by Mercator Océan but is operated by the Spanish Port Authority (Puertos del Estado, Spain) and, although the model domain mainly corresponds to the northeastern Atlantic Ocean, the output simulation also covers the WMED to as far as the 5∘ E meridian (blue line in Fig. ). The model grid is a subset of the global 1/12∘ ORCA tripolar grid also used by the parent system (that provides initial and lateral boundary conditions) but refined to 1/36∘ horizontal resolution (∼2 km). The system is based on an eddy-resolving NEMO model application run at 1/36∘ horizontal resolution with 50 vertical z levels. IBI does not include data assimilation; however, a downscaling methodology is applied that improves the solution near the open boundaries and the coasts . Lateral open boundary data (temperature, salinity, velocities and sea level) are interpolated from the daily GLO outputs (Sect. ). These are complemented by 11 tidal harmonics (M2, S2, N2, K1, O1, Q1, M4, K2, P1, Mf, Mm) built from FES2004 and TPXO7.1 tidal model solutions. River runoff consists of a combination of daily observations (PREVIMER project), simulated data (SMHI E-HYPE model), a monthly climatology (Global Runoff Data Centre; GRDC) and the French hydrographic database known as “Banque Hydro” (http://hydro.eaufrance.fr, last access: 1 January 2017). Topography is taken from the GEBCO08 dataset plus other local databases as reported by .

Tracks of detected eddies in the western Mediterranean indicate that the longest-lived eddies are typically found in the southern part of the WMED (Fig. ). Anticyclones tend to be longer lived than cyclones. The quantity and duration of long-lived eddies is higher in ALT and GLO, and lower in IBI. The long-lived ALT eddies are concentrated inside the Alboran gyres and the Algerian basin. There is also a small number of long-lived ALT anticyclones in the Balearic Sea. MFS and GLO have similar patterns of eddy distribution to ALT, but they have greater numbers of shorter-lived eddies (Fig. g, h). Large numbers of eddies are detected and tracked in IBI but they are of notably shorter duration than in the other products.

High levels of correspondence are found in eddy amplitude and radius distributions from the three models and altimetry over the western Mediterranean study region (Fig. ). Maps of mean eddy amplitude show that larger amplitudes are found consistently across the southern regions (up to ∼10 cm) and especially in the gyres of the Alboran Sea where amplitudes are ∼10 cm (Fig. a–h). Anticyclones in the south tend to have larger amplitudes and are more prevalent than cyclones which, aside from IBI, are somewhat smaller outside of the Alboran Sea. The distributions of the amplitude patterns between the products are quite similar for anticyclones, but the cyclones in IBI (Fig. d) have noticeably higher amplitudes along the Algerian current axis than they do in the other products. In the Balearic Sea, to the north, typical amplitude values are smaller at around 2.5 cm. There are only small differences between cyclones and anticyclones. Extreme amplitudes (>15 cm) are noticeable in the anticyclones of ALT and GLO at ∼37∘ N, 0∘ E (Fig. e, f). This position corresponds to the Jason-1/Jason-2 satellite track (not shown) which could explain detection of a strong eddy amplitude signal in this region; GLO assimilates altimetry, as does MFS, which also has a raised amplitude at ∼0∘ E (Fig. g). Note also that the eddy identified in GLO in Fig.  occupies this same position, and a large eddy here is visible in the corresponding gridded altimetry map (not shown).

Cyclone and anticyclone radii are generally larger in the southern parts of the study domain than they are in the north (Fig. i–p). The patterns between the models and altimetry are very similar for the anticyclones, aside from the Balearic Sea in ALT where the radii are slightly larger. There is more variability in the cyclones, where GLO has noticeably smaller radii in the Alboran gyres. ALT and IBI cyclone radii are marginally larger than their counterparts in GLO and MFS. Differences in radii for eddies of both signs between ALT and the models are most apparent in the Balearic Sea, where ALT eddies are consistently larger.

Eddy intensity (EI) maps from all products show progressive increases with resolution in both cyclones and anticyclones (Fig. a–h). EI is consistently at or above 0.2 cm km-1 within the Alboran Sea. In ALT, the Western and Eastern Alboran gyres are clearly distinguishable in the EI signal. ALT cyclones along the Algerian coast to the east have weak EI, whereas anticyclones have some of the largest values. Examination of Fig. a, e indicates this variability is largely determined by eddy amplitude rather than radius.

Horizontal anticyclonic eddy composites of ζ/f, T′ and S′ in Fig.  reveal the intensity of the eddy property anomalies of the three defined subregions of the Alboran Sea. Each variable is plotted at the median positions of the eddy coordinates that contribute to each subregion. The eddy positions between the models are very similar.

In the WAG, the median eddy positions for each model are located in the center of the gyre, which corresponds to the deepest water. GLO is found north of the Vizconde de Eza seamount (located at 35.8∘ N, ∼4∘ W in Fig. ), while MFS and IBI are to its west. In the EAG, the eddy positions, lying over the southern 1000 m isobath of the eastern Alboran basin, are virtually indistinguishable. The CRT coordinates are located about 0.75∘ further north in the broad deep water depression that opens into the Algerian basin with, again, little observable difference in median eddy position between the models. The plotting depth in Fig.  of each variable corresponds to the respective absolute maximum in the water column at the eddy center. These depths vary, being very shallow for ζ, some tens of meters deeper for T′ and generally below 100 m for S′. The anomalies tend to be approximately confined within the limits of the two radius estimates, L and Le. The anomalies are plotted out to a radial extent of 2L, with the region between L and 2L defined by as the eddy impact area

The eddy impact area as defined by is the area between 1 and 3 times the eddy radius around the eddy center; here, given the size of the Alboran gyres and the confined Alboran domain, we choose to use twice the radius.

The near-surface negative vorticity values inside the L and Le radii are variable according to both subregion and model in Fig.  (top row). For each model, |ζ| intensity in each subregion successively decreases from the west (WAG) to east (CRT). There is also an overall increase in |ζ| in each subregion between the models; GLO is weakest and IBI strongest. The model increases can be explained by the increasing model resolution. In the WAG, IBI ζ/f approaches 1, indicating the possible admittance of ageostrophic motions; however, the incoming Atlantic jet in IBI is suspected to be too strong such that these ζ values may be an overestimate . Outside of the eddy radii (i.e., from approximately L to 2L), the ζ values are uniformly positive.

The temperature anomalies in the middle row of Fig.  vary in depth between ∼20 and 155 m. There is inconsistency between the models in terms of the depths in each subregion. For example, the shallowest anomaly in MFS is in the WAG, whereas IBI has its deepest anomaly in this subregion. The most intense values of T′ are found in GLO in the WAG. In the eddy impact region of this eddy composite, there is intense negative T′ in the southern and western quadrants; on the eastern side there is an abrupt transition to an arc of positive T′ over the Alboran Trough at ∼3.5∘ W. The MFS WAG pattern is similar, although the strength of the anomaly is smaller. IBI has a strong T′ core, with a nearly continuous negative T′ in the eddy impact region. The EAG and CRT T′ patterns are quite consistent between the models, although the IBI CRT T′ is noticeably stronger than in the other models.

The salinity anomalies in the bottom row of Fig.  are the most consistent of the three variables. The deepest anomalies are in the WAG and the shallowest in the CRT. The fresh S′ composites in the eddy cores have similar magnitudes, and the same is true for the opposite sign in the eddy impact region. In contrast to temperature, the same sign S′ in the impact region is found both south and north of the eddy cores. The most intense S′ is in the WAG in IBI at a depth of 155 m; this contrasts with GLO and MFS minima at 130 and 123 m, respectively.

Vertical sections through zonal and meridional anticyclonic WAG eddy composites in Fig.  reveal good structural agreement between the models in ζ/f, T′ and S′. There are also some striking differences. The widths of the anomalies broadly correspond to the mean radii marked in orange in Fig.  for each eddy composite (Table ). The tilt of the eddies is described by the vertical brown lines; tilt is estimated based on the position of absolute maximum ζ within the eddy radius at each vertical z level for the respective models; see Sect.  and Figs. S2–S4. There is good agreement in eddy tilt between the models, especially in the meridional composites.

Concerning the eddy composite topography, the zonal plots indicate shoaling towards the Strait of Gibraltar in the west. The meridional plots show the eddies to be centered over the 200 m deep trough just to the north of the Alboran Ridge (see inset in Fig. ) at the bottom of the Alboran basin. Due to the successively higher model grid resolutions, more topographic details are visible in IBI and MFS than in GLO. The median IBI WAG position is to the west and south of the MFS and GLO positions; this explains the apparent shallower IBI topographic composite.

The intensity of surface-intensified negative ζ/f more than doubles between GLO and IBI, and the anomalies extend downward to between ∼150 m (GLO) and ∼200 m (IBI) (top row Fig. ).

GLO and MFS T′ sections are quite similar with two positive cores, one between the surface and about 50 m, and the other at 110 m (middle row in Fig. ). The IBI section is distinct, as it has just one core at 150 m and no expression at the surface. The zonal sections have weak negative T′ anomalies on their eastern flanks in the eddy impact area beyond the radius. The strongest T′ anomalies are seen in GLO (upper core) and IBI.

WAG S′ anomalies from the models have similar structure in Fig.  (bottom row). Single cores of negative S′ are centered at around 135 m. The upper surfaces of these anomalies shoal towards the north and east, producing a small surface expression within the northeast quadrant of each eddy.

Structural agreement similar to that of the Western Alboran Gyre above is also visible in the vertical sections of ζ/f, T′ and S′ in the Eastern Alboran Gyre (Fig. ). The eddies here have marginally larger radii than in the WAG (Table ) and lie in slightly deeper waters. The intensity of ζ/f progressively increases from GLO to IBI. Zonal sections of ζ/f are symmetric with weak tilt (top row Fig. ); the eddies are centered over topography that descends towards the east. The meridional sections of ζ/f are asymmetric with strong agreement between each model. The eddies tilt towards the north over the first ∼100–175 m, then back towards the south down to ∼600–700 m, where they begin to feel the topography on their southern flanks.

Both T′ and S′ anomalies in the EAG are slightly weaker than those of the WAG. In contrast to the WAG, zonal T′ in GLO and IBI has a surface signature comparable to that below; MFS, on the other hand, has a weak surface signature that only becomes significant at about 30 m. The zonal S′ structure is the reverse of T′: in GLO and IBI, the anomaly is centered between ∼50 and 150 m, whereas in MFS it reaches the surface. The meridional S′ sections emphasize the strong northward tilt of the eddies. Negative S′ is concentrated north of the eddy center between the surface and ∼100 m in each of the models.

Detected eddies in the Cartagena frontal region to the east of the EAG have weaker tracer and circulation anomalies than in the Alboran gyres (Fig. ). Eddy radii here from GLO and MFS are slightly smaller than in the WAG and EAG; the IBI CRT eddies meanwhile have the largest radii for all three subregions (Table ). Depths in the CRT reach 2500 m, and seafloor gradients are smaller than those in the Alboran gyres of Figs.  and . The same ζ/f intensity increase from GLO to IBI observed in the WAG and EAG is visible in Fig.  (top row). MFS and IBI ζ/f zonal sections are symmetric with small tilt; GLO has pronounced westward tilt down to about 150 m. The meridional ζ/f sections are again asymmetric, with agreement between the models. The eddies tilt northward between the surface and ∼125 m. The eddies are centered over the deepest isobath in both the zonal and meridional directions. Tracer T′ and S′ anomalies in the CRT are weaker than in the Alboran gyres. The cores with maximum T′ are found at around 100 m depth in the three models, with GLO slightly deeper (Fig. j) and MFS shallower (Fig. k). In the upper ∼30 m, T′ is near zero in GLO and MFS, while IBI has a weak positive T′ between the surface and ∼20 m. The vertical extents of the T′ anomalies progress from around 250 m (GLO) to 800 m (IBI). The anomalies are compensated by negative S′ anomalies of broadly similar structure (Fig. m–r).

Good agreement in the seasonal cycle of the WAG mixed layer depth between the models is evident in Fig. . The most interesting observation from the model estimates is the large variability, both seasonal as well as intra-seasonal, with the latter prominent in winter and autumn. As shortwave solar radiation increases from spring to summer, it induces strong stratification that is at its maximum at the end of the summer, leading to shallow MLDs of between ∼5 and 15 m. In autumn, with decreasing shortwave radiation forcing, the MLD deepens to maxima of around 50 m (75 m for IBI). In winter, under the influence of wind-forced mixing processes, the model MLD estimates in the WAG are the deepest over the seasonal cycle, with IBI again having the maximum values with depths below 100 m. Our MLD estimates from the model outputs are in good agreement (especially in summer and autumn), with climatological Mediterranean MLD values reported by that are based on density computed from observations. Small differences can be explained by (i) different methodological approaches here we use the density algorithm of and (ii) our estimates being, by design, biased in that we only sample eddies.

The large variability in MLD over the course of a year may have important implications for upper-layer processes, such as vertical motions associated with mesoscale structures (i.e., the WAG and EAG) that promote exchange of mass, heat and tracers between the surface and the ocean interior. Seasonal MLD variability for the EAG and CRT subregions is similar to that shown for the WAG in Fig. ; see Figs. S18 and S19.