The vertical component of geostrophic relative vorticity is derived from SSH as 1ζ=gf∇2SSH within each ensemble member and from the observational product, where g is the gravitational acceleration and f the Coriolis parameter. We computed vorticity from low-frequency SSH fields (see Sect. ), and averaged the result over localized boxes shown in Fig. . The resulting timeseries characterize the slow evolution of regional gyre-like features of interest.

The Mediterranean zonal overturning circulation provides a quantitative meridionally-integrated view of volume transports and water mass transformations within the basin, from their surface inflow to their subsurface outflow through Strait of Gibraltar . In order to assess the imprint of forced and intrinsic variability on the zonal transports in various density classes throughout the basin, we computed in each ensemble member the zonal overturning circulation (ZOC_σ, in Sverdrups: 106 m² s⁻¹) in density space from potential density referenced at the surface (σ0) and velocity fields saved as successive 5-daily averages, as described in : 2ZOCσ(x,σ0,t,n)=∫y1y2∫-h(x,y)ηu(x,y,z,t,n)×H(σ0(x,y,z,t,n)-σ0)dydz where y1 and y2 denote the basin's latitudinal boundaries (5 and 45° N), η the free surface height, h(x,y) the bottom depth, σ0 the reference isopycnal for transport integration, u(x,y,z,t,n) the zonal velocity at depth z and time t in member n, and H the Heaviside step function with H(x)=1 for x>0 and H(x)=0 otherwise. Time series of zonal transports are finally derived from ZOC_σ as explained in Sect. , post-processed as explained in the next two sections, and analyzed in the rest of the paper.

The 1979–2017 linear trends and mean seasonal cycles are removed from all SSH and ZOC-derived time series before decomposing them into temporal scales. Each of the resulting time series, noted X(x,t) at location x and time t, may be then decomposed following : 3X(x,t)=X‾(x)+XLF(x,t)+XHF(x,t), where

X‾(x) is the temporal average;

All variance estimates presented below were computed from demeaned, detrended, deseasonalized time series within all members, with or without decomposition into temporal scales (see Sect. ). Let Xn(t) be the time series of a variable of interest in the n-th ensemble member, with t∈[1,T], n∈[1,N], and N=30. Let overbars and brackets denote temporal and ensemble means, respectively: Xn‾=1T∑t=1TXn(t), and 〈X〉(t)=1N∑n=1NXn(t). These operators are used to split the total variability Xn(t) into its (externally-) forced and intrinsic components following .

The forced variability component is common to all members, and is thus estimated as the time-varying ensemble mean: XF(t)=〈X〉(t).

The variances of the total signal Xn, and of its forced (XF) and intrinsic (XI) components are estimated and compared as follows:

Mean variance of the total variability: σT2=〈(Xn(t)-Xn‾)2‾〉

Our choice of biased variance estimates applied on zero-mean detrended time series ensures that σT2=σF2+σI2 .

At first order, the Mediterranean surface circulation is characterized by cyclonic and anticyclonic gyres and semi-permanent jets. These coherent structures persist throughout the simulation and are clearly visible in both the time-averaged altimetric observations and the time-ensemble-averaged model fields, shown in Fig. a–b.

The model skillfully simulates the time-averaged general circulation in most parts of the basin, in particular large-scale features such as the inflow of Atlantic waters along the north African coast, the cyclonic gyres in the Gulf of Lions, in the Southern Adriatic Sea, and the Rhodes Gyre. The main simulation-observation difference appears in the Balearic sea (2° W to 1° E along the Spanish coast), where the observations reveal a weak cyclonic geostrophic circulation that has an opposite sign in the simulation. In the south and west of Crete, smaller circulation features – Ierapetra (35° N; 26° E) and Pelops (36° N; 22° E) gyres – appear less clearly in the model.

In both the observations and the simulations, the high-frequency (HF) total SSH variability reaches its maxima along the Algerian jet, and in the Levantine Sea (Fig. c, d). In these regions, the model slightly underestimates the observed HF total variability, as was reported by in a similar but non-ensemblist NEMO simulation; it is also possible in our case that the underestimation of local HF variability maxima is enhanced by the ensemble averaging process that smoothes out inter-member differences. Another discrepancy is found southeast of Crete, in the Ierapetra gyre, where the simulated HF variability is weaker than observed. On the opposite, HF variability maxima are simulated in coastal bands narrower than 100 km in the Gulf of Lions and of the Gulf of Gabès, which do not appear as clearly in the altimetric estimate whose effective resolution is likely too coarse. We will come back to the probable origin of these narrow bands in the following. Aside from these local differences, the model reproduces HF SSH variability reasonably well, with standard deviations of 3–4 cm matching observations.

The model correctly reproduces the low-frequency (LF) total SSH variability (Fig. e, f), capturing the main observed patterns and amplitudes. In particular, the North Ionian Gyre (NIG) stands out as one of the dominant modes of LF variability, both in the observations and the simulations. Observations reveal local LF variability maxima around the Cretan Sea, but their simulated counterparts appear too weak, suggesting a lack of energetic regional variability there. Conversely, the model overestimates the variability in the Balearic Sea (39.5° N; 2.5° E), as also reported by using earlier versions of the same model configuration. Based on these results, we excluded the Ierapetra, Pelops, and Balearic gyres from the subsequent analysis of vorticity in Sect. . These gyres either exhibit too small low-frequency variability in the observations, or significant discrepancies in their modeled representation–particularly in terms of amplitude and persistence. The five gyres retained for their subsequent analysis in terms of forced and intrinsic LF fluctuations are those that are correctly located and exhibit a substantial variability in both the simulated and observed datasets.

Figure a shows the time-ensemble-mean zonal overturning circulation in density space in the basin. ZOC_σ reaches its maximum around 28.4 kg m⁻³ near 6° E and around 28.9 kg m⁻³ around 19° E. This limit marks the center of the clockwise upper overturning cell, and the lower boundary of its upper limb (surface eastward flow). Atlantic Waters (AW) crossing the Strait of Gibraltar are carried eastwards within this branch, get progressively denser during their journey as evaporation salinizes and cools them. In the eastern basin, most of the surface waters have become dense enough to sink and flow back underneath towards the Strait of Gibraltar, within the lower limb of this upper cell (intermediate westward flow). Part of these westward-flowing waters get lighter and are upwelled back into the upper limb in the western basin, but most of them cross the Straits and overflow into the Atlantic Ocean.

The simulated transports at Gibraltar are evaluated at the longitude of the Tarifa narrow (5.5° W), as done by . The time-ensemble-mean eastward transport of Atlantic waters is 0.79 Sv, close to the 0.85 ± 0.05 Sv estimate deduced by combining current meter observations and basin-scale mass balance . The time-ensemble-mean deeper westward transport of Mediterranean waters is 0.74 Sv at the same longitude. This is also close to observed reconstructions, with an estimated outflow of 0.81 ± 0.05 Sv from INGRES measurements .

The time-ensemble-mean of the surface eastward transport (Fig. b) increases from about 0.74 Sv at Tarifa Narrows (5.5° W) to 1.2 Sv near 6° E (Gulf of Lions and Algerian basin), mostly due to the aforementioned upwelling of denser waters in the western basin . This transport smoothly decreases between 6 and 15° E and remains close to 1 Sv up to 27° E; it decreases to zero in the easternmost part of the basin as this 1 Sv of AW sinks, ultimately feeding the westward-flowing intermediate layer. This latter transport shows overall consistent zonal variations with the surface eastward transport, the bottom transport being largely second-order west of 25° E.

The time-ensemble-mean ZOC_σ upper cell structure and amplitude are qualitatively – if not quantitatively – consistent with those described by based on a 1/12° reanalysis. Their Fig. 3c shows a similar basin-wide upper cell in density coordinates, with a similar zonal profile of the surface eastward transport. Our ensemble captures the longitudinal alternation of small transport maxima (associated with secondary overturning cells), with peaks located around 5 and 11° E in the western basin, and 17, 18.5, and 24° E in the eastern Mediterranean – slightly shifted eastward relative to the reanalysis. Another difference is found in the maximum density of the surface eastward flow in the western basin, which is about 0.3–0.4 kg m⁻³ smaller in our simulation than in the reanalysis, likely reflecting some differences in buoyancy forcing, convection patterns or water mass properties. Overall, the model shows good agreement with the representation of Atlantic inflow into the Mediterranean, the eastward transport of AW throughout its longitudinal range, and the rate and location of AW sinking throughout the basin.

Slightly negative ZOC_σ extrema are found at largest densities at certain deep locations east of 3° E; they correspond to the counterclockwise bottom overturning cell, which feeds the bottom eastward flow, and locally intensifies the westward intermediate flow. This lower cell, which is very likely influenced by dense water formation in the Gulf of Lions, Aegean Sea and Adriatic Sea, is weaker than the upper cell: its lower limb drives an eastward mean bottom transport of about 0.1 Sv around 4° E, 0.2 Sv at 19° E and 0.34 Sv at 29° E. Its upper limb slightly intensifies the intermediate westward transport with the same time-mean amplitude, thus explaining the slight asymmetry between the black and blue lines in Fig. b.

The high-frequency standard deviation of the surface eastward and intermediate westward transports (Fig. a, blue and black lines) is of the same order of magnitude as their time-mean values (standard deviation of about 0.4 Sv and a mean value of about 1 Sv), indicating substantial HF fluctuations in the upper ZOC_σ cell. In the surface eastward branch, the HF standard deviation reaches its maximum (0.55 Sv) at 5° E, i.e. near the Gulf of Lions deep convection site, and remains close to 0.4 Sv from 19 to 31° E. Its low-frequency counterpart (Fig. b, black) is 3–5 times smaller, and exhibits an opposite zonal asymmetry with larger values in the eastern basin (up to 0.14 Sv at 23° E). This suggests that the atmospheric forcing and/or intrinsic ocean dynamics drive ZOC fluctuations with different time scales in both halves of the basin. This hypothesis is addressed in the next section, where total variability is split into forced and intrinsic components.

The total HF variability of the intermediate westward transport is about 20 % weaker than that of the eastward surface transport west of 10° E. This difference may be associated with the local maximum of HF variability of bottom eastward transport at 4° E. There, the instantaneous bottom transport can reach nearly three times its mean value, likely due to short and intense deep‐water formation events in the Gulf of Lions.

West of 10° E, the total HF variability of intermediate westward transports is smaller than that of surface eastward transport, suggesting that short-term anomalies of the upper and lower ZOC cells have the same sign (both clockwise or both counterclockwise). In the eastern basin, LF variability shows the opposite behaviour: intermediate transport fluctuations dominate over those at the surface, especially between 17–21 and 27–30° E, close to the Adriatic and Aegean deep convection sites. This suggests that long-term anomalies in the upper and lower ZOC cells often tend to have opposite signs, i.e. one clockwise and the other counterclockwise. These two longitude ranges are also those where low-frequency zonal transport fluctuations are weaker at the surface than at the bottom: intermediate zonal transports are thus mostly modulated there by the lower ZOC cell at low-frequency.

Explaining the dynamical origin of the signals described in this section lies beyond the scope of this study; these results however suggest that deep convection impacts zonal transport anomalies in contrasting ways depending on density, time scale, and longitude.

The forced high-frequency SSH variability (Fig. a) is strongest along the coasts. It reaches local maxima in the northeastern Aegean sea, in the Gulfs of Lions, Gabès and Venice, potentially favored by the concave geometry and shallow depth of these regions. SSH variability maxima may be driven by HF fluctuations of dominant winds in the latter regions (e.g. Tramontane, Mistral, Meltemi, Bora), as well as in the Alboran Sea subjected to fluctuations of the Levante and Poniente winds.

Intrinsic HF variability exhibits a very different spatial distribution, likely associated with eddy-active regions along the Algerian coast, the Ionian Basin and in the Levantine Basin (Fig. b). The strong intrinsic HF signal along the Algerian coast likely reflects the combined effect of baroclinic instability and the interaction of currents with complex coastal topography . These processes can lead to the spontaneous generation of energetic mesoscale structures whose high-frequency random fluctuations are relatively independent of direct atmospheric fluctuations. A marked intrinsic signal is also found near 29° E–36° N, within the northern part of the Rhodes Gyre. Intrinsic HF variability remains negligible in shallow regions such as the Adriatic and Aegean Seas, the Gulf of Lions, and over the Tunisian shelf; the model resolution may not be fine enough there to resolve hydrodynamic instabilities because of small Rossby radii.

The HF intrinsic variance ratio is shown in Fig. c. A ratio of 1 indicates that variability is entirely intrinsic, and a value of 0 reflects purely forced variability. Intrinsic processes account for about 20 % of the HF SSH variance over the shallow coastal areas (Aegean Sea, Adriatic Sea, Tunisian shelf), and about 40 %–50 % in the central Mediterranean. The largest HF ratios are found along the Algerian coast (up to 60 %), in the Levantine Basin and in the South Ionian Sea.

Maxima in forced LF variability (up to 7 cm) are found in the Balearic, Alboran and Ionian Seas (Fig. d). In these regions, intrinsic LF variability is about 2–3 times smaller (2–3 cm, Fig. e), indicating that low-frequency SSH anomalies there are mostly driven by the atmosphere. This intrinsic LF component exhibits a more homogeneous distribution across the central and southern Mediterranean, with notable maxima east of the Alboran Sea and within the Algerian Basin, and remains small in most shallow regions as reported at HF.

However, the intrinsic component explains more than 50 % of the LF SSH variance in several regions, including the Algerian Basin, the Tyrrhenian Sea, the southern Ionian Sea, and the Levantine Basin. Altogether, these areas represent approximately 17 % of the total basin area both at HF and LF, and are located in the same regions at both time scales with two exceptions: Ri exceeds 50 % at LF and not at HF in the Tyrrhenian Sea, and the opposite is found in the central Ionian Sea. Considerable LF intrinsic variance ratios are found along the Algerian coast, where up to 75 % of the LF SSH variance is of intrinsic origin. Small intrinsic variance ratios characterize shallow regions, where the LF variability is thus mostly paced by the atmospheric forcing.

The variance maps presented above provide a spatial view of SSH variability in two wide classes of time scales. We now extend our analysis to the entire frequency spectrum by computing the power spectral density (PSD) of SSH variability components between 2 d and 18 years, focusing on two latitudes where Ri is largest: 38° N in the western basin and 34° N in the eastern basin (Fig. c, f). Colors in Fig. a and b show along this line the longitude-dependent PSDs of the total and intrinsic variability, respectively.

The total and intrinsic SSH variability spectra are red throughout the basin. Consistently with Fig. d and f, the total spectrum shows moderate longitudinal contrasts at subannual periods at both latitudes, and localized peaks at periods longer than 1–2 years. The second spectrum reveals that high-frequency intrinsic variability (0.2–0.5 year periods) is much larger in the western basin where the 38° N line intersects the eddy-active Algerian current. More generally, the SSH intrinsic variability is strongest at periods longer than 1 year along both latitudes, except between 11 and 15° E above shallow topography south of Sicily.

The isolines in Fig.  represent the intrinsic-to-total PSD ratio. As for Ri, a ratio equal to 1 indicates that the variability at a given frequency and longitude is totally intrinsic, while a value of 0 corresponds to purely forced variability. More than 75 % of the SSH variability is paced by the atmosphere outside the thin black line (Ri<25%), i.e. at subannual periods throughout the eastern basin and at all frequencies south of Sicily.

Thick black contours surround the frequency–longitude domains where intrinsic variability dominates, i.e. where SSH variability is mostly random. The clear dominance of intrinsic processes is striking in the western basin, particularly between 2 and 10° E at all periods longer than two months. The highest ratios are concentrated near 7° E, where more than 75 % of the SSH variance is random (red shading), at all periods ranging from 3–4 months to 2 decades. In the eastern basin, intrinsic variability plays a less dominant role overall but still accounts for a substantial fraction of the SSH variance; it explains at least 25 % of the SSH variability at periods longer than 5–12 months east of 18° E, and more than half of its interannual variance around 18–22 and 30–32° E.

The forced and total HF variability of the surface eastward transport closely match each other (black lines in Figs. a and a), indicating the atmospheric pacing of most of its variance. Intrinsic variability remains modest (∼ 0.1 Sv, Fig. b), keeping Ri around 10 % throughout most of the basin. Similar values of Ri are found in the intermediate westward transport, except near 29° E where HF intrinsic fluctuations peak and raise Ri up to 37 % (blue lines in Fig. b–c).

In the western basin, forced HF fluctuations are slightly stronger at the surface than at the intermediate level (by about 0.05 Sv, Fig. a), suggesting positively-correlated, atmospherically-paced variations of the upper and lower ZOC cells. Intrinsic HF fluctuations exhibit the opposite pattern in the eastern basin, being larger at the intermediate level (Fig. b), which suggests anti-correlated random variations of the two cells (see Sect. ).

The strongest HF intrinsic variance ratio is found in the bottom eastward transport (green line in Fig. c): Ri at 6 and 19° E is 2–3 times larger than in the upper branches, and reaches 50 % at 29° E. These localized maxima incidentally coincide with deep convection sites (Gulf of Lions, Adriatic and eastern Levantine basins), raising the hypothesis that the ensemble spread associated with short-term convection events see propagates downward and induce random HF transport fluctuations. Testing this hypothesis is left for future studies.

Figure d–e shows that the forced and intrinsic LF variabilities of surface and intermediate transports are largest between 20 and 32° E, with more uniform and smaller amplitudes in the western basin. Forced fluctuations of both transports are smallest west of 1–2° W, probably since no LF variability is forced into the basin through the western buffer zone; this probably explains why intrinsic variance ratios Ri in the uppermost 2 layers reach a local maximum (about 30 %, black and blue lines in Fig. f) in the Alboran basin. Values of Ri decrease further east and get down to 10 % near 3° E, progressively increase again toward the east and reach another peak near 35° E.

The forced LF variability of bottom transports (green line in Fig. d) is maximum in the central and eastern basins, unlike its HF counterpart. In contrast, the LF intrinsic variability of bottom transports has the same zonal distribution as its HF counterpart with a 3–4 time smaller standard deviation. As at HF, the Ri of bottom transports at LF exceeds that of the other two layers east of 25° E, where 15 % to 50 % of the bottom transport variance has a random phase.

To summarize, the contribution of intrinsic processes on the HF and LF variance of zonal transports is globally largest in the eastern basin and in dense layers, with an additional maximum west of 3° E in the lightest two layers. More than 30 %–40 % of the variance of such transports can be random in phase locally, advocating for a more thorough analysis of their underlying dynamics, and for the need to keep in mind the importance of this intrinsic driver of random ZOC variability that competes with the atmospheric one.

Figure a shows over the whole longitudinal and frequency domains the total variability of the intermediate westward transport. In accordance with Fig. a, the total variability PSD exhibits localized minima at the eastern end of the domain, around 26° E where topography is shallow, and at its western boundary where the lateral forcing is purely seasonal and intrinsic variability is damped. The intrinsic variability of this intermediate transport (Fig. b) reaches two maxima at LF in the eastern basin, in particular in the eastern Levantine basin, close to the Aegean convective site (26–29° E). In this longitude range, the intrinsic-to-total PSD ratio decreases with increasing time scales: above 50 % in the submonthly range, 30 %–50 % between 2 months and 2 years, and above 20 % up to 5 years.

In the Ionian Sea (15–20° E) the intrinsic-to-total PSD ratio exceeds 20 % within the 5 months-3 year range. At 2° W in the Alboran Sea, this ratio exceeds 20 % at timescales longer than 4 years. We recall that all the results presented in this study only concern the intrinsic and forced components of the non-seasonal variability that is generated within the Mediterranean Sea: besides the climatological boundary forcing in the Gulf of Cadiz, no other potential influence of the Atlantic is injected into our domain.