In this section, the four regional simulations are compared to satellite-derived data covering the period 1993–2010. For the pre-altimetric period, only in the Mediterranean diagnostics (Sect. 4.2), we refer to the two reconstructions of Mediterranean sea level, represented by the grey shaded envelop in figures. The sea level signal prescribed in the Atlantic buffer zone is first analysed in terms of seasonal cycle and interannual variability. Then, we focus on the Mediterranean basin, looking at the seasonal cycle, the interannual variability, the spatial patterns and trends. For all the simulations we use monthly fields as done with the altimetry. To analyse the interannual variations yearly values are obtained by simple averaging. Trends are computed through a linear regression.
Near-Atlantic sea level variability
Seasonal cycle
The seasonal cycle of sea level averaged over the Atlantic buffer zone (from the western limit to Gibraltar) differs a lot in the different simulations, depending on the information prescribed. With the E–P–R water report method, LMDZ-MED shows an inverse seasonal cycle in the buffer zone simply because the net E–P–R water budget is larger in the Mediterranean during the winter season. This method had been designed to prevent the Mediterranean from emptying as there is a net freshwater loss over the basin. However, the downside of this approach is that the seasonal cycle modelled in the Atlantic box is wrong, as shown in Fig. 1. In the case of CNRM-RCSM4, the seasonal cycle is underestimated compared to the altimetry-derived dataset CCI-ECV because the COMBINE global ocean reanalysis does not assimilate altimeter-derived SLA. The MORCE-MED model prescribes, from 2002 on, sea level information from a global ocean reanalysis which assimilates SLA from satellite. MORCE-MED is therefore closer to the seasonal cycle of the reference CCI-ECV than the two previous simulations. However, MED12 is obviously the closest, since the seasonal cycle prescribed at the boundary corresponds to CCI-ECV, due to the correction applied to the data derived from ORAS4 in the MED12 simulation. However one can notice from the differences between the CCI-ECV and MED12 curves that the relaxation only happens on a small band of the Atlantic box of the model domain. After 6\(^\circ\)W, the model evolves freely.
Interannual variability
Table 1 Correlation coefficient and root mean square deviation (RMSD) with respect to CCI-ECV for the common period 1993–2008, for the interannual sea level variability in the Atlantic box
Figure 2 represents interannual sea level variations averaged over the Atlantic zone of the models. The absence of trend is noted for LMDZ-MED, which does not have Atlantic variable sea level conditions, as well as for CNRM-RCSM4 and MORCE-MED (before 2002) whose prescribed Atlantic conditions do not integrate SLA from satellites. Considering CCI-ECV as the reference, MED12 represents best the interannual variations and trend with a correlation of 0.91 with the CCI-ECV dataset (Table 1). Among the other three simulations, CNRM-RCSM4 performs best until 2003, because MORCE-MED uses the relaxation towards GLORYS-1 only from 2002 onward. The interannual variability of MORCE-MED before 2002 is thus very poor due to the experimental setup which does not take into account the Atlantic interannual variability before that year. By construction, the interannual variability displayed by LMDZ-MED follows the interannual variability of Mediterranean E–P–R, which is not correlated with the actual sea level variations in the North-East Atlantic. Therefore, the LMDZ-MED variations in the Atlantic box do not match CCI-ECV variability. The new simulation MED12, interanually driven by ORAS4 in terms of SSH, follows well the interannual variability of CCI-ECV with a very high correlation, but also performs best for the pre-altimetric period (before 1993), reflecting the quality of the ocean reanalysis used at the Atlantic boundary.
Mediterranean sea level variability
In order to assess to which extent the sea level signal prescribed west of the Strait of Gibraltar drives the sea level signal in the Mediterranean Sea, we analyse our four simulations over the basin, in terms of spatial average, spatial patterns and trends.
Seasonal cycle
Table 2 Amplitude, lag and root mean squared deviation (RMSD) of the Mediterranean cycle of each simulation
Figure 3 represents the seasonal cycle of the models and the reference. The “EPR water report” method used in LMDZ-MED leads to a flat seasonal cycle. For the three other models, the simulated seasonal cycle is highly dependent on the quality of the Atlantic dataset. The prescription of data from a reanalysis with no assimilation from satellite sea level information, as in CNRM-RCSM4, leads to a Mediterranean sea level which has an underestimated seasonal cycle. MORCE-MED and MED12 both use Atlantic data including satellites information: MED12 has a correction of the seasonal cycle toward CCI-ECV in the prescribed Atlantic dataset, and MORCE-MED prescribes data from the GLORYS-1 reanalysis which assimilates satellite data for the simulated period 2002–2008, and applies a correction to follow the seasonal cycle of GLORYS-1 for the simulated period 1989–2001. For these reasons, MED12 and MORCE-MED both have a Mediterranean seasonal cycle which is consistent with the reference. This is clearly depicted by the root mean squared deviation (RMSD) with the value of 1 cm for both MORCE-MED and MED12, 2.5 cm for CNRM-RCSM4 and 5 cm for LMDZ-MED (Table 2). MED12 presents a 1-month forward lag of the max, whereas MORCE-MED and CNRM-RCSM4 have no lag. Concerning the amplitude of the seasonal cycle, MED12 (13 cm) and MORCE-MED (12.5 cm) are both in good agreement with the reference (14 cm). CNRM-RCSM4 only simulates half of the amplitude displayed in satellite-derived data (Table 2).
Interannual variability
Figure 4a represents the interannual variations of sea level averaged over the Mediterranean basin for the different simulations, for reconstructions before the altimetric period, and for satellite-derived product from 1993 on. Figure 4b displays the impact of the different corrections applied to the LMDZ-MED time series. Table 3 summarizes the correlation of the detrended interannual timeseries of the simulations with CCI-ECV, and Table 4 compares the trends. Both tables refer to the common period 1993–2008. When comparing the SSH provided by the different models (Fig. 4a), it can be seen that LMDZ-MED is not producing any significant variability. Even if the correlation with altimetry is relatively high (Table 3), the range of variations is much smaller. Also the trends are negligible (Table 4). This was expected as by construction LMDZ-MED simulates an almost constant Mediterranean sea level. For CNRM-RCSM4 and MORCE-MED, the interannual variability is provided by the LBCs. Both simulations provide similar results in terms of variability and trends. The interannual variability is correlated to the observed variability (0.5 and 0.56 respectively) but the long-term trends are clearly wrong (Table 4). For MED12, which includes the improved signal from the Atlantic in its LBCs, the results are clearly better. The interannual variability shows the right magnitude and is highly correlated with the observations (0.80). Also, in MED12, the simulated trend for the common period is 1.62 mm year\(^{-1}\), close to the observational estimate (1.78 mm year\(^{-1}\)).
As mentioned previously, the SSH in the LMDZ-MED model is almost constant. In order to compensate this limitation of the modelling system, the typical solution is to add the Greatbach constant (Eq. (1)) to the model SSH. For the LMDZ-MED model (see Fig. 4b), the addition of the total steric component provides interannual variablity and a negative trend (−0.89 mm year\(^{-1}\)). This variability is induced by changes in the basin averaged temperature and salinity. When the mass changes due to salinity changes are included (Eq. (2)), and thus only the actual expansion is represented, the interannual variability is similar but a stong positive trend appears (4.48 mm year\(^{-1}\)). This is due to the warming trend present in LMDZ-MED and already identified by Llasses et al. (2016). This trend was driven by the warming of the deepest layers in the Levantine basin and attributed to a too short spin-up, thus being unrealistic. The conclusion of this comparison is twofold: (a) in cases where the models have fixed Atlantic conditions, the a-posteriori correction suggested by Jordà and Gomis (2013) improves the interannual variability but caution is required with the trends as model drifts can contaminate them; (b) in order to get an accurate simulation of Mediterranean sea level the mass transfer between the Atlantic and the Mediterranean has to be properly simulated as it is the driving mechanism of interannual to multidecadal Mediterranean variations.
Table 3 Correlation with CCI-ECV for the common period 1993–2008, for the interannual sea level variability in the Mediterranean
Table 4 Trend for the common period 1993–2008
Spatial patterns
Figure 5 compares the mean dynamic topography (MDT) patterns from Rio et al. (2014) (RIO 2014) as reference with the different simulations. The new MDT RIO 2014 was computed especially for the Mediterranean Sea from model outputs, altimeter measurements and oceanographic in situ data, and benefits from improvements made possible by the use of extended data sets and refined processing. It covers the 1993–2012 altimetric period. MDT patterns can be considered as proxies for the mean surface circulation. From this figure, we see that SSH spatial patterns are not necessarily improved with the revised near-Atlantic signal in MED12, but seem rather model-dependent. It is difficult to determine a “best” spatial representation among these four simulations; this shows that ORCSMs have difficulties to represent accurately sub-basin circulation variability (L’Hévéder et al. 2013; Sevault et al. 2014). One of the most distinct feature among the models occurs in the Alboran Sea. MORCE-MED and MED12 both have a sub-surface circulation with Atlantic waters flowing northward toward the Balearic Islands after entering through the strait of Gibraltar, which is likely unrealistic according to observations (Millot and Taupier-Letage 2005). However, a recent study by Pinardi et al. (2013) shows results from a retrospective reanalysis which displays a northward flowing segment. In LMDZ-MED, Atlantic waters entering at Gibraltar are trapped into gyres in the Alboran Sea and then stick to the North-African coast. Rio et al. (2014) propose a feature in between, quite close to the patterns displayed in CNRM-RCSM4 in the Alboran region. Concerning the North-Western Mediterranean, the low sea level feature associated to the large gyre in the convection area of the Gulf of Lions is well-represented in most of the models, but for MORCE-MED, where it remains weak.
In the eastern basin, MED12 shows the most consistent circulation compared to Rio et al. (2014). For example, in the other simulations, the Algerian current crosses the Sicily Channel but then circulates too far north in the Ionian, especially in MORCE-MED. MED12 displays the most realistic pattern for this feature. In the Levantine basin, the Rhodes cyclonic gyre, where winter convection occurs, is only accurately represented in MED12. The anticyclonic Ierapetra gyre (South-East of Crete) is nicely displayed in the reference dataset but this feature is absent in all the model simulations. The differences between the simulations and the altimetric data are mainly seen on spatial mesoscale patterns, the very large scale patterns being in agreement between both products. This is probably because the model spatial resolution ranges from 6 to 12 km and is not enough to properly simulate all the mesoscale and sub-mesoscale processes that play a role in the Mediterranean. Moreover, it has to be noted that the resolution of the models is not enough to properly model the hydraulic control and the water exchanges at the Strait of Gibraltar (Sannino et al. 2014). This would have a negative impact on the quality of the circulation around the Strait of Gibraltar as far as the transfer of momentum would not be accurate. However, in terms of Mediterranean sea level this is not a problem because the transport adjustments are set up at low frequency and thus unaffected by the details of the exchange [see for instance the quality of the results obtained with a 15 km model by Gomis et al. (2006)]. An in-depth anaysis of the causes for the differences and discrepancies of sub-surface circulation features among Mediterranean regional ocean models would be interesting but it remains beyond the scope of the present study.
Spatial trends
The basin-wide averaged trends have been presented in Table 4 and it has been shown that MED12 (1.62 mm year\(^{-1}\)) better agrees with CCI-ECV (1.78 mm year\(^{-1})\). Spatial trend anomalies with respect to basin average are represented in Fig. 6. CCI-ECV displays spatial trend anomalies which are negative around the Balearic Islands, in the Ionian, and in the south-west Levantine meaning that the local sea level rise in these regions is slower than the basin average trend, with even negative trends in the north-west Ionian (absolute values not shown). Positive trend anomalies are displayed around Crete. The trend patterns in the Ionian show the recovery after the Eastern Mediterranean Transient, which ends when the altimetric period begins. The changes in North Aegean trend patterns could reflect circulation changes related to changes in the Bosphorus fluxes. The positive/negative dipole south-east of Crete could be attributed to a shift of the Ierapetra gyre. In the western basin, the interpretation of the changes is more delicate.
Concerning models’ capability to represent spatial trends, we found that, except in MORCE-MED, local negative trend anomaly patterns of the western basin are in correct agreement with those displayed by the satellite-derived data despite the models’ difficulties to represent an adequate circulation in the Alboran region (see Sect. 4.2.3). For the eastern basin, the negative trend anomaly pattern of the north-west Ionian, attributed to the post-EMT recovery, is present in all models, although it is shifted southward in MORCE-MED. Concerning the absence of trend anomaly patterns in North Aegean in all models, the representation of the Bosphorus is too crude to be able to show the impact of changes in the Black Sea outflow on the circulation.
Local structures of sea level trend are driven by processes such as water mass changes, which are not necessarily influenced by the boundary conditions. The major improvement at Mediterranean global scale (see Sects. 4.2.1 and 4.2.2) is thus not clearly present at local scale. This might be a problem when analysing the spatial variability of the Mediterranean for the present climate, since the regional differences are up to \(\approx\)20 cm, thus larger than the basin scale temporal changes (\(\approx\)7 cm over the last 3 decades).
However, in future scenarios it is the opposite: sea level rise will be expressed as a basin-wide signal of 50–80 cm, while regional variability will change much less. In particular, Adloff et al. (2015) have shown that global warming could modify the circulation patterns. This would induce local differences in sea surface height of up to +10 cm. The gain from prescribing adequate sea level conditions at the Atlantic boundary is thus evident, even more for future longer time scales.