4.2. Contribution of Steric Sea Level to Sea Surface Height Trends
In this section, the steric component of the sea level in ocean reanalyses is estimated and inter-compared between five different products (ECCO-KFS, ECCOv4r3, GLORYS4, SODA3.12.2, and SODA 3.4.2), which were chosen because they are public datasets providing both temperature and salinity, and sea surface height. Table 1
(second part) includes some general characteristics of the reanalyses. The multi-product ensemble mean was also used to evaluate the overall performance of those products. Here, the period was focused on the satellite era (1993–2015) when altimetry data are usually assimilated in ocean reanalyses.
GMSL between 70° S–70° N was first calculated (Figure 6
). During 1993–2015, the multi-product ensemble mean of global SSH has a positive trend of 2.5mm year−1
, which is 79% of the observed trend for GMSL (3.2mm year−1
) for the same period (Figure 6
a). This suggests that ocean reanalyses slightly underestimate the GMSL rise rate. In the meantime, there is a divergence for the GMSL rise rate between the ocean reanalyses (Figure 6
b–f). GLORYS4 produces the fastest GMSL rise rate (3.8 mm year−1
), while SODA reanalyses have the smallest rates (2.1 and 1.9 mm year−1
), with ECCO products having a moderate rate (2.5 mm year−1
). Part of the difference might be due to altimetry data that are not consistently assimilated in the products.
We then estimated the contributions of steric height to GMSL rise in ocean reanalyses. For the multi-product ensemble mean, the steric component of the sea level has an increasing trend of 1.1 mm year−1
globally (Figure 6
a), which accounts for 44% of the total sea level trend. Steric heights at different depths (300 m, 700 m, 2000 m, full depth) were also calculated, with the 300-m depth having the largest relative contribution (0.6 mm year−1
). The contribution of steric height is varying within different ocean basins (Figure 7
a). In the Atlantic and the Southern Ocean, steric height contributes to 50% to 60% of the total SSH change rate; in the tropical Pacific and Indian Ocean, steric height has a lesser contribution (20%–40% of SSH change rate).
The effect of steric height to total SSH was also evaluated in individual reanalyses. Global steric height (full depth) is increasing during the period in all products (Figure 6
b–f), at a rate varying from 0.4 to 1.8 mm year−1
. Steric height has a stronger effect on the global SSH trend in SODA reanalyses, while it has a weaker effect in the ECCO reanalyses. In SODA, ocean is thermally expanding at a fast rate close to the total SSH increase rate. In ECCO, the thermal expanding rate of the ocean is less than 20% of the total SSH increase rate. This can be further demonstrated in the basin scale (Figure 7
b–f). In SODA products, steric height accounts for more than 80% of the total SSH change rate in the vast majority of the ocean. However, in ECCO products, the largest contribution of steric is reduced to 30% to 50%, which is in the western Pacific and eastern Indian Ocean. Moreover, in the eastern Pacific, the steric component of these products has negative trends, which are opposite to SSH trends. Thus, the contribution of steric to total sea level trend is region-dependent and product-dependent.
We found that the variety of steric contribution in reanalyses is associated with the deep ocean (>2000 m depth) (Figure 6
b–f), which is greatly warming in SODA but less warming or even slightly cooling in ECCO and GLORYS4, during the period. This is particularly true in the Pacific basin (not shown). The upper ocean (0–300 m depth) shows similar steric trends between these five products (not shown), especially at low latitudes. This suggests that assimilating ocean profile observations, which are widely observed in the upper ocean, reduces the differences of the ocean state produced by the models. However, in the deep ocean, due to the limited source of observations, ocean analysis makes little change for the steric sea level, which is in turn more likely to retain the variety of ocean models.
also shows that the contribution of the mass component (SSH minus steric) to the SSH trend varies between ocean reanalyses. For example, the ocean mass in ECCO and GLORYS4 is increasing at a higher rate than in SODA. Although the steric effect accounts more for the SSH trend in SODA, negligible contributions of ocean mass cause the SSH trend tot still be far less than other products and observations. More efforts are needed in the future to reconcile the representation of ocean mass in reanalyses.
4.3. Inter-Annual Variability
Inter-annual variability of observed GMSL was reasonably captured by the SSH of multi-product ensemble mean (Figure 8
), with a correlation equal to 0.40 (significant at 95% confidence level). The inter-annual variability is best re-produced in ECCOv4r3, with a correlation equal to 0.91. However, when not assimilating altimetry data, SODA products fail to reproduce the inter-annual variability of global SSH. In ECCO-KFS and GLORYS4, the correlation of SSH inter-annual variability is 0.60 and 0.54, respectively.
At the global scale, the contribution of steric sea level to the inter-annual variability of total SSH is essential in ocean reanalyses (Figure 8
). Regional SSH variations are provided in the Supplementary Material Figure S1
. The correlation between steric height at full depth and global SSH is 0.76 (significant at 95% confidence level) for the multi-product ensemble mean. For individual products, a correlation between steric and SSH anomaly is above 0.8, except ECCOv4r3, where r = 0.14 (not significant at 95% confidence level). The departure of steric height from SSH indicates other effects, e.g., the ocean mass. Like the SSH trend (Figure 6
), these effects have more impacts on SSH variability in ECCO products than in SODA products (Figure 8
It is worth noticing that the steric height inter-annual variability in the upper ocean (0–300 m) is consistently produced in those five ocean products, with an inter-product correlation greater than 0.5. This suggests that data assimilation corrects the modelled background of the ocean, and this correcting effect tends to make the analyzed ocean states from different ocean models resemble the observations. In the upper ocean, where the density of observations is high, steric height converges between products. However, in the ocean interior, where observations are rare, steric height is diverging between products due to the limited constraints of the models. This divergence is larger when ocean models are substantially different, such as those used in ECCO and SODA products.
We also evaluated the effect of steric height (full depth) on inter-annual variability of SSH at regional scales (Figure 9
). For the multi-product ensemble mean, the steric component of the sea level explains more than 60% of SSH variability in the vast majority of regions. In the tropical Pacific and Indian Ocean, over 90% of SSH variability is introduced by the local steric expansion. This feature is consistently produced in the reanalyses except GLORYS4 We further confirmed that the steric height above the 300-m depth is mostly responsible for SSH variability in those basins (Supplementary Material Figure S2
), and it is significantly modulated by ENSO at inter-annual timescales (Supplementary Material Figure S3
However, differences between the reanalyses still exist in some regions (Figure 9
). In the Southern Ocean, the steric component accounts for less than 50% of sea level variance in GLORYS4, but it does more than 70% to 80% in SODA products. Steric height has an intermediate effect in ECCO products (50%–70%). In the Atlantic, the discrepancy between GLORYS4 and SODA products becomes even larger. Some of those discrepancies are related to thermal expansion in the deep ocean. For example, in the Southern Ocean and the western boundary currents (i.e., the Gulf Stream and Kuroshio Extension), SSH variance is large in SODA products (Supplementary Material Figure S1
), and it is largely associated with the steric height below 300-m depths (Supplementary Material Figure S3
). However, in ECCO products, steric height lacks variability below the 300-m depth. This might be related to the ocean mixed layer depth, which is not deep enough to resolve the variability below the subsurface.
It is also worth noticing that GLORYS4 produces similar steric heights as SODA products across the basins, both in the subsurface and deep ocean (Supplementary Material Figures S2 and S3
). However, SSH variability in GLORYS4 is not explained by steric as much as in SODA (Figure 9
). This suggests that other effects, such as ocean mass, are also playing an important role in SSH variability in GLORYS4. This, again, indicates that efforts are needed in the future to vigorously evaluate those effects in ocean reanalyses.
4.4. Sea-Level Trends in Regional Reanalyses for the European Seas
In this section, we investigate the variability of the sea-level trend at the regional scales, starting from multi-resolution reanalyses for the European Seas: Baltic Sea (BAL), North Western Shelf (NWS), Iberian-Biscay-Ireland (IBI), and Mediterranean Sea (MED). In general, sea level trends obtained from multi-resolution reanalyses (Table 3
) show positive values, which were in agreement with the most recent estimates obtained for the European Seas from satellite altimetry [1
The sea level trend estimates obtained in the IBI (3.7 ± 0.15 mm year−1
) and NWS (2.12 ± 0.38 mm year−1
) regions were in the order (and in the uncertainty range) of those obtained in the literature [2
] from satellite altimetry data over the same regions and during the same period (1993–2016).
In the Baltic Sea, sea level trends can be strongly influenced by fresh water flux variations [97
]. A positive sea level rate was observed also in this basin (2.66 mm year−1
), where the halosteric component has a leading contribution compared to the thermosteric sea level trend. The largest uncertainty was observed in this region (>1 mm year−1
), which was in line with the findings of von Schukmann et al. [2
], who underlined the influence of salt inflow at the entrance of the basin on the mean sea level evolution in the Baltic Sea (Major Baltic Inflow; e.g., Hordoir et al. [98
]; Mohrholz et al. [99
]). Departures from the sea level trend estimates obtained from satellite altimetry [2
] can be explained through GIA-induced sea level rates typically applied to observation-based estimates, which can have a large contribution in the northern part of the basin [100
], and which are not represented in the OGCMs physics.
In the Mediterranean Sea, the sea level trend estimation (2.8 ± 0.26 mm year−1
) was consistent with the results of previous studies based on in-situ and remote-sensing observations [34
] when the resultant of the mass and thermosteric components was considered. This was not the case when the halosteric component was included, whose trends have high negative values that can lead to discrepancies when compared with the sea level trends obtained from observations (e.g., remote sensing), as underlined by Legeais et al. [34
In order to further investigate the sea-level trend variability in the European Seas, a merged high-resolution data-set was obtained interpolating each multi-resolution reanalysis over the spatial grid (1/12˚; 7 km) used by the CMEMS Global Monitoring and Forecasting Center global ocean operational analysis and forecast system (GLO-MFC; Lellouche et al. [102
]). During the merging, the sea level mass component in each (multi-resolution) reanalysis was reduced to a common reference considering the offset from a global mean, obtained as the temporal average of the CMEMS GLO-MFC fields over a 10-year period (2007–2017). A 10-year period was selected to consider a temporal window spanning both satellite altimetry [91
] and ARGO floats [103
shows the marked sea level (mass and steric components) trend spatial variability in the European Seas, as obtained from the merged dataset. Considering the steric contribution up to the 700-m depth, sea level trends during 1993 to 2016 ranged between −8 and +8 mm year−1
, showing how sea level trends at the regional scale can largely deviate from the global mean sea level trend (3.35 mm year−1
; e.g., Ablain et al. [9
]). This is in agreement with the findings of Legeais et al. [34
], who starting from satellite altimetry data, observed similar sea level trend ranges in the European Seas over the same period.
Considering the steric component up to the 300-m depth, positive homogeneous trends (2–3 mm year−1) were observed in the IBI and NWS regions, mostly due to thermosteric contributions (not shown). It is interesting to notice how sea level trends tended to increase (up to 8 mm year−1) in occurrence of the North Atlantic Drift and Azores Current when the steric component was considered up to a 700-m depth, showing the influence of the main features of the circulation in the upper ocean on the sea level trend spatial variability. Larger positive values, up to 6 mm year−1, were observed in the Baltic Sea considering the steric component (full depth), associated with large uncertainties (up to 3 mm year−1). In this basin, negative trends were also observed in the Gotland basin, due to halosteric contributions (not shown) in the deepest areas of the Baltic Sea.
In the Mediterranean Sea, sea level trends (up to 700-m depth) clearly showed the signature of the most prominent features of the ocean circulation in the basin (e.g., gyres and eddies; Pinardi et al. [104
]). Positive trends were found in the Adriatic Sea and Aegean Sea (up to 5 mm year−1
) and in the Levantine basin (up to 8 mm year−1
) where Pelops and Mersa-Matruh gyres occur. Smaller positive peaks were observed along the Lybian coasts, linked to the Syrte gyre. In agreement with the relevant studies acknowledged in this section, negative trends were observed in the Ionian Sea, as a consequence of an important change in the circulation observed in this basin since the beginning of the 1990s [105
], and south-east of Crete associated with the Ierapetra gyre.
Considering the steric height at full depth, sea level trends showed the contribution of the halosteric component in the Mediterranean Sea, which has high negative trends and that, as already mentioned considering multi-resolution reanalyses, can lead to unrealistic sea-level trend estimates. Results from the global reanalysis GLORYS12V1 performed at 1/12° degree of horizontal resolution [85
] (see also Table 1
) are shown in Figure S5
in order to provide a comparison for the merged regional reanalysis trends. Such maps indicate very large trends in the Baltic Sea, dominated by the halosteric contribution (not shown). On the contrary, sea level rise in the European north-western shelf area is attenuated compared to the regional reanalyses, and the Mediterranean Sea sea level fall, due again to the halosteric sea level, is also mitigated. The comparison confirms that diversity from reanalyses is mostly due to the freshwater budget representation. Considering as a reference the recent sea level trend estimates in the European Seas (1993–2016) obtained from satellite altimetry [2
], results from regional reanalyses appear more realistic in the Baltic Sea and less in the Mediterranean Sea in comparison with the global product.
Looking at the mean sea level trend, the results showed that during the period 1993–2016, the mean sea level in the European Seas rose, with rates that ranged between 1.6 and 2.6 mm year−1
(±0.3 mm year−1
), according to the depth ranges considered to integrate the steric contributions (Table 4
). In the upper ocean (up to 700 m), thermosteric sea level trends (positive) showed larger values than those due to the halosteric component (negative), while the opposite was observed considering steric contributions at full depth. The global reanalysis GLORYS12V1 (Table 5
) provides comparable estimates for the layer 0–300 m and 0–700 m, within the respective error bars. Below these layers, the halosteric contributions significantly differ between the merged and the global products, making the total sea level trend estimates larger in GLORYS12V1 by more than 1 mm year−1
in the 0–2000 m layer and the total column.
In the last part of this section, we focus on the European seas’ mean sea level variability and trend, considering steric contributions in the upper ocean (0–700 m). The top panel in Figure 11
shows the temporal evolution of total (red lines) and steric (black lines) sea level obtained from the merged reanalysis dataset during the period 1993–2016. In order to investigate the non-linear sea level variability and long-term trends of residual [101
] in the European Seas, empirical mode decompositions (EMDs) [108
] were used. EMD applied to sea level data decompose the signals in oscillatory modes (intrinsic mode functions, IMFs), representing different oceanic processes from the highest frequency to the lowest frequency oscillating mode. The remaining non-oscillating mode is the long-term trend of sea level residual [106
]. Considering 24 years of monthly data, EMD gave seven IMFs both for total and steric sea level signals. Total and steric sea level signals were significantly correlated (0.9) and had a similar temporal evolution and amplitude when the combination of IMFs that explains the low-frequency modes of oscillation (~10 years) was considered, underlining the contribution of the steric component to the sea level temporal evolution at these periodicities (not shown). EMD trends (Figure 11
, bottom panel) were also highly correlated (0.8), and both showed a non-linear trend with an increased slope in recent years. Interestingly, sea level residual trends were significantly correlated with those obtained considering the most prominent climate patterns in the North Atlantic (Figure 11
, dashed and dotted lines). The Atlantic Multidecadal Oscillation (AMO; e.g., Enfield et al. [111
]), which has its principal expression in the SST variability in the North Atlantic, showed a high positive correlation (0.9) with both sea level and steric height residuals. On the other hand, the North Atlantic Oscillation (NAO; e.g., Hurrell and Deser [112
]), which is mainly an atmospheric variation mode, showed a negative correlation (−0.6) with sea level residual, due to opposite temporal evolution patterns over the period 1993–2000. These results were in line with those observed by other authors in the Southern European Seas, starting from in-situ [113
] and remote-sensing [114
] sea-level estimates, and underlined the role of the North Atlantic climate as one of the main drivers of the long-term trends in the European Seas. Sea level residual trends from GLORYS12V1 (Figure S6
) match closely and are significantly correlated with the ones from the merged reanalysis product (with a correlation higher than 0.9), indicating the consistency between the two products in capturing the long-term sea level variability.