The potential recording of North Ionian Gyre’s reversals as a decadal signal in sea level during the instrumental period

In recent decades, the north Ionian Sea, central Mediterranean Sea, has witnessed shifts in surface current circulation from cyclonic to anticyclonic and vice versa at the quasi-decadal scale, a phenomenon termed the North Ionian Gyre (NIG) reversal. This process impacts parameters such as sea level by altering thermohaline properties and redistributing water masses at the sub-basin scale. Previous studies have shown that during anticyclonic (cyclonic) phases, the Ionian sea-level trend is falling (rising), the opposite of what is observed in other Mediterranean sub-basins. Assuming that sea level records reversals, this study employed signal decomposition to analyze satellite altimetry data and tide gauge observations across the region, some dating back to the 1900s. A distinct quasi-decadal periodicity emerges as the second dominant oscillatory mode from all independent observations, aligning its peaks and troughs (i.e., changes in sea-level trend) with known NIG reversals and associated changes in the state of North Ionian vorticity. Furthermore, this mode from altimetry data clearly depicts the spatial variability of sea level attributed to the opposite NIG states. This periodicity appears coherent among different sub-basins within the domain, especially in the eastern Mediterranean, with a shared generalized out of phase and weakening occurred from the 1930s to the 1950s. This study presents a century-scale reconstruction of NIG reversals, contributing to the understanding of this phenomenon prior to 1987 using direct observations from sea-level data.


Interannual and multi-decadal sea-level variability
The first IMFs obtained from the decomposition of both TGs and SA data primarily capture the interannual sea-level variability (Fig. S1).For this mode of variability, the regional and sub-basin ensemble mean of the TGs shows a dominant periodicity range between 3 and 4.3 years, with an average of 3.8 ± 1.4 years.The temporal evolution of this signal is notably variable, as expected.
The same observation can be made for the first IMF extracted from the SA (regional average periodicity of 3.7 ± 1.2 years), where the spatial variability appears large and chaotic (Fig. S2).
Consequently, aligning modes derived from the first IMFs, from both TGs and SA, with NIG reversal episodes is neither straightforward nor feasible in this context.Hence, this study focuses on longer periodicities of sea level, and the reader is referred to e.g.Mohamed et al. (2019), Menna et al. (2022) for a discussion on interannual sea-level variability.
The multi-decadal fluctuation (see IMF 3 in Fig. S6) in signals can only be observed within long TG datasets, e.g., more than 50/60 years of observations, and where smooth non-linearities in VLMs are not overly influential.Generally, a fluctuation within the range of 21-24 years has been detected, varying across the different sub-basins.In shorter time series, this signal is not detectable by the EEMD, which essentially forms an IMF representing the non-linear trend at any specific TG.Indeed, analyzing the multi-decadal (third IMF) or non-linear variability (second to last IMF) of sea level, as well as the residual linear variability (i.e., the last IMF), requires an in-depth examination.This analysis should focus on removing the influence of natural and anthropogenicinduced VLMs and accounting for the influence of mass-driven sea-level change.As a result, multi-decadal signals and residuals are not examined or discussed further in this study.The cyan and orange sectors, computed using the same approach as in Fig. 2 from the main text, are intended to symbolize the periods of cyclonic and anticyclonic patterns in the Ionian circulation.However, this reconstruction is shown to be not feasible for the IMF1 sea level.

Figure S2.
Annual mean value of sea level, associated with the first IMF, extracted from the signal decomposition using EEMD at each altimetry grid point.

The sea-surface salinity
Existing literature (refer to the main text for citations) establishes that NIG states, both cyclonic and anticyclonic, induce changes in water mass redistribution and thermohaline properties throughout the basin and its sub-basins.Fluctuations in seawater salinity in the Adriatic Sea have been observed periodically since the early 1900s, and recent studies attribute these changes to the effects of NIG reversal episodes.In this study, the observations align closely with the reconstructed reversals in the Adriatic.Specifically, the observed increases in water salinity (historically termed as 'ingressions') coincide with the commencement of cyclonic phases.As identified in previous studies, during the cyclonic state, the relatively fresher Atlantic Water is diverted directly towards the Levantine Basin after entering the Sicily Channel.This contrasts with its formerly northeastward deflection towards the Adriatic during anticyclonic phases.This results in a relative salinization of the sub-basin and consequently, a change in the halosteric component of sea level.This salinization leads to increased density, causing a localized sea level drop.This effect is further amplified by the reduced contribution of Atlantic Water mass, which is predominantly redistributed to the Levantine during cyclonic phases.Fig. S3 illustrates the variability of seasurface salinity across the Adriatic Sea from 1987 to 2020.The maps clearly depict a fluctuation in this parameter, with salinity decreasing during anticyclonic phases (1991-1998; 2006-2010; 2017-2020) and increasing during cyclonic phases (1987-1991; 1998-2006; 2010-2017).

The North Atlantic Oscillation
The Mediterranean quasi-decadal oscillation achieved from the signal decomposition on TGs has been compared (Fig. S4) with the principal-component (PC)-based indices of the North Atlantic Oscillation (NAO).The NAO PC-based indices serve to gauge the NAO all year round, following the seasonal shifts of the Icelandic low and the Azores high, over the sector 20°-80°N, 90°W-40°E.
To reduce noise and enhance comparability, the annual PC-based NAO indices were decomposed (dNAO) using the same approach as for TGs and SA data (refer to the main text).The processing results yielded both the second and third IMF with quasi-decadal periodicities (approximately 8 and 14 years, respectively).Consequently, these two modes were combined for comparison with the Mediterranean-averaged second IMF.In terms of visualization, the Mediterranean signal aligns well with the inverted dNAO, reflecting the well-known opposite sea level response to dNAO changes.Intriguingly, the signals are in phase during the 1930s-1950s period, with both experiencing a decrease in amplitude.In numerical terms, after accounting for the effective number of samples to remove the autocorrelation, the Kendall tau correlation analysis, based on 10,000 bootstrap repetitions, yields an average tau value of -0.27 and an average p-value of 0.03.This advises that the two signals under analysis are likely significantly correlated.Indeed, the crosscorrelation analysis between the two signals reveals significant negative correlations at lags -1 and -2.This suggests that, on a decadal scale, sea level negatively responds to dNAO changes within a period of just 1 or 2 years.Moreover, in terms of linear regression, the magnitude of this variability can be quantified as approximately -0.7 cm of sea level per dNAO unit.Finally, it should be noted that the nature of this correlation must be interpreted with caution.Dedicated studies, involving thorough analyses, are essential to accurately quantify and understand this correlation, as well as its potential link with NIG reversal occurrences.

The sea-level components
The sea-level variability observed at a specific location represents the change in a particular component (or multiple components simultaneously) within what is termed the total sea level ().The  term is essentially the sum of all components, also considered drivers: where  represents the variability induced by changes in temperature and salinity (steric term) and mass redistribution through circulation (dynamic term), ηGRD the effect of contemporary mass exchanges between the Antarctic and Greenland ice sheets, glaciers, water stored on land and the Ocean,  the glacial isostatic adjustment, i.e., the ongoing movement of land once loaded by ice-age glaciers,  the contribution of all vertical movements at a specific location induced by local tectonics, sediment compaction and underground fluids exploitation (this term does not affect altimetry), and  is the inverse barometer effect which accounts for the contribution of atmospheric loading on sea level.It is recognized in literature that shifts in the NIG state result in changes to both thermohaline properties and water mass distribution, essentially altering the sterodynamic component.Given that this study centers on the sea-level variability prompted by NIG reversal episodes, it is crucial to filter out all sea-level components except for the sterodynamic component.As described in the main text, the datasets used in this study have been corrected for both IB and GIA terms.Furthermore, it is assumed that, although VLMs on tide gauges can be non-linear in time, they do not affect oscillatory modes; thus, the influence of this component is considered negligible.The effect induced by GRD is therefore explored, finding that, in this case as well, the oscillatory modes are very minimally impacted with NRMSE values ranging from 2.6% to 8.8%, which vary across subbasins (Fig. S5).This component, similar to the VLM, strongly affects only the residuals, as observed in the full set of Trieste IMFs, for example (see Fig. S6).Thus, the GRD component can also be considered negligible when examining oscillatory modes.In this context, the signal being analyzed can be attributed solely to variations related to the sterodynamic component.Values on the y-axis represent sea-level changes in mm.

Observations of quasi-decadal sea-level changes within the Ionian Sea
As stated in the main text, the reconstructed signal for the second mode in the Ionian Sea level, averaged from five TGs (Fig. S7), cannot be considered reliable as this sub-basin is underrepresented by in-situ data and represents the epicenter of the reversal.The latter, essentially occurring in the open ocean, is not adequately captured by TGs, which are attached to the land, but they are still able to provide some interesting information.Since the reversal signal might also propagate towards certain land areas (see Fig. 3 in the main text), its influence on the nearest TGs cannot be excluded.If the quasi-decadal signal, decomposed from the sterodynamic sea level, were not related to reversals, a similar signal among TGs within the basin and with the adjacent subbasin would be expected.Conversely, as shown in Fig. S7, this signal is often out of phase among the five TGs available, also providing indications of opposite inflections in sea level, both in comparison to signals from other stations and especially to signals from TGs in adjacent sub-basins (Fig. 2 in the main text).This can be explained in terms of consequences related to the breathing oscillation pattern, linked to NIG reversals, which might actually influence some coastal areas around the north Ionian Sea by propagating towards the land and also moving in time and space.This consideration can strengthen the hypothesis of a direct link between the quasi-decadal oscillatory signal hidden in the Mediterranean sea level and NIG reversal occurrences.Additionally, it should also be considered that the averaged interannual sea-level signal over the Ionian, despite representing a general chaotic pattern, is much more coherent in time among the five stations (Fig. S1).Indeed, the interannual signal does not seem to be related to NIG reversals.

Figure S1 .
Figure S1.The ensemble mean of the first IMF at the sub-basin scale, computed from TGs, is represented by the solid black line, accompanied by the ± 1σ range (shaded in gray).The red hatched lines depict the basin average mean of the first IMF derived from the altimetry data, whereas the vertical black hatched lines are the same as those used in Fig.2(see the main text).The cyan and orange sectors, computed using the same approach as in Fig.2from the main text, are intended to symbolize the periods of cyclonic and anticyclonic patterns in the Ionian circulation.However, this reconstruction is shown to be not feasible for the IMF1 sea level.

Fig. S3 .
Fig. S3.Sea-surface salinity, corresponding to a depth of 10 meters, across the Adriatic Sea for the years 1987-2020.The colorbar is centered around the average Mediterranean salinity value of 38.26 psu for this period.The data used to produce this figure was retrieved from the Mediterranean Sea Physics Reanalysis, available on the Copernicus Marine Service website (https://doi.org/10.25423/CMCC/MEDSEA_MULTIYEAR_PHY_006_004_E3R1).

Fig. S5 .Fig. S6 .
Fig. S5.The ensemble mean of the second IMF sea level at the sub-basin scale, along with its related 1σ values (shaded areas), is shown both corrected (red hatched line) and non-corrected (black solid line) for GRD.The difference between the corrected and non-corrected time series is expressed in terms of NRMSE x 100, as indicated in parentheses.

Fig. S7 .
Fig. S7.The second IMF signal extracted from the SA and five TGs considered for the Ionian Sea.The vertical black hatched lines represent the occurrence of known reversals from the literature (see the main text).

Table S1 .
A detailed list of the tide gauges selected for this work.