Multi‐Approach Analysis of Baroclinic Internal Tide Perturbation in the Ionian Sea Abyssal Layer (Mediterranean Sea)

Despite being widely recognized, the importance of deep layers thermohaline and mixing processes in the ocean circulation and variability is still poorly investigated, especially in the Mediterranean Sea. This limits understanding and parametrizing deep dynamics, which result in evident biases in the global circulation representation by observations and numerical ocean simulations. Having access to hydrological datasets, collected on a whole water column, we investigated the abyssal stratification and its variability of the Ionian Sea (Central Mediterranean). Applying multiple analyses, we found a tidal‐period oscillation and the resulting activation of mixing, pointing out that the combined effect of stratification, morphology, and tides has a key role in enhancing local diapycnal diffusivity in the deepest layers, being a mechanism that connects the whole water column with a compelling impact on the vertical transport of heat and tracers.

Multi-approach analysis of baroclinic internal tide perturbation in the Ionian Sea abyssal layer (Mediterranean Sea).Geophysical Research Letters, 50, e2023GL104311.https://doi.org/10.1029/2023GL104311 10.1029/2023GL104311 2 of 10 crucial role of currents and mixing in the turbulent boundary layers over sloping rough bathymetry as well as the interaction with the inertial band of the internal wave spectrum in the abyssal circulation (De Lavergne et al., 2022;Ferrari et al., 2016;Rubino et al., 2007;St. Laurent et al., 2001;Wunsch & Ferrari, 2004).The baroclinic tidal component has been recognized in the ocean as the most eligible process to drive and explain deep circulation, enhancing abyssal mixing (MacKinnon et al., 2017;St. Laurent et al., 2001;Wüest & Lorke, 2003;Wunsch & Ferrari, 2004).These effects on the ocean interior and their consequences on the circulation have yet to be sufficiently investigated, especially in the Mediterranean basin, due to the area's limited amplitude of the tides (Cushman-Roisin & Naimie, 2002;Millot & Taupier-Letage, 2005).The tidal effects in this basin show an evident example in the Messina Strait, where they generate internal solitary waves propagating at ∼1 m/s observed both by in situ observations and by remote sensing (Artale et al., 1990;Cavaliere et al., 2021).Moreover, numerical model simulations with explicit tidal forcing demonstrated that tides have a non-negligible effect on intermediate circulation and in deep water convection processes, but less evidence on the abyssal layer, both in the global ocean (Arbic, 2022;Arbic et al., 2018;Z. Li et al., 2015;Müller et al., 2012;Waterhouse et al., 2014) and in the Mediterranean region (Sannino et al., 2015(Sannino et al., , 2022;;Tsimplis et al., 1995).
The horizontal and vertical circulations in the Ionian Sea are driven by the combined effect of wind stress and thermohaline components, are strongly affected by the basin geometry, and are characterized by sub-mesoscale gyres and variable currents (Pinardi et al., 2015;Robinson et al., 1991).During summer, the Modified Atlantic Water (MAW), which spreads eastward from the Sicily Strait in the surface layer, is well-defined and distinct from the warmer and saltier Ionian surface water, while they are mixed throughout the rest of the year.The MAW overlies the Levantine Intermediate Water (LIW) in the layer between 200 and 800 m, while the abyssal layers of the Ionian Sea are usually occupied by the Eastern Mediterranean Deep Water (EMDW), which originates from the mixing of Atlantic Deep Water and deep waters of Adriatic origin (Astraldi et al., 2002;Bensi et al., 2013;Budillon et al., 2010;Pinardi et al., 2015;Theocharis et al., 1993;Wüst, 1961).
In this letter, we investigate how tidal forcing influences diffusion in the deepest layers in the Ionian Sea.Our analysis is based on the unusual approach used in performing Conductivity-Temperature-Depth (CTD) casts, consisting of recurring full-depth profiles with a short time lag, which are unusually taken on hydrological cruises, mostly because of time-demanding operations and the need of monitoring larger areas.We combined this data set with a normal mode decomposition analysis, which has been widely used for studying internal waves in the ocean (Cao et al., 2015;Garrett & Munk, 1979;Gill, 1982;Griffiths & Grimshaw, 2007;Pauthenet et al., 2019), but rarely for deep-sea analysis (Alford, 2003;Artale et al., 2018), and estimates of the diapycnal diffusivity.Even though they have never been considered sufficient to resolve this type of dynamics, here we explore repeated CTD profiles finding comforting results and shedding light on abyssal mixing processes.

CTD Data
The data we use in this work refer to near-full-depth CTD profiles carried out in the Ionian abyssal plain of the Eastern Mediterranean Sea at about 70 km from the Malta Escarpment, at the ER-0121 site (36° 18′ N, 16° 6′ E), from 1999 to 2003 (see Figure 1; Table 1).The temperature and salinity profiles (Figure 2) used have been post-processed following the common quality control standards and the Intergovernmental Oceanographic Commission (IOC) recommendations (Bushnell et al., 2019;IOC et al., 2010).

Normal Mode Decomposition in Q-G Approximation
To study the oscillations of the water column we performed a normal mode decomposition on the assumption of Quasi-Geostrophic (Q-G) dynamics on the vertical profiles of buoyancy frequency (N 2 ), which was calculated directly from in-situ data.Modal shapes depend strongly on the amount of filtering applied to the profile.We obtained the best performances for real data input with a Savinsky-Golay filter of order 1 and frame length 15.
The Q-G equation in a continuously stratified fluid on a beta plane is (Gill, 1982;Pedlosky, 1996): where q is the potential vorticity, p is pressure, ρ is density, and the Coriolis parameter is f = f 0 + β 0 y, with |β 0 y| ≪ f 0 .By assuming a solution of the form:  (   ) = Ã() (  +  −) , substitution in Equation 1 yields to a Sturm-Liouville (S-L) problem: where the separation constant is: To solve the S-L problem we assumed that the fluid is bounded below by a horizontal surface, and above by a free surface.Together with its boundary conditions, the S-L equation defines an eigenvalue problem where the eigenvalues are determined by the vertical profiles of N 2 , and the eigenvectors are the vertical modes corresponding to each eigenvalue.The discretization used here was a straightforward finite-difference technique, with uniform spacing between vertical levels of ⁓10 m.
The resulting baroclinic modes from the solution of Equation 2 are the internal modes of oscillation associated with the vertical changes in the stratification.The zero-crossing intercepts the layer oscillation (Figure 3): each mode behaves as a step change moving out from the initial discontinuity.The first baroclinic mode, which is the most energetic, represents the oscillatory behavior due to the strong maximum of N 2 that is often found near the ocean surface, since generally the first 200 m are the most stratified (LeBlond & Mysak, 1978).The next vertical shapes of the modes are the different ranges of the scale of the stratification variability, and the fifth mode is the first able to capture the baroclinic structure of the deepest layer (Artale et al., 2018).

Diffusivity Estimation Method
The vertical eddy diffusivity coefficient is generally estimated and parametrized from CTD and velocity measurements since there are few direct observations and microstructure profiler measurements have many underlying difficulties (Nakano & Yoshida, 2019).The most physically consistent and well-established methodology to give estimates of the coefficient (Osborn, 1980;Osborn & Cox, 1972;Toole et al., 1994), is the Osborn relation under steady-state condition in a conventional turbulence system: K = ΓϵN −2 where ϵ is dissipation rate of turbulent kinetic energy, and the mixing efficiency Γ is taken constant (Koseff et al., 2016;Kunze et al., 2006;Oakey, 1982;Osborn, 1980).This equation allows estimating vertical diffusivity directly from dissipation rate and buoyancy.Most of the mixing is bounded to the internal wave field, so that is possible to express the dissipation rate as the anomaly of the strain variances from the background state of the internal wave field represented by the Garrett and Munk (hereafter GM) model (Artale et al., 2018;Gregg et al., 2003;Kunze et al., 2006): where and R ω = 7 (3 for the GM spectrum), is the latitude dependence, and K 0 = 0.05 • 10 −4 m 2 /s.
The internal wave strain can be estimated directly from N 2 , following the strain-based parametrization (Artale et al., 2018;Kunze et al., 2006): where   2 is the mean profile, in our case the time average.The ξ Z of each z-segment have been windowed at both ends with a 10% Tukey windowing before transforming to obtain strain spectrum, from which the strain  10.1029/2023GL104311 5 of 10 variances were obtained by integrating over rolling segments of 320 m to account for non-homogeneity in the statistical distribution of the water column properties and to have a more robust representation of the fine-scale variability.Integration has been done in the internal wave range corresponding to wavelengths of 160 and 20 m, ceiling the strain variance to 0.1 if it is above a minimum for the GM integration corresponding to 25 m to avoid saturation, which would lead to overestimated values (A.E. Gargett, 1990;Gregg et al., 2003;Kunze et al., 2006;Pollmann, 2020).

Results and Discussion
The seasonal variability of the Ionian Sea heavily affects circulation patterns at the surface and intermediate layers, with stronger winter flows (Millot & Taupier-Letage, 2005;Pinardi et al., 2015;Robinson et al., 1991).This seasonal variability can be recognized in the temperature and salinity profiles in Figures 2a and 2b, despite the casts being performed from 50 to 100 m above the surface.CTD profiles include all seasons, with M08 and M17 having a similar behavior, corresponding to winter periods with colder mean temperature values (Θ ∼ 13.9°C) and saltier mean salinity values (S A ∼ 38.98 g kg −1 ) in the upper 500 m.In contrast, M18, measured at the end of April, has higher mean temperatures (Θ ∼ 14.3°C) and lower mean salinity values (S A ∼ 38.96 g kg −1 ) in the  2c).The deeper layers have a small seasonal variation and are occupied by the EMDW, below the LIW until 2,000 m depth, where there is a smaller peak in the diagram that we identified as Ionian Abyssal Water (IAW) between 2,000 and 3,000 m to the bottom (Figure 2c).The introduction of IAW is meant to account for the significant change in the thermohaline structure in the deepest layer over 5 years (Figure 2).This is in accordance with the observed adjustment of the area to the EMT: the Ionian abyssal layer state was perturbed by the entrainment of Cretan Deep Water (CDW), which formed a thick homogeneous layer of warmer and saltier waters that stabilized between 2003 and 2011 (Artale et al., 2018;Bensi et al., 2013;Manca et al., 2006;Rubino et al., 2016).
In the EMT-induced stratification both EMDW and CDW are competing as bottom water sources for the Ionian basin, and the differences among them are complex to classify (Rubino et al., 2016).
We investigate the effects of the presence of the IAW in the behavior of the water column through the fifth mode of oscillation of the normal mode decomposition (Figure 3).The three M08 casts (Figure 3a) were measured ∼12 hr apart from each other and show little variations of the zero-crossing depths, of the order of 10 m, which correspond to the uncertainty on the mode calculation.The four M17 casts (Figure 3b) were taken at different time spans.The zero-crossings of the profiles with a time span larger than 11 hr remain almost at the same level, while the last two casts have a zero-crossing difference with the previous casts of a tenth meter.The cast CTD 14 and CTD 17 of M17 have a zero-crossing difference between them of ∼14 m for the equivalent depth of ⁓2,600 m, and ∼38 m for the equivalent depth of ⁓2,000 m.The three M18 casts (Figure 3c) show an evident oscillation in the deep layer, with ⁓183 m of variation for the equivalent depth of ∼2,500 m, and ⁓275 m for the equivalent depth of ∼1,700 m.These were the casts measured within the smallest time span.The three M20 casts (Figure 3d) were measured ⁓19 and ⁓38 hr apart respectively, and show little zero-crossing variations, of the order of 10 m.The two M22 casts (Figure 3e) were measured after ⁓12 hr from one another.The deepest zero-crossing, at an equivalent depth of ⁓2,900 m, goes up ∼22 m, and the above zero-crossing, corresponding to an equivalent depth of ⁓2,250, goes up ∼55 m.Therefore, what can be observed in Figure 3 is that the deepest zero-crossings of casts with a time span between one another smaller than ∼12 hr have a periodic variation that is not present when a long time has passed.
To further investigate the observed tidal-period oscillation of the deep layers in the M18 casts (Figure 3c) we reconstructed the isopycnal variability and estimated the diffusivity coefficient.From the potential density profiles at 1,500-3,000 m of depth (Figure 4a) we can identify a temporal sequence of density overturns, significantly, in the second profile (M18 CTD 09).The diffusivities associated with the overturns show a peak near and above 10 −5 (m 2 s −1 ), which is within the common observations and the expected values to sustain diapycnal circulation (Munk, 1966;Munk & Wunsch, 1998).The sorted M18 profiles (Figure 4a) are useful to identify instabilities and consequently significant density differences in the original profile (A.Gargett & Garner, 2008).This allowed highlighting the time variations: the third profile (M18 CTD 13) tends to realign with the first one (M18 CTD 04), while the second one (M18 CTD 09) departs from this behavior at ∼2,000-2,350 m, confirming that the profile catches isopycnals moving at that time under the tidal period (dotted lines in Figure 4a).This signal can be interpreted as a pre-condition of overturning, which would be confirmed by velocity field information, unluckily not available for this area.The presence of a high-density zone under 2,500 m in the second profile indicates that something must have lifted it up.Since the profiling location is 71.8 km from the Malta Escarpment (Figure 1), this should be due to bathymetry interaction with internal tides generated on the steep Escarpment, guided by the well-defined stratification of the deep layers (Ferrari et al., 2016).We exclude locally other mesoscale processes because the time scales needed for composite perturbation patterns generally range from a few days to a few weeks (Rubino et al., 2012), and the M18 profiles were acquired over 12 hr, which is above the near-inertial frequency peak observed in the area which is ∼17 hr (Giambenedetti et al., 2023).
To sustain our reasoning on the time dependence of the oscillation, we evaluated the diffusion coefficient (Equation 3) using a time-averaged   2 profile for the strain calculation in Equation 4 (Figure 4b).Nearby the IAW heights K iw has values of O(10 −5 ), greater than the background turbulence generally observed, and consistent with the baroclinic tidal influence which is a second-order effect with respect to the local dynamics.This suggests an activation of mixing in the M18 CTD 09 profile, with K iw values not extremely far from the GM reference values, validating all the analyses made so far.The K iw values estimated without applying the saturation criteria were overestimated in depth (red line in Figure 4b): the energy transfer at fine-scale activates before GM in observed strain variance spectra, and to evaluate the behavior correctly with respect to the model is necessary to put a condition on the total amount of energy available (A. E. Gargett, 1990;Pollmann, 2020).This diffusivity enhancement in the abyssal layer, combined with the tidal periodicity, clearly indicates that the observed perturbation is the consequence of a baroclinic tide wave breaking on the near Malta Escarpment.Its impact on activating energy exchange/mixing is therefore non-negligible when integrated over time in energy budgets, having direct consequences on the redistribution of heat and tracers in the water column.

Conclusions
The concurrence of several factors, that is, the unusual sampling method used for the CTD casts, the presence of a dense deep water mass (the IAW), and the multi-method approach, made it possible to undoubtedly identify a tidal-period variability in the deepest layer of the water column and the consequent activation of mixing at finer scales.
Tidal influence at 3,000 m of depth is not so straightforward to observe as well as inertial signals, and what we found is that it has a non-negligible role in the vertical transport of energy.To date, there are still few direct observations of deep mixing.However, by combining different indirect methodologies we can get a realistic representation of what happens at depths, even at smaller scales, exploiting the existing resources at best.These observations are consistent with the generally accepted idea that energy redistribution through morphology interaction requires tidal processes to explain the observed dissipation rates (MacKinnon et al., 2017;Meredith & Garbato, 2021;Wunsch & Ferrari, 2004), meaning that it is a process that has a non-negligible role even in the Mediterranean Sea, where tides amplitude is way less than in the global oceans (Cushman-Roisin & Naimie, 2002;Millot & Taupier-Letage, 2005).
Our results can be useful for driving future research in the Mediterranean region, pointing out that deep stratification and tidal forcing should be included in the numerical simulations, and that there is a need for exploring areas where their effect is greater, by performing continuous and more comprehensive measurements.(Crameri, 2018).
Conductivity-Temperature-Depth (CTD) casts data collected in the Ionian Sea with an unorthodox methodology allowed resolving tidal scale • The temperature and salinity diagram depicted typical water masses for the Ionian area including a dense abyssal water mass • The analyses showed a periodic pulsation and an activation of mixing in the abyssal layer due to the baroclinic internal tide Correspondence to:

Figure 2 .
Figure 2. Measured (a) conservative temperature (Θ) and (b) absolute salinity (S A ) profiles; (c) S A − Θ diagram.Water masses are indicated by their acronym.On the left, color legend according to the names and periods of the casts.On the bottom right side of the panel a zoom of the deepest zone corresponding to the Ionian Abyssal Water.Colormap by Crameri (Crameri, 2018).

Figure 3 .
Figure 3. Fifth modes of the normal mode decomposition for the casts performed during (a) December 1999, (b) March 2002, (c) April 2002, (d) August 2002, and (e) July 2003.Circles identify the zero-crossings, and for each of them are reported the corresponding equivalent depths.Black dashed lines indicate the zero line.Between the panels is reported approximately the time span between one cast and another of the same acquisition campaign.

Figure 4 .
Figure 4. (a) Vertical profiles of potential density (σ 0 ): dashed lines are the sorted profiles, gray curves and colored right panel show the contours of isopycnal levels; (b) diffusion coefficient (K iw ) evaluated for the M18 profiles, with boxplots performed on 320 m separated z-segments showing the uncertainty associated with the choice of segment lengths and position.Solid black line indicates the GM value, and in red is shown the K iw estimation without the saturation criteria.Colormap by Crameri(Crameri, 2018).

Table 1
Summary of the Conductivity-Temperature-Depth Casts Used in This Work, Performed at the ER-0121 Location