Technical note: tidal motions in the deep Mediterranean

van Haren, Hans

doi:10.5194/egusphere-2026-188

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https://doi.org/10.5194/egusphere-2026-188

Preprints

29 Jan 2026

| 29 Jan 2026

Technical note: tidal motions in the deep Mediterranean

Hans van Haren

Abstract. The Mediterranean Sea is known for its limited tidal motions. For example, surface barotropic tidal elevations have an amplitude of 0.1 m in the Northwestern Mediterranean. Nevertheless, these small tides are noticeable in temperature records at the 2500-m deep seafloor, but only under near-homogeneous conditions when buoyancy frequency N < f, the inertial frequency. After transfer of pressure to temperature units via the local adiabatic lapse rate, the observed internal-wave temperature signals may thus be corrected for 1.5x10^-5-°C amplitude semidiurnal barotropic tides. The remaining baroclinic tides are embedded in the broad and featureless inertio-gravity wave band, with some energy enhancement near its boundaries, also under tenfold-larger energetic stratified water conditions.

Received: 13 Jan 2026 – Discussion started: 29 Jan 2026

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Hans van Haren

Status: final response (author comments only)

EC1:
'Comment on egusphere-2026-188', Bernadette Sloyan, 02 Mar 2026

The comment was uploaded in the form of a supplement: https://egusphere.copernicus.org/preprints/2026/egusphere-2026-188/egusphere-2026-188-EC1-supplement.pdf

Citation: https://doi.org/10.5194/egusphere-2026-188-EC1
- AC1: 'Reply on EC1', Hans van Haren, 03 Mar 2026
  
  >>>I thank the editor for the time to comment the manuscript. My replies are behind >>>
  Review of manuscript
  Technical note: tidal motions in the deep Mediterranean by Hans van Haren
  
  The author analyses low tidal motions in the Mediterranean Sea. However, the author
  distinguishes small tides in the temperature records at a depth of 2500-m near the bottom. This
  happens only when the environmental conditions are near-homogeneous and the buoyancy
  frequency N is lower than the inertial frequency. The observations were performed with a set of
  almost 3000 precise temperature sensors. The author performs a transition of pressure to
  temperature units using the local adiabatic lapse rate like the atmospheric one. The author detects
  low amplitude semidiurnal barotropic tides.
  I generally like the paper and recommend publication.
  >>>Thank you for the appreciation.
  
  Two remarks.
  (1) It would be helpful to give a figure with a scheme of the experiment.
  >>>A scheme of the experimental set-up is now given in the new Appendix A.
  
  (2) A question to Fig. 1a. What if uncorrected temperature. Is this in situ temperature. And
  theta is it potential temperature. Please explain. Low temperature increase with depth can be
  found at larger depths, say 5000 m. In the case of 2500 m in the Mediterranean this requires
  explanation.
  >>>Yes, the ‘uncorrected’ temperature is the in situ temperature; with uncorrected ‘uncorrected for compression’ was meant. Conservative Temperature (upper case theta; TEOS-10) has indeed the same dynamical properties as potential temperature (lower case theta). Yes, a profile as plotted from 2000-2500 m in the Mediterranean has resemblance with much deeper profiles in the ocean. Good point. It may have to do with the lack of tides in the Mediterranean, and thus reduced turbulent mixing via internal wave breaking (by about a factor of 2 compared to the ocean; Wunsch and Ferrari, 2004). Also, the Mediterranean sea is an almost closed basin, nearly without connections to other basins whereby propagation from far away sources is likely reduced, in contrast with oceans. This is better explained in the text and figure caption.
  
  Citation: https://doi.org/10.5194/egusphere-2026-188-AC1
RC1:
'Comment on egusphere-2026-188', Anonymous Referee #1, 12 May 2026

This technical note presents observations from high‑resolution temperature measurements (approximately 2,900 sensors) together with data from three current meters deployed in the deep Mediterranean Sea. The instruments were located within the bottom 125 m of the water column at a total water depth of about 2,500 m. Different aspects of this extensive dataset have been reported in several publications by the same author, either submitted or currently in press. The present note focuses specifically on “tidal motions,” contrasting selected periods of weak stratification (referred to as “stratified water,” SW, in the manuscript) with near‑homogeneous (NH) conditions.
One of the main findings is that under SW conditions, the spectral variance of temperature is enhanced across the internal gravity wave (IGW) band. This enhancement is broadly distributed, without distinct spectral features, and includes a peak at frequencies lower than omega_min (the minimum frequency bound for internal gravity waves). This behavior appears inconsistent with the local stratification and instead suggests influence from a relatively weaker stratification, closer to that observed under NH conditions.
Overall, the observations and the topic are interesting, though their broader applicability may be somewhat limited. The manuscript could be suitable for publication after major revisions. In its current form, I find the quality of the presentation, both in terms of structure and figures (see specific comments below), to be relatively weak, and it would benefit from substantial improvement prior to publication. The main findings and conclusions could also be strengthened through a more detailed and systematic analysis of this rich dataset.
It is not entirely clear why correcting for the tidal signal in temperature is emphasized as a central issue, given that the signal appears to be near the noise level or measurement accuracy of most instruments (on the order of 10^−5 degC). Nevertheless, the abstract and the opening sections of the discussion and conclusions elevate this correction to a primary result. In my view, it would be more compelling to focus on contrasting the results obtained under NH and SW conditions and to highlight these differences more clearly in the abstract.
Since the manuscript claims to address tidal “motions,” it would also be valuable to integrate the current‑meter observations more fully into the analysis, using physical units. Is the reported variability in current amplitudes (currently shown in arbitrary units) significant relative to instrument noise?
Finally, a more systematic comparison between NH and SW conditions could be pursued. For example, the full time series could be subsampled into NH and SW segments, and composite spectra could be constructed for each regime. Such an approach may help to strengthen the conclusions drawn from Figure 6, particularly regarding the extension of omega_min.
Li 147–154 / Figure 3 (similarly Figure 5): The presentation of the data in these figures could be improved. The author might consider additionally showing the difference between T (panel a) and Tfilt (panel b), or alternatively replacing panel b with T−Tfilt . In its current form, the paragraph discussing turbulent convection and the apparent intensification near the seafloor is difficult to follow when referring to Figure 3. This issue becomes even more pronounced when the manuscript later discusses differences in processes between the two selected periods using Figures 3 and 5.
Li 182–186: The statements made in this section are not adequately supported by the results presented and should either be removed or more clearly substantiated. For example, the claim that “slantwise convection leads to a widening of the IGW range” is not clearly demonstrated in the analysis. Similarly, the statement that the “associated turbulence is elevated by one order of magnitude over open‑ocean values” is not supported by the figures or quantitative results shown. The author concludes by noting that this is a subject for future study.
DATA availability:
I find the data availability statement unsatisfactory. The temperature sensor data in physical units are clearly available to the author and should be made publicly accessible in accordance with journal data‑sharing expectations. I also note that in the related GRL paper, reference is made to the T-sensor data, provided as supplementary material to GRL Fig 2-4:
van Haren, H., & KM3NeT Collaboration (2025b). Supplementary materials to: Whipped and mixed warm clouds in the deep sea, figures 2-4. Mendeley Data, Version 2, [Dataset], https://doi.org/10.17632/jprhwpjh6y.1.
These are: “ASCII files of time series of moored temperature data and turbulence dissipation rate from Figure 2. Matlab files of 45-line temperature data from Figures 3 and 4”
If this dataset already covers the records used in the present submission, the author could simply refer to it explicitly. If not, a similar effort should be made to produce and make available the dataset used in this study.
Minor specifics:
Li 44: A citation would be helpful to support this statement (“..can be traced to the seafloor in weaker form”)
Li 47: trapping is not required for near-inertial motions to propagate as internal waves into the deep sea
Li 51-52: Here the link between tides to internal tides/waves and vertical mixing is not introduced. Some description from lines 56-60 could be moved upward.
Li 54: Could you reword “a sample”? E.g., “a test basin” or “a laboratory”?
Li 60-61: we shouldn’t forget “topography” for generating internal tides
Li 62- freely propagating linear internal wave bounds [f, N] should be mentioned somewhere here before the special cases of the deep Med Sea.
Li 68. This “is” because
Li 81: define the vertical component of relative vorticity (and specify that this is the vertical component)
Li 83: it would widen or shrink depending on the sign of relative vorticity
Li 95: it is not clear what is meant by “equally distributed over the mooring array”
Li 97: What is the height (above seafloor) of the CMs and the bottommost T-sensor?
Li 108-110: Some methods need more explanation: Please elaborate on “Instrumental bias was removed via vertical smoothing and via low-pass filtering”…Also please explain ”reference was made to…” Is this for offset correction / inter-calibration of sensors?
Li 130-131: please support this statement about the two deep-sea conditions with a reference.
Li 140: Why using 44 but not 45 lines?
Li 146: “pressure-data filtered” is not explained yet. It should be explained, perhaps in line 134.
Li 207: flow spectrum does NOT show a peak in 0.5f.
Fig 1: In panel c, days of the other two cases shown in figures 4 and 6 should also be marked.
Error bars in the spectra: They should be better placed and made better visible.
Figs 3 and 4: panel b is nearly identical to panel a and it is very difficult to interpret and join the discussing the author aims at.

Citation: https://doi.org/10.5194/egusphere-2026-188-RC1
- AC3: 'Reply on RC1', Hans van Haren, 14 May 2026
  
  >>>I thank the editor for the time to comment the manuscript. My replies are behind >>>
  
  This technical note presents observations from high‑resolution temperature measurements (approximately 2,900 sensors) together with data from three current meters deployed in the deep Mediterranean Sea. The instruments were located within the bottom 125 m of the water column at a total water depth of about 2,500 m. Different aspects of this extensive dataset have been reported in several publications by the same author, either submitted or currently in press. The present note focuses specifically on “tidal motions,” contrasting selected periods of weak stratification (referred to as “stratified water,” SW, in the manuscript) with near‑homogeneous (NH) conditions.
  
  One of the main findings is that under SW conditions, the spectral variance of temperature is enhanced across the internal gravity wave (IGW) band. This enhancement is broadly distributed, without distinct spectral features, and includes a peak at frequencies lower than omega_min (the minimum frequency bound for internal gravity waves). This behavior appears inconsistent with the local stratification and instead suggests influence from a relatively weaker stratification, closer to that observed under NH conditions.
  
  Overall, the observations and the topic are interesting, though their broader applicability may be somewhat limited. The manuscript could be suitable for publication after major revisions. In its current form, I find the quality of the presentation, both in terms of structure and figures (see specific comments below), to be relatively weak, and it would benefit from substantial improvement prior to publication. The main findings and conclusions could also be strengthened through a more detailed and systematic analysis of this rich dataset.
  >>>Thank you for the appreciation. The applicability is for other deep-sea areas where stratification is weak.
  
  It is not entirely clear why correcting for the tidal signal in temperature is emphasized as a central issue, given that the signal appears to be near the noise level or measurement accuracy of most instruments (on the order of 10^−5 degC). Nevertheless, the abstract and the opening sections of the discussion and conclusions elevate this correction to a primary result. In my view, it would be more compelling to focus on contrasting the results obtained under NH and SW conditions and to highlight these differences more clearly in the abstract.
  >>>I thank the reviewer for the interest in IGW-band broadening. However, the topic of this manuscript is indeed on tidal motions, while the contrast between NH and SW conditions is more extensively treated elsewhere (under submission). Here it is slightly strengthened now following the suggestion by the reviewer, including a new Fig. 7 displaying a second SW period, but the contrasting NH and SW is not the main topic of this technical note.
  
  Since the manuscript claims to address tidal “motions,” it would also be valuable to integrate the current‑meter observations more fully into the analysis, using physical units. Is the reported variability in current amplitudes (currently shown in arbitrary units) significant relative to instrument noise?
  >>>These were given in physical units, with typical overall amplitudes of 0.05 m/s (now with reference to van Haren et al. 2026). From the spectra and spectral slopes one can infer that the waterflow measurements are exceeding white noise for frequencies < 4 cpd. This is better indicated now.
  
  Finally, a more systematic comparison between NH and SW conditions could be pursued. For example, the full time series could be subsampled into NH and SW segments, and composite spectra could be constructed for each regime. Such an approach may help to strengthen the conclusions drawn from Figure 6, particularly regarding the extension of omega_min.
  >>>Yes that could be done, but it does not provide much more information that can be concluded from the presented spectra, compare the two NH spectra for instance and now also the two SW spectra with new Fig. 7, and it is not the main topic here, I am sorry.
  
  Li 147–154 / Figure 3 (similarly Figure 5): The presentation of the data in these figures could be improved. The author might consider additionally showing the difference between T (panel a) and Tfilt (panel b), or alternatively replacing panel b with T−Tfilt . In its current form, the paragraph discussing turbulent convection and the apparent intensification near the seafloor is difficult to follow when referring to Figure 3. This issue becomes even more pronounced when the manuscript later discusses differences in processes between the two selected periods using Figures 3 and 5.
  >>>I agree that the differences between the a and b panels in these figures are minimal, which is de facto the key result: Barotropic tides do not dominate IGW. Apologies, but ‘pressure-data filtering’ is from barotropic motions, and thus identical for all vertical levels. The suggested T-Tfilt will in fact display the pressure record, transferred to temperature variations, from Figs 2a and 4a. Thus, the figures are unchanged and a clarifying remark is made.
  
  Li 182–186: The statements made in this section are not adequately supported by the results presented and should either be removed or more clearly substantiated. For example, the claim that “slantwise convection leads to a widening of the IGW range” is not clearly demonstrated in the analysis. Similarly, the statement that the “associated turbulence is elevated by one order of magnitude over open‑ocean values” is not supported by the figures or quantitative results shown. The author concludes by noting that this is a subject for future study.
  >>>This sub-section is modified now for clarification, and the further study will be reported elsewhere (under submission). The modified paragraph now reads: ‘Slantwise convection under SW conditions (van Haren et al., 2026) may lead to a widening of the IGW range compared to that inferred from vertical stratification, because stratification is close to homogenous in the slanted direction. Following the present deep Mediterranean observations, apparently the IGW-widening occurs with some enhancements near its bounds including baroclinic semidiurnal internal wave motions. As the convection is governed by highly nonlinear processes, the associated relatively strong turbulence that is elevated by one order of magnitude over open-ocean values (van Haren et al., 2026) seems to be important for the replenishment of nutrients in the deep Mediterranean. The sub-inertial extent of the IGW-band may include sub-mesoscale eddies, of which the precise interaction with IGW is unknown. This is subject of future study.’
  
  DATA availability:
  I find the data availability statement unsatisfactory. The temperature sensor data in physical units are clearly available to the author and should be made publicly accessible in accordance with journal data‑sharing expectations. I also note that in the related GRL paper, reference is made to the T-sensor data, provided as supplementary material to GRL Fig 2-4:
  van Haren, H., & KM3NeT Collaboration (2025b). Supplementary materials to: Whipped and mixed warm clouds in the deep sea, figures 2-4. Mendeley Data, Version 2, [Dataset], https://doi.org/10.17632/jprhwpjh6y.1.
  These are: “ASCII files of time series of moored temperature data and turbulence dissipation rate from Figure 2. Matlab files of 45-line temperature data from Figures 3 and 4”
  If this dataset already covers the records used in the present submission, the author could simply refer to it explicitly. If not, a similar effort should be made to produce and make available the dataset used in this study.
  >>>Processed temperature are made available after acceptance of the manuscript for publication.
  
  Minor specifics:
  Li 44: A citation would be helpful to support this statement (“..can be traced to the seafloor in weaker form”)
  >>>Citation added (Albérola et al., 1995)
  
  Li 47: trapping is not required for near-inertial motions to propagate as internal waves into the deep sea
  >>>True, hence the ‘e.g.’ which is now changed into ‘also’.
  
  Li 51-52: Here the link between tides to internal tides/waves and vertical mixing is not introduced. Some description from lines 56-60 could be moved upward.
  >>>OK, paragraph moved up a few lines, as suggested.
  
  Li 54: Could you reword “a sample”? E.g., “a test basin” or “a laboratory”?
  >>>I chose ‘test basin’.
  
  Li 60-61: we shouldn’t forget “topography” for generating internal tides
  >>>’seafloor topography’ added now.
  
  Li 62- freely propagating linear internal wave bounds [f, N] should be mentioned somewhere here before the special cases of the deep Med Sea.
  >>>Modified now as suggested, including ‘[f, N] of freely propagating internal waves under open-ocean conditions of N >> f’
  
  Li 68. This “is” because
  >>>Yes, thank you.
  
  Li 81: define the vertical component of relative vorticity (and specify that this is the vertical component)
  >>>Done.
  
  Li 83: it would widen or shrink depending on the sign of relative vorticity
  >>>Sorry no, it widens the near-inertial band, as f_eff = 0.8f<omega<1.2f, instead of f only (for zeta=0).
  
  Li 95: it is not clear what is meant by “equally distributed over the mooring array”
  >>>Now ‘equally’ modified to ‘about 50 m over’. This is also made visible in new figure A1.
  
  Li 97: What is the height (above seafloor) of the CMs and the bottommost T-sensor?
  >>>The vertical lines are 125 m tall and the cable grid is on average at 1.5+/-0.4 m from the seafloor, as indicated in the new Appendix now.. The CMs are sampling at about h = 126 m above seafloor. As the CMs were pointing downward they were close to the same vertical position at the upper T-sensor. This is better indicated now.
  
  Li 108-110: Some methods need more explanation: Please elaborate on “Instrumental bias was removed via vertical smoothing and via low-pass filtering”…Also please explain ”reference was made to…” Is this for offset correction / inter-calibration of sensors?
  >>>The method of smoothing is extensively described in van Haren and Gostiaux, JMR2012 and van Haren, Sensors2018, cited. The filter cut-off wavelengths are indicated now, as well as the reference periods. Yes, for inter-calibration and bias-removal of the sensors, as absolute accuracy is not achievable with these sensors.
  
  Li 130-131: please support this statement about the two deep-sea conditions with a reference.
  >>>Citation added now (van Haren et al., GRL2026).
  
  Li 140: Why using 44 but not 45 lines?
  >>>One T-sensor was not working properly, as indicated in the caption of Fig. 2 now.
  
  Li 146: “pressure-data filtered” is not explained yet. It should be explained, perhaps in line 134.
  >>>This is explained now immediately after Eq. (2).
  
  Li 207: flow spectrum does NOT show a peak in 0.5f.
  >>>Indeed, more like a bulge elevation of variance. This is weakened now.
  
  Fig 1: In panel c, days of the other two cases shown in figures 4 and 6 should also be marked.
  >>>Indicated now.
  
  Error bars in the spectra: They should be better placed and made better visible.
  >>>Done as suggested.
  
  Figs 3 and 4: panel b is nearly identical to panel a and it is very difficult to interpret and join the discussing the author aims at.
  >>>Assuming the reviewer refers to Figs 3 and 5: Yes the corrections are small, which indicates the weak effect of tides. It was quite clearly explained in old l.147-154: the barotropic M2 is embedded in almost white noise, during a period when convection turbulence is dominant.
  
  Citation: https://doi.org/10.5194/egusphere-2026-188-AC3
EC2:
'Comment on egusphere-2026-188', Bernadette Sloyan, 14 May 2026

There are now two anonymous reviews of this manuscript.

Please consider these comments and prepare a revised manuscript and reply to reviewer's comments.

Citation: https://doi.org/10.5194/egusphere-2026-188-EC2
- AC2: 'Reply on EC2', Hans van Haren, 14 May 2026
  
  I am working on it.
  
  Citation: https://doi.org/10.5194/egusphere-2026-188-AC2

Hans van Haren

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Short summary

The Mediterranean Sea is known for its limited tidal motions. For example, surface barotropic tidal elevations have an amplitude of 0.1 m in the Northwestern Mediterranean. As is demonstrated in this paper, such small tides are noticeable in temperature records at the 2500-m deep seafloor, but only under near-homogeneous conditions. After correcting for pressure effects, the observed internal-wave temperature signals may thus be corrected for 1.5x10^-5-°C amplitude semidiurnal barotropic tides.


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Technical note: tidal motions in the deep Mediterranean

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