the Creative Commons Attribution 4.0 License.
the Creative Commons Attribution 4.0 License.
Semi-analytical approach to study the role of abyssal stratification in the propagation of potential vorticity in a four-layer ocean basin
Abstract. Observations of abyssal variability performed in the Ionian Sea (Mediterranean Sea) revealed the presence of a dense stable abyssal layer, whose thermohaline and dynamical properties changed drastically over a decade. Building upon these available observations, we aim to investigate the role that stratification can have on the propagation of vorticity throughout the water column to the abyss, and in turn on the redistribution of the energy stored in the deep sea, with a set of stationary states. A quasi-geostrophic equation with four coupled layers, a free surface, and a mathematical artifice for parametrizing decadal time evolution has been considered, proving that the relative layer thicknesses and the density difference among the layers are the two critical factors that determine the dynamical characteristics of this propagation. The variability of the ocean stratification is a relevant aspect that can activate the deep and intermediate dynamics engaging in the propagation and stabilization of signals throughout the water column. This demonstrates the non-negligible active connection of the dynamics of the bottom layers with the surface. The theoretical framework and the parametrization used were based on specific observations made in the Ionian Sea in the last decades, but without losing general applicability in all ocean basins that are characterized by the presence of a stratified dense water mass in the deep and intermediate layers.
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Notice on discussion status
The requested preprint has a corresponding peer-reviewed final revised paper. You are encouraged to refer to the final revised version.
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Preprint
(52901 KB)
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The requested preprint has a corresponding peer-reviewed final revised paper. You are encouraged to refer to the final revised version.
- Preprint
(52901 KB) - Metadata XML
- BibTeX
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- Final revised paper
Journal article(s) based on this preprint
Interactive discussion
Status: closed
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RC1: 'Comment on egusphere-2024-1580', Anonymous Referee #1, 02 Jul 2024
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AC1: 'Reply on RC1', Beatrice Giambenedetti, 14 Jul 2024
The comment was uploaded in the form of a supplement: https://egusphere.copernicus.org/preprints/2024/egusphere-2024-1580/egusphere-2024-1580-AC1-supplement.pdf
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RC3: 'Reply on AC1', Anonymous Referee #1, 16 Jul 2024
Thank you for your reply. I still don't understand the generation on PV in the layers. PV should be negligible in layers 2,3,4 at t=0 (assuming the initially the only PV there comes from the flow produced by the vortex in layer 1 and the coupling between layers (term A\psi in 8b)). Following equation (11) this very weak PV should only be advected layer-wise and horizontally diffused (if I correctly understand \nabla^2 as the horizontal Laplacian in equatoin (11)). I don't understand which term in the equation can explain the increase (in magnitude) of PV Â
Citation: https://doi.org/10.5194/egusphere-2024-1580-RC3 -
AC2: 'Reply on RC3', Beatrice Giambenedetti, 17 Jul 2024
Thank you for your prompt response. We apologize if we have misunderstood your initial comment and hope to clarify our explanation here.
You are correct that at t=0, the PV in layers 2, 3, and 4 can indeed be weak, and primarily comes from the coupling effect of the vortex in layer 1, as you mentioned, acting to redistribute PV throughout the different levels. The increase of PV is driven by the different configurations of relative thicknesses of the 3rd and 4th levels, which weigh the coupling differently for each explored configuration. We operate in a parametric space where we consider a set of stationary states. Eq. (11) describes the short-time evolution that we solve to let the PV redistribute for each configuration, in which each different choice of the ratio h3/h4 determines an equilibrium point of our phase space, and the dissipation terms are just a way to stabilize the computation, to filter out noise and reach correctly one of many of the possible stationary configurations. Our goal was to find a way to parametrize long-time stratification changes in the deep sea, as explained in the observation section. What we have then is a set of stationary states, and the increase in PV is given by the different configurations of the thicknesses and densities that weigh the coupling differently. The increase in PV is observed due to the different configurations of relative thicknesses and densities. Although initially small, these changes can lead to significant increases in PV, especially when perturbations are included. The term h3/h4 plays a crucial role in this, highlighting its impact on vorticity. Our numerical experiments aimed to explore this phase space and the idealized nature of these tests. We find that PV is redistributed to an equilibrium state, and changes in relative thicknesses reveal how this equilibrium shifts, findings that though qualitative, were consistent with observations.
We hope this clarifies the generation and evolution of PV in the layers. Please let us know if further details or explanations are needed.
Best regards,
Beatrice Giambenedetti, Vincenzo Artale, Nadia Lo Bue
Citation: https://doi.org/10.5194/egusphere-2024-1580-AC2 -
RC4: 'Reply on AC2', Anonymous Referee #1, 17 Jul 2024
Thank you for the clarification. It was a misunderstanding on my side.
Citation: https://doi.org/10.5194/egusphere-2024-1580-RC4 -
AC4: 'Reply on RC4', Beatrice Giambenedetti, 31 Jul 2024
We are glad we could clarify everything. Thank you again for your comments.
Citation: https://doi.org/10.5194/egusphere-2024-1580-AC4
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AC4: 'Reply on RC4', Beatrice Giambenedetti, 31 Jul 2024
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RC4: 'Reply on AC2', Anonymous Referee #1, 17 Jul 2024
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AC2: 'Reply on RC3', Beatrice Giambenedetti, 17 Jul 2024
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RC3: 'Reply on AC1', Anonymous Referee #1, 16 Jul 2024
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AC1: 'Reply on RC1', Beatrice Giambenedetti, 14 Jul 2024
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RC2: 'Comment on egusphere-2024-1580', Anonymous Referee #2, 07 Jul 2024
*General comments
This study examines the abyssal circulation of the Ionian Sea, specifically how vertical coupling between surface, intermediate, and abyssal layers might produce some observed decadal-scale changes in the circulation. The approach is based on sets of four-layer quasigeostrophic models with different stratifications (layer thicknesses) initialized with a Gaussian vortex. Some of the model results are qualitatively consistent with features found in current meter data. The results are very sensitive to the prescribed stratification, and this sensitivity is examined.
The text reads generally well, and most figures are clear. I think there are two major points (detailed below) and several other specific ones that need to be addressed.
I think a central issue in this work is that there is important sensitivity to the choices of layer thicknesses (and densities), as thoroughly examined in the manuscript. This is expected in QG systems with a few layers. Because the primary motivation of the manuscript is to understand decadal changes in the abyssal circulation with the simplest possible model, it would make sense to have experiments with more layers representing the observed density profile (Figure 2) more accurately. This would better approximate the continuously-stratified limit (see, e.g., Gulliver & Radko's 2022 Figure 4 with a ten-layer model based on an observed profile), and help determine at which point the discrete representation of the stratification is sufficiently realistic to reproduce the observed processes.
Another major point is the choice of a single vortex as initial condition. If the motivation is to explain some of the changes in the observed abyssal currents (Figure 1), decaying turbulence experiments with random broadband initial conditions would be more relevant. Even considering that the Intermediate Water eddies found in the Mediterranean have a Gaussian velocity profile, It seems unlikely that changes in individual eddy structure and propagation could be responsible for the observed changes in a real, broad-banded flow with a developed turbulent cascade. Diagnosing the changes in the baroclinic/barotropic energy fluxes in a turbulent four-layer system (with different stratifications like the authors do) could therefore be more helpful to find quantitative links with the observations.
*Specific comments
Figure 1c,d and paragraph starting at line 84: As seen in the hodographs and noted in the text, the amplitudes of the mean flow are similar, but there seems to be much less energy in the subinertial band in the SMO-1 rotary spectra than in GNDT-1. Is this low frequency/mesoscale kinetic energy drop reported in other observations in the literature, and if so, is the reason understood?
Line 47: I think it is important to note here that adding bottom topography with realistic roughness does produce more stable vortices with much longer lifetimes (across different density stratifications), as often observed in real vortices (Gulliver & Radko, 2022).
Lines 113-114: It is said here that compressibility effects were corrected for in the stratification frequency, so I think it would make more sense to have potential density in Figure 2b and in the layer density values reported. Using in situ density rather than potential density is very unusual, and I do not see a case for this choice here. Because only lateral density gradients matter in the QGPV equations, the extra density term due to compressibility effects should make no difference dynamically (apart from any potential numerical error propagation). But I still see no reason to use in situ density instead, especially since it obscures vertical structure in the observed profile (Figure 2b).
Lines 226-234: The relationship between the interfacial deformation radii in a layered QG model (as the one in this work and in Carton et al., 2014) and the modal deformation radii in a continuously stratified system (as in, e.g., Nittis et al. 1993) needs to be clarified here. This is important because the layer-wise deformation radii increase towards the bottom, and that seems to agree with the scale of the circulation features. But the modal deformation radii decrease with increasing mode number, and are associated with vertical modes with more zero crossings (i.e., shorter vertical wavelength). The modal analogues of the layered deformation radii involve combinations of the layer thicknesses (e.g., sqrt(g' * H1*H2/(H1 + H2))/f for the baroclinic mode in a two-layer model). It seems that the abyssal gyres in question are better described in the layered sense as locally equivalent-barotropic features, so I suggest trying to clarify that point.
Figure 5: The axis labels are very difficult to read without zooming in, the font sizes need to be increased.
*Minor corrections and editorial suggestions
Line 21: "in the deep layers process" -> "in abyssal processes", "in deep circulation", or something similar.
Line 31: catching -> observing.
Line 60: wants to -> aims to.
Line 85: to which this study refers -> which this study refers to.
Lines 124, 125, 167: adimensional -> nondimensional.
Line 168: was -> were.
Line 169: be of course worked around adding -> of course be worked around by adding.
Line 200: oscillation -> oscillations.
Line 253: among -> between.
Line 276: can be seen -> it can be seen.
Lines 331, 348: vortexes -> vortices.
Line 334: below ones -> ones below.
Lines 349-350: This last sentence is a bit confusing, perhaps a rewrite?
Line 358: the perturbation changes however the modal structure -> however, the perturbation changes the modal structure.
Line 359: Repeated closing parenthesis.
Line 361: emerges a symmetry in the modal structure around the critical value -> a symmetry in the modal structure around the critical value emerges.
Line 363: appear -> appears.
Line 372: variation -> variations.
Line 401: may be is too simplified for a completed representation of all the processes of the ocean water column -> is too simplified to represent the deep potential vorticity propagation considered here.
Line 405: critical thicknesses ratios values -> critical values of thickness ratios
Line 410: layers -> layer
Line 413: created the preconditions for -> favored
Line 414: The acronym IW is not defined, better to spell out internal waves since it is used only one other time (line 99)
Line 432: help -> helped*Gulliver & Radko (2022) reference: https://doi.org/10.1029/2021GL097686
Citation: https://doi.org/10.5194/egusphere-2024-1580-RC2 -
AC3: 'Reply on RC2', Beatrice Giambenedetti, 24 Jul 2024
The comment was uploaded in the form of a supplement: https://egusphere.copernicus.org/preprints/2024/egusphere-2024-1580/egusphere-2024-1580-AC3-supplement.pdf
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AC3: 'Reply on RC2', Beatrice Giambenedetti, 24 Jul 2024
Interactive discussion
Status: closed
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RC1: 'Comment on egusphere-2024-1580', Anonymous Referee #1, 02 Jul 2024
-
AC1: 'Reply on RC1', Beatrice Giambenedetti, 14 Jul 2024
The comment was uploaded in the form of a supplement: https://egusphere.copernicus.org/preprints/2024/egusphere-2024-1580/egusphere-2024-1580-AC1-supplement.pdf
-
RC3: 'Reply on AC1', Anonymous Referee #1, 16 Jul 2024
Thank you for your reply. I still don't understand the generation on PV in the layers. PV should be negligible in layers 2,3,4 at t=0 (assuming the initially the only PV there comes from the flow produced by the vortex in layer 1 and the coupling between layers (term A\psi in 8b)). Following equation (11) this very weak PV should only be advected layer-wise and horizontally diffused (if I correctly understand \nabla^2 as the horizontal Laplacian in equatoin (11)). I don't understand which term in the equation can explain the increase (in magnitude) of PV Â
Citation: https://doi.org/10.5194/egusphere-2024-1580-RC3 -
AC2: 'Reply on RC3', Beatrice Giambenedetti, 17 Jul 2024
Thank you for your prompt response. We apologize if we have misunderstood your initial comment and hope to clarify our explanation here.
You are correct that at t=0, the PV in layers 2, 3, and 4 can indeed be weak, and primarily comes from the coupling effect of the vortex in layer 1, as you mentioned, acting to redistribute PV throughout the different levels. The increase of PV is driven by the different configurations of relative thicknesses of the 3rd and 4th levels, which weigh the coupling differently for each explored configuration. We operate in a parametric space where we consider a set of stationary states. Eq. (11) describes the short-time evolution that we solve to let the PV redistribute for each configuration, in which each different choice of the ratio h3/h4 determines an equilibrium point of our phase space, and the dissipation terms are just a way to stabilize the computation, to filter out noise and reach correctly one of many of the possible stationary configurations. Our goal was to find a way to parametrize long-time stratification changes in the deep sea, as explained in the observation section. What we have then is a set of stationary states, and the increase in PV is given by the different configurations of the thicknesses and densities that weigh the coupling differently. The increase in PV is observed due to the different configurations of relative thicknesses and densities. Although initially small, these changes can lead to significant increases in PV, especially when perturbations are included. The term h3/h4 plays a crucial role in this, highlighting its impact on vorticity. Our numerical experiments aimed to explore this phase space and the idealized nature of these tests. We find that PV is redistributed to an equilibrium state, and changes in relative thicknesses reveal how this equilibrium shifts, findings that though qualitative, were consistent with observations.
We hope this clarifies the generation and evolution of PV in the layers. Please let us know if further details or explanations are needed.
Best regards,
Beatrice Giambenedetti, Vincenzo Artale, Nadia Lo Bue
Citation: https://doi.org/10.5194/egusphere-2024-1580-AC2 -
RC4: 'Reply on AC2', Anonymous Referee #1, 17 Jul 2024
Thank you for the clarification. It was a misunderstanding on my side.
Citation: https://doi.org/10.5194/egusphere-2024-1580-RC4 -
AC4: 'Reply on RC4', Beatrice Giambenedetti, 31 Jul 2024
We are glad we could clarify everything. Thank you again for your comments.
Citation: https://doi.org/10.5194/egusphere-2024-1580-AC4
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AC4: 'Reply on RC4', Beatrice Giambenedetti, 31 Jul 2024
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RC4: 'Reply on AC2', Anonymous Referee #1, 17 Jul 2024
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AC2: 'Reply on RC3', Beatrice Giambenedetti, 17 Jul 2024
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RC3: 'Reply on AC1', Anonymous Referee #1, 16 Jul 2024
-
AC1: 'Reply on RC1', Beatrice Giambenedetti, 14 Jul 2024
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RC2: 'Comment on egusphere-2024-1580', Anonymous Referee #2, 07 Jul 2024
*General comments
This study examines the abyssal circulation of the Ionian Sea, specifically how vertical coupling between surface, intermediate, and abyssal layers might produce some observed decadal-scale changes in the circulation. The approach is based on sets of four-layer quasigeostrophic models with different stratifications (layer thicknesses) initialized with a Gaussian vortex. Some of the model results are qualitatively consistent with features found in current meter data. The results are very sensitive to the prescribed stratification, and this sensitivity is examined.
The text reads generally well, and most figures are clear. I think there are two major points (detailed below) and several other specific ones that need to be addressed.
I think a central issue in this work is that there is important sensitivity to the choices of layer thicknesses (and densities), as thoroughly examined in the manuscript. This is expected in QG systems with a few layers. Because the primary motivation of the manuscript is to understand decadal changes in the abyssal circulation with the simplest possible model, it would make sense to have experiments with more layers representing the observed density profile (Figure 2) more accurately. This would better approximate the continuously-stratified limit (see, e.g., Gulliver & Radko's 2022 Figure 4 with a ten-layer model based on an observed profile), and help determine at which point the discrete representation of the stratification is sufficiently realistic to reproduce the observed processes.
Another major point is the choice of a single vortex as initial condition. If the motivation is to explain some of the changes in the observed abyssal currents (Figure 1), decaying turbulence experiments with random broadband initial conditions would be more relevant. Even considering that the Intermediate Water eddies found in the Mediterranean have a Gaussian velocity profile, It seems unlikely that changes in individual eddy structure and propagation could be responsible for the observed changes in a real, broad-banded flow with a developed turbulent cascade. Diagnosing the changes in the baroclinic/barotropic energy fluxes in a turbulent four-layer system (with different stratifications like the authors do) could therefore be more helpful to find quantitative links with the observations.
*Specific comments
Figure 1c,d and paragraph starting at line 84: As seen in the hodographs and noted in the text, the amplitudes of the mean flow are similar, but there seems to be much less energy in the subinertial band in the SMO-1 rotary spectra than in GNDT-1. Is this low frequency/mesoscale kinetic energy drop reported in other observations in the literature, and if so, is the reason understood?
Line 47: I think it is important to note here that adding bottom topography with realistic roughness does produce more stable vortices with much longer lifetimes (across different density stratifications), as often observed in real vortices (Gulliver & Radko, 2022).
Lines 113-114: It is said here that compressibility effects were corrected for in the stratification frequency, so I think it would make more sense to have potential density in Figure 2b and in the layer density values reported. Using in situ density rather than potential density is very unusual, and I do not see a case for this choice here. Because only lateral density gradients matter in the QGPV equations, the extra density term due to compressibility effects should make no difference dynamically (apart from any potential numerical error propagation). But I still see no reason to use in situ density instead, especially since it obscures vertical structure in the observed profile (Figure 2b).
Lines 226-234: The relationship between the interfacial deformation radii in a layered QG model (as the one in this work and in Carton et al., 2014) and the modal deformation radii in a continuously stratified system (as in, e.g., Nittis et al. 1993) needs to be clarified here. This is important because the layer-wise deformation radii increase towards the bottom, and that seems to agree with the scale of the circulation features. But the modal deformation radii decrease with increasing mode number, and are associated with vertical modes with more zero crossings (i.e., shorter vertical wavelength). The modal analogues of the layered deformation radii involve combinations of the layer thicknesses (e.g., sqrt(g' * H1*H2/(H1 + H2))/f for the baroclinic mode in a two-layer model). It seems that the abyssal gyres in question are better described in the layered sense as locally equivalent-barotropic features, so I suggest trying to clarify that point.
Figure 5: The axis labels are very difficult to read without zooming in, the font sizes need to be increased.
*Minor corrections and editorial suggestions
Line 21: "in the deep layers process" -> "in abyssal processes", "in deep circulation", or something similar.
Line 31: catching -> observing.
Line 60: wants to -> aims to.
Line 85: to which this study refers -> which this study refers to.
Lines 124, 125, 167: adimensional -> nondimensional.
Line 168: was -> were.
Line 169: be of course worked around adding -> of course be worked around by adding.
Line 200: oscillation -> oscillations.
Line 253: among -> between.
Line 276: can be seen -> it can be seen.
Lines 331, 348: vortexes -> vortices.
Line 334: below ones -> ones below.
Lines 349-350: This last sentence is a bit confusing, perhaps a rewrite?
Line 358: the perturbation changes however the modal structure -> however, the perturbation changes the modal structure.
Line 359: Repeated closing parenthesis.
Line 361: emerges a symmetry in the modal structure around the critical value -> a symmetry in the modal structure around the critical value emerges.
Line 363: appear -> appears.
Line 372: variation -> variations.
Line 401: may be is too simplified for a completed representation of all the processes of the ocean water column -> is too simplified to represent the deep potential vorticity propagation considered here.
Line 405: critical thicknesses ratios values -> critical values of thickness ratios
Line 410: layers -> layer
Line 413: created the preconditions for -> favored
Line 414: The acronym IW is not defined, better to spell out internal waves since it is used only one other time (line 99)
Line 432: help -> helped*Gulliver & Radko (2022) reference: https://doi.org/10.1029/2021GL097686
Citation: https://doi.org/10.5194/egusphere-2024-1580-RC2 -
AC3: 'Reply on RC2', Beatrice Giambenedetti, 24 Jul 2024
The comment was uploaded in the form of a supplement: https://egusphere.copernicus.org/preprints/2024/egusphere-2024-1580/egusphere-2024-1580-AC3-supplement.pdf
-
AC3: 'Reply on RC2', Beatrice Giambenedetti, 24 Jul 2024
Peer review completion
Journal article(s) based on this preprint
Data sets
Post-processed CTD Near-full-depth Data at ER-0121 Site Beatrice Giambenedetti https://zenodo.org/doi/10.5281/zenodo.7871734
NEMO-SN1 observatory data Nadia Lo Bue and Giuditta Marinaro http://www.moist.it/sites/western_ionian_sea/2
Model code and software
QG4L Beatrice Giambenedetti https://github.com/bgiambe/QG4L
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Beatrice Giambenedetti
Nadia Lo Bue
Vincenzo Artale
The requested preprint has a corresponding peer-reviewed final revised paper. You are encouraged to refer to the final revised version.
- Preprint
(52901 KB) - Metadata XML