the Creative Commons Attribution 4.0 License.
the Creative Commons Attribution 4.0 License.
Relative dispersion and kinematic properties of the coastal submesoscale circulation in the southeastern Ligurian Sea
PierreMarie Poulain
Luca Centurioni
Carlo Brandini
Stefano Taddei
Maristella Berta
Milena Menna
Abstract. An array of Lagrangian instruments (more than 100 drifters and a profiling float) was deployed for several days in the coastal waters of the southeastern Ligurian Sea to characterize the nearsurface circulation at the submesoscale (< 10 km). The drifters were trapped in an offshoreflowing filament and a cyclonic eddy that developed at the southwestern extremity of the filament. Drifter velocities are used to estimate differential kinematic properties (DKPs) and the relative dispersion of the nearsurface currents on scales as small as 100 m. The maximum drifter speed is ~50 cm/s. The DKPs within the cluster exhibit considerable spatial and temporal variability, with absolute values reaching the order of magnitude of the local inertial frequency. Vorticity prevails in the core of the cyclonic eddy, while strain is dominant at the outer edge of the eddy. Significant convergence was also found in the southwestern flow of the filament. The initial relative dispersion on small scales (100–200 m) is directly related to some of the DKPs (e.g., divergence, strain and instantaneous rate of separation): The mean squared separation distance (MSSD) grows exponentially with time and the finitesize Lyapunov exponent (FSLE) is independent of scale. After 5–10 h of drift or for initial separations greater than 500 m, the MSSD and FSLE show smaller relative dispersion that decreases slightly with scale.

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The requested preprint has a corresponding peerreviewed final revised paper. You are encouraged to refer to the final revised version.

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The requested preprint has a corresponding peerreviewed final revised paper. You are encouraged to refer to the final revised version.
 Preprint
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 Final revised paper
Journal article(s) based on this preprint
PierreMarie Poulain et al.
Interactive discussion
Status: closed

CC1: 'Comment on egusphere2023688', Roberto Iacono, 20 Apr 2023
I would like to suggest to the Authors that recent work focusing on the summer circulation in the Eastern Ligurian (https://doi.org/10.1016/j.dsr.2020.103407) by myself and E. Napolitano, appeared in 2021 in Deep Sea Research Part I, contains material that could be useful for their investigation.
Citation: https://doi.org/10.5194/egusphere2023688CC1 
AC1: 'Reply on CC1', PierreMarie Poulain, 20 Apr 2023
Thank you for letting us know about your work in the southern Ligurian Sea. We will read it and refer to it in the revised version of the manuscript.
Citation: https://doi.org/10.5194/egusphere2023688AC1

AC1: 'Reply on CC1', PierreMarie Poulain, 20 Apr 2023

RC1: 'Comment on egusphere2023688', Anonymous Referee #1, 10 Jun 2023
The authors investigate surface ocean dynamics in Ligurian Sea. The authors are all experts in such observations and analysis and very familiar with this interesting region. Their contribution is valuable and of interest to other researchers in the Med Sea region as well as elsewhere. Latest observing systems and analysis methods are used; the paper is concise and well written. I have no significent feedback to criticise or improve the manuscript. Thus I recommend publication as is.
Citation: https://doi.org/10.5194/egusphere2023688RC1 
AC2: 'Reply on RC1', PierreMarie Poulain, 31 Aug 2023
We thank Referee #1 for his/her comments on the original manuscript.
Citation: https://doi.org/10.5194/egusphere2023688AC2

AC2: 'Reply on RC1', PierreMarie Poulain, 31 Aug 2023

RC2: 'Comment on egusphere2023688', Anonymous Referee #2, 25 Jul 2023
Review Ms Egusphere2023688 ‘’ Relative dispersion and kinematic properties of the coastal submesoscale circulation in the southeastern Ligurian Sea’’ by Poulain et al.
The Ms present a 3day experiment aimed to characterize the sub mesoscale circulation in the Ligurian Sea using a large set of lagrangian drifters plus a profiling float. Drifter velocities were used to derive dispersion as well as different kinematic properties with the aim of explaining the dynamics in the area.
Although being a research area that is receiving increasing attention, the present manuscript has two major drawbacks ;
 First, the scientific problem is never stated. Although using several eulerian diagnostics (and one lagrangian), the scientific question is not clear. Besides providing a review of different metrics, largely used in the last two decades, the Ms as it is now, looks like a review of these techniques (technical report) used to describe the short term dynamics in a coastal area. For the reader it is not clear if the objective is to show how drifters arrange towards an eddy (a mesoscale structure), or towards the filaments shown in Figure 3 (scales between meso and submesoscale).
 Errors in the different metrics are not provided. For example, the slopes in the FSLE spectrum are not conclusive since the standard deviation for each initial separation distance is not given. Why not fit the FSLE spectrum data and compute the value of the slopes at the different spatial scales ranges?
 What is the error in the computation of the kinematic quantities due to the error in the drifter positions and to the least square approach?
Specific comments:
 The description and expression of Eq 2 can be improved. I would add, at least, a reference to the theoretical paper “Nonasymptotic properties of transport and mixing”,Boffetta et al., 2000, Chaos 10, 5060. Appendix A describes the correct operational definition of FSLE.
 I suggest the Authors discuss in some more detail the outcome of their FSLE computation. Did they consider the fastest growth time (as arbitrarily assumed by some authors) or the average growth time (as prescribed by the correct FSLE definition) ?
 Eq’s 3 and 4 correspond to the linear terms of the correction to the first order velocity of the taylor expansion (u_0 is missing)
 Figure 4. It will be helpful to superimpose currents from the CMEMS model together with the paths. Also the FSLE/FTLE maps would provide a good overview on the dynamics in the area.
 Figure 6. Plot each curve with a different color. Also discuss the implications of each relative dispersion on the dynamics of the area.
 Figure 7. Include errors.
 Figure 8. Can you explain in terms of the specific dynamical conditions the peaks on the speed?. A quick look at Figure 2 shows that this is nothing related to wind and waves.
 Figures 912. I suggest changing in a band near zero the green color to white (this will provide better insight on the different metrics presented in this small area. Besides, what is the difference between the DIV/f in figure 9 and Figure 10 a?. Show position of the eddy discussed in the text in Figure 9.
 Figures 1013. Why using Eulerian metrics instead of Lagrangian ones?. In particular, the use of the Lagrangian Divergence could give an indication of the upwelling/downwelling in the drifters path and confirm what is speculated in the document about the vertical velocities.
 Ln 226227. There are in the literature examples of such a comparison.
 Ln 262 > why?
 Ln 294 > This is something that an statistical analysis will ensure (only 8 pairs of drifters fall within this distance).
 Lns 320322. I agree totally on this.
 The references are largely biased towards the author's work and several relevant papers on the topic are missed.
Citation: https://doi.org/10.5194/egusphere2023688RC2 
AC3: 'Reply on RC2', PierreMarie Poulain, 31 Aug 2023
We thank Referee #2 for his/her helpful detailed comments on our original manuscript. We have addressed all the comments to improve the paper. Our responses to the individual comments are as follows. A pdf file is also attached with the updated figures.
 Major drawback
 The scientific objectives of the paper are now better stated in the introduction. The use of Eulerian and Lagrangian metrics to quantitatively describe surface dispersion is also better motivated.
 The errors on the MSSD, FLSE and DKPs due to the drifter GPS position error is now discussed in more detail, and relevant references are added. Bootstrapping is used to provide 95% confidence intervals on the mean values involved in the MSSD and FLSE calculations. We do not believe that the agreement with theoretical slopes would be better by fitting the FLSE spectrum.
For estimating the DKPs, the DIVA interpolation was used with a S/N of 10 (error of ~1 cm/s on velocities of ~10 cm/s) and decorrelation scales of 1 km. Spatially interpolated values with relative error larger than 50% are excluded.
The errors when estimating the DKPs using the least square approach are not discussed here since this method is not used.
 Specific comments
 The Boffetta et al. (2000) has been added and the definition of the FSLE has been expanded.
 We considered the average growth time rate.
 Indeed equations 3 and 4 correspond to the first order Taylor expansion. No mean flow is added because, as stated in the text, we consider the flow with respect to the center of mass of the drifters.
 The CMEMS currents have been added to all panels of Figure 4. Text on the qualitative comparison with the drifter velocities has been added. We have checked that FSLE from CMEMS (actually from AVISO) are too large scale and are not relevant for this study.
 Each curve has now a different color and the corresponding discussion has been expanded.
 95% confidence intervals based on bootstrapping have been added to the FSLE curve. In addition, the estimate using Boffetta et al (2000)’s method has been overlaid for comparison.
 Figure 8 has been removed because its information content was poor.
 Figure 9 has been removed because its information content was poor. The figures with the DKPs have been modified (more dates and better graphics). Color scaling was not changed, in particular the zero values have been kept in green to contrast them with the white areas with no data (outside the 50% S/N level).
 The use of mixed Eulerian (DKPs) and Lagrangian (MSSD, FLSE) metrics (or statistics) to describe the circulation and dispersion is now better motivated.
 Indeed, several papers in the literature deals with the comparison, but generally at larger scales than those considered here, and with better success. This has been added in the revised text.
 The horizontal divergence ranging between these values is a result, showing the significant spatial and temporal variations of the DKPs.
 We do not understand this comment!
 ok
 Several relevant references have been added to support the revised text.
Interactive discussion
Status: closed

CC1: 'Comment on egusphere2023688', Roberto Iacono, 20 Apr 2023
I would like to suggest to the Authors that recent work focusing on the summer circulation in the Eastern Ligurian (https://doi.org/10.1016/j.dsr.2020.103407) by myself and E. Napolitano, appeared in 2021 in Deep Sea Research Part I, contains material that could be useful for their investigation.
Citation: https://doi.org/10.5194/egusphere2023688CC1 
AC1: 'Reply on CC1', PierreMarie Poulain, 20 Apr 2023
Thank you for letting us know about your work in the southern Ligurian Sea. We will read it and refer to it in the revised version of the manuscript.
Citation: https://doi.org/10.5194/egusphere2023688AC1

AC1: 'Reply on CC1', PierreMarie Poulain, 20 Apr 2023

RC1: 'Comment on egusphere2023688', Anonymous Referee #1, 10 Jun 2023
The authors investigate surface ocean dynamics in Ligurian Sea. The authors are all experts in such observations and analysis and very familiar with this interesting region. Their contribution is valuable and of interest to other researchers in the Med Sea region as well as elsewhere. Latest observing systems and analysis methods are used; the paper is concise and well written. I have no significent feedback to criticise or improve the manuscript. Thus I recommend publication as is.
Citation: https://doi.org/10.5194/egusphere2023688RC1 
AC2: 'Reply on RC1', PierreMarie Poulain, 31 Aug 2023
We thank Referee #1 for his/her comments on the original manuscript.
Citation: https://doi.org/10.5194/egusphere2023688AC2

AC2: 'Reply on RC1', PierreMarie Poulain, 31 Aug 2023

RC2: 'Comment on egusphere2023688', Anonymous Referee #2, 25 Jul 2023
Review Ms Egusphere2023688 ‘’ Relative dispersion and kinematic properties of the coastal submesoscale circulation in the southeastern Ligurian Sea’’ by Poulain et al.
The Ms present a 3day experiment aimed to characterize the sub mesoscale circulation in the Ligurian Sea using a large set of lagrangian drifters plus a profiling float. Drifter velocities were used to derive dispersion as well as different kinematic properties with the aim of explaining the dynamics in the area.
Although being a research area that is receiving increasing attention, the present manuscript has two major drawbacks ;
 First, the scientific problem is never stated. Although using several eulerian diagnostics (and one lagrangian), the scientific question is not clear. Besides providing a review of different metrics, largely used in the last two decades, the Ms as it is now, looks like a review of these techniques (technical report) used to describe the short term dynamics in a coastal area. For the reader it is not clear if the objective is to show how drifters arrange towards an eddy (a mesoscale structure), or towards the filaments shown in Figure 3 (scales between meso and submesoscale).
 Errors in the different metrics are not provided. For example, the slopes in the FSLE spectrum are not conclusive since the standard deviation for each initial separation distance is not given. Why not fit the FSLE spectrum data and compute the value of the slopes at the different spatial scales ranges?
 What is the error in the computation of the kinematic quantities due to the error in the drifter positions and to the least square approach?
Specific comments:
 The description and expression of Eq 2 can be improved. I would add, at least, a reference to the theoretical paper “Nonasymptotic properties of transport and mixing”,Boffetta et al., 2000, Chaos 10, 5060. Appendix A describes the correct operational definition of FSLE.
 I suggest the Authors discuss in some more detail the outcome of their FSLE computation. Did they consider the fastest growth time (as arbitrarily assumed by some authors) or the average growth time (as prescribed by the correct FSLE definition) ?
 Eq’s 3 and 4 correspond to the linear terms of the correction to the first order velocity of the taylor expansion (u_0 is missing)
 Figure 4. It will be helpful to superimpose currents from the CMEMS model together with the paths. Also the FSLE/FTLE maps would provide a good overview on the dynamics in the area.
 Figure 6. Plot each curve with a different color. Also discuss the implications of each relative dispersion on the dynamics of the area.
 Figure 7. Include errors.
 Figure 8. Can you explain in terms of the specific dynamical conditions the peaks on the speed?. A quick look at Figure 2 shows that this is nothing related to wind and waves.
 Figures 912. I suggest changing in a band near zero the green color to white (this will provide better insight on the different metrics presented in this small area. Besides, what is the difference between the DIV/f in figure 9 and Figure 10 a?. Show position of the eddy discussed in the text in Figure 9.
 Figures 1013. Why using Eulerian metrics instead of Lagrangian ones?. In particular, the use of the Lagrangian Divergence could give an indication of the upwelling/downwelling in the drifters path and confirm what is speculated in the document about the vertical velocities.
 Ln 226227. There are in the literature examples of such a comparison.
 Ln 262 > why?
 Ln 294 > This is something that an statistical analysis will ensure (only 8 pairs of drifters fall within this distance).
 Lns 320322. I agree totally on this.
 The references are largely biased towards the author's work and several relevant papers on the topic are missed.
Citation: https://doi.org/10.5194/egusphere2023688RC2 
AC3: 'Reply on RC2', PierreMarie Poulain, 31 Aug 2023
We thank Referee #2 for his/her helpful detailed comments on our original manuscript. We have addressed all the comments to improve the paper. Our responses to the individual comments are as follows. A pdf file is also attached with the updated figures.
 Major drawback
 The scientific objectives of the paper are now better stated in the introduction. The use of Eulerian and Lagrangian metrics to quantitatively describe surface dispersion is also better motivated.
 The errors on the MSSD, FLSE and DKPs due to the drifter GPS position error is now discussed in more detail, and relevant references are added. Bootstrapping is used to provide 95% confidence intervals on the mean values involved in the MSSD and FLSE calculations. We do not believe that the agreement with theoretical slopes would be better by fitting the FLSE spectrum.
For estimating the DKPs, the DIVA interpolation was used with a S/N of 10 (error of ~1 cm/s on velocities of ~10 cm/s) and decorrelation scales of 1 km. Spatially interpolated values with relative error larger than 50% are excluded.
The errors when estimating the DKPs using the least square approach are not discussed here since this method is not used.
 Specific comments
 The Boffetta et al. (2000) has been added and the definition of the FSLE has been expanded.
 We considered the average growth time rate.
 Indeed equations 3 and 4 correspond to the first order Taylor expansion. No mean flow is added because, as stated in the text, we consider the flow with respect to the center of mass of the drifters.
 The CMEMS currents have been added to all panels of Figure 4. Text on the qualitative comparison with the drifter velocities has been added. We have checked that FSLE from CMEMS (actually from AVISO) are too large scale and are not relevant for this study.
 Each curve has now a different color and the corresponding discussion has been expanded.
 95% confidence intervals based on bootstrapping have been added to the FSLE curve. In addition, the estimate using Boffetta et al (2000)’s method has been overlaid for comparison.
 Figure 8 has been removed because its information content was poor.
 Figure 9 has been removed because its information content was poor. The figures with the DKPs have been modified (more dates and better graphics). Color scaling was not changed, in particular the zero values have been kept in green to contrast them with the white areas with no data (outside the 50% S/N level).
 The use of mixed Eulerian (DKPs) and Lagrangian (MSSD, FLSE) metrics (or statistics) to describe the circulation and dispersion is now better motivated.
 Indeed, several papers in the literature deals with the comparison, but generally at larger scales than those considered here, and with better success. This has been added in the revised text.
 The horizontal divergence ranging between these values is a result, showing the significant spatial and temporal variations of the DKPs.
 We do not understand this comment!
 ok
 Several relevant references have been added to support the revised text.
Peer review completion
Journal article(s) based on this preprint
PierreMarie Poulain et al.
PierreMarie Poulain et al.
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The requested preprint has a corresponding peerreviewed final revised paper. You are encouraged to refer to the final revised version.
 Preprint
(1717 KB)  Metadata XML