the Creative Commons Attribution 4.0 License.
the Creative Commons Attribution 4.0 License.
| 27 Jun 2025
Fractal Attractor of the Deep Convection Cycle in the Northwest Mediterranean Sea
Abstract. Deep convection in the Gulf of Lion is an important ocean mixing process in the western Mediterranean Sea caused by large cooling fluxes at the sea surface. It aids the Mediterranean thermohaline circulation, and promotes phytoplankton blooming. This work investigates the three different periods of the process: preconditioning, deep convecting, and restratification, through the lens of fractal attractor analysis with the local correlation dimension. From the analysis it was determined that preconditioning period is most predictable period, with a local correlation dimension of 10 to 30, followed by the deep convecting period, with a local correlation dimension of 30 to 45. However, the deep convecting period can also exhibit random process like behavior with local correlation dimensions growing exceedingly high in April and May. The least predictable period was the restratification period, with typical local correlation dimensions of 50 to 80 near the end of restratification.
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- RC1: 'Comment on egusphere-2025-2860', Anonymous Referee #1, 27 Jul 2025
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RC2: 'Comment on egusphere-2025-2860', Anonymous Referee #2, 21 Sep 2025
The pee-reviewed manuscript investigates the predictability of deep convection in the Gulf of Lion, a complex oceanic phenomenon characterized by intense vertical mixing. The study specifically focuses on examining the three distinct phases of its evolution. To achieve this, the authors analyze the system's fractal attractor, utilizing a methodology based on local correlation analysis as developed in prior research of other authors. The author briefly, yet clearly, examines the physics of the process and its underlying causes. This allows the reader to fully understand the essence of the phenomenon, without unnecessary detail or omissions.
The article left a positive impression. First of all, it's written at a high scientific level and well structured. I have no questions about the scientific aspect. Overall, it's clear what problem the author is addressing and how he addresses it. In this regard, however, I'd like to make the following comment. The author does not provide a clear enough explanation as to why he chose the fractal attractor as the main subject of study. Other methods and approaches exist for studying the predictability of geophysical processes. From my view point, the author needs to explain why the fractal attractor was chosen as the subject of this study.
Second comment is as follows. A reader unfamiliar with the authors' papers, the developers of method used in this study, can only assume that other methods will not allow a detailed investigation of the predictability of all phases of oceanic deep convection. Therefore, some explanations should be provided. The third comment concerns the discussion of the results. The author needs to clarify which parameter values are considered ’’good’’ and which are ‘’bad’’. It may be difficult for the reader to interpret Figures 4 and 5. It is clear that ocean convection is chaotic in nature due to several factors.
The third comment concerns the discussion of the results. The author needs to clarify which values of local correlation dimension are considered ’’good’’ and which are ‘’bad’’. Therefore, it may be difficult for the reader to interpret Figures 4 and 5. It is clear that ocean convection is chaotic in nature due to several factors. Readers should be confident that if the local correlation dimension exceeds a certain (critical) value, the system's behaviour becomes more chaotic than before. However, this does not allow one to draw conclusions about the predictability of the system in either case. One can only perform a comparative analysis, nothing more.
Next comment: The author uses mixed layer depth as the primary parameter characterizing the convention. However, there are some other parameters used for this purpose. Therefore, the author could provide a ranking of the relative importance of input characteristics. This would robustly demonstrate that mixed layer depth alone is the most significant predictor, justifying its sole use in this study.
It would be interesting to know whether the obtained results can be scaled to other regions of the world's oceans.
Citation: https://doi.org/10.5194/egusphere-2025-2860-RC2 -
EC1: 'Comment on egusphere-2025-2860', Norbert Marwan, 22 Sep 2025
The results depend strongly on the reanalysis data and the Argo profiles, both of which carry uncertainties (model biases, sampling gaps, etc.). Since these data directly feed into the dimensionality estimates, the results must also be uncertain. At the moment, this is not really addressed beyond the dataset revision. I suggest the authors discuss these uncertainties more explicitly and, if possible, show how they affect the results (e.g. with confidence ranges or sensitivity/ robustness tests).
In addition, reproducibility is not fully ensured, as also mentioned by referee 1: while the data sources are public, the code and workflow used for the local correlation dimension analysis are not available. I suggest that the authors provide code or at least detailed instructions, ideally mentioned in the Data availability section, so that others can reproduce the results.Citation: https://doi.org/10.5194/egusphere-2025-2860-EC1
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- 1
The manuscript estimates the local dimension of the attractor of the dynamics of the mixed layer depth in the Mediterranean region close to the Gulf of Lion. This is relevant as this area experience frequent and intense events of deep convection that lead to the formation of Western Mediterranean Deep Water. The methodology used is taken from Lucarini et al, 2012 and Faranda et al, 2017, which uses the statistics of close recurrences near each point in the attractor, mapped into a problem of extreme values. The author describes the implications of the different annual values of the dimension on the predictability of the different regimes.
The paper contains interesting results and the discussion seems sound, which provides insight into different aspects of deep convection in the area. Nevertheless, it seems to me that the methodology is not presented with sufficient detail as to guarantee reproducibility by other researchers. Thus, before recommending publication, I ask the author to expand and clarify the following aspects:
- The only mention to the state variable used to reconstruct the attractor properties is the sentence ‘’the MLD (=Mixed Layer Depth) will be taken as the representative system state of deep convection in the Gulf of Lion”. I interpret that the time-dependent vector x(t) which is used in the dimension estimation method is the vector made with all values of MLD, one for each horizontal grid point in the reanalysis, at a given time. And that the Euclidean distance mentioned later acts on this vector. It seems to me that this is the reasonable interpretation of the methodology in the paper, but I feel that given the basic role this vector takes in the whole paper, its characteristics need to be more explicitly described: for example, to mention its dimensionality (number of grid points used). The need for this type of clarification is stressed by the fact that MLD configurations are never plotted, and only the ‘maximum values’ are mentioned plotted in Figs. 2 and 4-7. This exclusive reference to the ‘max MLD’ makes the reader to doubt if really the whole MLD configuration is being used as system state or just the time series of maxima.
- The definition of ‘max MLD’ is also not very precise. The reanalysis provides daily values of MLD at each horizontal grid point, so that it seems natural to interpret the ‘max MLD’ as the maximal depth in the MLD spatial configuration each day. But this is never explicitly said and other interpretations could point to the maximum value in a space-time interval. This is further supported by the comment at the end of the caption of Fig. 2, which mentions ‘monthly maximum and median’ for the Argo data. Please explicitly state, for each data source, over which spatial, temporal, or spatio-temporal window are the maxima taken.
- Data on deep convection from the reanalysis and from Argo profiles are very different. The author ‘corrects’ reanalysis data by comparing them with Argo, Somot and Marginier data. But no details are given on how the correction is done, which set of time steps are ‘removed’ and under which criteria. It seems that ‘too discrepant’ data are ‘removed’ from the reanalysis data set. But in the text and fig. 2, 19 years are said to be removed but in table 1 only 18 are moved from the ‘deep-convection’ to the ‘not-deep-convection’ category. Please explain in detail which objective criteria are used to ‘correct’ which time-steps (daily?) of the reanalysis, and the rationale for this.
- Despite the large differences between reanalysis and Argo data, Fig. 3 seem to imply that they give very similar results for the dimension estimation. The reason for this needs some explicit explanation.
- There are essentially no details on the path between the MLD data and the final d estimation. A threshold value of 98% percentile for g1 is used without justification. Some sensibility analysis is in order to demonstrate that this is an appropriate threshold, for example by showing results for other values, or showing that the distribution of z for this threshold is indeed a Generalized Pareto (in fact, a simple exponential in this case), or other data that can convince the reader that the hypothesis needed for the validity of the methodology are indeed satisfied here to a good extent.
- As a minor point, the color scales used in Fig. 7 b and c are quite confusing: First, at difference with panels a and d, here reddish/violet colors, easily confused, appear at both ends of the scale, which leads to difficult reading of the data in the plots. Second, the orientation of the colors is exactly opposite (red for low values in b, red for high values in c), which is really confusing. Please use in panels b and c a color scale of the type used in a or d.