the Creative Commons Attribution 4.0 License.
the Creative Commons Attribution 4.0 License.
| 30 Apr 2025
Multiscale statistical analysis of thermal and non-thermal components of seawater pCO2 in the Western English Channel: scaling, time-reversibility, and dependence
Abstract. The partial pressure of carbon dioxide (pCO2) has been measured on the ASTAN cardinal buoy (Brittany, west coast of France) with at 30-minute intervals by Gac et al. (2020), yielding a dataset of 32,582 data points collected over a period of nearly five years. These measurements were then coupled with others of sea surface temperature and salinity, chlorophyll a, oxygen saturation and atmospheric pressure. The aim of this study was to consider the statistical properties of the thermal and non-thermal component of pCO2, based on its relation with temperature established by Takahashi et al. (2009). Using Fourier spectral analysis, it was demonstrated that all marine scalars exhibited scaling properties with power-law slopes ranging from 1.73 to 1.85 for timescales spanning from 12 hours to at least 80-100 days. The results obtained from this analysis indicate a turbulent and intermittent dynamics for all the considered scalars, including sea surface temperature and salinity, chlorophyll a, oxygen saturation, pCO2, and pCO2 thermal and non-thermal components. A time-reversibility analysis evidenced the irreversibility of the pCO2 components above 30 days. The irreversibility exhibited by the thermal component was found to be higher than that of the non-thermal component, with an average value of the associated irreversibility index that was approximately 3.5 times higher than that of the non-thermal component over the period of 50 to 70 days. Furthermore, a methodology known as the Probability Density Function quotient was employed, a method that has not been widely utilized. This approach enabled the identification of values for which there were statistical relationships between variables. This facilitated the quantification of the influence of primary production on the non-thermal pCO2, or the influence of periods of depression on supersaturation due to atmospheric or terrigenous inputs. This provided new insights into the stochastic coupling between biological and physical processes, when considering high-frequency pCO2 variability.
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Status: final response (author comments only)
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EC1: 'Comment on egusphere-2025-972', Liuqian Yu, 09 May 2025
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CC1: 'Reply on EC1', Kévin Robache, 18 May 2025
Dear Editor,The database has been published as requested in Bozec et al. (2025; https://doi.org/10.17882/106537) and Robache and Schmitt (2025; https://doi.org/10.17882/106550), and will be referenced in the dedicated data availability section of the manuscript.Best regards,Kévin Robache and François G. SchmittCitation: https://doi.org/
10.5194/egusphere-2025-972-CC1
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CC1: 'Reply on EC1', Kévin Robache, 18 May 2025
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RC1: 'Comment on egusphere-2025-972', Anonymous Referee #1, 11 Jun 2025
Robache and Schmidt apply statistical approaches, that are more commonly used in other fields, to a high-frequency surface ocean biogeochemical data set collected on the coastal shelf off Brittany, France. These approaches are able to quantify relationships between different measured parameters as supporting evidence for the thermal vs non-thermal (e.g., primary production, river input of DIC) drivers of surface ocean pCO2 variability. The manuscript is well-written, targeted to an audience with some existing expertise in these statistical approaches. I recommend publication of this manuscript after a few issues are addressed.
Major comments:
The data set used in this analysis is 5 years long, with gaps (Table 1). At best, these statistical analyses address sub-annual pCO2 variability and its potential drivers. This needs to be clearly stated and incorporated into the interpretation of results. For example, how does the lack of a longer-term data set impact the finding that some of the time series are irreversible at time scales longer than one month? Could this be influenced by lack of data that would have longer-term signals, like interannual signals? How do the results of this analysis challenge or build upon past studies that have looked at these signals, such as the long-term memory processes that drive ocean biogeochemistry (e.g., the higher-order auto-regressive processes shown by Séférian et al., 2013, doi.org/10.5194/esd-4-109-2013, or the diurnal to seasonal processes shown by Torres et al., 2021, doi.org/10.1029/2020GL090228)?
This manuscript is written for a reader with some knowledge of advanced statistical approaches. In order to reach a wider audience of ocean biogeochemists, it would be useful to ensure all statistical and mathematical jargon is defined, such as conditional means (section 3.2.1) and power-law slopes and passive scalar turbulence (section 3.1.3).
The authors note the importance of large observation databases such as SOCAT (line 30). One benefit of a quality-controlled, internally-consistent data synthesis effort such as SOCAT is data accessibility for regional comparisons. The impact of this work would be enhanced by submitting the ASTAN buoy data to SOCAT and exploring pCO2 variability and drivers of similar time series found in SOCAT, especially high-frequency time series like from the Thornton buoy 10km off Belgium coast that measures the same parameters and may have similar local drivers such as nearby freshwater sources.
Minor comments:
Lines 65-72: States what depths and heights these measurements are collected. Also describe the data quality assurance and control process. Were outliers identified and flagged? With a fluorometer deployed at the surface, how is interference from ambient light addressed?
Line 184: Explain why the daily cycle influence is avoided in the Fourier analysis but included elsewhere (e.g., tidal signal in lines 193-195 and in the reversibility section)?
Line 192: Clarify what is meant by “small-scale” here.
Line 229: Remove “and thus the oceanic biological pump.” The relationship between pCO2 and chl a only suggest the effects of primary production in surface waters. The biological pump involves several other processes connecting those surface processes to sinking organic carbon, remineralization, and eventual sequestration at depth. The data presented here do not capture those subsurface processes.
Line 331: Remove “one” at the end of the sentence.
Line 361: Update database citation to the citation for the actual data and metadata.
Citation: https://doi.org/10.5194/egusphere-2025-972-RC1 - AC1: 'Reply on RC1 and RC2', Kévin Robache, 17 Sep 2025
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RC2: 'Comment on egusphere-2025-972', Anonymous Referee #2, 28 Aug 2025
The study ‘Multiscale statistical analysis of thermal and non-thermal components of seawater pCO2 in the Western English Channel: scaling, time-reversibility, and dependence’ statistically analyzes the pCO2 data from the ASTAN cardinal buoy (Brittany, west coast of France) with at 30-minute intervals. The total data is available for 5 years. The author applies various statistical approaches to quantify the relationship between the ocean state variables influencing the thermal and non-thermal components of the pCO2 variability. The paper is overall well written but is statistically too heavy. But depreciating the scientific explanations or essence for performing these statistical analyses. In general, any statistical analysis is performed to explain an underlying problem. This study lacks these explanations and seems like a statistical methodology that was simply applied to a set of variables, for the sake of applying. However, I believe the manuscript could be an important contribution if the authors are able to enhance the explanation highlighting the need for this hefty statistical analysis to understand the physics-based connection between different variables. My major and minor comments are as follows.
Major comments
Although the authors claim to have analyzed 5 years of data, Table 1 clearly shows that the primary variable, i.e., pCO2 of this study, have >60% gap. This raises a serious question on the significance of the statistics performed in this study. The authors should explain these limitations and how does it impact the overall outcome of this study.
Table 1 also highlights that the data gap varies for different variables. The authors perform PDF quotient which is based on joint probability. The variable data availability across the different variables may have a significant impact on such statistical analysis. The authors should make equal data length and then perform such PDF quotient. This may or may not change the outcome of this study, but such analysis is quint essential to show. Also, please provide figures showing the available data count for different time periods. This will give an idea how the distribution of data may impact the seasonality or the interannual or higher order variabilities.
Please explain the meaning of the time-reversal symmetry and asymmetry. Also, explain why such analysis is important. What scientific problem is addressed or highlighted, with such analysis? Especially keeping in mind variables such as pCO2. The return period analysis is generally performed for storms, cyclones, sea level rise, etc. These suggest the time required for reoccurrence of such events that may impact the coastal population/society.
Between lines 145-150 ‘This provides information that complements what is obtained from the correlation. While the correlation is a single numerical...’ authors present some key conclusions. However, it is important to highlight why is it important to know which values are in (x,y) plane exhibit weak or strong relationship.
Lines 159-160 ‘The CV of pCO2.....’ this could be because of the high missing values in pCO2.
Minor comments
Provide full form of ASTAN and WEC on its first occurrence in the manuscript.
Improve Fig. 2, why is it required?
Line 161 ‘.. X sat time series still exhibits significant fluctuations..’ How does the author decide that the fluctuations are significant?
Elongate Fig. 3 along X-axis for clarity of image.
Line 171 ‘In general, this indicates that the non-thermal component...’ Explain how does the author reach this conclusion?
Lines 175-177 ‘On the contrary..’ The results reported should be visible from Fig. 3
Line 178 should be Figs 4a and 4b
Lines 179-180 ‘More...’ The conclusion presented here is subjected to the amount of data availability and could change if more data is available. Authors should consider this.
Line 184 says that for scaling data below daily was discarded, more explanation is required for this statement. Especially, when the authors have very high-resolution data.
Line 192, please explain ‘small-scale intermittency’ in detail. What is the physical relevance of the same?
Lines 217-218 ‘As for the Fourier spectra...’ Explain the physical relevance to obtain information at such small scales. Also, since pCO2 = f(SST) isn’t the observation reported in this line but obvious?
Line 229, please remove the ‘biological pump’ reference. This data is only at surface, and a detailed analysis of the sub-surface data is required to confirm the role of the ‘biological pump’.
Citation: https://doi.org/10.5194/egusphere-2025-972-RC2 - AC1: 'Reply on RC1 and RC2', Kévin Robache, 17 Sep 2025
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Dear Authors,
During the review process, we identified an important issue regarding data accessibility that requires your attention.
According to the Biogeosciences Data policy (https://www.biogeosciences.net/policies/data_policy.html), authors are requested to deposit data that correspond to journal articles in reliable (public) data repositories, assign digital object identifiers (DOIs), and properly cite data sets as individual contributions.
Currently, your manuscript references Gac et al. (2020) for dataset access, which is not a formal data citation. Additionally, the URL provided in Gac et al. (2020) (http://somlit-db.epoc.u-bordeaux1.fr/bdd.php?serie=ST&sm=3) is no longer functional, and the described "discrete data" does not appear to include the buoy data central to your study.
To assist the review process, please deposit the dataset used in your study in a FAIR-aligned repository, assign a DOI to it, and provide that information in your response.
Best regards,
Liuqian