the Creative Commons Attribution 4.0 License.
the Creative Commons Attribution 4.0 License.
| 05 Mar 2024
Scaling and intermittent properties of oceanic and atmospheric pCO2 time series and their difference
Abstract. In this study the multi-scale dynamics of 38 oceanic and atmospheric pCO2 time series from fixed Eulerian buoys recorded with three-hour resolution are considered. The difference between these time series, the sea surface temperature and the sea surface salinity data were also studied. These series possess multi-scale turbulent-like fluctuations and display scaling properties from three hours to the annual scale. Scaling exponents are estimated through Fourier analysis and their average quantities considered globally for all parameters, as well as for different ecosystems (e.g. coastal shelf, coral reefs, open ocean). Sea surface temperature is the only parameter for which a spectral slope close to 5/3 is found, corresponding to a passive scalar in homogeneous and isotropic turbulence. The other parameters had smaller spectral slopes, from 1.18 to 1.35. By using empirical mode decomposition of the time series, together with generalized Hilbert spectral analysis, the intermittency of the time series was considered in the multifractal framework. Concave moment functions were estimated and Hurst index and intermittency parameters estimated in the framework of a lognormal multifractal fit. It is the first time that atmospheric and oceanic pCO2 and their difference ∆pCO2 are studied using such intermittent turbulence framework. The ∆pCO2 time series was shown to possess power-law scaling with an exponent of β = 1.32 ± 0.2.
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RC1: 'Comment on npg-2024-7', Anonymous Referee #1, 23 Apr 2024
The manuscript presents an analysis of the scaling properties of 38 oceanic and atmospheric pCO2 time series at 3-hr resolution to uncover similarities and differences between different ecosystems, as well as, to shed new insights on the role of turbulence (both of passive and active nature). The paper is well-written and also logically organized. It is appropriate for the scope of NPG. However, at the present stage I would not recommend it for publication but I would suggest for major revisions as outlined below.
Major comments
- The authors firstly present results based on Fourier PSD for spectral exponents, while later they use EMD/HSA to provide more insights on high-order statistics, as well as, to also reduce effects of periodicity in time series that could destroy scaling behavior. Why not to directly use EMD/HSA for also investigating spectral slopes by using the second-order moment of the generalized Hilbert spectra? This would directly overcome limitations provided by Fourier PSD. Concerning the second-order moment it is expected to observe an agreement between the spectral slope evaluated via Fourier PSD and those evaluated via EMD/HSA. This agreement seems to be missed if one looks at the second-order exponents for SSS in Figure 8 for Gulf of Maine and especially for pCO2 air time series.
- Concerning the scaling exponents of pCO2 air time series it seems that, especially for Gulf of Maine, a plateau is reached for high-order statistics that could be related to missing statistics for proper evaluation or to the choice of the range of scales where scaling exponents are evaluated. This needs to be fixed or explained.
- One of the main result is that multifractal intermittency is shown for the first time for oceanic and atmospheric pCO2 air time series. However, by looking at Table 5 I would say that intermittency is almost zero, considering average values of the µ parameter and its error range. Could this be related to the choice of the multifractal model, i.e., the log-normal one?
- A general comment on Figs. 4, 5, 7, 8: it would be desirable to add error bars on the estimated quantities (exponents) since this would allow directly to see if they are really different or can be comparable in the range of uncertainty. Furthermore, I would suggest to add in Fig. 4 both errors on ß as well as the indication of the range of frequencies where the spectral law is evaluated. The latter can be really useful to estimate the goodness of the fit, especially if looking at lower-middle panel when peaks appear at high frequencies.
- Figure 7. More than a comment it is a suggestion. It is an interesting result that seems to suggest that something occurs at northern mid latitudes. What about to see if there are variations in the slope of the low frequency regime that could be related to some large-scale forcing affecting that region? What about similar analysis for SST and SSS?
Minor comments (line by line)
- Line 16: "mitigated" seems to not be appropriate.
- Line 26: please clearly state which temporal and spatial scales are referring to.
- Line 29: "flux" -> "mixing"?
- Eq. (3): does it hold for current measurements? Is ß a function of the depth and of the frequency? Please clarify.
- Lines 124 and 125: "Pikes" -> "Peaks"?
- Figure 6: what are the dots?
- Line 199: linear interpolation could introduce some kinds of spurious high-frequency intermittent-like bursts where it is performed. Is it the case? If yes, these time intervals are removed for the evaluation of slopes?
- Eq. (6): there is a missing "Principal Value".
- Line 234: I do not see this agreement for pCO2 air time series (see Major Comments 1 and 2).
Citation: https://doi.org/10.5194/npg-2024-7-RC1 -
RC2: 'Comment on npg-2024-7', Anonymous Referee #2, 05 Sep 2024
Review of the manuscript titled ‘Scaling and intermittent properties of oceanic and atmospheric pCO2 time series and their difference’ by Robache et al.
This manuscript addresses the intermittent properties of pCO2 from high resolution time series to ascertain turbulent fluctuations that influence the uptake of pCO2 at the air sea interface. Measurements in different oceanic regions are used to determine the characteristics of pCO2 from coastal to open ocean from different methods and analysis tools. The content, methodology, the analysis and the results fit well into the scope of the journal Nonlinear Processes in Geophysics (NPG). The manuscript is well written and straight-forward to follow. The conclusions drawn are supported by the analysis and results presented.
I think it is a good paper, and I recommend it subject to minor revisions along the comments mentioned below. My comments below are mostly editorial but necessary to clarify certain parts of the text. In the end, the paper can also be useful in its present form. However, I recommend the manuscript for publication in NPG after a minor revision.
Minor comments:
- I suggest to include ‘in a turbulence framework’ at the end of the title, especially since it is the first time this is done in this study.
- The abstract should include some important results. At the moment the abstract mostly lists what was done with very little information on what was found as a result.
- Line 5: Remove brackets: ‘…ecosystems such as coastal shelf,..’
- Line 18: In context of the anthropogenic CO2 uptake by the ocean, the authors should also cite Sabine et al. 2004: The Oceanic Sink for Anthropogenic CO2. Science 305,367-371(2004). DOI:10.1126/science.1097403
- Line 29 influence of small scale turbulence
- Line 38: partial pressures
- Line 43: Here it is unclear whether the authors refer to the small scale or large scale turbulence, given that it is shown to evolve over a large period up to 3 months. Authors should clarify which kind of turbulence they refer to here, and also at other instances in the manuscript where turbulence appears.
- Line 44: ‘…their scaling properties’. Whose scaling properties? Clarify.
- Line 59: ‘…by the authors’. Which authors does this phrase correspond to: the present authors or the authors of a different manuscript? Please specify.
- Line 62: ‘The data paper presenting the database…’. Please cite the publication instead of such a phrase.
- Line 86: ‘…proportion of time in negative or positive values.’ This is unclear, please clarify the sentence.
- Line 86: ‘It indicates..’. It refers to what?
- Line 88: …sinks than sources…
- Line 89: what is reversed? Clarify.
- Line 95: …a proportion that is reversed… Fix the typo.
- Line 95: ‘…a proportion that is reversed…’ . Is the proportion reversed exactly also in percentages? Please clarify.
- Line 132: Please rewrite this sentence to make it clearer.
- Lines 175 and 244: Here and elsewhere: please be consistent with the user of either CO2 or carbon dioxide throughout the manuscript.
- Line 245: …these quantities…
- Line 246: …on multiscales…
- Section 5: The main results should be mentioned in this section more clearly which are currently missing or somehow unclear to the reader.
- Table A1: Is there another way of depicting the information in this table? Or if it is already published, perhaps it can be simply referred to the published dataset as a citation?
Citation: https://doi.org/10.5194/npg-2024-7-RC2 - AC1: 'Final author comments', Kévin Robache, 03 Oct 2024
Status: closed
-
RC1: 'Comment on npg-2024-7', Anonymous Referee #1, 23 Apr 2024
The manuscript presents an analysis of the scaling properties of 38 oceanic and atmospheric pCO2 time series at 3-hr resolution to uncover similarities and differences between different ecosystems, as well as, to shed new insights on the role of turbulence (both of passive and active nature). The paper is well-written and also logically organized. It is appropriate for the scope of NPG. However, at the present stage I would not recommend it for publication but I would suggest for major revisions as outlined below.
Major comments
- The authors firstly present results based on Fourier PSD for spectral exponents, while later they use EMD/HSA to provide more insights on high-order statistics, as well as, to also reduce effects of periodicity in time series that could destroy scaling behavior. Why not to directly use EMD/HSA for also investigating spectral slopes by using the second-order moment of the generalized Hilbert spectra? This would directly overcome limitations provided by Fourier PSD. Concerning the second-order moment it is expected to observe an agreement between the spectral slope evaluated via Fourier PSD and those evaluated via EMD/HSA. This agreement seems to be missed if one looks at the second-order exponents for SSS in Figure 8 for Gulf of Maine and especially for pCO2 air time series.
- Concerning the scaling exponents of pCO2 air time series it seems that, especially for Gulf of Maine, a plateau is reached for high-order statistics that could be related to missing statistics for proper evaluation or to the choice of the range of scales where scaling exponents are evaluated. This needs to be fixed or explained.
- One of the main result is that multifractal intermittency is shown for the first time for oceanic and atmospheric pCO2 air time series. However, by looking at Table 5 I would say that intermittency is almost zero, considering average values of the µ parameter and its error range. Could this be related to the choice of the multifractal model, i.e., the log-normal one?
- A general comment on Figs. 4, 5, 7, 8: it would be desirable to add error bars on the estimated quantities (exponents) since this would allow directly to see if they are really different or can be comparable in the range of uncertainty. Furthermore, I would suggest to add in Fig. 4 both errors on ß as well as the indication of the range of frequencies where the spectral law is evaluated. The latter can be really useful to estimate the goodness of the fit, especially if looking at lower-middle panel when peaks appear at high frequencies.
- Figure 7. More than a comment it is a suggestion. It is an interesting result that seems to suggest that something occurs at northern mid latitudes. What about to see if there are variations in the slope of the low frequency regime that could be related to some large-scale forcing affecting that region? What about similar analysis for SST and SSS?
Minor comments (line by line)
- Line 16: "mitigated" seems to not be appropriate.
- Line 26: please clearly state which temporal and spatial scales are referring to.
- Line 29: "flux" -> "mixing"?
- Eq. (3): does it hold for current measurements? Is ß a function of the depth and of the frequency? Please clarify.
- Lines 124 and 125: "Pikes" -> "Peaks"?
- Figure 6: what are the dots?
- Line 199: linear interpolation could introduce some kinds of spurious high-frequency intermittent-like bursts where it is performed. Is it the case? If yes, these time intervals are removed for the evaluation of slopes?
- Eq. (6): there is a missing "Principal Value".
- Line 234: I do not see this agreement for pCO2 air time series (see Major Comments 1 and 2).
Citation: https://doi.org/10.5194/npg-2024-7-RC1 -
RC2: 'Comment on npg-2024-7', Anonymous Referee #2, 05 Sep 2024
Review of the manuscript titled ‘Scaling and intermittent properties of oceanic and atmospheric pCO2 time series and their difference’ by Robache et al.
This manuscript addresses the intermittent properties of pCO2 from high resolution time series to ascertain turbulent fluctuations that influence the uptake of pCO2 at the air sea interface. Measurements in different oceanic regions are used to determine the characteristics of pCO2 from coastal to open ocean from different methods and analysis tools. The content, methodology, the analysis and the results fit well into the scope of the journal Nonlinear Processes in Geophysics (NPG). The manuscript is well written and straight-forward to follow. The conclusions drawn are supported by the analysis and results presented.
I think it is a good paper, and I recommend it subject to minor revisions along the comments mentioned below. My comments below are mostly editorial but necessary to clarify certain parts of the text. In the end, the paper can also be useful in its present form. However, I recommend the manuscript for publication in NPG after a minor revision.
Minor comments:
- I suggest to include ‘in a turbulence framework’ at the end of the title, especially since it is the first time this is done in this study.
- The abstract should include some important results. At the moment the abstract mostly lists what was done with very little information on what was found as a result.
- Line 5: Remove brackets: ‘…ecosystems such as coastal shelf,..’
- Line 18: In context of the anthropogenic CO2 uptake by the ocean, the authors should also cite Sabine et al. 2004: The Oceanic Sink for Anthropogenic CO2. Science 305,367-371(2004). DOI:10.1126/science.1097403
- Line 29 influence of small scale turbulence
- Line 38: partial pressures
- Line 43: Here it is unclear whether the authors refer to the small scale or large scale turbulence, given that it is shown to evolve over a large period up to 3 months. Authors should clarify which kind of turbulence they refer to here, and also at other instances in the manuscript where turbulence appears.
- Line 44: ‘…their scaling properties’. Whose scaling properties? Clarify.
- Line 59: ‘…by the authors’. Which authors does this phrase correspond to: the present authors or the authors of a different manuscript? Please specify.
- Line 62: ‘The data paper presenting the database…’. Please cite the publication instead of such a phrase.
- Line 86: ‘…proportion of time in negative or positive values.’ This is unclear, please clarify the sentence.
- Line 86: ‘It indicates..’. It refers to what?
- Line 88: …sinks than sources…
- Line 89: what is reversed? Clarify.
- Line 95: …a proportion that is reversed… Fix the typo.
- Line 95: ‘…a proportion that is reversed…’ . Is the proportion reversed exactly also in percentages? Please clarify.
- Line 132: Please rewrite this sentence to make it clearer.
- Lines 175 and 244: Here and elsewhere: please be consistent with the user of either CO2 or carbon dioxide throughout the manuscript.
- Line 245: …these quantities…
- Line 246: …on multiscales…
- Section 5: The main results should be mentioned in this section more clearly which are currently missing or somehow unclear to the reader.
- Table A1: Is there another way of depicting the information in this table? Or if it is already published, perhaps it can be simply referred to the published dataset as a citation?
Citation: https://doi.org/10.5194/npg-2024-7-RC2 - AC1: 'Final author comments', Kévin Robache, 03 Oct 2024
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