the Creative Commons Attribution 4.0 License.
the Creative Commons Attribution 4.0 License.
| 08 Mar 2023
ESD Ideas: A 6-year oscillation in the whole Earth system?
Abstract. An oscillation of about 6 years has been reported in Earth’s fluid core motions, magnetic field, rotation, and crustal deformations. Recently, a 6-year cycle has also been detected in several climatic parameters (e.g., sea level, surface temperature, precipitation, land ice, land hydrology, and atmospheric angular momentum). Here we suggest that the 6-year oscillations detected in the Earth’s deep interior, mantle rotation, and atmosphere are linked together, and that the core processes previously proposed as drivers of the 6-year cycle in the Earth’s rotation, cause in addition the atmosphere to oscillate together with the mantle, inducing fluctuations in the climate system with similar periodicities.
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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.
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Preprint
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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.
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Journal article(s) based on this preprint
Interactive discussion
Status: closed
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CC1: 'Comment on egusphere-2023-312', Paul PUKITE, 09 Mar 2023
This is such an interesting ESD Idea candidate. The 6 year period is a magic number in terms of the Earth. As an integer it aligns perfectly as a multiple of the annual cycle (obviously) and with the wavenumber=0 symmetry of the lunar nodal cycle Tn=27.2122 days interfering with the lunar anomalistic cycle Ta=27.5545 days. So that 1/Tn - 1/Ta = 1/ (6 y), to amazing precision assuming 365.25 days -- something like 5.9999 years ! What does this imply? As a longitidudinally independent measure it can describe a point in the Moon's orbit whereby the Moon's declination and distance wrt to the Earth are extremes (as well as the Sun given the annual multiple alignment), implying a cyclical extreme torque applied to the axis.
The other 6 year conection pertains to the Chandler wobble, whereby the lunar nodal cycle synchronizes with a semi-annual impulse with an envelope of ~6.4 years, according to modular arithmetic mod(365.25/ 27.2122, 0.5) = 1/433d (Chandler wobble cycle) and so beat envelope of 1/433d - 1/365.25d = 1/6.4y when mixed with the annual cycle. This value is observed in all Chandler wobble measurements when the Chandler wobble is mixed with and thus interferes with the annual wobble, see e.g. https://agupubs.onlinelibrary.wiley.com/doi/pdf/10.1029/98JB02527
Neither of these alignments are often invoked in the literature, as the nodal or draconic cycle is largely dismissed in favor of the tropical or synodic lunar cycle of 27.32 days , which is a longitudinally-centric measure, and thus irrelevant to the spherical symmetry of the Earth's mantle, atmosphere, and axis of rotation inertial moment. See Mathematical Geoenergy (Wiley/AGU, 2018).
Citation: https://doi.org/10.5194/egusphere-2023-312-CC1 -
AC1: 'Reply on CC1', Anny Cazenave, 18 Mar 2023
We thak Dr Pukite for his comment. It is interesting to learn that a 6-year cycle has also been found in some parameters of the Earth-Moon system. However it is not clear to us what type of mechanism linked to the dynamics of the Earth-Moon system could explain our observations. More detailed suggestions would be welcome.
Citation: https://doi.org/10.5194/egusphere-2023-312-AC1
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AC1: 'Reply on CC1', Anny Cazenave, 18 Mar 2023
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RC1: 'Comment on egusphere-2023-312', Jianli Chen, 06 Apr 2023
This article provides a fairly comprehensive review of the 6-year oscillations in the Earth system and proposes that the core processes, widely believed as the driver of the 6-year oscillations in LOD and magnetic field, is also responsible for the newly discovered similar 6-year oscillations in the climate system. This article is well written, and the authors have demonstrated a thorough understanding of the current progress in the field. I only have a few minor comments.
- In the abstract (line 18), the newly discovered 6-year oscillations are not just in the atmosphere, but also in the hydrosphere, ocean and cryosphere. I would suggest replacing “atmosphere” with “climate system” or “surface geophysical fluids”.
- Lines 44-45, “A recent study by Watkins et al. (2018) …”: It was a study published almost 5 years ago and should not really counted as a recent study. Also there was a parallel paper (Ding and Chao, 2018) published at about the same time on the same topic (6-year oscillation in surface deformation). The authors may want to cite this one as well, which provides some insights on the likely coupling mechanism.
Ding, H. & Chao, B. F. (2018). A 6-year westward rotary motion in the Earth: Detection and possible MICG coupling mechanism, Earth and Planetary Science Letters., 495, 50-55, https://doi.org/10.1016/j.epsl.2018.05.009
- Unlike the well-known 6-year oscillations in Earth rotation and magnetic field, the similar 6-year oscillations in the climate system have only been recently reported. Can the authors elaborate a little bit on how significant those signals are or how confident people are on detection of those signals?
- Line 92, “As LOD changes are well explained by deep Earth processes”: This is not really true. Although we believe that deep Earth processes are responsible for LOD changes at several years and longer time scales, the mechanisms are still not clear. The authors may want to rephrase the wording here.
Citation: https://doi.org/10.5194/egusphere-2023-312-RC1 -
CC2: 'Reply on RC1', Julia Pfeffer, 13 Apr 2023
We thank Reviewer Jianli Chen for his positive comments on this short note. We provide below our responses to each comment.
- Comment 1: We will replace the term "atmosphere" by "superficial fluid envelopes" .
- Comment 2: We will remove the word "recent" when quoting Watkins et al., 2018. We did not quote Ding and Chao, (2018) due to the limited number of references (15) allowed in ESD Ideas. We provide a more comprehensive litterature review in Pfeffer et al., 2023 (submitted, http://dx.doi.org/10.2139/ssrn.4388237).
- Comment 3: A detailed description of the 6-yr cycle in the climate system is provided in Moreira et al., (2021) and Pfeffer et al., (2023). These two studies, quoted in this note, show that the 6-yr cycle is quite significant, well above the noise level, in particular in the GMSL rate, precipitation, TWS, etc.
- Comment 4: We will rephrase the sentence as: " According to the current litterature, core dynamics is the favored mechanism to explain the 6-yr cycle in LOD. We thus may conclude [...]"
Updated reference:
Pfeffer et al., 2023 has been updated into: "Pfeffer, J., Cazenave, A., Rosat, S., Moreira, L., Mandea, M. and Dehant, V. (2023), A 6-Year Cycle in the Earth System. Submitted to Global Planetary Change. Available at SSRN: http://dx.doi.org/10.2139/ssrn.4388237"
Citation: https://doi.org/10.5194/egusphere-2023-312-CC2 -
AC2: 'Reply on RC1', Anny Cazenave, 13 Apr 2023
We thank Reviewer Jianli Chen for his positive comments on this short note. We provide below our responses to each comment.
- Comment 1: We will replace the term "atmosphere" by "superficial fluid envelopes" .
- Comment 2: We will remove the word "recent" when quoting Watkins et al., 2018. We did not quote Ding and Chao, (2018) due to the limited number of references (15) allowed in ESD Ideas. We provide a more comprehensive litterature review in Pfeffer et al., 2023 (submitted, http://dx.doi.org/10.2139/ssrn.4388237).
- Comment 3: A detailed description of the 6-yr cycle in the climate system is provided in Moreira et al., (2021) and Pfeffer et al., (2023). These two studies, quoted in this note, show that the 6-yr cycle is quite significant, well above the noise level, in particular in the GMSL rate, precipitation, TWS, etc.
- Comment 4: We will rephrase the sentence as: " According to the current litterature, core dynamics is the favored mechanism to explain the 6-yr cycle in LOD. We thus may conclude [...]"
Updated reference:
Pfeffer et al., 2023 has been updated into: "Pfeffer, J., Cazenave, A., Rosat, S., Moreira, L., Mandea, M. and Dehant, V. (2023), A 6-Year Cycle in the Earth System. Submitted to Global Planetary Change. Available at SSRN: http://dx.doi.org/10.2139/ssrn.4388237"
ReplyCitation: https://doi.org/10.5194/egusphere-2023-312-CC2Citation: https://doi.org/10.5194/egusphere-2023-312-AC2
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RC2: 'Comment on egusphere-2023-312', Richard Holme, 05 Jun 2023
There does seem to be a whole range of phenomena in the Earth system with a "period" of about 6 years. My own work suggested a very clear 6 year period (actually 5.88 year period) for \Delta LOD from 1962-2011. This fit appeared very imptessive - certainly enough to solidify my career! In retrospect, I think I did this work and published the paper at exactly the right time - but for my career, not for broader scientific understanding! By looking at the LOD series in detail post 2011, it seems that the 6 year period breaks down, with peaks in 2010,2014 and 2019 or so. So it was a good thing that I investigated when I did, otherwise things would have been much more complicated!
More generally, looking at LOD prior to 1962 (occultation data constrained) shows power at around 6 year, but generally at periods slightly greater than 6 years. This means that an assumption of a modal interaction seems more complex than I had suggested. Perhaps this is not surprising - with so many different elements making a contribution at about this period, there is a likelihood of a disruption of the simple oscillation. and most significantly, this disruption is uneven - suggesting that the signal is non-stationary. In this case, more complex Fourier analysis will not help with further understanding - I do not suggest wavelets aren't wonderful, but when the changes happen on the same time scale as the oscillation, overinterpretation is a risk.
As a result, this paper is to be welcomed as a start, but only as a start. With no clear methodology as to a mechanism of the coupling, a phenomonological approach is necessary - while correlation does not imply correlation, lack of correlation is certainly likely to allow rejection of causation. So it is interesting to start with the different phenomena with the similar periods, but what is the phase difference bewteen these "oscillations"? And is that phase diffrence consistent over time? Hopefully this paper will drive more detailed and intensive analysis of the data time-series to address this question.
Citation: https://doi.org/10.5194/egusphere-2023-312-RC2 -
AC3: 'Reply on RC2', Anny Cazenave, 13 Jun 2023
We thank Rev.2 for his comments about our ESD Ideas manuscript. Due to the limited number of references allowed in ESD Ideas, we could not quote the Home & de Viron (2013) paper but we are well aware of Rev.2 pioneering analysis of the 6-year cycle in LOD. Recent analyses of LOD data updated to present still show the presence of a 6-year cycle. Recent publications as well as our own work show that a 6-year cycle is detectable in the atmospheric angular momentum (AAM) that is out of phase with the 6-year cycle in LOD (this suggesting that the atmosphere oscillates in phase with the solid Earth mantle at this particular frequency.
In a longer manuscript (Pfeffer et al., A 6-year cycle in the Earth system, in review at Global and Planetary Change ; manuscript available on the SSRN platform –see reference below-), we provide a more comprehensive review of previous studies on the 6-year cycle (including from Holme & de Viron, 2013). We also investigate in detail the significance of the 6-year cycle detected in the deep Earth (waves in the liquid core, magnetic field), in the gravity field and in several climate parameters. We find phase (or phase) consistency at the 6 year frequency between magnetic field, gravity field, LOD, AAM and some climate parameters (e.g., mean Earth temperature). In land hydrology (i.e. vertically integrated water storage), the phase of the 6 year cycle is not geographically uniform, which can be explained by the complex response of the regional water balance to meteorological forcing and the potential delay in water propagation in soil from the surface to the underground aquifers. This issue will be mentionned in the revised version of Pfeffer et al.’s manuscript.
Finally we agree with Rev.2’s comment saying that our paper is just a start that needs to be followed by deeper investigations, in particular in terms of physical mechanism able to explain what drives the coupled system «mantle + atmosphere» at the 6-year frequency. As our study is clearly pluridisciplinary involving dynamical processes occuring in the deep Earth (core flow and magnetic field), geodesy (Earth rotation and gravity field), atmospheric and climate sciences as well as land hydrology, we think that this short note should motivate novel interdisciplinary studies from a wide research community.
Reference : Pfeffer, J., Cazenave, A., Rosat, S., Moreira, L., Mandea, M. and Dehant V. (2023). A 6-Year Cycle in the Earth System. In review, Global and Planetary Change. Preprint available at SSRN: http://dx.doi.org/10.2139/ssrn.4388237.
Citation: https://doi.org/10.5194/egusphere-2023-312-AC3 -
AC4: 'Reply on AC3', Anny Cazenave, 04 Jul 2023
Dear Editor
I have uploaded the revised version of our ESD Ideas manuscript entitled : ‘ A 6-year oscillation in the whole Earth system?.
With my co-authors, I made a number of corrections to account for the minor comments made by the two reviewers. A document ‘Responses to the reviewers’ has also been uploaded.
I hope this revised version will be acceptable for publication.
Sincerely Yours,
Anny Cazenave
Senior Scientist at LEGOS
(Laboratoire de Recherche en Geophysique et Oceanographie Spatiales, Toulouse, France)
New email: anny.cazenave@gmail.com
Citation: https://doi.org/10.5194/egusphere-2023-312-AC4
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AC4: 'Reply on AC3', Anny Cazenave, 04 Jul 2023
-
AC3: 'Reply on RC2', Anny Cazenave, 13 Jun 2023
Interactive discussion
Status: closed
-
CC1: 'Comment on egusphere-2023-312', Paul PUKITE, 09 Mar 2023
This is such an interesting ESD Idea candidate. The 6 year period is a magic number in terms of the Earth. As an integer it aligns perfectly as a multiple of the annual cycle (obviously) and with the wavenumber=0 symmetry of the lunar nodal cycle Tn=27.2122 days interfering with the lunar anomalistic cycle Ta=27.5545 days. So that 1/Tn - 1/Ta = 1/ (6 y), to amazing precision assuming 365.25 days -- something like 5.9999 years ! What does this imply? As a longitidudinally independent measure it can describe a point in the Moon's orbit whereby the Moon's declination and distance wrt to the Earth are extremes (as well as the Sun given the annual multiple alignment), implying a cyclical extreme torque applied to the axis.
The other 6 year conection pertains to the Chandler wobble, whereby the lunar nodal cycle synchronizes with a semi-annual impulse with an envelope of ~6.4 years, according to modular arithmetic mod(365.25/ 27.2122, 0.5) = 1/433d (Chandler wobble cycle) and so beat envelope of 1/433d - 1/365.25d = 1/6.4y when mixed with the annual cycle. This value is observed in all Chandler wobble measurements when the Chandler wobble is mixed with and thus interferes with the annual wobble, see e.g. https://agupubs.onlinelibrary.wiley.com/doi/pdf/10.1029/98JB02527
Neither of these alignments are often invoked in the literature, as the nodal or draconic cycle is largely dismissed in favor of the tropical or synodic lunar cycle of 27.32 days , which is a longitudinally-centric measure, and thus irrelevant to the spherical symmetry of the Earth's mantle, atmosphere, and axis of rotation inertial moment. See Mathematical Geoenergy (Wiley/AGU, 2018).
Citation: https://doi.org/10.5194/egusphere-2023-312-CC1 -
AC1: 'Reply on CC1', Anny Cazenave, 18 Mar 2023
We thak Dr Pukite for his comment. It is interesting to learn that a 6-year cycle has also been found in some parameters of the Earth-Moon system. However it is not clear to us what type of mechanism linked to the dynamics of the Earth-Moon system could explain our observations. More detailed suggestions would be welcome.
Citation: https://doi.org/10.5194/egusphere-2023-312-AC1
-
AC1: 'Reply on CC1', Anny Cazenave, 18 Mar 2023
-
RC1: 'Comment on egusphere-2023-312', Jianli Chen, 06 Apr 2023
This article provides a fairly comprehensive review of the 6-year oscillations in the Earth system and proposes that the core processes, widely believed as the driver of the 6-year oscillations in LOD and magnetic field, is also responsible for the newly discovered similar 6-year oscillations in the climate system. This article is well written, and the authors have demonstrated a thorough understanding of the current progress in the field. I only have a few minor comments.
- In the abstract (line 18), the newly discovered 6-year oscillations are not just in the atmosphere, but also in the hydrosphere, ocean and cryosphere. I would suggest replacing “atmosphere” with “climate system” or “surface geophysical fluids”.
- Lines 44-45, “A recent study by Watkins et al. (2018) …”: It was a study published almost 5 years ago and should not really counted as a recent study. Also there was a parallel paper (Ding and Chao, 2018) published at about the same time on the same topic (6-year oscillation in surface deformation). The authors may want to cite this one as well, which provides some insights on the likely coupling mechanism.
Ding, H. & Chao, B. F. (2018). A 6-year westward rotary motion in the Earth: Detection and possible MICG coupling mechanism, Earth and Planetary Science Letters., 495, 50-55, https://doi.org/10.1016/j.epsl.2018.05.009
- Unlike the well-known 6-year oscillations in Earth rotation and magnetic field, the similar 6-year oscillations in the climate system have only been recently reported. Can the authors elaborate a little bit on how significant those signals are or how confident people are on detection of those signals?
- Line 92, “As LOD changes are well explained by deep Earth processes”: This is not really true. Although we believe that deep Earth processes are responsible for LOD changes at several years and longer time scales, the mechanisms are still not clear. The authors may want to rephrase the wording here.
Citation: https://doi.org/10.5194/egusphere-2023-312-RC1 -
CC2: 'Reply on RC1', Julia Pfeffer, 13 Apr 2023
We thank Reviewer Jianli Chen for his positive comments on this short note. We provide below our responses to each comment.
- Comment 1: We will replace the term "atmosphere" by "superficial fluid envelopes" .
- Comment 2: We will remove the word "recent" when quoting Watkins et al., 2018. We did not quote Ding and Chao, (2018) due to the limited number of references (15) allowed in ESD Ideas. We provide a more comprehensive litterature review in Pfeffer et al., 2023 (submitted, http://dx.doi.org/10.2139/ssrn.4388237).
- Comment 3: A detailed description of the 6-yr cycle in the climate system is provided in Moreira et al., (2021) and Pfeffer et al., (2023). These two studies, quoted in this note, show that the 6-yr cycle is quite significant, well above the noise level, in particular in the GMSL rate, precipitation, TWS, etc.
- Comment 4: We will rephrase the sentence as: " According to the current litterature, core dynamics is the favored mechanism to explain the 6-yr cycle in LOD. We thus may conclude [...]"
Updated reference:
Pfeffer et al., 2023 has been updated into: "Pfeffer, J., Cazenave, A., Rosat, S., Moreira, L., Mandea, M. and Dehant, V. (2023), A 6-Year Cycle in the Earth System. Submitted to Global Planetary Change. Available at SSRN: http://dx.doi.org/10.2139/ssrn.4388237"
Citation: https://doi.org/10.5194/egusphere-2023-312-CC2 -
AC2: 'Reply on RC1', Anny Cazenave, 13 Apr 2023
We thank Reviewer Jianli Chen for his positive comments on this short note. We provide below our responses to each comment.
- Comment 1: We will replace the term "atmosphere" by "superficial fluid envelopes" .
- Comment 2: We will remove the word "recent" when quoting Watkins et al., 2018. We did not quote Ding and Chao, (2018) due to the limited number of references (15) allowed in ESD Ideas. We provide a more comprehensive litterature review in Pfeffer et al., 2023 (submitted, http://dx.doi.org/10.2139/ssrn.4388237).
- Comment 3: A detailed description of the 6-yr cycle in the climate system is provided in Moreira et al., (2021) and Pfeffer et al., (2023). These two studies, quoted in this note, show that the 6-yr cycle is quite significant, well above the noise level, in particular in the GMSL rate, precipitation, TWS, etc.
- Comment 4: We will rephrase the sentence as: " According to the current litterature, core dynamics is the favored mechanism to explain the 6-yr cycle in LOD. We thus may conclude [...]"
Updated reference:
Pfeffer et al., 2023 has been updated into: "Pfeffer, J., Cazenave, A., Rosat, S., Moreira, L., Mandea, M. and Dehant, V. (2023), A 6-Year Cycle in the Earth System. Submitted to Global Planetary Change. Available at SSRN: http://dx.doi.org/10.2139/ssrn.4388237"
ReplyCitation: https://doi.org/10.5194/egusphere-2023-312-CC2Citation: https://doi.org/10.5194/egusphere-2023-312-AC2
-
RC2: 'Comment on egusphere-2023-312', Richard Holme, 05 Jun 2023
There does seem to be a whole range of phenomena in the Earth system with a "period" of about 6 years. My own work suggested a very clear 6 year period (actually 5.88 year period) for \Delta LOD from 1962-2011. This fit appeared very imptessive - certainly enough to solidify my career! In retrospect, I think I did this work and published the paper at exactly the right time - but for my career, not for broader scientific understanding! By looking at the LOD series in detail post 2011, it seems that the 6 year period breaks down, with peaks in 2010,2014 and 2019 or so. So it was a good thing that I investigated when I did, otherwise things would have been much more complicated!
More generally, looking at LOD prior to 1962 (occultation data constrained) shows power at around 6 year, but generally at periods slightly greater than 6 years. This means that an assumption of a modal interaction seems more complex than I had suggested. Perhaps this is not surprising - with so many different elements making a contribution at about this period, there is a likelihood of a disruption of the simple oscillation. and most significantly, this disruption is uneven - suggesting that the signal is non-stationary. In this case, more complex Fourier analysis will not help with further understanding - I do not suggest wavelets aren't wonderful, but when the changes happen on the same time scale as the oscillation, overinterpretation is a risk.
As a result, this paper is to be welcomed as a start, but only as a start. With no clear methodology as to a mechanism of the coupling, a phenomonological approach is necessary - while correlation does not imply correlation, lack of correlation is certainly likely to allow rejection of causation. So it is interesting to start with the different phenomena with the similar periods, but what is the phase difference bewteen these "oscillations"? And is that phase diffrence consistent over time? Hopefully this paper will drive more detailed and intensive analysis of the data time-series to address this question.
Citation: https://doi.org/10.5194/egusphere-2023-312-RC2 -
AC3: 'Reply on RC2', Anny Cazenave, 13 Jun 2023
We thank Rev.2 for his comments about our ESD Ideas manuscript. Due to the limited number of references allowed in ESD Ideas, we could not quote the Home & de Viron (2013) paper but we are well aware of Rev.2 pioneering analysis of the 6-year cycle in LOD. Recent analyses of LOD data updated to present still show the presence of a 6-year cycle. Recent publications as well as our own work show that a 6-year cycle is detectable in the atmospheric angular momentum (AAM) that is out of phase with the 6-year cycle in LOD (this suggesting that the atmosphere oscillates in phase with the solid Earth mantle at this particular frequency.
In a longer manuscript (Pfeffer et al., A 6-year cycle in the Earth system, in review at Global and Planetary Change ; manuscript available on the SSRN platform –see reference below-), we provide a more comprehensive review of previous studies on the 6-year cycle (including from Holme & de Viron, 2013). We also investigate in detail the significance of the 6-year cycle detected in the deep Earth (waves in the liquid core, magnetic field), in the gravity field and in several climate parameters. We find phase (or phase) consistency at the 6 year frequency between magnetic field, gravity field, LOD, AAM and some climate parameters (e.g., mean Earth temperature). In land hydrology (i.e. vertically integrated water storage), the phase of the 6 year cycle is not geographically uniform, which can be explained by the complex response of the regional water balance to meteorological forcing and the potential delay in water propagation in soil from the surface to the underground aquifers. This issue will be mentionned in the revised version of Pfeffer et al.’s manuscript.
Finally we agree with Rev.2’s comment saying that our paper is just a start that needs to be followed by deeper investigations, in particular in terms of physical mechanism able to explain what drives the coupled system «mantle + atmosphere» at the 6-year frequency. As our study is clearly pluridisciplinary involving dynamical processes occuring in the deep Earth (core flow and magnetic field), geodesy (Earth rotation and gravity field), atmospheric and climate sciences as well as land hydrology, we think that this short note should motivate novel interdisciplinary studies from a wide research community.
Reference : Pfeffer, J., Cazenave, A., Rosat, S., Moreira, L., Mandea, M. and Dehant V. (2023). A 6-Year Cycle in the Earth System. In review, Global and Planetary Change. Preprint available at SSRN: http://dx.doi.org/10.2139/ssrn.4388237.
Citation: https://doi.org/10.5194/egusphere-2023-312-AC3 -
AC4: 'Reply on AC3', Anny Cazenave, 04 Jul 2023
Dear Editor
I have uploaded the revised version of our ESD Ideas manuscript entitled : ‘ A 6-year oscillation in the whole Earth system?.
With my co-authors, I made a number of corrections to account for the minor comments made by the two reviewers. A document ‘Responses to the reviewers’ has also been uploaded.
I hope this revised version will be acceptable for publication.
Sincerely Yours,
Anny Cazenave
Senior Scientist at LEGOS
(Laboratoire de Recherche en Geophysique et Oceanographie Spatiales, Toulouse, France)
New email: anny.cazenave@gmail.com
Citation: https://doi.org/10.5194/egusphere-2023-312-AC4
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AC4: 'Reply on AC3', Anny Cazenave, 04 Jul 2023
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AC3: 'Reply on RC2', Anny Cazenave, 13 Jun 2023
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Anny Cazenave
Julia Pfeffer
Mioara Mandea
Véronique Dehant
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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