Interactions between ocean heat budget terms in HighResMIP climate models measured by the rate of information transfer

Docquier, David; Vannitsem, Stéphane; Bellucci, Alessio; Frankignoul, Claude

doi:https://doi.org/10.5194/egusphere-2022-1340

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https://doi.org/10.5194/egusphere-2022-1340

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02 Dec 2022

| 02 Dec 2022

Status: this preprint has been withdrawn by the authors.

Interactions between ocean heat budget terms in HighResMIP climate models measured by the rate of information transfer

David Docquier, Stéphane Vannitsem, Alessio Bellucci, and Claude Frankignoul

Abstract. The Liang-Kleeman rate of information transfer is used to quantify interactions between the different terms of the ocean heat budget at monthly time scale over the period 1988–2017 in three coupled global climate models participating in the High Resolution Model Intercomparison Project (HighResMIP), as well as in the Ocean Reanalysis System 5 (ORAS5). In particular, we focus on the influences of ocean heat transport convergence (dynamical influence) and net surface heat flux (thermodynamical influence) on ocean heat content tendency. At least two different configurations are used for each model, allowing to investigate the impact of ocean resolution on these causal relationships. A very small number of regions with a dynamical influence is found at high ocean resolution (≤ 0.25°) and ORAS5 reanalysis when considering the upper 50 m, while a thermodynamical influence is present in a large number of regions. The number of regions with a dynamical influence increases when taking into account the upper 300 m and becomes comparable to the thermodynamical influence. Interestingly, low-resolution model configurations (1° in the ocean) show a much larger number of regions with a significant dynamical influence for both depth integrations (upper 50 m and 300 m) compared to high-resolution model configurations. The reason for the large difference in dynamical influence between low and high resolutions partly comes from the spatial distribution of ocean velocity field, which is highly variable at high resolution, leading to a smaller dynamical influence. High resolution is therefore key in representing realistically the causal interactions between the ocean and atmosphere.

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David Docquier, Stéphane Vannitsem, Alessio Bellucci, and Claude Frankignoul

Interactive discussion

Status: closed

RC1:
'Comment on egusphere-2022-1340', Justin Small, 01 Feb 2023
Review of Docquier, Vannitsem, Belluci and Frankignoul, Interactions between ocean heat budget terms in HighResMIP climate models measured by rate of information transfer, submitted to EGUSphere/Ocean Science.
This paper addresses the question of what processes drive upper ocean heat content variability in models and an ocean reanalysis. Low and high-resolution models from the HighResMIP suite are considered, and depths of 50m and 300m are analyzed. They aim to determine the role of surface heat fluxes and of ocean heat transport convergence. A novel aspect is that they use a form of information transfer theory to derive the connections between ocean heat content variability and the candidate driving mechanisms.
The authors are to be applauded for applying a novel method (information theory) to address the above question. However I believe there is a major flaw in this work (detailed next) which leads me to recommend rejection. I strongly encourage the authors to correct the flaw and resubmit at a later time for it is an interesting study. I am lead author of the Small et al. (2020) study cited in the paper so I have a keen interest in this subject and would like to see best methods applied.
The flaw is this: the OHT convergence computation (lines 132-138) must have an error to lead to the results you show. In my view the problem is that you have not included the vertical component and only consider horizontal convergence. The vertical component is very important and often of similar magnitude to the horizontal (and they often partly-cancel). A more secondary problem may be the lack of sub-monthly data.
It is possible that some HighResMIP models may output ocean heat transport convergence terms which, if true, would make this easier. A good person to ask is Malcolm Roberts, co-lead of HighResMIP.
Some comments which support my viewpoint:
Should the contributions from all terms add up to 100% ? When I look at figures like Fig. 1, 2,3, the sum of the ocean forcing and the atmosphere forcing can often be ~ 0% or negative.

In my work with high-resolution models, I always find that ocean forcing is more dominant in western boundary currents. This is not the case in your figures.

When you apply a more common method of Pearson correlation coefficient (Fig. 8), we now get surprisingly high correlations, and weaker values in high-resolution, all counter to my expectation.

I have discussed this with other experts who have supported my opinion and contributed to the above comments.
I am very keen to discuss and help interpretation. Once corrected, the manuscript could be a very important contribution to the field.
Justin Small, jsmall@ucar.edu
There are some other recent papers on similar topics that should be referenced:
Laurindo, L. , R. Justin Small, L.A. Thompson et al., 2022. Role of ocean and atmosphere variability in scale-dependent thermodynamic air-sea interaction. J. Geophys. Res. Ocean. https://agupubs.onlinelibrary.wiley.com/doi/10.1029/2021JC018340
Patrizio, C et al. - https://doi.org/10.1175/JCLI-D-20-0476.1 , also https://doi.org/10.1175/JCLI-D-21-0184.1
Citation: https://doi.org/10.5194/egusphere-2022-1340-RC1
- AC1:
  'Reply on RC1', David Docquier, 10 Feb 2023
  
  We would like to thank the reviewer Justin Small for hisvery interesting and insightful comments. We completely agree with Dr. Small that the non-inclusion of the vertical component of OHT convergence is a limitation of our study and might lead to an error in our estimates of dynamical dependencies between OHT convergence, OHC tendency and air-sea fluxes (Qnet).
  In our manuscript, we tried to take the missing processes (such as vertical and horizontal mixing and sub-monthly variations) into account by computing a residual term in the upper 50 m as the difference between OHC tendency and the sum of OHT convergence and Qnet, as explained in the end of Section 2.2 (L173-177). This approach showed that the “residual” influence was very similar to the “dynamical” (OHT convergence) influence (Section 3.4).
  However, we acknowledge that such an approach cannot replace the missing vertical component of OHT convergence and we agree with the reviewer that we should take this effect explicitly into account. Therefore, in our revision, we will take this vertical component into account and will re-compute the rate of information transfer between variables. We expect this will greatly improve the findings of our study. We will provide a more detailed response to this comment when this inclusion has been done.
  Concerning the three other comments of Dr. Small:
  1. The sum of the different contributions we show in the figures do not add up to 100% as we do not show in our paper the self-influences (e.g. influence of OHC tendency on itself), which are usually the largest, and the influences from OHT tendency to OHT convergence and Qnet. Taking all these contributions into account, the sum becomes closer to 100% but does not reach this value as there is also a noise component in the computation of the relative rate of information transfer (see eq. (5)).
  2. We agree with the reviewer that this difference between our study and his study (ocean forcing is more dominant in western boundary currents) has not been investigated in detail in our study. We will provide a more detailed response to this comment when the inclusion of the vertical component of OHT has been done.
  3. This illustrates well the fact that correlation does not necessarily imply causation. You can have a large number of regions with a significant correlation between OHC tendency and OHT convergence (such as in Fig. 8) but only a few of these regions show a causal dependence from OHT convergence to OHC tendency (Fig. 1a for LR and Fig. 2a for HR). The reason for the lower correlation at high resolution (Fig. 8b) compared to low resolution (Fig. 8a) is explained in Section 3.3: this is partly due to the “noisier” spatial distribution of ocean velocity at high resolution compared to low resolution (Fig. 7). Depending on the result we find with the inclusion of the OHT vertical component, we will update this part.
  We thank the reviewer again and will take all his comments into account in our revised manuscript.
  D. Docquier, S. Vannitsem, A. Bellucci, C. Frankignoul
  
  Citation: https://doi.org/10.5194/egusphere-2022-1340-AC1
  - RC2: 'Reply on AC1', Justin Small, 10 Feb 2023
    
    Dear Drs Doocquier, Vannitsem, Belluci, Frankignoul
    It is good that you find my comments helpful and I look forward to further feedback.
    Justin Small
    
    Citation: https://doi.org/10.5194/egusphere-2022-1340-RC2
    
    AC1: 'Reply on RC1', David Docquier, 10 Feb 2023
    
    We would like to thank the reviewer Justin Small for hisvery interesting and insightful comments. We completely agree with Dr. Small that the non-inclusion of the vertical component of OHT convergence is a limitation of our study and might lead to an error in our estimates of dynamical dependencies between OHT convergence, OHC tendency and air-sea fluxes (Qnet).
    In our manuscript, we tried to take the missing processes (such as vertical and horizontal mixing and sub-monthly variations) into account by computing a residual term in the upper 50 m as the difference between OHC tendency and the sum of OHT convergence and Qnet, as explained in the end of Section 2.2 (L173-177). This approach showed that the “residual” influence was very similar to the “dynamical” (OHT convergence) influence (Section 3.4).
    However, we acknowledge that such an approach cannot replace the missing vertical component of OHT convergence and we agree with the reviewer that we should take this effect explicitly into account. Therefore, in our revision, we will take this vertical component into account and will re-compute the rate of information transfer between variables. We expect this will greatly improve the findings of our study. We will provide a more detailed response to this comment when this inclusion has been done.
    Concerning the three other comments of Dr. Small:
    1. The sum of the different contributions we show in the figures do not add up to 100% as we do not show in our paper the self-influences (e.g. influence of OHC tendency on itself), which are usually the largest, and the influences from OHT tendency to OHT convergence and Qnet. Taking all these contributions into account, the sum becomes closer to 100% but does not reach this value as there is also a noise component in the computation of the relative rate of information transfer (see eq. (5)).
    2. We agree with the reviewer that this difference between our study and his study (ocean forcing is more dominant in western boundary currents) has not been investigated in detail in our study. We will provide a more detailed response to this comment when the inclusion of the vertical component of OHT has been done.
    3. This illustrates well the fact that correlation does not necessarily imply causation. You can have a large number of regions with a significant correlation between OHC tendency and OHT convergence (such as in Fig. 8) but only a few of these regions show a causal dependence from OHT convergence to OHC tendency (Fig. 1a for LR and Fig. 2a for HR). The reason for the lower correlation at high resolution (Fig. 8b) compared to low resolution (Fig. 8a) is explained in Section 3.3: this is partly due to the “noisier” spatial distribution of ocean velocity at high resolution compared to low resolution (Fig. 7). Depending on the result we find with the inclusion of the OHT vertical component, we will update this part.
    We thank the reviewer again and will take all his comments into account in our revised manuscript.
    D. Docquier, S. Vannitsem, A. Bellucci, C. Frankignoul
    
    Citation: https://doi.org/10.5194/egusphere-2022-1340-AC1
RC3:
'Comment on egusphere-2022-1340', Anonymous Referee #2, 15 Feb 2023

The authors, Docquier et al., analyse the causal relationship between different

components contributing to the tendency of depth-integrated ocean heat content

(OHC) using a somewhat ‘forgotten’, but important, metric introduced

by Liang and Kleeman (KL): the rate of information transfer. The main

purpose of the paper is to investigate the role of resolution in the

strength and direction of the causal relationship of different components

contributing to the ‘tendency budget’. A suite of couple climate models

and observational products of various resolutions are called upon.
Major comments
As mentioned by Small (RC1), neglecting the impact of the vertical

component in closing the OHC tendency ‘budget’ is problematic and

compounded by the fact that 1) not only the strength of oceanic

vertical transport, but also 2) the geographic locations of where

both significant vertical and horizontal (tracer) transport occurs, is

tightly linked to model resolution according to recent findings (see

for example, Rosso et al. 2014 and Langlais et al. 2015). As the

authors pointed out in the last sentence of the abstract, model

resolution is key in the realistic representation of ocean-atmospheric

interactions and, as a consequence, for realistic modelling of tracers

transport in climate models.
As vertical transport is of importance, the more so for higher

horizontal resolution model as mentioned above, it begs the question

of what is the influence of the vertical resolution as well.
I find challenging reconciling the 50m results, especially, with the

results presented by Bach et al. 2019 for SST and surface

atmospheric fields, who uses the Granger causality formalism,

extended to the frequency domain by Barnett and Seth, 2014.

Comparing the KL information transfer and Granger causality

approaches for the OHC tendency budget would be of value here.
Minor comments
For clarity, it would be informative to give the OHC tendency equation

with all relevant terms used by the authors (as well as the ones

collected under the residuals) and described such as in Small et al.

2020 or Roberts et al. 2016.
In the method section (L150-165), the readers would benefit from a

short illustration on how 1) the matrix co-factors are computed and

2) an explanation of what they represent.
More details on how 1) to compute the noise terms in the Z

‘normalizer’ and 2) to what these terms physically represent

(L160-165) would also be beneficial.
In the appendix, all self-interaction maps should be included for a

complete picture on how the KL method apportioned information

transfer as only information transfer between different variables have

been presented by the authors so far
Recommendations
In view of both the major and minor points mentioned above, I

recommend a major revision for the paper.
The published work on the impact of resolution on tracer transport

and Granger causality mentioned above are:
Rosso, Isabella, and Hogg, Andrew McC., and Strutton, Peter G.,

and Kiss, Andrew E., and Matear, Richard, and Klocker, Andreas,

and van Sebille, Erik. 2014. Vertical Transport in the Ocean Due to

Sub-Mesoscale Structures: Impacts in the Kerguelen Region. Ocean

Modelling. DOI: 10.1016/j.ocemod.2014.05.001.
Langlais, C. E. and Lenton, A. and Matear, R. and Monselesan, D.

and Legresy, B. and Cougnon, E. and Rintoul, S. 2017. Stationary

Rossby Waves Dominate Subduction of Anthropogenic Carbon in

the Southern Ocean. Scientific Reports. DOI:

10.1038/s41598-017-17292-3.
Barnett, Lionel and Seth, Anil K. 2014. The MVGC Multivariate

Granger Causality Toolbox: A New Approach to Granger-Causal

Inference. Journal of Neuroscience Methods. DOI:

10.1016/j.jneumeth.2013.10.018.
Bach, Eviatar, and Motesharrei, Safa, and Kalnay, Eugenia, and

Ruiz-Barradas, Alfredo. 2019. Local Atmosphere–Ocean

Predictability. Journal of Climate. DOI: 10.1175/JCLI-D-18-0817.1

Citation: https://doi.org/10.5194/egusphere-2022-1340-RC3
- AC2: 'Reply on RC3', David Docquier, 23 Feb 2023
  
  We would like to thank the reviewer for thevery interesting comments. As already mentioned in our reply to Referee #1 (Dr. Justin Small), we completely agree that the non-inclusion of the vertical component of OHT convergence is a limitation of our study and might lead to an error in our estimates of dynamical dependencies between OHT convergence, OHC tendency and air-sea fluxes (Qnet). We are actively working on integrating this vertical component in our computation and we will take it into account in our revision.
  Regarding the role of vertical resolution, HighResMIP model simulations focused on the impact of horizontal resolution, so all model configurations of the same model use the same number of vertical levels. Thus, we cannot really provide an answer to this question in our study. However, following the reviewer’s comment, we will provide a brief discussion regarding this aspect in our revision.
  We also thank the reviewer for pointing out the study from Bach et al. (2019) and we will provide a discussion of differences between their results using the Granger causality and our study.
  Regarding the remaining minor comments from the reviewer:
  - we will provide the OHC tendency equation in our revised manuscript as suggested by the reviewer;
  - we will provide further explanation about the computation of the matrix cofactors as well as the noise terms in the computation of the rate of information transfer;
  - we will provide some supplementary figures to provide the full picture of influences between the three different variables analyzed (including self-influences) in our revised manuscript;
  - we will integrate the different papers recommended by the reviewer.
  We thank the reviewer again and will take all the comments into account in our revised manuscript.
  D. Docquier, S. Vannitsem, A. Bellucci, C. Frankignoul
  
  Citation: https://doi.org/10.5194/egusphere-2022-1340-AC2

Interactive discussion

Status: closed

RC1:
'Comment on egusphere-2022-1340', Justin Small, 01 Feb 2023
Review of Docquier, Vannitsem, Belluci and Frankignoul, Interactions between ocean heat budget terms in HighResMIP climate models measured by rate of information transfer, submitted to EGUSphere/Ocean Science.
This paper addresses the question of what processes drive upper ocean heat content variability in models and an ocean reanalysis. Low and high-resolution models from the HighResMIP suite are considered, and depths of 50m and 300m are analyzed. They aim to determine the role of surface heat fluxes and of ocean heat transport convergence. A novel aspect is that they use a form of information transfer theory to derive the connections between ocean heat content variability and the candidate driving mechanisms.
The authors are to be applauded for applying a novel method (information theory) to address the above question. However I believe there is a major flaw in this work (detailed next) which leads me to recommend rejection. I strongly encourage the authors to correct the flaw and resubmit at a later time for it is an interesting study. I am lead author of the Small et al. (2020) study cited in the paper so I have a keen interest in this subject and would like to see best methods applied.
The flaw is this: the OHT convergence computation (lines 132-138) must have an error to lead to the results you show. In my view the problem is that you have not included the vertical component and only consider horizontal convergence. The vertical component is very important and often of similar magnitude to the horizontal (and they often partly-cancel). A more secondary problem may be the lack of sub-monthly data.
It is possible that some HighResMIP models may output ocean heat transport convergence terms which, if true, would make this easier. A good person to ask is Malcolm Roberts, co-lead of HighResMIP.
Some comments which support my viewpoint:
Should the contributions from all terms add up to 100% ? When I look at figures like Fig. 1, 2,3, the sum of the ocean forcing and the atmosphere forcing can often be ~ 0% or negative.

In my work with high-resolution models, I always find that ocean forcing is more dominant in western boundary currents. This is not the case in your figures.

When you apply a more common method of Pearson correlation coefficient (Fig. 8), we now get surprisingly high correlations, and weaker values in high-resolution, all counter to my expectation.

I have discussed this with other experts who have supported my opinion and contributed to the above comments.
I am very keen to discuss and help interpretation. Once corrected, the manuscript could be a very important contribution to the field.
Justin Small, jsmall@ucar.edu
There are some other recent papers on similar topics that should be referenced:
Laurindo, L. , R. Justin Small, L.A. Thompson et al., 2022. Role of ocean and atmosphere variability in scale-dependent thermodynamic air-sea interaction. J. Geophys. Res. Ocean. https://agupubs.onlinelibrary.wiley.com/doi/10.1029/2021JC018340
Patrizio, C et al. - https://doi.org/10.1175/JCLI-D-20-0476.1 , also https://doi.org/10.1175/JCLI-D-21-0184.1
Citation: https://doi.org/10.5194/egusphere-2022-1340-RC1
- AC1:
  'Reply on RC1', David Docquier, 10 Feb 2023
  
  We would like to thank the reviewer Justin Small for hisvery interesting and insightful comments. We completely agree with Dr. Small that the non-inclusion of the vertical component of OHT convergence is a limitation of our study and might lead to an error in our estimates of dynamical dependencies between OHT convergence, OHC tendency and air-sea fluxes (Qnet).
  In our manuscript, we tried to take the missing processes (such as vertical and horizontal mixing and sub-monthly variations) into account by computing a residual term in the upper 50 m as the difference between OHC tendency and the sum of OHT convergence and Qnet, as explained in the end of Section 2.2 (L173-177). This approach showed that the “residual” influence was very similar to the “dynamical” (OHT convergence) influence (Section 3.4).
  However, we acknowledge that such an approach cannot replace the missing vertical component of OHT convergence and we agree with the reviewer that we should take this effect explicitly into account. Therefore, in our revision, we will take this vertical component into account and will re-compute the rate of information transfer between variables. We expect this will greatly improve the findings of our study. We will provide a more detailed response to this comment when this inclusion has been done.
  Concerning the three other comments of Dr. Small:
  1. The sum of the different contributions we show in the figures do not add up to 100% as we do not show in our paper the self-influences (e.g. influence of OHC tendency on itself), which are usually the largest, and the influences from OHT tendency to OHT convergence and Qnet. Taking all these contributions into account, the sum becomes closer to 100% but does not reach this value as there is also a noise component in the computation of the relative rate of information transfer (see eq. (5)).
  2. We agree with the reviewer that this difference between our study and his study (ocean forcing is more dominant in western boundary currents) has not been investigated in detail in our study. We will provide a more detailed response to this comment when the inclusion of the vertical component of OHT has been done.
  3. This illustrates well the fact that correlation does not necessarily imply causation. You can have a large number of regions with a significant correlation between OHC tendency and OHT convergence (such as in Fig. 8) but only a few of these regions show a causal dependence from OHT convergence to OHC tendency (Fig. 1a for LR and Fig. 2a for HR). The reason for the lower correlation at high resolution (Fig. 8b) compared to low resolution (Fig. 8a) is explained in Section 3.3: this is partly due to the “noisier” spatial distribution of ocean velocity at high resolution compared to low resolution (Fig. 7). Depending on the result we find with the inclusion of the OHT vertical component, we will update this part.
  We thank the reviewer again and will take all his comments into account in our revised manuscript.
  D. Docquier, S. Vannitsem, A. Bellucci, C. Frankignoul
  
  Citation: https://doi.org/10.5194/egusphere-2022-1340-AC1
  - RC2: 'Reply on AC1', Justin Small, 10 Feb 2023
    
    Dear Drs Doocquier, Vannitsem, Belluci, Frankignoul
    It is good that you find my comments helpful and I look forward to further feedback.
    Justin Small
    
    Citation: https://doi.org/10.5194/egusphere-2022-1340-RC2
    
    AC1: 'Reply on RC1', David Docquier, 10 Feb 2023
    
    We would like to thank the reviewer Justin Small for hisvery interesting and insightful comments. We completely agree with Dr. Small that the non-inclusion of the vertical component of OHT convergence is a limitation of our study and might lead to an error in our estimates of dynamical dependencies between OHT convergence, OHC tendency and air-sea fluxes (Qnet).
    In our manuscript, we tried to take the missing processes (such as vertical and horizontal mixing and sub-monthly variations) into account by computing a residual term in the upper 50 m as the difference between OHC tendency and the sum of OHT convergence and Qnet, as explained in the end of Section 2.2 (L173-177). This approach showed that the “residual” influence was very similar to the “dynamical” (OHT convergence) influence (Section 3.4).
    However, we acknowledge that such an approach cannot replace the missing vertical component of OHT convergence and we agree with the reviewer that we should take this effect explicitly into account. Therefore, in our revision, we will take this vertical component into account and will re-compute the rate of information transfer between variables. We expect this will greatly improve the findings of our study. We will provide a more detailed response to this comment when this inclusion has been done.
    Concerning the three other comments of Dr. Small:
    1. The sum of the different contributions we show in the figures do not add up to 100% as we do not show in our paper the self-influences (e.g. influence of OHC tendency on itself), which are usually the largest, and the influences from OHT tendency to OHT convergence and Qnet. Taking all these contributions into account, the sum becomes closer to 100% but does not reach this value as there is also a noise component in the computation of the relative rate of information transfer (see eq. (5)).
    2. We agree with the reviewer that this difference between our study and his study (ocean forcing is more dominant in western boundary currents) has not been investigated in detail in our study. We will provide a more detailed response to this comment when the inclusion of the vertical component of OHT has been done.
    3. This illustrates well the fact that correlation does not necessarily imply causation. You can have a large number of regions with a significant correlation between OHC tendency and OHT convergence (such as in Fig. 8) but only a few of these regions show a causal dependence from OHT convergence to OHC tendency (Fig. 1a for LR and Fig. 2a for HR). The reason for the lower correlation at high resolution (Fig. 8b) compared to low resolution (Fig. 8a) is explained in Section 3.3: this is partly due to the “noisier” spatial distribution of ocean velocity at high resolution compared to low resolution (Fig. 7). Depending on the result we find with the inclusion of the OHT vertical component, we will update this part.
    We thank the reviewer again and will take all his comments into account in our revised manuscript.
    D. Docquier, S. Vannitsem, A. Bellucci, C. Frankignoul
    
    Citation: https://doi.org/10.5194/egusphere-2022-1340-AC1
RC3:
'Comment on egusphere-2022-1340', Anonymous Referee #2, 15 Feb 2023

The authors, Docquier et al., analyse the causal relationship between different

components contributing to the tendency of depth-integrated ocean heat content

(OHC) using a somewhat ‘forgotten’, but important, metric introduced

by Liang and Kleeman (KL): the rate of information transfer. The main

purpose of the paper is to investigate the role of resolution in the

strength and direction of the causal relationship of different components

contributing to the ‘tendency budget’. A suite of couple climate models

and observational products of various resolutions are called upon.
Major comments
As mentioned by Small (RC1), neglecting the impact of the vertical

component in closing the OHC tendency ‘budget’ is problematic and

compounded by the fact that 1) not only the strength of oceanic

vertical transport, but also 2) the geographic locations of where

both significant vertical and horizontal (tracer) transport occurs, is

tightly linked to model resolution according to recent findings (see

for example, Rosso et al. 2014 and Langlais et al. 2015). As the

authors pointed out in the last sentence of the abstract, model

resolution is key in the realistic representation of ocean-atmospheric

interactions and, as a consequence, for realistic modelling of tracers

transport in climate models.
As vertical transport is of importance, the more so for higher

horizontal resolution model as mentioned above, it begs the question

of what is the influence of the vertical resolution as well.
I find challenging reconciling the 50m results, especially, with the

results presented by Bach et al. 2019 for SST and surface

atmospheric fields, who uses the Granger causality formalism,

extended to the frequency domain by Barnett and Seth, 2014.

Comparing the KL information transfer and Granger causality

approaches for the OHC tendency budget would be of value here.
Minor comments
For clarity, it would be informative to give the OHC tendency equation

with all relevant terms used by the authors (as well as the ones

collected under the residuals) and described such as in Small et al.

2020 or Roberts et al. 2016.
In the method section (L150-165), the readers would benefit from a

short illustration on how 1) the matrix co-factors are computed and

2) an explanation of what they represent.
More details on how 1) to compute the noise terms in the Z

‘normalizer’ and 2) to what these terms physically represent

(L160-165) would also be beneficial.
In the appendix, all self-interaction maps should be included for a

complete picture on how the KL method apportioned information

transfer as only information transfer between different variables have

been presented by the authors so far
Recommendations
In view of both the major and minor points mentioned above, I

recommend a major revision for the paper.
The published work on the impact of resolution on tracer transport

and Granger causality mentioned above are:
Rosso, Isabella, and Hogg, Andrew McC., and Strutton, Peter G.,

and Kiss, Andrew E., and Matear, Richard, and Klocker, Andreas,

and van Sebille, Erik. 2014. Vertical Transport in the Ocean Due to

Sub-Mesoscale Structures: Impacts in the Kerguelen Region. Ocean

Modelling. DOI: 10.1016/j.ocemod.2014.05.001.
Langlais, C. E. and Lenton, A. and Matear, R. and Monselesan, D.

and Legresy, B. and Cougnon, E. and Rintoul, S. 2017. Stationary

Rossby Waves Dominate Subduction of Anthropogenic Carbon in

the Southern Ocean. Scientific Reports. DOI:

10.1038/s41598-017-17292-3.
Barnett, Lionel and Seth, Anil K. 2014. The MVGC Multivariate

Granger Causality Toolbox: A New Approach to Granger-Causal

Inference. Journal of Neuroscience Methods. DOI:

10.1016/j.jneumeth.2013.10.018.
Bach, Eviatar, and Motesharrei, Safa, and Kalnay, Eugenia, and

Ruiz-Barradas, Alfredo. 2019. Local Atmosphere–Ocean

Predictability. Journal of Climate. DOI: 10.1175/JCLI-D-18-0817.1

Citation: https://doi.org/10.5194/egusphere-2022-1340-RC3
- AC2: 'Reply on RC3', David Docquier, 23 Feb 2023
  
  We would like to thank the reviewer for thevery interesting comments. As already mentioned in our reply to Referee #1 (Dr. Justin Small), we completely agree that the non-inclusion of the vertical component of OHT convergence is a limitation of our study and might lead to an error in our estimates of dynamical dependencies between OHT convergence, OHC tendency and air-sea fluxes (Qnet). We are actively working on integrating this vertical component in our computation and we will take it into account in our revision.
  Regarding the role of vertical resolution, HighResMIP model simulations focused on the impact of horizontal resolution, so all model configurations of the same model use the same number of vertical levels. Thus, we cannot really provide an answer to this question in our study. However, following the reviewer’s comment, we will provide a brief discussion regarding this aspect in our revision.
  We also thank the reviewer for pointing out the study from Bach et al. (2019) and we will provide a discussion of differences between their results using the Granger causality and our study.
  Regarding the remaining minor comments from the reviewer:
  - we will provide the OHC tendency equation in our revised manuscript as suggested by the reviewer;
  - we will provide further explanation about the computation of the matrix cofactors as well as the noise terms in the computation of the rate of information transfer;
  - we will provide some supplementary figures to provide the full picture of influences between the three different variables analyzed (including self-influences) in our revised manuscript;
  - we will integrate the different papers recommended by the reviewer.
  We thank the reviewer again and will take all the comments into account in our revised manuscript.
  D. Docquier, S. Vannitsem, A. Bellucci, C. Frankignoul
  
  Citation: https://doi.org/10.5194/egusphere-2022-1340-AC2

David Docquier, Stéphane Vannitsem, Alessio Bellucci, and Claude Frankignoul

Model code and software

Liang Index to quantify interactions between ocean heat budget terms David Docquier https://doi.org/10.5281/zenodo.7358097

David Docquier, Stéphane Vannitsem, Alessio Bellucci, and Claude Frankignoul

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Short summary

Understanding whether variations in ocean heat content are driven by air-sea heat fluxes or by ocean dynamics is of crucial importance to enhance climate projections. We use a relatively novel causal method to quantify interactions between ocean heat budget terms based on climate models. We find that low-resolution models overestimate the influence of ocean dynamics in the upper ocean, and that changes in ocean heat content are dominated by air-sea fluxes at high resolution.


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