Estimates of Atlantic meridional heat transport from spatiotemporal fusion of Argo, altimetry and gravimetry data

Calafat, Francisco M.; Vallivattathillam, Parvathi; Frajka-Williams, Eleanor

doi:https://doi.org/10.5194/egusphere-2025-1216

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https://doi.org/10.5194/egusphere-2025-1216

Preprints

21 Mar 2025

| 21 Mar 2025

Estimates of Atlantic meridional heat transport from spatiotemporal fusion of Argo, altimetry and gravimetry data

Francisco M. Calafat, Parvathi Vallivattathillam, and Eleanor Frajka-Williams

Abstract. Understanding how changes in Atlantic meridional heat transport (MHT) and the Earth’s climate relate to one another is crucial to our ability to predict the future climate response to anthropogenic forcing. Attaining this understanding requires continuous and accurate records of MHT across the whole Atlantic. While such records can be obtained through direct ocean observing systems, these systems are expensive to install and maintain and thus, in practice, records of MHT derived in this way are restricted to a few latitudes. An alternative approach, based on hydrographic and satellite components of the global ocean observing system, consists of inferring heat transport convergence as a residual from the difference between ocean heat content (OHC) changes and surface heat flux. In its simplest form, this approach derives the OHC from hydrographic observations alone, however these observations are spatially sparse and unevenly distributed, which can introduce significant errors and biases into the MHT estimates. Here, we combine data from hydrography, satellite altimetry and satellite gravimetry through joint spatiotemporal modelling to generate probabilistic estimates of MHT for the period 2004–2020 at 3-month resolution across 12 latitudinal sections of the Atlantic Ocean between 65° N and 35° S. Our approach leverages the higher spatial sampling of the satellite observations to compensate for the sparseness and irregular distribution of the hydrographic data, leading to significantly improved estimates of MHT compared to those derived from hydrographic data alone. The fusion of the various data sets is done using rigorous Bayesian statistical methods that account for the spatial resolution mismatch between data sets and ensure an adequate representation and propagation of uncertainty. Our estimates of MHT at 26° N agree remarkably well with estimates based on direct ocean observations from the RAPID array, in terms of both the magnitude and phase of the variability, with a correlation of 0.77 for quarterly (3-monthly) time series and 0.93 after applying a 5-quarter running mean. The time-mean MHT at 26° N is also captured by our approach, with a value of 1.17 PW [1.04,1.30] (5–95 % credible interval). Estimates of MHT at other latitudes are also consistent with what we expect based on earlier estimates as well as on our current understanding of MHT in the Atlantic Ocean.

Received: 14 Mar 2025 – Discussion started: 21 Mar 2025

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Francisco M. Calafat, Parvathi Vallivattathillam, and Eleanor Frajka-Williams

Status: closed

RC1:
'Comment on egusphere-2025-1216', Anonymous Referee #1, 18 Apr 2025
Review of “Estimates of Atlantic meridional heat transport from spatiotemporal fusion of Argo, altimetry and gravimetry data” by Calafat et al.

This paper aims to estimate the meridional heat transport (MHT) at transatlantic sections throughout the Atlantic Ocean. Mainly, it uses hydrographic and satellite data via a Bayesian hierarchical model (BHM) to calculate the ocean heat content (OHC) tendency. The latter is then combined with air-sea heat flux data product to derive the ocean heat divergence and the MHT (as a residual from heat budgets). Accurate MHT estimates are critical for understanding the ocean’s role in our climate system. Overall, the paper reads well, and the results are presented. However, there is potential confusion about the goals and motivations of this study, which would make it hard to follow what is presented and what one can learn from it. I recommend it for publication after the following minor comments are addressed.

Main comments:

The main goal of this paper is to provide MHT estimates that maximize the use of hydrographic and satellite data, via a new framework (BHM). However, I have difficulties in understanding the argument of not using the RAPID data to derive the MHT at other latitudes. Instead, the authors make assumptions about the MHT at the northern boundaries, which introduce uncertainties in the MHT estimates across all latitudes. In my opinion, it undermines the deliverables from this study.

Another source of uncertainty in the MHT estimates is from surface heat flux. However, surface heat flux itself likely contains larger uncertainty than the heat divergence derived from this study – as that is indicated by the discrepancies between BHM solutions. I would suggest that the authors provide a thorough uncertainty estimate that takes into consideration errors in surface heat flux.

If the goal of this paper is to prove the efficacy of the new BHM framework that combines hydrographic and satellite observations, should it be compared with one that just uses hydrographic data? That would highlight the advantages of the BHM.

This is related to comment#3. Much of this paper is centered on the discrepancies between BHM solutions (see Figures 4, 5, 6, 7 and the related text). Those comparisons are useful as an evaluation of how different surface heat flux data impact the MHT estimates. But such an evaluation itself is not well motivated. In addition, the MHT estimates are validated against Trenberth et al. (2019). But it is not clear we gain from this analysis that is distinct from Trenberth et al. which uses atmospheric reanalyses (surface heat flux) and hydrographic data (the OHC tendency).

Other comments:

Line 90: TS and HS are anomalies relative to the climatology density. Other terms should also be anomalies? Please be specific about each term.
Line 133: ‘interesting oceanographically’ reads odd.
Line 148: How large is the volume transport? If it is large, it affects the mass conservation and thus the MHT estimate. Such effects on the related sections need to be discussed.
Line 172: Uniform l= 100m spatially and vertically? How valid are such assumptions?
Line 215: Are the two reanalysis products only used onward 12/2017? If yes, how?
Line 218: Are the reanalysis products averaged together with DEEP-C? This appears to contradict the previous statement that ‘it is preferable to’ the reanalysis products.
Line 228: ‘effective spatial resolution is much lower than what such grids imply’ Hard to understand what it means – please reword.
Line 240: If the goal is for an integrated value over the region between two latitudes (11 regions in total, Fig. 1), why does one need spatial grids anyway? Why not consider the enclosed basin as a whole?
Line 281: Setting rhoij= 0 requires justifications. The decorrelation time scale should be evaluated separately for each dataset, which is likely longer than a month.
Line 288 and Figure 2: What are the different arrows in Figure 2? For example, those black arrows within the right red box indicate that Q is derived by H minus HTC. But that is opposite to what’s described in the text.
Line 298: Why are the reanalysis products used separately? This is related to my comment above.
Line 315: How exactly are uncertainties determined? It is the key to providing a meaningful estimate.
Line 520: What does it mean by ‘will be accurate at any latitude’? How to quantify this accuracy? Also, why is the true transport at a given latitude is ‘large relative to the true transport at 65N’?
Line 524: ‘four time larger at RAPID than at OSNAP’ – are the comparisons only based on the MHT estimates from this study?
Line 529: What kind of error is this referring to? The mean value of MHT1 is not supposed to affect the derived variations.
Line 532: How representative is the 2014-2018 mean? over a longer period 2004-2020?
Line 536: I am not sure about this assumption that is based on a 4-year time series.
Line 540-546: I found the explanations inadequate – this is related to my main comment above. First, the observed MHT from RAPID is most likely the best estimate one can get, so why does depending on it become an issue? I cannot follow the reasoning behind the second point. Why does the observed MHT from RAPID introduce large errors? It is understandable that the RAPID data may be used to first validate this method. But after that validation, could and should it be used to improve the estimates?
Line 549: Once again, it is unclear why three surface heat flux (Qsfc) datasets are used separately, which are over different time periods.
Line 573: Please justify ‘very significant’ – what is p-value?
Line 575: Why is a discrepancy only occurring in 2020?
Line 577: ‘This discrepancy is … entire period.’ Hard to understand what it means – please rephrase.
Line 588: Figure 4: How are the CIs determined? It is worth a dedicated subsection in Methods on uncertainty in the MHT estimates.
Line 599: As mentioned above, is the difference in the mean MHT between BMH solutions mostly related to Qsfc?
Line 600: ‘To complete our comparison’ may not be a good motivation. E.g., why apply 5-quarter running averages? How does it help complete the comparison, or how does it help understand the discrepancies?
Line 609: The data are 5-year averages. What do the differences during 2005-2007 represent?
Line 626: For the comparing purposes, why not apply the same 12-month (4-quarter) running averages to the MHT estimates from this study? That would help make meaningful comparisons.
Line 628: ‘several interesting features’ reads odd.
Line 628 and the whole paragraph: Those features are related to the similarities and differences between BHM solutions. But it is not clear what we will gain from those comparisons. Please refer to my main comments.
Line 658: As mentioned earlier, would it be better to use the 12-month smoothed data when comparing with Trenberth et al. (2019)?
Line 667: The mean is obtained over different lengths of record and different periods. Given the strong interannual and decadal variations in the OHC and probably in the MHT, the time-mean estimates could be biased and cannot be compared directly to each other. Please justify the choices of those estimates to compare with and discuss the comparisons to avoid misinterpretation.
Line 686: Is it because of a similar method (MHT as a residual from heat budgets)?
Line 688: Why compare to GW03? What can we learn from this comparison?
Line 706: What is the main objective of this study? A data set (MHT estimates) or a valid method? Please refer to my main comments.
Line 710: It is not clear why three solutions are needed.
Line 719: This seems to be a hasty conclusion. Those correlations are based on data for different time periods and are based on different assumptions.
Line 726: It simply indicates that surface heat flux is a major source of uncertainty in the MHT estimates. Please refer to my main comments.
Citation: https://doi.org/10.5194/egusphere-2025-1216-RC1
- AC1: 'Reply on RC1', Francisco Mir Calafat, 31 Jul 2025
  
  The comment was uploaded in the form of a supplement: https://egusphere.copernicus.org/preprints/2025/egusphere-2025-1216/egusphere-2025-1216-AC1-supplement.pdf
  
  Citation: https://doi.org/10.5194/egusphere-2025-1216-AC1
RC2:
'Comment on egusphere-2025-1216', Anonymous Referee #2, 14 May 2025
This study tackles the challenge of estimating variations in Atlantic meridional heat transport (MHT) using satellite data and in situ temperature and salinity profiles across 12 latitudinal cross-sections. The authors propose a method to estimate MHT by combining changes in ocean heat content (OHC) with surface heat flux (HF) data. Recognizing the limitations imposed by sparse hydrographic observations, the study advances traditional methods by integrating hydrographic data with satellite altimetry and gravimetry within a joint spatiotemporal Bayesian framework. This fusion enables the generation of probabilistic MHT estimates from 2004 to 2020 across 12 Atlantic latitudinal sections, from 65°N to 35°S. The methodology effectively leverages the comprehensive spatial coverage of satellite data to compensate for the uneven distribution of in situ observations, thereby improving the quality of MHT estimates. Validation against independent measurements from the RAPID array at 26°N (which were not used in the derivation of the MHT estimates) shows good agreement in both the magnitude and timing of variability (with correlations of 0.77 for the raw series and 0.93 for the smoothed series), as well as in the mean transport value (1.17 PW). Results at other latitudes are consistent with prior estimates.

This work addresses the critical issue of variability in Atlantic meridional heat transport—a key component of global and regional ocean heat transport influencing climate. Continuous and precise measurements of Atlantic MHT are essential but limited by the high costs and logistical challenges associated with direct ocean observation systems, which currently provide data at only a few latitudes (e.g., through the RAPID and OSNAP arrays). The authors manage to overcome this limitation here by infering ocean heat transport convergence (HTC) as a residual from the imbalance between OHC changes and surface heat fluxes, using all available data to estimate OHC (i.e., satellite altimetry, gravimetry, and hydrographic observations) within a Bayesian framework. As such, this study is original and highly relevant to the climate science community. The ocean energy budget approach used to derive HTC is not new, nor is the combination of satellite altimetry, gravimetry, and hydrography to estimate OHC. The novelty of this study lies in its application of a Bayesian statistical framework that explicitly accounts for uncertainties in each dataset.
While the overall approach is sound and the results are promising, there are several significant limitations in the current version of the manuscript that must be addressed for the study to be fully convincing.

Major Concerns
Surface Heat Flux (HF) Datasets:

The datasets used to estimate HF are not state-of-the-art. The authors rely on outputs from atmospheric reanalyses, whose surface flux estimates are known to suffer from inconsistencies and large biases due to the weak observational constraints on the short-term forecasts used to generate them. A more robust alternative involves estimating surface fluxes from the atmospheric energy budget using CERES observations at the top of the atmosphere (TOA) and computing the divergence of atmospheric energy transport from reanalysis fields (e.g., winds and temperature), which are more strongly constrained through data assimilation than the short-term forecasts. This approach has been adopted by Mayer et al. (2017, 2021, 2022, 2024) and Meyssignac et al. (2024), and is now widely accepted as yielding net surface fluxes with smaller large-scale biases than reanalysis output-based or satellite-derived model outputs. The authors are strongly encouraged to apply this method, which would substantially increase the reliability of their MHT estimates.

Uncertainty Estimation in GRACE Data:

Given the central role of uncertainty quantification in this study, it is concerning that the uncertainty associated with space gravimetry data is only partially addressed. The authors rely on uncertainties from the mascon product, which do not account for critical error sources in GRACE data, such as the glacial isostatic adjustment (GIA), geocenter motion, and C20 corrections. These components are known to dominate the error budget in ocean mass estimates from GRACE (see Quinn & Ponte 2010; Blazquez et al. 2018; Uebbing et al. 2019) and significantly impact thermal expansion estimates. The authors should incorporate these additional uncertainty sources into their analysis.

Thermosteric Sea Level (TS) and OHC Relationship:

The assumed relationship between thermosteric sea level and vertically integrated ocean heat content in the process layer involves important simplifications. Specifically, the neglect of the deep ocean (below 1500 m) and the linearity assumption between TS and vertically integrated OHC (see Eq. 17) could introduce significant inconsistencies. These approximations should be explicitly discussed and, if possible, their impact quantified.

Comparison with Outdated MHT Estimates:

The authors compare their results with an outdated MHT estimate based on ERA-Interim and CERES surface fluxes. ERA-Interim, in particular, is known to suffer from a negative radiation budget at TOA, which inevitably biases surface flux estimates. More recent and accurate estimates using ERA5 are available (e.g., Meyssignac et al. 2024; Mayer et al. 2022; Liu et al. 2020). The authors should compare their results against one of these more recent and reliable datasets.

Detailed Comments
L204: Is the GIA correction used in GRACE consistent with that used in the altimetry analysis?

L205: The GRACE error budget is dominated by uncertainties in GIA and geocenter corrections, which are not currently accounted for in the analysis (see major concern #2).

L217: surface fluxes derived from the output of reanalyses are biased. Use instead a combination of CERES TOA data and vertically integrated atmospheric energy divergence estimated from reanalyses, as in Mayer et al. (2022). (See major concern #1.)

L240: For the effective resolution of satellite altimetry, refer to the updated analysis in Ballarotta et al. (2019).

L271: More satellites are currently operating with ~30-day repeat cycles (e.g., Sentinel-3A/B, AltiKa, CryoSat) than with 10-day cycles. The term “most” should be removed or corrected.

L333: Clarify the term “reference datum.” If referring to the altimetry reference ellipsoid, note that all altimetry satellites use the same reference ellipsoid. Biases across satellite altimeters’ data arise rather because of biases in the radar signal characterization (e.g. biases in the radar signal delay characterisation, biases in the antenna center positioning relative to the center of mass of the satellite, etc…).

L396: Is c(Rj) computed over the full water column or limited to 0–1500 m? How is the deep ocean contribution addressed? This is important, especially since changes in deep ocean heat content can affect the α–C relationship not only on the time-mean but also over time. (See major concern #3.)

L598: BHM2 is likely biased low due to the negative TOA radiation budget in ERA-Interim. Why compare to such an outdated estimate (Trenberth et al. 2019) instead of more recent ones using ERA5? (See major concern #4.)

References:
Ballarotta, M., Ubelmann, C., Pujol, M.-I., Taburet, G., Fournier, F., Legeais, J.-F., Faugère, Y., Delepoulle, A., Chelton, D., Dibarboure, G., and Picot, N.: On the resolutions of ocean altimetry maps, Ocean Sci., 15, 1091–1109, https://doi.org/10.5194/os-15-1091-2019, 2019.
A Blazquez, B Meyssignac, JM Lemoine, E Berthier, A Ribes, A Cazenave, Exploring the uncertainty in GRACE estimates of the mass redistributions at the Earth surface: implications for the global water and sea level budgets, Geophysical Journal International, Volume 215, Issue 1, October 2018, Pages 415–430, https://doi.org/10.1093/gji/ggy293
Liu C et al (2020) Variability in the global energy budget and transports 1985-2017. Climate Dyn 55:3381–3396. https://doi.org/10.1007/s00382-020-05451-8
Mayer M, Haimberger L, Edwards JM, Hyder P (2017) Toward consistent diagnostics of the coupled atmosphere and ocean energy budgets. J Climate 30:9225–9246. https://doi.org/10.1175/ JCLI-D-17-0137.1
Mayer J, Mayer M, Haimberger L (2021) Mass-consistent atmospheric energy and moisture budget monthly data from 1979 to present derived from ERA5 reanalysis. Copernic Clim Change Serv (C3S) Clim Data Store (CDS). https://doi.org/10.24381/cds.c2451f6b
Mayer J, Mayer M, Haimberger L, Liu C (2022) Comparison of surface energy fluxes from global to local scale. J Clim. https://doi.org/10.1175/JCLI-D-21-0598.1
Mayer M, Kato S, Bosilovich M et al (2024) Assessment of atmospheric and surface energy budgets using observation-based data products. Surv Geophys. https://doi-org.insu.bib.cnrs.fr/10.1007/ s10712-024-09827-x
Meyssignac, B., Fourest, S., Mayer, M. et al. North Atlantic Heat Transport Convergence Derived from a Regional Energy Budget Using Different Ocean Heat Content Estimates. Surv Geophys 45, 1855–1874 (2024). doi 10.1007/s10712-024-09865-5
Katherine J. Quinn, Rui M. Ponte, Uncertainty in ocean mass trends from GRACE, Geophysical Journal International, Volume 181, Issue 2, May 2010, Pages 762–768, https://doi.org/10.1111/j.1365-246X.2010.04508.x
Trenberth, K. E., Y. Zhang, J. T. Fasullo, and L. Cheng, 2019: Observation-Based Estimates of Global and Basin Ocean Meridional Heat Transport Time Series. J. Climate, 32, 4567–4583, https://doi.org/10.1175/JCLI-D-18-0872.1.
Uebbing, B., Kusche, J., Rietbroek, R., & Landerer, F. W. (2019). Processing choices affect ocean mass estimates from GRACE. Journal of Geophysical Research: Oceans, 124, 1029–1044. doi 10.1029/2018JC014341
Citation: https://doi.org/10.5194/egusphere-2025-1216-RC2
- AC2: 'Reply on RC2', Francisco Mir Calafat, 31 Jul 2025
  
  The comment was uploaded in the form of a supplement: https://egusphere.copernicus.org/preprints/2025/egusphere-2025-1216/egusphere-2025-1216-AC2-supplement.pdf
  
  Citation: https://doi.org/10.5194/egusphere-2025-1216-AC2
EC1:
'Comment on egusphere-2025-1216', Meric Srokosz, 20 May 2025

Both reviewers are positive regarding the manuscript so I would encourage the authors to respond to comments and submit a revised version.

Citation: https://doi.org/10.5194/egusphere-2025-1216-EC1
- AC3: 'Reply on EC1', Francisco Mir Calafat, 31 Jul 2025
  
  We thank the Editor for their positive assessment of our paper. We have provided a point-by-point response to each of the reviewers’ comments.
  
  Citation: https://doi.org/10.5194/egusphere-2025-1216-AC3

Status: closed

RC1:
'Comment on egusphere-2025-1216', Anonymous Referee #1, 18 Apr 2025
Review of “Estimates of Atlantic meridional heat transport from spatiotemporal fusion of Argo, altimetry and gravimetry data” by Calafat et al.

This paper aims to estimate the meridional heat transport (MHT) at transatlantic sections throughout the Atlantic Ocean. Mainly, it uses hydrographic and satellite data via a Bayesian hierarchical model (BHM) to calculate the ocean heat content (OHC) tendency. The latter is then combined with air-sea heat flux data product to derive the ocean heat divergence and the MHT (as a residual from heat budgets). Accurate MHT estimates are critical for understanding the ocean’s role in our climate system. Overall, the paper reads well, and the results are presented. However, there is potential confusion about the goals and motivations of this study, which would make it hard to follow what is presented and what one can learn from it. I recommend it for publication after the following minor comments are addressed.

Main comments:

The main goal of this paper is to provide MHT estimates that maximize the use of hydrographic and satellite data, via a new framework (BHM). However, I have difficulties in understanding the argument of not using the RAPID data to derive the MHT at other latitudes. Instead, the authors make assumptions about the MHT at the northern boundaries, which introduce uncertainties in the MHT estimates across all latitudes. In my opinion, it undermines the deliverables from this study.

Another source of uncertainty in the MHT estimates is from surface heat flux. However, surface heat flux itself likely contains larger uncertainty than the heat divergence derived from this study – as that is indicated by the discrepancies between BHM solutions. I would suggest that the authors provide a thorough uncertainty estimate that takes into consideration errors in surface heat flux.

If the goal of this paper is to prove the efficacy of the new BHM framework that combines hydrographic and satellite observations, should it be compared with one that just uses hydrographic data? That would highlight the advantages of the BHM.

This is related to comment#3. Much of this paper is centered on the discrepancies between BHM solutions (see Figures 4, 5, 6, 7 and the related text). Those comparisons are useful as an evaluation of how different surface heat flux data impact the MHT estimates. But such an evaluation itself is not well motivated. In addition, the MHT estimates are validated against Trenberth et al. (2019). But it is not clear we gain from this analysis that is distinct from Trenberth et al. which uses atmospheric reanalyses (surface heat flux) and hydrographic data (the OHC tendency).

Other comments:

Line 90: TS and HS are anomalies relative to the climatology density. Other terms should also be anomalies? Please be specific about each term.
Line 133: ‘interesting oceanographically’ reads odd.
Line 148: How large is the volume transport? If it is large, it affects the mass conservation and thus the MHT estimate. Such effects on the related sections need to be discussed.
Line 172: Uniform l= 100m spatially and vertically? How valid are such assumptions?
Line 215: Are the two reanalysis products only used onward 12/2017? If yes, how?
Line 218: Are the reanalysis products averaged together with DEEP-C? This appears to contradict the previous statement that ‘it is preferable to’ the reanalysis products.
Line 228: ‘effective spatial resolution is much lower than what such grids imply’ Hard to understand what it means – please reword.
Line 240: If the goal is for an integrated value over the region between two latitudes (11 regions in total, Fig. 1), why does one need spatial grids anyway? Why not consider the enclosed basin as a whole?
Line 281: Setting rhoij= 0 requires justifications. The decorrelation time scale should be evaluated separately for each dataset, which is likely longer than a month.
Line 288 and Figure 2: What are the different arrows in Figure 2? For example, those black arrows within the right red box indicate that Q is derived by H minus HTC. But that is opposite to what’s described in the text.
Line 298: Why are the reanalysis products used separately? This is related to my comment above.
Line 315: How exactly are uncertainties determined? It is the key to providing a meaningful estimate.
Line 520: What does it mean by ‘will be accurate at any latitude’? How to quantify this accuracy? Also, why is the true transport at a given latitude is ‘large relative to the true transport at 65N’?
Line 524: ‘four time larger at RAPID than at OSNAP’ – are the comparisons only based on the MHT estimates from this study?
Line 529: What kind of error is this referring to? The mean value of MHT1 is not supposed to affect the derived variations.
Line 532: How representative is the 2014-2018 mean? over a longer period 2004-2020?
Line 536: I am not sure about this assumption that is based on a 4-year time series.
Line 540-546: I found the explanations inadequate – this is related to my main comment above. First, the observed MHT from RAPID is most likely the best estimate one can get, so why does depending on it become an issue? I cannot follow the reasoning behind the second point. Why does the observed MHT from RAPID introduce large errors? It is understandable that the RAPID data may be used to first validate this method. But after that validation, could and should it be used to improve the estimates?
Line 549: Once again, it is unclear why three surface heat flux (Qsfc) datasets are used separately, which are over different time periods.
Line 573: Please justify ‘very significant’ – what is p-value?
Line 575: Why is a discrepancy only occurring in 2020?
Line 577: ‘This discrepancy is … entire period.’ Hard to understand what it means – please rephrase.
Line 588: Figure 4: How are the CIs determined? It is worth a dedicated subsection in Methods on uncertainty in the MHT estimates.
Line 599: As mentioned above, is the difference in the mean MHT between BMH solutions mostly related to Qsfc?
Line 600: ‘To complete our comparison’ may not be a good motivation. E.g., why apply 5-quarter running averages? How does it help complete the comparison, or how does it help understand the discrepancies?
Line 609: The data are 5-year averages. What do the differences during 2005-2007 represent?
Line 626: For the comparing purposes, why not apply the same 12-month (4-quarter) running averages to the MHT estimates from this study? That would help make meaningful comparisons.
Line 628: ‘several interesting features’ reads odd.
Line 628 and the whole paragraph: Those features are related to the similarities and differences between BHM solutions. But it is not clear what we will gain from those comparisons. Please refer to my main comments.
Line 658: As mentioned earlier, would it be better to use the 12-month smoothed data when comparing with Trenberth et al. (2019)?
Line 667: The mean is obtained over different lengths of record and different periods. Given the strong interannual and decadal variations in the OHC and probably in the MHT, the time-mean estimates could be biased and cannot be compared directly to each other. Please justify the choices of those estimates to compare with and discuss the comparisons to avoid misinterpretation.
Line 686: Is it because of a similar method (MHT as a residual from heat budgets)?
Line 688: Why compare to GW03? What can we learn from this comparison?
Line 706: What is the main objective of this study? A data set (MHT estimates) or a valid method? Please refer to my main comments.
Line 710: It is not clear why three solutions are needed.
Line 719: This seems to be a hasty conclusion. Those correlations are based on data for different time periods and are based on different assumptions.
Line 726: It simply indicates that surface heat flux is a major source of uncertainty in the MHT estimates. Please refer to my main comments.
Citation: https://doi.org/10.5194/egusphere-2025-1216-RC1
- AC1: 'Reply on RC1', Francisco Mir Calafat, 31 Jul 2025
  
  The comment was uploaded in the form of a supplement: https://egusphere.copernicus.org/preprints/2025/egusphere-2025-1216/egusphere-2025-1216-AC1-supplement.pdf
  
  Citation: https://doi.org/10.5194/egusphere-2025-1216-AC1
RC2:
'Comment on egusphere-2025-1216', Anonymous Referee #2, 14 May 2025
This study tackles the challenge of estimating variations in Atlantic meridional heat transport (MHT) using satellite data and in situ temperature and salinity profiles across 12 latitudinal cross-sections. The authors propose a method to estimate MHT by combining changes in ocean heat content (OHC) with surface heat flux (HF) data. Recognizing the limitations imposed by sparse hydrographic observations, the study advances traditional methods by integrating hydrographic data with satellite altimetry and gravimetry within a joint spatiotemporal Bayesian framework. This fusion enables the generation of probabilistic MHT estimates from 2004 to 2020 across 12 Atlantic latitudinal sections, from 65°N to 35°S. The methodology effectively leverages the comprehensive spatial coverage of satellite data to compensate for the uneven distribution of in situ observations, thereby improving the quality of MHT estimates. Validation against independent measurements from the RAPID array at 26°N (which were not used in the derivation of the MHT estimates) shows good agreement in both the magnitude and timing of variability (with correlations of 0.77 for the raw series and 0.93 for the smoothed series), as well as in the mean transport value (1.17 PW). Results at other latitudes are consistent with prior estimates.

This work addresses the critical issue of variability in Atlantic meridional heat transport—a key component of global and regional ocean heat transport influencing climate. Continuous and precise measurements of Atlantic MHT are essential but limited by the high costs and logistical challenges associated with direct ocean observation systems, which currently provide data at only a few latitudes (e.g., through the RAPID and OSNAP arrays). The authors manage to overcome this limitation here by infering ocean heat transport convergence (HTC) as a residual from the imbalance between OHC changes and surface heat fluxes, using all available data to estimate OHC (i.e., satellite altimetry, gravimetry, and hydrographic observations) within a Bayesian framework. As such, this study is original and highly relevant to the climate science community. The ocean energy budget approach used to derive HTC is not new, nor is the combination of satellite altimetry, gravimetry, and hydrography to estimate OHC. The novelty of this study lies in its application of a Bayesian statistical framework that explicitly accounts for uncertainties in each dataset.
While the overall approach is sound and the results are promising, there are several significant limitations in the current version of the manuscript that must be addressed for the study to be fully convincing.

Major Concerns
Surface Heat Flux (HF) Datasets:

The datasets used to estimate HF are not state-of-the-art. The authors rely on outputs from atmospheric reanalyses, whose surface flux estimates are known to suffer from inconsistencies and large biases due to the weak observational constraints on the short-term forecasts used to generate them. A more robust alternative involves estimating surface fluxes from the atmospheric energy budget using CERES observations at the top of the atmosphere (TOA) and computing the divergence of atmospheric energy transport from reanalysis fields (e.g., winds and temperature), which are more strongly constrained through data assimilation than the short-term forecasts. This approach has been adopted by Mayer et al. (2017, 2021, 2022, 2024) and Meyssignac et al. (2024), and is now widely accepted as yielding net surface fluxes with smaller large-scale biases than reanalysis output-based or satellite-derived model outputs. The authors are strongly encouraged to apply this method, which would substantially increase the reliability of their MHT estimates.

Uncertainty Estimation in GRACE Data:

Given the central role of uncertainty quantification in this study, it is concerning that the uncertainty associated with space gravimetry data is only partially addressed. The authors rely on uncertainties from the mascon product, which do not account for critical error sources in GRACE data, such as the glacial isostatic adjustment (GIA), geocenter motion, and C20 corrections. These components are known to dominate the error budget in ocean mass estimates from GRACE (see Quinn & Ponte 2010; Blazquez et al. 2018; Uebbing et al. 2019) and significantly impact thermal expansion estimates. The authors should incorporate these additional uncertainty sources into their analysis.

Thermosteric Sea Level (TS) and OHC Relationship:

The assumed relationship between thermosteric sea level and vertically integrated ocean heat content in the process layer involves important simplifications. Specifically, the neglect of the deep ocean (below 1500 m) and the linearity assumption between TS and vertically integrated OHC (see Eq. 17) could introduce significant inconsistencies. These approximations should be explicitly discussed and, if possible, their impact quantified.

Comparison with Outdated MHT Estimates:

The authors compare their results with an outdated MHT estimate based on ERA-Interim and CERES surface fluxes. ERA-Interim, in particular, is known to suffer from a negative radiation budget at TOA, which inevitably biases surface flux estimates. More recent and accurate estimates using ERA5 are available (e.g., Meyssignac et al. 2024; Mayer et al. 2022; Liu et al. 2020). The authors should compare their results against one of these more recent and reliable datasets.

Detailed Comments
L204: Is the GIA correction used in GRACE consistent with that used in the altimetry analysis?

L205: The GRACE error budget is dominated by uncertainties in GIA and geocenter corrections, which are not currently accounted for in the analysis (see major concern #2).

L217: surface fluxes derived from the output of reanalyses are biased. Use instead a combination of CERES TOA data and vertically integrated atmospheric energy divergence estimated from reanalyses, as in Mayer et al. (2022). (See major concern #1.)

L240: For the effective resolution of satellite altimetry, refer to the updated analysis in Ballarotta et al. (2019).

L271: More satellites are currently operating with ~30-day repeat cycles (e.g., Sentinel-3A/B, AltiKa, CryoSat) than with 10-day cycles. The term “most” should be removed or corrected.

L333: Clarify the term “reference datum.” If referring to the altimetry reference ellipsoid, note that all altimetry satellites use the same reference ellipsoid. Biases across satellite altimeters’ data arise rather because of biases in the radar signal characterization (e.g. biases in the radar signal delay characterisation, biases in the antenna center positioning relative to the center of mass of the satellite, etc…).

L396: Is c(Rj) computed over the full water column or limited to 0–1500 m? How is the deep ocean contribution addressed? This is important, especially since changes in deep ocean heat content can affect the α–C relationship not only on the time-mean but also over time. (See major concern #3.)

L598: BHM2 is likely biased low due to the negative TOA radiation budget in ERA-Interim. Why compare to such an outdated estimate (Trenberth et al. 2019) instead of more recent ones using ERA5? (See major concern #4.)

References:
Ballarotta, M., Ubelmann, C., Pujol, M.-I., Taburet, G., Fournier, F., Legeais, J.-F., Faugère, Y., Delepoulle, A., Chelton, D., Dibarboure, G., and Picot, N.: On the resolutions of ocean altimetry maps, Ocean Sci., 15, 1091–1109, https://doi.org/10.5194/os-15-1091-2019, 2019.
A Blazquez, B Meyssignac, JM Lemoine, E Berthier, A Ribes, A Cazenave, Exploring the uncertainty in GRACE estimates of the mass redistributions at the Earth surface: implications for the global water and sea level budgets, Geophysical Journal International, Volume 215, Issue 1, October 2018, Pages 415–430, https://doi.org/10.1093/gji/ggy293
Liu C et al (2020) Variability in the global energy budget and transports 1985-2017. Climate Dyn 55:3381–3396. https://doi.org/10.1007/s00382-020-05451-8
Mayer M, Haimberger L, Edwards JM, Hyder P (2017) Toward consistent diagnostics of the coupled atmosphere and ocean energy budgets. J Climate 30:9225–9246. https://doi.org/10.1175/ JCLI-D-17-0137.1
Mayer J, Mayer M, Haimberger L (2021) Mass-consistent atmospheric energy and moisture budget monthly data from 1979 to present derived from ERA5 reanalysis. Copernic Clim Change Serv (C3S) Clim Data Store (CDS). https://doi.org/10.24381/cds.c2451f6b
Mayer J, Mayer M, Haimberger L, Liu C (2022) Comparison of surface energy fluxes from global to local scale. J Clim. https://doi.org/10.1175/JCLI-D-21-0598.1
Mayer M, Kato S, Bosilovich M et al (2024) Assessment of atmospheric and surface energy budgets using observation-based data products. Surv Geophys. https://doi-org.insu.bib.cnrs.fr/10.1007/ s10712-024-09827-x
Meyssignac, B., Fourest, S., Mayer, M. et al. North Atlantic Heat Transport Convergence Derived from a Regional Energy Budget Using Different Ocean Heat Content Estimates. Surv Geophys 45, 1855–1874 (2024). doi 10.1007/s10712-024-09865-5
Katherine J. Quinn, Rui M. Ponte, Uncertainty in ocean mass trends from GRACE, Geophysical Journal International, Volume 181, Issue 2, May 2010, Pages 762–768, https://doi.org/10.1111/j.1365-246X.2010.04508.x
Trenberth, K. E., Y. Zhang, J. T. Fasullo, and L. Cheng, 2019: Observation-Based Estimates of Global and Basin Ocean Meridional Heat Transport Time Series. J. Climate, 32, 4567–4583, https://doi.org/10.1175/JCLI-D-18-0872.1.
Uebbing, B., Kusche, J., Rietbroek, R., & Landerer, F. W. (2019). Processing choices affect ocean mass estimates from GRACE. Journal of Geophysical Research: Oceans, 124, 1029–1044. doi 10.1029/2018JC014341
Citation: https://doi.org/10.5194/egusphere-2025-1216-RC2
- AC2: 'Reply on RC2', Francisco Mir Calafat, 31 Jul 2025
  
  The comment was uploaded in the form of a supplement: https://egusphere.copernicus.org/preprints/2025/egusphere-2025-1216/egusphere-2025-1216-AC2-supplement.pdf
  
  Citation: https://doi.org/10.5194/egusphere-2025-1216-AC2
EC1:
'Comment on egusphere-2025-1216', Meric Srokosz, 20 May 2025

Both reviewers are positive regarding the manuscript so I would encourage the authors to respond to comments and submit a revised version.

Citation: https://doi.org/10.5194/egusphere-2025-1216-EC1
- AC3: 'Reply on EC1', Francisco Mir Calafat, 31 Jul 2025
  
  We thank the Editor for their positive assessment of our paper. We have provided a point-by-point response to each of the reviewers’ comments.
  
  Citation: https://doi.org/10.5194/egusphere-2025-1216-AC3

Francisco M. Calafat, Parvathi Vallivattathillam, and Eleanor Frajka-Williams

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Short summary

Understanding how heat moves through the ocean is crucial to predicting future climate change confidently. This requires accurate records of heat transport throughout the ocean, but these are challenging to obtain by direct ocean observation. Here, we combine in-situ and satellite-based observations to generate estimates of meridional heat transport for the period 2004–2020 at 3-month resolution across the Atlantic Ocean with improved accuracy compared to existing indirectly inferred estimates.


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