An optimal transformation method applied to diagnosing the ocean carbon sink

Mackay, Neill; Zika, Jan; Sohail, Taimoor; Williams, Richard; Andrews, Oliver; Watson, Andrew

doi:https://doi.org/10.5194/egusphere-2023-2448

Preprints

https://doi.org/10.5194/egusphere-2023-2448

Preprints

11 Mar 2024

| 11 Mar 2024

An optimal transformation method applied to diagnosing the ocean carbon sink

Neill Mackay, Jan Zika, Taimoor Sohail, Richard Williams, Oliver Andrews, and Andrew Watson

Abstract. The ocean carbon sink plays a critical role in climate, absorbing anthropogenic carbon from the atmosphere and mitigating climate change. The sink shows significant variability on decadal timescales, but estimates from models and observations disagree with one another, raising uncertainty over the magnitude of the sink, its variability, and its driving mechanisms. There is a need to reconcile observationally-based estimates of air-sea CO₂ fluxes with those of the changing ocean carbon inventory in order to improve our understanding of the sink, and doing so requires knowledge of how carbon is transported within the interior by the ocean circulation. Here we employ a recently developed Optimal Transformation Method (OTM) that uses water mass theory to relate interior changes in tracer distributions to transports and mixing and boundary forcings, and extend its application to include carbon using synthetic data. We validate the method using model outputs from a biogeochemical state estimate, and test its ability to recover boundary carbon fluxes and interior transports consistent with changes in heat, salt and carbon. Our results show that OTM effectively reconciles boundary carbon fluxes with interior carbon distributions when given a range of prior fluxes. OTM shows considerable skill in its reconstructions, reducing root-mean-squared errors from biased priors between model ‘truth’ and reconstructed boundary carbon fluxes by up to 71 %, with bias of the reconstructions consistently ≤ 0.06 mol-Cm⁻² yr⁻¹ globally. Inter-basin transports of carbon also compare well with the model truth, with residuals < 0.25 Pg C yr⁻¹ for reconstructions produced using a range of priors. OTM has significant potential for application to reconciling observational estimates of air-sea CO₂ fluxes with the interior accumulation of anthropogenic carbon.

Received: 20 Oct 2023 – Discussion started: 11 Mar 2024

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13 Aug 2024

An optimal transformation method applied to diagnose the ocean carbon budget

Neill Mackay, Taimoor Sohail, Jan David Zika, Richard G. Williams, Oliver Andrews, and Andrew James Watson

Geosci. Model Dev., 17, 5987–6005, https://doi.org/10.5194/gmd-17-5987-2024,https://doi.org/10.5194/gmd-17-5987-2024, 2024

Short summary

Neill Mackay, Jan Zika, Taimoor Sohail, Richard Williams, Oliver Andrews, and Andrew Watson

Interactive discussion

Status: closed

RC1:
'Comment on egusphere-2023-2448', Anonymous Referee #1, 03 Apr 2024

Review invitation : 22-3-2024
Review accepted: 27-3-2024
Review sent: 3-4-2024
Review of the MS egusphere-2023-2448: An optimal transformation method applied to diagnosing the ocean carbon sink, by Neill Mackay et al.
General comment:
The air-sea exchange and oceanic cycle of carbon dioxide (CO2) is important in controlling the evolution of the climate and the chemistry (acidification). Significant progresses have been made over the last 10 years or so in observing, understanding and developing methods (models and data-based approaches) to quantify the ocean CO2 sink and its temporal variation. It is now well established that the global ocean is a major sink for CO2 but there are still uncertainties on the inter-annual to decadal scales and on the processes that drive the change of CO2 in both the surface and at depth. Detecting and understanding the drivers of ocean properties is challenging given the climate change and associated multiple forcing (wind, circulation, warming, including volcanoes, e.g. Fay et al, 2023). Thanks to the synthesis of observations (e.g. GLODAP), the decadal change of DIC and anthropogenic CO2 (Cant) in the ocean is now estimated at global scale (e.g. Gruber et al, 2019; Müller et al 2023) although there are regions where the data are sparse and the origin of the changes and drivers uncertain, such as in the southern ocean and in the deep layers.
In this context, Neill Mackay and co-authors present a new method (OTM) to reconstruct ocean CO2 concentrations in surface and the water column. They describe the OTM that has been detailed by Zika and Taimoor (2023, paper in revision) for heat and freshwater budgets. Here they extend OTM for the carbon budget. Concerning the CO2 sink, as noted by the authors, there are uncertainties between model and most data-based products and their method, when applied with observations, is probably promising to understand the origin of the bias and interpreting the DIC and C* changes. For example, after year 2000 GOBMs simulate a CO2 sink lower compared to the data-products as identified in several GCB reports (Friedlingstein et al, 2020, 2022) and recently recalled in the RECCAP2 stories (De Vries et al, 2023; Terhaar et al, 2024).
The introduction of the submitted paper is clear, results well presented, figures and references adapted. I am not specialist of the OTM method but I think compared to previous method dedicated to surface fields (e.g. Rodenbeck et al, 2015; Watson et al, 2020 among other) this offers a new view, especially in the water column including internal carbon transport.
The results, here based on the ECCO model, are convincing and I wondered how this could be applied to real world with observations. Quoting authors: “Once validated, OTM’s extension to carbon can be applied to observations to produce a globally consistent estimate of ocean carbon uptake, transports and mixing. ». It would be useful to inform the observations needed and that could be used for applying the OTM (data, periods, region…) and derived carbon change at global scale.
The paper is pleasant to read and probably suitable for publication in GMD once the paper from Zika and Taimoor (2023, submitted) is accepted in the same journal. Below are listed specific comments.
Specific comments:
C-01: Line 23: “…but with significant variability (Hauck et al., 2020).” Maybe also refer to De Vries et al (2023) and Terhaar et al (2024).
C-02: Line 25: “…have also suggested greater decadal variability and a steeper rate of increasing sink since the turn of the 21st century than GOBMs,”. Maybe recall that the difference could reach 1 PgC/yr (compared to 2.9 PgC/yr listed line 7).
C-03: Line 36: “The rate of change of the global inventory of Canth has been estimated at 2.6 ± 0.3 PgCyr−1 for the period 1994-2007 (Gruber et al., 2019)”. Maybe also refer to Müller et al (2023) who estimate change from 1994 to 2004 by 29 ± 3 PgC/decade but to 27 ± 3 PgC/decade from 2004 to 2014 (i.e. a weakening of the uptake ?). Also, I think these estimates where calculated for the layer 0-3000m only, not the full depth, and these results should be extended to the bottom (as proposed using OTM).
C-04: Line 290: « This mismatch indicates that OTM is unable to recover the correct transports of carbon solely from information about the changes in temperature and salinity and associated boundary fluxes of heat and salt/freshwater ». This is an important result suggesting that for carbon one need to use apriori fluxes as well (correct ?).
C-05: Line 298: « The net inter-basin carbon transports from the case 2 OTM solution are shown on Fig. 8… ». Figure 8 and 9 show the total carbon transport for 1995-2015; could you also show the same for the difference between 1995-2005 and 2010-2015 to highlight the power of OTM to derive carbon budget changes?
C-06: Figure 8: Compared to the carbon transport from Mikaloff Fletcher et al (2007), there is a difference of the carbon flux in the Indian Ocean and at the Indonesian throughflow. On Line 145 you informed that “the Indonesian throughflow is set to a net transport of 15 Sv westwards, based on volume transports from ECCO-Darwin ». Mikaloff Fletcher et al (2007) showed a natural carbon flux toward the Pacific whereas Mikaloff Fletcher et al (2006) presented a Cant flux toward the Indian Ocean. Could you comment ?
C-07: Line 350: « the method therefore does not resolve either tracer or flux gradients within a water mass. The effect of the latter is illustrated on Fig. 5, where we compare the unaltered ECCO-Darwin boundary carbon fluxes with the result of binning the fluxes into water mass space and then remapping them back into geographical coordinates using a mask ». Maybe specify where the large differences occur: e.g. NE-PAC, SE-PAC, SO-ATL and Indian (source versus sink ?). Would those differences be the same when applying OTM with observations?
C-08: Line 370: « for example in the case of the South Pacific/Indian Ocean, it could be beneficial to further split the Southern Ocean in a manner that allows the imposition of an Antarctic Circumpolar Current. ». A suggestion for future analysis: select the Drake Passage for the transport using observations available at this boundary (Meredith et al, 2011; Munro et al, 2015)?
C-09: Line 407: « We are working on producing our own global, full-depth, time-evolving estimates of DIC and C∗ in the ocean, using machine learning with satellite and GLODAP data, which we hope by combining with OTM will enable us to produce the first global estimate of the uptake, transport and storage of carbon directly from observations. ». Why not starting/testing OTM using MOBO-DIC (Keppler et al)? Is the MOBO-DIC period 2004-2017 too short to test OTM and because MOBO-DIC is not extended to the bottom? Is your new global data-based product already developed? Could you specify the data that would be needed for applying OTM (T, AT, DIC, O2, nutrients, other ?). Are the existing data synthesis available enough for your future analysis or would you recommend to extend GLODAP, SOCAT, etc… ?
C-09: Figure 2: curiosity: what, where are the outliers at high salinity 38 (Red Sea, MedSea, Arabian Sea?)
C-10: Figure 5: In the legend maybe recall that (b) is for Case 2.
C-11: Title: “An optimal transformation method applied to diagnosing the ocean carbon sink.”
As there are also sources in some regions (EqPAC), maybe change the title: “An optimal transformation method applied to diagnosing the ocean carbon budget”.
;;;;;;;;; Reference in this review not listed in the MS
DeVries, T., Yamamoto, K., Wanninkhof, R., Gruber, N., Hauck, J., Müller, J. D., et al. (2023). Magnitude, trends, and variability of the global ocean carbon sink from 1985-2018. Global Biogeochemical Cycles, 37, e2023GB007780, doi:10.1029/2023GB007780
Fay, A. R., McKinley, G. A., Lovenduski, N. S., Eddebbar, Y., Levy, M. N., Long, M. C., Olivarez, H. C., and Rustagi, R. R.: Immediate and Long-Lasting Impacts of the Mt. Pinatubo Eruption on Ocean Oxygen and Carbon Inventories, Global Biogeochem. Cy., 37, e2022GB007513, https://doi.org/10.1029/2022GB007513, 2023.
Friedlingstein, P., et al: Global Carbon Budget 2020, Earth Syst. Sci. Data, 12, 3269–3340, https://doi.org/10.5194/essd-12-3269-2020, 2020.
Meredith, M. P., and Coauthors, 2011: Sustained monitoring of the Southern Ocean at Drake Passage: past achievements and future priorities. Rev. Geophys., 1-36.
Mikaloff Fletcher, et al: Inverse estimates of the oceanic sources and sinks of natural CO2 and the implied oceanic carbon transport, Global biogeochemical cycles, GB1010, doi:10.1029/2006GB002751, 2007
Müller, J. D., Gruber, N., Carter, B., Feely, R., Ishii, M., Lange, N., et al. (2023). Decadal trends in the oceanic storage of anthropogenic carbon from 1994 to 2014. AGU Advances, 4, e2023AV000875. https://doi.org/10.1029/2023AV000875
Munro,D. R., N. S. Lovenduski, T. Takahashi, B. B. Stephens, T. Newberger, and C. Sweeney (2015), Recent evidence for a strengthening CO2 sink in the Southern Ocean from carbonate system measurements in the Drake Passage (2002–2015), Geophys. Res. Lett., 42, doi:10.1002/2015GL065194.
Terhaar, J., Goris, N., Müller, J. D., DeVries, T., Gruber, N., Hauck, J., et al. (2024). Assessment of global ocean biogeochemistry models for ocean carbon sink estimates in RECCAP2 and recommendations for future studies. Journal of Advances in Modeling Earth Systems, 16, e2023MS003840. https://doi.org/10.1029/2023MS003840
;;;;;;;; end review

Citation: https://doi.org/10.5194/egusphere-2023-2448-RC1
- AC1: 'Reply on RC1', Neill Mackay, 10 Jun 2024
  
  Many thanks for the considerate review. Please see our responses in bold type below the original pasted comments.
  
  The results, here based on the ECCO model, are convincing and I wondered how this could be applied to real world with observations. Quoting authors: “Once validated, OTM’s extension to carbon can be applied to observations to produce a globally consistent estimate of ocean carbon uptake, transports and mixing. ». It would be useful to inform the observations needed and that could be used for applying the OTM (data, periods, region…) and derived carbon change at global scale.
  We have added the following text to the last paragraph of section 4.1: “The boundary fluxes for heat and freshwater could be explored using multiple products such as the ERA5 reanalysis (global coverage from 1940 to present; Hersbach et al. (2020)) and the JRA55 reanalysis (global coverage from 1958 to present; Kobayashi et al. (2015)), and for CO₂ with the compilation of data products by Fay and McKinley (2021) that were used to assess the flux uncertainty in section 2.3.”
  We also added a detail in the second sentence of section 4.2, which now reads: “Temperature and salinity in the ocean is comparatively well observed, and their time evolution in the ocean interior has been mapped based on a combination of shipboard and Argo float observations in the Met Office EN4 objective analysis (Good et al., 2013), in a gridded product with monthly global fields spanning 1900-present.”
  Finally, we added some more detail about the carbon reconstructions in section 4.2, as outlined below in response to C-09.
  
  C-01: Line 23: “…but with significant variability (Hauck et al., 2020).” Maybe also refer to De Vries et al (2023) and Terhaar et al (2024).
  
  We have added the suggested references.
  
  C-02: Line 25: “…have also suggested greater decadal variability and a steeper rate of increasing sink since the turn of the 21st century than GOBMs,”. Maybe recall that the difference could reach 1 PgC/yr (compared to 2.9 PgC/yr listed line 7).
  
  We added the following sentence, including a reference to the latest GCB paper: “According to the Global Carbon Budget (Friedlingstein et al., 2023, Table 6), the discrepancy between GOBMs and data products reached 0.6 Pg C yr⁻¹ in 2022, or a fifth of the contemporary sink.” We also updated the reference in line 7 and added the uncertainty to the contemporary sink estimate.
  
  C-03: Line 36: “The rate of change of the global inventory of Canth has been estimated at 2.6 ± 0.3 PgCyr−1 for the period 1994-2007 (Gruber et al., 2019)”. Maybe also refer to Müller et al (2023) who estimate change from 1994 to 2004 by 29 ± 3 PgC/decade but to 27 ± 3 PgC/decade from 2004 to 2014 (i.e. a weakening of the uptake ?). Also, I think these estimates where calculated for the layer 0-3000m only, not the full depth, and these results should be extended to the bottom (as proposed using OTM).
  
  Thank you for the suggestion. The Gruber and Müller estimates are, in fact, full depth, with a scaling factor applied to derive the accumulation below 3000 m. We have altered the text to “The rate of change of the global inventory of C_anth has been estimated at 2.6 ± 0.3 Pg C yr⁻¹ for the period 1994-2007 by Gruber et al. (2019), and 2.9 ± 0.3 Pg C yr⁻¹ for 1994-2004 and 2.7 ± 0.3 Pg C yr⁻¹ for 2004-2014 by Müller et al. (2023), with the latter estimate indicating a reduction in ocean’s carbon uptake efficiency in the more recent decade in the context of the continuing rise in atmospheric CO₂.”
  
  C-04: Line 290: « This mismatch indicates that OTM is unable to recover the correct transports of carbon solely from information about the changes in temperature and salinity and associated boundary fluxes of heat and salt/freshwater ». This is an important result suggesting that for carbon one need to use apriori fluxes as well (correct ?).
  
  Yes, that’s correct! We have modified the text to “This mismatch indicates that OTM is unable to recover the correct transports of carbon solely from information about the changes in temperature and salinity and associated boundary fluxes of heat and salt/freshwater, and that the additional information provided by the a priori CO₂ flux estimates in cases 2-5 is needed.”
  We have also emphasised this point at the start of the discussion: “When given information limited to changes in temperature and salinity distributions and their boundary forcings, OTM obtains a transport matrix that is broadly consistent with changes in carbon, and which can be used to obtain reasonable basin-integrated carbon uptake. However, inter-basin meridional carbon transports from OTM are inconsistent with the model truth using this setup, indicating that more information is needed for a realistic solution. With the addition of prior information about the distribution of boundary carbon fluxes, OTM shows considerable skill in recovering carbon fluxes that are closer to the model truth than the prior, while also diagnosing inter-basin carbon transports consistent with the model.”
  
  C-05: Line 298: « The net inter-basin carbon transports from the case 2 OTM solution are shown on Fig. 8… ». Figure 8 and 9 show the total carbon transport for 1995-2015; could you also show the same for the difference between 1995-2005 and 2010-2015 to highlight the power of OTM to derive carbon budget changes?
  
  In fact we are not able to plot trends with the current setup, because our solution derives from the transition between the time average of the early period (1995-2005) and the time average of the late period (2005-2015). We have added some text to make this clearer: “Note that it is the transition between the state of the ocean in the early period and its state in the later one that we use to infer the carbon uptake and transport. In this case, the OTM solution could be regarded as representing an average for the time period between the midpoint of 1995-2005 and the midpoint of 2005-2015 (i.e. for the change from 2000 to 2010).”
  
  C-06: Figure 8: Compared to the carbon transport from Mikaloff Fletcher et al (2007), there is a difference of the carbon flux in the Indian Ocean and at the Indonesian throughflow. On Line 145 you informed that “the Indonesian throughflow is set to a net transport of 15 Sv westwards, based on volume transports from ECCO-Darwin ». Mikaloff Fletcher et al (2007) showed a natural carbon flux toward the Pacific whereas Mikaloff Fletcher et al (2006) presented a Cant flux toward the Indian Ocean. Could you comment ?
  
  Thank you for pointing out those studies, we have now added some text to the discussion comparing what we find with their results: “A possible impact of the lack of mass transport constraint was seen in the large counter-clockwise circulation of carbon on Fig. 8 between the Southern Ocean, South Pacific, and Indian Ocean. These transports do not seem consistent with, for example, a westward Indonesian Throughflow (ITF) C_anth transport of 0.05 Pg C yr⁻¹ as reported by Mikaloff Fletcher et al. (2006) or an eastward ITF C_nat transport of 0.1 Pg C yr⁻¹ as reported by Mikaloff Fletcher et al. (2007). We have diagnosed a transport of C^∗, which contains both C_anth and a portion of C_nat, but the OTM transports nonetheless do not appear reconcilable with the ITF estimates”.
  
  C-07: Line 350: « the method therefore does not resolve either tracer or flux gradients within a water mass. The effect of the latter is illustrated on Fig. 5, where we compare the unaltered ECCO-Darwin boundary carbon fluxes with the result of binning the fluxes into water mass space and then remapping them back into geographical coordinates using a mask ». Maybe specify where the large differences occur: e.g. NE-PAC, SE-PAC, SO-ATL and Indian (source versus sink ?). Would those differences be the same when applying OTM with observations?
  
  We have added some explanation: “There are differences, for example off the west coast of North America where ECCO-Darwin has outgassing (Fig. 5a) and the remapped fluxes show uptake (Fig. 5b); a similar situation off the west coast of the southern tip of South America; and also in the north of the Indian Ocean. Fig. 5b is the closest we can get to the true model fluxes with this configuration (with the caveat noted in section 2.4 that we have remapped surface fluxes into three-dimensional water masses)”.
  We also now note that “a closer match to the ‘true’ field may be achieved by combining the remapped term q(x, y, z)^adjust with the true fluxes; therefore here we present a worst-case scenario where the detail of the true fluxes is not assumed to be reliable”. This alternative method is a recent development that was not applied during the analysis for this paper.
  
  C-08: Line 370: « for example in the case of the South Pacific/Indian Ocean, it could be beneficial to further split the Southern Ocean in a manner that allows the imposition of an Antarctic Circumpolar Current. ». A suggestion for future analysis: select the Drake Passage for the transport using observations available at this boundary (Meredith et al, 2011; Munro et al, 2015)?
  
  Thank you for the suggestion, indeed such constraints may be useful!
  
  C-09: Line 407: « We are working on producing our own global, full-depth, time-evolving estimates of DIC and C∗ in the ocean, using machine learning with satellite and GLODAP data, which we hope by combining with OTM will enable us to produce the first global estimate of the uptake, transport and storage of carbon directly from observations. ». Why not starting/testing OTM using MOBO-DIC (Keppler et al)? Is the MOBO-DIC period 2004-2017 too short to test OTM and because MOBO-DIC is not extended to the bottom?
  
  We added some further explanation about the potential of application using MOBO-DIC earlier in the paragraph, as follows: “….Unfortunately, these two estimates are limited, respectively, to the top 1500 m of the ocean, and to the Southern Ocean only. MOBO-DIC could form the basis for an application of OTM, but it would be necessary to somehow extend it to full depth.”
  
  Is your new global data-based product already developed? Could you specify the data that would be needed for applying OTM (T, AT, DIC, O2, nutrients, other ?). Are the existing data synthesis available enough for your future analysis or would you recommend to extend GLODAP, SOCAT, etc… ?
  
  We have made significant progress with the application of OTM to observations in the last few months, including in the machine learning reconstructions which have been validated and on which a paper is in preparation. We modified part of the final paragraph of section 4.2 as follows: “We are developing our own global, full-depth, time-evolving reconstructions from 1990-present of DIC and C^∗ in the ocean that we hope to combine with OTM in future work. The reconstructions use deep neural networks trained on GLODAP DIC, Total Alkalinity, and nutrient data, with predictors of temperature and salinity from EN4, location, depth, and atmospheric CO₂ concentration.”
  
  C-09: Figure 2: curiosity: what, where are the outliers at high salinity 38 (Red Sea, MedSea, Arabian Sea?)
  
  This is the Mediterranean (see e.g. https://journals.ametsoc.org/view/journals/phoc/42/5/jpo-d-11-0139.1.xml Fig 5).
  
  C-10: Figure 5: In the legend maybe recall that (b) is for Case 2.
  
  We have added this detail; the caption now reads: “Boundary carbon fluxes (air-sea CO2 flux - sediment flux) for the ECCO-Darwin 1995-2015 time-mean (a) and the BSP-binned fluxes remapped back into geographical coordinates (b). Note that (b) is the ‘ECCO Darwin’ flux against which the prior and solution are compared on Figure 4 and is also the prior for case 2.”
  
  C-11: Title: “An optimal transformation method applied to diagnosing the ocean carbon sink.”
  As there are also sources in some regions (EqPAC), maybe change the title: “An optimal transformation method applied to diagnosing the ocean carbon budget”.
  
  Thank you for the title suggestion; we agree it is an improvement and have adopted it.
  
  Citation: https://doi.org/10.5194/egusphere-2023-2448-AC1
RC2:
'Comment on egusphere-2023-2448', Anonymous Referee #2, 05 May 2024

This manuscript presents the application of the Optimal Transformation Method (OTM) to estimate air-sea carbon fluxes and interior carbon transport. The method is applied to output from the ECCO-Darwin biogeochemical state estimate, and results are compared with the state estimate (model "truth") for five different priors to valid the method and its sensitivity to the choice of prior. It is shown the method has good skill at reproducing the model truth, and hence has good potential for estimating the fluxes and transport using observations. The application to observations will add uncertainties, but these are discussed in the manuscript. The manuscript is well written, the figures are clear, and I think it is publishable in it current form.

Citation: https://doi.org/10.5194/egusphere-2023-2448-RC2
- AC2: 'Reply on RC2', Neill Mackay, 10 Jun 2024
  
  Many thanks for your comments - we are glad you liked the manuscript!
  
  Citation: https://doi.org/10.5194/egusphere-2023-2448-AC2

Interactive discussion

Status: closed

RC1:
'Comment on egusphere-2023-2448', Anonymous Referee #1, 03 Apr 2024

Review invitation : 22-3-2024
Review accepted: 27-3-2024
Review sent: 3-4-2024
Review of the MS egusphere-2023-2448: An optimal transformation method applied to diagnosing the ocean carbon sink, by Neill Mackay et al.
General comment:
The air-sea exchange and oceanic cycle of carbon dioxide (CO2) is important in controlling the evolution of the climate and the chemistry (acidification). Significant progresses have been made over the last 10 years or so in observing, understanding and developing methods (models and data-based approaches) to quantify the ocean CO2 sink and its temporal variation. It is now well established that the global ocean is a major sink for CO2 but there are still uncertainties on the inter-annual to decadal scales and on the processes that drive the change of CO2 in both the surface and at depth. Detecting and understanding the drivers of ocean properties is challenging given the climate change and associated multiple forcing (wind, circulation, warming, including volcanoes, e.g. Fay et al, 2023). Thanks to the synthesis of observations (e.g. GLODAP), the decadal change of DIC and anthropogenic CO2 (Cant) in the ocean is now estimated at global scale (e.g. Gruber et al, 2019; Müller et al 2023) although there are regions where the data are sparse and the origin of the changes and drivers uncertain, such as in the southern ocean and in the deep layers.
In this context, Neill Mackay and co-authors present a new method (OTM) to reconstruct ocean CO2 concentrations in surface and the water column. They describe the OTM that has been detailed by Zika and Taimoor (2023, paper in revision) for heat and freshwater budgets. Here they extend OTM for the carbon budget. Concerning the CO2 sink, as noted by the authors, there are uncertainties between model and most data-based products and their method, when applied with observations, is probably promising to understand the origin of the bias and interpreting the DIC and C* changes. For example, after year 2000 GOBMs simulate a CO2 sink lower compared to the data-products as identified in several GCB reports (Friedlingstein et al, 2020, 2022) and recently recalled in the RECCAP2 stories (De Vries et al, 2023; Terhaar et al, 2024).
The introduction of the submitted paper is clear, results well presented, figures and references adapted. I am not specialist of the OTM method but I think compared to previous method dedicated to surface fields (e.g. Rodenbeck et al, 2015; Watson et al, 2020 among other) this offers a new view, especially in the water column including internal carbon transport.
The results, here based on the ECCO model, are convincing and I wondered how this could be applied to real world with observations. Quoting authors: “Once validated, OTM’s extension to carbon can be applied to observations to produce a globally consistent estimate of ocean carbon uptake, transports and mixing. ». It would be useful to inform the observations needed and that could be used for applying the OTM (data, periods, region…) and derived carbon change at global scale.
The paper is pleasant to read and probably suitable for publication in GMD once the paper from Zika and Taimoor (2023, submitted) is accepted in the same journal. Below are listed specific comments.
Specific comments:
C-01: Line 23: “…but with significant variability (Hauck et al., 2020).” Maybe also refer to De Vries et al (2023) and Terhaar et al (2024).
C-02: Line 25: “…have also suggested greater decadal variability and a steeper rate of increasing sink since the turn of the 21st century than GOBMs,”. Maybe recall that the difference could reach 1 PgC/yr (compared to 2.9 PgC/yr listed line 7).
C-03: Line 36: “The rate of change of the global inventory of Canth has been estimated at 2.6 ± 0.3 PgCyr−1 for the period 1994-2007 (Gruber et al., 2019)”. Maybe also refer to Müller et al (2023) who estimate change from 1994 to 2004 by 29 ± 3 PgC/decade but to 27 ± 3 PgC/decade from 2004 to 2014 (i.e. a weakening of the uptake ?). Also, I think these estimates where calculated for the layer 0-3000m only, not the full depth, and these results should be extended to the bottom (as proposed using OTM).
C-04: Line 290: « This mismatch indicates that OTM is unable to recover the correct transports of carbon solely from information about the changes in temperature and salinity and associated boundary fluxes of heat and salt/freshwater ». This is an important result suggesting that for carbon one need to use apriori fluxes as well (correct ?).
C-05: Line 298: « The net inter-basin carbon transports from the case 2 OTM solution are shown on Fig. 8… ». Figure 8 and 9 show the total carbon transport for 1995-2015; could you also show the same for the difference between 1995-2005 and 2010-2015 to highlight the power of OTM to derive carbon budget changes?
C-06: Figure 8: Compared to the carbon transport from Mikaloff Fletcher et al (2007), there is a difference of the carbon flux in the Indian Ocean and at the Indonesian throughflow. On Line 145 you informed that “the Indonesian throughflow is set to a net transport of 15 Sv westwards, based on volume transports from ECCO-Darwin ». Mikaloff Fletcher et al (2007) showed a natural carbon flux toward the Pacific whereas Mikaloff Fletcher et al (2006) presented a Cant flux toward the Indian Ocean. Could you comment ?
C-07: Line 350: « the method therefore does not resolve either tracer or flux gradients within a water mass. The effect of the latter is illustrated on Fig. 5, where we compare the unaltered ECCO-Darwin boundary carbon fluxes with the result of binning the fluxes into water mass space and then remapping them back into geographical coordinates using a mask ». Maybe specify where the large differences occur: e.g. NE-PAC, SE-PAC, SO-ATL and Indian (source versus sink ?). Would those differences be the same when applying OTM with observations?
C-08: Line 370: « for example in the case of the South Pacific/Indian Ocean, it could be beneficial to further split the Southern Ocean in a manner that allows the imposition of an Antarctic Circumpolar Current. ». A suggestion for future analysis: select the Drake Passage for the transport using observations available at this boundary (Meredith et al, 2011; Munro et al, 2015)?
C-09: Line 407: « We are working on producing our own global, full-depth, time-evolving estimates of DIC and C∗ in the ocean, using machine learning with satellite and GLODAP data, which we hope by combining with OTM will enable us to produce the first global estimate of the uptake, transport and storage of carbon directly from observations. ». Why not starting/testing OTM using MOBO-DIC (Keppler et al)? Is the MOBO-DIC period 2004-2017 too short to test OTM and because MOBO-DIC is not extended to the bottom? Is your new global data-based product already developed? Could you specify the data that would be needed for applying OTM (T, AT, DIC, O2, nutrients, other ?). Are the existing data synthesis available enough for your future analysis or would you recommend to extend GLODAP, SOCAT, etc… ?
C-09: Figure 2: curiosity: what, where are the outliers at high salinity 38 (Red Sea, MedSea, Arabian Sea?)
C-10: Figure 5: In the legend maybe recall that (b) is for Case 2.
C-11: Title: “An optimal transformation method applied to diagnosing the ocean carbon sink.”
As there are also sources in some regions (EqPAC), maybe change the title: “An optimal transformation method applied to diagnosing the ocean carbon budget”.
;;;;;;;;; Reference in this review not listed in the MS
DeVries, T., Yamamoto, K., Wanninkhof, R., Gruber, N., Hauck, J., Müller, J. D., et al. (2023). Magnitude, trends, and variability of the global ocean carbon sink from 1985-2018. Global Biogeochemical Cycles, 37, e2023GB007780, doi:10.1029/2023GB007780
Fay, A. R., McKinley, G. A., Lovenduski, N. S., Eddebbar, Y., Levy, M. N., Long, M. C., Olivarez, H. C., and Rustagi, R. R.: Immediate and Long-Lasting Impacts of the Mt. Pinatubo Eruption on Ocean Oxygen and Carbon Inventories, Global Biogeochem. Cy., 37, e2022GB007513, https://doi.org/10.1029/2022GB007513, 2023.
Friedlingstein, P., et al: Global Carbon Budget 2020, Earth Syst. Sci. Data, 12, 3269–3340, https://doi.org/10.5194/essd-12-3269-2020, 2020.
Meredith, M. P., and Coauthors, 2011: Sustained monitoring of the Southern Ocean at Drake Passage: past achievements and future priorities. Rev. Geophys., 1-36.
Mikaloff Fletcher, et al: Inverse estimates of the oceanic sources and sinks of natural CO2 and the implied oceanic carbon transport, Global biogeochemical cycles, GB1010, doi:10.1029/2006GB002751, 2007
Müller, J. D., Gruber, N., Carter, B., Feely, R., Ishii, M., Lange, N., et al. (2023). Decadal trends in the oceanic storage of anthropogenic carbon from 1994 to 2014. AGU Advances, 4, e2023AV000875. https://doi.org/10.1029/2023AV000875
Munro,D. R., N. S. Lovenduski, T. Takahashi, B. B. Stephens, T. Newberger, and C. Sweeney (2015), Recent evidence for a strengthening CO2 sink in the Southern Ocean from carbonate system measurements in the Drake Passage (2002–2015), Geophys. Res. Lett., 42, doi:10.1002/2015GL065194.
Terhaar, J., Goris, N., Müller, J. D., DeVries, T., Gruber, N., Hauck, J., et al. (2024). Assessment of global ocean biogeochemistry models for ocean carbon sink estimates in RECCAP2 and recommendations for future studies. Journal of Advances in Modeling Earth Systems, 16, e2023MS003840. https://doi.org/10.1029/2023MS003840
;;;;;;;; end review

Citation: https://doi.org/10.5194/egusphere-2023-2448-RC1
- AC1: 'Reply on RC1', Neill Mackay, 10 Jun 2024
  
  Many thanks for the considerate review. Please see our responses in bold type below the original pasted comments.
  
  The results, here based on the ECCO model, are convincing and I wondered how this could be applied to real world with observations. Quoting authors: “Once validated, OTM’s extension to carbon can be applied to observations to produce a globally consistent estimate of ocean carbon uptake, transports and mixing. ». It would be useful to inform the observations needed and that could be used for applying the OTM (data, periods, region…) and derived carbon change at global scale.
  We have added the following text to the last paragraph of section 4.1: “The boundary fluxes for heat and freshwater could be explored using multiple products such as the ERA5 reanalysis (global coverage from 1940 to present; Hersbach et al. (2020)) and the JRA55 reanalysis (global coverage from 1958 to present; Kobayashi et al. (2015)), and for CO₂ with the compilation of data products by Fay and McKinley (2021) that were used to assess the flux uncertainty in section 2.3.”
  We also added a detail in the second sentence of section 4.2, which now reads: “Temperature and salinity in the ocean is comparatively well observed, and their time evolution in the ocean interior has been mapped based on a combination of shipboard and Argo float observations in the Met Office EN4 objective analysis (Good et al., 2013), in a gridded product with monthly global fields spanning 1900-present.”
  Finally, we added some more detail about the carbon reconstructions in section 4.2, as outlined below in response to C-09.
  
  C-01: Line 23: “…but with significant variability (Hauck et al., 2020).” Maybe also refer to De Vries et al (2023) and Terhaar et al (2024).
  
  We have added the suggested references.
  
  C-02: Line 25: “…have also suggested greater decadal variability and a steeper rate of increasing sink since the turn of the 21st century than GOBMs,”. Maybe recall that the difference could reach 1 PgC/yr (compared to 2.9 PgC/yr listed line 7).
  
  We added the following sentence, including a reference to the latest GCB paper: “According to the Global Carbon Budget (Friedlingstein et al., 2023, Table 6), the discrepancy between GOBMs and data products reached 0.6 Pg C yr⁻¹ in 2022, or a fifth of the contemporary sink.” We also updated the reference in line 7 and added the uncertainty to the contemporary sink estimate.
  
  C-03: Line 36: “The rate of change of the global inventory of Canth has been estimated at 2.6 ± 0.3 PgCyr−1 for the period 1994-2007 (Gruber et al., 2019)”. Maybe also refer to Müller et al (2023) who estimate change from 1994 to 2004 by 29 ± 3 PgC/decade but to 27 ± 3 PgC/decade from 2004 to 2014 (i.e. a weakening of the uptake ?). Also, I think these estimates where calculated for the layer 0-3000m only, not the full depth, and these results should be extended to the bottom (as proposed using OTM).
  
  Thank you for the suggestion. The Gruber and Müller estimates are, in fact, full depth, with a scaling factor applied to derive the accumulation below 3000 m. We have altered the text to “The rate of change of the global inventory of C_anth has been estimated at 2.6 ± 0.3 Pg C yr⁻¹ for the period 1994-2007 by Gruber et al. (2019), and 2.9 ± 0.3 Pg C yr⁻¹ for 1994-2004 and 2.7 ± 0.3 Pg C yr⁻¹ for 2004-2014 by Müller et al. (2023), with the latter estimate indicating a reduction in ocean’s carbon uptake efficiency in the more recent decade in the context of the continuing rise in atmospheric CO₂.”
  
  C-04: Line 290: « This mismatch indicates that OTM is unable to recover the correct transports of carbon solely from information about the changes in temperature and salinity and associated boundary fluxes of heat and salt/freshwater ». This is an important result suggesting that for carbon one need to use apriori fluxes as well (correct ?).
  
  Yes, that’s correct! We have modified the text to “This mismatch indicates that OTM is unable to recover the correct transports of carbon solely from information about the changes in temperature and salinity and associated boundary fluxes of heat and salt/freshwater, and that the additional information provided by the a priori CO₂ flux estimates in cases 2-5 is needed.”
  We have also emphasised this point at the start of the discussion: “When given information limited to changes in temperature and salinity distributions and their boundary forcings, OTM obtains a transport matrix that is broadly consistent with changes in carbon, and which can be used to obtain reasonable basin-integrated carbon uptake. However, inter-basin meridional carbon transports from OTM are inconsistent with the model truth using this setup, indicating that more information is needed for a realistic solution. With the addition of prior information about the distribution of boundary carbon fluxes, OTM shows considerable skill in recovering carbon fluxes that are closer to the model truth than the prior, while also diagnosing inter-basin carbon transports consistent with the model.”
  
  C-05: Line 298: « The net inter-basin carbon transports from the case 2 OTM solution are shown on Fig. 8… ». Figure 8 and 9 show the total carbon transport for 1995-2015; could you also show the same for the difference between 1995-2005 and 2010-2015 to highlight the power of OTM to derive carbon budget changes?
  
  In fact we are not able to plot trends with the current setup, because our solution derives from the transition between the time average of the early period (1995-2005) and the time average of the late period (2005-2015). We have added some text to make this clearer: “Note that it is the transition between the state of the ocean in the early period and its state in the later one that we use to infer the carbon uptake and transport. In this case, the OTM solution could be regarded as representing an average for the time period between the midpoint of 1995-2005 and the midpoint of 2005-2015 (i.e. for the change from 2000 to 2010).”
  
  C-06: Figure 8: Compared to the carbon transport from Mikaloff Fletcher et al (2007), there is a difference of the carbon flux in the Indian Ocean and at the Indonesian throughflow. On Line 145 you informed that “the Indonesian throughflow is set to a net transport of 15 Sv westwards, based on volume transports from ECCO-Darwin ». Mikaloff Fletcher et al (2007) showed a natural carbon flux toward the Pacific whereas Mikaloff Fletcher et al (2006) presented a Cant flux toward the Indian Ocean. Could you comment ?
  
  Thank you for pointing out those studies, we have now added some text to the discussion comparing what we find with their results: “A possible impact of the lack of mass transport constraint was seen in the large counter-clockwise circulation of carbon on Fig. 8 between the Southern Ocean, South Pacific, and Indian Ocean. These transports do not seem consistent with, for example, a westward Indonesian Throughflow (ITF) C_anth transport of 0.05 Pg C yr⁻¹ as reported by Mikaloff Fletcher et al. (2006) or an eastward ITF C_nat transport of 0.1 Pg C yr⁻¹ as reported by Mikaloff Fletcher et al. (2007). We have diagnosed a transport of C^∗, which contains both C_anth and a portion of C_nat, but the OTM transports nonetheless do not appear reconcilable with the ITF estimates”.
  
  C-07: Line 350: « the method therefore does not resolve either tracer or flux gradients within a water mass. The effect of the latter is illustrated on Fig. 5, where we compare the unaltered ECCO-Darwin boundary carbon fluxes with the result of binning the fluxes into water mass space and then remapping them back into geographical coordinates using a mask ». Maybe specify where the large differences occur: e.g. NE-PAC, SE-PAC, SO-ATL and Indian (source versus sink ?). Would those differences be the same when applying OTM with observations?
  
  We have added some explanation: “There are differences, for example off the west coast of North America where ECCO-Darwin has outgassing (Fig. 5a) and the remapped fluxes show uptake (Fig. 5b); a similar situation off the west coast of the southern tip of South America; and also in the north of the Indian Ocean. Fig. 5b is the closest we can get to the true model fluxes with this configuration (with the caveat noted in section 2.4 that we have remapped surface fluxes into three-dimensional water masses)”.
  We also now note that “a closer match to the ‘true’ field may be achieved by combining the remapped term q(x, y, z)^adjust with the true fluxes; therefore here we present a worst-case scenario where the detail of the true fluxes is not assumed to be reliable”. This alternative method is a recent development that was not applied during the analysis for this paper.
  
  C-08: Line 370: « for example in the case of the South Pacific/Indian Ocean, it could be beneficial to further split the Southern Ocean in a manner that allows the imposition of an Antarctic Circumpolar Current. ». A suggestion for future analysis: select the Drake Passage for the transport using observations available at this boundary (Meredith et al, 2011; Munro et al, 2015)?
  
  Thank you for the suggestion, indeed such constraints may be useful!
  
  C-09: Line 407: « We are working on producing our own global, full-depth, time-evolving estimates of DIC and C∗ in the ocean, using machine learning with satellite and GLODAP data, which we hope by combining with OTM will enable us to produce the first global estimate of the uptake, transport and storage of carbon directly from observations. ». Why not starting/testing OTM using MOBO-DIC (Keppler et al)? Is the MOBO-DIC period 2004-2017 too short to test OTM and because MOBO-DIC is not extended to the bottom?
  
  We added some further explanation about the potential of application using MOBO-DIC earlier in the paragraph, as follows: “….Unfortunately, these two estimates are limited, respectively, to the top 1500 m of the ocean, and to the Southern Ocean only. MOBO-DIC could form the basis for an application of OTM, but it would be necessary to somehow extend it to full depth.”
  
  Is your new global data-based product already developed? Could you specify the data that would be needed for applying OTM (T, AT, DIC, O2, nutrients, other ?). Are the existing data synthesis available enough for your future analysis or would you recommend to extend GLODAP, SOCAT, etc… ?
  
  We have made significant progress with the application of OTM to observations in the last few months, including in the machine learning reconstructions which have been validated and on which a paper is in preparation. We modified part of the final paragraph of section 4.2 as follows: “We are developing our own global, full-depth, time-evolving reconstructions from 1990-present of DIC and C^∗ in the ocean that we hope to combine with OTM in future work. The reconstructions use deep neural networks trained on GLODAP DIC, Total Alkalinity, and nutrient data, with predictors of temperature and salinity from EN4, location, depth, and atmospheric CO₂ concentration.”
  
  C-09: Figure 2: curiosity: what, where are the outliers at high salinity 38 (Red Sea, MedSea, Arabian Sea?)
  
  This is the Mediterranean (see e.g. https://journals.ametsoc.org/view/journals/phoc/42/5/jpo-d-11-0139.1.xml Fig 5).
  
  C-10: Figure 5: In the legend maybe recall that (b) is for Case 2.
  
  We have added this detail; the caption now reads: “Boundary carbon fluxes (air-sea CO2 flux - sediment flux) for the ECCO-Darwin 1995-2015 time-mean (a) and the BSP-binned fluxes remapped back into geographical coordinates (b). Note that (b) is the ‘ECCO Darwin’ flux against which the prior and solution are compared on Figure 4 and is also the prior for case 2.”
  
  C-11: Title: “An optimal transformation method applied to diagnosing the ocean carbon sink.”
  As there are also sources in some regions (EqPAC), maybe change the title: “An optimal transformation method applied to diagnosing the ocean carbon budget”.
  
  Thank you for the title suggestion; we agree it is an improvement and have adopted it.
  
  Citation: https://doi.org/10.5194/egusphere-2023-2448-AC1
RC2:
'Comment on egusphere-2023-2448', Anonymous Referee #2, 05 May 2024

This manuscript presents the application of the Optimal Transformation Method (OTM) to estimate air-sea carbon fluxes and interior carbon transport. The method is applied to output from the ECCO-Darwin biogeochemical state estimate, and results are compared with the state estimate (model "truth") for five different priors to valid the method and its sensitivity to the choice of prior. It is shown the method has good skill at reproducing the model truth, and hence has good potential for estimating the fluxes and transport using observations. The application to observations will add uncertainties, but these are discussed in the manuscript. The manuscript is well written, the figures are clear, and I think it is publishable in it current form.

Citation: https://doi.org/10.5194/egusphere-2023-2448-RC2
- AC2: 'Reply on RC2', Neill Mackay, 10 Jun 2024
  
  Many thanks for your comments - we are glad you liked the manuscript!
  
  Citation: https://doi.org/10.5194/egusphere-2023-2448-AC2

Peer review completion

AR: Author's response | RR: Referee report | ED: Editor decision | EF: Editorial file upload

AR by Neill Mackay on behalf of the Authors (10 Jun 2024) Author's response Author's tracked changes Manuscript

ED: Referee Nomination & Report Request started (14 Jun 2024) by Vassilios Vervatis

RR by Anonymous Referee #1 (15 Jun 2024)

ED: Publish as is (18 Jun 2024) by Vassilios Vervatis

AR by Neill Mackay on behalf of the Authors (21 Jun 2024)

Post-review adjustments

AA: Author's adjustment | EA: Editor approval

AA by Neill Mackay on behalf of the Authors (06 Aug 2024) Author's adjustment Manuscript

EA: Adjustments approved (07 Aug 2024) by Vassilios Vervatis

Journal article(s) based on this preprint

13 Aug 2024

An optimal transformation method applied to diagnose the ocean carbon budget

Neill Mackay, Taimoor Sohail, Jan David Zika, Richard G. Williams, Oliver Andrews, and Andrew James Watson

Geosci. Model Dev., 17, 5987–6005, https://doi.org/10.5194/gmd-17-5987-2024,https://doi.org/10.5194/gmd-17-5987-2024, 2024

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Neill Mackay, Jan Zika, Taimoor Sohail, Richard Williams, Oliver Andrews, and Andrew Watson

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The ocean absorbs carbon dioxide from the atmosphere, mitigating climate change, but estimates of the uptake do not always agree. There is a need to reconcile these differing estimates, and to improve our understanding of ocean carbon uptake. We present a new method for estimating ocean carbon uptake and test it with model data. The method effectively diagnoses the ocean carbon uptake from limited data, and therefore shows promise for reconciling different observational estimates.


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