the Creative Commons Attribution 4.0 License.
the Creative Commons Attribution 4.0 License.
| 13 Jan 2025
Global air-sea heat and freshwater fluxes constrained by ocean observations
Abstract. A substantial portion of the transport of heat and freshwater in the climate system occurs through the ocean. Heat and fresh water enter the ocean as air-sea fluxes, which are typically estimated based on observationally constrained ‘reanalyses’ of the atmosphere. However, these estimates are uncertain, with broad differences in space and time between different products, and do not align with estimates of integrated ocean temperature and salinity. As a result, inferred global heat and freshwater transport, including transport trends, remain unclear. In this work, we use a novel water mass-based inverse modelling method, the Optimal Transformation Method (OTM), to reconcile reanalysis-based changes in surface heat and freshwater fluxes with changes in observed ocean temperature and salinity. We present estimates of air-sea surface fluxes since the 1970s, derived from reanalysis products ERA5, JRA-55 and COREv2, which are adjusted to be physically consistent with observation-based 3D ocean temperature and salinity products EN4 and IAP. OTM adjusts air-sea surface fluxes in a consistent manner, thereby also enabling estimation of meridional heat and freshwater transports. Inferred mean meridional heat transport is relatively consistent, and aligns with independent ocean transport observations and the spread of estimates from historical reconstructions from the 6th Climate Model Intercomparison Project. Mean freshwater transport and trends in both heat and freshwater transport are less consistent. Either a narrowing of the range of estimates provided by reanalyses and/or additional constraints to OTM (in addition to the thermodynamic constraints currently provided) are therefore still needed.
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RC1: 'Comment on essd-2024-545', Sjoerd Groeskamp, 14 Feb 2025
Review of “Global air-sea heat and freshwater fluxes constrained by ocean Observations”
Authors: Sohail and Zika
Review by Sjoerd Groeskamp
Recommendation: Major Revisions.
This paper uses a previously developed inverse method (by the same authors), called the Optimal Transformation Method (OTM) to estimate the correction needed for air-sea freshwater and heatfluxes, to have an improved global balance and related air-sea flux products. The method uses fundamental ocean thermodynamical constraints that are available from readily available observations of T&S and air-sea fluxes. Given a beginning and end-state of the ocean volume in S&T space, and air-sea T&S fluxes, they calculate the required mixing between water masses. The residual is then used to calculate the required adaptation of surface fluxes to obtain the final water masses from the initial water masses. The inversion is done in T&S coordinates and translated back into geographical coordinates. The method is applied to different combination of gridded hydrography’s and air-sea flux products. This study is used to understand if the method performs as expected, to see where adaptations need to be made to surface fluxes and to understand how this impacts meridional heat transport.
I believe this work is of interest because air-sea fluxes are notoriously hard to estimate due to a lack of observational constraints. This method aims to further constraint estimates of air-sea fluxes (where we could otherwise not), using thermodynamical constraints that can be applied to observation of the ocean state and have implications for the overlaying air-se fluxes. In that sense, I welcome the line of work by these authors, and I think this paper is a worthwhile continuation of that work that intends to improve air-sea flux estimates and study how, why and where they lack information. All in all, I thus recommend publication of this work, but only after some extra work related to both improving the method, discussing or assessing uncertainty of the method and related to clarifying exactly what happens. These improvements are also needed for reproducibility. In addition, a better explanation is needed what the advance is of this paper compared to previous work by the authors. Below are my specific comments that include specification of the more general comments above.
Comments related to the method
It is not exactly clear what the advances are compared to Zika and Sohail 2023. This should be made clear.
Eq. 6 – Can you specify what is meant with adjacent regions? Are they touching each other? These are specifically horizontal right?
What about “adjacent water masses” in the vertical. You don’t want surface waters to mix with bottom waters directly and skip the water in between. Is there a constraint applied for this?
L93 - It is clearly discussed in the manuscript that the weighing factor influences the result. However, there is no quantification how it does so. It is discussed that, for example, consistency in adjustment in the SO can be due to this weighing factor. This is unfortunate, because I thought the consistency in adjustment would be exactly what would provide a solid argument for the use of this method. Is there a way to quantify the impact of modelers choices of the weighing factor and teas out the useful results from modeling choices?
The current choice of the weighing factors seems a clever one, but perhaps a broader discussion of what its impacts are is also helpful. Imagine doing no weighing for example.
More general than the weighing factor, the result of an inverse method can depend strongly on modelers choices and constraints. For example, that of the BSP and a-priori knowledge. Some of this is studies by having multiple products, but a discussion and possibly quantification of the influence of the modelers choices on the result can be improved and is maybe essential for interpreting the results.
Section 2 - The result of gij will be sensitive to weighing, BSP and given constraints. But also, to input datasets. This will result in imperfect mixing between water masses and related gij and eventually changes in Q^adjust. I guess this comes back to the sensitivity question before. Because how does this influence the results?
How is shortwave radiation depth penetration included? Groeskamp and Iudicone 2018 showed it has a huge impact on Watermass transformation. This means that the vertical distribution of SWR changes the thermodynamic state of the ocean below the surface. This effect should be included in Qij and will impact which water masses (and how much) need to be mixed, and thus eventually the resulting gij and Q^adjust.
Other comments
L73 – What is BSP? Can you give a quick explanation? Is it based on equal mass partitioning or so?
Eq. (2)-(6) – As with Eq 6, it would be great if you can add one sentence behind each equation, what the constraint implies.
L90 - Space between Ai and
L100 and before and after - I had to go back and read Zika en Sohail 2023 to understand the OTM. Now in principle this is not a problem, but I guess some more explanation of what is going on would be really helpful for some readers. Also, in reading that paper and then going back to this paper, I was not 100% how this works. Am I correct that you first do an inversion with the given air-sea fluxes (Q^prior), which then provides gij. Then this gij is used to calculate Qij in Eq(1), from which Q^adjust is obtained as Q – Q^prior? Anyway, I think some clarification is warranted, especially as there is no Q^adjust (the thing you ultimately want to know) in your cost function.
Figure 9 and 10 are key figures, but it does not show how the adjustment improves the results. This is the key point of the paper and I think this figure should somehow show the improvements made with the OTM. Also, please highlight the zero line (thick black line or so).
L248 - figure 7e and f
Comments fig 7 and around - The goals is for the surface fluxes to be adjusted thermodynamically and such that they have smaller biases when integrated globally. If I’m correct, global warming requires 0.3W/m2 warming. Why not include this in the inversion as a constraint?
On that note, do the adjustments lead to lower globally integrated air-sea flux biases? Can you provide a number that shows the globally integrated results?
Fig 7 has changing y axis, which is somewhat misleading in the comparison. Maybe have a panel or SM-figure where all green lines are in one panel?
Figure 8 was really confusing to read. There are multiple things stacked on each other, but sometimes not. It is hard to compare the flux products to each other and it is hard to separate the basins. I think an alternative way should be found to present this information.
L-287 – two times adjusted
L375 – The inverse method is no longer novel I think, it seems there are several papers quoted using this.
Reading the conclusion, I realized I was not exactly sure how the adjustment to the air-sea fluxes is added over time. If you calculate the adjustment over, say 6 years, you linearly add it over that period? Is this done at all?
Citation: https://doi.org/10.5194/essd-2024-545-RC1 -
RC2: 'Comment on essd-2024-545', Anonymous Referee #2, 03 Apr 2025
This is an interesting paper that seeks to apply an inverse method approach to adjust air-sea heat and freshwater flux fields to resolve long-standing and well-recognised major biases in various surface flux products. Use of inverse methods to address this problem is not new but the authors application of changes in T and S as constraints is novel. Their approach promises to move on this field which has not seen much development since the application of ocean heat transport estimates as constraints more than twenty years ago. The method is described in an earlier paper and its application here certainly merits publication.
My main concerns are centered on the analysis of the results which at times is lacking in the quantitative detail needed to support some of the qualitative conclusions that are reached. Also, the analysis falls short of addressing one of the key points, namely how much has the inter-product variance been reduced as a result of applying the inverse method analysis. In particular, are we now in a position - following the analysis - that uncertainty in the surface flux fields has been reduced to a level where they can be reliably used and, if so, where is this the case? Or is the level of uncertainty still uncomfortably large? The authors should address this key issue in their discussion which, at the moment, is rather short and doesn’t give this topic the amount of attention it needs.
In addition to these high-level points, the following issues need to be addressed:
- Line 2. Abstract. ‘…typically estimated based on observationally constrained ‘reanalyses’…’. The existence of other approaches should be noted too, either here or in the main text, in particular combined reanalysis/satellite-based products e.g. OAFlux (Lisan Yu, WHOI).
- Line 24. Intro. ‘Rich and accurate’, why rich (i.e. large number)? One would be enough if it’s accurate.
- Line 35. It would be good to balance the reference list by adding some of the early papers that attempted to adjust air-sea flux fields using inverse methods e.g., Isemer et al., 1989 (https://journals.ametsoc.org/view/journals/clim/2/10/1520-0442_1989_002_1173_faolsa_2_0_co_2.xml) and Grist and Josey, 2003 (https://journals.ametsoc.org/view/journals/clim/16/20/1520-0442_2003_016_3274_iaaots_2.0.co_2.xml)
- Line 93. Could do with a few more details on the OTM for the non-specialist and to avoid having to refer to back to the earlier paper. So, please broaden the treatment a little. In addition, clarify the following points: the Qi prior is defined at line 76 but where is the definition of the Qij prior needed for (7)? Also, where does the j info come into the definition of wj following (7)?
- Line 138. ‘COREv2 (Large and Yeager, 2009), the latter being an ocean/atmosphere reanalysis product’. This is an inaccurate description as COREv2 is an adjusted atmospheric reanalysis product with the adjustments largely being based on satellite observations. A more accurate description is needed here.
- Line 140. ‘ERA5 fluxes too much heat into the ocean, JRA-55 cools the ocean too much, and COREv2 is biased warm, though not by as much as ERA5.’ Needs to be backed up by some numbers here in addition to Fig.2. So, please include a table showing the global mean net heat flux and E-P values for each of these products, for each window.
- Figure 2. JRA55 and COREv2 have heat and freshwater content time series with the same sign for rate of change but ERA5 has opposite sign. This needs to be noted and possible reasons for this difference discussed. Is it related to differences between reanalyses in the relative importance of E&P trends in the freshwater budget and latent heat (E) in the heat budget?
- Figure 3. How is heat flux tendency defined? Is it a linear fit to the relevant local time series over the period considered? Or is some other method employed?
- Line 200. The authors note problems with data sparseness prior to the Argo period. Do they get similar heat and freshwater convergence tendency maps if they consider the most recent 20 year period which is spanned by Argo? Please include an extra set of maps for this period in the Supplementary and comment on any differences from Fig.3g-h and 4g-h.
- Figs 5 and 6 and associated discussion. Are the adjustments that are shown an average for the whole period considered? The text on rolling windows earlier in the text suggests that different adjustments are obtained for different sub-periods of the whole period. If so, are the adjustments for the different periods consistent with the whole period mean?
- Figs 5 and 6 and associated discussion. I can see the need to keep the color scale the same in each column but it’s very hard to see the details of the central column adjustments. So, an extra figure is needed in the Supplementary showing just the adjustments and a different color scale that better fits the range of the adjustments e.g., +/- 50 W/m2 or less for the heat flux.
- Figure 7 and associated discussion. This figure is interesting but why are the y-axes not chosen to have the same range? As it stands, the figure is a bit misleading because it looks like the variations are similar for each product but if a common y-axis scale was chosen it would be clear e.g., in the Tropics, that COREv2 has more than 3 times as much heat (for Prior + Adjustment) going into the ocean (0.2 PW/deg) than ERA5 (0.06 PW/deg). Maybe there’s an error here (or I’ve misunderstood something) because from Fig.5 it looks like the 3 products have a broadly similar amount of heat going into the ocean in the Tropics. If this is the case, why are they so different on Fig.7? So, some clarification is needed and a common y-axis scale should be employed on Fig.7 for heat. Likewise for freshwater.
- Fig. 7 and associated discussion. Does the inverse method employed (OTM) provide an uncertainty range on the adjustment? If so, please include this on the figure together with some discussion of what it implies e.g., are the IAP and EN4-based adjustments the same within the error range provided by the inverse method?
- Fig. 8. The y-axis range also varies between panels on this plot making it very difficult to compare the results for different products. So, the figure needs to be revised to have a common y-axis to enable the reader to make an intercomparison.
- Fig. 8. Also, there’s a lot of information on the figure and the dOTC, and divergence terms aren’t fully discussed in the text. So, they could be moved to an extra figure (with some discussion of what they show) and that would make Fig.8 simpler and easier to interpret.
- Line 296-297. ‘The time-mean ocean heat transports inferred from OTM match closely with prior research using the ECCO state estimate (Forget and Ferreira, 2019).’ This statement needs to be supported by including the ECCO state estimate transports on Figs.9 and 10.
- Fig. 9a It’s interesting that the JRA transports are weaker than those of CORE and ERA5. Does the large negative global mean heat flux bias in JRA55 in some way prevent it’s adjusted fluxes from being strong enough to generate a strong heat transport even though the global heat budget is closed?
- Line 311. Is there any value in using repeat hydrography estimates from other ocean basins as points of comparison in addition to RAPID and OSNAP for the North Atlantic? Of course, they’re not continuous like RAPID and OSNAP but surely they have some value as observational comparators? Valdivieso et al. (2017) include WOCE-based inverse model estimates at control sections from Ganachaud and Wunsch (2003) and Lumpkin and Speer (2007) on their heat transport plots. Please include these values on your plot too or argue why they are not useful as points of comparison.
- Line 358-359. ‘While the inter-product variance of the time-mean OTM-adjusted air-sea fluxes is relatively small (i.e., the adjusted fields are similar),…’. Some quantitative detail is needed here to support this qualitative statement, in particular the inter-product variance has not been shown as a map in the preceding text – so please include such a figure here to support this point. By adding and discussing a three-panel figure with maps of the inter-product variance before and after application of the inverse method, together with their difference, the authors will be able to address the point I made at the start of the review. Specifically, following application of the inverse method, has the uncertainty in the surface flux fields been reduced to a level (e.g. < 10 Wm-2 or some larger threshold depending on the application) where they can be reliably used and, if so, where is this the case?
Citation: https://doi.org/10.5194/essd-2024-545-RC2 -
RC3: 'Comment on essd-2024-545', R. Marsh, 08 Apr 2025
The authors have demonstrated that surface net heat and freshwater fluxes, and implied meridional transports and divergences, can be corrected (for global balance) in relation to the regional heat and freshwater budgets associated with water masses. This relies on the Optimal Transformation Method (OTM), established in previous publications by the same authors. The utility of this approach – applied to three reanalysis products and two observation-based 3D ocean temperature and salinity products – is evident in reasonable results, which are clearly presented. Specifically useful are maps of correction in surface heat and freshwater fluxes, and meridional profiles of the associated heat and freshwater transports, globally and separated between Atlantic and Indo-Pacific basins. While improvements in heat fluxes and transports are encouraging, it is evidently more challenging to obtain agreement with long-term trends associated with freshwater transport and trends in both budgets (across datasets and compared to other sources).
The Method (Sect. 2) is rather tricky to follow for readers unfamiliar with the water mass space and the OTM, given the abstract concept of extracting a geographical and time-varying correction to surface fluxes from transformation in T-S space of N (=144) water masses. As I understand, the two times, t0 and t1, define a timescale over which the prior (uncorrected) surface fluxes act to bias T and S of a given water mass (away from observed changes between t0 and t1) while mixing also transforms water masses (in T-S space); OTM provides the adjustment of surface fluxes to agree with observed changes of T and S, accounting for mixing. The transport matrix (g) transforms ‘early’ water masses (at t0) to ‘late’ water masses (at t1) via surface fluxes and mixing. The definition of t0 and t1, could be made clearer, defining (as I understand) the time elapsed for mixing that modifies T and S and the (corrected) trends in T and S attributed to (corrected) surface fluxes over this period.
The Data (Sect. 3) is clearly outlined. Figure 2 provides compelling motivation for this study, evidencing the serious and contrasting heat and freshwater flux biases relative to hydrographic observations, in terms of ocean heat and freshwater content.
The Results (Sect. 4) are clearly and concisely presented, although there is scope for some clarification. Regarding the rate of change of air-sea heat fluxes (1979-onwards tendencies) across the three reanalysis products (Fig. 3d-f), ‘with all three products showing a deceleration of surface warming over the majority of the ocean surface except high latitudes’, how does this relate to Fig. 2a, in which JRA-55 implies strong cooling while ERA5 implies strong warming? The heat flux adjustment maps in Fig. 5 are more clearly consistent with these biases, correcting JRA-55 with extra surface warming and ERA5 with extra surface cooling. Other results are largely supportive of the method, while the Discussion and Conclusions provide a clear synthesis and summary of the study and caveats.
I have some specific comments that relate to clarification and potential fuller explanation of results:
- Lines 32-33: Reference to heat as a tracer seems awkward to me; it is perhaps more straightforward to refer to ‘air-sea fluxes’ and ‘ocean heat and freshwater content’, or ‘ocean state’
- Line 67: In this context, should the indices of C be ‘1,j’?
- Line 70, Equation (1) and preceding text: Volumes ‘V’ are added to air-sea fluxes ‘Q’; as introduced, it is unclear how two different quantities (a volume and a flux) can be thus added, although by line 76, it is clear that Q is time and area integrated, which makes sense (Q thus becoming a volumetric change). Perhaps the authors can more carefully introduce and define Q, so that it is clear that this is an incremental change of volume?
- Lines 77-78: Is q(x,y,t), the ‘two-dimensional, time-varying surface air-sea flux field representing combined freshwater and heat fluxes’ otherwise a vector in T-S space? If so, perhaps further explain accordingly.
- Figure 2 caption: Presumably the cumulative heat and freshwater content changes are global – please add this clarification to the caption.
- Figure 8 caption: It is hard for the reader to appreciate how the six combined measures (the six bars) correspond to each basin; it appears that they are combined in four bars, centred about the tick on the x axes; please clarify this in the caption.
- Lines 330-333: Regarding divergence and convergence of freshwater transport, this is normally taken as a derivative, here implicitly in latitude; I think you are interpreting transports as divergences if < 0 (or convergences, if > 0), taken as the difference from zero (at a given latitude), but this could be more clearly explained for those unfamiliar with freshwater transport/divergence.
- Figure 10: Regarding the tendency (10b) compared to the mean (10a), the former shares broadly similar profile to the latter, implying that freshwater transports (divergences/convergences) have amplified, consistent with an intensifying water cycle. Is this correct? If so, perhaps note this in Sect. 4.3
Citation: https://doi.org/10.5194/essd-2024-545-RC3
Data sets
Adjusted ERA5, COREv2 and JRA-55 products constrained by ocean observations Taimoor Sohail and Jan D. Zika https://doi.org/10.5281/zenodo.14004938
Model code and software
Adjusted ERA5, COREv2 and JRA-55 products constrained by ocean observations Taimoor Sohail and Jan D. Zika https://doi.org/10.5281/zenodo.14004938
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