Long-Wavelength Steric Sea Level and Heat Storage Anomaly Maps by Combining Argo Temperature and Salinity Profiles with Satellite Altimetry and Gravimetry

Chambers, Don P.; Reinelt, Sara J.

doi:https://doi.org/10.5194/essd-2025-510

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https://doi.org/10.5194/essd-2025-510

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09 Sep 2025

| 09 Sep 2025

Status: this preprint is currently under review for the journal ESSD.

Long-Wavelength Steric Sea Level and Heat Storage Anomaly Maps by Combining Argo Temperature and Salinity Profiles with Satellite Altimetry and Gravimetry

Don P. Chambers and Sara J. Reinelt

Abstract. Argo profiles of temperature/salinity (T/S) at specific times and locations from January 2003 through December 2023 are mapped into monthly maps of steric sea level (SSL), thermosteric sea level (TSL), and Ocean Heat Content (OHC) anomalies at long wavelengths. The mapping uses a monthly satellite reference computed from the difference between satellite altimetry and gravimetry, so that in periods where there is not sufficient global Argo coverage (generally before 2007), the satellite estimate is used instead of a mean climatology. Longwave mapping is done to reduce large errors introduced by poor sampling of mesoscale eddies by the Argo floats. We demonstrate that on global- and basin-scales, the longwave mapping does not substantially affect calculations of mean SSL, TSL, or OHC changes. Monthly standard error maps from the mapping are also provided. These maps are intended for users interested in understanding global- and basin-scale sea level budgets, as well as understanding changes in ocean heat uptake.

Received: 20 Aug 2025 – Discussion started: 09 Sep 2025

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Don P. Chambers and Sara J. Reinelt

Status: final response (author comments only)

RC1:
'Comment on essd-2025-510', Anonymous Referee #1, 09 Oct 2025
In this paper, the authors use temperature and salinity data from Argo floats (2003–2023) to produce monthly maps of steric sea level (SSL), thermosteric sea level (TSL), and ocean heat content (OHC) anomalies, focusing on long-wavelength signals. A satellite-based reference, derived from the combination of satellite altimetry and space gravimetry, is used as a first a priori field and helps fill data gaps in Argo coverage, particularly before 2007. A long-wavelength mapping approach is applied to reduce errors in the monthly maps caused by the sparse sampling of mesoscale variability by Argo. The authors claim that the resulting dataset, including associated error maps, enables analysis of sea level and ocean heat variations on both global and basin scales.

Major comments:
This study addresses the important issue of SSL, TSL, and OHC variability at regional and global scales—key components of the global and regional sea level budget. Continuous and accurate estimates of SSL, TSL, and OHC are essential for closing the sea level budget and understanding sea level variability. However, precise estimates are limited by the number of Argo floats, which sparsely sample the high-variance mesoscale variability induced by eddies and fronts, introducing significant regional errors in TSL and SSL relative to the true mean state. The authors partly overcome this limitation by using a long wave length optimal smoother with a background climatology (a priori estimate) based on a combination of satellite altimetry and gravimetry, and correlation coefficients derived from satellite altimetry data, thereby damping the noise induced by mesoscale variability. As such, this study is relevant to the climate science community.
The use of satellite altimetry to derive the correlation coefficients for the smoother and as a first-guess field is not new—it has been previously employed by Willis et al. (2003 JGR, 2004 JGR ocean) and further by Lyman and Johnson (2008 JCLI, 2023 JAOT) The novelty of the present work lies in combining satellite altimetry with GRACE data instead of relying solely on altimetry. This addition likely has a limited (possibly insignificant) impact on the calculation of correlation coefficients, since GRACE cannot resolve mesoscale variability. However, it may improve the final solution by providing a first-guess field more consistent with Argo data. Unfortunately, this potential benefit is not analyzed in the paper: the authors do not compare solutions with and without gravimetry data to assess any improvement. Another new aspect of the study is the production of maps of interpolation-induced long-wavelength errors. Although these “error maps” do not represent total uncertainty, they are valuable as they indicate where and when satellite reference data are used to fill gaps and where Argo data dominate the reconstruction. This is a welcome addition, as most processing centers do not provide such information. Aside from these aspects, I do not identify significant novelty compared to previous literature. The authors claim that using altimetry in the optimal interpolation improves SSL, TSL, and OHC estimates, particularly before 2008. This is true, but it is already well established (e.g., Lyman and Johnson 2008).
The general approach of interpolating Argo profiles with satellite data to estimate SSL, TSL, and OHC used in this work, is standard and reasonable. However, in this work, it presents several important limitations that need to be addressed for the results to be convincing and fully comprehensible.
The methodology is not clearly explained.

a) The authors provide “long-wavelength” OHC, SSL, and TSL estimates down to 2000 m depth, but this depth limitation is never clearly stated in the abstract or the main text. It should be explicitly mentioned, ideally in the title.
b) The term “long wavelength,” which is central to the approach, is never quantitatively defined. While Equation 8 provides some indication of the targeted scales, the concept is not clearly explained or discussed in the abstract or main text. There is also no discussion of whether these intended long wavelengths are effectively resolved in the final estimates.
c) The overall workflow of the method is unclear. It took several readings to infer that the optimal interpolation (OI) scheme is applied multiple times—first to satellite data, then to Argo profile anomalies relative to the satellite field. While the equations are clear, the narrative is not. A schematic diagram of the workflow would greatly aid comprehension.
d) Some key assumptions underlying the OI approach are not explicitly stated or discussed (see, for instance, my detailed comment on Equation 8 regarding the assumption that the signal is uncorrelated with the errors).
e) The resulting SSL, TSL, and OHC estimates are compared against an OI field based on Argo data only (the SIO estimate). Since Argo-only reconstructions are known to provide suboptimal representations of OHC and TSL this comparison is of limited relevance. Other products combining Argo and satellite altimetry for optimal interpolation exist (e.g., Lyman and Johnson 2008, the PMEL product; Lyman and Johnson 2023, the RFROM product) and they show significantly better results (Meyssignac et al., 2019 Frontiers ; Hakuba et al., 2024 survey of geophysics). They should be included in the comparison.

f) When making comparisons, the authors should separate the annual cycle from the interannual and longer-term variability (in particular in figures 5,6, 8 and 9). This is essential to assess whether the interannual and low-frequency components of SSL, TSL, and OHC are adequately resolved.
2. The study lacks a validation section.
The proposed estimates are not validated against any independent data. Validation is crucial to demonstrate the reliability of the results. A suitable validation approach would be a “leave-one-out” experiment, where the analysis is repeated multiple times excluding one or more Argo profiles; the omitted profiles can then serve as independent references. Another useful validation could involve comparing the global mean OHC estimates with surface flux-derived ocean heat uptake estimates from the combination of CERES TOA radiation (EBAF product) and the vertically integrated divergence of atmospheric energy (TDIV product), as in Mayer et al. (2022 JCLI). This method provides precise global-scale validation. To achieve a state-of-the-art assessment of OHC, both approaches should be implemented.
In summary, although the work presented here is not particularly novel, the inclusion of GRACE data in addition to altimetry for interpolating Argo profiles is an interesting idea, and the provision of “uncertainty” or “error” maps representing the interpolation error is a valuable contribution. Overall, the approach is sound, but several significant limitations must be addressed for the study to be convincing. In particular, the absence of validation against independent data is a major shortcoming. I believe the paper could be suitable for publication, but only after all major comments listed above have been satisfactorily addressed.
Detailed Comments :
Title and Abstract: The term “longwave length” must be clearly defined with a specific quantitative range.
The study provides estimates of SSL, STL, and OHC only down to 2000 m depth. This critical limitation is not stated until line 404, which is too late and may cause confusion. It should be made explicit from the beginning.
Line 18: There appears to be a missing word. Please check the grammar.
Line 23: The term “deep ocean” may be incorrect in this context. You likely mean “open ocean.”
Line 29: Key recent literature is missing. Consider citing the following: Lyman and Johnson (2008 JCLI, 2023 JAOT), Meyssignac et al. (2019 Fronteirs in Marine science ), Hakuba et al. (2024, survey of geophysics)
Lines 28–42: The "non-exhaustive list" includes several datasets known to have biases due to missing state-of-the-art corrections (e.g., use of climatologies that relax to zero in data-sparse regions, as with Ishii et al.; or lack of salinity drift correction in Argo before 2019, as in EN4). At the same time, key datasets that use satellite altimetry for interpolation and are more accurate (e.g., Lyman and Johnson 2008; Hakuba et al. 2021; Marti et al. 2022 essd) are omitted. See Hakuba et al. (2024 survey of geophysics) for a comparative assessment.
Please also consider including: Cheng et al. (2024 essd) (IAP estimate)
Line 50: Marti et al. (2022 essd) also employ this technique. Please include this reference.
Line 58: A more recent paper by the same authors addresses deep and abyssal warming: Johnson & Purkey (2024 GRL)
Line 60: A Recent community effort compare various OHC estimation methods: Hakuba et al. (2024 survey in geophysics)
Lines 151–152: "Necessary corrections applied" is too vague. Specify whether corrections to altimetry are consistent with those in the GRACE mascon solution. In particular:
Was a consistent GIA correction used?

Were corrections such as Frederikse et al. (2017, GRL) applied to altimetry to address ocean crustal elastic response to contemporary ice mass loss?

Line 202: Clarify what “normally” refers to. What standards or norms are implied? In which cases is temporal variability ignored, and how does that apply here? What are the implications?
Lines 205–207: Using Wunsch (2003)'s method assumes uncorrelated signal and noise within the control radius (i.e., ⟨signal(i), error(j)⟩ = 0 for all i, j). This assumption may not hold in practice. For example, salinity drift affecting profilers from the same manufacturer (deployed in the same regions) introduces a correlation between signal and error. This assumption must be explained and its limitations discussed in more details.
Lines 216–217:
Estimating the autocovariance from satellite data incorporates altimetry and GRACE error covariance into the interpolation error. In some regions, this can dominate the total error. Publicly available datasets provide uncertainty and error covariance for satellite data; They should be used to evaluate the impact. The authors should consider incorporating these error sources directly into the error budget (e.g., equations 8 and 9) for a more robust analysis.

In the same way, the interpolation approach introduces the covariance of deep ocean signals—present in satellite data but missing in Argo— into the interpolation error in equation 11. This signal may be significant and temporally correlated (see Zilberman et al., 2024 GRL). This effect should be evaluated

The same issue arises when sea level is used as a proxy for STL (line 290–291), especially in high latitudes where salinity signals are non-negligible. Please discuss.

Line 230: While random error may be assumed in equation 6, in reality, altimetry and GRACE data exhibit significant spatial and temporal correlations (see Prandi et al., 2021 Sci data). This correlation should be explicitly included in equation 8 via non-diagonal terms in C_sat^error.
Line 233:The strategy of treating shortwave signals as correlated noise in order to smooth them out via the optimal interpolation scheme is central to the method. The author should give more details on how this works. They should expand on how exactly the approach work, which wavelengths are filtered and whether all shortwave signals are treated equally
Line 260: You are likely referring to equation 6 here, not equation 5.
Line 261: Since Argo profiles OI is used here, the error covariance should reflect the structure of Argo data signal and error, not satellite data signal and error. Please address this inconsistency or discuss the limitations implied by replacing one by the other
Line 282: Step 3 removes any deep ocean signal present in altimetry/GRACE that is absent in Argo (limited to 2000 m). This makes it clear—albeit belatedly—that SSL, STL, and OHC are limited to 0–2000 m. This should be stated clearly and early in the manuscript. The implications are significant: the dataset cannot capture full-depth ocean heat uptake. This other limitation must be acknowledged and discussed.
Line 285: The equations become unclear here. For instance, ΔSSL_sat^oi_corr(x,y,t) is referenced but never appear in the equations. Likely, it should appear in equation 10, but this is not explicit. A clear workflow diagram with consistent notation would certainly adress this issue. And by clarifying the actual overall computation process, it would greatly improve reproducibility.
Line 305: In the figure 2 caption, you likely meant “thermosteric sea level” instead of “steric sea level.”
Line 329: High correlation values mostly reflect the agreement between annual cycles. Readers also need to know what the correlation numbers are when the annual and semi-annual signal are removed. This also applies to figures 5, 6, 8, and 9.
Line 331: The statement that “longwave maps are sufficiently accurate to resolve global and regional sea level budgets” is overstated. Accuracy depends on the specific scientific application. If the goal is to identify contributions to sea level rise, these maps may not be suitable, as they cannot estimate deep ocean warming or confirm its absence. Please revise this claim accordingly.
Line 335: The caption of figure 3 is unclear. Clarify what is meant by “eddy covariance as signal” vs. “eddy covariance as error (longwave signal).”
Line 395: If only one dataset is used for comparison, the results should ideally be compared with Lyman and Johnson (2008 JCLI) or Lyman and Johnson (2023 JAOT), which also used altimetry to interpolate Argo profiles. This would assess whether the current estimate matches the state of the art and whether adding GRACE data improves accuracy.
Line 414 & Figure 9: TSL from USF and SIO aligns better with altimetry+GRACE-derived SSL than their own SSL estimate. This implies persistent salinity issues, even in recent data. Please comment.
Line 429: Note that actually an open international comparison effort is ongoing: ME4OH, led by M. Palmer (UK Met Office) and D. Giglio (NCAR) in which all raw data from different groups is available.
Line 433: OHU cannot be estimated accurately here, as the analysis omits OHC below 2000 m. This must be stated explicitly.
Figure 10: The figure would be more convincing if compared with independent OHU estimates such as Mayer et al. (2022 JCLI), which use CERES and ERA5 data.
Line 462: I think the statement “useful benefits for scientists working on sea level-budget and ocean heat uptake studies “ is overstated and not supported by the analysis. The deep ocean contribution to sea level is arguably the most important unknown contribution (in amplitude) to the sea level budget. As deep ocean estimate is simply lacking here, the benefit for sea level budget science is limited. Even regionally the absence of deep ocean estimate is very limiting. Recent studies based on deep argo reveal that deep ocean signal is actually a significant contributor to the regional sea level variability (up to 30% in some regions, Zilbermann et al. 2024 GRL Johnson et al. 2019 GRL). As for the OHU studies , this is impossible to do with the proposed dataset as it does not provide any estimate of the OHU it only provides an estimate of the ocean heat content changes from 0 to 2000 m depth.
Citation: https://doi.org/10.5194/essd-2025-510-RC1
RC2:
'Comment on essd-2025-510', Anonymous Referee #2, 11 Oct 2025
Report on ‘Long-wavelength steric sea level and heat storage…’ by D.P. Chambers and S.J. Reinelt
This study proposes a new data set of steric sea level and ocean heat content (OHC) based on Argo data for the 0-2000m depth range and 2003-2023 time span. From my understanding, the two main differences with other existing Argo-based steric data sets are: (1) the use of a ‘geodetic’ steric climatology as reference-or first guess- (defined as the difference between the altimetry-based global mean sea level/GMSL and GRACE-based ocean mass), and (2) a long-wavelength mapping for reducing uncertainty due to meso-scale eddies not well observed by Argo.
Such a new data set could be of great value for some studies that investigate the long-term upper ocean warming. It could be also considered as a useful new indicator of the contribution of the upper ocean to the Earth energy imbalance. However (and this is not mentioned in the manuscript), I would be more cautious about using it for assessing global and regional sea level budget closure, as explained below.
While such a data set may be worth to be published, the manuscript needs substantial revision and clarification.
The authors do not explain well the novelty of their results neither the specific applications of their data set. To me, such a data set would be useful as an indicator of upper ocean warming but should not be used for sea level budget closure assessments. In effect, the use altimetry-based GMSL corrected for the ocean mass contribution (equivalent to the steric sea level) as first guess (or reference) will have a strong weight during the first 5 years of the record in any sea level budget assessment because of the poor Argo data coverage, hence the limited information brought by Argo data in the optimal interpolation process. Over this time span, the computed steric sea level will thus be dominated by the ‘Altimetry minus GRACE’ signal. As a result, one may expect that the GMSL budget of the early part of the record will be artificially closed because the estimated steric sea level from this study will be - by construction- essentially equal to the ‘Altimetry minus GRACE’ time series.

Several steps of the processing need clarification (see detailed comments below).

The term ‘long-wavelength’ is unexplained (500 km?, 1000km? more?…).

Above all, the results need thorough validation in order to convince users about the interest of using this new data set. Only a single comparison with one Argo product is proposed in the manuscript. More is needed. For example, the derived OHC data set could be compared with CERES data.

It is a pity that all presented steric sea level curves include the seasonal cycle while one is likely more interested in the interannual variability. The discussion about trend differences is quite superficial.

Finally, while the authors are well aware of the Argo-based salinity measurement errors as of 2015, there is no discussion on the reliability of their halosteric data set. This is an important limitation of this study.

Detailed comments
Abstract, line 9: indicate the wavelength range. What means ‘long-wavelength’?

Abstract, line 11: explain what is a ‘mean climatology’

Introduction, line 23: I suppose that you mean ‘open ocean’ rather than ‘deep ocean’?

Introduction, lines 49-62: indicate here that your altimetry data set does not account for the Jason-3 radiometer drift (a problem that may impact your results, especially at the end of the record)

Introduction, lines 57-58: deep ocean warming may no more be negligible (e.g., Johnson and Purkey, 2024).

Section 2.1, lines 116-118: the sentence ‘we kept only profiles deeper than 750 dba’ is unclear. Which depth? Why?

Section 2, line 145, I suppose that ‘who which’ should read ‘who wish’…

Section 2.2: line 152: indicate which corrections are applied (and mention that the Jason-3 radiometer drift is not accounted for)

Section 2.2: lines 173-174: mention (for readers not familiar with the sea level budget) that ‘altimetry-based sea level minus GRACE-based ocean mass’ represents the steric sea level

Section 2.3, Optimal interpolation: this section is not easy to read. The numerical values mentioned in the equations seem to have been pulled out of a hat…

Section 2.3, line 215: what means ‘4-10x’?

Section 2.3, line 272: what means ‘mean surface’ for GRACE data? (and Argo); line 289: ‘corrected’ for what?

Section 3, Table 1: since you do not remove the seasonal cycle, the correlation essentially refers to this dominant seasonal cycle. What about the correlations at interannual time scale?

Section 3, Table 1: trend differences around 0.3 mm/yr are not negligible at all (same order of magnitude as the GIA signal in the altimetry-based GMSL)

Section 3, Figures 5 and 6: Show difference time series!!! Remove the seasonal cycle

Section 3, lines 59-362: The trend difference over 2005-2024 (1.04 versus 1.17 mm/yr) is not significantly larger than the one over 2011-2024 (0.08 mm/yr), so that the use of the geodetic reference has limited impact.

Section 3, results: Why not show maps of regional trend differences? I suppose that the regional trend differences are not uniform but may depend on the regional Argo data sampling

Section 3, line 380: ‘The satellite data tend to dominate the mapping from 2003 to 2008…’: see my comment above

Section 3, lines 400-404: the discussion about the corrections should appear much earlier in the manuscript (see comment above)

Section 3, figures 8 and 9: show difference time series!!! Remove the seasonal cycle

Section 3 figures 8 and 9: what is the impact of salinity measurement errors on the USF SSL curves? Please discuss

Section 3, figure 10: there is no explanation for the 2015 difference between USF and SIO OHC. Please discuss

Section3, figure 10: the OHC time series show clear quasi periodic variation. Could you compute the periodogram and discuss the observed quasi periodicity?
Citation: https://doi.org/10.5194/essd-2025-510-RC2

Don P. Chambers and Sara J. Reinelt

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https://doi.org/10.5194/essd-2025-510-supplement

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Steric Sea Level and Heat Storage Anomalies from Argo Profiles and Satellite Altimetry and Gravimetry Don P. Chambers and Sara J. Reinelt https://doi.org/10.17632/dsjkkhvywr.1

Don P. Chambers and Sara J. Reinelt

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Monthly maps of steric sea level, thermometric sea level, and ocean heat content anomalies from January 2003 through December 2023 are described. The maps were created from a statistical combination of satellite altimetry, satellite gravimetry, and in situ Argo profiles of temperature/salinity to 2000 m depth. Data are mapped at long wavelengths to reduce contamination from mesoscale eddies. The data are intended for the study of sea level budgets and changes in ocean heat uptake.


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