the Creative Commons Attribution 4.0 License.
the Creative Commons Attribution 4.0 License.
| 23 Feb 2026
An Improvement to short term variability in Global Mean Sea level reconstruction
Abstract. We hypothesise that there is an overestimation of Global Mean Sea Level (GMSL) variability from GMSL empirical orthogonal function (EOF) reconstructions due to differences between the tide gauge observations and their corresponding altimetry data. We show that these differences are correlated well with local winds along coastlines, suggesting that observations from tide gauges at the coast and satellite altimetry near the coast could partially be explained by the wind forcing. Correcting these differences through a mainly wind-driven regression model prior to the EOF reconstruction, reduces the standard deviation (SD) of the reconstructed GMSL variability by 26 % and significantly increases the correlation to 0.46 with respect to the observed averaged GMSL calculated from altimetry grid points (1994 to 2020). The model was used to extrapolate these differences prior to 1993 and a corrected GMSL reconstruction is presented.
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Notice on discussion status
The requested preprint has a corresponding peer-reviewed final revised paper. You are encouraged to refer to the final revised version.
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Preprint
(2389 KB)
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The requested preprint has a corresponding peer-reviewed final revised paper. You are encouraged to refer to the final revised version.
- Preprint
(2389 KB) - Metadata XML
- BibTeX
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- Final revised paper
Journal article(s) based on this preprint
Interactive discussion
Status: closed
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RC1: 'Comment on egusphere-2026-846', John Church, 04 Mar 2026
- AC1: 'Reply on RC1', Svetlana Jevrejeva, 19 Jun 2026
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RC2: 'Comment on egusphere-2026-846', Anonymous Referee #2, 24 May 2026
The study addresses a limitation of EOF-based GMSL reconstructions in capturing interannual variability. The proposed approach of examining and modelling the Signal Differences between tide gauges and nearby altimetry is well motivated, and the reported improvement in the reconstructed GMSL variability is promising. The manuscript is generally clearly structured, and the topic is meaningful to the sea-level reconstruction community.
Two methodological details require clarification before publishing. In particular, the treatment of GIA corrections and reference frames, and the possible contribution of non-linear and periodical vertical land motion signal to the estimated Signal Differences.
- Please clarify the treatment of GIA corrections and reference frames. The manuscript states that the tide-gauge records are corrected for GIA, while the altimetry data are also corrected using the drad250 GIA correction. Since tide gauges measure relative sea level whereas satellite altimetry measures absolute sea level, it is unclear whether these two GIA corrections place the two datasets into the same reference frame. The manuscript seems to apply two different GIA-related corrections: a relative sea-level GIA correction to tide gauges and a drad250 radial-deformation correction to altimetry. Please explain how their application ensures that the corrected tide-gauge and corrected altimetry records are comparable in a common reference frame before calculating the Signal Differences.
- Recent studies have shown that vertical land motion (VLM) at tide-gauge sites cannot always be represented as a purely linear process, and that nonlinear VLM can affect tide-gauge relative sea-level records and their interpretation (Oelsmann et al., 2024). In addition, GNSS studies have identified quasi-periodic surface displacement signals near a 6-year period, including vertical components (e.g., Ding and Chao, 2018). Similar signals have also been reported in satellite-altimetry-minus-tide-gauge residuals and have been considered when aligning tide-gauge and altimetry records for sea-level reconstruction (Wang et al., 2025). Because the Signal Differences in this study are defined as the difference between tide gauge and altimetry, it would be useful for the authors to clarify whether such vertical land-motion-related signals could contribute to the estimated differences. If these land-motion-related signals can be incorporated into the framework, they may further improve the resulting GMSL reconstruction. It will be better if the authors test this possibility. If such an analysis is beyond the scope of the present study, the authors should acknowledge this issue as a potential limitation and discuss how it may affect the interpretation of the regression-based correction.
Other comments
Line 117:
“though linear regression” should be “through linear regression.”Line 158:
The sentence “A total of seven yearly observations were removed from the entire data set during this procedure” is somewhat unclear. Please specify whether these seven removed observations correspond to seven station-years across different tide gauges, seven years from a single tide gauge, or another configuration. It would also be helpful to list the affected tide-gauge stations and years, or provide this information in a table or supplement.Line 160:
The manuscript states that the quality-controlled tide-gauge stations were spatially averaged into 1° × 1° tide-gauge bins. Please clarify the exact binning procedure. For example, were all stations falling within the same 1° × 1° grid cell averaged directly, or was an additional distance criterion used? Please also specify how stations with overlapping or different temporal coverage were combined within each bin.Lines 221-223: The notation may be visually confusing because the summation operator ∑ and the covariance matrix ∑ appear very similar. I suggest better to distinguish it clearly from the summation symbol.
Line 296:
There is an extra period after “reconstruction.” Please change “reconstruction..” to “reconstruction.”Line 315:
“using 229 tide gauge” should be “using 229 tide gauges”Line 425:
“less of factor” should be “less of a factor.”Line 582:
“large scale” should be hyphenated as “large-scale” when used adjectivally.References:
Oelsmann, J., Marcos, M., Passaro, M., Sanchez, L., Dettmering, D., Dangendorf, S., & Seitz, F. (2024). Regional variations in relative sea-level changes influenced by nonlinear vertical land motion. Nature Geoscience, 17(2), 137–144. https://doi.org/10.1038/s41561-023-01357-2
Ding, H., & Chao, B. F. (2018). A 6-year westward rotary motion in the Earth: Detection and possible MICG coupling mechanism. Earth and Planetary Science Letters, 495, 50–55. https://doi.org/10.1016/j.epsl.2018.05.009
Wang, S., Shum, C. K., Bevis, M., He, X., Zhang, Y., Ding, Y., Zhang, C., & Montillet, J.-P. (2025). Sea level reconstruction reveals improved separation of regional climate and trend patterns over the last seven decades. Earth System Science Data, 17(12), 7055–7077. https://doi.org/10.5194/essd-17-7055-2025
Citation: https://doi.org/10.5194/egusphere-2026-846-RC2 - AC2: 'Reply on RC2', Svetlana Jevrejeva, 19 Jun 2026
Peer review completion
Interactive discussion
Status: closed
-
RC1: 'Comment on egusphere-2026-846', John Church, 04 Mar 2026
General Comments:
This manuscript proposes a correction to the Empirical Orthogonal Function (EOF) model used for estimating historical global mean sea level prior to the satellite altimeter period. This correction relies on local winds, the SOI and the signal of tide gauges to “correct” for these local effects impacting coastal sea level that are not captured by the large scale altimeter signal, particularly as expressed through EOFs.
I think this is a useful approach and it is well described in the manuscript. Congratulations to the authors.
I was a little surprised that there was not a larger difference between the corrected and uncorrected GMSL estimates (Figure 12). Perhaps further improvements would result from correcting for the effect of Gravity, Rotational and Deformational (GRD) impacts from changes in the distribution of mass of water stored on land on sea levels, during ENSO events for example. Note Wang et al. (2024) has attempted to include these GRD impacts on reconstructions. There are alternate (possibly better) ways of including these effects the authors might wish to investigate in subsequent studies.
I was surprised that there was no discussion of coastal trapped waves known to be important on the American and Australian coasts. These waves are consistent with the idea behind these corrections of winds affected coastal sea levels with a much reduced impact on sea levels off shore at altimeter grid points. These waves also allow the impacts of remote winds affecting local sea levels, again as studied on the American and Australian coasts. Similarly, ENSO impacts can travel very large distances on the American and Australian coasts. I think the authors should discuss the implication of coastal trapped waves and propagation of remote signal such as those associated with ENSO and distant coastal winds.
There remains some trend differences in Figure 12. Although they are not significant, it would be useful to understand the reasons for the differences. I suspect that GIA differences may be at the heart of these differences. Could the authors comment please rather than just state they are not significantly different.
I recommend that the paper is published after consideration of these comments.
Detailed Comments for the authors to consider:
Lines 60-64: It may be useful to note that Wang et al. (2024) has extended the EOF technique by dispensing with mode zero and instead including spatially variable fingerprints.
Lines 269-282: Would using winds parallel and perpendicular to the coast be useful?
Line 559-560: Can you make the quantitative (and statistical) reasons for preferring on model 3 clearer. I did not pick up this clear preference given the additional parameters used in this more complex model.
References
Wang, Jinping, et al. 2024. Improved sea-level reconstruction from 1900 to 2019. Journal of Climate, 37 (24), 6453-6474. DOI 10.1175/JCLI-D-23-0410.1
Citation: https://doi.org/10.5194/egusphere-2026-846-RC1 - AC1: 'Reply on RC1', Svetlana Jevrejeva, 19 Jun 2026
-
RC2: 'Comment on egusphere-2026-846', Anonymous Referee #2, 24 May 2026
The study addresses a limitation of EOF-based GMSL reconstructions in capturing interannual variability. The proposed approach of examining and modelling the Signal Differences between tide gauges and nearby altimetry is well motivated, and the reported improvement in the reconstructed GMSL variability is promising. The manuscript is generally clearly structured, and the topic is meaningful to the sea-level reconstruction community.
Two methodological details require clarification before publishing. In particular, the treatment of GIA corrections and reference frames, and the possible contribution of non-linear and periodical vertical land motion signal to the estimated Signal Differences.
- Please clarify the treatment of GIA corrections and reference frames. The manuscript states that the tide-gauge records are corrected for GIA, while the altimetry data are also corrected using the drad250 GIA correction. Since tide gauges measure relative sea level whereas satellite altimetry measures absolute sea level, it is unclear whether these two GIA corrections place the two datasets into the same reference frame. The manuscript seems to apply two different GIA-related corrections: a relative sea-level GIA correction to tide gauges and a drad250 radial-deformation correction to altimetry. Please explain how their application ensures that the corrected tide-gauge and corrected altimetry records are comparable in a common reference frame before calculating the Signal Differences.
- Recent studies have shown that vertical land motion (VLM) at tide-gauge sites cannot always be represented as a purely linear process, and that nonlinear VLM can affect tide-gauge relative sea-level records and their interpretation (Oelsmann et al., 2024). In addition, GNSS studies have identified quasi-periodic surface displacement signals near a 6-year period, including vertical components (e.g., Ding and Chao, 2018). Similar signals have also been reported in satellite-altimetry-minus-tide-gauge residuals and have been considered when aligning tide-gauge and altimetry records for sea-level reconstruction (Wang et al., 2025). Because the Signal Differences in this study are defined as the difference between tide gauge and altimetry, it would be useful for the authors to clarify whether such vertical land-motion-related signals could contribute to the estimated differences. If these land-motion-related signals can be incorporated into the framework, they may further improve the resulting GMSL reconstruction. It will be better if the authors test this possibility. If such an analysis is beyond the scope of the present study, the authors should acknowledge this issue as a potential limitation and discuss how it may affect the interpretation of the regression-based correction.
Other comments
Line 117:
“though linear regression” should be “through linear regression.”Line 158:
The sentence “A total of seven yearly observations were removed from the entire data set during this procedure” is somewhat unclear. Please specify whether these seven removed observations correspond to seven station-years across different tide gauges, seven years from a single tide gauge, or another configuration. It would also be helpful to list the affected tide-gauge stations and years, or provide this information in a table or supplement.Line 160:
The manuscript states that the quality-controlled tide-gauge stations were spatially averaged into 1° × 1° tide-gauge bins. Please clarify the exact binning procedure. For example, were all stations falling within the same 1° × 1° grid cell averaged directly, or was an additional distance criterion used? Please also specify how stations with overlapping or different temporal coverage were combined within each bin.Lines 221-223: The notation may be visually confusing because the summation operator ∑ and the covariance matrix ∑ appear very similar. I suggest better to distinguish it clearly from the summation symbol.
Line 296:
There is an extra period after “reconstruction.” Please change “reconstruction..” to “reconstruction.”Line 315:
“using 229 tide gauge” should be “using 229 tide gauges”Line 425:
“less of factor” should be “less of a factor.”Line 582:
“large scale” should be hyphenated as “large-scale” when used adjectivally.References:
Oelsmann, J., Marcos, M., Passaro, M., Sanchez, L., Dettmering, D., Dangendorf, S., & Seitz, F. (2024). Regional variations in relative sea-level changes influenced by nonlinear vertical land motion. Nature Geoscience, 17(2), 137–144. https://doi.org/10.1038/s41561-023-01357-2
Ding, H., & Chao, B. F. (2018). A 6-year westward rotary motion in the Earth: Detection and possible MICG coupling mechanism. Earth and Planetary Science Letters, 495, 50–55. https://doi.org/10.1016/j.epsl.2018.05.009
Wang, S., Shum, C. K., Bevis, M., He, X., Zhang, Y., Ding, Y., Zhang, C., & Montillet, J.-P. (2025). Sea level reconstruction reveals improved separation of regional climate and trend patterns over the last seven decades. Earth System Science Data, 17(12), 7055–7077. https://doi.org/10.5194/essd-17-7055-2025
Citation: https://doi.org/10.5194/egusphere-2026-846-RC2 - AC2: 'Reply on RC2', Svetlana Jevrejeva, 19 Jun 2026
Peer review completion
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Andrew Shaw
Francisco Calafat
The requested preprint has a corresponding peer-reviewed final revised paper. You are encouraged to refer to the final revised version.
- Preprint
(2389 KB) - Metadata XML
General Comments:
This manuscript proposes a correction to the Empirical Orthogonal Function (EOF) model used for estimating historical global mean sea level prior to the satellite altimeter period. This correction relies on local winds, the SOI and the signal of tide gauges to “correct” for these local effects impacting coastal sea level that are not captured by the large scale altimeter signal, particularly as expressed through EOFs.
I think this is a useful approach and it is well described in the manuscript. Congratulations to the authors.
I was a little surprised that there was not a larger difference between the corrected and uncorrected GMSL estimates (Figure 12). Perhaps further improvements would result from correcting for the effect of Gravity, Rotational and Deformational (GRD) impacts from changes in the distribution of mass of water stored on land on sea levels, during ENSO events for example. Note Wang et al. (2024) has attempted to include these GRD impacts on reconstructions. There are alternate (possibly better) ways of including these effects the authors might wish to investigate in subsequent studies.
I was surprised that there was no discussion of coastal trapped waves known to be important on the American and Australian coasts. These waves are consistent with the idea behind these corrections of winds affected coastal sea levels with a much reduced impact on sea levels off shore at altimeter grid points. These waves also allow the impacts of remote winds affecting local sea levels, again as studied on the American and Australian coasts. Similarly, ENSO impacts can travel very large distances on the American and Australian coasts. I think the authors should discuss the implication of coastal trapped waves and propagation of remote signal such as those associated with ENSO and distant coastal winds.
There remains some trend differences in Figure 12. Although they are not significant, it would be useful to understand the reasons for the differences. I suspect that GIA differences may be at the heart of these differences. Could the authors comment please rather than just state they are not significantly different.
I recommend that the paper is published after consideration of these comments.
Detailed Comments for the authors to consider:
Lines 60-64: It may be useful to note that Wang et al. (2024) has extended the EOF technique by dispensing with mode zero and instead including spatially variable fingerprints.
Lines 269-282: Would using winds parallel and perpendicular to the coast be useful?
Line 559-560: Can you make the quantitative (and statistical) reasons for preferring on model 3 clearer. I did not pick up this clear preference given the additional parameters used in this more complex model.
References
Wang, Jinping, et al. 2024. Improved sea-level reconstruction from 1900 to 2019. Journal of Climate, 37 (24), 6453-6474. DOI 10.1175/JCLI-D-23-0410.1