the Creative Commons Attribution 4.0 License.
the Creative Commons Attribution 4.0 License.
| 16 May 2025
Sea level reconstruction reveals improved separations of regional climate and trend patterns over the last seven decades
Abstract. Rapidly rising sea level is one of the major adverse consequences of anthropogenic climate change. Sea level rise poses an existential threat to coastal populations, particularly for urban settlements with accelerating growth rates. Contemporary empirical sea level reconstructions have been used to conflate short-term (~3 decades) satellite altimetry geocentric sea level data and long-term (50 years or longer) tide gauge records to better estimate reliable sea level rise towards multi-decadal to centennial time scales. However, adequate separations and quantifications of low-frequency climate patterns and sea level trends globally at regional scales remain elusive. Here, we propose a new sea level reconstruction framework that incorporates Empirical Orthogonal Function (EOF) into the contemporary Cyclostationary EOF with Reduced Space Optimal Interpolation (CSEOF-OI) algorithm to better reconstruct sea level fields. Using 225 selected long-term gap-filled tide gauge records with vertical land motion adjusted and satellite altimetry, our global reconstructed monthly sea level time series, January 1950– January 2022, exhibit distinct delineations between modeled climate patterns and sea level trends at regional scales. The separated sea level patterns include trends, modulated annual cycles, the El Niño Southern Oscillation (ENSO), and the Pacific Decadal Oscillation (PDO). The third principal component of the reconstructed sea level exhibits a Pearson correlation coefficient of 0.87 with the Niño 3.4 ENSO index, and the fourth principal component correlates at 0.75 with the PDO index, indicating excellent agreement. The global mean sea level trend, accounting for the predominant climate periodicities, is 1.9 ± 0.2 mm yr⁻¹ (95 % confidence), and the estimate during the satellite altimetry era (January 1993–December 2021) is 3.2 ± 0.3 mm yr⁻¹ (95 % confidence). Compared with previous studies, we conclude that our 72-year sea-level reconstruction allows us to better separate the ENSO and PDO climate patterns, as well as the sea level they induced. Finally, we show that the short-term (5-year) rates of ENSO and PDO patterns significantly affect sea level both on a global and regional scale, altering global mean sea level trends by up to 1.1 ± 0.5 mm yr¹ (January 2011–January 2016). Over the past seven decades, the climate pattens exerted a minor impact on sea level trends, but substantially modulated apparent regional sea level accelerations, particularly in the western Pacific (e.g., 0.09 ± 0.05 mm yr⁻² at the Kuroshio Current), and in the east and central equatorial Pacific Ocean (e.g., −0.04 ± 0.03 mm yr⁻² near Costa Rica). The reconstructed sea level and analysis results datasets are available at https://doi.org/10.5281/zenodo.15288817 (Wang, 2025).
- Preprint
(33773 KB) - Metadata XML
-
Supplement
(31767 KB) - BibTeX
- EndNote
Status: closed
-
RC1: 'Comment on essd-2025-251', Anonymous Referee #1, 24 Jun 2025
- AC1: 'Reply on RC1', Shengdao Wang, 10 Nov 2025
-
RC2: 'Comment on essd-2025-251', Anonymous Referee #2, 07 Oct 2025
This manuscript introduces a modified spatial-temporal sea-level reconstruction method/product that combines two complementary decomposition techniques with reduced-space optimal interpolation, extending geocentric (absolute) sea-level anomalies back to 1950. The manuscript provides two main improvements. First, the reconstruction products support more cleanly separating climate-related sea level variability (e.g., ENSO, PDO) from the long-term trend within a spatiotemporal framework. Second, after quantifying climate-related variabilities, the authors assess their influence on regional short-term trend estimates as well as on regional long-term trends and accelerations. Other minor contributions include testing different gap-filling methods for tide gauge records to increase record availability. Comparison between different ways to correct vertical land motion at tide gauges to better match tide-gauge and satellite altimetry sea level. Overall, the datasets and their derived results are likely to benefit the sea-level and climate communities. The authors have provided both the products and core plotting/analysis codes at the data availability link, which facilitates a user-friendly experience. However, I still have several comments/concerns that, once addressed, should make the manuscript suitable for publication.
- The manuscript tests three gap-filling approaches (regularized EM, PPCA, AR) for tide gauges by using 48 nearly complete 70-year records and concludes that regularized EM performs best, as illustrated in Figure 2. Since the reconstruction process uses many more gap-filled tide gauges, please include a robustness test on a broader sample, e.g., considering setting the gauge record length shorter to include a larger set of near-complete gauge records, and report whether the ranking of methods is stable.
- In the section GNSS-derived vertical land motion at tide-gauge locations compared with the results from the altimetry minus tide-gauge (SA-TG) approach, this comparison should provide the GNSS data selection criterion used in Figure 3, e.g., collocation criteria, time spans, etc. More generally, in this section, please refocus SA-TG approach, which was used in the reconstruction, and present the other two correction approaches briefly. This will avoid letting side methods overshadow the main workflow and will make the procedure easier to follow.
- For the validation on the modified sea level reconstruction product in Figure 6d, the manuscript emphasizes applying long-term tide gauge records excluded from the reconstruction as independent validations, which is good. However, it should also report the comparison between the gauges used in the reconstruction process and their collocated reconstruction series to assess whether potential overfitting exists. For Figure 6g, since produced from this study in 1° × 1° resolution, please also compare the full-resolution 70-year trends with other gridded reconstruction over their common period if comparable-resolution product exists.
- In Figure 9, the 70-year combined ENSO–PDO induced sea-level acceleration is spatially prominent. To better serve users who are interested in multi-decadal sea level acceleration studies, the authors should also include separate spatial maps showing the ENSO-induced and PDO-induced acceleration coefficients, respectively.
- Add a flowchart of the modified reconstruction procedure to highlight the steps implemented in the reconstruction section more clearly.
Minor suggestions:
Line 25, exhibit -> exhibits
Line 68, spatiotemporal sea level changes -> spatiotemporal changes in sea level
Line 103, the estimate of -> estimating, difficult -> challenging
Line 112, mirrors -> was similar to
Line 134, PSMSL, first time showing in the main text, should provide the full name.
Line 162, mitigate -> address
Line 189, needed-> necessary
Line 218, long-> largely
Line 225, to be estimated -> estimation
Line 227 to Line 229, “An issue that might be regarded as a mere matter of language is examined here … entails circular logic or tautological reasoning.” Should simplify/reorganize these two sentences.
Line 234, not -> rather than
Line 324, corresponding the -> the corresponding
Line 335, In Figure 4, the author should add the trend values of the CSEOF trend mode estimated regional trends, and trend values from the further refined trend mode. Also, anomlies -> anomalies
Line 393, initial and terminal -> near beginning and end
Line 450, and respective reconstruction -> and their respective reconstructions
Line 464 to Line 466 “This validation was performed over 40 years (January 1982 to December 2021; 224 gauges) and 65 years (January 1967 to December 2021; 34 gauges), yielding a consistent median r0.85 (85.19% for 40 years and 84.76% for 65 years).” Since the reconstructed sea level is from January 1950 to January 2022, consider updating this comparison to also include January 2022.
Line 541, in line -> consistent
Line 560, before -> prior to the
Line 577, suggesting -> suggest, meet -> meeting
Line 578, partly -> have been partly
Line 586, ENSO, PDO‐induced sea level -> ENSO and PDO-induced sea level
Line 621, increased -> increasing
Line 627, evident by most of the strong rising areas concentrating on the low-latitude Pacific -> as evident by the concentration of the strongest rising areas in the low-latitude Pacific.
Line 641, contrasted by -> in contrast to
Line 642, western -> West
Line 652, the critical need to account for both ENSO and PDO influences for understanding short-term sea level changes. -> the importance of considering both ENSO and PDO influences in understanding short-term sea level changes.
Line 658, during -> over
Line 705, generally between 1 and 2 mm yr⁻¹ -> typically ranging from 1 to 2 mm yr⁻¹
Line 730, estimate -> estimating
Line 750, scales -> timescales
Line 762, multi-decades -> multiple decades
Citation: https://doi.org/10.5194/essd-2025-251-RC2 -
AC2: 'Reply on RC2', Shengdao Wang, 10 Nov 2025
Thank you very much for reviewing our manuscript and for your constructive comments. We sincerely appreciate the time and effort you devoted to our work. We have carefully considered each of your points and have provided corresponding responses. For the detailed, point-by-point replies, please refer to the attached PDF document.
Status: closed
-
RC1: 'Comment on essd-2025-251', Anonymous Referee #1, 24 Jun 2025
The manuscript presents a global sea level reconstruction spanning 1950–2022 at a 1° × 1° resolution, using a combined dataset of tide gauge records (corrected for vertical land motion) and satellite altimetry, implemented through an enhanced CSEOF-OI framework incorporating EOF decomposition. The authors emphasize improved separation of climate modes (e.g., ENSO, PDO) and long-term trends.
While the study contributes to an important topic and provides a potentially valuable dataset to the sea level and climate research community, several key aspects of the methodology and validation require further clarification. In particular, the validation appears limited to coarser 5° × 5° spatial scales, and insufficient attention is given to the accuracy of reconstructed data in the pre-altimetry era (especially before 1993) and in open-ocean regions lacking tide gauge constraints. These issues, along with others detailed below, should be addressed to ensure the robustness and usability of the dataset.
- The manuscript reports strong correlations (r = 0.87 and r = 0.75) between reconstructed principal components and ENSO/PDO indices. However, the interpretation as “excellent agreement” should be moderated, and the authors should clarify whether statistical significance tests were performed and how preprocessing (e.g., detrending) was handled.
- In Fig. 1(a), how many tide gauge stations are included in total? Since the data record lengths vary across stations, the authors should also clarify the proportion of stations within each time span category as shown in the figure. In Fig. 1(b), the authors present the percentage distribution of tide gauge records covering the 1950–2022 period. However, it would be helpful to specify the actual number of stations corresponding to each percentage category.
- The manuscript refers to the data time span as both “January 1950 to December 2021” and “January 1950 to January 2022” in different sections. The authors should ensure consistency and clarify the exact temporal coverage of the reconstructed dataset.
- Lines 141–142 refer to Figs. S1–S3, and line 165 mentions Fig. S4. However, these figures are not provided in the manuscript. The authors should ensure that all referenced supplementary figures are included at the end of the paper.
- The manuscript states that missing data in tide gauge records were filled using AR, PPCA, and EM methods, with EM identified as the optimal approach based on validation experiments. However, it is unclear how the authors handled records with substantial data gaps at the beginning or end of the time series. What was the quality of the gap-filling in such cases? As Fig. 1(b) indicates, some stations have more than 50% missing data — were these records also gap-filled and subsequently used in the sea level reconstruction? Further clarification is needed regarding the treatment and reliability of heavily gapped records.
- The sentence “GIA models have been extensively used to harmonize measurements between altimetry and tide gauge sea level” is misleading. GIA corrections are primarily used to account for long-term vertical land motion, not to harmonize the two types of measurements. The authors should revise this statement to more accurately reflect the role of GIA models.
- The manuscript discusses the limitations of GIA models and emphasizes that GIA is not the sole contributor to vertical land motion at tide gauge locations. However, it remains unclear how GIA corrections were specifically implemented in the reconstruction. The authors should explicitly state which GIA model was used, how the corrections were applied, and whether additional vertical land motion sources (e.g., tectonics, anthropogenic subsidence) were considered or corrected for in the analysis.
- The discussion on vertical land motion (LVM) from lines 209 to 226 reads more like a general literature review and would be more appropriately placed in the Introduction section. The Methods section should focus on describing the specific data sources and procedures used in this study.
- The sentence in lines 227–228 (“An issue that might be regarded as a mere matter of language is examined here; however, imprecise terminology can give rise to subtle yet conceptual misunderstandings”) is vague in both meaning and context. It is unclear what specific issue the authors are referring to in this section. The authors should clarify the intended point or consider removing or relocating the sentence for better coherence.
- What is the spatial resolution of the AVISO Level 4 monthly gridded sea level product used in this study? How are the sea level changes at the tide gauge locations derived from the gridded data? Specifically, what spatial matching or interpolation methods are applied to relate the gridded data to the tide gauge positions?
- The comparison between SA–TG-derived and GNSS-derived VLM estimates shows a median difference of 0.88 mm/yr (r = 0.86) across 253 sites. Even in the subset with the smallest GNSS uncertainties, the median difference remains 0.64 mm/yr. These differences are non-negligible and may influence long-term sea level trend estimates. The authors should discuss the implications of such discrepancies on their reconstruction results. Additionally, the manuscript does not report the average (mean) VLM rates estimated separately by SA–TG and GNSS methods over the 253 sites; this information should be provided to better understand the characteristics of both estimates.
- Lines 283–285: The procedure for transforming the tide gauge time series onto the reference frame of the nearby altimetry point is not clearly explained. Could the authors provide more detail on how this transformation is performed?
- To improve clarity and reproducibility, I suggest the authors include a schematic flowchart of the data processing workflow. This would provide a more intuitive and comprehensive overview than text descriptions alone.
- The manuscript describes the reconstruction of sea level trends from 1950 to 1993 by combining tide gauge and altimetry-derived rates. However, it is unclear how the fusion between tide gauge records and satellite altimetry data is achieved, given that the AVISO dataset begins in 1993. Specifically, how is the 1°×1° gridded product generated for the pre-altimetry period, and how are data gaps filled in offshore or deep-ocean regions where tide gauges are absent or sparse?
- The manuscript refers to the application of a Reduced Space Optimal Interpolation method based on CSEOFs (CSEOF-OI), but the underlying algorithm is not clearly described. For reproducibility and clarity, I suggest the authors provide a concise explanation of how the CSEOF decomposition and the subsequent optimal interpolation are implemented, and how this approach improves upon traditional EOF-OI methods. A schematic or reference to a methodological appendix would be helpful.
- In Figure 6, panels (a) and (b) appear to show very similar results, despite panel (b) involving additional processing steps such as EOF or CSEOF decomposition. Since both panels are based on the same altimetry data, this comparison mainly reflects differences introduced by the processing itself rather than demonstrating any improvement in the quality of the reconstructed data. I suggest that the authors clarify the purpose of this comparison and provide more rigorous evidence to support claims of improved data quality.
- Line 265 mentions that GNSS-derived and SA–TG-derived VLM time series are not consistent. However, the manuscript does not clarify the temporal coverage of GNSS observations used for validation. What is the time period of the GNSS-derived VLM estimates across the 253 tide gauge sites? Are these periods consistent across stations? Moreover, temporal inconsistencies between GNSS and SA–TG estimates may lead to biased trend comparisons, especially if GNSS observations cover shorter or non-overlapping periods with significant non-linear land motion. This potential impact should be addressed and quantified. We note that comparisons of vertical land motion should be conducted over consistent time periods; otherwise, the comparison becomes fundamentally invalid and cannot reliably assess the agreement between the two methods.
- The reconstructed dataset is provided at a 1° × 1° resolution; however, the validation analyses are primarily conducted at 5° × 5° or coarser spatial scales. It is important to assess the accuracy and stability of the reconstruction at the native grid resolution, especially for users interested in regional-scale applications. Furthermore, the quality assessment largely focuses on trend estimates and correlations with known climate indices. While useful, these do not sufficiently address the reliability of the reconstructed sea level fields in the pre-altimetry era (before 1993), particularly in the open ocean where tide gauge constraints are absent. Greater emphasis should be placed on evaluating the uncertainty and credibility of the reconstructed fields in such data-sparse regions.
Citation: https://doi.org/10.5194/essd-2025-251-RC1 - AC1: 'Reply on RC1', Shengdao Wang, 10 Nov 2025
-
RC2: 'Comment on essd-2025-251', Anonymous Referee #2, 07 Oct 2025
This manuscript introduces a modified spatial-temporal sea-level reconstruction method/product that combines two complementary decomposition techniques with reduced-space optimal interpolation, extending geocentric (absolute) sea-level anomalies back to 1950. The manuscript provides two main improvements. First, the reconstruction products support more cleanly separating climate-related sea level variability (e.g., ENSO, PDO) from the long-term trend within a spatiotemporal framework. Second, after quantifying climate-related variabilities, the authors assess their influence on regional short-term trend estimates as well as on regional long-term trends and accelerations. Other minor contributions include testing different gap-filling methods for tide gauge records to increase record availability. Comparison between different ways to correct vertical land motion at tide gauges to better match tide-gauge and satellite altimetry sea level. Overall, the datasets and their derived results are likely to benefit the sea-level and climate communities. The authors have provided both the products and core plotting/analysis codes at the data availability link, which facilitates a user-friendly experience. However, I still have several comments/concerns that, once addressed, should make the manuscript suitable for publication.
- The manuscript tests three gap-filling approaches (regularized EM, PPCA, AR) for tide gauges by using 48 nearly complete 70-year records and concludes that regularized EM performs best, as illustrated in Figure 2. Since the reconstruction process uses many more gap-filled tide gauges, please include a robustness test on a broader sample, e.g., considering setting the gauge record length shorter to include a larger set of near-complete gauge records, and report whether the ranking of methods is stable.
- In the section GNSS-derived vertical land motion at tide-gauge locations compared with the results from the altimetry minus tide-gauge (SA-TG) approach, this comparison should provide the GNSS data selection criterion used in Figure 3, e.g., collocation criteria, time spans, etc. More generally, in this section, please refocus SA-TG approach, which was used in the reconstruction, and present the other two correction approaches briefly. This will avoid letting side methods overshadow the main workflow and will make the procedure easier to follow.
- For the validation on the modified sea level reconstruction product in Figure 6d, the manuscript emphasizes applying long-term tide gauge records excluded from the reconstruction as independent validations, which is good. However, it should also report the comparison between the gauges used in the reconstruction process and their collocated reconstruction series to assess whether potential overfitting exists. For Figure 6g, since produced from this study in 1° × 1° resolution, please also compare the full-resolution 70-year trends with other gridded reconstruction over their common period if comparable-resolution product exists.
- In Figure 9, the 70-year combined ENSO–PDO induced sea-level acceleration is spatially prominent. To better serve users who are interested in multi-decadal sea level acceleration studies, the authors should also include separate spatial maps showing the ENSO-induced and PDO-induced acceleration coefficients, respectively.
- Add a flowchart of the modified reconstruction procedure to highlight the steps implemented in the reconstruction section more clearly.
Minor suggestions:
Line 25, exhibit -> exhibits
Line 68, spatiotemporal sea level changes -> spatiotemporal changes in sea level
Line 103, the estimate of -> estimating, difficult -> challenging
Line 112, mirrors -> was similar to
Line 134, PSMSL, first time showing in the main text, should provide the full name.
Line 162, mitigate -> address
Line 189, needed-> necessary
Line 218, long-> largely
Line 225, to be estimated -> estimation
Line 227 to Line 229, “An issue that might be regarded as a mere matter of language is examined here … entails circular logic or tautological reasoning.” Should simplify/reorganize these two sentences.
Line 234, not -> rather than
Line 324, corresponding the -> the corresponding
Line 335, In Figure 4, the author should add the trend values of the CSEOF trend mode estimated regional trends, and trend values from the further refined trend mode. Also, anomlies -> anomalies
Line 393, initial and terminal -> near beginning and end
Line 450, and respective reconstruction -> and their respective reconstructions
Line 464 to Line 466 “This validation was performed over 40 years (January 1982 to December 2021; 224 gauges) and 65 years (January 1967 to December 2021; 34 gauges), yielding a consistent median r0.85 (85.19% for 40 years and 84.76% for 65 years).” Since the reconstructed sea level is from January 1950 to January 2022, consider updating this comparison to also include January 2022.
Line 541, in line -> consistent
Line 560, before -> prior to the
Line 577, suggesting -> suggest, meet -> meeting
Line 578, partly -> have been partly
Line 586, ENSO, PDO‐induced sea level -> ENSO and PDO-induced sea level
Line 621, increased -> increasing
Line 627, evident by most of the strong rising areas concentrating on the low-latitude Pacific -> as evident by the concentration of the strongest rising areas in the low-latitude Pacific.
Line 641, contrasted by -> in contrast to
Line 642, western -> West
Line 652, the critical need to account for both ENSO and PDO influences for understanding short-term sea level changes. -> the importance of considering both ENSO and PDO influences in understanding short-term sea level changes.
Line 658, during -> over
Line 705, generally between 1 and 2 mm yr⁻¹ -> typically ranging from 1 to 2 mm yr⁻¹
Line 730, estimate -> estimating
Line 750, scales -> timescales
Line 762, multi-decades -> multiple decades
Citation: https://doi.org/10.5194/essd-2025-251-RC2 -
AC2: 'Reply on RC2', Shengdao Wang, 10 Nov 2025
Thank you very much for reviewing our manuscript and for your constructive comments. We sincerely appreciate the time and effort you devoted to our work. We have carefully considered each of your points and have provided corresponding responses. For the detailed, point-by-point replies, please refer to the attached PDF document.
Data sets
Modified Sea Level Reconstruction Reveals Improved Separation of Climate and Trend Patterns Shengdao Wang https://doi.org/10.5281/zenodo.15288817
Model code and software
Modified Sea Level Reconstruction Reveals Improved Separation of Climate and Trend Patterns Shengdao Wang https://doi.org/10.5281/zenodo.15288817
Viewed
| HTML | XML | Total | Supplement | BibTeX | EndNote | |
|---|---|---|---|---|---|---|
| 1,491 | 116 | 31 | 1,638 | 85 | 35 | 64 |
- HTML: 1,491
- PDF: 116
- XML: 31
- Total: 1,638
- Supplement: 85
- BibTeX: 35
- EndNote: 64
Viewed (geographical distribution)
| Country | # | Views | % |
|---|
| Total: | 0 |
| HTML: | 0 |
| PDF: | 0 |
| XML: | 0 |
- 1
The manuscript presents a global sea level reconstruction spanning 1950–2022 at a 1° × 1° resolution, using a combined dataset of tide gauge records (corrected for vertical land motion) and satellite altimetry, implemented through an enhanced CSEOF-OI framework incorporating EOF decomposition. The authors emphasize improved separation of climate modes (e.g., ENSO, PDO) and long-term trends.
While the study contributes to an important topic and provides a potentially valuable dataset to the sea level and climate research community, several key aspects of the methodology and validation require further clarification. In particular, the validation appears limited to coarser 5° × 5° spatial scales, and insufficient attention is given to the accuracy of reconstructed data in the pre-altimetry era (especially before 1993) and in open-ocean regions lacking tide gauge constraints. These issues, along with others detailed below, should be addressed to ensure the robustness and usability of the dataset.