The study „Attributing decadal climate variability in coastal sea-level trends“ aims to relate the variability in decadal sea-level trends in coastal regions to climate variability. Based on a high resolution ocean model, the authors reconstruct coastal, sea-level trends via linear relationships with climate indices.

Based on their reconstruction, the authors can confirm and quantify the dominance of manometric over steric sea-level trends at coastal locations and pinpoint locations where the GRD signal is of importance. They quantify the sea-level trend variance explained by climate variability and show that in one-third of all coastal locations almost half the variance can be explained by climate variability. Finally, their results suggest that climate variability has suppressed sea-level rise during the period 2008-2018.

The results are well presented, the paper is relevant to the scientific community and doesn’t present any major flaws. I recommend the article to be accepted, after some minor revisions.

General comments

1. The authors used a series of climate indices to establish the relation between sea-level trends and climate variability. It is my understanding that, except for the AMOC index, the indices are based on observations, or reanalysis data. Wouldn’t it be more consistent to use indices that are derived from the model output or the atmospheric forcing data set to infer the relation between those indices and the modeled sea level? The reconstructed sea-level trends that are compared to observed trends should still be based on the observed indices, of course.

2. The authors limit their analysis to a coastal region within 25 km of the coastline. As they point out the translation of steric to manometric sea-level anomalies depends on the water depth. I am wondering if a criterion based on water depth to identify coastal region would be more appropriate?

3. The authors should make sure to use the terms “intrinsic variability”, “internal variability” and “climate variability” consistently, and properly introduce them in order to avoid confusion. For the most part of the manuscript, the authors use “intrinsic variability” whenever they refer to variability intrinsic to the ocean, i.e. not directly forced by the atmosphere and “climate variability” when they refer to variability intrinsic to the climate system, i.e. not related to long term (anthropogenic) change. I second this choice but suggest to make sure the terms are used consistently throughout the manuscript and avoid other terms like “internal variability” for example.

4. The authors should make sure the term “sea level” is hyphenated when used as an adjective.

Specific comments

L38-39: Please add a reference.

L50-54: This seems to motivate the choice of the climate indices used for the reconstruction. The Arctic Oscillation is also listed in Table S1 but not mentioned here. It would be nice to see a list of all climate indices that were under consideration and not only the ones that were used in the end. Either here or as a supplement.

L52: Frankcombe et al., 2015 does not distinguish between interannual and decadal variability in case of the IOD. So the reported impact of the IOD is likely due to interannual variability. Are there any publications that shows an impact of the IOD in the Pacific on longer timescales?

L57-59: The statement is true in general and not only for intrinsic sea-level variability.

L87: I’m not sure what is meant by “real” atmospheric forcing.

L112: What exactly is meant by a non-significant PC?

L117: Is there a reason for this particular period 2008-2018? Altimeter data would allow for a longer period or an additional period of similar length.

L122-124: The data is not corrected for VLM of any kind other than GIA, right? Not just GRD-induced VLM.

L127: The authors refer to Marzocchi et al. 2015 and Moat et al. 2016 for a detailed model description. I understand that this is very subjective matter, but I suggest to include a few more details of the model setup that are relevant for this specific study on sea-level variability. I am thinking of issues like a fresh water budget correction or restoring of temperature or salinity to a climatology which are commonly used in ocean models but have the potential to affect sea level variability.

L130: “The NEMO Working Group (2019)” refers to NEMO4.0 but from the year of publication of the other two reference a assume the experiment is based on NEMO3.6 or older.

L136-138: I suggest to avoid the term “correction” in this case. My understanding of “correcting for the Boussineq approximation” is to diagnose the global mean steric sea level by considering the mass budget (see Greatbatch 1994, Madec and NEMO System Team, 2016), but the authors merely subtract the spurious global mean trend, which is of course sufficient in this case.

L146-147: I am not sure what is meant here. “Internal ocean variability” in this case refers to variability of oceanic parameters intrinsic to the climate system, which is diagnosed from the ensemble spread, correct? The “internal/intrinsic/chaotic” variability of the ocean model represents variability intrinsic to the ocean, i.e. not directly forced by the atmosphere. Something very different and impossible to diagnose from a climate model. So what exactly is going to be compared?

L150: I suggest to use the term “monthly means” rather than “monthly time stamps”.

L203: The following sentence lacks a reference: This effect in climate models is typical in semi-enclosed seas.

L232-234: For the benefit of the reader, please clarify with which timeseries the reconstruction has been correlated.

L247-253: This is in large parts a repetition of what has been said in the paragraph starting at line 57.

L247-L259: Please clarify why this paragraph is necessary here. Did you use ARGO Data to compute steric sea level?

L261-262: Can you speculate as to why the addition of contributions from each component improves the result? It’s not obvious to me.

L261: Please refer to a specific table or figure, like Table S1 for example, rather to “Supplementary Information” in general.

L281-282: "The variance explained at coastal grid cell locations in the Atlantic and Indian Oceans is increased, although the variance is decreased by the reconstruction in the Pacific." Is this shown somewhere?

L300-301: I expected some results after this sentence and I actually find the results shown in Table S1 worth to be mentioned in the manuscript. I would not have expected such a strong influence of the AMOC index on the Indian Ocean for example.

Figure 4: What does the envelope around the gray line show?

Figure 4: What is shown in panel f? The caption says global mean but the title says Helsinki.

Figure S1: I guess the reference to AVISO is incorrect?

Technical comments

L12: Introduce GRD

L18: “sea level variability”

L22: “sea level change”

L33: “sea level rise”

L33: The sentence is very long and could be read as if locations of fronts and ML/thermocline depth induce variations to the GRD equipotential.

L35: “sea level change”

L57: “sea level trends”

L58: “sea level changes”

L53: “sea level variability”

L69: “sea level variability”

L86: “sea-level”

L108: “sea level trend”

L133: Please check sentence

L203: “In contract”

L226: “sea level variability”

L243: “areally”

L302: “sea level variability”

L306: “sea level variability”

L352: Correct sentence

Figure 5: The label of panel c overlaps with the labels of the x-axis.

Figures S4 – S17: Panels lack labels

Figures S5,S8,S12,S13: The ignored pattern are still shown here.

The authors showed the effect of climate modes on the decadal sea level rise in the coast using the sea level modeling results of the high-resolution ocean model and the CMIP6 models. In general, the ideas are clear and scientifically supported. However, some corrections are suggested to aid the reader's understanding. 

1. Why don't the authors show the mean value of decadal trends in Figure 1 or 2? 
2. In Figure 1, there is not enough explanation for each panel. Adding more information about each picture to the picture caption is suggested. 
3. In Figure 2, since opaque rectangles are overlapped, information distortion is possible. Instead, it is recommended to minimize the overlap by averaging several boxes. 
4. It is proposed to add the total sea level rise rate to Figure 2. If the sea level rise rate is very low, this classification may not have much meaning. 
5. In Figure 3, it is proposed to verify and show the results of reconstruction and NEMO for Tide Gauge. The authors did not show their level of accuracy.

Summary: The manuscript by Royston et al., explores the mechanisms responsible for sea level variability at decadal time-scales using a combination of ocean general circulation model (NEMO), climate model predictions (CMIP6 ensemble), satellite altimetry observations and tide gauge observations. The authors attempt a reconstruction of sea level trend anomalies using a regression between climate indices and the correlated components of a decomposition in empirical orthogonal functions of the NEMO sea level outputs. These reconstructions are compared with tide gauge and satellite altimetry observations, to estimate how climate modes contribute to decadal sea level variations. 

Recommendation: The thematic treatment is of great interest for the scientific community, as the internal sea level variability has been identified as a major source of uncertainties in climate models, especially in the near-future. It is therefore important to advance knowledge in the identification of the mechanisms responsible for sea level variations in a changing climate. The study brings some useful insights in this regard, and should be considered for publication after consideration of the following comments.

General comments: 

• The description of the method lacks clarity in the manuscript. It is difficult to follow step by step what has been done with which data. It is unclear to me how the CMIP6 predictions are used. The reconstruction seems to be applied on the manometric, steric and GRD outputs of the NEMO predictions, but the method is still unclear. Have the eof decompositions been applied on the total, manometric, steric and GRD contributions individually? Then correlations are estimated between the PCs of the eof decompositions and the climate indices. Finally, a regression analysis is performed, though it is unclear how. A few equations would help to better understand this final stage. The text should be clarified and a flow chart would help to picture the steps of the analysis. 
• There are a few methodological hindrances in the approach of the authors that have not been acknowledged. In particular, the authors calculate the correlations with climate indices based on the results of an eof decomposition. The eof decomposition will pull apart physical signals and redistribute them into statistical models explaining less and less variance as you increase the order. As a consequence, the correlation between sea level changes and individual climate indices might be lost because it has been divided into several modes of variation. To avoid this issue, a multivariate regression is usually carried out directly on the variable of interest (here sea level changes). To deal with the issue of intercorrelated climate indices, a regularisation can be applied (see Pfeffer et al., 2018 and 2022). The multivariate regression also allows the identification of climate indices contributing to the sea level variations at each grid point, which is only possible with limitations with the author's approach. The authors should acknowledge these limitations to allow the reader to assess the relevance of the approach. 
• The description of the data lacks clarity in the manuscript. In particular the description of processing applied on the altimetry and tide gauge measurements is imprecise. It is not clear that adequate corrections have been applied for the various datasets for GIA and GRD. 
• The description of the results is clear and interesting. However, more precision would be appreciated. In particular, the authors restitute the performance of the sea level reconstruction based on climate modes by reporting the percentage of variance explained above a certain threshold. It would be much more informative to have a range of variance, with a minimum and maximum bounds for a given region. The authors also use several time expressions like “explain much of this” or “explain well”, it would be useful to have a metric, so that the reader can assess what “much” or “well” means. 
• The conclusion is clear, but fails to compare the results with Pfeffer et al., (2018) and (2022) dealing with the attribution of climate modes contributions to steric and manometric sea level changes. 

Detailed comments:

Abstract: Define GRD or use full words

L28-29: formulation not excessively clear

L33: “A proportion of regional variation in sea level rise”: change rather than rise. The full sentence is not clear. 

L44: The two following references are lacking. Pfeffer et al., 2018 has shown the influence of the PDO, ENSO, AMO, NPGO and IOBM on steric sea level changes, with significant influence at pluri-decadal time scales. Pfeffer et al., (2022) has shown the influence of ENSO, PDO, AO, NAO and SAM modes in the barystatic component of sea level measured by GRACE.

L70: sentence not clear 

L70-72: see general comment on eof decomposition

L78-81: reformulate to increase clarity

L102: not a huge fan of rolling pin, that will generate an aliasing of many different signals and modes of variability

L117: why not using the full altimetry period?

L110-122: verb missing. Reformulate the sentence for clarity

L113-115: Not clear reformulate. 

L123-124: not clear why GRD correction is not applied. It does not rely on GPS measurements. 

L133:typo “noting” 

L157-158: This sentence is very confusing. GRD and GIA are observed by satellite radar altimetry and by tide gauges, but not in the same way since tide gauges are attached to the coast. The corrections applied on the various datasets must be consistent one with another. If you wish to remove these effects from altimetry, you need to remove the global mean correction if it has been applied if it has been applied (it depends on the product chosen, but usually gridded altimetry products are not corrected for GIA), and then apply an appropriate correction at each grid point. Maybe consider writing this paragraph after the description of the datasets. So it would be easier for the reader to understand what data processing is applied to which data.

L169: “Absolute sea level is defined from a multi-mission” → Absolute sea level is defined from the ESA SLCCI v2 multi-mission

L171-173: it is not clear that appropriate correction has been applied for gia. As stated earlier,altimetry-based gridded SLA products do not usually (check specific product) correct for GIA. The GIA correction is usually only applied on the GMSL. Please reference the altimetry product in greater detail (exact product name, version and doi) and explain what GIA correction has been applied in it. Then, state what specific correction you applied, so that it is consistent with other datasets.

L186: This approach has flaws. An eof decomposition will pull apart the physical signal into a suite of statistical modes. As a consequence, coherent physical signals will be separated into several modes. If the sea level is influenced by one or several climate modes at one location, the part of variance explained by climate indices is likely to be separated into several modes as well. Therefore, you will not be able to retrieve a strong correlation with a single PC, but are more likely to get partial correlations with a lot of different PCs. This is why multivariate regression is preferred. To deal with the issue of correlated indices a regularisation might be applied. Alternatively, statistical tests have also been applied to determine the robustness of a correlation between two time series.

L192: Why are tide gauges not corrected for GRD? Admittedly there are other sources of deformation that cannot be easily modelled and require GPS observations that are very sparse and usually very limited in time, but non-linear GRD effects can be estimated with models.

L200: it would be interesting to see the differences between the NEMO run and the CMIP6 mean prediction. It would be easier to compare to the spread, in order to assess if both approaches are consistent within uncertainties.

Section 4.1: clear and interesting

L231-246: The results might be inflated to some extent in this section. The proportions of variance explained are credible and exhibit similar order of magnitudes than previous studies. It is perfectly fine to report an explained variance of 20 or 30%. It is still significant when compared with the accuracy of model and observations, but also with other physical signals present in sea level observations, predictions and reconstructions. It would probably be better to give a range of explained variance for a given region, rather than a minimum explained variance. The regions where the percentage of explained variance is small (~ <30%) cover most of the coastal areas of the world (orange areas in Fig. 3b). It is important to state that in most coastal areas of the world climate modes explain a small but significant part of the variance. Similarly in Table 1, it would be better to report the percentage of locations with a variance in the first (0-25%), second (25-50%), third (50-75%) and fourth (75-100%) quartiles. That way, the reader would have a better picture of the statistical distribution of the results.

L265: name the regions where coastally trapped wave are expected

L272: Some precisions would help here. Which region are you referring to? What constitutes large magnitude variability? Is it above a certain threshold of RMS? Which one? What constitutes “much of that decadal signal” (proportion?)?

L278-279: the reconstructed trend anomaly seems to capture the pattern well but not the amplitude. It should be said. A figure of the difference would help. For regions where the observed trends anomalies are large (e;g. tropical Pacific, west coast of North and South America etc.) it would be good to estimate the ratio between the reconstructed and observed trend anomaly. Also be careful about the vocabulary, it is a trend anomaly not a trend.

L311-313: this has also been shown by Pfeffer et al., 2018 for the steric component, with in particular the influence of AMO emerging in ocean reanalyses, only with a sufficient time coverage (~ 50 years). Other modes such as ENSO, PDO, NPGO (North Pacific Gyre Oscillation), IOD and IOBM (Indian Ocean Basin Mode) have been shown to have a strong influence on the interannual-variability of steric sea levels over a 57 time period. The NPGO is not often considered, though it has been shown to have a very large influence on SSH (see articles by Di Lorenzo including but not limited to Di Lorenzo et al., 2008) and on the manometric component (Pfeffer et al., 2022).

Section 5 Conclusion: please provide metrics in your conclusion to support the soundness of your approach

References:

Pfeffer, J., Tregoning, P., Purcell, A., & Sambridge, M. (2018). Multitechnique assessment of the interannual to multidecadal variability in steric sea levels: A comparative analysis of climate mode fingerprints. Journal of Climate, 31(18), 7583-7597. https://doi.org/10.1175/JCLI-D-17-0679.1

Pfeffer, J., Cazenave, A., & Barnoud, A. (2021). Analysis of the interannual variability in satellite gravity solutions: detection of climate modes fingerprints in water mass displacements across continents and oceans. Climate Dynamics, 1-20. https://doi.org/10.1007/s00382-021-05953-z

Di Lorenzo, E., Schneider, N., Cobb, K. M., Franks, P. J. S., Chhak, K., Miller, A. J., ... & Rivière, P. (2008). North Pacific Gyre Oscillation links ocean climate and ecosystem change. Geophysical Research Letters, 35(8).