General Comments

This paper quantifies the contribution to Common Era global mean sea level (GMSL) from changes in ocean volume caused by temperature (salinity is not evaluated with justification provided) and from changes in ocean mass (Antarctica, Greenland, and glaciers are separated; land-water storage is not evaluated with justification provided). Each of these contributions is estimated, with uncertainty, through modeling. The sum of the components (GMSL) is reconciled with two, closely-related (and previously published) estimates of GMSL generated through application of a spatio-temporal model to proxy reconstructions. The similarity between modeled and reconstructed GMSL is compelling, except for a notable underestimate for GMSL change since ~1800 CE.

As the authors note, previous efforts to connect Common Era GMSL changes with other parts of the climate system (e.g., ice mass) largely focused on correlations (or lack of) with other proxy data. The application of process-based models in this paper therefore represents a welcome scientific advance and a substantive contribution toward our understanding of how and why GMSL changed during the Common Era. I recommend that it be published in Earth System Dynamics and hope that the open review forum will attract input from others to strengthen the paper further.

I am familiar with the proxy sea-level reconstructions that modeled GMSL is compared to and therefore my review focuses on that aspect of the paper. I am wholly unfamiliar with process-based models and cannot provide an expert evaluation of choices made within and among the models used.

Specific Comments

1. Section 2.4 provides a short summary of the proxy-based GMSL reconstructions. I think that this section would benefit from a modest expansion to include some missing (but potentially important) information and some material that appears elsewhere in the paper already.

The Kopp (2016), Kemp (2018), and Walker (2021) GMSL reconstructions are largely iterations of a spatio-temporal statistical model applied to a growing database of Common Era proxy reconstructions. The authors might emphasize a little more that the GMSL reconstructions are less different models and more an evolution in the underlying data. Notably the GSML reconstruction became smoother over these sequential publications. The authors may also want to highlight that the geographic distribution of proxy records is very uneven, but that Kopp (2016) performed sensitivity tests to explore this influence. It is also important to recognize that GMSL is not a quantity that was reconstructed from a proxy, but is rather one component of the relative sea-level signal that is estimated during the record decomposition performed by the spatio-temporal model.

Text on lines 363-365 and 374-375 could be moved into section 2.4.

In this section it might also be appropriate to highlight when notable differences exist between the two GMSL reconstructions (e.g., before ~600 CE).

2. Sea-level fingerprints. Changing the mass of water stored on land as ice results a in fingerprint of sea level change. Although its beyond the paper’s focus on GMSL, I think it would be interesting and helpful to show the fingerprints (from individual sources and their sum) that occur as a consequence of the modeled changes in mass from Greenland, Antarctica, and the 18 regions of glaciers. The fingerprints could be compared to the distribution of proxy records, or to estimates of regional sea level trends. It is possible that fingerprinting could help inform model choice if proxy records support/refute particular melt histories. As minimum could the regional contributions from glaciers be provided as a supplemental output for others to convert into sea-level fingerprints.

3. Glaciers appear to be the single most important driver of Common Era GMSL change, but also the most problematic to model and quantify. Please could the authors show the contributions from the 18 different regions of glaciers. In Figure 3D the glacier contribution is shown against global temperature, which the paper does acknowledge (line 460) is an imperfect comparison since glaciers respond to regional climate. Could the glacier contribution from the 18 regions be compared to regional climate from Neukom et al (2019)?

The modeled glacier contribution is large (even described as “remarkable” on line 456), which presumably indicates that some proportion of the 18 regions were behaving in a temporally-coherent fashion (growing/melting at the same time as one another), or possibly that a subset of regions dominate the glacier signal. Simultaneous contributions across multiple regions in the pre-anthropogenic Common Era might be surprising since a principal conclusion of Neukom et al. (2019) is that temperature trends were not spatially-coherent during this time. I was therefore surprised to see such a large and sustained glacier contribution, because the Neukom et al (2019) analysis led me to think that as one region warmed, another cooled and therefore that the change in glacier mass (and its contribution to GMSL) would be moderated. This is even more surprising because Neukom et al. (2019) conclude that 20^th century warming is the only temperature signal which is globally coherent and therefore would effect all the glacier regions simultaneously, yet the contribution to GMSL from glaciers is smaller and slower that it was during times of incoherent temperature variability. I think some regional analysis of glaciers by region would be a useful addition to this paper.

The authors note that modeled GMSL is considerably less than observed and reconstructed 20^th century rise. The difference is attributed to underestimating the barystatic contribution, especially from glaciers. In particular, the distribution and size of glaciers at the start of the Common Era was set (by necessity) to be the same as that observed in ~2000 CE, despite anthropogenic warming having already impacted them significantly by ~2000 CE (including some glaciers being lost – line 425 –  and therefore missing from the modeled contribution throughout the Common Era presumably). The authors discuss how this effects modeled GMSL since ~1800 CE, but offer less insight into how the problem could bias GMSL estimates before 1800 CE (other than suggesting that the very large contribution from glaciers before ~400 CE could be a spin-up effect from using ~2000 CE as the initial state). I would be interested to read an expanded discussion about how modeled GMSL appears to be an underestimate for the past 200 years, but agrees well with reconstructed GMSL at least for ~800-1800 CE despite the difficulties with glaciers. For example, the difference between GMSL as modeled and reconstructed by Walker is large before ~600 CE. Could (and how) might glaciers solve/cause this discrepancy? If some glaciers are missing, does this mean that the modeled contribution from glaciers is a minimum, and would somehow adding them back in to the GMSL calculation fix the discrepancy since ~1800 CE at the expense of creating a new discrepancy before ~1800 CE?

Technical Corrections

Line 49: The Walker et al. paper is cited as a 2020 publication, but it is listed (correctly) as a 2021 publication in the reference list.

Line 217: Title needs a capital letter.

The 20^th century is variously referred to as “20thC” (section 4.1), “twentieth century” (e.g., line 30), or “20^th century” (e.g., line 204). These could me made consistent throughout the manuscript.

Line 196: “R” should be changed to “r” for consistency with other titles.

I found Figure 1 to be a little confusing. Readers might find it easier if a third panel was added to show the “below 700m” component rather than including it in panel B which is described initially in the caption as the “top 700m”. Or alternatively place the below 700 m, above 700m and total in a single panel.

The use of two y-axes in figure 5a to show the same quantity (sea level, cm) at different scales made the figure difficult to use.

General comments

This manuscript produces a new analysis of global-mean sea level change over the common era using process-based modeling with an examination of thermosteric and barystatic (Antarctic, Greenland, and glaciers) contributions through time. The authors compare their modeled GMSL with proxy reconstructions of global sea level and find general agreement, although the model-based estimate underestimates 20^th century GMSL. They find that glaciers acted as the dominant source of GMSL changes during the common era; however, the uncertainties were large especially in the last millennium.

The paper is generally clear and well written and while there are some large uncertainties in the results, it is valuable to have new process model-based estimates of GMSL to compare with proxy reconstructions and to further understand the relative contributions of processes driving GMSL changes over longer timescales through the common era.

I would recommend the manuscript to be published in Earth System Dynamics if the following several points could be addressed to improve the discussion of the results and comparison with proxy reconstructions. My comments focus on these aspects of the paper, as I cannot expertly comment on the intricacies of the process modeling methods themselves.

Specific comments

The last paragraph of the introduction mainly refers to analysis during the PCE (except for Ln 71 which says “changes over the CE”) which is inconsistent. However, the results and discussion do cover the entire CE, not just the PCE, so I would suggest altering the text accordingly.

Because the authors clearly state questions in the introduction that the paper will attempt to answer (Ln 71-73), I would expect clearer answers to each of these questions in the discussion or at the conclusion of the paper. Especially concerning the major sources of uncertainty – while the large uncertainties are referenced throughout the paper, it would be helpful to clearly state the sources of these uncertainties at the conclusion of the paper and suggestions for how to minimize them in future work.

Section 2.4 could be strengthened to explain the proxy-based reconstructions of global sea level – such as the proxy data that was used, the basic methods with spatiotemporal modeling. Specific details like Ln 361-365 describing the different curves could be moved to section 2.4 instead. It would also be helpful to more completely explain the Kopp/Kemp/Walker global reconstruction – that it is an estimate of global sea level via the signal common to all of the sea-level records in the Common Era proxy database. It is therefore the “globally uniform” term among sites from the spatiotemporal model, and not exactly an estimate of GMSL. The Kopp/Kemp/Walker method could give a true estimate of “GMSL” in the presence of spatially complete data.

The descriptions of the proxy-based reconstructions of global sea level need to be corrected. In Ln 361-365 describing the methodological constraint, it is correct that Kemp et al. (2018) used this constraint. However, Walker et al. (2021) also utilized this constraint so this needs to be corrected in Ln 365. The constraint was used for all of the analysis in Walker et al. (2021) and the global curve shown in that paper uses the constraint. A supplemental figure in Walker et al. (2021) shows the global curve without using the constraint – which is the curve that is shown in this paper in comparison to the process model estimate. This needs to be made clear throughout this manuscript and in Figure 4. Alternatively, Walker et al. (2022) could be referenced, which did remove the constraint for the analysis and so the global sea-level results do not include the constraint – this would be the equivalent global curve to what is actually shown in this paper.

Walker, J.S., Kopp, R.E., Little, C.M. et al. Timing of emergence of modern rates of sea-level rise by 1863. Nat Commun 13, 966 (2022). https://doi.org/10.1038/s41467-022-28564-6

In Ln 339-342, could the authors speculate as to what would cause the differing response of the Greenland and Antarctic ice sheets to surface temperature changes? Or provide any references that also support these findings?

In Ln 360 (and throughout the paper) I think it would be more clear and helpful to refer to “reconstructions” as “proxy-based reconstructions” instead.

In Ln 405-409, first a positive contribution is related to GMSL rise in Ln 405, meaning a negative contribution is related to GMSL fall in Ln 406. So how is in Ln 408-409 “All the GMSL components except Antarctic ice sheet have a positive contribution to net GMSL fall during 1200-1800 CE” supposed to be interpreted?

I understand the uncertainties and limitations using the process-based model, but I find it difficult to put too much weight on the results for the PCE, when the 20^th century global sea-level estimates are inconsistent with reconstructions and observations and are underestimated to a degree that there is not even overlap within the uncertainties. If the model was altered/improved to match the observations/reconstructions in the 20^th century, how would this change GMSL and the relative contributions of driving processes (especially glaciers) over the rest of the PCE? Can a more formal list of improvements be recommended to address this discrepancy? How much of this is due to the initial conditions in the model and is there a way that these could be adjusted? I think these questions need to be addressed more completely in the discussion.

Technical corrections

Ln 49, 50, 361, 365: these should reference Walker et al. 2021, not 2020

Ln 424: ‘focused’ spelled incorrectly

Figure 1: the caption says the Zanna et al., (2019) reconstruction is blue, but it is green on the figure

Figure 4b: would be helpful to show the uncertainties in the rates for the Kemp/Walker/Neukom curves

A review of “Process-based Estimate of Global-mean Sea-level Changes in the Common Era” by Nidheesh, Goosse, Parkes, Goelzer, Maussion, and Marzeion

The authors use models to quantify thermosteric effects from ocean heat storage and barystatic effects from land ice changes on long-term global-mean sea-level (GMSL) fluctuations during the preindustrial Common Era (PCE). They compare their results to proxy reconstructions of PCE GMSL changes from Kopp, Kemp, and Walker. One of the authors’ main conclusions is that glaciers made dominant contributions to GMSL changes during the PCE.

I’m a sea-level scientist with training in physical oceanography. I don’t have expertise in modeling land ice. Thus, I restrict my review mainly to sections on thermosteric effects, and recommend the editor solicits reviews from experts in ice-sheet and glacier modeling.

I really liked this study. Something like it has been needed for a while. The past decade has seen real advances in the community’s ability to quantify PCE GMSL changes from proxy reconstructions (from the likes of Kemp, Kopp, Walker, and others). But there’s been a total lack of modeling studies to complement those observational studies. This paper starts to fill that gap: it won’t be the last word on the subject, but it takes the logical first steps, and therefore deserves to be published after some minor revisions.

Specific comments

References to Walker et al. (2020) should be to Walker et al. (2021)

Section 2.1. The authors describe how they estimate global-mean thermosteric sea level from PMIP3/CMIP5 temperature and salinity. Why not just use the zostoga global-mean thermosteric sea-level diagnostic variable made available by several PMIP3/CMIP5 groups? Also, the authors should identify precisely which PMIP3/CMIP5 model simulations they use (they only identify GISS-ES-R; were other models used?).

The authors consider LOVECLIM, PMIP/CMIP models, and the reconstruction of Zanna et al. (2019). Is that all of the relevant data sources for ocean warming and thermosteric effects during the Common Era? Are there other ocean reconstructions that could also be brought in to corroborate the story they're telling?

Section 2.5.2 Uncertainty on rest of the processes. I find this whole section unclear, ad hoc, and arbitrary. Can the authors please explain more the basic rationale and provide references for their methods when possible? In particular, I’m confused what their uncertainty quantification is supposed to represent. What missing process do they imagine they’re accounting for by adding the autocorrelated noise, for example?

Section 3.1

Line 266ff. Can the authors speculate on the high-frequency (decadal) global-mean thermosteric variability apparent in the LOVECLIM solution that is unrelated to volcanism? Is it related to ENSO or another global mode of natural climate variation (e.g., Hamlington et al., 2020, PNAS)?

Lines 283ff. Can the authors speculate on the mechanisms of these changes and when or why upper-ocean and deep-ocean effects may be opposing or reinforcing? More generally, some discussion of the physics involved, rather than just a tabulation of numbers, would be informative.

Line 290. What are the plus/minus values?

Line 302 and elsewhere. Why the italics on Roman Warm Period? Also on the next line it should be Antiquity not Antique.

Line 305ff. Is LOVECLIM model output available to say more about what drove these multicentennial changes? Were they the long-term effects of volcanism? Changes in insolation? Again, some physical insights would be useful.

Line 373ff. The more muted variability in the Walker et al. (2021) results relative to the Kemp et al. (2018) result may be owing to different prior assumptions made in the two studies with regard to dominant timescales of variability (i.e., what time smoothing is implied by the respective versions of the empirical spatiotemporal model).

Line 393ff. Have the authors identified why their model results with respect to global-mean thermosteric versus barystatic contributions during the twentieth century differ so greatly from estimates of Slangen et al. (2017; Surveys in Geophysics) and Frederikse et al. (2020; Nature)? The authors point out the differences several times, but it would be good to know why these differences exist, and whether they bear on the confidence we have in their simulations of the PCE.