Data Revisions and the Statistical Relation of Global Mean Sea Level and Surface Temperature
Round 1
Reviewer 1 Report
This manuscript tested the sensitivity of estimation parameters from three semi-empirical models to various dataset versions, for both sea surface temperature and sea level. The analyses showed that the statistical relationships are sensitive to data revisions (vintages) but the sensitivity varies depending on model, outliers and time period (particularly during 1910-1960 and 1990s). Authors advocate for publication of dataset revisions for reproducibility.
Although the manuscript is well-written, authors did not:
(1) translate the impact of their results in terms of sea level projections.
(2) include a more in depth discussion of their findings, and also with respect to similar previous studies (eg https://0-link-springer-com.brum.beds.ac.uk/article/10.1007/s00382-011-1226-7).
Recommendation: major review to address the two issues raised above which will greatly benefit the manuscript content.
Author Response
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Author Response File: 
Author Response.pdf
Reviewer 2 Report
Summary
The aim of this paper is to demonstrate the stability, or not of three different empirical methods that have been used in the literature to link two important climate metrics: global mean sea level with global mean surface temperature. The inter-comparison explores how results from these three methods are affected by using two versions of each metric, one from 2009 extending 1880-2001 and one from 2018 extending 1880-2013 – the later an update to the former, including updates within the period of overlap. The authors find that all three methods are affected by data revisions but that Vermeer & Rahmstorf (2009) [linear regression of dH/dt with T and dT/dt] and Grassi et al. (2013) [state-space model with linear trend models for each of H and T] are more sensitive to data revisions than Schmith et al. (2012) [vector auto-regression of dH/dt and dT/dt].
General comments
This is an interesting paper, which provides a useful and I think original inter-comparison between empirical methods. However, since the paper goes no further than identifying the extent to which data revisions affect model stability and do not show how this impacts GSL projections, it is not particularly impactful at this stage. It should be noted that semi-empirical sea-level models were originally designed as a pragmatic way of projecting GSL to “evade unknowns pertaining to individual components” (Grinsted et al. 2010) and including behaviour as yet un-modelled in process-based sea-level models.
It should also be noted that this paper appears to be an updated version of a discussion paper published by the University of Copenhagen, Department of Economics in June 2015 (Doi: http://0-dx-doi-org.brum.beds.ac.uk/10.2139/ssrn.2612924 ), yet there is no mention of this in the manuscript. The conclusions are not different, and much of the text is the same.
I feel that this paper holds a great deal of potential in terms of the premise of exploring the impact of data revisions, but since it does the whole analysis on “real” data, where the “known” regression coefficient is not truly “known”, the authors cannot say which of the three methods provides the best solution (or closest to the truth, were they to create a synthetic set of “sea level” and “temperature” data).
Furthermore, the paper is not really up-to-date, as a number of research groups have published different global sea-level reconstructions (e.g. Jevrejeva et al. 2008, Hay et al. 2015, Dangendorf et al. 2017, Hamlington et al., ), global temperature series (e.g. HadCRUT, GISS) and new versions of the semi-empirical sea level model (e.g. Kopp et al. 2016 [PNAS] – which also uses a global reconstruction for GSL back to ~1000 AD, Mengel et al. 2016 [PNAS]).
I would encourage the authors to bring the paper fully up-to-date, and bring in as many data “vintages” and methods as possible. For a start they might include Rahmstorf (2007) from which Vermeer & Rahmstorf (2009) was developed, Grinsted et al. (2010) and . Alternatively, they might perform a better comparison by using synthetic datasets with prescribed relations to demonstrate the same point.
Finally, there is no interpretation of the results derived in terms of physical plausibility – and this also should form part of the inter-comparison (Schmith et al. 2012 propose alternative physical mechanisms to Rahmstorf (2007), V&R (2009) which are important when studying differences between the models).
Specific comments
L5. Rahmstorf (2007) to Vermeer & Rahmstorf (2009)
L18. Citation following “ramifications for societies”
L19. “an” to “thermal”
L19. Citation following “upper ocean”
L19. There is increasing evidence of expansion occurring in the deep ocean (e.g. Zanna et al. 2019, PNAS)
L19. Citation following “glaciers and ice sheets”
L23. Modelling the ice sheets remains difficult and in some cases controversial. Much of this has occurred since Church et al. (2013) as process modelling has advanced, thus additional citations here please – this is also important given the readership for Econometrics will not be the same as those in Climate Journals
L24-25. Whilst this is broadly true, their purpose is clearly stated in Grinsted et al (2010) as a pragmatic response to close present-day sea-level budgets (which process-based models didn’t do in IPCC AR4) and make GSL projections pertaining to the whole system (PB models had missing physical components in IPCC AR4 and AR5 – many of these components, particularly components of ice sheet dynamics are now being incorporated).
L27-28. “Since both … clearly” This appears out of place here because the focus has been entirely upon global metrics, now you are introducing the idea of spatial variability as justification for aggregation to use global metrics. This is better placed in the data section when you make it clear to readers the provenance of data sources used in the analysis.
L48. Add “)” to “1981”
L47-55. Explicitly mention all data (temperature and sea level) downloaded and analyses are performed with annually averaged series.
On place to access additional sea level reconstructions is here: https://www.psmsl.org/products/reconstructions/
The authors would need to contact Carling Hay for her GSL reconstruction (see Hay et al. 2015, Nature), or Sonke Dangendorf for his GSL reconstruction (see Dangendorf et al. 2017, PNAS) – Sonke also has an updated GSL reconstruction merging methods from Hay and Jevrejeva to look out for.
L78-79. This point is addressed in Church & White (2011) p.587
L122. Cite Moore et al. (2005), this is also commented upon in Schmith et al. (2012) and should be outlined because it is potentially a factor affecting the regression coefficients
L129, 131, Table 1 and elsewhere – these coefficients have units (cm a-1 K-1) – so please state them. Whether econometricians are bothered by this I don’t know, but physical scientists will take umbrage with such omissions.
Section 3.1 – also needs to include a brief discussion of the results for parameter b, because the sign implies a mechanism where a rise in global temperature gives an instantaneous fall in GSL, or lagged behaviour. Neither do confidence intervals overlap implying vintages of GSL and T influence the relationship.
Table 2 – please check values, as regression coeff in Galassi et al. (2013) for Hold and Told appears to be 0.4565. Also, not only does the “new vintage” have uncertainties that no longer cross zero, but the range is narrower too – worth mentioning?
Table 3 – do the results here alter the conclusions of Schmith et al. (2012) section 6a? It should be pointed out that a change in temperature vintage appears to have a stronger influence than a change in sea-level vintage.
L183. In the context of this discussion, Schmith et al. (2012)’s conclusions should be discussed alongside Rahmstorf (2007), V&R (2009) interpretations of the physical basis for such a relationship, given that the two have alternative physical explanations as to the causal mechanisms. This should be developed in a separate section of the Discussion, as it has a bearing upon the results presented in the paper. Furthermore, it should also be mentioned that utilising longer time series of temperature and sea level may allow better estimation of the equilibrium timescale for adjustment (see Grinsted et al. 2010, Kopp et al. 2016).
L226. This time period is also highlighted in Schmith et al. (2012), and is not explained by adding a weakly exogenous radiative forcing term to the VAR.
Section 4 – while the data replacement approach taken here highlights periods of time that additionally influence model stability between vintages, there is still no independent analysis of the three approaches on temperature and sea level series with knownregression relationship. And additional analysis using synthetic time series with a suite of prescribed regression relationships would allow such comparison. For an example from GPS data see Gazeaux et al. (2013) [https://0-doi-org.brum.beds.ac.uk/10.1002/jgrb.50152]
Figures 6-8: the change in scale means that the robustness of the
Schmith et al (2012) model is not immediately apparent, perhaps set all to the
same scale, or highlight this fact in the text.
Author Response
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Author Response File: Author Response.pdf
Reviewer 3 Report
General Comments:
This manuscript assesses three different semi-empirical models that could potentially be used for projections of future sea level. Overall, the manuscript is well written and clear. I have a few detailed comments below.
The manuscript finds that all of the models are somewhat sensitive to different input/training data sets. The abstract refers to significant sensitivities in the projections of future sea level. However, the text of the manuscript makes no reference as to how sensitive these projections are. This would seem to be an important element to include in the manuscript.
The conclusion is rather short and incomplete. It makes no comment on how useful these methods might be for projections of future sea level, despite this being the reported objectives on the semi-empirical models. This seems a significant emission and reduces the value of the manuscript. The IPCC AR5 assessment expressed only low confidence in the semi-empirical model projections and thus they were not included in the formal projections for the 21stcentury (and beyond). Is this assessment valid? Given the sensitivities discussed here, superficially, it would seem this manuscript does support this conclusion. Furthermore, it is hard to understand how any of these schemes that are trained on historical data can be used for robust projections when we know that there are changing sources for sea level rise in the 21stcentury and beyond, compared to the 20thcentury.
Before publication, I think the manuscript should be revised to take account of the above issues. The authors should also consider the detailed comments below.
Detailed comments:
Lines 74-75: This is not quite correct. The time series of the observed EOFs are not used/. Only the spatial distributions of the EOFs are used. These EOFs are fitted to the available observations to determine the temporally varying magnitude of the EOFs.
Lines 97-98: Yes the time series are different – but not very different – the correlation in these plots must be high. I suggest quote it, or some other measure of the differences. The issue is how sensitive are the projections given differences of this magnitude. I also note that the first differences in sea level appear to have a slightly smaller variance, possibly related to a longer altimeter time series and thus more robust EOFs or more available tide gauges.
Table 1: Are these uncertainties 90% confidence limits as in Table 2?
Line 131: This would seem to suggest that the uncertainties are estimated, possibly as a result of low frequency differences between the time series that is not adequately included in the uncertainty estimates.
Lines 230-236: These conclusions are rather short with nothing said at all about the implications of the study for projections. The IPCC AR5 assessment expressed only low confidence in the semi-empirical model projections and thus they were not included in the formal projections for the 21stcentury (and beyond). Indeed, it is hard to understand how any of these schemes that are trained on historical data can be sued for robust projections when we know that there are changing sources for sea level rise in the 21stcentury and beyond.
Author Response
Please see attachment
Author Response File: Author Response.pdf
Round 2
Reviewer 2 Report
Manuscript Review: Data Revisions and the Statistical Relation of Global Mean Sea-Level and Surface Temperature
Authors: Eric Hillebrand, Soren Johansen and Torben Schmith
Summary:
This paper assesses the extent to which revisions in reconstructed global average surface temperature and global average sea level affect the statistical relation between them for four published models. The old (1880-2001) and new (1880-2013) datasets for temperature and sea level are supplied by the same research groups respectively. The authors find that the coefficient linking the two climate metrics is affected by the different vintages of data. Furthermore, by applying the coefficients for different vintages derived from the different models to future temperature scenarios they show substantial differences in long term projections of global sea level rise. The authors advocate for all data vintages to be made available to allow for greater replicability.
Of the four models, two use standard regression between smoothed differences in sea level and levels of temperature, one uses a state-space model with time-varying linear trend models for sea level and temperature coupled by a “coefficient of influence” between these two time-varying linear trends, and one uses a vector-autoregressive model on differences in both sea level and temperature given the level of both series are non-stationary.
General comments:
The authors have revised the manuscript to a certain degree by adding a simpler regression model (Rahmstorf, 2007), which preceded VR09 and making GSL projections for the global surface temperature pathway based on RCP4.5 and RCP6.0, though not for the S12 model. The authors have now added reference to the earlier versions of this paper in the acknowledgements. The authors have also added a brief discussion of the alternate physical mechanism implied by S12. Finally the authors have made a number of adjustments to figures, tables and text to accommodate the specific comments.
There remain, however, a number of issues with the manuscript.
A number of the specific comments do not appear to have been addressed after comparing the previous and current versions of the manuscript – details are below, but there is no justification provided by the authors as to why these changes have or have not been made.
One of the main conclusions is to “advocate making all data vintages available” to allow for greater replicability. While the reviewer agrees with this, it can be strongly argued that vintages are already available – comment L359 – the authors give no example as to where data was not available prohibiting them from analysis.
Much of the language is qualitative, not quantitative when talking about the projections – details in specific comments – which seems strange given that the empirical models provide exact quantities and well defined uncertainties.
A number of Figures need revising, and perhaps removed/moved to supplementary information.
There is limited description of the changes/differences between data vintages and interpreting the difference between the model findings in light of these insights (details in the specific comments).
Specific Comments (including those relating to previous review, marked with a *)
L4: “different vintages” – be more specific – include time lengths and overlapping coverage
L4: “data updates” – be more specific – temperature, sea level or both
L4/5: “substantial” – be quantitative – how much do coefficients and their associated projections change.
L6: State which scenarios are used for projections.
L6/7: While I endorse that data vintages should be made available, there is no evidence in your paper to support this conclusion because all the data vintages you wanted/intended to use were available (and in fact more than you wanted to use).
L12/13: remove “which is … and coefficient estimates”
L14: “projections vary” to “projections derived using these coefficient estimates vary”
L14-15: remove “We suggest … be replicated”
L16-21: before a paragraph on global sea level, include a complimentary paragraph on global temperature
L18: move (Zanna et al. 2019) to “thermal expansion of the ocean (Zanna et al. 2019)”
L19: remove “and by”
*L20: include citation for “glaciers and ice sheets”
L20: add “, and land water storage change (plus citation)” after “glaciers and ice sheets”
L21: “ocean, land, atmosphere, and cryosphere” to “atmosphere-ocean, land, and cryosphere”
L21: cite IPCC AR5 and IPCC SROCC (citations on the IPCC website of each publication)
L25: “to shortfalls in” to “to the current limitations of”
L26: “accurately predict observed” to “project future”
L26: remove “and a tool … projections”
L29: change “Church et al. (2013)” to “Gregory et al. (2013)”
L29: move “For a general … see Church [now Gregory]” to end of line 21.
L47-50: update paper organisation to include projections
L60: You include the website as a footnote, but GISS have a clear citation policy that you should use
L62: “downloaded … at different times” or is it that different versions are made available by GISS at different times – their documentation, and a comparison between R07, VR09 temperature data and the different GISS vintages available should help to clarify this.
L64: “It was downloaded …” Who downloaded it, you or VR09?
L66-67: Move references to sea-level and selection of analysis periods to after the sea level data description.
L69: “inhomogeneity-adjusted” what does this mean? There is no citation in this paragraph. The GISTEMP history page describes the changes involved between the SEVEN vintages it has produced and supplied.
L75: “seems to be” It either is or isn’t, this is also a one sentence paragraph – append to previous paragraph and include citations.
L80-81: “Finally … we call new_2001^H” Move to after the SL description
L80: You include the website as a footnote, but this hasn’t been updated since 2016 and is no longer CSIRO’s primary data archive for sea level – use https://research.csiro.au/slrwavescoast/sea-level/measurements-and-data/sea-level-data/
L84: “open ocean” Island based tide gauges begin to appear from 1950’s onwards
L85: “The CSIRO dataset …” rephrase to include the RSOI methodology
L86: Remove “p.587” from citation – this was to help you the authors find the relevant material, read it and update your text accordingly. The important subject needs a bit more development in the text. Please cite Holgate et al. (2013) if talking about PSMSL tide gauges and the network evolution. Please cite (and read) Calafat et al. (2014), who rigorously assess Church and White’s (2011) methodology.
L90: “Figure 2 shows …” Not correct, it shows first-differences for both vintages over their full periods, not just 1880-2001 – change the Figure or the text.
L93: explain the reservoir correction – no econometrician will know what it is.
L95: supply un-reservoir-corrected results as part of Supplementary Information
L101: “Panel a” – none of the graphs (in ANY of the Figures) have been labelled a, b, etc.. Update figures to allow for consistency in the text. Then in Line 101 you can say, for example, “Figure 4a shows…” No need to refer to “panel”, or have that first sentence.
L102-103: Remove “Panels c … differenced series.” See comments in Figure 4 (below)
L105: Discuss time series period selection etc. in this paragraph (see comments L66-67, L80-81)
L116: Remove “to those … old_2001^T)”
L117: “sea level” to “sea level (Figure 2b)”
L118: “temperature” to “temperature (Figure 1a)”
L118-120: Remove “The right panel … of Figure 1”
L121: “temperature” to “temperature (Figure 1)”
L123-125: Remove “repeating the … left panel of Figure 1”
L128: “trend” – keep consistent terminology
*L128: cite Moore et al. (2005) for SSA and n-year binning, this is also commented upon in Schmith et al. (2012) and should be mentioned in the discussion because it is also a factor affecting the regression coefficients.
L129-132: move to end of the introduction to section 3 – this is something you are going to do for all the methods, not just R07.
L140: “It seems” – the regression coefficients you obtain imply this is the case, but if you don’t want to state this as fact, then perhaps say something like “In this case, the revision of sea level data has a larger influence than that of temperature …”
L144-158: This section does not present any results from your analysis, but read like a discussion and comparison of your results with the rest of the literature – therefore it should be moved into a discussion section separate from the section regarding influential periods in the revisions. Furthermore, Bolin et al. (2015) and Rahmstorf et al. (2012) do not feature in the discussion sections currently, but are important studies attempting to assess the impact of vintages – they do not feature in the introduction either, and probably should.
L159-172: Move into introduction – you make projections for 3 of the 4 models therefore this description of a method shouldn’t been under 3.1.
L163: citation for IPCC AR3
L167: “RCP6” – this should be RCP6.0 – however results presented here do not show significant differences to RCP4.5 (line 173). Use RCP8.5 instead of RCP6.0 as this will give distinct results, provide more opportunities to compare with Rahmstorf et al. (2012) and IPCC AR5. Alternatively (though I say this reluctantly) you could just drop the RCP6.0 analysis from the manuscript.
L175: “just above” – please be exact – you have empirical models and results in your Figures that are lines (not distributions), therefore you should specify the number rounded to the nearest centimetre for each scenario (depending upon how you respond to comment L167).
L178: “only about 10cm” – the range quoted in Rahmstorf et al. (2012) is 20 cm (±10 cm).
L179: “Vermeer (2007)” to “Rahmstorf (2007)”
L179: “year-to-year changes in” to “instantaneous responses of sea level to”
L181: Cite Moore et al. (2005)
L186: “are replications of the ones” to “replicate those”
L187: “overlap. The” to “overlap and the”
L188: “It seems that” to “Again”
L191: Remove “again”
*L192/Table 2: There is still no mention of the results of “b” in the main text. The VR09 model design implies that this component is important and this is shown in your results where “b” shows a strong reduction but a weakening of significance – this seems to come mainly from the revision in T. Please include a summary of “b” (do not just copy and paste the above sentence).
L197, L198, L201: “just over”, “just over”, “about”, “just under” – be exact
L202: “coefficient of influence” – rather than using different terminology for the models, can you keep consistency, at least for models 1-3 where the inferred physical mechanisms are the same.
L210: Remove “We estimate … new data.”
L212: “five combinations” to “five data combinations”
L213: “0.20” to “0.02”??
L227: “to Table 2” to “Tables 1 and 2”
L229: “as on the old vintages” to “as the old vintages though with significantly lower uncertainty”
L238: Remove “can”
L255: “RCP2.5” to “RCP4.5” – the temperature you select needs a citation, especially as you are using a slightly different reference period than those used typically.
L259, L260, L261, L262: “just over”, “just under”, “at around”, “just below” – be exact.
L272/273: “changing the vintage of T has an effect on the coefficients” – Is this because the temperature adjusts to the cointegrating relationship (alpha_T) whereas alpha_H is insignificant. Also worth stating that as alpha_T increases, beta decreases relative to the old vintage.
L284: While you do not report projections here, the simulation approach taken for G13 could be applied here too. If it is sea level driving temperature, then simulate sea level pathways and derive temperature pathways associated with them, then narrow sea level pathways to those for which a set of temperature pathways satisfy the RCP4.5 range.
*L291: “Summary” You do not need a summary of results. But you do need a discussion of the results in the form of an inter-comparison – model assumptions, comparison of results with wider literature, including process-models (use IPCC AR5 [2013] and IPCC SROCC [2019]), etc. This section can be relabelled to something like “4.1 Model assumptions and comparative approaches”. It should also be mentioned that utilising longer time series of temperature and sea level may allow better estimation of the equilibrium timescale for adjustment (see Grinsted et al. 2010, Kopp et al. 2016).
L308: Are both sea level and temperature vintages I(1)? The acceleration in both parameters in the early 21st century has been published in a number of places, even over just the altimetry era (e.g. Nerem et al. 2018). Might this imply that sea level is possibly I(2) as argued by Stern et al. (2019).
L308: Can G13’s assumptions about T being I(2) and H being I(3) be reconciled with S12?
L316, L317: “about”, “roughly”, “about” – be exact
L318: In this section you should refer to the differences in the updated Figure 4 (which should become Figure 3 if you remove/move the reservoir correction Figure to a Supplement).
L318: The analysis conducted here still doesn’t reveal whether revision to H or T more heavily influence the relations. We might interpret that changes in H dominate, but this is only from the full replacement of new with old vintage time series in Section 3. You need to keep old vintage T, and estimate the models while replacing H_new with H_old for h-snippets, and then visa-versa.
L323: “We estimate the models” – does this mean the smoothing is done before or after the replacement of data?
L329: “b” - move results for “b” into supplement to help the reader focus upon comparisons between SL-T coefficient
L335-337: This reads as if you are implying that the “true” a,b values lie between the vintages.
*L341-342: “family of curves … intersect” – do you mean the period where they overlap each other? This is only true for h>9. Also, switching new vintage into the old vintage appears much more sensitive than old into new – can you explain this behaviour and quantify it too – perhaps versions of the updated Figure 4 with but with switched data might illustrate this point? The time period 1910s to 1950s is also highlighted in Schmith et al. (2012), and is not explained by adding a weakly exogenous radiative forcing term to the VAR.
L344-346: This is an interesting observation, but again has no interpretation or attempt to explain why this would be the case.
L355: “substantial” – quantify this statement
L358: “policy makers” – who has been informed by these statistical studies and where has it been published?
L359: “[make] all vintages of data revisions available” – where should they be made available? If through Journal submission – this has become the norm is data has been created, or just correctly cited if it has been obtained from elsewhere – including the date of download – hence the importance of using the suppliers citation policy. Furthermore, GISS already supply seven vintages of their temperature reconstructions and most of the sea-level reconstructions are freely available too, either from: https://www.psmsl.org/products/reconstructions/, or the most recent merged product by Dangendorf et al (2019) [https://0-www-nature-com.brum.beds.ac.uk/articles/s41558-019-0531-8#Sec12].
Figure 3: I do not think it’s inclusion in the main text adds anything to the manuscript, in fact it makes things more confusing for a non-sea level reader. I suggest you present the reservoir corrected old and new vintages in Figure 1b, instead of the uncorrected data. Then provide Figure 3 in a supplement with the model results as mentioned above in comment L95.
Figure 4: These graphs are very difficult to interpret because there is no allusion to time in them and the inference you make in L103-104 is not clear at all from these plots. Furthermore, plotting the first differences doesn’t add any new information that isn’t clear from just the levels. I suggest you replot this Figure with two panels (a and b), where a is Tnew minus Told, with time along the x-axis, and b is Hnew minus Hold, again with time along the x-axis. This will reveal (I know because I have done it) the clear position in time where the new vintage differs from the old, and will go some way to supporting the analysis you make in section 4 – you should refer to Figure 4 during this discussion and also Calafat et al. (2014) and Holgate et al. (2013) who both discuss revisions to the tide gauge network, and the relevant GISS citations.
Figure 7: Specify the temperature and associated scenario these projections adhere to.
Figure 10: it is not clear what values of h cause the outliers around 1908.
Figures 8, 10-11: the change in scale means that the robustness of the Schmith et al (2012) model is not immediately apparent, set all to the same scale, or highlight this fact in the text.
Figures 8-11 are plotted with lines of the same colour and pattern for old (and new) across all h-values. This makes reading the graphs extremely hard, particularly given the degree of crossing that occurs. For new replaced with old, the line pattern makes the graph look like a scatter graph with little to no interpretability, except for the large scale features. Please alter these graphs to improve their legibility.
Table 1: Copy layout in Table 3
Table 2: Copy layout in Table 3
Table 3: Can you simplify the 90% confidence intervals to be directly comparable to Tables 1, 2 and 4? The co-effs look to be in the centre of each 90% range.
References (not already used in manuscript)
Calafat, F.M., Chambers, D.P. and Tsimplis, M.N., 2014. On the ability of global sea level reconstructions to determine trends and variability. Journal of Geophysical Research: Oceans, 119(3), pp.1572-1592.
Holgate, S.J., Matthews, A., Woodworth, P.L., Rickards, L.J., Tamisiea, M.E., Bradshaw, E., Foden, P.R., Gordon, K.M., Jevrejeva, S. and Pugh, J., 2013. New data systems and products at the permanent service for mean sea level. Journal of Coastal Research, 29(3), pp.493-504.
Kopp, R.E., Kemp, A.C., Bittermann, K., Horton, B.P., Donnelly, J.P., Gehrels, W.R., Hay, C.C., Mitrovica, J.X., Morrow, E.D. and Rahmstorf, S., 2016. Temperature-driven global sea-level variability in the Common Era. Proceedings of the National Academy of Sciences, 113(11), pp.E1434-E1441.
Bruns, S.B., Csereklyei, Z. and Stern, D.I., 2020. A multicointegration model of global climate change. Journal of Econometrics, 214(1), pp.175-197.Nerem et al. (2018)
IPCC AR5: cited as Church et al. (2013) -
Church, J.A., P.U. Clark, A. Cazenave, J.M. Gregory, S. Jevrejeva, A. Levermann, M.A. Merrifield, G.A. Milne, R.S. Nerem, P.D. Nunn, A.J. Payne, W.T. Pfeffer, D. Stammer and A.S. Unnikrishnan, 2013: Sea Level Change. In: Climate Change 2013: The Physical Science Basis. Contribution of Working Group I to the Fifth Assessment Report of the Intergovernmental Panel on Climate Change [Stocker, T.F., D. Qin, G.-K. Plattner, M. Tignor, S.K. Allen, J. Boschung, A. Nauels, Y. Xia, V. Bex and P.M. Midgley (eds.)]. Cambridge University Press, Cambridge, United Kingdom and New York, NY, USA.
IPCC SROCC: cited as Oppenheimer et al. (2019) -
Oppenheimer, M., B.C. Glavovic , J. Hinkel, R. van de Wal, A.K. Magnan, A. Abd-Elgawad, R. Cai, M. Cifuentes-Jara, R.M. DeConto, T. Ghosh, J. Hay, F. Isla, B. Marzeion, B. Meyssignac, and Z. Sebesvari, 2019: Sea Level Rise and Implications for Low-Lying Islands, Coasts and Communities. In: IPCC Special Report on the Ocean and Cryosphere in a Changing Climate [H.-O. Pörtner, D.C. Roberts, V. Masson-Delmotte, P. Zhai, M. Tignor, E. Poloczanska, K. Mintenbeck, A. Alegría, M. Nicolai, A. Okem, J. Petzold, B. Rama, N.M. Weyer (eds.)]. In press.
Dangendorf, S., Hay, C., Calafat, F.M., Marcos, M., Piecuch, C.G., Berk, K. and Jensen, J., 2019. Persistent acceleration in global sea-level rise since the 1960s. Nature Climate Change, 9(9), pp.705-710.
Moore, J.C., Grinsted, A. and Jevrejeva, S., 2005. New tools for analyzing time series relationships and trends. Eos, Transactions American Geophysical Union, 86(24), pp.226-232.
Author Response
Please see the attachment.
Author Response File: Author Response.pdf
Reviewer 3 Report
General Comments:
The revised manuscript is a substantial improvement on the original manuscript and addresses the key criticisms in my earlier review. The conclusions are still somewhat limited and I would have preferred to see a more detailed discussion of the values of the various approaches, particularly in the light of different physical contributions to sea level rise that are becoming clearer over time.
I recommend publication after the authors consider my further comments.
Detailed comments:
Line 19: It is the “loss of mass” that is important. Glaciers are always melting.
Lines 92-96: Note there are now estimates of the sea-level contribution for the extraction of water from aquifers, to complement the terrestrial reservoir storage estimates.
Line 173: Here and elsewhere, the authors should note that the IPCC projections for these two scenarios are little different in 2100, even though the path to 2100 and the longer term implications are somewhat different.
Table 1: How were these confidence limits determined? They seem tiny given the strong autocorrelation of the input data sets, especially for the low frequency variability that is critically important. A similar comment would apply to Table 2.
Figure 5: Specify what New/old means – new T/old H? Similar for other terms. This also applies to subsequent figures.
Lines 359-360 and the abstract: I agree that the various revisions of the data sets should be freely available. But isn’t that the case already?
Author Response
Please see the attachment.
Author Response File: Author Response.pdf
Round 3
Reviewer 2 Report
Summary
The authors have made quite a number of changes to improve the manuscript. They have continued to remain ambiguous in stating the values of their projections, which I do not understand and which needs to be dealt with. A number of previous comments/suggestions were chosen to be ignored. I have removed all those from the author’s reply that I could accept as the author’s prerogative, however there remain a few outstanding points that I really want to see addressed both in reply and evidenced in the manuscript. Furthermore, there is one new point related to the G13 analysis that needs to be resolved related to the temperature threshold selection for projections.
I am happy to see this manuscript move on to publication stage should these points be satisfactorily resolved.
Specific Comments
L26: “loss of mass of glaciers, by melting of ice sheets” to “loss of mass of glaciers and ice sheets (include citation)”
L71/72: While I agree that your language is relatively clear I would point out that the different vintages are available online from GISS in a single zip file here (please add this link): https://data.giss.nasa.gov/gistemp/history/output/loti_used.zip
L90: “1950?s” to “1950’s”
L92: cite Holgate et al. (2013)
L183: “around 90 cm” – remove “around” and replace 90 cm with the actual value.
L185: “above 60 cm” – remove “above” and replace 60 cm with actual value.
L187: “about 20 cm” – remove “about”.
L211: “over 60 cm” – remove “over” and replace 60 cm with actual value.
L212: “over 100 cm” – remove “over” and replace 100 cm with actual value.
L212: “about 40 cm” – remove “about” and replace 40 cm with actual value.
L214: “under 70 cm” – remove “under” and replace 70 cm with actual value.
L268: “RCP2.5” to “RCP2.6” – I have read Meinshausen et al. (2011) and there is no mention of RCP2.5 but there is RCP2.6. Change text “RCP2.6”.
L268: Why did you select the temperature cut-off (1.38°C relative to 1951-1980 baseline) using the RCP2.6 scenario? This is a strong mitigation scenario and thus the end-of-century mean global temperature is lower than that of RCP4.5 or RCP6 (which you use for R07 and VR09 projections). In fact, although the probability of a negative temperature trend in 2100 is non-zero (as stated in L268) it is not physically implausible (as stated in L266) and cannot just be discarded if you want to stick to using RCP2.6 as your baseline threshold. This can be seen in Figure 6c of Meinshausen et al. (2011), Figure SPM7a and Table 12.2 of IPCC (2013) – the probability is low, but it is non-zero. If you are not going to select from your simulations a set of temperature pathways adhering to the likely range of RCP4.5 or RCP6, then you should at least have a second threshold at RCP8.5 (0.38°C + 3.7°C = 4.08°C) above which you discard simulations too. Otherwise, projections you calculate will be biased high.
L272: “over 20 cm” – remove “over” and replace 20 cm with actual value
L273: “under 80 cm” – remove “under” and replace 80 cm with actual value
L274: “approximately 55 cm” – remove “approximately” and replace 55 cm with actual value (or keep 55 cm if that is the value to the nearest centimetre)
L275: “below 70 cm” – remove “below” and replace 70 cm with actual value
L285/286: “changing the vintage of T has an effect on the coefficients” – Is this because the temperature adjusts to the cointegrating relationship (alpha_T) whereas alpha_H is insignificant? Please reply with an answer to the question and how you have adjusted the text to include a brief explanation.
L321: Are both sea level and temperature vintages I(1)? The acceleration in both parameters in the early 21st century has been published in a number of places, even over just the altimetry era (e.g. Nerem et al. 2018). Might this imply that sea level is possibly I(2) as argued by Stern et al. (2019). Please reply with an answer to the question and how you have adjusted the text to include a brief explanation.
L314: Can G13’s assumptions about T being I(2) and H being I(3) be reconciled with S12?
Author’s response: Schmith et al. (2012) test whether and then specify that both T and H are I(1), whereas Grassi et al. (2013) assume that T is I(2) and H is I(3). These approaches are in contradiction with each other. Unit roots are conceptualized and utilized in state space models in a manner different from cointegration analysis. In Grassi et al. (2013), the second unit root in T, for example, is introduced simply to smooth the extracted trend component, which is shown in Grassi et al. (2013) to be very similar to the first singular spectrum component used in Rahmstorf (2007). Cointegration analysis, on the other hand, puts emphasis on statistical inference about levels of integration, which state space analysis does not to the same extent. If one was satisfied with a random walk as trend component in temperature, a local level model, it would suffice to model T as I(1), and a model in the spirit of Grassi et al. (2013) would then indeed conclude that H was I(2), relating to your reference to Stern et al. (2019) above.
Reviewer: Please include some part of this response in the summary section.
L361-362: “family of curves … intersect” – do you mean the period where they overlap each other? This is only true for h>9. Also, switching new vintage into the old vintage appears much more sensitive than old into new – can you explain this behaviour and quantify it too – perhaps versions of the updated Figure 4 with but with switched data might illustrate this point? The time period 1910s to 1950s is also highlighted in Schmith et al. (2012), and is not explained by adding a weakly exogenous radiative forcing term to the VAR. Please reply with an answer to the questions and how you have adjusted the text to include a brief explanation.
L362-364: What does having a narrower range of the estimated coefficient mean about the S12 and G13 methods compared to R07/VR09? Please reply with an answer to the questions, how you have adjusted the text to include a brief explanation.
Figure 4: These graphs remain very difficult to interpret because there is no allusion to time in them. The inference you make in L113-114 is not clear at all from these plots. Furthermore, plotting the first differences doesn’t add any new information that isn’t clear from just the levels. Please replot this Figure with two panels, where one is Tnew minus Told, with time along the x-axis, and the other is Hnew minus Hold, again with time along the x-axis. This will reveal (I know because I have done it) the clear positions in time where the new vintage differs from the old, and will go some way to supporting the analysis you make in section 4 – you should refer to Figure 4 during this discussion and also Calafat et al. (2014) and Holgate et al. (2013) who both discuss revisions to the tide gauge network.
Figure 10: it is not clear what values of h cause the outliers around 1908.
Author’s response: We have decided not to add another “h=…” label to those outliers in order not to clutter the figure.
Reviewer: Labelling this outlier region to show which values of h this is associated would absolutely not clutter the Figure given the outlier region (by definition) is distant from the main sensitivity pathways. Please state what these values are either in the Figure, or in the main text.
Figures 8-11 are plotted with lines of the same colour and pattern for old (and new) across all h-values. This makes reading the graphs extremely hard, particularly given the degree of crossing that occurs. For new replaced with old, the line pattern makes the graph look like a scatter graph with little to no interpretability, except for the large scale features. Please alter these graphs to improve their legibility.
Author’s response: We have kept the figure organization
Reviewer: Please explain why you have made this decision.
References (not already used in manuscript)
Holgate, S.J., Matthews, A., Woodworth, P.L., Rickards, L.J., Tamisiea, M.E., Bradshaw, E., Foden, P.R., Gordon, K.M., Jevrejeva, S. and Pugh, J., 2013. New data systems and products at the permanent service for mean sea level. Journal of Coastal Research, 29(3), pp.493-504.
Kopp, R.E., Kemp, A.C., Bittermann, K., Horton, B.P., Donnelly, J.P., Gehrels, W.R., Hay, C.C., Mitrovica, J.X., Morrow, E.D. and Rahmstorf, S., 2016. Temperature-driven global sea-level variability in the Common Era. Proceedings of the National Academy of Sciences, 113(11), pp.E1434-E1441.
Bruns, S.B., Csereklyei, Z. and Stern, D.I., 2020. A multicointegration model of global climate change. Journal of Econometrics, 214(1), pp.175-197.
Author Response
see enclosed
Author Response File: Author Response.pdf
