Current observed global mean sea level rise and acceleration estimated from satellite altimetry and the associated uncertainty

Guérou, Adrien; Meyssignac, Benoit; Prandi, Pierre; Ablain, Michaël; Ribes, Aurélien; Bignalet-Cazalet, François

doi:https://doi.org/10.5194/egusphere-2022-330

Preprints

https://doi.org/10.5194/egusphere-2022-330

Preprints

01 Jun 2022

| 01 Jun 2022

Current observed global mean sea level rise and acceleration estimated from satellite altimetry and the associated uncertainty

Adrien Guérou, Benoit Meyssignac, Pierre Prandi, Michaël Ablain, Aurélien Ribes, and François Bignalet-Cazalet

Abstract. We present the latest released of the Global Mean Sea Level (GMSL) record produced by the French space agency CNES and distributed on the AVISO+ website. This dataset is based on reprocessed along-track data, so-called L2P 21, of the reference missions Topex-Poseïdon, Jason-1/-2 and -3. The L2P 21 CNES/AVISO GMSL record covers the period January-1993 to December-2021 and is now delivered with an estimate of its uncertainties following the method presented in Ablain et al. (2019). Based on the latest Calibration and Validation (Cal/Val) knowledge, we updated the uncertainty budget of the reference altimetry missions and demonstrate that the CNES/AVISO GMSL record now achieves stability performances of ±0.3 mm/yr at the 90 % confidence level (C. L. ) for its trend and ±0.05 mm/yr² (90 %C. L. ) for its acceleration over the 29-years of the altimetry record. Thanks to an analysis of the relative contribution of each uncertainty budget contributor, i.e. , the altimeter, the radiometer, the orbit determination, the geophysical corrections, we identified the current limiting factors to the GMSL monitoring stability and accuracy. We find that the radiometer Wet Troposphere Correction (WTC) and the high-frequency errors with timescales shorter than 1-year are the major contributors to the GMSL uncertainty over periods of 10-years (30–70 %), both for the trend and acceleration estimations. For longer periods of 20-years, the TP data quality is still a limitation but more interestingly, the International Terrestrial Reference Frame (ITRF) realisation uncertainties becomes dominant over all the others sources of uncertainty. Such a finding challenges the altimetry observing system as it is designed today and highlights clear topics of research to be explored in the future to help the altimetry community to improve the GMSL accuracy and stability.

Received: 16 May 2022 – Discussion started: 01 Jun 2022

Adrien Guérou et al.

Status: closed

RC1:
'Comment on egusphere-2022-330', Thomas Frederikse, 22 Jun 2022

Review of “Current observed global mean sea level rise and acceleration estimated from satellite altimetry and the associated uncertainty”

This manuscript describes an updated version of the global-mean sea-level record distributed by CNES/AVISO and provides an update of the uncertainty assessment from Ablain et al. (2019). The paper is complete, well-written, and shows the progress in estimating GMSL from altimetry over the past few years. I didn’t see any major issue with the current manuscript and I recommend it for publication in Ocean Science. I do have some minor points, which I have listed below.

Thomas Frederikse

General:

There are currently a few different altimetry GMSL curves available from various processing groups (For example NASA GSFC: https://podaac-tools.jpl.nasa.gov/drive/files/allData/merged_alt/L2/TP_J1_OSTM/global_mean_sea_level/GMSL_TPJAOS_5.1_199209_202203.txt or NOAA STAR: https://www.star.nesdis.noaa.gov/socd/lsa/SeaLevelRise/LSA_SLR_timeseries_global.php). It would be nice to compare the new GMSL curve against these products: do they all agree within the uncertainty estimates, and are there differences in the trends/accelerations over various periods?

Line-by-line

L3 and throughout the whole manuscript: I wonder about the double dots/trema on Poseidon. The trema should not be there: when transcribing the ancient Greek name Ποσειδá¿¶ν into the Latin alphabet, the ι (iota) should not get a trema as the iota does not start a new syllable: it’s Po-sei-don and not Po-se-i-don.

L22-23: The accuracy numbers, where do they come from? I think this statement needs a source. Also, the daily ¼ by ¼ degree resolution, that is just the resolution at which the along-track data has been interpolated. The spatio-temporal resolution at which features can be extracted will be much lower.

L72 and L79: To avoid confusion with the +/- 82 degree spatial coverage mentioned in line 22, state explicitly here (or at L22/23) that the TOPEX/Jason missions only cover +/- 66 degree latitude.

L134: The ocean bottom deformation correction mentioned here is not just a correction needed to match altimetry with Argo/GRACE: GMSL changes are defined as global-mean relative sea-level changes (See equation 42 in Gregory et al. 2019 and the discussion in the same section), while satellite altimetry provides global-mean geocentric sea-level change (GMGSL). Both GIA and contemporary mass redistribution cause the ocean bottom to subside on average, which leads to a difference between GMSL and GMGSL that is corrected by adding 0.3 mm/yr (GIA) and 0.1 mm/yr (Contemporary) to the GMGSL trend. Hence to estimate GMSL from altimetry, both corrections serve the same purpose. One could argue that the GIA correction is larger and thus more important. However, due to the increasing rate of barystatic sea-level rise, the contemporary mass change-induced ocean bottom correction is about 0.2 mm/yr since 2005, which is on the same order as the GIA correction, see the supplement of Hakuba et al., 2021.

L178: why apply a low-pass filter before estimating the trend? That does not make the estimated trend any more accurate, and in the worst case even degrades the estimate because of edge effects at the beginning and end of the time series. I suggest to estimate the trend/acceleration without low-pass filtering.

Figure 5 and Figure 6: the trends and accelerations for the longest periods in this figure don’t match with the numbers in Figure 3. In Figure 5, the trend for the longest period is 3.5 mm/yr and the acceleration < 0.1 mm/yr^2, while in Figure 3, there’s a trend of 3.3 mm/yr and acceleration of 0.12 mm/yr^2. The only possible difference could be the different period: the caption notes here that these figures only show data until October 2021 and Figure 3 notes December 2021. However, since the mean seasonal cycle has been removed, the difference cannot be this big. So there must be something wrong with either Figure 5/6 or Figure 3. I also recommend using a single record length for both.

L294: I’d be cautious with stating that the ITRF uncertainty is fully linear. It is an assumption made here, which is fine, but in reality, the error probably is non-linear. That is because ITRF frames refer to the center of mass (CM), while most observations that go into ITRF are in the center-of-figure frame (CF). The difference between the two, geocenter motion, is to a large extent driven by ice mass loss, which is rapidly accelerating, while in ITRF frames, geocenter motion is approximated by a linear trend, which induces a non-linear error. Fully quantifying this error is way out of scope for the current manuscript, but it might be good to notice here.

I assume in this paper, ITRF2014 has been used. ITRF2020 has recently been released. Could the authors provide any information on whether this updated reference frame can help with reducing the reference-frame uncertainties?

L409: I encourage the authors to share the scripts used to calculate the uncertainties on a public repository.

References:

Gregory, J. M., Griffies, S. M., Hughes, C. W., Lowe, J. A., Church, J. A., Fukimori, I., Gomez, N., Kopp, R. E., Landerer, F., Cozannet, G. L., Ponte, R. M., Stammer, D., Tamisiea, M. E., & van de Wal, R. S. W. (2019). Concepts and Terminology for Sea Level: Mean, Variability and Change, Both Local and Global. Surveys in Geophysics. https://doi.org/10.1007/s10712-019-09525-z

Hakuba, M. Z., Frederikse, T., & Landerer, F. (2021). Earth’s Energy Imbalance from the ocean perspective (2005 â 2019). Geophysical Research Letters. https://doi.org/10.1029/2021GL093624

Citation: https://doi.org/10.5194/egusphere-2022-330-RC1
- AC1: 'Reply on RC1', Adrien Guerou, 01 Jul 2022
  
  Dear Thomas,
  Thank you very much for your review.
  We started to take into considerations your suggestions and comments and will answer your questions as soon as we receive the second review to optimize the modifications of the paper.
  Regards,
  Adrien et al.
  
  Citation: https://doi.org/10.5194/egusphere-2022-330-AC1
- AC2: 'Reply on RC1', Adrien Guerou, 20 Oct 2022
  
  Dear Thomas,
  
  Please find below our complete answer to your comments:
  
  General
  
  We have included to the revised version of the paper the comparison of our GMSL record to the GMSL curves you mentionned. See paragraph l.238 and associated figure 5.
  
  Line-by-Line
  
  L.3 / The syntax of Poseidon has been modified accordingly
  L.22-23 / We modified the sentence to make the distinction between sampling and accuracy. We also add references to the accuracy numbers. See Lines 23-25.
  L.72 and 79 / Modifications as follow has been added: “ ... all grid cells within +/-66 degrees N/S (the Topex and Jasons coverage) are spatially averaged..." See L.82 now.
  L.134 / We modified the sentence according to your comment, see l.145-148
  L. 178 / We estimated the trend and acceleration over the 29 years period of the GMSL record, with and without filtering, and the results are identical. This was expected since the 2 months cut off period of the filter is low as compared to the total lenght of the record (i.e, 29 years). The border effects are thus not significant. This is also true for estimations over 5 years periods.
  We apply such a fitlering on the AVISO GMSL record as we consider that we remove some high frequency noise and that we still do not degrade the trend and acceleration estimations. We nevertheless note that raw GMSL time series could be publicly provided. This will be done in a future release.
  Figure 5 and 6 / Thank you for having noticed this point. We were using the wrong GMSL timeseries for Figure 5 and 6 (i.e., not corrected for the Topex-A drift). We now obtain, naturally, consistent values between Figure 3, 5 and 6.
  L.294/ The ITRF uncertainty is certainly non-liear, this is a good point. We modified l.324 accordingly. We used the uncertainties published for the ITRF2014, indeed. The updated reference frame ITRF2020 should help reducing the associated uncertainties as: time series are longer, seasonal signals are now considered in the local movements of the ITRF2020, the models are enriched as well as more data is used to constraints the model (I.e., Galileo). Information has been added to the manuscript L.358.
  L.409 / We are currently discussing publishing the scripts used to calculate the trend, acceleration and uncertainties. Unfortunately, it will take some time. In the meantime, Prandi et al. (2021) made public similar scripts to perform OLS estimation with uncertainties in the context of regional MSL. This code is based on the same theoretical approach as ours and can be used to reproduce our analysis. We added this information l.207.
  
  Citation: https://doi.org/10.5194/egusphere-2022-330-AC2
RC2:
'Comment on egusphere-2022-330', Huseyin Baki Iz, 19 Jul 2022

Please refer to the attached PDF file.

Citation: https://doi.org/10.5194/egusphere-2022-330-RC2
- AC3: 'Reply on RC2', Adrien Guerou, 20 Oct 2022
  
  Dear Huseyin,
  There is here, from the start, a misunderstanding of the objective of the present study (and of Ablain et al., 2019). This study (and Ablain et al. 2019) does NOT intend to estimate the “systematic components” of the observed GMSL anomalies. We only intend to characterize the uncertainty in GMSL measurements due to the instrumental errors. We state it clearly in the manuscript on line 37 (and also in Ablain et al. 2019 page 1190, 2nd column, 3rd paragraph).
  Our group produces sea level measurements from satellite altimetry level 1 data. We are involved in this activity with CNES managers and CNES engineers who developed the radar altimeters onboard the satellite altimeters because we are in charge of the delivery of the sea level scientific product for CNES. We deliver sea level products and associated uncertainties (which is a pure instrumental uncertainty) as a service to the scientific community who can then use these products and their associated uncertainty to evaluate further different elements such as the geostrophic circulation, the mean dynamic topography and its changes, the GMSL anomalies and, if they wish, the “systematic components of the observed GMSL anomalies”. Here we certainly do not evaluate ourselves the “systematic components of the observed GMSL anomalies”, we only provide the updated GMSL anomalies derived from satellite altimetry and its associated instrumental uncertainty. We also provide an estimate of the 1993-2022 trend and acceleration with associated uncertainties as a metric for the low frequency changes in GMSL. The uncertainty on this trend and this acceleration is an uncertainty ONLY due to instrumental errors. We never claim the trend or the acceleration represent any “systematic component” of the GMSL. We provide the trend and the acceleration with uncertainty just as a reference for the scientific community so they can realize the actual amplitude of the instrumental errors on such metrics that are largely used for many different purposes in the science community. Note that our objective is also to provide a reference calculation of the trend uncertainty and the acceleration uncertainty so people can check their own calculation of the instrumental errors on their trend and acceleration estimate when they use our error variance/covariance matrix.
  The confusion here is very common in the community that analyses sea level rise. We believe this is because this community is very focused on the detection and attribution of the forced response of global mean sea level to anthropogenic forcing on the climate system. This forced response is expected to take the shape of a parabolic signal on global mean sea level at decadal time scales (according to climate model simulation). For this reason people in this community tend to interpret any parabolic signal in GMSL as a “systematic component” of the GMSL that has some predictive value.
  Here we DO NOT do such things. We are addressing a community that is much larger than the single community that analyses sea level rise. We are providing an update of GMSL anomalies with instrumental uncertainties for all the science communities that use GMSL products. These communities range from the Earth water cycle community to the Energy cycle community and it includes many communities as different as the ocean circulation community (which intend to assimilate the GMSL anomalies in ocean models for example) and the geophysics communities (like GIA people or solid earth people who use GMSL anomalies as observational constraint). Many of these communities compute trends or accelerations in their application. For this reason, we compute here one trend and one acceleration (the one trend and the one acceleration over 1993-2022) with the associated instrumental uncertainty derived from the error variance covariance matrix. This is as a reference so they can get a rapid idea of the actual amplitude of the instrumental error on such metrics. This is also a reference against which they can check their own uncertainty calculation when they use our error variance covariance matrix.
  From this review, we suppose that the parabolic signal of the observed GMSL anomalies has been interpreted as “systematic components “ of the GMSL. This is something that should NOT be done. A simple trend calculation or a simple acceleration calculation on the measured GMSL time series that we are providing here, does not give an estimate of any “systematic component”. There is a misunderstanding of the GMSL data in this interpretation. We are not totally clear on what is meant by the term “systematic component”. We suspect he means the forced response of GMSL to the anthropogenic forcing on the climate system. If so, there is actually a long way to isolate the “systematic component” out of the GMSL measurement we are providing here. To isolate this signal, one needs to estimate the internal variability of the climate system and also to estimate the response to other forcings on the climate system such as the sun variability and the long term tides from other planets of the solar system. One also needs to isolate the intrinsic variability generated by the ocean circulation.
  We clearly and explicitly explained this point in Ablain et al. 2019 (page 1190, 2nd column, 3rd paragraph). We repeat here in this paper that we are addressing only instrumental uncertainties and we are not trying to isolate the forced response to anthropogenic forcing. Reading your review, we understand that we have not been clear enough in the introduction of this manuscript. We thank you for pointing out this issue unintentionally. We have now added a supplementary paragraph in the introduction to clarify this positioning. See paragraph from line 40.
  Because we were not clear enough in the introduction that we are addressing only instrumental uncertainties and do not estimate any “systematic components”, we believe that several comments of the review are actually not relevant. We explain this below.
  Comment #1
  We explained in detail in Ablain et al. (2019) why we use an OLS rather than a GLS. OLS estimate is known to be less accurate than GLS in terms of the mean square error, because its variance is larger. A generalized least square estimate would probably help in narrowing slightly the trend uncertainty, but the difference is expected to be small, in particular when the V/C matrix is not far from identity (Ribes et al. 2016). Important advantages of using OLS are that (i) OLS is consistent with previous estimators of GMSL trends as well as estimators of trends in other essential climate variables than GMSL (indeed OLS with V/C matrices is the approach used in the IPCC, see for example Hartmann, et al., 2014,) and that (ii) the OLS best estimate does not depend on the estimated variance–covariance matrix Σ. Reasons why the OLS estimate could be prefered, even if the V/C matrix is not the identity, were also discussed in the IPCC AR5 (e.g., Chapter 2, Box 2.2)
  We tested a GLS estimate on a yearly average GMSL time series (for which the V/C matrix is now invertible) and checked that the result is very close to the OLS estimate. We do find very similar results with both estimates. See plot below. We added this information in the manuscript now on line 204.
  Comment #2
  There is a confusion here. We do not assume that a linear signal or a parabolic signal represent the GMSL time series and then test these simplistic models against the zero assumption. This approach is used by people trying to isolate the GMSL signal forced by anthropogenic emissions assuming it is a linear trend or a parabolic signal. Here we are not interested in this. Here we intend to provide the most accurate estimate of the observed GMSL. Then we consider the GMSL time series and try to derive the trend and the acceleration of the time series over the record length as metrics of the lowest frequencies included in the time series. In this sense we do not expect the disturbances to be zero and in this sense the OLS estimator itself is an unbiased estimator (see Ribes et al. 2016 and demonstration in the reference therein). Note that linear trend models are also used (and useful) in cases where the underlying shift is not linear in time (and so the “expected value” of the residual is non-zero; see again IPCC AR5, Box 2.2). In such cases, trends are used to measure the rate of increase in a time-series.
  Comment #3
  We never assume the quadratic model captures “the systematic variations in the observed GMSL”. This interpretation is biased towards interpreting the GMSL physical signals. Again, we estimate the trend and acceleration of the observed GMSL as metrics of the lowest frequencies included in the time series. See our answer to point #2.
  Comment #4
  We agree with this comment and we refer to our response of point #1 (where we checked that the GLS estimate and the OLS estimate lead to the same estimate) as well as point #2.
  Comment #5
  We would like to make two comments in response to this point. First, the estimated V/C matrix is taken into account in the uncertainty analysis, i.e., quantification of the standard error of the trend and acceleration coefficients. As a result, this uncertainty analysis is valid and reliable – and fully consistent with our V/C estimate. Second, our uncertainty analysis only accounts for the measurement uncertainty – this is now made clearer in the revised version of the manuscript (see our response to the review’s introduction for more details). In particular, any uncertainty related to internal variability within the climate system (which can be large) is not taken into account here. So, our confidence range is not representative of uncertainty on human-induced SLR.
  Comment #6
  Indeed, if the objective of this study was to isolate the forced response of sea level to anthropogenic emissions we would need to account for the internal variability and the natural variability in GMSL in the least square approach. And the review is right, we would need to model the serial correlation in the GMSL time series. But that is not our objective. Our objective here is only to deliver to the community the most accurate GMSL time series possible from satellite altimetry with associated instrumental uncertainty and to estimate the uncertainty due to instruments on the 1993-2020 trend and acceleration of the GMSL time series. For this reason we believe this comment is not relevant here.
  Comment #7
  See answer of the previous point #6.
  Comment #8
  Of course we expect the forced response of GMSL to anthropogenic forcing to be a response that is more complex than just a parabolic signal. For this reason, the acceleration and the trends are expected to change with time, we agree. But here we do not tackle this problem. We simply want to give metrics for the lowest frequency included in the 1993-2020 GMSL record derived from satellite altimetry. For this reason we focus on one unique trend and one unique acceleration : the 1993-2020 trend and acceleration corresponding to the full satellite altimetry era. Once again, because of the different perspective, we believe the comment here is not relevant.
  Comment #9
  See our answer to the previous comment #8.
  Comment #10
  That is the point here. We use the trend and acceleration as simple metrics for the low frequency and do not make any predictions with it. This would be indeed “an extremely costly blunder in climate mitigation decision making”. Any other metric could/should be used for sure to achieve this goal. We choose one metric and are clear about it so people in the community can test their own calculation against ours.
  We DO NOT pretend those metrics represent any “systematic component” of the GMSL and we CERTAINLY NOT pretend those metrics have any predictive skills. For your recollection , we are only providing an observed estimate of the GMSL and low frequency metrics with the INSTRUMENTAL uncertainty. We clarified this point in the paper l. 197-198.
  Comment #11
  We do not make any predictive model in this study. See answer to comments #10.
  Comment #12
  Thank you for pointing out that “the efforts to build a full V/C matrix is a worthy endeavor for optimal analyses of GMSL anomalies”. We believe so as well. Indeed this is the goal of the paper and we insist on that point: for the altimetry measurements only.
  But please note that we DO NOT intend to provide a full V/C matrix that represents the errors of the forced response of GMSL to anthropogenic emissions. Our work is much more modest. We ONLY provide a V/C matrix of INSTRUMENTAL errors in GMSL. Providing a description of the GMSL instrumental errors is a very important step for scientists of all communities that use the GMSL time series and not only for the sea level rise community. For the sea level rise community, our work provides the very first brick over which scientists can further build a complete V/C matrix of the forced signal. This is not our intention. We understand from this review that we were not clear enough. Now we clarify this in a whole new paragraph in the introduction (see lines 40-48). We hope this makes our objective clearer to the sea level rise community.
  
  Citation: https://doi.org/10.5194/egusphere-2022-330-AC3

Status: closed

RC1:
'Comment on egusphere-2022-330', Thomas Frederikse, 22 Jun 2022

Review of “Current observed global mean sea level rise and acceleration estimated from satellite altimetry and the associated uncertainty”

This manuscript describes an updated version of the global-mean sea-level record distributed by CNES/AVISO and provides an update of the uncertainty assessment from Ablain et al. (2019). The paper is complete, well-written, and shows the progress in estimating GMSL from altimetry over the past few years. I didn’t see any major issue with the current manuscript and I recommend it for publication in Ocean Science. I do have some minor points, which I have listed below.

Thomas Frederikse

General:

There are currently a few different altimetry GMSL curves available from various processing groups (For example NASA GSFC: https://podaac-tools.jpl.nasa.gov/drive/files/allData/merged_alt/L2/TP_J1_OSTM/global_mean_sea_level/GMSL_TPJAOS_5.1_199209_202203.txt or NOAA STAR: https://www.star.nesdis.noaa.gov/socd/lsa/SeaLevelRise/LSA_SLR_timeseries_global.php). It would be nice to compare the new GMSL curve against these products: do they all agree within the uncertainty estimates, and are there differences in the trends/accelerations over various periods?

Line-by-line

L3 and throughout the whole manuscript: I wonder about the double dots/trema on Poseidon. The trema should not be there: when transcribing the ancient Greek name Ποσειδá¿¶ν into the Latin alphabet, the ι (iota) should not get a trema as the iota does not start a new syllable: it’s Po-sei-don and not Po-se-i-don.

L22-23: The accuracy numbers, where do they come from? I think this statement needs a source. Also, the daily ¼ by ¼ degree resolution, that is just the resolution at which the along-track data has been interpolated. The spatio-temporal resolution at which features can be extracted will be much lower.

L72 and L79: To avoid confusion with the +/- 82 degree spatial coverage mentioned in line 22, state explicitly here (or at L22/23) that the TOPEX/Jason missions only cover +/- 66 degree latitude.

L134: The ocean bottom deformation correction mentioned here is not just a correction needed to match altimetry with Argo/GRACE: GMSL changes are defined as global-mean relative sea-level changes (See equation 42 in Gregory et al. 2019 and the discussion in the same section), while satellite altimetry provides global-mean geocentric sea-level change (GMGSL). Both GIA and contemporary mass redistribution cause the ocean bottom to subside on average, which leads to a difference between GMSL and GMGSL that is corrected by adding 0.3 mm/yr (GIA) and 0.1 mm/yr (Contemporary) to the GMGSL trend. Hence to estimate GMSL from altimetry, both corrections serve the same purpose. One could argue that the GIA correction is larger and thus more important. However, due to the increasing rate of barystatic sea-level rise, the contemporary mass change-induced ocean bottom correction is about 0.2 mm/yr since 2005, which is on the same order as the GIA correction, see the supplement of Hakuba et al., 2021.

L178: why apply a low-pass filter before estimating the trend? That does not make the estimated trend any more accurate, and in the worst case even degrades the estimate because of edge effects at the beginning and end of the time series. I suggest to estimate the trend/acceleration without low-pass filtering.

Figure 5 and Figure 6: the trends and accelerations for the longest periods in this figure don’t match with the numbers in Figure 3. In Figure 5, the trend for the longest period is 3.5 mm/yr and the acceleration < 0.1 mm/yr^2, while in Figure 3, there’s a trend of 3.3 mm/yr and acceleration of 0.12 mm/yr^2. The only possible difference could be the different period: the caption notes here that these figures only show data until October 2021 and Figure 3 notes December 2021. However, since the mean seasonal cycle has been removed, the difference cannot be this big. So there must be something wrong with either Figure 5/6 or Figure 3. I also recommend using a single record length for both.

L294: I’d be cautious with stating that the ITRF uncertainty is fully linear. It is an assumption made here, which is fine, but in reality, the error probably is non-linear. That is because ITRF frames refer to the center of mass (CM), while most observations that go into ITRF are in the center-of-figure frame (CF). The difference between the two, geocenter motion, is to a large extent driven by ice mass loss, which is rapidly accelerating, while in ITRF frames, geocenter motion is approximated by a linear trend, which induces a non-linear error. Fully quantifying this error is way out of scope for the current manuscript, but it might be good to notice here.

I assume in this paper, ITRF2014 has been used. ITRF2020 has recently been released. Could the authors provide any information on whether this updated reference frame can help with reducing the reference-frame uncertainties?

L409: I encourage the authors to share the scripts used to calculate the uncertainties on a public repository.

References:

Gregory, J. M., Griffies, S. M., Hughes, C. W., Lowe, J. A., Church, J. A., Fukimori, I., Gomez, N., Kopp, R. E., Landerer, F., Cozannet, G. L., Ponte, R. M., Stammer, D., Tamisiea, M. E., & van de Wal, R. S. W. (2019). Concepts and Terminology for Sea Level: Mean, Variability and Change, Both Local and Global. Surveys in Geophysics. https://doi.org/10.1007/s10712-019-09525-z

Hakuba, M. Z., Frederikse, T., & Landerer, F. (2021). Earth’s Energy Imbalance from the ocean perspective (2005 â 2019). Geophysical Research Letters. https://doi.org/10.1029/2021GL093624

Citation: https://doi.org/10.5194/egusphere-2022-330-RC1
- AC1: 'Reply on RC1', Adrien Guerou, 01 Jul 2022
  
  Dear Thomas,
  Thank you very much for your review.
  We started to take into considerations your suggestions and comments and will answer your questions as soon as we receive the second review to optimize the modifications of the paper.
  Regards,
  Adrien et al.
  
  Citation: https://doi.org/10.5194/egusphere-2022-330-AC1
- AC2: 'Reply on RC1', Adrien Guerou, 20 Oct 2022
  
  Dear Thomas,
  
  Please find below our complete answer to your comments:
  
  General
  
  We have included to the revised version of the paper the comparison of our GMSL record to the GMSL curves you mentionned. See paragraph l.238 and associated figure 5.
  
  Line-by-Line
  
  L.3 / The syntax of Poseidon has been modified accordingly
  L.22-23 / We modified the sentence to make the distinction between sampling and accuracy. We also add references to the accuracy numbers. See Lines 23-25.
  L.72 and 79 / Modifications as follow has been added: “ ... all grid cells within +/-66 degrees N/S (the Topex and Jasons coverage) are spatially averaged..." See L.82 now.
  L.134 / We modified the sentence according to your comment, see l.145-148
  L. 178 / We estimated the trend and acceleration over the 29 years period of the GMSL record, with and without filtering, and the results are identical. This was expected since the 2 months cut off period of the filter is low as compared to the total lenght of the record (i.e, 29 years). The border effects are thus not significant. This is also true for estimations over 5 years periods.
  We apply such a fitlering on the AVISO GMSL record as we consider that we remove some high frequency noise and that we still do not degrade the trend and acceleration estimations. We nevertheless note that raw GMSL time series could be publicly provided. This will be done in a future release.
  Figure 5 and 6 / Thank you for having noticed this point. We were using the wrong GMSL timeseries for Figure 5 and 6 (i.e., not corrected for the Topex-A drift). We now obtain, naturally, consistent values between Figure 3, 5 and 6.
  L.294/ The ITRF uncertainty is certainly non-liear, this is a good point. We modified l.324 accordingly. We used the uncertainties published for the ITRF2014, indeed. The updated reference frame ITRF2020 should help reducing the associated uncertainties as: time series are longer, seasonal signals are now considered in the local movements of the ITRF2020, the models are enriched as well as more data is used to constraints the model (I.e., Galileo). Information has been added to the manuscript L.358.
  L.409 / We are currently discussing publishing the scripts used to calculate the trend, acceleration and uncertainties. Unfortunately, it will take some time. In the meantime, Prandi et al. (2021) made public similar scripts to perform OLS estimation with uncertainties in the context of regional MSL. This code is based on the same theoretical approach as ours and can be used to reproduce our analysis. We added this information l.207.
  
  Citation: https://doi.org/10.5194/egusphere-2022-330-AC2
RC2:
'Comment on egusphere-2022-330', Huseyin Baki Iz, 19 Jul 2022

Please refer to the attached PDF file.

Citation: https://doi.org/10.5194/egusphere-2022-330-RC2
- AC3: 'Reply on RC2', Adrien Guerou, 20 Oct 2022
  
  Dear Huseyin,
  There is here, from the start, a misunderstanding of the objective of the present study (and of Ablain et al., 2019). This study (and Ablain et al. 2019) does NOT intend to estimate the “systematic components” of the observed GMSL anomalies. We only intend to characterize the uncertainty in GMSL measurements due to the instrumental errors. We state it clearly in the manuscript on line 37 (and also in Ablain et al. 2019 page 1190, 2nd column, 3rd paragraph).
  Our group produces sea level measurements from satellite altimetry level 1 data. We are involved in this activity with CNES managers and CNES engineers who developed the radar altimeters onboard the satellite altimeters because we are in charge of the delivery of the sea level scientific product for CNES. We deliver sea level products and associated uncertainties (which is a pure instrumental uncertainty) as a service to the scientific community who can then use these products and their associated uncertainty to evaluate further different elements such as the geostrophic circulation, the mean dynamic topography and its changes, the GMSL anomalies and, if they wish, the “systematic components of the observed GMSL anomalies”. Here we certainly do not evaluate ourselves the “systematic components of the observed GMSL anomalies”, we only provide the updated GMSL anomalies derived from satellite altimetry and its associated instrumental uncertainty. We also provide an estimate of the 1993-2022 trend and acceleration with associated uncertainties as a metric for the low frequency changes in GMSL. The uncertainty on this trend and this acceleration is an uncertainty ONLY due to instrumental errors. We never claim the trend or the acceleration represent any “systematic component” of the GMSL. We provide the trend and the acceleration with uncertainty just as a reference for the scientific community so they can realize the actual amplitude of the instrumental errors on such metrics that are largely used for many different purposes in the science community. Note that our objective is also to provide a reference calculation of the trend uncertainty and the acceleration uncertainty so people can check their own calculation of the instrumental errors on their trend and acceleration estimate when they use our error variance/covariance matrix.
  The confusion here is very common in the community that analyses sea level rise. We believe this is because this community is very focused on the detection and attribution of the forced response of global mean sea level to anthropogenic forcing on the climate system. This forced response is expected to take the shape of a parabolic signal on global mean sea level at decadal time scales (according to climate model simulation). For this reason people in this community tend to interpret any parabolic signal in GMSL as a “systematic component” of the GMSL that has some predictive value.
  Here we DO NOT do such things. We are addressing a community that is much larger than the single community that analyses sea level rise. We are providing an update of GMSL anomalies with instrumental uncertainties for all the science communities that use GMSL products. These communities range from the Earth water cycle community to the Energy cycle community and it includes many communities as different as the ocean circulation community (which intend to assimilate the GMSL anomalies in ocean models for example) and the geophysics communities (like GIA people or solid earth people who use GMSL anomalies as observational constraint). Many of these communities compute trends or accelerations in their application. For this reason, we compute here one trend and one acceleration (the one trend and the one acceleration over 1993-2022) with the associated instrumental uncertainty derived from the error variance covariance matrix. This is as a reference so they can get a rapid idea of the actual amplitude of the instrumental error on such metrics. This is also a reference against which they can check their own uncertainty calculation when they use our error variance covariance matrix.
  From this review, we suppose that the parabolic signal of the observed GMSL anomalies has been interpreted as “systematic components “ of the GMSL. This is something that should NOT be done. A simple trend calculation or a simple acceleration calculation on the measured GMSL time series that we are providing here, does not give an estimate of any “systematic component”. There is a misunderstanding of the GMSL data in this interpretation. We are not totally clear on what is meant by the term “systematic component”. We suspect he means the forced response of GMSL to the anthropogenic forcing on the climate system. If so, there is actually a long way to isolate the “systematic component” out of the GMSL measurement we are providing here. To isolate this signal, one needs to estimate the internal variability of the climate system and also to estimate the response to other forcings on the climate system such as the sun variability and the long term tides from other planets of the solar system. One also needs to isolate the intrinsic variability generated by the ocean circulation.
  We clearly and explicitly explained this point in Ablain et al. 2019 (page 1190, 2nd column, 3rd paragraph). We repeat here in this paper that we are addressing only instrumental uncertainties and we are not trying to isolate the forced response to anthropogenic forcing. Reading your review, we understand that we have not been clear enough in the introduction of this manuscript. We thank you for pointing out this issue unintentionally. We have now added a supplementary paragraph in the introduction to clarify this positioning. See paragraph from line 40.
  Because we were not clear enough in the introduction that we are addressing only instrumental uncertainties and do not estimate any “systematic components”, we believe that several comments of the review are actually not relevant. We explain this below.
  Comment #1
  We explained in detail in Ablain et al. (2019) why we use an OLS rather than a GLS. OLS estimate is known to be less accurate than GLS in terms of the mean square error, because its variance is larger. A generalized least square estimate would probably help in narrowing slightly the trend uncertainty, but the difference is expected to be small, in particular when the V/C matrix is not far from identity (Ribes et al. 2016). Important advantages of using OLS are that (i) OLS is consistent with previous estimators of GMSL trends as well as estimators of trends in other essential climate variables than GMSL (indeed OLS with V/C matrices is the approach used in the IPCC, see for example Hartmann, et al., 2014,) and that (ii) the OLS best estimate does not depend on the estimated variance–covariance matrix Σ. Reasons why the OLS estimate could be prefered, even if the V/C matrix is not the identity, were also discussed in the IPCC AR5 (e.g., Chapter 2, Box 2.2)
  We tested a GLS estimate on a yearly average GMSL time series (for which the V/C matrix is now invertible) and checked that the result is very close to the OLS estimate. We do find very similar results with both estimates. See plot below. We added this information in the manuscript now on line 204.
  Comment #2
  There is a confusion here. We do not assume that a linear signal or a parabolic signal represent the GMSL time series and then test these simplistic models against the zero assumption. This approach is used by people trying to isolate the GMSL signal forced by anthropogenic emissions assuming it is a linear trend or a parabolic signal. Here we are not interested in this. Here we intend to provide the most accurate estimate of the observed GMSL. Then we consider the GMSL time series and try to derive the trend and the acceleration of the time series over the record length as metrics of the lowest frequencies included in the time series. In this sense we do not expect the disturbances to be zero and in this sense the OLS estimator itself is an unbiased estimator (see Ribes et al. 2016 and demonstration in the reference therein). Note that linear trend models are also used (and useful) in cases where the underlying shift is not linear in time (and so the “expected value” of the residual is non-zero; see again IPCC AR5, Box 2.2). In such cases, trends are used to measure the rate of increase in a time-series.
  Comment #3
  We never assume the quadratic model captures “the systematic variations in the observed GMSL”. This interpretation is biased towards interpreting the GMSL physical signals. Again, we estimate the trend and acceleration of the observed GMSL as metrics of the lowest frequencies included in the time series. See our answer to point #2.
  Comment #4
  We agree with this comment and we refer to our response of point #1 (where we checked that the GLS estimate and the OLS estimate lead to the same estimate) as well as point #2.
  Comment #5
  We would like to make two comments in response to this point. First, the estimated V/C matrix is taken into account in the uncertainty analysis, i.e., quantification of the standard error of the trend and acceleration coefficients. As a result, this uncertainty analysis is valid and reliable – and fully consistent with our V/C estimate. Second, our uncertainty analysis only accounts for the measurement uncertainty – this is now made clearer in the revised version of the manuscript (see our response to the review’s introduction for more details). In particular, any uncertainty related to internal variability within the climate system (which can be large) is not taken into account here. So, our confidence range is not representative of uncertainty on human-induced SLR.
  Comment #6
  Indeed, if the objective of this study was to isolate the forced response of sea level to anthropogenic emissions we would need to account for the internal variability and the natural variability in GMSL in the least square approach. And the review is right, we would need to model the serial correlation in the GMSL time series. But that is not our objective. Our objective here is only to deliver to the community the most accurate GMSL time series possible from satellite altimetry with associated instrumental uncertainty and to estimate the uncertainty due to instruments on the 1993-2020 trend and acceleration of the GMSL time series. For this reason we believe this comment is not relevant here.
  Comment #7
  See answer of the previous point #6.
  Comment #8
  Of course we expect the forced response of GMSL to anthropogenic forcing to be a response that is more complex than just a parabolic signal. For this reason, the acceleration and the trends are expected to change with time, we agree. But here we do not tackle this problem. We simply want to give metrics for the lowest frequency included in the 1993-2020 GMSL record derived from satellite altimetry. For this reason we focus on one unique trend and one unique acceleration : the 1993-2020 trend and acceleration corresponding to the full satellite altimetry era. Once again, because of the different perspective, we believe the comment here is not relevant.
  Comment #9
  See our answer to the previous comment #8.
  Comment #10
  That is the point here. We use the trend and acceleration as simple metrics for the low frequency and do not make any predictions with it. This would be indeed “an extremely costly blunder in climate mitigation decision making”. Any other metric could/should be used for sure to achieve this goal. We choose one metric and are clear about it so people in the community can test their own calculation against ours.
  We DO NOT pretend those metrics represent any “systematic component” of the GMSL and we CERTAINLY NOT pretend those metrics have any predictive skills. For your recollection , we are only providing an observed estimate of the GMSL and low frequency metrics with the INSTRUMENTAL uncertainty. We clarified this point in the paper l. 197-198.
  Comment #11
  We do not make any predictive model in this study. See answer to comments #10.
  Comment #12
  Thank you for pointing out that “the efforts to build a full V/C matrix is a worthy endeavor for optimal analyses of GMSL anomalies”. We believe so as well. Indeed this is the goal of the paper and we insist on that point: for the altimetry measurements only.
  But please note that we DO NOT intend to provide a full V/C matrix that represents the errors of the forced response of GMSL to anthropogenic emissions. Our work is much more modest. We ONLY provide a V/C matrix of INSTRUMENTAL errors in GMSL. Providing a description of the GMSL instrumental errors is a very important step for scientists of all communities that use the GMSL time series and not only for the sea level rise community. For the sea level rise community, our work provides the very first brick over which scientists can further build a complete V/C matrix of the forced signal. This is not our intention. We understand from this review that we were not clear enough. Now we clarify this in a whole new paragraph in the introduction (see lines 40-48). We hope this makes our objective clearer to the sea level rise community.
  
  Citation: https://doi.org/10.5194/egusphere-2022-330-AC3

Adrien Guérou et al.

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Short summary

Based on the latest satellite observations published by the French CNES space agency, we present the current state of the sea level at the scale of the planet and assess its rise and acceleration over the past 29 years. To support stakeholders decisions we provide updated quantified estimations of our confidence on our estimations and highlight key technological and scientific fields to make progress on that will help to better characterise the sea level evolution in the future.


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