The authors present a synchronization of Greenland ice core (NGRIP Ca2+) and Asian Speleothem (d18O) data using an automated algorithm for Bayesian inversion. Contrary to previous studies, this study does not only focus on stadial-interstadial transitions to estimate the timescale differences, but exploits the entire record for a continuous inference of the timescale differences. Their results agree with estimates based on cosmogenic radionuclides within errors but are more precise. Further, the authors find that the differences between GICC05 and the U/Th-timescale grow quickly between 15-22 kaBP and decline even more rapidly between 24-26 kaBP. Assuming that U/Th is absolute, this implies an underestimation of the GICC05 counting uncertainty. The authors discuss reasons for the overcounting between LGM and GI-3 and hypothesize a relation to the high dust deposition and the seasonality of snow deposition which leads to additional bands in the visual stratigraphy and the erroneous identification of annual layers.

General Comments

The paper is well written, easy to follow and the figures are appropriate. However, I think the approach and the results must be discussed more with respect to the underlying assumptions and the mismatches with previous attempts.

The synchronization of proxy data from different archives has a long tradition and obvious drawbacks. Previous studies have only used large climate transitions/events for synchronization which has the underlying assumption that an event occurred/was recorded synchronously in all records. This study goes one step further, as it has the underlying assumption that all climate records are indeed the same (equation in line 228). Spelled out, this means that NGRIP Ca2+ = Speleothem d18O, which is obviously not true as they are very different physical quantities, controlled by different processes. Admittedly, some of the controlling processes may be shared, but the assumption of the applied method is much stronger: It implies the existence of a linear function that relates NGRIP Ca2+ and speleothem d18O. Considering the chain of processes that contribute to aerosol transport and deposition in Greenland and speleothem d18O, of which many are non-linear, this seems very unlikely. In the model, standardized NGRIP Ca2+ and speleothem d18O should agree within the uncertainty of the PC1 of the speleothem records, if aligned correctly. Figure 4 clearly shows that this is not the case. Especially between 15-24 kaBP NGRIP Ca2+ and speleothem d18O show simply very different variations: EASM PC1 is increasing between from 20 to 19 kaBP, while NGRIP Ca2+ is more or less constant. The subsequent decrease in NGRIP Ca2+ lasts for a century or so, while EASM d18O is steadily decreasing for ~4,000 years until the onset of GI-1. These discrepancies occur during the period, where the authors infer the largest ice core layer counting errors, raising doubt about the robustness of this discussion.

In summary, the basic assumption underlying the approach presented here (i.e., NGRIP Ca2+ = speleothem d18O) is incorrect and should hence not be used.

If the authors nonetheless want to follow this approach, they need to i) clearly state that their model assumptions are not fulfilled and ii) discuss these drawbacks and provide additional tests to demonstrate the robustness of the results:

1. What determines the inferred timescale shift during the LGM, when there is little co-variability between NGRIP Ca and EASM PC1 (see figure 4)?
2. Which timescale offset is inferred when only the period between 15 – 22 kaBP (or other subsections) is synchronized (and both records are standardized only for this period)?
3. How would the results differ if NGRIP d18O was used instead of Ca2+?
4. How would the results (and uncertainties) differ if the uncertainty sigma_ui in the model was increased sufficiently to fulfil the model assumption (NGRIP Ca2+ = speleothem d18O within error).

Further, the results need to be evaluated more critically with respect to previous studies:

1. Please include the timescale differences by Corrick et al. into figures 4 & 5.
2. It appears that most other studies (Buizert et al. / Corrick et al. / Martin et al) found systematically smaller timescale differences then the results presented here. Why?

The points above should be included as new sections (sensitivity experiments / comparison to previous studies) in the main part of the manuscript so that the reader understands the caveats of the method and results. A synchronization function like this will likely be used by many, and it is important to be transparent with its shortcomings and not oversell this.

Specific Comments:

L13-14: “which are currently not detectable…” Why wouldn’t they be?

L19-20: “a bias attributable…” The paper provides a reasonable discussion around this, but it is not conclusive. Please add “possibly” or similar.

L37-38: “much smaller uncertainty in the absolute ages”. During the glacial.

L85-87: But it is not quite clear which part of this chain of events is recorded by the data (see e.g., Beck et al., 2018; Liu et al., 2014; Pausata et al., 2011).

L95-96: Please also mention the advantage, that this is a relatively low-level assumption, that only requires synchroneity and not a linear relationship as assumed by the model applied here. Further, the discrete tie-points have typically a high signal to noise ratio, while the method applied here, employs also low signal to noise variations for matching. Please be critical with the assumptions of your method.

L103-111: In principle, I agree with the problems of the alignment technique, but I am not sure what this has to do with (which?) autocorrelation. 10Be is autocorrelated over time - so are most climate and forcing records. The autocorrelation argument would also be true for pure 14C-wiggle match-dating. In my opinion, the crux is the window-length: If there is one large peak within a window, it will dominate the obtained pdf as long as it is in the window. Hence, we used only non-overlappting windows in Adolphi & Muscheler 2016. But that obviously affects the resolution we can obtain, as we need a certain window length to have a signal.

L117-119: This is not an issue of the alignment technique, but of the lack of convincing tie-points. In Adolphi et al. 2018 we only chose one tie-point around 21 kaBP which we called “tentative” but which forms the basis of much of what is discussed here. The lack of tie-points (or co-variability) is similar in this study. Looking at figure 4 there seems little agreement between the records. See major comments.

L143-145: There are many processes that contribute to Ca deposition in Greenland. Please discuss in more detail.

L167-169: Maybe point out the advantages too: The assumption that the timing of a major climate transition synchronous is much more conservative than assuming a linear relationship between the proxies on all timescales which is clearly proven wrong during the LGM.

L180: “in response to changes in accumulation” since you’re not modelling accumulation, maybe better “in response to miscounting”?

L181-182: “simulated ice core depositional history”. See above, you’re not modelling deposition but only the timescale.

L205 (eq. 1): Maybe I got this wrong but looking at this equations and trying to put in [units]: m must be [years/m]; so t must be [m] not time; so tau is defined on depth? If so, please use a different symbol as t is time later on.

L213-214: “…distinct depositional environments…” But you only model the ice core alignement and their accumulation rates are certainly autorcorrelated? It is ok to do it like that, but I am not sure I agree with the explanation.

L214-216: Isn't it that: You are not modelling the timescale (or ice accumulation) but only minor modifications of it (counting errors), which do not need to be autorcorrelated.

L228: “u(ti) = g(tau(ti))” See major comments. This is obviously not true and should be discussed.

L244 (Eq. 3): This was defined for comparing 14C-dates to a 14C-calibration. I.e., similar physical quantities. Because your sigma_ui is too small to fulfil the model (u=g) the vast majority of the data is essentially treated as outliers in the gamma-distribution. See major comments.

L257: “integrates” better “reflects” as this is the derivative of the MCE which may cause confusion.

L258-259: but that shift is absolute? Why is the RCE a good measure here?

L268-269: “exceeds the range allowed by the MCE (as is generally the case for the Holocene)”. This is not true. We also discuss, that the RCE is only exceeded very briefly. The exceeded MCE is inhereted from this early mistake. See figure 12 in Adolphi and Muscheler 2016

L318: 0.97 is 50% more than 0.63! Is that “comparable”?

L321: Please compare the Delta T to Muscheler et al. 2008

L322: “younger” within error this is consistent?

L331-332: See major comments. The agreement between the records is not very convincing. Please discuss critically. What is the correlation coefficient? What is the error of the model (u=g) after alignment?

L334-335: “the error is large”. It appears that the error is actually smaller than during MIS-3?

L345: There seems to be quite some disagreement with Martin et al. 2023. Please discuss.

L346: Please include the re-assessment of the LGM tie-point by Sinnl et al., (2023) into the figures

L361: Please also cite Sinnl et a. (2023)

Figure 4: Please include Corrick et al. 2023 tie-points

References

Beck, J. W., Zhou, W., Li, C., Wu, Z., White, L., Xian, F., Kong, X., & An, Z. (2018). A 550,000-year record of East Asian monsoon rainfall from 10Be in loess. Science, 360(6391), 877–881. https://doi.org/10.1126/science.aam5825

Liu, Z., Wen, X., Brady, E. C., Otto-Bliesner, B., Yu, G., Lu, H., Cheng, H., Wang, Y., Zheng, W., Ding, Y., Edwards, R. L., Cheng, J., Liu, W., & Yang, H. (2014). Chinese cave records and the East Asia Summer Monsoon. Quaternary Science Reviews, 83, 115–128. https://doi.org/https://doi.org/10.1016/j.quascirev.2013.10.021

Pausata, F. S. R., Battisti, D. S., Nisancioglu, K. H., & Bitz, C. M. (2011). Chinese stalagmite δ18O controlled by changes in the Indian monsoon during a simulated Heinrich event. Nature Geoscience, 4(7), 474–480. https://doi.org/10.1038/ngeo1169

Sinnl, G., Adolphi, F., Christl, M., Welten, K. C., Woodruff, T., Caffee, M., Svensson, A., Muscheler, R., & Rasmussen, S. O. (2023). Synchronizing ice-core and U\,$/$\,Th timescales in the Last Glacial Maximum using Hulu Cave $^{14}$C and new $^{10}$Be measurements from Greenland and Antarctica. Climate of the Past, 19(6), 1153–1175. https://doi.org/10.5194/cp-19-1153-2023

The manuscript is concerned with the construction of a transfer function between the Greenland GICC05 time scale and the U-Th based time scale for a number of East Asian stalagmites and in particular that of the Hulu Cave. The work is based on the assumption that there is a one-to-one correspondence between the variability in Greenland dust/Ca concentration and that of water isotopes in the Asian/Hulu cave(s). This assumption seems justified for major abrupt climate transitions, such as onsets of DO events, as most climate proxies change across those transitions and there is support for this assumption in a number of other studies. For the LGM/GS-2 section, approx. 15-23 ka, however, it is somewhat more uncertain if the relation holds, as there are few or no characteristic events to match up in that period.

As one of the main authors behind the construction of the glacial section of GICC05, I generally agree to the finding of this and previous studies that there is some quite strong bias in the GICC05 layer counting for the 15-28 ka section that was fairly unconstrained at the time. In some sections, the bias appears larger than the stated MCE, and quite likely, the bias goes in both directions for different periods ending up at a close-to-correct absolute age for much of the 30-40 ka section. Still, I would think there is also the possibility that the U-Th stalagmite ages may sometimes have their accuracy issues although they are often published with very small error bars. Alone the observed scatter among different stalagmites covering the same events points in this direction. I think we have an example of this for the applied stalagmite records at around GI-10, where they ‘exhibit some temporal inconsistencies’ (Figure 4). Therefore, I would be careful to assume that all of the observed disagreement in absolute ages between the ice core and U-Th chronologies can be attributed issues related to the ice-core time scale(s). In any case, a long-term absolute error of about 1% is certainly much smaller than we thought it possible some 15-20 years ago, when GICC05 was put together.

The following recent papers may be relevant to mention or discuss in the manuscript:

Dong et al., 2022, is concerned with GS-3 and introduces some accurately dated Asian stalagmites that allow for a detailed comparison of ice core and U-Th ages across that interval. The paper is supportive of the ice-core Ca/dust – Asian monsoon relationship for significant and abrupt climate events and it identifies biases of the ice-core chronologies in the same direction as the present manuscript although with somewhat smaller amplitudes.

Sinnl et al., 2023, identifies new 10Be bipolar links between G and A in the older part of the difficult GS-2 interval. The study is thus relevant for comparison in a similar way to that of Martin et al., 2023.

I am not commenting on the applied Bayesian inversion algorithm that is not my expertise.

Specific comments:

Lines 331-341: To test the robustness of the suggested similarity of the Greenland and East Asian records across GS-2 it may be an idea to apply a different Greenland record for the inversion algorithm. The NGRIP dust record is available in 5cm resolution, but it has rather poor quality when it comes to details. NEEM has available high-resolution records available for both Ca and dust concentrations. It may be worth trying to match the dust record and maybe the Ca using a log scale as the dust concentration varies exponentially with Greenland water isotopes (see attached figure).

Lines 242-248: This may be a good place also to discuss the Sinnl et al., 2023, bipolar 10Be match points. Please also elaborate a bit on the relevance of the Martin et al, 2023, study. It may not be evident for the reader why the G – A synchronization is relevant in a context that is otherwise entirely NH.

Line 361: Clearly, there is god agreement between the results of the present study and that of Martin et al., 2023, at around 18 ka in Figure 5, but for younger and particularly for older ages, there are large discrepancies, so what are the implications of this? Again, it may not be evident to the reader how Antarctica fits into the otherwise NH picture. The Dong et al., 2022, study could be relevant for this discussion.

Figure 3: A convincing comparison (although not surprising) but something must be wrong with figure titles or the caption. Should be right-hand figure be showing GS onsets? Not sure which reversed scale is referred to in the caption.

Figure 4 caption: Which blue line is referred to in caption of Figure 3c? In Figure 3d, I can also not distinguish the mentioned colors.

Figure 6 caption: There seems to be some remains of previous versions of this figure in the caption? At least, I do not find the mentioned annual layer thickness profile in the figure.

Figure 6: In the attached figure, I compare the Sieben Hengste Cave (SHC) isotope record to the Ca and dust profiles of NGRIP and NEEM (all ice core records are on log scales). The SHC record is shown on its original time scale without application of the transfer function. Shown on those time scales, there appears to be a good correspondence between the ice core records and the SHC isotopes for the 22-28 ka period. In particular, the sharp transition associated with the onset of the younger of the Greenland dust spikes close to 24 ka and the adjacent structures seem to be well aligned between all records. Therefore, assuming there is a one-to-one relationship between ice-core dust/Ca and European stalagmite d18O, it appears that the transfer function makes things worse for this interval. If there are common events between the two records at around 18 ka, the transfer function may do a better job here?

References:

Dong, X., Kathayat, G., Rasmussen, S. O., Svensson, A., Severinghaus, J. P., Li, H., Sinha, A., Xu, Y., Zhang, H., Shi, Z., Cai, Y., Pérez-Mejías, C., Baker, J., Zhao, J., Spötl, C., Columbu, A., Ning, Y., Stríkis, N. M., Chen, S., Wang, X., Gupta, A. K., Dutt, S., Zhang, F., Cruz, F. W., An, Z., Lawrence Edwards, R., and Cheng, H.: Coupled atmosphere-ice-ocean dynamics during Heinrich Stadial 2, Nature Communications, 13, 10.1038/s41467-022-33583-4, 2022.

Sinnl, G., Adolphi, F., Christl, M., Welten, K. C., Woodruff, T., Caffee, M., Svensson, A., Muscheler, R., and Rasmussen, S. O.: Synchronizing ice-core and U ∕ Th timescales in the Last Glacial Maximum using Hulu Cave 14C and new 10Be measurements from Greenland and Antarctica, Clim. Past, 19, 1153-1175, 10.5194/cp-19-1153-2023, 2023.