The manuscript aims at characterizing the variability in temperature and dust concentration of globally distributed records from over the last glacial cycle. Furthermore, it investigates if there is any co-variability of such records located at different latitudes.

The manuscript has a strong focus on the applied frequency analysis method and less attention is paid to the applied datasets and the climate of the last glacial period. Having submitted the manuscript to a climate journal, I would suggest those priorities should be different. For this journal, the primary focus should be on the climate of the last glacial period and what we can learn about it. Below I give some suggestions for how this could be done.

General comments:

To put a bit more focus on the applied datasets, it would be great to see all of the applied records shown on a common time scale in a figure. Maybe one figure for the temperature records and one for the dust records? That will allow the reader to visually compare the records and better judge the outcome of your subsequent analysis. For dust records, a log scale may give a better overview of the record variability. It would also be great to include some orbital forcing records for comparison, for example the 60N insolation curve. Figure 3 is a step in this direction, but it is hard to judge if the millennium-scale variability is well synchronized between the records. It would therefore be useful if the figure uses the full page width to show the details of the 120 ka profiles. Also, you only show high resolution ice-core records, what do the lower resolution records from lower latitudes look like?

Another important point to mention is the time scales you are applying for each record. There is a large number of different time scales available for the last glacial period, often related to individual archives and quite often not in agreement. For ice cores alone, there are several generations of time scales that have developed over decades. When you start comparing records from different archives and investigating co-variability among records, you are assuming that the records from different archives are synchronized, eg that their times scales are in agreement, but in general, they are not. For ice cores for example, different versions of time scales for the same ice core will typically deviate by centuries to millennia, which will easily bring DO-event out of phase from one core to the next. You therefore need to discuss time scales of the applied records and state for each applied record which time scale has been applied. Possibly, references for the applied time scales could be included in table 1? If you plot the applied records in high-resolution on the applied time scales, we may be able to judge visually how well some of the records are synchronized.

It would also be helpful to show the time resolution of the applied records throughout the 120 ka period you investigate. I see an average sample resolution presented in Table 1, but sample resolution may vary greatly throughout over time. I also see an attempt of presenting the varying sample resolution in Figure 2, but it is not clear to me what ‘Proportional age’ and ‘first part of the age’ refers to. Why not show the actual sample resolution for each record on an absolute age scale from 0 to 120 ka in one figure? This may provide us with some background information about how well suited the different records are for the analysis.

Are you aware that there are high resolution water isotope and dust records available for the Greenland NEEM ice core? You may want to apply those? You find them here (Schüpbach et al., 2018;Gkinis et al., 2021). It may be an idea to substitute the RECAP record that has very low temporal resolution of the last glacial period?

An alternative interpretation of Figure 5 would be that the variability in correlation among records does not reflect climate variability, but rather that time scales of the applied records tend to disagree more the longer the record is, in particular between ice cores and lower latitude records. You therefore first need to convince us that that the applied records are well synchronized, before we can trust the current interpretation of the figure.

Figure 6: Very strange that the analysis gives so different results for GRIP and NGRIP as the records are practically identical. This makes me suspicious about the suitability of the Haar analysis for those records. Are the two ice cores on the same time scale? Please have a look at the high-resolution figure in (Rasmussen et al., 2014) to see just how similar both the temperature records (in terms of d18O) and in particular the dust records (in terms of Ca concentration that is often used as a dust proxy) are for the Greenland ice cores. It may be an idea to run your analysis on the d18O and Ca of the GRIP, GISP2 and NGRIP ice cores to see how well the results compare? In my opinion they should lead to very similar results, otherwise something is fundamentally wrong.

Around line 265, a discussion of DO and AIM events suddenly starts without previous introduction. Those events are so defining for the climate of the last glacial period that their nature and relation needs to be introduced and discussed in the introduction of the paper. A lot is known about the relative phasing of those events within Greenland, within Antarctica, and between the two poles (see eg (Buizert et al., 2015)). Also the well-known relation between temperature and dust in both Greenland and Antarctica would be good to introduce at an earlier stage. Likewise, the knowledge about the origin of ice core dust is relevant for your interpretation and should have been mentioned earlier. I think it would be relevant to introduce to those topics in the introduction section and then to comment on them in the discussion and compare to the results of your analysis?

Detailed comments:

Please double-check your reference for the GRIP dust record in Table 1. I am quite certain, it has nothing to do with the record you are applying. Also, the GRIP record does not reach back continuously 248 kyr as stated in the table. It may have been wrongly published like that, but see (Rasmussen et al., 2014) for how long back in time the GRIP core can be synchronized to the NGRIP ice core that holds the longest continuous Greenland profile.

Statement in lines 266-268 about polar amplification needs to be supported. An alternative reason for the better pole-to-pole correlation could be that the time resolution of the polar records is generally much superior to that of records from the lower latitudes? The reader will be able to judge this if the applied records were presented in an overview figure.

Statement line 278 about the importance of ice sheet height for temperature is rather incomplete. What about DO-events, glacial-interglacial periods, and sea ice extent in the North Atlantic? Are those factors not important for the site temperature on the ice sheet?

References:

Buizert, C., Adrian, B., Ahn, J., Albert, M., Alley, R. B., Baggenstos, D., Bauska, T. K., Bay, R. C., Bencivengo, B. B., Bentley, C. R., Brook, E. J., Chellman, N. J., Clow, G. D., Cole-Dai, J., Conway, H., Cravens, E., Cuffey, K. M., Dunbar, N. W., Edwards, J. S., Fegyveresi, J. M., Ferris, D. G., Fitzpatrick, J. J., Fudge, T. J., Gibson, C. J., Gkinis, V., Goetz, J. J., Gregory, S., Hargreaves, G. M., Iverson, N., Johnson, J. A., Jones, T. R., Kalk, M. L., Kippenhan, M. J., Koffman, B. G., Kreutz, K., Kuhl, T. W., Lebar, D. A., Lee, J. E., Marcott, S. A., Markle, B. R., Maselli, O. J., McConnell, J. R., McGwire, K. C., Mitchell, L. E., Mortensen, N. B., Neff, P. D., Nishiizumi, K., Nunn, R. M., Orsi, A. J., Pasteris, D. R., Pedro, J. B., Pettit, E. C., Price, P. B., Priscu, J. C., Rhodes, R. H., Rosen, J. L., Schauer, A. J., Schoenemann, S. W., Sendelbach, P. J., Severinghaus, J. P., Shturmakov, A. J., Sigl, M., Slawny, K. R., Souney, J. M., Sowers, T. A., Spencer, M. K., Steig, E. J., Taylor, K. C., Twickler, M. S., Vaughn, B. H., Voigt, D. E., Waddington, E. D., Welten, K. C., Wendricks, A. W., White, J. W. C., Winstrup, M., Wong, G. J., and Woodruff, T. E.: Precise interpolar phasing of abrupt climate change during the last ice age, Nature, 520, 661-665, 10.1038/nature14401, 2015.

Gkinis, V., Vinther, B. M., Popp, T. J., Quistgaard, T., Faber, A.-K., Holme, C. T., Jensen, C.-M., Lanzky, M., Lütt, A.-M., Mandrakis, V., Ørum, N.-O., Pedersen, A.-S., Vaxevani, N., Weng, Y., Capron, E., Dahl-Jensen, D., Hörhold, M., Jones, T. R., Jouzel, J., Landais, A., Masson-Delmotte, V., Oerter, H., Rasmussen, S. O., Steen-Larsen, H. C., Steffensen, J.-P., Sveinbjörnsdóttir, Á.-E., Svensson, A., Vaughn, B., and White, J. W. C.: A 120,000-year long climate record from a NW-Greenland deep ice core at ultra-high resolution, Scientific Data, 8, 141, 10.1038/s41597-021-00916-9, 2021.

Rasmussen, S. O., Bigler, M., Blockley, S. P., Blunier, T., Buchardt, S. L., Clausen, H. B., Cvijanovic, I., Dahl-Jensen, D., Johnsen, S. J., Fischer, H., Gkinis, V., Guillevic, M., Hoek, W. Z., Lowe, J. J., Pedro, J. B., Popp, T., Seierstad, I. K., Steffensen, J. P., Svensson, A. M., Vallelonga, P., Vinther, B. M., Walker, M. J. C., Wheatley, J. J., and Winstrup, M.: A stratigraphic framework for abrupt climatic changes during the Last Glacial period based on three synchronized Greenland ice-core records: Refining and extending the INTIMATE event stratigraphy, Quaternary Science Reviews, 106, 14-28, 10.1016/j.quascirev.2014.09.007, 2014.

Schüpbach, S., Fischer, H., Bigler, M., Erhardt, T., Gfeller, G., Leuenberger, D., Mini, O., Mulvaney, R., Abram, N. J., Fleet, L., Frey, M. M., Thomas, E., Svensson, A., Dahl-Jensen, D., Kettner, E., Kjaer, H., Seierstad, I., Steffensen, J. P., Rasmussen, S. O., Vallelonga, P., Winstrup, M., Wegner, A., Twarloh, B., Wolff, K., Schmidt, K., Goto-Azuma, K., Kuramoto, T., Hirabayashi, M., Uetake, J., Zheng, J., Bourgeois, J., Fisher, D., Zhiheng, D., Xiao, C., Legrand, M., Spolaor, A., Gabrieli, J., Barbante, C., Kang, J. H., Hur, S. D., Hong, S. B., Hwang, H. J., Hong, S., Hansson, M., Iizuka, Y., Oyabu, I., Muscheler, R., Adolphi, F., Maselli, O., McConnell, J., and Wolff, E. W.: Greenland records of aerosol source and atmospheric lifetime changes from the Eemian to the Holocene, Nature Communications, 9, 10.1038/s41467-018-03924-3, 2018.

The manuscript proposes a framework for analyzing climate (dust and temperature proxies) variability across time scales covering at least in part the last glacial period using a few high resolution paleoclimate archives and a statistical technique called Haar fluctuation analysis.

The idea behind this study is indeed very interesting and mounts on a technique previously developed. However, there a few important points that need further clarification – including a more thorough climatic interpretation of the results beyond the description of the analysis outcomes in terms of metrics.

Comments

Clarify whether the specific methodological approach is novel or the technique was already presented in previous papers (beyond the application to a broader/different dataset).

Also, to what extent this work is an extension of Lambert & Lovejoy 2019?

Figure 2 and related text: it is not very clear to me what this variable represents, please give a clearer definition

Why does delta-t in Figure 4d,e have negative values? What does that represent?

Line 177. “low-frequency peak somewhere between 17.8 to 31.6 kyr” > where can we see that?

Line 247. Concerning NGRIP, I thought dust and d18O were essentially co-varying on millennial time scales, so I would expect to read something different at least concerning dust on these time scales. Could you comment on that?

Sections 4 and 5: spend more time describing and discussing the meaning of your findings

The authors utilize a range of existing paleoclimate proxy data from the last glacial period to analyze temperature and dust variability on a range of temporal scales. They incorporate a Haar-based algorithm to evaluate spatial variability and deal with the non-uniform sampling inherent in many of the records. I appreciated the detailed Methodology and Results section, and am impressed with the depth of detail the authors generated with non-uniformly sampled data; in this regard the Haar approach seems like a valuable tool to have in the paleoclimate community toolkit. The climate interpretations in the manuscript are a bit more limited. A more robust comparison to other glacial-age interpretations would strengthen the authors findings and interpretations. Regardless, this is an interesting manuscript with an innovative approach that will be of interest to the paleoclimate community.