Patterns of Centennial-to-Millennial Holocene Climate Variation in the North American Mid-Latitudes

Shuman, Bryan N.

doi:https://doi.org/10.5194/cp-2022-89

Preprints

https://doi.org/10.5194/cp-2022-89

Preprints

28 Nov 2022

| 28 Nov 2022

Status: a revised version of this preprint was accepted for the journal CP and is expected to appear here in due course.

Patterns of Centennial-to-Millennial Holocene Climate Variation in the North American Mid-Latitudes

Bryan N. Shuman

Abstract. Noise in Holocene paleoclimate reconstructions can hamper detection of centennial-to-millennial climate variations and diagnoses of the dynamics involved. This paper uses multiple ensembles of reconstructions to separate signal and noise and determine what, if any, centennial-to-millennial variations influenced North America during the past 7000 yr. To do so, ensembles of temperature and moisture reconstructions were compared across four different spatial scales: continental, regional, sub-regional, and local scales. At each scale, two independent multi-record ensembles were compared to detect any centennial-to-millennial departures from the long Holocene trends, which correlate more than expected from random patterns. In all cases, the potential centennial-to-millennial variations had small magnitudes. However, at least two patterns of centennial-to-millennial variability appear evident. First, large-scale variations included a prominent Mid-Holocene anomaly from 5600–4500 YBP that increased mean effective moisture and produced temperature anomalies of different signs in different regions. The changes steepened the north-south temperature gradient in mid-latitude North America with a pattern similar to the positive mode of the North Atlantic Oscillation (NAO). Second, correlated multi-century (~500 yr) variations produce a distinct spectral signature in temperature and hydroclimate records along the western Atlantic margin. Both patterns differ from random autocorrelated variations but expressed distinct spatiotemporal characteristics consistent with separate controlling dynamics.

Received: 14 Nov 2022 – Discussion started: 28 Nov 2022

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Bryan N. Shuman

Status: closed

RC1:
'Review of cp-2022-89', Anonymous Referee #1, 07 Feb 2023

The comment was uploaded in the form of a supplement: https://cp.copernicus.org/preprints/cp-2022-89/cp-2022-89-RC1-supplement.pdf

Citation: https://doi.org/10.5194/cp-2022-89-RC1
- AC2:
  'Reply on RC1', Bryan Shuman, 24 Oct 2023
  I appreciate that the review understood the main goals of the manuscript and supported the value of considering approaches such as described in the manuscript. I hope that the manuscript can stimulate useful discussion of some of the patterns described as well as similar analyses of other datasets.
  The critiques of the manuscript are useful and appreciated. The discussion of different geographic scales and regions is clearly cumbersome and hard to follow in portions of the text.
  I will revise by
  Including site maps showing the locations of records and the extents of the different regions;
  
  Revising the naming of the different regions/scales to make each one clearly distinct and improve referencing them;
  
  Revising or replacing the scatter plots in Fig. 4 with a simpler table of the relationships;
  
  Revising Section 4.4 to better address the broad applicability of the approaches discussed here. I had focused on limitations of the approach to calibrated datasets with linear relationships to specific climate variables, but I can revisit the section to better articulate how similar methods could be broadly applied.
  
  Clarifying that European data were used at times to test whether the patterns of variation had parallels across continents (and thus were more likely to be significant).
  
  I will also make the minor corrections suggested.
  
  Citation: https://doi.org/10.5194/cp-2022-89-AC2
RC2:
'Comment on cp-2022-89', Raphael Hébert, 13 Apr 2023

General comments:
The paper presents an interesting analysis of selected records and is highly relevant to the study of centennial to millennial scale natural variability, providing some valuable insights into the space-time dynamics of the North American climate over the Holocene. I think that most of the prominent features discussed are convincing, but I think that limitations of the data and analysis can explain why little coherent variability is observed otherwise.
First, I think that a more formal definition of cen-mil variations could be given. When amplitudes of variations are given, it should be clear that those are (if I understood correctly) the standard deviation of the 50-year interpolated series over the last 7000 years after removing a loess trend with span of 6/11. If that is indeed the definition usually assumed, then I would question it since lots (or virtually all) of the records will have a resolution lower than 50 years, and the resulting standard variation will be underestimated. In addition, time-uncertainty will further smooth variability when taking such averages after interpolation. Therefore, the amplitude of the resulting cen-mil variations can only be seen as a lower bound for true variations (assuming that non-climate variations are small and mostly averaged out, which might not be exactly true, but I think this is still very challenging to quantify).
Quantifying variability at a given timescale could also be achieved by integrating the power spectrum over a given timescale/frequency band to obtain the variance. That said, removing the LOESS is an effective high-pass filter (although the frequency cutoff is not precisely defined) and will give similar results, with the advantage of being in temperature units. Having variability in temperature unis could also be achieved using Haar fluctuations (Lovejoy & Schertzer, 2013), which incidentally works quite well with irregular data (Hébert et al., 2022, NPG).
Second, the null expectation model could be improved. On line 156-157, it is stated that LOESS filtering white noise gives time series with temporal autocorrelation characteristics similar to paleoclimate timeseries, well, not really. The LOESS is quite an abrupt low-pass filter, so if you apply it to white noise, the result is mostly white noise at a lower resolution with a smoother interpolation between, the temporal autocorrelation isn’t changed above a certain timescale. Why not generate data that already has realistic autocorrelation (e.g. fractional noise with an exponent estimated from paleo data, which often hovers around beta=1/H=0) and then low-pass filter it (as in Hébert et al., 2021, NPG for example)? I would consult Reschke et al. (2019): https://doi.org/10.1016/j.cageo.2018.11.009, which wholly focus on the method aspect of creating an appropriate null expectation model and provides tools for testing the significance of correlations when dealing with irregular paleoclimate data.
I think the null expectation model used by the author is pedagogically useful and helps getting a conceptual understanding of the characteristics of paleoclimate data. It is not however a state-of-the-art representation of paleoclimate data, I would say.
Detailed comments:
Section numbers 1.1 and 1.2 should read as 2.1 and 2.2 I believe.
Figure 2: The shading should be described, are we looking at the spread between the single curves used in the average?
Line 254: Unclear to me where the range of random expectations comes from, Fig. 3a, which is cited, is not showing that. Are we talking about the histogram on Fig. 1a? Or are we averaging a different white noise on both series and calculating the correlation 1000 times and using this as the range as in Fig 1b? I would consider using the “corit” package from Reschke et al. (2019) to calculate the correlations and their significance.
Line 264: Again would be important to specify how the range is obtained.
figure 3B: The blue curve appears to go outside of the shading around 1000 year BP or so. Unclear how the shadding is calculated.
Line 286: Meaning of sentence is unclear to me.
Figure 4: I would write the correlation coefficient with the same size font as the information on the strength of the correlation is already in the value itself. Maybe adding a colour code for whether they are significant or not would be useful. I think the figure could generally be improved. Are we learning a lot from the scatter plots and the distribution of detrended residuals?
Figure 5: The use of shading instead of a curve to reproduce the MAT spectrum is confusing I'd say, why not keep the black curve reproduced? There is likely very little signal left on these curves since we are looking at a temporal average of curves with time-uncertainty (see e.g. Hébert et al., 2022, Nat Geosc, Extended Data Fig. 1 for a surrogate experiment with time-uncertainty), which smooths out drastically the high-frequency signal, and the LOESS detrending removes the low-frequency signal. The steep scaling on the high-frequency side is very likely the result of power-loss due to combining time-uncertain series. I would only expect a narrow band between 2000-4000 (maybe 1000-4000) to be somewhat reliable. Also, power spectral density is not unitless, I would advocate showing the actual units rather than the log (but keeping log spacing); as a result, it is unclear to me how the series with different units are compared, was the spectrum computed on something like the z-score of the residual timeseries?
One last point on this figure, the uncertainty given for the scaling exponents are quite meaningless, and I would advocate giving approximate values (e.g. beta≈0.7). There is nothing wrong with taking a linear fit of logs to get an approximation of the scaling exponent, but many assumptions that do not hold are made when doing so, e.g. about the distribution of the residuals being independent and normal. If we really wanted to make meaningful estimates of uncertainty here, I would recommend designing a surrogate model for the series and using a Monte-Carlo approach (e.g. Hébert et al., 2021, NPG), ideally also accounting for time-uncertainty and other proxy processes (Kunz et al., 2022, Clim Past; Dolman et al., 2021, Clim Past). However, I would also be satisfied by approximate values without any uncertainty given (e.g. beta≈0.7).
Figure 6: B) The map could use a colour scale. I would also use only two colours on a divergent scale (blue to red for example) rather than orange-green-white-blue-purple. The colour scale for the colour of the triangles would also be useful. A) The shading should be described, are we looking at the spread between the single curves used in the average? In the caption, I would quickly mention those are the ENA sites.
Line 358: Not sure I am convinced by the significance of the "Evidence of the 8200 YBP cool event" on Fig. 6A.
Line 359: Maybe "warming phase" would be more accurate than "warm phase”, although it is not warming much, but rather stays constant until it rejoins de long-term cooling trend. I would generally avoid describing minor wiggles as I am not convinced they are robust.
Line 364: How robust is this correlation? It seems to me like there is very little correlation outside the first 1000 years (when we have a very steep change) and the 5500-4800 period, which was used to discriminate the records. Could the apparently event in the 5500-4800 period be produced by construction? Say we would take the same set of records and average them based on their trends in another arbitrary time period, would’t we also get a similar result but for a different time period, i.e. the records with (randomly) positive trends averaged together will create an average series with a stronger trend over the selected time period and average out elsewhere? I did a quick experiment and simulated 20 fractional noise series with beta=1/H=0 (following out method in Hébert et al., 2021, NPG) covering 11ka, low-pass filtered and sub-sampled at 250 years resolution, then calculated trends over a 1000-year long period in the middle the series, and then stacked the series with a positive trend together, and the ones with negative trends together. This yielded an average correlation of -0.14+/-0.27 between the two stacks, and -0.15+/-0.17 between the two stacks after a 6k loess trends was removed in each. Thus, I expect that the method may induce a negative bias on the correlation and would suggest to run a similar surrogate experiment to assess the significance of the correlation, and also to try out stacking the records with respect to the trends estimated over different reference period and see whether we can easily get such events.
Line 367: How do we know that this standard deviation difference is due to different variability? Then why are the warming/cooling events around 5500 BP of similar magnitude? Isn’t it possible that they are the result of different different resolutions (and also time-uncertainty) in the input timeseries? It would be easy to check whether the mean resolution of the northern records is lower than that of the southern ones.
Line 369: Why is this slope relevant?
Line 384: “appear evident” rather than “appear evidence”? Revise sentence.
Line 385: Unclear what are those small temperature fluctuations that are discussed, is that with respect to the standard deviation of individual detrended series after interpolation at a 50-year resolution? Seems to contradict line 239 where 0.25-0.5 variations are discussed. Cen-mil variations could be formally defined.
Line 391: Not sure that the null model can be described as autoregressive, which is defined (on Wikipedia) by: “ The autoregressive model specifies that the output variable depends linearly on its own previous values and on a stochastic term (an imperfectly predictable term); thus the model is in the form of a stochastic difference equation (or recurrence relation which should not be confused with differential equation).” As the LOESS filter is not causal, this means that it also depends on future values.
Line 409: I would see this drop in high-frequency variability as a consequence of averaging time-uncertain records together, having bioturbation or sediment mixing, and interpolation of lower resolution sediments.
Figure 8: MBM is written mbm on the axis of the top panel.
Line 501: Not sure if this statement is substantiated.
Line 504: I’d say “relatively” well-dated.

References:
Dolman, A.M., Kunz, T., Groeneveld, J., Laepple, T., 2020. Estimating the timescale-dependent uncertainty of paleoclimate records – a spectral approach. Part II: Application and interpretation. Climate of the Past Discussions 1–22. https://doi.org/10.5194/cp-2019-153
Hébert, R., Herzschuh, U., Laepple, T., 2022. Millennial-scale climate variability over land overprinted by ocean temperature fluctuations. Nat. Geosci. 15, 899–905. https://doi.org/10.1038/s41561-022-01056-4
Hébert, R., Rehfeld, K., Laepple, T., 2021. Comparing estimation techniques for timescale-dependent scaling of climate variability in paleoclimate time series. Nonlinear Processes in Geophysics Discussions 1–26. https://doi.org/10.5194/npg-2021-7
Kunz, T., Dolman, A.M., Laepple, T., 2020. A spectral approach to estimating the timescale-dependent uncertainty of paleoclimate records – Part 1: Theoretical concept. Climate of the Past 16, 1469–1492. https://doi.org/10.5194/cp-16-1469-2020
Lovejoy, S., Schertzer, D., 2012. Haar wavelets, fluctuations and structure functions: convenient choices for geophysics. Nonlinear Processes in Geophysics 19, 513–527. https://doi.org/10.5194/npg-19-513-2012
Reschke, M., Kunz, T., Laepple, T., 2019. Comparing methods for analysing time scale dependent correlations in irregularly sampled time series data. Computers & Geosciences 123, 65–72. https://doi.org/10.1016/j.cageo.2018.11.009

Citation: https://doi.org/10.5194/cp-2022-89-RC2
- AC1:
  'Reply on RC2', Bryan Shuman, 24 Oct 2023
  I am very appreciative of the comments from Dr. Hébert. They have been stimulating and helpful.
  As noted by the review, my driving question was understanding the specific space-time patterns of climate variation in North America that may have driven potential impacts (e.g., ecological or hydrological changes). I appreciate the feedback that the major features discussed seem convincing and will revise with an eye toward limiting discussion of less robust elements, particularly those linked to the limitations of the data and analyses.
  In this context, I am glad to be pointed toward up-to-date methods that can be applied to determine the significant patterns; I had been planning to cite some of these newer papers (e.g., Hébert et al., 2022) even before seeing this review. I will strive to update the analyses as much as I reasonably can within the scope of this revision, particularly by
  applying ‘corit’ to test the significance of the correlations,
  
  using a Gaussian filter in place of the LOESS, and
  
  further following Reschke et al. (2019) to improve the null models.
  
  One issue that probably also needs clarification is that most of the datasets used in the manuscript already existed as uniform timestep (50-yr) series and are not irregular raw proxy data because they represent previously published stacks of many records, compiled after linear interpolation (consistent with Reschke et al., 2019’s guidance). Only the SST record from the Scotian Margin is based on data from a single core. The thinking here was that any signal remaining after interpolating and averaging to create stacks is potentially a significant signal (albeit muted by the sampling and averaging process). The signals may be particularly significant if they are reproduced across multiple independent data stacks, which would be prone to different variability from non-climate sources. However, testing such a hypothesis may require use of null models. In this context, I am excited to apply and cite the surrogate-record methods suggested by the review to improve the null models.
  Other major points of revision will include the following:
  I will provide a more formal definition of cen-mil variations consistent with that defined in the review, but updated to reference the use of a Gaussian filter instead of the LOESS.
  
  I agree and will also clarify that the standard deviation metric calculated after removing the loess only provides a lower bound on the magnitude of the variations because of the averaging of irregular and infrequent sampling in much of the underlying data. I will clarify this caveat.
  
  Figure 4 – Given the agreement among reviewers about making this figure more concise, I will replace it with an alternative that emphasizes the most meaningful correlations (or lack of correlations).
  
  Figure 5 – The suggestions for improvement make sense and I appreciate the point about approximating the scaling exponents rather than providing the uncertainties.
  
  Figure 5 and related text in line 409 - I respect the discussion about meaningful climate information possibly being restricted to the 2000-4000 yr band and that factors like “averaging time-uncertain records together, having bioturbation or sediment mixing, and interpolation of lower resolution sediments” would reduce the likelihood of variations in the 1000-500 yr band. However, I will revise to clarify that multi-centennial (~500-yr band) signals represent first-order (even visually apparent) stratigraphic features in some of the underlying raw data; they can be tracked across sites and captured different proxies and reconstruction methods at the local-to-regional scale (see e.g., Newby et al., 2014; Shuman et al., 2019 cited in the manuscript). The moisture reconstructions, in particular, represent composites of data with sample resolution of 15-40 yrs/sample, which should limit the power loss at the high frequency end of the scale.
  
  The novel contribution here is not that the coastal records contain multi-century variability, but rather that it differs from patterns seen in other regions and at other scales. To the degree that the resolution of the records and impacts of averaging do not change meaningfully across the stacks from different scales or regions, the multi-century variability only appear to represent much of the spectral power in the coastal records. This point from Figure 5 and in line 409 parallels some geographic differences in variability at the interannual scale across the study area.
  
  I agree that the averaging across records should reduce the signal amplitudes as shown by Hébert et al., 2021 experiment, but if so, then all of the different spectra should have similar slopes. Or at least, the independent data ensembles from each region or scale (in each panels in the figure) should be as variable from each other as from the other regions/scales (other figure panels). However, both the temperature and moisture data from the NE coast (far right panel) show a markedly different trend from the other spectra; I will revise to clarify that this aspect of the analyses may be the most meaningful.
  
  I can also clarify that the spectra were calculated using z-scores to make the temperature and moisture reconstructions directly comparable. I will also remove the gray shading.
  
  Figure 6 – I will improve the figure color scale as suggested and clarify the confidence interval shading.
  
  Figure 6-7 and related text – Regarding the changes at 5500-4800 YBP, I appreciate the point that arbitrarily selecting any time period and dividing the data into positive and negative change groups would likely construct spurious anomaly patterns. I will further evaluate the relationship and provide caveats as suggested using a surrogate experiment as proposed; it does seem possible to me that the only significant signal is, in fact, the shift at 5500-4800 and not the other variations throughout the rest of the Holocene.
  
  I should also clarify that the time period was not selected arbitrarily but was found previously to represent the largest rate of change in multiple proxies in eastern North American data over the past 8000 years (see Shuman and Marsicek, 2016). I can now cite a more in-depth analysis of the spatial patterns of this change in a separate dataset with a greater number of records: Shuman, B. N., Stefanescu, I. C., Grigg, L. D., Foster, D. R., & Oswald, W. W. (2023). A millennial-scale oscillation in latitudinal temperature gradients along the western North Atlantic during the mid-Holocene. Geophysical Research Letters, 50, e2022GL102556. https://doi.org/10.1029/2022GL102556.
  
  Also related to the 5500-4800 YBP change in line 367: I will revise the text to clarify the point that the two magnitudes are not significantly different. Their ratio of 0.67 could indicate a value greater (closer to one) than expected by chance alone produced in the null models used in manuscript (0.27-0.41 in Fig. 1A). As Dr. Hébert proposes, the ratio is within the range (0.41-1.0) expected if factors like sampling frequency and other sources of noise degrade two common signals (as in Fig. 1B). I will improve on the null modeling using the useful guidance from Dr. Hébert, but the point made here was not that these represent different patterns. Instead, the two stacks could instead share a common signal, which is indicated by the high ratio of the standard deviations. Even if the standard deviations represent only an approximation of the lower bound of the true magnitude of variation, their ratio would be much lower if produced by chance only.
  
  I respect that not all of the analyses here represent state-of-the-art analyses, but one motivation for the manuscript was to make a pedagogical contribution as much as an analytical contribution. The paper was inspired specifically by some conversations with other paleoclimate researchers about the significance of apparent centennial-millennial variations. I may not have satisfactorily achieved the goal of balancing pedagogy and approachable analysis for practitioners without deep time series backgrounds, but I will improve the manuscript by better inclusion and referencing of the types of approaches that were suggested in the review.
  
  Citation: https://doi.org/10.5194/cp-2022-89-AC1

Status: closed

RC1:
'Review of cp-2022-89', Anonymous Referee #1, 07 Feb 2023

The comment was uploaded in the form of a supplement: https://cp.copernicus.org/preprints/cp-2022-89/cp-2022-89-RC1-supplement.pdf

Citation: https://doi.org/10.5194/cp-2022-89-RC1
- AC2:
  'Reply on RC1', Bryan Shuman, 24 Oct 2023
  I appreciate that the review understood the main goals of the manuscript and supported the value of considering approaches such as described in the manuscript. I hope that the manuscript can stimulate useful discussion of some of the patterns described as well as similar analyses of other datasets.
  The critiques of the manuscript are useful and appreciated. The discussion of different geographic scales and regions is clearly cumbersome and hard to follow in portions of the text.
  I will revise by
  Including site maps showing the locations of records and the extents of the different regions;
  
  Revising the naming of the different regions/scales to make each one clearly distinct and improve referencing them;
  
  Revising or replacing the scatter plots in Fig. 4 with a simpler table of the relationships;
  
  Revising Section 4.4 to better address the broad applicability of the approaches discussed here. I had focused on limitations of the approach to calibrated datasets with linear relationships to specific climate variables, but I can revisit the section to better articulate how similar methods could be broadly applied.
  
  Clarifying that European data were used at times to test whether the patterns of variation had parallels across continents (and thus were more likely to be significant).
  
  I will also make the minor corrections suggested.
  
  Citation: https://doi.org/10.5194/cp-2022-89-AC2
RC2:
'Comment on cp-2022-89', Raphael Hébert, 13 Apr 2023

General comments:
The paper presents an interesting analysis of selected records and is highly relevant to the study of centennial to millennial scale natural variability, providing some valuable insights into the space-time dynamics of the North American climate over the Holocene. I think that most of the prominent features discussed are convincing, but I think that limitations of the data and analysis can explain why little coherent variability is observed otherwise.
First, I think that a more formal definition of cen-mil variations could be given. When amplitudes of variations are given, it should be clear that those are (if I understood correctly) the standard deviation of the 50-year interpolated series over the last 7000 years after removing a loess trend with span of 6/11. If that is indeed the definition usually assumed, then I would question it since lots (or virtually all) of the records will have a resolution lower than 50 years, and the resulting standard variation will be underestimated. In addition, time-uncertainty will further smooth variability when taking such averages after interpolation. Therefore, the amplitude of the resulting cen-mil variations can only be seen as a lower bound for true variations (assuming that non-climate variations are small and mostly averaged out, which might not be exactly true, but I think this is still very challenging to quantify).
Quantifying variability at a given timescale could also be achieved by integrating the power spectrum over a given timescale/frequency band to obtain the variance. That said, removing the LOESS is an effective high-pass filter (although the frequency cutoff is not precisely defined) and will give similar results, with the advantage of being in temperature units. Having variability in temperature unis could also be achieved using Haar fluctuations (Lovejoy & Schertzer, 2013), which incidentally works quite well with irregular data (Hébert et al., 2022, NPG).
Second, the null expectation model could be improved. On line 156-157, it is stated that LOESS filtering white noise gives time series with temporal autocorrelation characteristics similar to paleoclimate timeseries, well, not really. The LOESS is quite an abrupt low-pass filter, so if you apply it to white noise, the result is mostly white noise at a lower resolution with a smoother interpolation between, the temporal autocorrelation isn’t changed above a certain timescale. Why not generate data that already has realistic autocorrelation (e.g. fractional noise with an exponent estimated from paleo data, which often hovers around beta=1/H=0) and then low-pass filter it (as in Hébert et al., 2021, NPG for example)? I would consult Reschke et al. (2019): https://doi.org/10.1016/j.cageo.2018.11.009, which wholly focus on the method aspect of creating an appropriate null expectation model and provides tools for testing the significance of correlations when dealing with irregular paleoclimate data.
I think the null expectation model used by the author is pedagogically useful and helps getting a conceptual understanding of the characteristics of paleoclimate data. It is not however a state-of-the-art representation of paleoclimate data, I would say.
Detailed comments:
Section numbers 1.1 and 1.2 should read as 2.1 and 2.2 I believe.
Figure 2: The shading should be described, are we looking at the spread between the single curves used in the average?
Line 254: Unclear to me where the range of random expectations comes from, Fig. 3a, which is cited, is not showing that. Are we talking about the histogram on Fig. 1a? Or are we averaging a different white noise on both series and calculating the correlation 1000 times and using this as the range as in Fig 1b? I would consider using the “corit” package from Reschke et al. (2019) to calculate the correlations and their significance.
Line 264: Again would be important to specify how the range is obtained.
figure 3B: The blue curve appears to go outside of the shading around 1000 year BP or so. Unclear how the shadding is calculated.
Line 286: Meaning of sentence is unclear to me.
Figure 4: I would write the correlation coefficient with the same size font as the information on the strength of the correlation is already in the value itself. Maybe adding a colour code for whether they are significant or not would be useful. I think the figure could generally be improved. Are we learning a lot from the scatter plots and the distribution of detrended residuals?
Figure 5: The use of shading instead of a curve to reproduce the MAT spectrum is confusing I'd say, why not keep the black curve reproduced? There is likely very little signal left on these curves since we are looking at a temporal average of curves with time-uncertainty (see e.g. Hébert et al., 2022, Nat Geosc, Extended Data Fig. 1 for a surrogate experiment with time-uncertainty), which smooths out drastically the high-frequency signal, and the LOESS detrending removes the low-frequency signal. The steep scaling on the high-frequency side is very likely the result of power-loss due to combining time-uncertain series. I would only expect a narrow band between 2000-4000 (maybe 1000-4000) to be somewhat reliable. Also, power spectral density is not unitless, I would advocate showing the actual units rather than the log (but keeping log spacing); as a result, it is unclear to me how the series with different units are compared, was the spectrum computed on something like the z-score of the residual timeseries?
One last point on this figure, the uncertainty given for the scaling exponents are quite meaningless, and I would advocate giving approximate values (e.g. beta≈0.7). There is nothing wrong with taking a linear fit of logs to get an approximation of the scaling exponent, but many assumptions that do not hold are made when doing so, e.g. about the distribution of the residuals being independent and normal. If we really wanted to make meaningful estimates of uncertainty here, I would recommend designing a surrogate model for the series and using a Monte-Carlo approach (e.g. Hébert et al., 2021, NPG), ideally also accounting for time-uncertainty and other proxy processes (Kunz et al., 2022, Clim Past; Dolman et al., 2021, Clim Past). However, I would also be satisfied by approximate values without any uncertainty given (e.g. beta≈0.7).
Figure 6: B) The map could use a colour scale. I would also use only two colours on a divergent scale (blue to red for example) rather than orange-green-white-blue-purple. The colour scale for the colour of the triangles would also be useful. A) The shading should be described, are we looking at the spread between the single curves used in the average? In the caption, I would quickly mention those are the ENA sites.
Line 358: Not sure I am convinced by the significance of the "Evidence of the 8200 YBP cool event" on Fig. 6A.
Line 359: Maybe "warming phase" would be more accurate than "warm phase”, although it is not warming much, but rather stays constant until it rejoins de long-term cooling trend. I would generally avoid describing minor wiggles as I am not convinced they are robust.
Line 364: How robust is this correlation? It seems to me like there is very little correlation outside the first 1000 years (when we have a very steep change) and the 5500-4800 period, which was used to discriminate the records. Could the apparently event in the 5500-4800 period be produced by construction? Say we would take the same set of records and average them based on their trends in another arbitrary time period, would’t we also get a similar result but for a different time period, i.e. the records with (randomly) positive trends averaged together will create an average series with a stronger trend over the selected time period and average out elsewhere? I did a quick experiment and simulated 20 fractional noise series with beta=1/H=0 (following out method in Hébert et al., 2021, NPG) covering 11ka, low-pass filtered and sub-sampled at 250 years resolution, then calculated trends over a 1000-year long period in the middle the series, and then stacked the series with a positive trend together, and the ones with negative trends together. This yielded an average correlation of -0.14+/-0.27 between the two stacks, and -0.15+/-0.17 between the two stacks after a 6k loess trends was removed in each. Thus, I expect that the method may induce a negative bias on the correlation and would suggest to run a similar surrogate experiment to assess the significance of the correlation, and also to try out stacking the records with respect to the trends estimated over different reference period and see whether we can easily get such events.
Line 367: How do we know that this standard deviation difference is due to different variability? Then why are the warming/cooling events around 5500 BP of similar magnitude? Isn’t it possible that they are the result of different different resolutions (and also time-uncertainty) in the input timeseries? It would be easy to check whether the mean resolution of the northern records is lower than that of the southern ones.
Line 369: Why is this slope relevant?
Line 384: “appear evident” rather than “appear evidence”? Revise sentence.
Line 385: Unclear what are those small temperature fluctuations that are discussed, is that with respect to the standard deviation of individual detrended series after interpolation at a 50-year resolution? Seems to contradict line 239 where 0.25-0.5 variations are discussed. Cen-mil variations could be formally defined.
Line 391: Not sure that the null model can be described as autoregressive, which is defined (on Wikipedia) by: “ The autoregressive model specifies that the output variable depends linearly on its own previous values and on a stochastic term (an imperfectly predictable term); thus the model is in the form of a stochastic difference equation (or recurrence relation which should not be confused with differential equation).” As the LOESS filter is not causal, this means that it also depends on future values.
Line 409: I would see this drop in high-frequency variability as a consequence of averaging time-uncertain records together, having bioturbation or sediment mixing, and interpolation of lower resolution sediments.
Figure 8: MBM is written mbm on the axis of the top panel.
Line 501: Not sure if this statement is substantiated.
Line 504: I’d say “relatively” well-dated.

References:
Dolman, A.M., Kunz, T., Groeneveld, J., Laepple, T., 2020. Estimating the timescale-dependent uncertainty of paleoclimate records – a spectral approach. Part II: Application and interpretation. Climate of the Past Discussions 1–22. https://doi.org/10.5194/cp-2019-153
Hébert, R., Herzschuh, U., Laepple, T., 2022. Millennial-scale climate variability over land overprinted by ocean temperature fluctuations. Nat. Geosci. 15, 899–905. https://doi.org/10.1038/s41561-022-01056-4
Hébert, R., Rehfeld, K., Laepple, T., 2021. Comparing estimation techniques for timescale-dependent scaling of climate variability in paleoclimate time series. Nonlinear Processes in Geophysics Discussions 1–26. https://doi.org/10.5194/npg-2021-7
Kunz, T., Dolman, A.M., Laepple, T., 2020. A spectral approach to estimating the timescale-dependent uncertainty of paleoclimate records – Part 1: Theoretical concept. Climate of the Past 16, 1469–1492. https://doi.org/10.5194/cp-16-1469-2020
Lovejoy, S., Schertzer, D., 2012. Haar wavelets, fluctuations and structure functions: convenient choices for geophysics. Nonlinear Processes in Geophysics 19, 513–527. https://doi.org/10.5194/npg-19-513-2012
Reschke, M., Kunz, T., Laepple, T., 2019. Comparing methods for analysing time scale dependent correlations in irregularly sampled time series data. Computers & Geosciences 123, 65–72. https://doi.org/10.1016/j.cageo.2018.11.009

Citation: https://doi.org/10.5194/cp-2022-89-RC2
- AC1:
  'Reply on RC2', Bryan Shuman, 24 Oct 2023
  I am very appreciative of the comments from Dr. Hébert. They have been stimulating and helpful.
  As noted by the review, my driving question was understanding the specific space-time patterns of climate variation in North America that may have driven potential impacts (e.g., ecological or hydrological changes). I appreciate the feedback that the major features discussed seem convincing and will revise with an eye toward limiting discussion of less robust elements, particularly those linked to the limitations of the data and analyses.
  In this context, I am glad to be pointed toward up-to-date methods that can be applied to determine the significant patterns; I had been planning to cite some of these newer papers (e.g., Hébert et al., 2022) even before seeing this review. I will strive to update the analyses as much as I reasonably can within the scope of this revision, particularly by
  applying ‘corit’ to test the significance of the correlations,
  
  using a Gaussian filter in place of the LOESS, and
  
  further following Reschke et al. (2019) to improve the null models.
  
  One issue that probably also needs clarification is that most of the datasets used in the manuscript already existed as uniform timestep (50-yr) series and are not irregular raw proxy data because they represent previously published stacks of many records, compiled after linear interpolation (consistent with Reschke et al., 2019’s guidance). Only the SST record from the Scotian Margin is based on data from a single core. The thinking here was that any signal remaining after interpolating and averaging to create stacks is potentially a significant signal (albeit muted by the sampling and averaging process). The signals may be particularly significant if they are reproduced across multiple independent data stacks, which would be prone to different variability from non-climate sources. However, testing such a hypothesis may require use of null models. In this context, I am excited to apply and cite the surrogate-record methods suggested by the review to improve the null models.
  Other major points of revision will include the following:
  I will provide a more formal definition of cen-mil variations consistent with that defined in the review, but updated to reference the use of a Gaussian filter instead of the LOESS.
  
  I agree and will also clarify that the standard deviation metric calculated after removing the loess only provides a lower bound on the magnitude of the variations because of the averaging of irregular and infrequent sampling in much of the underlying data. I will clarify this caveat.
  
  Figure 4 – Given the agreement among reviewers about making this figure more concise, I will replace it with an alternative that emphasizes the most meaningful correlations (or lack of correlations).
  
  Figure 5 – The suggestions for improvement make sense and I appreciate the point about approximating the scaling exponents rather than providing the uncertainties.
  
  Figure 5 and related text in line 409 - I respect the discussion about meaningful climate information possibly being restricted to the 2000-4000 yr band and that factors like “averaging time-uncertain records together, having bioturbation or sediment mixing, and interpolation of lower resolution sediments” would reduce the likelihood of variations in the 1000-500 yr band. However, I will revise to clarify that multi-centennial (~500-yr band) signals represent first-order (even visually apparent) stratigraphic features in some of the underlying raw data; they can be tracked across sites and captured different proxies and reconstruction methods at the local-to-regional scale (see e.g., Newby et al., 2014; Shuman et al., 2019 cited in the manuscript). The moisture reconstructions, in particular, represent composites of data with sample resolution of 15-40 yrs/sample, which should limit the power loss at the high frequency end of the scale.
  
  The novel contribution here is not that the coastal records contain multi-century variability, but rather that it differs from patterns seen in other regions and at other scales. To the degree that the resolution of the records and impacts of averaging do not change meaningfully across the stacks from different scales or regions, the multi-century variability only appear to represent much of the spectral power in the coastal records. This point from Figure 5 and in line 409 parallels some geographic differences in variability at the interannual scale across the study area.
  
  I agree that the averaging across records should reduce the signal amplitudes as shown by Hébert et al., 2021 experiment, but if so, then all of the different spectra should have similar slopes. Or at least, the independent data ensembles from each region or scale (in each panels in the figure) should be as variable from each other as from the other regions/scales (other figure panels). However, both the temperature and moisture data from the NE coast (far right panel) show a markedly different trend from the other spectra; I will revise to clarify that this aspect of the analyses may be the most meaningful.
  
  I can also clarify that the spectra were calculated using z-scores to make the temperature and moisture reconstructions directly comparable. I will also remove the gray shading.
  
  Figure 6 – I will improve the figure color scale as suggested and clarify the confidence interval shading.
  
  Figure 6-7 and related text – Regarding the changes at 5500-4800 YBP, I appreciate the point that arbitrarily selecting any time period and dividing the data into positive and negative change groups would likely construct spurious anomaly patterns. I will further evaluate the relationship and provide caveats as suggested using a surrogate experiment as proposed; it does seem possible to me that the only significant signal is, in fact, the shift at 5500-4800 and not the other variations throughout the rest of the Holocene.
  
  I should also clarify that the time period was not selected arbitrarily but was found previously to represent the largest rate of change in multiple proxies in eastern North American data over the past 8000 years (see Shuman and Marsicek, 2016). I can now cite a more in-depth analysis of the spatial patterns of this change in a separate dataset with a greater number of records: Shuman, B. N., Stefanescu, I. C., Grigg, L. D., Foster, D. R., & Oswald, W. W. (2023). A millennial-scale oscillation in latitudinal temperature gradients along the western North Atlantic during the mid-Holocene. Geophysical Research Letters, 50, e2022GL102556. https://doi.org/10.1029/2022GL102556.
  
  Also related to the 5500-4800 YBP change in line 367: I will revise the text to clarify the point that the two magnitudes are not significantly different. Their ratio of 0.67 could indicate a value greater (closer to one) than expected by chance alone produced in the null models used in manuscript (0.27-0.41 in Fig. 1A). As Dr. Hébert proposes, the ratio is within the range (0.41-1.0) expected if factors like sampling frequency and other sources of noise degrade two common signals (as in Fig. 1B). I will improve on the null modeling using the useful guidance from Dr. Hébert, but the point made here was not that these represent different patterns. Instead, the two stacks could instead share a common signal, which is indicated by the high ratio of the standard deviations. Even if the standard deviations represent only an approximation of the lower bound of the true magnitude of variation, their ratio would be much lower if produced by chance only.
  
  I respect that not all of the analyses here represent state-of-the-art analyses, but one motivation for the manuscript was to make a pedagogical contribution as much as an analytical contribution. The paper was inspired specifically by some conversations with other paleoclimate researchers about the significance of apparent centennial-millennial variations. I may not have satisfactorily achieved the goal of balancing pedagogy and approachable analysis for practitioners without deep time series backgrounds, but I will improve the manuscript by better inclusion and referencing of the types of approaches that were suggested in the review.
  
  Citation: https://doi.org/10.5194/cp-2022-89-AC1

Bryan N. Shuman

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Short summary

A gap in understanding climate variation exists at centennial-to-millennial scales, particularly for warm climates. Such variations challenge detection. They exceed direct observation but are geologically short. Centennial-to-millennial variations that may have influenced North America were examined over the past 7000 yr. Significant patterns were detected from fossil pollen and sedimentary lake-level changes, indicating ecological, hydrological, and likely human significance.


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