Characterisation of Dansgaard-Oeschger events in palaeoclimate time series using the Matrix Profile

Barbosa, Susana; Silva, Maria Eduarda; Rousseau, Denis-Didier

doi:https://doi.org/10.5194/npg-2024-13

Preprints

https://doi.org/10.5194/npg-2024-13

Preprints

21 May 2024

| 21 May 2024

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

Characterisation of Dansgaard-Oeschger events in palaeoclimate time series using the Matrix Profile

Susana Barbosa, Maria Eduarda Silva, and Denis-Didier Rousseau

Abstract. Palaeoclimate time series, reflecting the state of Earth's climate in the distant past, display occasionally very large and rapid shifts, evidencing abrupt climate variability. The identification and characterisation of these abrupt transitions in palaeoclimate records is of particular interest as it allows the understanding of millennial climate variability and the identification of potential tipping points in the context of current climate change. Methods that are able to characterise these events in an objective and automatic way, in a single time series or across two proxy records, are therefore of particular interest. In our study the matrix profile approach is used to describe Dansgaard-Oeschger (DO) events, abrupt warmings detected in Greenland ice core, and Northern Hemisphere marine and continental records. The results indicate that canonical events DO-19 and DO-20, occurring at around 72 and 76 ka, are the most similar events over the past 110,000 years. These transitions are characterised by matching transitions corresponding to events DO-1, DO-8 and DO-12. These transitions are abrupt, resulting in a rapid shift to warmer conditions, followed by a gradual return to cold conditions. The joint analysis of the δ¹⁸O and Ca²⁺ time series indicates that the transition corresponding to the DO-19 event is the most similar event across the two time series.

Received: 13 May 2024 – Discussion started: 21 May 2024

Publisher's note: Copernicus Publications remains neutral with regard to jurisdictional claims made in the text, published maps, institutional affiliations, or any other geographical representation in this preprint. The responsibility to include appropriate place names lies with the authors.

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Susana Barbosa, Maria Eduarda Silva, and Denis-Didier Rousseau

Status: closed

RC1:
'Comment on npg-2024-13', Anonymous Referee #1, 24 Jun 2024

In the manuscript "Characterisation of Dansgaard-Oeschger events in palaeoclimate time series using the Matrix Profile" Susana Barbosa, Maria Eduarda Silva, and Denis-Didier Rousseau use the matrix profile method to analyse isotope time series from the NGRIP ice cores. The aim of the study is not to date the various tipping points in the record but rather to demonstrate the potential of a purely data-driven approach in charaterise the abrupt transition. Using the matrix profile approach allows a quantitative identification of typical transition motifs that are associated with the DO transitions the authors focus on. Moreover, the method allows to measure the similarity between transitions and not surprising the transition motifs for DO-19 and DO-20 are identified as the most similar.
The manuscript is nicely written and the results are given by meaningful figures and tables. Overall, I enjoyed reading the manuscript. The authors give a good summary of the matrix profile method. This section is detailed enough to understand the method applied and the references given to the original works allow a deep-dive into the method if required. delta-O-18 and Ca2+ records are analysed, first by themself (finding self-similarity) and then together (focussing on "cross"-similarity/join matrix profile). The investigations follow a logical structure and in combination show the strength of the method studied. The study is completed by testing the limits and dependencies of the method on only parameter the method depends on and on including an artificial time shift between the delta-O-18 and Ca2+ records.
While the manuscript is a good example of how novel time series analysis methods can be applied in a paleoclimate context, research never ends and consequently I missed two main points in the manuscript. Firstly, the strength of the matrix profile method is to find motifs in time series in a computational efficient way. The authors should make clear how the record under consideration with only 4869 data points requires such an advanced method and why traditional methods are computational not tractable. Second, while the manuscript contains some test demonstrating the stability of the methods and results, strictly speaking there is no consideration given with respect to the statistical significance of the results. While bootstrapping would not make sense in the context of this study, more advanced surrogate data methods, like the Small-shuffle technique (T. Nakamura & M. Small Phys. Rev. E 72, 056216 (2005)), could be used. With such methods one could investigate how destroying for example the short term correlation in the data changes the distance matrix. I understand that such an investigation might well be beyond a simple revision and might by itself be the basis for a future publication.
I also found a small number of typos in the manuscript:

l67: taht -> that

l181: vales -> values

l245: by by -> by

Citation: https://doi.org/10.5194/npg-2024-13-RC1
- AC1: 'Reply on RC1', Susana Barbosa, 09 Jul 2024
  
  We attach a supplementary document with a point-by-point reply to the referee's comments.
  
  Citation: https://doi.org/10.5194/npg-2024-13-AC1
RC2:
'Comment on npg-2024-13', Anonymous Referee #2, 25 Jun 2024

Review of "Characterisation of Dansgaard-Oeschger events in palaeoclimate

time series using the Matrix Profile" by Barbosa et al
Barbosa and colleagues apply the pattern-recognition algorithm called the Matrix Profile on NGRIP ice-core measurements of d18O and Ca+ in order to provide an objective ad automatic characterisation of Dansgaard-Oeschger warming events. The algorithm sucessfully identifies and matches a number of events according to their similarity. The identification of so-called motifs works within one time series as well as across different time series. It is even able to identify corresponding patterns if the compared records are of different length or if the time axis is shifted.
While the method seems to work well with the presented data set, the implications and relevance of the study remain unclear. The discussion of the results remains superficial and very much within the space/jargon of the matrix profile. It does not become clear to me what the method can achieve that could not have been achieved by other means. I outline my major comments below and suggest that these comments need to be addressed before the paper can be considered for publication.

=========================

Major Comments

=========================

1. Relevance/Novelty and physical interpretation ------
- The objective of the study was to "characterise the abrupt transitions, in a purely data-driven manner, based on the shape of the corresponding DO patterns". I have learned a lot about similarity between different DO-events, but the resulting interpretation does not add any new information to what we already new about DO-events. The only physical characterisation is given as "an abrupt transition to warm conditions preceded by approximately stable stadial conditions and followed by a slow return to cold conditions" for d18O and "distinguished by an abrupt decrease in terrestrial dust concentration, followed by a period of stable dust conditions." for Ca+. Both of these statements seem established knowledge and could have been obtained almost purely by eye. I believe the relevance of the study could be greatly improved by giving more physical context and interpretation to the obtained results. I list some example questions below that could help in giving this context:
(1) What is the actual advantage of the method with respect to previous methods? The authors mention that it can be a powerful alternative to "wiggle matching" (see also major comment 2). I can see this, but most of the performed analysis was done within one time series, what is the advantage here?

(2) What do I gain from knowing which events are most similar to each other? Can the information help with stacking or with classification? Here, the authors give a small hint in their conclusion, stating that the identified similarity could be an indication of similar underlying mechanisms. Can this claim be backed up/elaborated upon? And what about the other (shorter) unidentified transitions?

(3) What is the physical interpretation/relevance of an event being a top motif or a neighbouring motif?

(4) What does it imply that the matrix profile identiefies different top motifs in d18O and Ca+?
2. Possible limitations ---------------------------------

I think possible limitations of the method need to be discussed in more detail, especially when it comes to the joint matrix profile. The test data set used here are two records on the same age model from a similar location. These seem very favourable conditions. What if the records have different temporal resolution as is often the case? How would the method be used to synchronise two records if they have different age models? And as I understand it, the method can only be used to synchronise two time series if the manifestation of the events follows a similar pattern. What if there is a phase shift or if the pattern is not as pronounced as in the Greenland ice cores?
Also, as I understand from the discussion, the window size does not seem to have a big effect on the identification of main motifs in the range of 2500-3500 years. But what about the smaller window sizes and shorter DO-events? Currently only long events are captured and shorter events (e.g. events 3-7, 9 and 10) are probabaly ignored because of the chosen window length. Where is the lower bound for meaningful results?
3. Clarity ----------------------------------------------

In parts, it is difficult to follow the method description and interpretation, especially because the word "close" is used for being similar and for being close in time. I suggest to use "similarity" instead of "distance" thoughout the text to avoid confusion between close/distant in time and similar/dissimilar according to the Euclidian distance. E.g. line 53-54 would become: "The matrix profile [...] that stores the Euclidian distance [...] to its most similar sub-sequence. The similarity is measured using the Euclidian distance [...]."

=========================

Minor Comments

=========================

paragraph starting in l52 - it might be good to specifiy early on how the different sub-sequences are defined. That information only comes in l72 but would be good to have earlier.
l73-76 - in my understanding, applying the joint matrix profile to two timeseries is where the real power and benefit of this method lies. I think this should be highlighted more!
l94-100 - this seems to be a more specific version/repetition of the method section. Think about incorporating it there instead?
l103-112 - is the matrix profile symmetric? If yes, should there not be matrix profile of the two closest sub-sequences not be identical, resulting in two global minima? How do you decide which one to pick as the top motif?
l114-124 - I find this very confusing. Please explain more carefully. It may also be good to have d18O, the matrix profile and the matrix profile index all in one figure. The distances in Table 2 are not the same distances as shown in Fig1, right? So to identify neighbouring motifs you have to perform additional calculations to get the distance between the top motif and all other possible sub-sequences? What is the difference of neighbouring motifs to 1st and 2nd order motifs mentioned in the method section?
l190-207 - same as comment on l114-124: I am again confused. Is the approach for selecting the neighbouring motifs in Figure 12 the same as in Table 2? First you describe in length one way of using R and even discuss you results in the context. But then you say that you are actually using another approach. Also a lot of these two paragraphs seems to repeat itself. Please rewrite more clearly!
=========================

Some Editorial Comments

=========================

l17 - word missing: serves *as* an indirect proxy

l23-25 - hard to read because of too many parentheses, please rephrase

l57 - typos: That *location* is stored in the profile index. [...] vector *that* stores [...].

l74 and many other places - should it be *joint* matrix/motif instead of "join matrix/motif" ?

l98 - the *smallest* value

l134 - remove "Thus,"

l144 - what do you mean by "on the plot"?

l205 - *than* that instead of "that that"

Citation: https://doi.org/10.5194/npg-2024-13-RC2
- AC2: 'Reply on RC2', Susana Barbosa, 09 Jul 2024
  
  We attach a supplementary document with a point-by-point reply to the referee's comments.
  
  Citation: https://doi.org/10.5194/npg-2024-13-AC2

Status: closed

RC1:
'Comment on npg-2024-13', Anonymous Referee #1, 24 Jun 2024

In the manuscript "Characterisation of Dansgaard-Oeschger events in palaeoclimate time series using the Matrix Profile" Susana Barbosa, Maria Eduarda Silva, and Denis-Didier Rousseau use the matrix profile method to analyse isotope time series from the NGRIP ice cores. The aim of the study is not to date the various tipping points in the record but rather to demonstrate the potential of a purely data-driven approach in charaterise the abrupt transition. Using the matrix profile approach allows a quantitative identification of typical transition motifs that are associated with the DO transitions the authors focus on. Moreover, the method allows to measure the similarity between transitions and not surprising the transition motifs for DO-19 and DO-20 are identified as the most similar.
The manuscript is nicely written and the results are given by meaningful figures and tables. Overall, I enjoyed reading the manuscript. The authors give a good summary of the matrix profile method. This section is detailed enough to understand the method applied and the references given to the original works allow a deep-dive into the method if required. delta-O-18 and Ca2+ records are analysed, first by themself (finding self-similarity) and then together (focussing on "cross"-similarity/join matrix profile). The investigations follow a logical structure and in combination show the strength of the method studied. The study is completed by testing the limits and dependencies of the method on only parameter the method depends on and on including an artificial time shift between the delta-O-18 and Ca2+ records.
While the manuscript is a good example of how novel time series analysis methods can be applied in a paleoclimate context, research never ends and consequently I missed two main points in the manuscript. Firstly, the strength of the matrix profile method is to find motifs in time series in a computational efficient way. The authors should make clear how the record under consideration with only 4869 data points requires such an advanced method and why traditional methods are computational not tractable. Second, while the manuscript contains some test demonstrating the stability of the methods and results, strictly speaking there is no consideration given with respect to the statistical significance of the results. While bootstrapping would not make sense in the context of this study, more advanced surrogate data methods, like the Small-shuffle technique (T. Nakamura & M. Small Phys. Rev. E 72, 056216 (2005)), could be used. With such methods one could investigate how destroying for example the short term correlation in the data changes the distance matrix. I understand that such an investigation might well be beyond a simple revision and might by itself be the basis for a future publication.
I also found a small number of typos in the manuscript:

l67: taht -> that

l181: vales -> values

l245: by by -> by

Citation: https://doi.org/10.5194/npg-2024-13-RC1
- AC1: 'Reply on RC1', Susana Barbosa, 09 Jul 2024
  
  We attach a supplementary document with a point-by-point reply to the referee's comments.
  
  Citation: https://doi.org/10.5194/npg-2024-13-AC1
RC2:
'Comment on npg-2024-13', Anonymous Referee #2, 25 Jun 2024

Review of "Characterisation of Dansgaard-Oeschger events in palaeoclimate

time series using the Matrix Profile" by Barbosa et al
Barbosa and colleagues apply the pattern-recognition algorithm called the Matrix Profile on NGRIP ice-core measurements of d18O and Ca+ in order to provide an objective ad automatic characterisation of Dansgaard-Oeschger warming events. The algorithm sucessfully identifies and matches a number of events according to their similarity. The identification of so-called motifs works within one time series as well as across different time series. It is even able to identify corresponding patterns if the compared records are of different length or if the time axis is shifted.
While the method seems to work well with the presented data set, the implications and relevance of the study remain unclear. The discussion of the results remains superficial and very much within the space/jargon of the matrix profile. It does not become clear to me what the method can achieve that could not have been achieved by other means. I outline my major comments below and suggest that these comments need to be addressed before the paper can be considered for publication.

=========================

Major Comments

=========================

1. Relevance/Novelty and physical interpretation ------
- The objective of the study was to "characterise the abrupt transitions, in a purely data-driven manner, based on the shape of the corresponding DO patterns". I have learned a lot about similarity between different DO-events, but the resulting interpretation does not add any new information to what we already new about DO-events. The only physical characterisation is given as "an abrupt transition to warm conditions preceded by approximately stable stadial conditions and followed by a slow return to cold conditions" for d18O and "distinguished by an abrupt decrease in terrestrial dust concentration, followed by a period of stable dust conditions." for Ca+. Both of these statements seem established knowledge and could have been obtained almost purely by eye. I believe the relevance of the study could be greatly improved by giving more physical context and interpretation to the obtained results. I list some example questions below that could help in giving this context:
(1) What is the actual advantage of the method with respect to previous methods? The authors mention that it can be a powerful alternative to "wiggle matching" (see also major comment 2). I can see this, but most of the performed analysis was done within one time series, what is the advantage here?

(2) What do I gain from knowing which events are most similar to each other? Can the information help with stacking or with classification? Here, the authors give a small hint in their conclusion, stating that the identified similarity could be an indication of similar underlying mechanisms. Can this claim be backed up/elaborated upon? And what about the other (shorter) unidentified transitions?

(3) What is the physical interpretation/relevance of an event being a top motif or a neighbouring motif?

(4) What does it imply that the matrix profile identiefies different top motifs in d18O and Ca+?
2. Possible limitations ---------------------------------

I think possible limitations of the method need to be discussed in more detail, especially when it comes to the joint matrix profile. The test data set used here are two records on the same age model from a similar location. These seem very favourable conditions. What if the records have different temporal resolution as is often the case? How would the method be used to synchronise two records if they have different age models? And as I understand it, the method can only be used to synchronise two time series if the manifestation of the events follows a similar pattern. What if there is a phase shift or if the pattern is not as pronounced as in the Greenland ice cores?
Also, as I understand from the discussion, the window size does not seem to have a big effect on the identification of main motifs in the range of 2500-3500 years. But what about the smaller window sizes and shorter DO-events? Currently only long events are captured and shorter events (e.g. events 3-7, 9 and 10) are probabaly ignored because of the chosen window length. Where is the lower bound for meaningful results?
3. Clarity ----------------------------------------------

In parts, it is difficult to follow the method description and interpretation, especially because the word "close" is used for being similar and for being close in time. I suggest to use "similarity" instead of "distance" thoughout the text to avoid confusion between close/distant in time and similar/dissimilar according to the Euclidian distance. E.g. line 53-54 would become: "The matrix profile [...] that stores the Euclidian distance [...] to its most similar sub-sequence. The similarity is measured using the Euclidian distance [...]."

=========================

Minor Comments

=========================

paragraph starting in l52 - it might be good to specifiy early on how the different sub-sequences are defined. That information only comes in l72 but would be good to have earlier.
l73-76 - in my understanding, applying the joint matrix profile to two timeseries is where the real power and benefit of this method lies. I think this should be highlighted more!
l94-100 - this seems to be a more specific version/repetition of the method section. Think about incorporating it there instead?
l103-112 - is the matrix profile symmetric? If yes, should there not be matrix profile of the two closest sub-sequences not be identical, resulting in two global minima? How do you decide which one to pick as the top motif?
l114-124 - I find this very confusing. Please explain more carefully. It may also be good to have d18O, the matrix profile and the matrix profile index all in one figure. The distances in Table 2 are not the same distances as shown in Fig1, right? So to identify neighbouring motifs you have to perform additional calculations to get the distance between the top motif and all other possible sub-sequences? What is the difference of neighbouring motifs to 1st and 2nd order motifs mentioned in the method section?
l190-207 - same as comment on l114-124: I am again confused. Is the approach for selecting the neighbouring motifs in Figure 12 the same as in Table 2? First you describe in length one way of using R and even discuss you results in the context. But then you say that you are actually using another approach. Also a lot of these two paragraphs seems to repeat itself. Please rewrite more clearly!
=========================

Some Editorial Comments

=========================

l17 - word missing: serves *as* an indirect proxy

l23-25 - hard to read because of too many parentheses, please rephrase

l57 - typos: That *location* is stored in the profile index. [...] vector *that* stores [...].

l74 and many other places - should it be *joint* matrix/motif instead of "join matrix/motif" ?

l98 - the *smallest* value

l134 - remove "Thus,"

l144 - what do you mean by "on the plot"?

l205 - *than* that instead of "that that"

Citation: https://doi.org/10.5194/npg-2024-13-RC2
- AC2: 'Reply on RC2', Susana Barbosa, 09 Jul 2024
  
  We attach a supplementary document with a point-by-point reply to the referee's comments.
  
  Citation: https://doi.org/10.5194/npg-2024-13-AC2

Susana Barbosa, Maria Eduarda Silva, and Denis-Didier Rousseau

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Short summary

The characterisation of abrupt transitions in palaeoclimate records allows the understanding of millennial climate variability and of potential tipping points in the context of current climate change. In our study an algorithmic method, the matrix profile, is employed to characterise abrupt warmings designated as Dansgaard-Oeschger (DO) events and to identify the most similar transitions in the palaeoclimate time series.


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