Bifurcations and tipping points (TPs) are an important part of the Earth system’s behavior. These critical points represent thresholds at which small changes in the system’s parameters or in the forcing abruptly switch it from one state or type of behavior to another. Current concern with TPs is largely due to the potential of slow anthropogenic forcing to bring about abrupt, and possibly irreversible, change to the physical climate system and impacted ecosystems. Paleoclimate proxy records have been shown to contain abrupt transitions, or “jumps,” which may represent former instances of such dramatic climate change events. These transitions can provide valuable information for identifying critical TPs in current and future climate evolution. Here, we present a robust methodology for detecting abrupt transitions in proxy records that is applied to ice core and speleothem records of the last climate cycle. This methodology is based on the nonparametric Kolmogorov–Smirnov (KS) test for the equality, or not, of the probability distributions associated with two samples drawn from a time series, before and after any potential jump. To improve the detection of abrupt transitions in proxy records, the KS test is augmented by several other criteria and it is compared with recurrence analysis. The augmented KS test results show substantial skill when compared with more subjective criteria for jump detection. This test can also usefully complement recurrence analysis and improve upon certain aspects of its results.
REFERENCES
1.
M.
Alho
, C. S.
Wedlund
, H.
Nilsson
, E.
Kallio
, R.
Jarvinen
, and T.
Pulkkinen
, “Hybrid modeling of cometary plasma environments—II. Remote-sensing of a cometary bow shock
,” Astron. Astrophys.
630
, A45
(2019
). 2.
P.
Ashwin
, S.
Wieczorek
, R.
Vitolo
, and P.
Cox
, “Tipping points in open systems: Bifurcation, noise-induced and rate-dependent examples in the climate system
,” Philos. Trans. R. Soc. A
370
(1962
), 1166
–1184
(2012
). 3.
W.
Bagniewski
, K. J.
Meissner
, and L.
Menviel
, “Exploring the oxygen isotope fingerprint of Dansgaard–Oeschger variability and Heinrich events
,” Quat. Sci. Rev.
159
, 1
–14
(2017
). 4.
W.
Bagniewski
, D.-D.
Rousseau
, and M.
Ghil
, “PaleoJump database for research on rapid climate transitions,” EGU General Assembly, EGU21-9968, 2021.5.
S.
Barker
, J.
Chen
, X.
Gong
, L.
Jonkers
, G.
Knorr
, and D.
Thornalley
, “Icebergs not the trigger for North Atlantic cold events
,” Nature
520
(7547
), 333
–336
(2015
). 6.
C.
Beaulieu
, J.
Chen
, and J. L.
Sarmiento
, “Change-point analysis as a tool to detect abrupt climate variations
,” Philos. Trans. R. Soc. A
370
(1962
), 1228
–1249
(2012
). 7.
N.
Boers
, M.
Ghil
, and D.-D.
Rousseau
, “Ocean circulation, ice shelf, and sea ice interactions explain Dansgaard–Oeschger cycles
,” Proc. Natl. Acad. Sci. U.S.A.
115
(47
), E11005
–E11014
(2018
). 8.
N.
Boers
, B.
Goswami
, and M.
Ghil
, “A complete representation of uncertainties in layer-counted paleoclimatic archives
,” Clim. Past
13
(9
), 1169
–1180
(2017
). 9.
W. S.
Broecker
, D. M.
Peteet
, and D.
Rind
, “Does the ocean–atmosphere system have more than one stable mode of operation?
,” Nature
315
(6014
), 21
–26
(1985
). 10.
M. A.
Cane
, “A role for the tropical Pacific
,” Science
282
(5386
), 59
–61
(1998
). 11.
E.
Carlstein
et al., “Nonparametric change-point estimation
,” Ann. Stat.
16
(1
), 188
–197
(1988
). 12.
H.
Cheng
, R. L.
Edwards
, A.
Sinha
, C.
Spötl
, L.
Yi
, S.
Chen
, M.
Kelly
, G.
Kathayat
, X.
Wang
, X.
Li
et al., “The Asian monsoon over the past 640 000 years and ice age terminations
,” Nature
534
(7609
), 640
–646
(2016
). 13.
A. C.
Clement
, M. A.
Cane
, and R.
Seager
, “An orbitally driven tropical source for abrupt climate change
,” J. Clim.
14
(11
), 2369
–2375
(2001
). 14.
G. W.
Cobb
, “The problem of the Nile: Conditional solution to a changepoint problem
,” Biometrika
65
(2
), 243
–251
(1978
). 15.
16.
W.
Dansgaard
, H.
Clausen
, N.
Gundestrup
, C.
Hammer
, S.
Johnsen
, P.
Kristinsdottir
, and N.
Reeh
, “A new Greenland deep ice core
,” Science
218
(4579
), 1273
–1277
(1982
). 17.
W.
Dansgaard
, S. J.
Johnsen
, H. B.
Clausen
, D.
Dahl-Jensen
, N.
Gundestrup
, C.
Hammer
, C.
Hvidberg
, J.
Steffensen
, A.
Sveinbjörnsdottir
, J.
Jouzel
et al., “Evidence for general instability of past climate from a 250-kyr ice-core record
,” Nature
364
(6434
), 218
–220
(1993
). 18.
J. F.
Donges
, R. V.
Donner
, M. H.
Trauth
, N.
Marwan
, H. -J.
Schellnhuber
, and J.
Kurths
, “Nonlinear detection of paleoclimate-variability transitions possibly related to human evolution
,” Proc. Natl. Acad. Sci. U.S.A.
108
(51
), 20422
–20427
(2011
). 19.
J.-P.
Eckmann
, S. O.
Kamphorst
, and D.
Ruelle
, “Recurrence plots of dynamical systems
,” Europhys. Lett.
4
(9
), 973
–977
(1987
). 20.
B.
Efron
, “Nonparametric estimates of standard error: The jackknife, the bootstrap and other methods
,” Biometrika
68
(3
), 589
–599
(1981
). 21.
B.
Efron
and R.
Tibshirani
, “Bootstrap methods for standard errors, confidence intervals, and other measures of statistical accuracy
,” Stat. Sci.
1
(1
), 54
–75
(1986
).22.
D.
Eroglu
, N.
Marwan
, S.
Prasad
, and J.
Kurths
, “Finding recurrence networks’ threshold adaptively for a specific time series
,” Nonlinear Process. Geophys.
21
(6
), 1085
–1092
(2014
). 23.
D.
Eroglu
, F. H.
McRobie
, I.
Ozken
, T.
Stemler
, K.-H.
Wyrwoll
, S. F.
Breitenbach
, N.
Marwan
, and J.
Kurths
, “See-saw relationship of the Holocene East Asian-Australian summer monsoon
,” Nat. Commun.
7
, 12929
(2016
).24.
T.
Fawcett
, “An introduction to ROC analysis
,” Pattern Recognit. Lett.
27
(8
), 861
–874
(2006
). 25.
26.
C.
Gallagher
, R.
Lund
, and M.
Robbins
, “Changepoint detection in climate time series with long-term trends
,” J. Clim.
26
(14
), 4994
–5006
(2013
). 27.
A.
Ganopolski
and S.
Rahmstorf
, “Rapid changes of glacial climate simulated in a coupled climate model
,” Nature
409
(6817
), 153
–158
(2001
). 28.
M.
Ghil
, “A century of nonlinearity in the geosciences
,” Earth Space Sci.
6
, 1007
–1042
(2019
). 29.
M.
Ghil
and S.
Childress
, Topics in Geophysical Fluid Dynamics: Atmospheric Dynamics, Dynamo Theory, and Climate Dynamics
(Springer Science+Business Media
, Berlin
, 1987
), Reissued as an eBook in 2012.30.
M.
Ghil
and V.
Lucarini
, “The physics of climate variability and climate change
,” Rev. Mod. Phys.
92
(3
), 035002
(2020
). 31.
B.
Goswami
, N.
Boers
, A.
Rheinwalt
, N.
Marwan
, J.
Heitzig
, S. F.
Breitenbach
, and J.
Kurths
, “Abrupt transitions in time series with uncertainties
,” Nat. Commun.
9
(1
), 1
–10
(2018
). 32.
J.
Griffié
, L.
Boelen
, G.
Burn
, A. P.
Cope
, and D. M.
Owen
, “Topographic prominence as a method for cluster identification in single-molecule localisation data
,” J. Biophoton.
8
(11-12
), 925
–934
(2015
). 33.
T.
Hastie
, R.
Tibshirani
, and J.
Friedman
, The Elements of Statistical Learning: Data Mining, Inference, and Prediction
(Springer Science+Business Media
, 2009
).34.
H.
Heinrich
, “Origin and consequences of cyclic ice rafting in the Northeast Atlantic Ocean during the past 130 000 years
,” Quat. Res.
29
(2
), 142
–152
(1988
). 35.
A.
Helman
, The Finest Peaks: Prominence and Other Mountain Measures
(Trafford Publishing
, 2005
).36.
C.
Huber
, M.
Leuenberger
, R.
Spahni
, J.
Flückiger
, J.
Schwander
, T. F.
Stocker
, S.
Johnsen
, A.
Landais
, and J.
Jouzel
, “Isotope calibrated Greenland temperature record over Marine Isotope stage 3 and its relation to CH
,” Earth Planet. Sci. Lett.
243
(3–4
), 504
–519
(2006
). 37.
S.
Johnsen
, H.
Clausen
, W.
Dansgaard
, K.
Fuhrer
, N.
Gundestrup
, C.
Hammer
, P.
Iversen
, J.
Jouzel
, B.
Stauffer
et al., “Irregular glacial interstadials recorded in a new Greenland ice core
,” Nature
359
(6393
), 311
–313
(1992
). 38.
A.
Kolmogorov
, “Sulla determinazione empirica di una legge di distribuzione
,” Giornale IIA
4
, 83
–91
(1933
).39.
C.
Kuehn
, “A mathematical framework for critical transitions: Bifurcations, fast-slow systems and stochastic dynamics
,” Physica D
240
(12
), 1020
–1035
(2011
). 40.
T. M.
Lenton
, H.
Held
, E.
Kriegler
, J. W.
Hall
, W.
Lucht
, S.
Rahmstorf
, and H. J.
Schellnhuber
, “Tipping elements in the Earth’s climate system
,” Proc. Natl. Acad. Sci. U.S.A.
105
(6
), 1786
–1793
(2008
). 41.
L. E.
Lisiecki
and M. E.
Raymo
, “A Pliocene-Pleistocene stack of 57 globally distributed benthic 18O records
,” Paleoceanography
20
(1
), PA1003
, (2005
). 42.
L. E.
Lisiecki
and M. E.
Raymo
, “Plio–Pleistocene climate evolution: Trends and transitions in glacial cycle dynamics
,” Quat. Sci. Rev.
26
(1-2
), 56
–69
(2007
). 43.
D.
MacAyeal
, “Binge/purge oscillations of the Laurentide Ice Sheet as a cause of the North Atlantic’s Heinrich events
,” Paleoceanography
8
(6
), 775
–784
, (1993
). 44.
B. R.
Markle
, E. J.
Steig
, C.
Buizert
, S. W.
Schoenemann
, C. M.
Bitz
, T.
Fudge
, J. B.
Pedro
, Q.
Ding
, T. R.
Jones
, J. W.
White
et al., “Global atmospheric teleconnections during Dansgaard–Oeschger events
,” Nat. Geosci.
10
(1
), 36
–40
(2017
). 45.
N.
Marwan
, M. C.
Romano
, M.
Thiel
, and J.
Kurths
, “Recurrence plots for the analysis of complex systems
,” Phys. Rep.
438
(5-6
), 237
–329
(2007
). 46.
N.
Marwan
, S.
Schinkel
, and J.
Kurths
, “Recurrence plots 25 years later—Gaining confidence in dynamical transitions
,” Europhys. Lett.
101
(2
), 20007
(2013
). 47.
N.
Marwan
, M.
Thiel
, and N. R.
Nowaczyk
, “Cross recurrence plot based synchronization of time series
,” Nonlinear Process. Geophys.
9
(3/4
), 325
–331
(2002
). 48.
S. J.
Mason
and N. E.
Graham
, “Areas beneath the relative operating characteristics (ROC) and relative operating levels (ROL) curves: Statistical significance and interpretation
,” Q. J. R. Meteorol. Soc.
128
(584
), 2145
–2166
(2002
). 49.
F. J.
Massey
, Jr., “The Kolmogorov-Smirnov test for goodness of fit
,” J. Am. Stat. Assoc.
46
(253
), 68
–78
(1951
). 50.
L.
Menviel
, A.
Timmermann
, T.
Friedrich
, and M.
England
, “Hindcasting the continuum of Dansgaard–Oeschger variability: Mechanisms, patterns and timing
,” Clim. Past
10
(1
), 63
–77
(2014
). 51.
G. M.
Mindlin
and R.
Gilmore
, “Topological analysis and synthesis of chaotic time series
,” Physica D
58
(1-4
), 229
–242
(1992
). 52.
J. M.
Mitchell
, Jr., “An overview of climatic variability and its causal mechanisms
,” Quat. Res.
6
(4
), 481
–493
(1976
). 53.
J. M.
Murphy
, D. M.
Berwick
, M. C.
Weinstein
, J. F.
Borus
, S. H.
Budman
, and G. L.
Klerman
, “Performance of screening and diagnostic tests: Application of receiver operating characteristic analysis
,” Arch. Gen. Psychiatry
44
(6
), 550
–555
(1987
). 54.
I.
Ozken
, D.
Eroglu
, T.
Stemler
, N.
Marwan
, G. B.
Bagci
, and J.
Kurths
, “Transformation-cost time-series method for analyzing irregularly sampled data
,” Phys. Rev. E
91
(6
), 062911
(2015
). 55.
F.
Parrenin
, J.-M.
Barnola
, J.
Beer
, T.
Blunier
, E.
Castellano
, J.
Chappellaz
, G.
Dreyfus
, H.
Fischer
, S.
Fujita
, J.
Jouzel
, K.
Kawamura
, B.
Lemieux-Dudon
, L.
Loulergue
, V.
Masson-Delmotte
, B.
Narcisi
, J.-R.
Petit
, G.
Raisbeck
, D.
Raynaud
, U.
Ruth
, J.
Schwander
, M.
Severi
, R.
Spahni
, J. P.
Steffensen
, A.
Svensson
, R.
Udisti
, C.
Waelbroeck
, and E.
Wolff
, “The EDC3 chronology for the EPICA Dome C ice core
,” Clim. Past
3
(3
), 485
–497
(2007
). 56.
F.
Pearce
, With Speed and Violence: Why Scientists Fear Tipping Points in Climate Change
(Beacon Press
, 2007
).57.
W. W. T. G.
Peterson
, T.
Birdsall
, and W.
Fox
, “The theory of signal detectability
,” Trans. IRE Prof. Group Inf. Theory
4
(4
), 171
–212
(1954
). 58.
S. O.
Rasmussen
, M.
Bigler
, S. P.
Blockley
, T.
Blunier
, S. L.
Buchardt
, H. B.
Clausen
, I.
Cvijanovic
, D.
Dahl-Jensen
, S. J.
Johnsen
, H.
Fischer
et al., “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
,” Quat. Sci. Rev.
106
, 14
–28
(2014
). 59.
J.
Reeves
, J.
Chen
, X. L.
Wang
, R.
Lund
, and Q. Q.
Lu
, “A review and comparison of changepoint detection techniques for climate data
,” J. Appl. Meteorol. Climatol.
46
(6
), 900
–915
(2007
). 60.
D.-D.
Rousseau
, W.
Bagniewski
, and M.
Ghil
, “Abrupt climate changes and the astronomical theory,” Clim. Past, (2021
).61.
M.
Scheffer
, J.
Bascompte
, W. A.
Brock
, V.
Brovkin
, S. R.
Carpenter
, V.
Dakos
, H.
Held
, E. H.
Van Nes
, M.
Rietkerk
, and G.
Sugihara
, “Early-warning signals for critical transitions
,” Nature
461
(7260
), 53
–59
(2009
). 62.
B.
Schölkopf
, A. J.
Smola
, F.
Bach
et al., Learning With Kernels: Support Vector Machines, Regularization, Optimization, and Beyond
(MIT Press
, 2002
).63.
R.
Seager
and D. S.
Battisti
, “Challenges to our understanding of the general circulation: Abrupt climate change
,” Global Circ. Atmos.
331
, 371
(2007
).64.
J. P.
Severinghaus
, T.
Sowers
, E. J.
Brook
, R. B.
Alley
, and M. L.
Bender
, “Timing of abrupt climate change at the end of the Younger Dryas interval from thermally fractionated gases in polar ice
,” Nature
391
(6663
), 141
–146
(1998
). 65.
A.
Singh
, M. A.
Papa
, H.-B.
Eggenstein
, and S.
Walsh
, “Adaptive clustering procedure for continuous gravitational wave searches
,” Phys. Rev. D
96
(8
), 082003
(2017
). 66.
N.
Smirnov
, “Ob uklonenijah empiriceskoi krivoi raspredelenija
,” Recl. Math. Mat. Sbornik (N.S.)
6
(48
), 3
–26
(1939
).67.
68.
M.
Thiel
, M. C.
Romano
, J.
Kurths
, R.
Meucci
, E.
Allaria
, and F. T.
Arecchi
, “Influence of observational noise on the recurrence quantification analysis
,” Physica D
171
(3
), 138
–152
(2002
). 69.
M. H.
Trauth
, A.
Asrat
, W.
Duesing
, V.
Foerster
, K. H.
Kraemer
, N.
Marwan
, M. A.
Maslin
, and F.
Schaebitz
, “Classifying past climate change in the Chew Bahir Basin, Southern Ethiopia, using recurrence quantification analysis
,” Clim. Dyn.
53
(5
), 2557
–2572
(2019
). 70.
C.
Truong
, L.
Oudre
, and N.
Vayatis
, “Selective review of offline change point detection methods
,” Signal Process.
167
, 107299
(2020
). 71.
J.
Verbesselt
, R.
Hyndman
, G.
Newnham
, and D.
Culvenor
, “Detecting trend and seasonal changes in satellite image time series
,” Remote Sens. Environ.
114
(1
), 106
–115
(2010
). 72.
Y.
Wang
, H.
Cheng
, R. L.
Edwards
, X.
Kong
, X.
Shao
, S.
Chen
, J.
Wu
, X.
Jiang
, X.
Wang
, and Z.
An
, “Millennial-and orbital-scale changes in the East Asian monsoon over the past 224 000 years
,” Nature
451
(7182
), 1090
–1093
(2008
). 73.
Y.-J.
Wang
, H.
Cheng
, R. L.
Edwards
, Z.
An
, J.
Wu
, C.-C.
Shen
, and J. A.
Dorale
, “A high-resolution absolute-dated late Pleistocene monsoon record from Hulu Cave, China
,” Science
294
(5550
), 2345
–2348
(2001
). 74.
T.
Westerhold
, N.
Marwan
, A. J.
Drury
, D.
Liebrand
, C.
Agnini
, E.
Anagnostou
, J. S.
Barnet
, S. M.
Bohaty
, D.
De Vleeschouwer
, F.
Florindo
et al., “An astronomically dated record of Earth’s climate and its predictability over the last 66 million years
,” Science
369
(6509
), 1383
–1387
(2020
). 75.
C.
Wunsch
, “Abrupt climate change: An alternative view
,” Quat. Res.
65
(2
), 191
–203
(2006
). 76.
W. J.
Youden
, “Index for rating diagnostic tests
,” Cancer
3
(1
), 32
–35
(1950
). 77.
D.
Yuan
, H.
Cheng
, R. L.
Edwards
, C. A.
Dykoski
, M. J.
Kelly
, M.
Zhang
, J.
Qing
, Y.
Lin
, Y.
Wang
, J.
Wu
et al., “Timing, duration, and transitions of the last interglacial Asian monsoon
,” Science
304
(5670
), 575
–578
(2004
). 78.
J. P.
Zbilut
and C. L.
Webber Jr
, “Embeddings and delays as derived from quantification of recurrence plots
,” Phys. Lett. A
171
(3-4
), 199
–203
(1992
). 79.
X.
Zhang
, G.
Knorr
, G.
Lohmann
, and S.
Barker
, “Abrupt North Atlantic circulation changes in response to gradual CO2 forcing in a glacial climate state
,” Nat. Geosci.
10
(7
), 518
–523
(2017
). © 2021 Author(s). Published under an exclusive license by AIP Publishing.
2021
Author(s)
You do not currently have access to this content.
