Palaeoclimate dynamics : a voyage through scales

Transcription

1 Palaeoclimate dynamics : a voyage through scales Michel Crucifix, Takahito Mitsui, Guillaume Lenoir EGU General Assembly April 2015 EGU

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3 other is that the small control eccentricthe last interglacial on the basis of these curvestests have ranged from 80,000 to ty exerts on the total annual insolation is Time-Domain 180,000 years ago (22). significant climatically (59). The second and more critical problem in testing the orbital theory has been the An apparently independent confirmaassumptions. frequencyuncertaintyas of with geologicalthe chronology. Until the of recently inaccuracy dating ion of our conclusions about spectral we start here with the asin the Variations Earth's Orbit:domain test, methods limited the interval over which peaks b and c can be found in reports of sumption that a meaningful test could be made to the systhe radiation-climate last 150,000 years. Hence the most conpacemaker of the Ice Ages limatic periodicities in the 8180 record tem is time-invariant and linear. vincing arguments advanced in support One of the orbital to date theory beena losely For matching thosemajor of obliquity well-knownbased and have characteristic ofhave such 500,000 years, climatic changes on the ages of 80,000, 105,000, and sysrecession (14, variations 16, 20, 26, 69). However, tem forms 125,000 the basis years obtained for coral terraces for our time-domain followed in obliquity and precession. and on New first on Barbados later (15) he time scale used in these investiga- tests: any Guinea frequency component (23) and Hawaii (24). These struc-of the J. D. Hays, John Imbrie, N. J. Shackleton For more than a century the cause of fluctuations in the Pleistocene ice sheets has remained an intriguing and unsolved scientific mystery. Interest in this problem has generated a number of possible explanations (1, 2). One group of theories invokes factors external to the climate system, including variations in the output of the sun, or the amount of solar energy reaching the earth caused by changing concentrations of interstellar dust (3); the seasonal and latitudinal disu 1. of incoming radiation caused by tribution c changes in the earth's orbital geometry to the volcanic dust content of the atmo(4); sphere (5); and the earth's magnetic field (6). Other theories are based on internal oo elements of the system believed to have response times sufficiently long to yield fluctuations in the range 104 to 106 years. Such features include the growth and ZCI decay of ice sheets (7), the surging of the 0 Antarctic ice sheet (8); the ice cover of the Arctic Ocean (9); the distribution of -carbon dioxide between atmosphere and ocean (10); and the deep circulation of the ocean (11). Additionally, it has been argued that as an almost intransitive system, climate could alternate between different states on an appropriate time scale without the intervention of any exstimulus16 or internal time constant ternal Thursday April 15 (12). b-3 hypothesis has been formulated so as to predict the frequencies of major Pleistocene glacial fluctuations. Thus it is the only explanation that can be tested geologically by determining what these frequencies are. Our main purpose here is to make such a test. Previous work has provided strong suggestive evidence that orbital changes induced climatic change (13-20). However, two primary obstacles have led to continuing controversy. The first is the uncertainty in identifying which aspects of the radiation budget are critical to climatic change. Depending on the latitude and season considered most significant, grossly different climatic records can be predicted from the same astronomical data. Milankovitch (4) followed Koppen and Wegener's (21) view that the distribution of summer insolation (solar radiation received at the top of the atmosphere) at 65 N should be critical to the growth and decay of ice sheets. Hence the curve of summer insolation at this latitude has been taken by many as a prediction of the world climate curve. Kukla (19) has pointed out weaknesses in Koppen and Wegener's proposal and has suggested that the critical time may be September and October in both hemispheres. However, several other curves have been supported by plausible argu- tures record episodes of high sea level (and therefore low ice volume) at times predicted by the Milankovitch theory. Unfortunately, dates for older terraces are too uncertain to yield a definitive test (25). More climatic information is provided by the continuous records from deep-sea cores, especially the oxygen isotope record obtained by Emiliani (26). However, the quasi-periodic nature of both the isotopic and insolation curves, and the uncertain chronology of the older geologic records, have combined to render plausible different astronomical interpretations of the same geologic data (13, 14, 17, 27). Strategy All versions of the orbital hypothesis of climatic change predict that the obliquity of the earth's axis (with a period of about 41,000 years) and the precession of the equinoxes (period of about 21,000 years) are the underlying, controlling variables that influence climate through their impact on planetary insolation. Most of these hypotheses single out The authors are all members of the CLIMAP project. J. D. Hays is professor of geology at Columbia University, New York 10027, and is on the staff of the Lamont-Doherty Geological Observatory, Palisades, New York John Imbrie is Henry L. Doherty professor of oceanography, Brown University, Providence, Rhode Island N. J. Shackleton is on the staff of the Sub-department of Quaterna- Downloaded from on March 21, 2007 approximately 100,000 years (Table 5). Downloaded from on March 21, 2007 ly (68) to changes in the geographic and seasonal distribution of insolation. An-

4 approximately 100,000 years (Table 5). J. D. Hays, John Imbrie, N. J. Shackleton For more than a century the cause of fluctuations in the Pleistocene ice sheets has remained an intriguing and unsolved scientific mystery. Interest in this problem has generated a number of possible explanations (1, 2). One group of theories invokes factors external to the climate system, including variations in the output of the sun, or the amount of solar energy reaching the earth caused by changing concentrations of interstellar dust (3); the seasonal and latitudinal disu 1. of incoming radiation caused by tribution c changes in the earth's orbital geometry to the volcanic dust content of the atmo(4); sphere (5); and the earth's magnetic field (6). Other theories are based on internal oo elements of the system believed to have response times sufficiently long to yield fluctuations in the range 104 to 106 years. Such features include the growth and ZCI decay of ice sheets (7), the surging of the 0 Antarctic ice sheet (8); the ice cover of the Arctic Ocean (9); the distribution of -carbon dioxide between atmosphere and ocean (10); and the deep circulation of the ocean (11). Additionally, it has been argued that as an almost intransitive system, climate could alternate between different states on an appropriate time scale without the intervention of any exstimulus16 or internal time constant ternal Thursday April 15 (12). b-3 tures record episodes of high sea level (and therefore low ice volume) at times predicted by the Milankovitch theory. Unfortunately, dates for older terraces are too uncertain to yield a definitive test Downloaded from on March 21, 2007 other is that the small control eccentricthe last interglacial on the basis of these curvestests have ranged from 80,000 to ty exerts on the total annual insolation is Time-Domain 180,000 years ago (22). significant climatically (59). The second and more critical problem in testing the orbital theory has been the An apparently independent confirmaassumptions. frequencyuncertaintyas of with geologicalthe chronology. Until the of recently inaccuracy dating ion of our conclusions about spectral we start here with the asin the Variations Earth's Orbit:domain test, methods limited the interval over which peaks b and c can be found in reports of sumption that a meaningful test could be made to the systhe radiation-climate last 150,000 years. Hence the most conpacemaker of the Ice Ages limatic periodicities in the 8180 record tem is time-invariant and linear. vincing arguments advanced in support One of the orbital to date theory beena losely For matching thosemajor of obliquity well-knownbased and have characteristic ofhave such 500,000 years, climatic changes on the ages of 80,000, 105,000, and sysrecession (14, variations 16, 20, 26, 69). However, tem forms 125,000 the basis years obtained for coral terraces for our time-domain followed in obliquity and precession. and on NewMitchell first on Barbados later (15) J. M. he time scale used in these investiga- tests: any Guinea frequency component (23) and Hawaii (24). These struc-of the Downloaded from on March 21, 2007 ly (68) to changes in the geographic and seasonal distribution of insolation. An- I I I I. MO 1DAY 3.HR hypothesis has been formulated so as to predict the frequencies of major Pleisto- (25). cene glacial fluctuations. Thus it is the More climatic information is provided only explanation that can be tested geo- by the continuous records from deep-sea logically by determining what these fre- cores, especially the oxygen isotope recquencies are. Our main purpose here is ord obtained by Emiliani (26). However, to make such a test. the quasi-periodic nature of both the isoprevious work has provided strong topic and insolation curves, and the unsuggestive evidence that orbital changes certain chronology of the older geologic induced climatic change (13-20). How- records, have combined to render plauever, two primary obstacles have led to sible different astronomical interprecontinuing controversy. The first is the tations of the same geologic data (13, 14, uncertainty in identifying which aspects 17, 27). of the radiation budget are critical to climatic change. Depending on the latitude and season considered most signifi- Strategy cant, grossly different climatic records can be predicted from the same astroall versions of the orbital hypothesis 1O nomical data. Milankovitch (4) followed of climatic change predict that the obliqphtiod IN YEARS Koppen and Wegener's (21) view thatfig. uity of the ofearth's (withof aclimate periodoverof all periods (wavelengths) of variation, from those comparable to the age of the Earth 1. Estimate relative axis variance about one hour.41,000 Stippledyears) area and represents total varianceofon all spatial scales of variation. the distribution of summer insolation (sothe precession about Dashed curves in lower part of the figure indicate the tributions to the total variance from processes characterized spatial scales less than those indicated (in kilometers). Strictly periodic componen lar radiation received at the top of the the equinoxes (period of about width. Solidby triangles of variation are represented by spikes of arbitrary 21,000 indicate scaling relationship between the spikes and the amplitude of ot atmosphere) at 65 N should be critical features to years) are the(seeunderlying, controlling of the spectrum text). the growth and decay of ice sheets. variables that influence climate through Hence the curve of summer insolation at their impact on planetary insolation. this latitude has been taken by many as a Most of these hypotheses single out prediction of the world climate curve. Kukla (19) has pointed out weaknesses The authors are all members of the CLIMAP J. D. Hays is professor of geology at Columin Koppen and Wegener's proposal and project. bia University, New York 10027, and is on the staff has suggested that the critical time may of the Lamont-Doherty Geological Observatory, Palisades, New York John Imbrie is Henry L. be September and October in both hemi- Doherty professor of oceanography, Brown Universpheres. However, several other curves sity, Providence, Rhode Island N. J. Shackleis ton on the staff of the Sub-department of Quaternahave been supported by plausible argu-

5 approximately 100,000 years (Table 5). J. D. Hays, John Imbrie, N. J. Shackleton tures record episodes of high sea level (and therefore low ice volume) at times predicted by the Milankovitch theory. Unfortunately, dates for older terraces are too uncertain to yield a definitive test Downloaded from on March 21, 2007 other is that the small control eccentricthe last interglacial on the basis of these curvestests have ranged from 80,000 to ty exerts on the total annual insolation is Time-Domain 180,000 years ago (22). significant climatically (59). The second and more critical problem in testing the orbital theory has been the An apparently independent confirmaassumptions. frequencyuncertaintyas of with geologicalthe chronology. Until the of recently inaccuracy dating ion of our conclusions about spectral we start here with the asin the Variations Earth's Orbit:domain test, methods limited the interval over which peaks b and c can be found in reports of sumption that a meaningful test could be made to the systhe radiation-climate last 150,000 years. Hence the most conpacemaker of the Ice Ages limatic periodicities in the 8180 record tem is time-invariant and linear. vincing arguments advanced in support One of the orbital to date theory beena losely For matching thosemajor of obliquity well-knownbased and have characteristic ofhave such 500,000 years, climatic changes on the ages of 80,000, 105,000, and sysrecession (14, variations 16, 20, 26, 69). However, tem forms 125,000 the basis years obtained for coral terraces for our time-domain followed in obliquity and precession. and on NewMitchell first on Barbados later (15) J. M. he time scale used in these investiga- tests: any Guinea frequency component (23) and Hawaii (24). These struc-of the Downloaded from on March 21, 2007 ly (68) to changes in the geographic and seasonal distribution of insolation. An- I I I I. MO 1DAY 3.HR For more than a century the cause of hypothesis has been formulated so as to fluctuations in the Pleistocene ice sheets predict the frequencies of major Pleisto- (25). has remained an intriguing and unsolved cene glacial fluctuations. Thus it is the More climatic information is provided scientific mystery. Interest in this prob- only explanation that can be tested geo- by the continuous records from deep-sea lem has generated a number of possible logically by determining what these fre- cores, especially the oxygen isotope recexplanations (1, 2). One group of theo- quencies are. Our main purpose here is ord obtained by Emiliani (26). However, ries invokes factors external to the cli- to make such a test. the quasi-periodic nature of both the isomate system, including variations in the Previous work has provided strong topic and insolation curves, and the unoutput of the sun, or the amount of solar suggestive evidence that orbital changes certain chronology of the older geologic energy reaching the earth caused by induced climatic change (13-20). How- records, have combined to render plauchanging concentrations of interstellar ever, two primary obstacles have led to sible different astronomical interpredust (3); the seasonal and latitudinal dis- continuing controversy. The first is the tations of the same geologic data (13, 14, U 1. of incoming radiation caused by uncertainty in identifying which aspects 17, 27). tribution c changes in the earth's orbital geometry of the radiation budget are critical to to the volcanic dust content of the atmoclimatic change. Depending on the lati(4); sphere (5); and the earth's magnetic field tude and season considered most signifi- Strategy (6). Other theories are based on internal cant, grossly different climatic records oo elements of the system believed to have can be predicted from the same astroall versions of the orbital hypothesis 1O response times sufficiently long to yield nomical data. Milankovitch (4) followed of climatic change predict that the obliqphtiod IN YEARS fluctuations in the range 104 to 106 years. Koppen and Wegener's (21) view thatfig. uity of the ofearth's (withof aclimate periodoverof all periods (wavelengths) of variation, from those comparable to the age of the Earth 1. Estimate relative axis variance Such about one hour.41,000 Stippledyears) area and represents total varianceofon all spatial scales of variation. features include the growth and the distribution of summer insolation (sothe precession about Dashed curves in lower part of the figure indicate the ZCI tributions to the total variance from processes characterized spatial scales less than those indicated (in kilometers). Strictly periodic componen decay of ice sheets (7), the surging of the lar radiation received at the top of the 0 the equinoxes (period of about width. Solidby triangles of variation are represented by spikes of arbitrary 21,000 indicate scaling relationship between the spikes and the amplitude of ot Antarctic ice sheet (8); the ice coverstochastic of atmosphere) at 65 N should be critical features to years) are the(seeunderlying, controlling of the spectrum text). climate models the Arctic Ocean (9); the distribution of the growth and decay of ice sheets. variables that influence climate through -carbon dioxide between atmosphere and Hence the curve of summer insolation at their impact on planetary insolation. Theory ocean (10); and the deep circulation of this Part latitudei.has been taken by many as a Most of these hypotheses single out the ocean (11). Additionally, it has been prediction of the world climate curve. argued that as an almost intransitive Kukla (19) has pointed out weaknesses The authors are all members of the CLIMAP By K.alternate HASSELMANN, fiir Meteurologie, Hamburg, J. D. Hays is professor of geology at Columproject.FRQ! in Koppen and Wegener's between Mm-Phnck-I?znstitut$~& proposal and system, climate could bia University, New York 10027, and is on the staff different states on an appropriate time has suggested that the critical time may of the Lamont-Doherty Geological Observatory, (Manuscript received January 19;and in final formin April 1976) Palisades, New York John Imbrie is Henry L. of any exbe September scale without the intervention October both6,hemiprofessor of oceanography, Brown Universtimulus16 or internal time constant spheres. However, several other curves Doherty ternal sity, Providence, Rhode Island N. J. ShackleThursday April 15 is ton on the staff of the Sub-department of Quaternahave been supported by plausible argu(12). b-3

6 Huybers and Curry 2006 period : years period 1 year note also : Pestiaux et al Pelletier 1998 Lovejoy et al. 2013

7 Temperature spectrum: 40 x 1000 x period : years period 1000 year

8 Result consistent across data and methods DSDP 607 EPICA CO2 EPICA Deuterium Spectral slope of the order of 2 Ratio between 100,000 year and 1,000 year power of the order of 1000 nota : ice volume will have a larger slope if it indeed integrates temperature.

9 Ice Volume Red-Sea Level reconstruction : Siddall et al., Nature, 2003 (red sea record based on oxygen isotopes)

10 Lomb-Scargle periodogram Lomb-Scargle (raw) Lomb-Scargle with smoothing E(w) 1e 01 1e+01 1e+03 1e x E(w) 1e 02 1e+00 1e+02 1e+04 1e 04 1e 03 1e 02 1e 01 1e+00 1e 04 1e 03 1e 02 1e 01 1e+00 Frequency (kyr 1) Frequency (kyr 1) ( Lomb-Scargle + WOSA spectrum (Hanning (sin^2) window - 50% overlap - 49 windows. Supplied by G. Lenoir)

11 Conceptual models of ice ages

12 Forced Van der Pol Oscillator as a conceptual model of ice ages forcing 1 5 x 0 4 LR04 (obs.) y time (ka) dx ( y + b + gf(t)) = dt t dy dt = a(y3 /3 y x). t

13 This deterministic oscillator has way too little high-frequency power Van-der-pol : Fast Variable (Y) E(w) 1e-07 1e-05 1e-03 1e-01 1e+01 period : years 5e-04 5e-03 5e-02 5e-01 5e+00 Frequency (kyr -1) 1000 x period 1000 years power gap

14 Saltzman and Maasch 1991 Paillard 1998 Le Treut and Ghil 1983 The ratio between 100,000 yr and 1,000 yr power is, in all these models, incompatible with what we learned from data analysis Discussion on EMICS left for discussion time,... if we have

15 We can fix this by noising it up... Van der pol model + noise dx = 1 dy = ( + F (t) y)dt (y + x)dt + dw

16 Enough added noise this (sort of) fixes the spectrum... Van-der-pol + sigma^2 = 0.04 yr-1 : Fast Variable (Y) E(w) 1e-04 1e-02 1e+00 1e+02 period : years period 1000 years 1000 x power gap 5e-04 5e-03 5e-02 5e-01 5e+00 Frequency (kyr -1)

17 ... but we loose trajectory stability VDP with sigma^2 = 0.27 kyr 1 X Time (kyr) (colors = different noise realisations) (mecanism of desynchronisation : perturbation of Strange Non Chaotic Attractor)

18 Other example: the Paillard 1998 model: time (kyr)

19 The Paillard 1998 model P98 without added noise P98 with sigma^2 = kyr-1 E(w) 1e-09 1e-06 1e-03 1e+00 E(w) 1e-08 1e-06 1e-04 1e-02 1e+00 effect of adding Gaussian Noise 5e-04 5e-03 5e-02 5e-01 5e+00 5e-04 5e-03 5e-02 5e-01 5e+00 Frequency (kyr -1) Frequency (kyr -1)

20 Again : noising up = messing up P98 with sigma^2 = kyr 1 X Time (kyr) (mecanism of desynchronisation : piece-wise discontinuity of attractor)

21 Conclusions and further thoughts

22 Conclusions and further thoughts As we already knew: adding noise to a deterministic system alters periodicity, reduces predictability, excites metastable states... adding a lot of noise destroys the deterministic structure (and may produce interesting effects)

23 Conclusions and further thoughts As we already knew: adding noise to a deterministic system alters periodicity, reduces predictability, excites metastable states... adding a lot of noise destroys the deterministic structure (and may produce interesting effects) It was shown here that these are relevant issues for ice ages!

24 Conclusions and further thoughts As we already knew: adding noise to a deterministic system alters periodicity, reduces predictability, excites metastable states... adding a lot of noise destroys the deterministic structure (and may produce interesting effects) It was shown here that these are relevant issues for ice ages! Stochastic effects have not yet been quantitively explored at the ice age time scale

25 Conclusions and further thoughts As we already knew: adding noise to a deterministic system alters periodicity, reduces predictability, excites metastable states... adding a lot of noise destroys the deterministic structure (and may produce interesting effects) It was shown here that these are relevant issues for ice ages! Stochastic effects have not yet been quantitively explored at the ice age time scale We currently do not know the variability spectrum of sea-level at ice age scales (is there really so much millennial variability?)

26 Conclusions and further thoughts As we already knew: adding noise to a deterministic system alters periodicity, reduces predictability, excites metastable states... adding a lot of noise destroys the deterministic structure (and may produce interesting effects) It was shown here that these are relevant issues for ice ages! Stochastic effects have not yet been quantitively explored at the ice age time scale We currently do not know the variability spectrum of sea-level at ice age scales (is there really so much millennial variability?) and we currently do not have a theory stochastic parameterisations at these time scales (Which noise? multiplicative, alpha-stable, long-memory?)

27 Further reading published M. Crucifix, How can a glacial inception be predicted?, The Holocene, 21, M. Crucifix, Oscillators and relaxation phenomena in Pleistocene climate theory, Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences, 370, M. Crucifix, Why could ice ages be unpredictable?, Climate of the Past, 9, B. De Saedeleer, M. Crucifix, and S. Wieczorek, Is the astronomical forcing a reliable and unique pacemaker for climate? A conceptual model study, Climate Dynamics, 40, T. Mitsui and K. Aihara, Dynamics between order and chaos in conceptual models of glacial cycles, Climate Dynamics, 42, in prep T. Mitsui, M. Crucifix, K. Aihara, Physica D, Bifurcations and strange nonchaotic attractors in a phase oscillator model of glacial-interglacial cycles in review T. Mitsui and M. Crucifix, InDAM, Effects of noise on the dynamics of glacial cycles in review G. Lenoir and M. Crucifix, Significance testing for spectra of unevenly spaced data POSTER FRIDAY Y22 EGU VISIT US at :

28 Saltzman - Maash 91 : Ice Volume S91 Ice Vol. Auto regressive fit (Burg) y Power density AR(42) slope= Time Modulus of Morlet CWT Period SSA spectrum Period Frac. of explained variance AR1 model L= Time 40 kyr 10 1 Period all times in kyr

29 Saltzman - Maash 91 : CO2 S91 CO2 Auto regressive fit (Burg) y Power density AR(19) slope= Time Modulus of Morlet CWT Period SSA spectrum Period Frac. of explained variance AR1 model L= Time 40 kyr 10 1 Period all times in kyr

30 LeTreut - Ghil 1983 GL83 Ice Vol. Auto regressive fit (Burg) y Power density AR(66) slope= Time Modulus of Morlet CWT Period SSA spectrum Period Frac. of explained variance AR1 model L= Time 40 kyr 10 1 Period all times in kyr