On the (Nonlinear) Causes of Abrupt Climate Change During the Last Ice Age

Transcription

1 On the (Nonlinear) Causes of Abrupt Climate Change During the Last Ice Age J.A. Rial Wave Propagation Lab, University of North Carolina-Chapel Chapel Hill

2 The Astronomical Theory of the Ice Ages Precession Tilt Eccentricity

3 The Milankovitch Eccentricity Periodicities Eccentricity Tilt or Obliquity 41,000years 100,000years Precession of the Equinoxes 21,000years

4 Evidence of Climate's Nonlinear Response to Astronomical Forcing Frequency shifts Frequency (or phase) modulation Fast warming, slow cooling and 'self-similarity' similarity'

5 Frequency shift at the Mid-Pleistocene Transition

6 Frequency Modulation Tilt Eccentricity Rial,J.A., Science, 285 (1999)

7 Saw-tooth self-similarity: similarity: Fast Warming-Slow Cooling Dansgaard- Oeschger oscillations Rial et al., Climatic Change, 2004

8 A toy model to visualize the sawtooth asymmetry and FM Wave Propagation Lab, UNC-Chapel Hill

9 (No external forcing required) Sawtooth waveform

10 Frequency Modulation

11 Ice Volume and Temperature

12 Fitting the long-period records

13 Modeling the Greenland (GRIP) Short-Period Time Series

14 Greenland ice core w w w w w w today 100,000 yrs ago W: Abrupt warming (10 o C or more)

15 FREQUENCY DEMODULATION OF GRIP REVEALS A 2.75ky 'CARRIER'

16 Modulating Phase or "Intelligence" Best Fitting Periods 72.1ky and 41ky Modulating Phase (LP filtered) 1/75 ~ 1/41-1/95 1/72.1 = 1/41-1/95 (combination tone) 1/35 ~ 1/19-1/41

17 Heinrich events-> 1

18 The thermal oscillator has the form of a Van der Pol nonlinear equation Wave Propagation Lab, UNC-Chapel Hill

19 The Van der Pol Equation (Self-exciting exciting oscillations with a limit cycle) d 2 x/dt 2 + v(x 2-1)dx/dt + ω 2 o x = 0 Is equivalent to dx/dt = y - v (x 3 /3 -x) dy/dt = - ω 2 o x Wave Propagation Lab, UNC-Chapel Hill

20 In a simplified climate model An energy balance equation C T dt/dt = -αl -βt + Q(1+ε coswt) Coupled to a logistic growth equation for the sea ice C L dl/dt = T/α - (a L 3 /3 -bl) Become a Van der Pol equation for the sea ice extent d 2 L/dt 2 + v(l 2-1) dl/dt + ω 2 o L = G(1+ε coswt) and with G=0, it gives Saltzman's nonlinear thermal oscillator C T, C L, Q, α, β, β a, b are positive constants

21 Saltzman's NONLINEAR THERMAL OSCILLATOR L(t) 0 ICE AGE ATMOSPHERE SEA ICE T(t) OCEAN θ(t)

22 Saltzman's NONLINEAR THERMAL OSCILLATOR L(t) 0 ICE AGE ATMOSPHERE SEA ICE T(t) OCEAN θ(t)

23 Saltzman's NONLINEAR THERMAL OSCILLATOR L(t) 0 ICE AGE ATMOSPHERE SEA ICE T(t) OCEAN θ(t)

24 Saltzman's NONLINEAR THERMAL OSCILLATOR L(t) 0 SEA ICE ICE AGE ATMOSPHERE T(t) OCEAN θ(t)

25 Saltzman's NONLINEAR THERMAL OSCILLATOR L(t) 0 ICE AGE ATMOSPHERE SEA ICE T(t) OCEAN θ(t)

26 The self-sustained, relaxation oscillation of the thermal oscillator

27 Forcing Saltzman's Oscillator with Milankovitch Cycles

28 Linear, forced by cosine QuickTime and a Animation decompressor are needed to see this picture. Nonlinear, forced by cosine QuickTime and a Animation decompressor are needed to see this picture. Time (arbitrary units)

29 Nonlinear, forced by simulated Insolation QuickTime and a Animation decompressor are needed to see this picture. Time (arbitrary units)

30 GRIP vs VdPol Model

31 VdPol Model is Robust

32 GRIP vs VdPol Model

33 Kyears B.P. GRIP

34 Prediction GRIP vs VdPol Model Kyears B.P.

35 Concluding Remarks A simplified climate model describing the nonlinear oscillations of sea ice driven by deep ocean temperature closely reproduces the GRIP data. A natural free period of 2.75ky retrieved form the data by demodulation appears to be the free period of the sea ice/atmosphere/ocean system. Frequency modulation of this free oscillation by the insolation (tilt and precession) generates time-series features consistent with many of the puzzling features of the GRIP time series. The model is deterministic, and it can be chaotic. Though the origin of the 2.75ky period is not resolved, it is commensurate with predictions made by Saltzman's sea ice oscillator. We shall use GCMs to understand the origin and physics of this period.

36 Research supported by NSF grant ATM Wave Propagation Laboratory, University of North Carolina-Chapel Hill

37 Ice core data from Greenland (millennial scale) Dansgaard-Oeschger Oscillations. -16

38 FM in the D/O

39 FM in the D/O Relative Temp ( o C) Carrier: 2.7ky Modulator: 7.5ky

40 The Paleoclimate Time Series A Complex tale of Fast warming-slow cooling Frequency Modulation Non-Stationarity Chaos and Order

41 Sawtooth Mid-Pleistocene Transition FM

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43 What does self-similarity similarity mean? The abrupt warming episodes of the last Ice Age and the Dow Jones crash of 1987

44 What does self-similarity similarity mean? The abrupt warming episodes of the last Ice Age and the Dow Jones crash of 1987

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46 Fast Warming - Slow Cooling and The Younger Dryas (YD) event

47 Milankovitch Forcing and Ice Core Data ~ 21ky ky Tilt 41ky

48 QuickTime and a Animation decompressor are needed to see this picture.

49 QuickTime and a Animation decompressor are needed to see this picture. QuickTime and a Animation decompressor are needed to see this picture. Time (arbitrary units)

50 Global temperature over the last Millennium T (o C) 1 0 and during the last Ice Age Normal abrupt climate change, or CO 2 warming?

51 Time series from the Antarctic Ice cap Today 400,000 years ago

52 The self-sustained, relaxation oscillation of the thermal oscillator

53 Frequency modulation (FM) in millennial-scale climate series 7.5ky

54 1/74 ~ 1/41-1/95 1/37 ~ 1/19-1/41

55 Deep-sea sediment Ice core Sea-surface Temp

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