The authors conclude, "the presence of chaos in the present model suggests that this could be manifested in the climate system itself in a so-called climatic butterfly effect: a small perturbation, or even just the internal climatic noise, might cause a significant shift in the glacial cycles. Obviously, this could impose fundamental limitations on long-term climate predictability."
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1Johannes Kepler University, Institute of Semiconductor and Solid State Physics, Altenbergerstrasse 69, 4040 Linz, Austria
2Centre for Ice and Climate, Niels Bohr Institute, University of Copenhagen, Juliane Maries Vej 30, 2100 Copenhagen, Denmark
Abstract. Milankovitch's astronomical theory of glacial cycles, attributing ice age climate oscillations to orbital changes in Northern Northern-Hemisphere insolation, is challenged by the paleoclimatic record. The climatic response to the variations in insolation is far from trivial. In general the glacial cycles are highly asymmetric in time, with slow cooling from the interglacials to the glacials (inceptions) and very rapid warming from the glacials to the interglacials (terminations). We shall refer to this fast-slow dynamics as the "saw-tooth" shape of the paleoclimatic record. This is non-linearly related to the time-symmetric variations in the orbital forcing. However, the most pronounced challenge to the Milankovitch theory is the Mid-Pleistocene Transition (MPT) occurring about one million years ago. During that event, the prevailing 41 kyr glacial cycles, corresponding to the almost harmonic obliquity cycle were replaced by longer saw-tooth shaped cycles with a time scale around 100 kyr. The MPT must have been driven by internal changes in climate response, since it does not correspond to any apparent changes in the orbital forcing. In order to identify possible mechanisms causing the observed changes in glacial dynamics, it is relevant to study simplified models with the capability of generating temporal behavior similar to the observed records. We present a simple oscillator type model approach, with two variables, a temperature anomaly and an ice volume analogous, climatic memory term. The generalization of the ice albedo feedback is included in terms of an effective multiplicative coupling between this latter climatic memory term (representing the internal degrees of freedom) and the external drive. The simple model reproduces the temporal asymmetry of the late Pleistocene glacial cycles and suggests that the MPT can be explained as a regime shift, aided by climatic noise, from a period 1 frequency locking to the obliquity cycle to a period 2–3 frequency locking to the same obliquity cycle. The change in dynamics has been suggested to be a result of a slow gradual decrease in atmospheric greenhouse gas concentration. The presence of chaos in the (non-autonomous) glacial dynamics and a critical dependence on initial conditions raises fundamental questions about climate predictability.
Conclusions
We have formulated a semi-conceptual model to describe the Mid-Pleistocene
Transition, 5 which we propose to be a period two and period three response to the 41 kyr
obliquity forcing. This resolves the “100 and 400 kyr problems” of the Milankovitch
theory, since the eccentricity cycle is proposed to be insignificant, and is omitted all
together in the forcing. The change at the MPT is caused by a long term, gradual
decrease of some parameter of the system. With the conceptual model approach, we
10 can only point to dynamical mechanisms and not to the real environmental change.
However, the idea of a gradual change aligns with the decrease in global CO2 or
tectonic re-arrangements as proposed in the literature.
The model does not in itself possess an internal frequency of oscillation, thus
suggesting that the time scale of the glacial cycles is determined solely by the non15
linear response to the frequency of the obliquity pacing. We observe that the model
also reproduces the observed saw-tooth shaped time reversal asymmetry observed in
the record, which is not present in the forcing. In the model this is related to the larger
amplitude of the glacial cycles after the MPT in comparison to the more symmetric
cycles prior to the MPT. With the larger cycles, the system experience the non-linearity
20 in the internal dynamical response (the skewed climate potential in the model) much
stronger than in the case of small, almost harmonic oscillations. As we have shown,
the modulations in the forcing amplitude can also lead to a change in the periodicity of
the response, rendering an intrinsically non-linear climatic behaviour.
Despite its simplicity, the model shows a surprisingly wide range of behaviours
25 depending on the forcing, the initial conditions and the values of the parameters. The
observed variety of possible climatic responses in the model raises the perplexing
question: How robust is the climatic history of the Earth? We are obviously not in the
position, where we can rerun the past. Thus we must ask in which sense, we should
be able to model the past, by reproducing the evolution, which has been realised, or by
reproducing the past in some statistical sense.
Furthermore, the presence of chaos in the present model suggests that this could
5 be manifested in the climate system itself in a so-called climatic butterfly effect: a small
perturbation, or even just the internal climatic noise, might cause a significant shift in
the glacial cycles. Obviously, this could impose fundamental limitations on long-term
climate predictability.
Clim. Past Discuss., 10, 1101-1127, 2014
www.clim-past-discuss.net/10/1101/2014/ doi:10.5194/cpd-10-1101-2014 |
1Johannes Kepler University, Institute of Semiconductor and Solid State Physics, Altenbergerstrasse 69, 4040 Linz, Austria
2Centre for Ice and Climate, Niels Bohr Institute, University of Copenhagen, Juliane Maries Vej 30, 2100 Copenhagen, Denmark
Abstract. Milankovitch's astronomical theory of glacial cycles, attributing ice age climate oscillations to orbital changes in Northern Northern-Hemisphere insolation, is challenged by the paleoclimatic record. The climatic response to the variations in insolation is far from trivial. In general the glacial cycles are highly asymmetric in time, with slow cooling from the interglacials to the glacials (inceptions) and very rapid warming from the glacials to the interglacials (terminations). We shall refer to this fast-slow dynamics as the "saw-tooth" shape of the paleoclimatic record. This is non-linearly related to the time-symmetric variations in the orbital forcing. However, the most pronounced challenge to the Milankovitch theory is the Mid-Pleistocene Transition (MPT) occurring about one million years ago. During that event, the prevailing 41 kyr glacial cycles, corresponding to the almost harmonic obliquity cycle were replaced by longer saw-tooth shaped cycles with a time scale around 100 kyr. The MPT must have been driven by internal changes in climate response, since it does not correspond to any apparent changes in the orbital forcing. In order to identify possible mechanisms causing the observed changes in glacial dynamics, it is relevant to study simplified models with the capability of generating temporal behavior similar to the observed records. We present a simple oscillator type model approach, with two variables, a temperature anomaly and an ice volume analogous, climatic memory term. The generalization of the ice albedo feedback is included in terms of an effective multiplicative coupling between this latter climatic memory term (representing the internal degrees of freedom) and the external drive. The simple model reproduces the temporal asymmetry of the late Pleistocene glacial cycles and suggests that the MPT can be explained as a regime shift, aided by climatic noise, from a period 1 frequency locking to the obliquity cycle to a period 2–3 frequency locking to the same obliquity cycle. The change in dynamics has been suggested to be a result of a slow gradual decrease in atmospheric greenhouse gas concentration. The presence of chaos in the (non-autonomous) glacial dynamics and a critical dependence on initial conditions raises fundamental questions about climate predictability.
Conclusions
We have formulated a semi-conceptual model to describe the Mid-Pleistocene
Transition, 5 which we propose to be a period two and period three response to the 41 kyr
obliquity forcing. This resolves the “100 and 400 kyr problems” of the Milankovitch
theory, since the eccentricity cycle is proposed to be insignificant, and is omitted all
together in the forcing. The change at the MPT is caused by a long term, gradual
decrease of some parameter of the system. With the conceptual model approach, we
10 can only point to dynamical mechanisms and not to the real environmental change.
However, the idea of a gradual change aligns with the decrease in global CO2 or
tectonic re-arrangements as proposed in the literature.
The model does not in itself possess an internal frequency of oscillation, thus
suggesting that the time scale of the glacial cycles is determined solely by the non15
linear response to the frequency of the obliquity pacing. We observe that the model
also reproduces the observed saw-tooth shaped time reversal asymmetry observed in
the record, which is not present in the forcing. In the model this is related to the larger
amplitude of the glacial cycles after the MPT in comparison to the more symmetric
cycles prior to the MPT. With the larger cycles, the system experience the non-linearity
20 in the internal dynamical response (the skewed climate potential in the model) much
stronger than in the case of small, almost harmonic oscillations. As we have shown,
the modulations in the forcing amplitude can also lead to a change in the periodicity of
the response, rendering an intrinsically non-linear climatic behaviour.
Despite its simplicity, the model shows a surprisingly wide range of behaviours
25 depending on the forcing, the initial conditions and the values of the parameters. The
observed variety of possible climatic responses in the model raises the perplexing
question: How robust is the climatic history of the Earth? We are obviously not in the
position, where we can rerun the past. Thus we must ask in which sense, we should
be able to model the past, by reproducing the evolution, which has been realised, or by
reproducing the past in some statistical sense.
Furthermore, the presence of chaos in the present model suggests that this could
5 be manifested in the climate system itself in a so-called climatic butterfly effect: a small
perturbation, or even just the internal climatic noise, might cause a significant shift in
the glacial cycles. Obviously, this could impose fundamental limitations on long-term
climate predictability.
It seems like ages ago that I asked Peter Huybers by email a similar question about Milankovitch cycles. http://eps.harvard.edu/people/peter-huybers
ReplyDeleteMy recollection is that he said it was one of the interests he shared with Carl Wunsch. http://en.wikipedia.org/wiki/Carl_Wunsch
I had been reading a paper by two Chinese astronomers who asserted that the Milankovitch cycles are actually pseudo-cycles that are derived from chaotic celestial movements.
I recalled that you can fit a polynomial to any sort of data if you have sufficient terms of high enough order. The same is true of sine waves. You can decompose any signal into sine waves and then convince yourself you have discovered regularities in nature.
Part of the problem is computational. With just the giant planets the Sun and the Earth we have a multi-body problem. But the Mars and the inner planets are closer so they complicate the computations.
And then there are the perturbations of the asteroid belt to take account of.
There is really no way of resolving the issue of determination or indeterminacy (chaos) by observation and calculation.
We are in the position of the Cargo Cult people who cannot tell the difference between magic and technology. We may never know if the Milankovitch cycles are of any predictive value.
Financial models have been built to predict the stock market using the same approach and failed for the same reason, inability to distinguish chaos from cyclicity.