Stable non-Gaussian random processes , by G. Samorodnitsky and M. S. Taqqu. Pp. 632. £49.50. 1994. ISBN 0-412-05171-0 (Chapman and Hall).

Tipping points in complex systems may imply risks of unwanted collapse, but also opportunities for positive change. Our capacity to navigate such risks and opportunities can be boosted by combining emerging insights from two unconnected fields of research. One line of work is revealing fundamental architectural features that may cause ecological networks, financial markets, and other complex systems to have tipping points. Another field of research is uncovering generic empirical indicators of the proximity to such critical thresholds. Although sudden shifts in complex systems will inevitably continue to surprise us, work at the crossroads of these emerging fields offers new approaches for anticipating critical transitions.

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Anticipating Critical Transitions

A copy of Guangbo jiemu bao [Broadcast Program Report] was being passed from hand to hand among a group of young people eager to be the first to read the article introducing the program "What Is Revolutionary Love?" It said: "… Young friends, you are certainly very concerned about this problem'. So, we would like you to meet the young women workers Meng Xiaoyu and Meng Yamei and the older cadre Miss Feng. They are the three leading characters in the short story ‘The Place of Love.’ Through the description of the love lives of these three, the story induces us to think deeply about two questions that merit further examination.

This is How the Discussion Started

Polar temperatures over the last several million years have, at times, been slightly warmer than today, yet global mean sea level has been 6-9 metres higher as recently as the Last Interglacial (130,000 to 115,000 years ago) and possibly higher during the Pliocene epoch (about three million years ago). In both cases the Antarctic ice sheet has been implicated as the primary contributor, hinting at its future vulnerability. Here we use a model coupling ice sheet and climate dynamics-including previously underappreciated processes linking atmospheric warming with hydrofracturing of buttressing ice shelves and structural collapse of marine-terminating ice cliffs-that is calibrated against Pliocene and Last Interglacial sea-level estimates and applied to future greenhouse gas emission scenarios. Antarctica has the potential to contribute more than a metre of sea-level rise by 2100 and more than 15 metres by 2500, if emissions continue unabated. In this case atmospheric warming will soon become the dominant driver of ice loss, but prolonged ocean warming will delay its recovery for thousands of years.

Contribution of Antarctica to past and future sea-level rise

https://boris.unibe.ch/62575/1/1-s2.0-S0277379114003485-main.pdf

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

The rapid climate shifts observed in the glacial climate are analyzed. The transitions into the warm interstadial states, the onsets, are easily identifiable in the record. The distribution of waiting times between consecutive onsets is well fitted, assuming that the remaining residence time in each state is independent of the past. This implies that it has a simple no-memory exponential waiting time distribution, but with the mean waiting time depending on the climate state. The mean waiting time from one onset to the next is around 2400 yr. The most likely (maximum likelihood) distribution derived solely from the onset sequence is rather insensitive to the mean waiting time in the warm interstadials in the range of 400–1200 yr. When extending the analysis to include the transitions from the warm interstadials to the cold stadials observed with a larger uncertainty, the distributions in the two states are well fitted to exponential distributions, with mean waiting times of around 800 yr in the w...

On the Stochastic Nature of the Rapid Climate Shifts during the Last Ice Age

https://www.gfy.ku.dk/%7Epditlev/papers/surf_sci292.pdf

Molecular modeling of ethylene decomposition on platinum surfaces

Natural climate variability and persistency are reflected in the scaling properties of climate records. Here, the authors show that the scaling properties of interglacial and glacial climates are distinctively different: The former is monofractal while the latter is multifractal with much longer range memory.

/pdf/contrasting-scaling-properties-of-interglacial-and-glacial-32fbynbsio.pdf

Contrasting scaling properties of interglacial and glacial climates.

We present an independent test of recently developed methods of potential analysis and degenerate fingerprinting which aim, respectively, to identify the number of states in a system, and to forecast bifurcations. Several samples of modelled data of unknown origin were provided by one author, and the methods were used by the two other authors to investigate these properties. The main idea of the test was to investigate whether the techniques are capable to identify the character of the data of unknown origin, which includes potentiality, possible transitions and bifurcations. Based on the results of the analysis, models were proposed that simulated data equivalent to the test samples. The results obtained were compared with the initial simulations for critical evaluation of the performance of the methods. In most cases, the methods successfully detected the number of states in a system, and the occurrence of transitions between states. The derived models were able to reproduce the test data accurately. However, noise-induced abrupt transitions between existing states cannot be forecast due to the lack of any change in the underlying potential.

https://www.gfy.ku.dk/~pditlev/papers/physicaA_391_2012.pdf

An independent test of methods of detecting system states and bifurcations in time-series data

Milankovitch’s astronomical theory of glacial cycles, attributing ice age climate oscillations to orbital changes in 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 middle 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 a 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 critical dependence on initial conditions in the (non-autonomous) glacial dynamics raises fundamental questions about climate predictability.

Peter D. Ditlevsen

Papers

On the Stochastic Nature of the Rapid Climate Shifts during the Last Ice Age

Molecular modeling of ethylene decomposition on platinum surfaces

Contrasting scaling properties of interglacial and glacial climates.

An independent test of methods of detecting system states and bifurcations in time-series data

A conceptual model for glacial cycles and the middle Pleistocene transition