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.

/pdf/anticipating-critical-transitions-4zp7hd84hx.pdf

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 existence of partially conserved enstrophy-like quantities is conjectured to cause embedded, inverse magnetic energy cascades to develop in magnetohydrodynamical (MHD) turbulence. By decomposing the velocity and magnetic fields in spectral space onto helical modes, we show that two new quantities exist which are partially conserved among a set of three-wave (triad) interactions in MHD turbulence. In a subset of these helical triad interactions, the quantities become enstrophy-like, which, by analogy to enstrophy-conserving triad interactions in two-dimensional, nonconducting hydrodynamical turbulence, are conjectured to cause embedded, inverse magnetic energy cascades to develop. We test the resulting predictions by constructing a nonlocal helical MHD shell model (reduced wave-space numerical model) of the minimal set of triad interactions (MTIs) required to conserve the ideal MHD invariants, energy, magnetic helicity, and cross-helicity. The numerically simulated MTIs demonstrate that, for a range of forcing configurations, the partial invariants are indeed useful for understanding the embedded energy cascade contributions to the total spectral energy flux, which has potential implications for the turbulent dynamo action, central to the evolution of astrophysical magnetic fields.

Inverse magnetic energy cascades embedded in magnetohydrodynamical turbulence

An investigation into the dynamics of a two-parameter family of non-linear differential equations inspired by MacAyeal (1979) reveals the utility of simple conceptual models in understanding climate response to forcing. A slow-fast model is used to explain the non-linear response of the climate to insolation forcing after the Mid-Pleistocene Transition (MPT) which produces the saw-toothed glacial cycles in the paleoclimate record. Global ice volume is taken to be a function of two independently varying parameters, the solar insolation and &amp;#8216;alpha&amp;#8217;, a secondary control parameter. The pleated cusp geometry of the model, due to the addition of the second control allows the system to exhibit both smooth changes and sudden discontinuous transitions from one stable solution to another, producing the gradual increase and sudden decrease in global ice volume observed in the paleoclimate record. &amp;#160;The control parameter alpha is suggested to be related to internal dynamics of the climate system, proposed to be a measure of glacial-oceanic interaction, which varies due to glacial isostatic adjustments of the bedrock. &amp;#160;The transition in period of glacial cycles at the MPT is suggested to occur as a result of northern hemisphere glaciers exceeding a critical threshold, which allows alpha to become larger, causing the asymmetric, higher amplitude glacial cycles with quasi-period of 100kyr of the late Pleistocene.&amp;#160;ReferenceR. MacAyeal, &amp;#8216;A Catastrophe Model of the Paleoclimate Record&amp;#8217; , Journal of Glaciology , Volume 24 , Issue 90 , 1979 , pp. 245 &amp;#8211; 257.&amp;#160; 

Investigating the dynamics of cusp bifurcations: A conceptual model for glacial-interglacial cycles

Summary. The cause for and possible prediction of rapid climate changes is poorly understood. The most pronounced changes observed, beside the glacial terminations, are the Dansgaard-Oeschger (DO) events. Present day general circulation climate models simulating glacial conditions are not capable of reproduci ng these rapid shifts. It is thus not known if they are due to bi furcations in the structural stability of the climate or if they are induced by stochastic fluctuations. From analysis of a high resolution ice core record the bifurcation scenario can be excluded. This strongly suggests that they are noise induced and thus have very limited predictability. The DO climate events in the last glacial period, shown in figu re 1, are observed in a variety of paleoclimatic records with an almost global extend. They are abrupt jumps between a distinct cold climatic state (the stadial) and a warm state (the interstadial). By time scale separation the climate dynamics can be split into a slow component and a fast component. The dynamics is then described as an effective non-linear stochastic proces in which the fast chaotic variations are treate d as a stochastic noise forcing the slow climate dynamics [1] This description is, even in the linear approximation, very successful in explaining the red noise spectra observed in climate records [2] The observation that the extremely complex dynamics of the climate system seems to exhibit bifurcations, which are usually associated with low order non-linear dynamical systems, is remarkable. It is thus a fundamental question if the rapid climate changes are due to bifurcations, where the system becomes structurally unstable as a function of some control parameter, or if the jumps between two quasi-stable states are purely stochastic and noise induced. At present we do not have final t heories for which scenario describes the observed rapid climate changes. On the contrary, climate models in favor of both scenarios or even induced - or self-sustained oscillat ions have been proposed. The goal here is then to extract enough information from the observations to discriminate between the different possible scenarios. The observations to be an alyzed are the new high temporal resolution NGRIP ice-core. The two generic characteristics of the approach to a bifurcation point in a noisy system are increased variance of the observed signal, following from the fluctuation-dissipati on theorem and the corresponding increased autocorrelation related to critical slow down. In order to identify a bifurcati on from observations the two signals; increased variance and increased autocorrelation, should be detectable. The dynamics of the effective variable x are governed by the Langevin

/pdf/s-tructural-and-stochastic-transitions-in-the-climate-1c8qm8nfpq.pdf

S tructural and stochastic transitions in the climate

In this paper two paleoclimatic ice core records are analyzed. These, the water isotope, d18O, and the dust concentration records are analyzed for the period 59-27 kyr BP, which is the glacial period dominated by regular occurrences of Dansgaard-Oeschger events. There are two major points in the paper: Firstly, the data are modelled as a stochastic process using the Kramers-Moyal equation to investigate the importance of (discontinuous) jumps in the noise. Secondly, the two records are modelled as a two-dimensional joined process.

Answers: green Comments by reviewer: violet Comment on esd-2021-95

Here we present a simple stochastic threshold model consisting of a deterministic slowly decaying term and a fast stochastic noise term. The process shows a pseudo-resonance, in the sense that for small and large intensities of the noise the signal is irregular and the distribution of threshold crossings is broad, while for a tuned intermediate value of noise intensity the signal becomes quasi-periodic and the distribution of threshold crossings is narrow. The mechanism captured by the model might be relevant for explaining apparent quasi-periodicity of observed climatic variations where no internal or external periodicities can be identified.

Peter D. Ditlevsen

Papers

Inverse magnetic energy cascades embedded in magnetohydrodynamical turbulence

Investigating the dynamics of cusp bifurcations: A conceptual model for glacial-interglacial cycles

S tructural and stochastic transitions in the climate

Answers: green Comments by reviewer: violet Comment on esd-2021-95

Pseudo resonance induced quasi-periodic behavior in stochastic threshold dynamics