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 increase in glacial cycle length from approximately 41 to on average 100 thousand years around 1 million years ago, called the middle Pleistocene transition (MPT), lacks a conclusive explanation. We describe a dynamical mechanism which we call ramping with frequency locking (RFL), that explains the transition by an interaction between the internal period of a self-sustained oscillator and forcing that contains periodic components. This mechanism naturally explains the abrupt increase in cycle length from approximately 40 to 80 thousand years observed in proxy data, unlike some previously proposed mechanisms for the MPT. A rapid increase in durations can be produced by a rapid change in an external parameter, but this assumes rather than explains the abruptness. In contrast, models relying on frequency locking can produce a rapid change in durations assuming only a slow change in an external parameter. We propose a scheme for detecting RFL in complex, computationally expensive models, and motivate the search for climate variables that can gradually increase the internal period of the glacial cycles.

https://link.springer.com/content/pdf/10.1007/s00382-019-04679-3.pdf

The middle Pleistocene transition by frequency locking and slow ramping of internal period

The power spectrum provides a compact representation of the scale dependence of the variability in time series. At multi-millennial time scales the spectrum of the Pleistocene climate is composed of a set of narrow band spectral modes attributed to the regularly varying changes in insolation from the astronomical change in Earth’s orbit and rotation superimposed on a continuous background generally attributed to stochastic variations. Quantitative analyses of paleoclimatic records indicate that the continuous part comprises a dominant part of the variance. It exhibits a power-law dependency typical of stochastic, self-similar processes, but with a scale break at the frequency of glacial-interglacial cycles. Here we discuss possible origins of this scale break, the connection between the continuous background and the narrow bands, and the apparently modest spectral power above the continuum at these scales. We demonstrate that the observed scale break around 100 ka can have a variety of different origins and does not imply an internal time scale of correlation as implied by the simplest linear stochastic model.

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Crossover and peaks in the Pleistocene climate spectrum; understanding from simple ice age models

. During the last glacial period, climate records from the North Atlantic region exhibit a pronounced spectral component corresponding to a period of about 1470 years, which has attracted much attention. This spectral peak is closely related to the recurrence pattern of Dansgaard-Oeschger (DO) events. In previous studies a red noise random process, more precisely a first-order autoregressive (AR1) process, was used to evaluate the statistical significance of this peak, with a reported significance of more than 99%. Here we use a simple mechanistic two-state model of DO events, which itself was derived from a much more sophisticated ocean-atmosphere model of intermediate complexity, to numerically evaluate the spectral properties of random (i.e., solely noise-driven) events. This way we find that the power spectral density of random DO events differs fundamentally from a simple red noise random process. These results question the applicability of linear spectral analysis for estimating the statistical significance of highly non-linear processes such as DO events. More precisely, to enhance our scientific understanding about the trigger of DO events, we must not consider simple "straw men" as, for example, the AR1 random process, but rather test against realistic alternative descriptions.

/pdf/limitations-of-red-noise-in-analysing-dansgaard-oeschger-725jp03y23.pdf

Limitations of red noise in analysing Dansgaard-Oeschger events

Fully developed homogeneous isotropic turbulence in two dimensions is fundamentally different from that in three dimensions. In two dimensions, the simultaneous inviscid conservation of both kinetic energy and enstrophy within the inertial range of scales leads to a forward cascade of enstrophy and a reverse cascade of energy. In three dimensions, helicity, the integral of the scalar product of velocity and vorticity, is also an inviscid flow invariant along with the energy. Unlike the enstrophy, however, the helicity does not block the forward cascade of energy to small scales. Energy and helicity are conserved not only globally but also within each nonlinear triadic interaction between three plane waves in the spectral form of the Navier-Stokes equation (NSE). By decomposing each plane wave into two helical modes of opposite helicities, each triadic interaction is split into a set of eight helical triadic interactions between helical modes [F. Waleffe, Phys. Fluids A 4, 350 (1992)]. Recently it was found that a subset of these helical interactions, which render both signs of helicity separately conserved (enstrophy-like), leads to an inverse cascade of (part of) the energy [L. Biferale et al., Phys. Rev. Lett. 108, 164501 (2012)]. Motivated by this finding we introduce a new shell model, obtained from the NSE expressed in the helical basis, allowing the eight helical interactions to be coupled as in the NSE and their relative contributions evaluated as a function of both the net helicity input and triad geometry. By numerically integrating the new model, we find that the intermittency of the energy cascade decreases with the net helicity input. Studying the partitioning of the energy cascade between the eight helical interactions, we find that the decrease in intermittency is related to a shift in the dominating helical interactions when helically forced, two of which exhibit a larger cascade intermittency than the other six interactions. Among the relatively local triad geometries considered here, the partitioning of the energy and helicity cascades between the eight helical interactions shows no sign of change with triad geometry.

Role of helicity in triad interactions in three-dimensional turbulence investigated by a new shell model.

Measurements of δ18O and insoluble dust in the Greenland Ice Core Project ice core reveal that the concentration of dust is about 100 times higher in ice from the last glacial maximum than it is today. In order to understand the glacial climate it is of importance to establish to what extent this increased level was due to changes in the source areas and to what extent it was due to changes in the atmospheric transportation. We here present a one-dimensional model evaluating the effect of changes in the zonally averaged atmospheric circulation on the atmospheric hydrological cycle and dust transportation. The main characteristics of the altered climate during glacial periods are assumed to be increased baroclinicity, an equatorward displacement of the baroclinic zone, and reduced evaporation. The model reproduces the zonally averaged hydrological cycle of the present climate reasonably well, and it produces a halving of snow accumulation in polar areas for glacial periods. From the ice core data we obtain a power law dependence between the concentration of dust in the ice and the accumulation related to long-term climate variations. With the input of dust to the atmosphere being independent of the simulated climate, the model reproduces this power law. The obtained power is strongly dependent on the assumed position of the dust sources. For reasonable estimates of the present-day dust sources the simulated mechanism may account for a twofold to sixfold increase in dust concentration in polar ice from interglacial to full glacial conditions. Concurrently, the atmospheric content of dust is increased at all latitudes during the glacial period.

/pdf/glacial-interglacial-variations-of-meridional-transport-and-zjdc9kheo1.pdf

Peter D. Ditlevsen

Papers

The middle Pleistocene transition by frequency locking and slow ramping of internal period

Crossover and peaks in the Pleistocene climate spectrum; understanding from simple ice age models

Limitations of red noise in analysing Dansgaard-Oeschger events

Role of helicity in triad interactions in three-dimensional turbulence investigated by a new shell model.

Glacial/interglacial variations of meridional transport and washout of dust: A one‐dimensional model