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

In helical turbulence a linear cascade of helicity accompanying the energy cascade has been suggested. Since energy and helicity have different dimensionality we suggest the existence of a characteristic inner scale, ξ=kH−1, for helicity dissipation in a regime of hydrodynamic fully developed turbulence and estimate it on dimensional grounds. This scale is always larger than the Kolmogorov scale, η=kE−1, and their ratio η/ξ vanishes in the high Reynolds number limit, so the flow will always be helicity free in the small scales.

https://www.gfy.ku.dk/%7Epditlev/papers/PhysFluids_13_3508.pdf

Dissipation in helical turbulence

Rapid climate changes during the last glacial period were first observed in ice-core records (Dansgaard and others, 1982). These shifts between interstadials, called Dansgaard–Oeschger (D-O) events, and stadials or deep glaciation were later seen in Atlantic sediment records (Bond and others, 1993), pointing to the ocean circulation as a strong component in the dynamics of these shifts (Wright and Stocker, 1991). the interstadial states are observed to have a characteristic ``sawtooth’’ shape, indicating a gradual drift of the stable interstadial state toward the stable stadial state. In order to contrast the two climate states, we have separated the δ18O signal from the Greenland Icecore Project ice core into periods corresponding to the two states. the climate variability in the two different climatic states is different (Johnsen and others, 1997). We find that the standard deviation is significantly larger in the stadial than in the interstadial state. Both states are found to have a larger standard deviation than the Holocene part of the record. the correlation times in the different states are difficult to obtain because of limited data resolution and diffusion of the isotopic signal. However, using a statistical technique, we have estimated the correlation times. We do not find significant differences in the correlation times, which are of the order of months, in the different climatic states. These findings are interpreted in the context of a simple linear stochastic model which provides information about the relative roles of the climatic forcing and the stability of the climate state governing the climate variability.

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The fast climate fluctuations during the stadial and interstadial climate states

We study the GOY shell model simulating the cascade processes of turbulent flow. The model has two inviscid invariants governing the dynamical behavior. Depending on the choice of interaction coefficients, or coupling parameters, the two invariants are either both positive definite, analogous to energy and enstrophy of 2D flow, or only one is positive definite and the other not, analogous to energy and helicity of 3D flow. In the 2D like model the dynamics depend on the spectral ratio of enstrophy to energy. That ratio depends on wave-number as $k^{\alpha}$. The enstrophy transfer through the inertial sub-range can be described as a forward cascade for $\alpha 2$. The $\alpha =2$ case, corresponding to 2D turbulence, is a borderline between the two descriptions. The difference can be understood in terms of the ratio of typical timescales in the inertial sub-range and in the viscous sub-range. The multi fractality of the enstrophy dissipation also depends on the parameter $\alpha$, and seems to be related to the ratio of typical timescales of the different shell velocities.

https://www.gfy.ku.dk/%7Epditlev/papers/pre53_1996.pdf

Cascades and statistical equilibrium in shell models of turbulence.

A discussion of the H-H interactions in a metal is given. Based on self-consistent total-energy calculations within the local-density approximation for ${\mathrm{H}}_{2}$ in a homogeneous electron gas, we show that metallic electrons make the H-H interaction more repulsive than in vacuum. Using effective-medium theory to calculate total energies we show the same tendency for the short-range part of the H-H interaction when two H atoms are squeezed into a single site in Pd or PdH. At longer range (of the order a lattice constant) there is an attractive, lattice-mediated H-H interaction. On the basis of the calculated energetics, the thermodynamical properties of various palladium hydrides are modeled.

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H-H interactions in Pd

[1] We investigate the effect of precipitation weighting on annual d values of stable water isotopes in ice cores from Greenland. This effect can explain the observation from ice cores that d values in northwestern Greenland are less related to annual coastal temperatures than are the d values in southern and central Greenland ice cores. Furthermore, the precipitation weighting can explain the result of Vinther et al. (2010) that exclusion of summer layers increases information about annual temperature in Greenland ice core records. We study these effects by comparing arithmetic annual means of a regional temperature signal to annual means of the same signal weighted by local precipitation. Specifically, we apply the ERA‐40 reanalysis of meteorological observations to compute time series of southwest Greenland temperatures in annual means and in annual precipitation weighted means. We find that the correlation between these temperature series is highest in southern Greenland, decreasing toward the north, and that the correlation is controlled by the seasonal time scale precipitation weighting. A statistical model is developed to understand the role of climatic parameters in this correlation. The low correlation in northwestern Greenland is caused in equal parts by a relatively lower mean fraction of precipitation during winter in this sector and a larger year‐to‐year variability of this fraction.

https://www.gfy.ku.dk/%7Epditlev/papers/Persson.etal.JGR.2011.pdf

Peter D. Ditlevsen

Papers

Dissipation in helical turbulence

The fast climate fluctuations during the stadial and interstadial climate states

Cascades and statistical equilibrium in shell models of turbulence.

H-H interactions in Pd

The influence of precipitation weighting on interannual variability of stable water isotopes in Greenland