scholarly journals Oscillators and relaxation phenomena in Pleistocene climate theory

2012 ◽  
Vol 370 (1962) ◽  
pp. 1140-1165 ◽  
Author(s):  
Michel Crucifix
Keyword(s):  
Limit Cycle ◽  
Relaxation Oscillator ◽  
Homoclinic Orbits ◽  
Ice Age ◽  
Glacial Cycles ◽  
Stochastic Dynamical Systems ◽  
Pleistocene Climate ◽  
Stochastic Fluctuations ◽  
Earth’S Climate ◽  
Almost All

Ice sheets appeared in the northern hemisphere around 3 Ma (million years) ago and glacial–interglacial cycles have paced Earth's climate since then. Superimposed on these long glacial cycles comes an intricate pattern of millennial and sub-millennial variability, including Dansgaard–Oeschger and Heinrich events. There are numerous theories about these oscillations. Here, we review a number of them in order to draw a parallel between climatic concepts and dynamical system concepts, including, in particular, the relaxation oscillator, excitability, slow–fast dynamics and homoclinic orbits. Namely, almost all theories of ice ages reviewed here feature a phenomenon of synchronization between internal climate dynamics and astronomical forcing. However, these theories differ in their bifurcation structure and this has an effect on the way the ice age phenomenon could grow 3 Ma ago. All theories on rapid events reviewed here rely on the concept of a limit cycle excited by changes in the surface freshwater balance of the ocean. The article also reviews basic effects of stochastic fluctuations on these models, including the phenomenon of phase dispersion, shortening of the limit cycle and stochastic resonance. It concludes with a more personal statement about the potential for inference with simple stochastic dynamical systems in palaeoclimate science.

Emergence of critical climate states during the Pleistocene

2021 ◽  
Author(s):  
Nicholas Golledge
Keyword(s):  
Dynamical Systems ◽  
Late Pleistocene ◽  
Dominant Frequency ◽  
Climate System ◽  
Ice Age ◽  
Early Pleistocene ◽  
Glacial Cycles ◽  
Pleistocene Climate ◽  
System Nodes ◽  
Systems Framework

<p>During the Pleistocene (approximately 2.6 Ma to present) glacial to interglacial climate variability evolved from dominantly 40 kyr cyclicity (Early Pleistocene) to 100 kyr cyclicity (Late Pleistocene to present). Three aspects of this period remain poorly understood: Why did the dominant frequency of climate oscillation change, given that no major changes in orbital forcing occurred? Why are the longer glacial cycles of the Late Pleistocene characterised by a more asymmetric form with abrupt terminations? And how can the Late Pleistocene climate be controlled by 100 kyr cyclicity when astronomical forcings of this frequency are so much weaker than those operating on shorter periods? Here we show that the decreasing frequency and increasing asymmetry that characterise Late Pleistocene ice age cycles both emerge naturally in dynamical systems in response to increasing system complexity, with collapse events (terminations) occuring only once a critical state has been reached. Using insights from network theory we propose that evolution to a state of criticality involves progressive coupling between climate system 'nodes', which ultimately allows any component of the climate system to trigger a globally synchronous termination. We propose that the climate state is synchronised at the 100 kyr frequency, rather than at shorter periods, because eccentricity-driven insolation variability controls mean temperature change globally, whereas shorter-period astronomical forcings only affect the spatial pattern of thermal forcing and thus do not favour global synchronisation. This dynamical systems framework extends and complements existing theories by accomodating the differing mechanistic interpretations of previous studies without conflict.</p>

Greenhouses, hot water bottles, cycles and the future of New Zealand climate

2009 ◽  
pp. 61-67
Author(s):  
W.P. De Lange
Keyword(s):  
New Zealand ◽  
Thermal Energy ◽  
Infrared Radiation ◽  
Little Ice Age ◽  
Hot Water ◽  
Ice Age ◽  
The Sun ◽  
Weather Patterns ◽  
Time Periods ◽  
Almost All

The Greenhouse Effect acts to slow the escape of infrared radiation to space, and hence warms the atmosphere. The oceans derive almost all of their thermal energy from the sun, and none from infrared radiation in the atmosphere. The thermal energy stored by the oceans is transported globally and released after a range of different time periods. The release of thermal energy from the oceans modifies the behaviour of atmospheric circulation, and hence varies climate. Based on ocean behaviour, New Zealand can expect weather patterns similar to those from 1890-1922 and another Little Ice Age may develop this century.

LIMIT CYCLE BIFURCATIONS IN NEAR-HAMILTONIAN SYSTEMS BY PERTURBING A NILPOTENT CENTER

2008 ◽  
Vol 18 (10) ◽  
pp. 3013-3027 ◽  
Author(s):  
MAOAN HAN ◽  
JIAO JIANG ◽  
HUAIPING ZHU
Keyword(s):  
Limit Cycle ◽  
Limit Cycles ◽  
Unperturbed System ◽  
Bifurcation Theorem ◽  
First Order ◽  
Cubic System ◽  
Limit Cycle Bifurcation ◽  
Almost All ◽  
Nilpotent Center ◽  
Computing Method

As we know, Hopf bifurcation is an important part of bifurcation theory of dynamical systems. Almost all known works are concerned with the bifurcation and number of limit cycles near a nondegenerate focus or center. In the present paper, we study a general near-Hamiltonian system on the plane whose unperturbed system has a nilpotent center. We obtain an expansion for the first order Melnikov function near the center together with a computing method for the first coefficients. Using these coefficients, we obtain a new bifurcation theorem concerning the limit cycle bifurcation near the nilpotent center. An interesting application example & a cubic system having five limit cycles & is also presented.

Into the Icehouse

2012 ◽  
Author(s):  
Jan Zalasiewicz ◽  
Mark Williams
Keyword(s):  
The Body ◽  
Ice Age ◽  
Polar Regions ◽  
Earth System ◽  
The North ◽  
The World ◽  
The Face ◽  
Ancient Times ◽  
Almost All ◽  
Popular Image

The frozen lands of the north are an unforgiving place for humans to live. The Inuit view of the cosmos is that it is ruled by no one, with no gods to create wind and sun and ice, or to provide punishment or forgiveness, or to act as Earth Mother or Father. Amid those harsh landscapes, belief is superfluous, and only fear can be relied on as a guide. How could such a world begin, and end? In Nordic mythology, in ancient times there used to be a yet greater kingdom of ice, ruled by the ice giant, Ymir Aurgelmir. To make a world fit for humans, Ymir was killed by three brothers—Odin, Vilje, and Ve. The blood of the dying giant drowned his own children, and formed the seas, while the body of the dead giant became the land. To keep out other ice giants that yet lived in the far north, Odin and his brothers made a wall out of Ymir’s eyebrows. One may see, fancifully, those eyebrows still, in the form of the massive, curved lines of morainic hills that run across Sweden and Finland. We now have a popular image of Ymir’s domain—the past ‘Ice Age’—as snowy landscapes of a recent past, populated by mammoths and woolly rhinos and fur-clad humans (who would have been beginning to create such legends to explain the precarious world on which they lived). This image, as we have seen, represents a peculiarly northern perspective. The current ice age is geologically ancient, for the bulk of the world’s land-ice had already grown to cover almost all Antarctica, more than thirty million years ago. Nevertheless, a mere two and a half million years ago, there was a significant transition in Earth history—an intensification of the Earth’s icehouse state that spread more or less permanent ice widely across the northern polar regions of the world. This intensification— via those fiendishly complex teleconnections that characterize the Earth system—changed the face of the entire globe. The changes can be detected in the sedimentary strata that were then being deposited around the world.

Abiotic and biotic responses to Milankovitch-forced megamonsoon and glacial cycles recorded in South China at the end of the Late Paleozoic Ice Age

2018 ◽  
Vol 163 ◽  
pp. 97-108 ◽  
Author(s):  
Qiang Fang ◽  
Huaichun Wu ◽  
Linda A. Hinnov ◽  
Wenqian Tian ◽  
Xunlian Wang ◽  
...  
Keyword(s):  
South China ◽  
Ice Age ◽  
Late Paleozoic ◽  
Glacial Cycles ◽  
Late Paleozoic Ice Age

scholarly journals Predicting Pleistocene climate from vegetation in North America

2007 ◽  
Vol 3 (1) ◽  
pp. 109-118 ◽  
Author(s):  
C. Loehle
Keyword(s):  
North America ◽  
Ice Age ◽  
Temperate Species ◽  
Eastern North America ◽  
Biogeographic Patterns ◽  
Free Zone ◽  
Low Co2 ◽  
Pleistocene Climate ◽  
Co2 Levels ◽  
Climate Indicator

Abstract. Climates at the Last Glacial Maximum have been inferred from fossil pollen assemblages, but these inferred climates are colder for eastern North America than those produced by climate simulations. It has been suggested that low CO2 levels could account for this discrepancy. In this study biogeographic evidence is used to test the CO2 effect model. The recolonization of glaciated zones in eastern North America following the last ice age produced distinct biogeographic patterns. It has been assumed that a wide zone south of the ice was tundra or boreal parkland (Boreal-Parkland Zone or BPZ), which would have been recolonized from southern refugia as the ice melted, but the patterns in this zone differ from those in the glaciated zone, which creates a major biogeographic anomaly. In the glacial zone, there are few endemics but in the BPZ there are many across multiple taxa. In the glacial zone, there are the expected gradients of genetic diversity with distance from the ice-free zone, but no evidence of this is found in the BPZ. Many races and related species exist in the BPZ which would have merged or hybridized if confined to the same refugia. Evidence for distinct southern refugia for most temperate species is lacking. Extinctions of temperate flora were rare. The interpretation of spruce as a boreal climate indicator may be mistaken over much of the region if the spruce was actually an extinct temperate species. All of these anomalies call into question the concept that climates in the zone south of the ice were extremely cold or that temperate species had to migrate far to the south. An alternate hypothesis is that low CO2 levels gave an advantage to pine and spruce, which are the dominant trees in the BPZ, and to herbaceous species over trees, which also fits the observed pattern. Thus climate reconstruction from pollen data is probably biased and needs to incorporate CO2 effects. Most temperate species could have survived across their current ranges at lower abundance by retreating to moist microsites. These would be microrefugia not easily detected by pollen records, especially if most species became rare. These results mean that climate reconstructions based on terrestrial plant indicators will not be valid for periods with markedly different CO2 levels.

scholarly journals Nonlinear softening as a predictive precursor to climate tipping

2012 ◽  
Vol 370 (1962) ◽  
pp. 1205-1227 ◽  
Author(s):  
Jan Sieber ◽  
J. Michael T. Thompson
Keyword(s):  
Time Series ◽  
Basin Of Attraction ◽  
Stable State ◽  
Ice Age ◽  
Geological Time ◽  
Nonlinear Features ◽  
Last Ice Age ◽  
Earth’S Climate ◽  
Increasing Temperature ◽  
Linear Decay

Approaching a dangerous bifurcation, from which a dynamical system such as the Earth's climate will jump (tip) to a different state, the current stable state lies within a shrinking basin of attraction. Persistence of the state becomes increasingly precarious in the presence of noisy disturbances. We argue that one needs to extract information about the nonlinear features (a ‘softening’) of the underlying potential from the time series to judge the probability and timing of tipping. This analysis is the logical next step if one has detected a decrease of the linear decay rate. If there is no discernible trend in the linear analysis, nonlinear softening is even more important in showing the proximity to tipping. After extensive normal-form calibration studies, we check two geological time series from palaeo-climate tipping events for softening of the underlying well. For the ending of the last ice age, where we find no convincing linear precursor, we identify a statistically significant nonlinear softening towards increasing temperature.

On the astronomical forcing of simple conceptual ice age models

2020 ◽  
Author(s):  
Gaëlle Leloup ◽  
Didier Paillard
Keyword(s):  
Conceptual Model ◽  
Climate Model ◽  
Ice Age ◽  
Early Pleistocene ◽  
Model Parameters ◽  
Ice Ages ◽  
Glacial Cycles ◽  
Orbital Parameters ◽  
Ice Volume ◽  
Astronomical Forcing

<p>Variations of the Earth’s orbital parameters are known to pace the ice volume variations of the last million year [1], even if the precise mechanisms remain unknown.<br>Several conceptual models have been used to try to better understand the connection between ice-sheet changes and the astronomical forcing. An often overlooked question is to decide which astronomical forcing can best explain the observed cycles.</p><p>A rather traditional practice was to use the insolation at a some specific day of the year, for instance at mid-july [2] or at the june solstice [3].<br>But it was also suggested that the integrated forcing above some given threshold could be a better alternative [4]. In a more recent paper, Tzedakis et al. [5] have shown that simple rules, based on the original Milankovitch forcing or caloric seasons, could also be used to explain the timing of ice ages.<br>Here we adapt and simplify the conceptual model of Parrenin and Paillard 2003 [6], to first reduce the set of parameters.<br>Like in the original conceptual model from [6], this simplified conceptual model is based on climate oscillations between two states: glaciation and deglaciation. It switches to one another when crossing a defined threshold. While the triggering of glaciations is only triggered by orbital parameters, the triggering of deglaciations is triggered by a combination of orbital parameters and ice volume. <br>Then, we apply the different possible forcings listed above and we try to adapt the model parameters to reproduce the ice volume record, at least in a qualitative way. This allows us to discuss which kind of astronomical forcing better explains the Quaternary ice ages, in the context of such simple threshold-based models.</p><p>[1] Variations in the Earth's Orbit: Pacemaker of the Ice Ages, Hays et al., 1976, Science
</p><p>[2] Modeling the Climatic Response to Orbital Variations, Imbrie and Imbrie, 1980, Science
</p><p>[3] The timing of Pleistocene glaciations from a simple multiple-state climate model, Paillard, 1998, Nature</p><p>[4] Early Pleistocene Glacial Cycles and the Integrated Summer Insolation Forcing, Huybers et al., 2006, Science</p><p>[5] A simple rule to determine which insolation cycles lead to interglacials, Tzedakis et al., 2017, Nature</p><p>[6] Amplitude and phase of glacial cycles from a conceptual model, Parrenin Paillard, 2003, EPSL.</p>

scholarly journals How can a glacial inception be predicted?

The Holocene ◽  
2011 ◽  
Vol 21 (5) ◽  
pp. 831-842 ◽  
Author(s):  
Michel Crucifix
Keyword(s):  
Greenhouse Gas ◽  
Numerical Models ◽  
Climate System ◽  
Ice Age ◽  
Glacial Cycles ◽  
The Holocene ◽  
Stochastic Dynamical System ◽  
Northern Summer ◽  
External Forcings ◽  
Inference Network

The Early Anthropogenic Hypothesis considers that greenhouse gas concentrations should have declined during the Holocene in absence of humankind activity, leading to glacial inception around the present. It partly relies on the fact that present levels of northern summer incoming solar radiation are close to those that, in the past, preceded a glacial inception phenomenon, associated with declines in greenhouse gas concentrations. However, experiments with various numerical models of glacial cycles show that next glacial inception may still be delayed by several tens of thousands of years, even with the assumption of a decline in greenhouse gas concentrations during the Holocene. Furthermore, as we show here, conceptual models designed to capture the gross dynamics of the climate system as a whole suggest also that small disturbances may sometimes cause substantial delays in glacial events, causing a fair level of unpredictability on ice age dynamics. This suggests the need for a validated mathematical description of climate system dynamics that allows us to quantify uncertainties on predictions. Here, it is proposed to organise our knowledge about the physics and dynamics of glacial cycles through a Bayesian inference network. Constraints on the physics and dynamics of climate can be encapsulated into a stochastic dynamical system. These constraints include, in particular, estimates of the sensitivity of the components of climate to external forcings, inferred from plans of experiments with large simulators of the atmosphere, oceans and ice sheets. On the other hand, palaeoclimate observations are accounted for through a process of parameter calibration. We discuss promises and challenges raised by this programme.

Sign in / Sign up

Export Citation Format

Share Document