The climate record preserved in polar glaciers, mountain glaciers, and widespread cave deposits shows repeated occurrence of abrupt global transitions between cold/dry stadial and warm/wet interstadial states during glacial periods. These abrupt transitions occur on millennial time scale and in the absence of any known global-scale forcing. Here a theory is advanced implicating a feedback between atmospheric dust and the hydrological cycle in producing these abrupt transitions. Calculations are performed using a radiative-convective model that includes the interaction of aerosols with radiation to reveal the mechanism of the dust/precipitation interaction feedback process and a Langevin equation is used to model glacial climate destabilization by this mechanism. This theory explains the observed bimodal, stochastic, and abrupt nature of the transitions as well as their intrinsic connection with the hydrological cycle.
The last glacial period was punctuated by a series of abrupt climate shifts, the so-called Dansgaard-Oeschger (DO) events. The frequency of DO events varied in time, supposedly because of changes in background climate conditions. Here, the influence of external forcings on DO events is investigated with statistical modelling. We assume two types of simple stochastic dynamical systems models (double-well potential-type and oscillator-type), forced by the northern hemisphere summer insolation change and/or the global ice volume change. The model parameters are estimated by using the maximum like…
Here we use a very simple conceptual model in an attempt to reduce essential parts of the complex nonlinearity of abrupt glacial climate changes (the so-called Dansgaard-Oeschger events) to a few simple principles, namely (i) a threshold process, (ii) an overshooting in the stability of the system and (iii) a millennial-scale relaxation. By comparison with a so-called Earth system model of intermediate complexity (CLIMBER-2), in which the events represent oscillations between two climate states corresponding to two fundamentally different modes of deep-water formation in the North Atlantic, we…
Following the mid-Pleistocene transition, the dominant period of glacial cycles changed from 40 ka to ~100 ka. It is broadly accepted that the 40 ka glacial cycles were driven by cyclical changes in obliquity. However, this forcing does not explain the ~100 ka glacial cycles. Mechanisms have been proposed for ~100 ka cycles, but none are universally accepted. Any proposed mechanism for ~100 ka glacial cycles must give the Earth's climate system a memory of tens-of-thousands-of-years. This timescale is difficult to achieve for surface processes, however it is possible for the solid Earth. Recen…
Stochastic coupling of climate variables and ice volume over the Late Pleistocene glacial cycles
Nordita, KTH Royal Institute of Technology and Stockholm University（诺尔迪塔，瑞典皇家理工学院和斯德哥尔摩大学）；Department of Mathematics, Massachusetts Institute of Technology（麻省理工学院数学系）；Departments of Mathematics, Earth & Planetary Sciences, and Physics, Yale University（耶鲁大学数学、地球与行星科学及物理系）
The dynamics of glacial cycles is studied in terms of the dynamical systems theory. We explore the dependence of the climate state on the phase of astronomical forcing by examining five conceptual models of glacial cycles proposed in the literature. The models can be expressed as quasiperiodically forced dynamical systems. It is shown that four of them exhibit a strange nonchaotic attractor (SNA), which is an intermediate regime between quasiperiodicity and chaos. Then, the dependence of the climate state on the phase of astronomical forcing is not given by smooth relations, but constitutes a …
Over the last few decades, climate scientists have devoted much effort to the development of large numerical models of the atmosphere and the ocean. While there is no question that such models provide important and useful information on complicated aspects of atmosphere and ocean dynamics, skillful prediction also requires a phenomenological approach, particularly for very slow processes, such as glacial-interglacial cycles. Phenomenological models are often represented as low-order dynamical systems. These are tractable, and a rich source of insights about climate dynamics, but they also igno…
A review of the recent refereed literature fails to confirm quantitatively that carbon dioxide (CO2) radiative forcing was the prime mover in the changes in temperature, ice-sheet volume, and related climatic variables in the glacial and interglacial periods of the past 650,000 years, even under the "fast response" framework where the convenient if artificial distinction between forcing and feedback is assumed. Atmospheric CO2 variations generally follow changes in temperature and other climatic variables rather than preceding them. Likewise, there is no confirmation of the often-posited signi…
Conceptual climate models provide an approach to understanding climate processes through a mathematical analysis of an approximation to reality. Recently, these models have also provided interesting examples of nonsmooth dynamical systems. Here we discuss a conceptual model of glacial cycles consisting of a system of three ordinary differential equations defining a discontinuous vector field. We show that this system has a large periodic orbit crossing the discontinuity boundary. This orbit can be interpreted as an intrinsic cycling of the Earth's climate giving rise to alternating glaciations…
The glacial cycles are attributed to the climatic response of the orbital changes in the irradiance to the Earth. These changes in the forcing are to small to explain the observed climate variations as simple linear responses. Non-linear amplifications are necessary to account for the glacial cycles. Here an empirical model of the non-linear response is presented. From the model it is possible to assess the role of stochastic noise in comparison to the deterministic orbital forcing of the ice ages. The model is based on the bifurcation structure derived from the climate history. It indicates t…
The Earth, like other planets with a relatively thick atmosphere, is not locally in radiative equilibrium and the transport of energy by the geophysical fluids (atmosphere and ocean) plays a fundamental role in determining its climate. Using simple energy-balance models, it was suggested a few decades ago that the meridional energy fluxes might follow a thermodynamic Maximum Entropy Production (MEP) principle. In the present study, we assess the MEP hypothesis in the framework of a minimal climate model based solely on a robust radiative scheme and the MEP principle, with no extra assumptions.…
Climate variability over the past million years shows a strong glacial-interglacial cycle of ~100,000 years as a combined result of Milankovitch orbital forcing and climatic resonance. It has been suggested that anthropogenic contributions to radiative forcing may extend the length of the present interglacial, but the effects of anthropogenic forcing on the periodicity of glacial-interglacial cycles has received little attention. Here I demonstrate that moderate anthropogenic forcing can act to damp this 100,000 year cycle and reduce climate variability from orbital forcing. Future changes in …
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 to 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 ten thousands of years, even with…
An intriguing problem in climate science is the existence of Earth's glacial cycles. We show that it is possible to generate these periodic changes in climate by means of the Earth's carbon cycle as the main determinant factor. The carbon exchange between the Ocean, the Continent and the Atmosphere is modeled by means of a tridimensional Lotka-Volterra system and the resulting atmospheric carbon cycle is used as the unique radiative forcing mechanism. It is shown that the carbon dioxide (CO$_{2}$) and temperature anomaly curves, which are thus obtained, have the same first-order structure as t…
We present a new conceptual model of the Earth's glacial-interglacial cycles, one leading to governing equations for which the vector field has a hyperplane of discontinuities. This work extends the classic Budyko- and Sellers-type conceptual energy balance models of temperature-albedo feedback by removing the standard assumption of planetary symmetry about the equator. The dynamics of separate Northern and Southern Hemisphere ice caps are coupled to an equation representing the annual global mean surface temperature. The system has a discontinuous switching mechanism based on mass balance pri…
Glacial-interglacial cycles are large variations in continental ice mass and greenhouse gases, which have dominated climate variability over the Quaternary. The dominant periodicity of the cycles is $\sim $40 kyr before the so-called middle Pleistocene transition between $\sim$1.2 and $\sim$0.7 Myr ago, and it is $\sim $100 kyr after the transition. In this paper, the dynamics of glacial-interglacial cycles are investigated using a phase oscillator model forced by the time-varying incoming solar radiation (insolation). We analyze the bifurcations of the system and show that strange nonchaotic …
Palaeo data have been frequently used to determine the equilibrium (Charney) climate sensitivity $S^a$, and - if slow feedback processes (e.g. land ice-albedo) are adequately taken into account - they indicate a similar range as estimates based on instrumental data and climate model results. Most studies implicitly assume the (fast) feedback processes to be independent of the background climate state, e.g., equally strong during warm and cold periods. Here we assess the dependency of the fast feedback processes on the background climate state using data of the last 800 kyr and a conceptual cli…
A stable hothouse triggered by a tipping mechanism
Brevan Howard Centre for Financial Analysis, Imperial College Business School, Imperial College London（帝国理工学院商业学院布雷文·霍华德金融分析中心）；Laboratoire de Météorologie Dynamique (CNRS & IPSL), Ecole Polytechnique（巴黎综合理工学院动力气象学实验室（法国国家科学研究中心与IPSL））；Unit of Theoretical Chronobiology, Faculty of Sciences, Université Libre de Bruxelles（布鲁塞尔自由大学理学院理论时间生物学单元）；Geosciences Department and Laboratoire de Météorologie Dynamique (CNRS & IPSL), Ecole Normale Supérieure and PSL University（巴黎高等师范学院和PSL大学地质科学系及动力气象学实验室（法国国家科学研究中心与IPSL））；Department of Atmospheric and Oceanic Sciences, University of California, Los Angeles（加州大学洛杉矶分校大气与海洋科学系）；Department of Mathematics, Imperial College London（帝国理工学院数学系）
The Milankovitch theory states that the orbital eccentricity, precession, and obliquity of the Earth influence our climate by modulating the summer insolation at high latitudes in the northern hemisphere. Despite considerable success of this theory in explaining climate change over the Pleistocene epoch (2.6 to 0.01 Myr ago), it is inconclusive with regard to which combination of orbital elements paced the 100 kyr glacial-interglacial cycles over the late Pleistocene. Here we explore the role of the orbital elements in pacing the Pleistocene deglaciations by modeling ice-volume variations in a…
The solution of energy-balance model of the Earth global climate and the EPICA Dome C and Vostok experimental data of the Earth surface palaeotemperature evolution over past 420 and 740 kyr are compared. In the framework of proposed bifurcation model (i) the possible sharp warmings of the Dansgaard-Oeschger type during the last glacial period due to stochastic resonance is theoretically argued; (ii) the concept of climatic sensitivity of water in the atmosphere, whose temperature instability has the form of so-called hysteresis loop, is proposed, and based of this concept the time series of gl…
The detection of cause-effect relationships from the analysis of paleoclimatic records is a crucial step to disentangle the main mechanisms at work in the climate system. Here, we show that the approach based on the generalized Fluctuation-Dissipation Relation, complemented by the analysis of the Transfer Entropy, allows the causal links to be identified between temperature, CO2 concentration and astronomical forcing during the glacial cycles of the last 800 kyr based on Antarctic ice core records. When considering the whole spectrum of time scales, the results of the analysis suggest that tem…
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 pr…
A striking correlation has recently been observed between global cloud cover and the flux of incident cosmic rays. The effect of natural variations in the cosmic ray flux is large, causing estimated changes in the Earth's energy radiation balance that are comparable to those attributed to greenhouse gases from the burning of fossil fuels since the Industrial Revolution. However a direct link between cosmic rays and cloud formation has not been unambiguously established. We therefore propose to experimentally measure cloud (water droplet) formation under controlled conditions in a test beam at …
The Mid-Pleistocene Transition, the shift from 41 kyr to 100 kyr glacial-interglacial cycles that occurred roughly 1 Myr ago, is often considered as a change in internal climate dynamics. Here we revisit the model of Quaternary climate dynamics that was proposed by Saltzman and Maasch (1988). We show that it is quantitatively similar to a scalar equation for the ice dynamics only when combining the remaining components into a single delayed feedback term. The delay is the sum of the internal times scales of ocean transport and ice sheet dynamics, which is on the order of 10 kyr. We find that, …
