Oscillators and relaxation phenomena in Pleistocene climate theory

Ice sheets appeared in the northern hemisphere around 3 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 theses 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 synchronisation between internal climate dynamics and the 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 million years ago. All theories on rapid events reviewed here rely on the concept of a limit cycle in the ocean circulation, which may be excited by changes in the surface freshwater surface balance. 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. Keywords: palaeoclimates, dynamical systems, limit cycle, ice ages, Dansgaard-Oeschger eventsComment: Published in the Transactions of the Philosophical Transactions of the Royal Society (Series A, Physical Mathematical and Engineering Sciences), as a contribution to the Proceedings of the workshop on Stochastic Methods in Climate Modelling, Newton Institute (23-27 August). Philosophical Transactions of the Royal Society (Series A, Physical Mathematical and Engineering Sciences), vol. 370, pp. xx-xx (2012); Source codes available on request to author and on http://www.uclouvain.be/ito

Bayesian model selection for the glacial-interglacial cycle

A prevailing viewpoint in paleoclimate science is that a single paleoclimate record contains insufficient information to discriminate between typical competing explanatory models. Here we show that by using SMC 2 (sequential Monte Carlo squared) combined with novel Brownian bridge type proposals for the state trajectories, it is possible to estimate Bayes factors to sufficient accuracy to be able to select between competing models, even with relatively short time series. The results show that Monte Carlo methodology and computer power have now advanced to the point where a full Bayesian analysis for a wide class of conceptual climate models is now possible. The results also highlight a problem with estimating the chronology of the climate record prior to further statistical analysis, a practice which is common in paleoclimate science. Using two datasets based on the same record but with different estimated chronologies, results in conflicting conclusions about the importance of the astronomical forcing on the glacial cycle, and about the internal dynamics generating the glacial cycle, even though the difference between the two estimated chronologies is consistent with dating uncertainty. This highlights a need for chronology estimation and other inferential questions to be addressed in a joint statistical procedure

Quantifying age and model uncertainties in palaeoclimate data and dynamical climate models with a joint inferential analysis

The study of palaeoclimates relies on information sampled in natural archives such as deep sea cores. Scientific investigations often use such information in multi-stage analyses, typically with an age model being fitted to a core to convert depths into ages at stage one. These age estimates are then used as inputs to develop, calibrate or select climate models in a second stage of analysis. Here, we show that such multi-stage approaches can lead to misleading conclusions, and develop a joint inferential approach for climate reconstruction, model calibration and age estimation. As an illustration, we investigate the glacial–interglacial cycle, fitting both an age model and dynamical climate model to two benthic sediment cores spanning the past 780 kyr. To show the danger of a multi-stage analysis, we sample ages from the posterior distribution, then perform model selection conditional on the sampled age estimates, mimicking standard practice. Doing so repeatedly for different samples leads to model selection conclusions that are substantially different from each other, and from the joint inferential analysis. We conclude that multi-stage analyses are insufficient when dealing with uncertainty, and that to draw sound conclusions the full joint inferential analysis should be performed

On the Sensitivity of the Devonian Climate to Continental Configuration, Vegetation Cover, Orbital Configuration, CO 2 Concentration, and Insolation

During the Devonian (419 to 359 million years ago), life on Earth witnessed decisive evolutionary breakthroughs, most prominently the colonization of land by vascular plants and vertebrates. However, it was also a period of major marine extinctions coinciding with marked changes in climate. The cause of these changes remains unknown, and it is therefore instructive to explore systematically how the Devonian climate responds to changes in boundary conditions. Here we use coupled climate model simulations to investigate separately the influence of changes in continental configuration, vegetation cover, carbon dioxide (CO2) concentrations, the solar constant, and orbital parameters on the Devonian climate. The biogeophysical effect of changes in vegetation cover is small, and the cooling due to continental drift is offset by the increasing solar constant. Variations of orbital parameters affect the Devonian climate, with the warmest climate states at high obliquity and high eccentricity. The prevailing mode of decadal to centennial climate variability relates to temperature fluctuations in high northern latitudes which are mediated by coupled oscillations involving sea ice cover, ocean convection, and a regional overturning circulation. The temperature evolution during the Devonian is dominated by the strong decrease in atmospheric CO2. Albedo changes due to increasing vegetation cover cannot explain the temperature rise found in Late Devonian proxy data. Finally, simulated temperatures are significantly lower than estimates based on oxygen isotope ratios, suggesting a lower d18O ratio of Devonian seawater. ©2019. The Authors

Obliquity pacing of the late Pleistocene glacial terminations

Author Posting. © The Authors, 2005. This is the author's version of the work. It is posted here by permission of Nature Publishing Group for personal use, not for redistribution. The definitive version was published in Nature 434 (2005): 491-494, doi:10.1038/nature03401.The timing of glacial/interglacial cycles at intervals of about 100,000 yr (100 kyr) is commonly attributed to control by Earth orbital configuration variations. This “pacemaker” hypothesis has inspired many models, variously depending upon Earth obliquity, orbital eccentricity, and precessional fluctuations, with the latter usually emphasized. A contrasting hypothesis is that glacial cycles arise primarily because of random internal climate variability. Progress requires distinguishing between the more than 30 proposed models of the late Pleistocene glacial variations. Here we present a formal test of the pacemaker hypothesis, focusing on the rapid deglaciation events known as terminations. The null hypothesis that glacial terminations are independent of obliquity can be rejected at the 5% significance level. In contrast, for eccentricity and precession, the corresponding null-hypotheses cannot be rejected. The simplest inference, consistent with the observations, is that ice-sheets terminate every second (80 kyr) or third (120 kyr) obliquity cycle — at times of high obliquity — and similar to the original Milankovitch assumption. Hypotheses not accounting for the obliquity pacing are unlikely to be correct. Both stochastic and deterministic variants of a simple obliquity-paced model describe the observations.PH is supported by the NOAA Postdoctoral Program in Climate and Global Change and CW in part by the National Ocean Partnership Program (ECCO)

Climatic control on palaeohydrology and cyclical sediment distribution in the Plio-Quaternary deposits of the Guadix Basin (Betic Cordillera, Spain)

A cyclical pattern can be observed in the central sector of the Guadix Basin (southern Spain) in the Late Pliocene-Quaternary alluvial fan deposits prograding into its axial valley. A climatic significance has been attributed to this cyclicity on the basis of sedimentological and preliminary isotopic studies. The progradation phases of the alluvial fans are here attributed to more arid time intervals in which the vegetation cover would be less developed, erosion and sediment supply would be higher, and base level would be lower. In contrast, the time intervals during which the fluvial system sediments dominated the area are inferred to be wetter and base level higher, with vegetation cover retaining the soils and preventing erosion. Permanent water supply to the river would therefore facilitate the aggradation of the floodplain and prevent progradation of the fans. Starting from a litho-, bio- and magnetostratigraphical frame provided for the area, an age is assigned to the alternation of the reddish sediments of the transverse alluvial fans and the greyish to white fluvio-lacustrine sediments of the axial drainage system. A cyclicity of ca. 100 ky has been identified in most of the alluvial fan progradation phases, falling within Milankovitch high-frequency eccentricity periodicities. Correlation of the phases with insolation curves is accordingly discussed as a possible origin for the cyclicity. Finally, the results offer new insights into early hominin occupation patterns in the region, through the identification of predictable resources of permanent fresh water that would have remained available throughout the recorded time span (that includes the Early–Middle Pleistocene transition) even during times of aridification.The study was supported by the Project CGL2009-07830/BTE and the Working Group RNM-369JA

Paleoclimate Implications for Human-Made Climate Change

Paleoclimate data help us assess climate sensitivity and potential human-made climate effects. We conclude that Earth in the warmest interglacial periods of the past million years was less than 1{\deg}C warmer than in the Holocene. Polar warmth in these interglacials and in the Pliocene does not imply that a substantial cushion remains between today's climate and dangerous warming, but rather that Earth is poised to experience strong amplifying polar feedbacks in response to moderate global warming. Thus goals to limit human-made warming to 2{\deg}C are not sufficient - they are prescriptions for disaster. Ice sheet disintegration is nonlinear, spurred by amplifying feedbacks. We suggest that ice sheet mass loss, if warming continues unabated, will be characterized better by a doubling time for mass loss rate than by a linear trend. Satellite gravity data, though too brief to be conclusive, are consistent with a doubling time of 10 years or less, implying the possibility of multi-meter sea level rise this century. Observed accelerating ice sheet mass loss supports our conclusion that Earth's temperature now exceeds the mean Holocene value. Rapid reduction of fossil fuel emissions is required for humanity to succeed in preserving a planet resembling the one on which civilization developed.Comment: 32 pages, 9 figures; final version accepted for publication in "Climate Change at the Eve of the Second Decade of the Century: Inferences from Paleoclimate and Regional Aspects: Proceedings of Milutin Milankovitch 130th Anniversary Symposium" (eds. Berger, Mesinger and Sijaci

Is the astronomical forcing a reliable and unique pacemaker for climate? A conceptual model study

There is evidence that ice age cycles are paced by astronomical forcing, suggesting some kind of synchronisation phenomenon. Here, we identify the type of such synchronisation and explore systematically its uniqueness and robustness using a simple paleoclimate model akin to the van der Pol relaxation oscillator and dynamical system theory. As the insolation is quite a complex quasiperiodic signal involving different frequencies, the traditional concepts used to define synchronisation to periodic forcing are no longer applicable. Instead, we explore a different concept of generalised synchronisation in terms of (coexisting) synchronised solutions for the forced system, their basins of attraction and instabilities. We propose a clustering technique to compute the number of synchronised solutions, each of which corresponds to a different paleoclimate history. In this way, we uncover multistable synchronisation (reminiscent of phase- or frequency-locking to individual periodic components of astronomical forcing) at low forcing strength, and monostable or unique synchronisation at stronger forcing. In the multistable regime, different initial conditions may lead to different paleoclimate histories. To study their robustness, we analyse Lyapunov exponents that quantify the rate of convergence towards each synchronised solution (local stability), and basins of attraction that indicate critical levels of external perturbations (global stability). We find that even though synchronised solutions are stable on a long term, there exist short episodes of desynchronisation where nearby climate trajectories diverge temporarily (for about 50 kyr). (...)Comment: 22 pages, 18 figure

On the maintenance of the axisymmetric part of the flow in the atmosphere

The maintenance of the axisymmetric component of the flow in the atmosphere is investigated by means of a steady-state, quasi-geostrophic formulation of the meteorological equations. It is shown that the meridional variations in the time-averaged axisymmetric variables can be expressed as the sum of three contributions, one being due to the eddy heat transport, another to the eddy momentum transport, and a third to the convective-radiative equilibrium temperature which enters the problem through the specification of a Newtonian form of diabatic heating. The contributions by the large scale eddies are evaluated through the use of observed values for the eddy heat and momentum transports.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/43251/1/24_2004_Article_BF00878865.pd