The Mid-Pleistocene Transition induced by delayed feedback and bistability

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, in the absence of astronomical forcing, the delayed feedback leads to bistable behaviour, where stable large-amplitude oscillations of ice volume and an equilibrium coexist over a large range of values for the delay. We then apply astronomical forcing. We perform a systematic study to show how the system response depends on the forcing amplitude. We find that over a wide range of forcing amplitudes the forcing leads to a switch from small-scale oscillations of 41 kyr to large-amplitude oscillations of roughly 100 kyr without any change of other parameters. The transition in the forced model consistently occurs near the time of the Mid-Pleistocene Transition as observed in data records. This provides evidence that the MPT could have been primarily a forcing-induced switch between attractors of the internal dynamics. Small additional random disturbances make the forcing-induced transition near 800 kyr BP even more robust. We also find that the forced system forgets its initial history during the small-scale oscillations, in particular, nearby initial conditions converge prior to transitioning. In contrast to this, in the regime of large-amplitude oscillations, the oscillation phase is very sensitive to random perturbations, which has a strong effect on the timing of the deglaciation events

Signatures consistent with multi-frequency tipping in the Atlantic meridional overturning circulation

The early detection of tipping points, which describe a rapid departure from a stable state, is an important theoretical and practical challenge. Tipping points are most commonly associated with the disappearance of steady state or periodic solutions at fold bifurcations and are often associated with hysteresis loops. We discuss here multi-frequency tipping (M-tipping), which is tipping due to the disappearance of an attracting torus. M-tipping is a generic phenomenon in systems with at least two intrinsic or external frequencies that can interact and, hence, relevant to a wide variety of systems of interest. We show that the more complicated sequence of bifurcations involved in M-tipping provides a possible consistent explanation for as yet unexplained behaviour observed near tipping in climate models for the Atlantic meridional overturning circulation. More generally, this work provides a path towards identifying possible early-warning signs of tipping in multiple-frequency systems.Comment: 14 pages, 4 figure

Early warning signals of tipping points in periodically forced systems

This is the final version of the article. Available from the European Geosciences Union via the DOI in this record.The prospect of finding generic early warning signals of an approaching tipping point in a complex system has generated much interest recently. Existing methods are predicated on a separation of timescales between the system studied and its forcing. However, many systems, including several candidate tipping elements in the climate system, are forced periodically at a timescale comparable to their internal dynamics. Here we use alternative early warning signals of tipping points due to local bifurcations in systems subjected to periodic forcing whose timescale is similar to the period of the forcing. These systems are not in, or close to, a fixed point. Instead their steady state is described by a periodic attractor. For these systems, phase lag and amplification of the system response can provide early warning signals, based on a linear dynamics approximation. Furthermore, the Fourier spectrum of the system's time series reveals harmonics of the forcing period in the system response whose amplitude is related to how nonlinear the system's response is becoming with nonlinear effects becoming more prominent closer to a bifurcation. We apply these indicators as well as a return map analysis to a simple conceptual system and satellite observations of Arctic sea ice area, the latter conjectured to have a bifurcation type tipping point. We find no detectable signal of the Arctic sea ice approaching a local bifurcation.The research leading to these results has received funding from the European Union Seventh Framework Programme FP7/2007-2013 under grant agreement no. 603864 (HELIX). We are grateful to Peter Ashwin, Peter Cox, Michel Crucifix, Vasilis Dakos, Henk Dijkstra, Jan Sieber, Marten Scheffer and Appy Sluijs for the fruitful discussions over beers and balls

A morphometric analysis of vegetation patterns in dryland ecosystems

Vegetation in dryland ecosystems often forms remarkable spatial patterns. These range from regular bands of vegetation alternating with bare ground, to vegetated spots and labyrinths, to regular gaps of bare ground within an otherwise continuous expanse of vegetation. It has been suggested that spotted vegetation patterns could indicate that collapse into a bare ground state is imminent, and the morphology of spatial vegetation patterns, therefore, represents a potentially valuable source of information on the proximity of regime shifts in dryland ecosystems. In this paper, we have developed quantitative methods to characterize the morphology of spatial patterns in dryland vegetation. Our approach is based on algorithmic techniques that have been used to classify pollen grains on the basis of textural patterning, and involves constructing feature vectors to quantify the shapes formed by vegetation patterns. We have analysed images of patterned vegetation produced by a computational model and a small set of satellite images from South Kordofan (South Sudan), which illustrates that our methods are applicable to both simulated and real-world data. Our approach provides a means of quantifying patterns that are frequently described using qualitative terminology, and could be used to classify vegetation patterns in large-scale satellite surveys of dryland ecosystems

JULES-BE:Representation of bioenergy crops and harvesting in the Joint UK Land Environment Simulator vn5.1

We describe developments to the land surface model JULES, allowing for flexible user-prescribed harvest regimes of various perennial bioenergy crops or natural vegetation types. Our aim is to integrate the most useful aspects of dedicated bioenergy models into dynamic global vegetation models, in order that assessment of bioenergy options can benefit from state-of-the-art Earth system modelling. A new plant functional type (PFT) representing Miscanthus is also presented. The Miscanthus PFT fits well with growth parameters observed at a site in Lincolnshire, UK; however, global observed yields of Miscanthus are far more variable than is captured by the model, primarily owing to the model's lack of representation of crop age and establishment time. Global expansion of bioenergy crop areas under a 2 ?C emissions scenario and balanced greenhouse gas mitigation strategy from the IMAGE integrated assessment model (RCP2.6- SSP2) achieves a mean yield of 4.3 billion tonnes of dry matter per year over 2040-2099, around 30 % higher than the biomass availability projected by IMAGE. In addition to perennial grasses, JULES-BE can also be used to represent short-rotation coppicing, residue harvesting from cropland or forestry and rotation forestry

A modeling case for high atmospheric oxygen concentrations during the Mesozoic and Cenozoic

Changes in atmospheric oxygen concentration over Earth history are commonly related to the evolution of animals and plants. But there is no direct geochemical proxy for O2 levels, meaning that estimations rely heavily on modeling approaches. The results of such studies differ greatly, to the extent that today's atmospheric mixing ratio of 21% might be either the highest or lowest level during the past 200 m.y. Long-term oxygen sources, such as the burial in sediments of reduced carbon and sulfur species, are calculated in models by representation of nutrient cycling and estimation of productivity, or by isotope mass balance (IMB)—a technique in which burial rates are inferred in order to match known isotope records. Studies utilizing these different techniques produce conflicting estimates for paleoatmospheric O2, with nutrient-weathering models estimating concentrations close to, or above, that of the present day, and IMB models estimating low O2, especially during the Mesozoic. Here we re-assess the IMB technique using the COPSE biogeochemical model. IMB modelling is confirmed to be highly sensitive to assumed carbonate δ13C, and when this input is defined following recent compilations, predicted O2 is significantly higher and in reasonable agreement with that of non-IMB techniques. We conclude that there is no model-based support for low atmospheric oxygen concentrations during the past 200 m.y. High Mesozoic O2 is consistent with wildfire records and the development of plant fire adaptions, but links between O2 and mammal evolution appear more tenuous

The limits to global-warming mitigation by terrestrial carbon removal

Massive near‐term greenhouse gas emissions reduction is a precondition for staying “well below 2°C” global warming as envisaged by the Paris Agreement. Furthermore, extensive terrestrial carbon dioxide removal (tCDR) through managed biomass growth and subsequent carbon capture and storage is required to avoid temperature “overshoot” in most pertinent scenarios. Here, we address two major issues: First, we calculate the extent of tCDR required to “repair” delayed or insufficient emissions reduction policies unable to prevent global mean temperature rise of 2.5°C or even 4.5°C above pre‐industrial level. Our results show that those tCDR measures are unable to counteract “business‐as‐usual” emissions without eliminating virtually all natural ecosystems. Even if considerable (Representative Concentration Pathway 4.5 [RCP4.5]) emissions reductions are assumed, tCDR with 50% storage efficiency requires >1.1 Gha of the most productive agricultural areas or the elimination of >50% of natural forests. In addition, >100 MtN/yr fertilizers would be needed to remove the roughly 320 GtC foreseen in these scenarios. Such interventions would severely compromise food production and/or biosphere functioning. Second, we reanalyze the requirements for achieving the 160–190 GtC tCDR that would complement strong mitigation action (RCP2.6) in order to avoid 2°C overshoot anytime. We find that a combination of high irrigation water input and/or more efficient conversion to stored carbon is necessary. In the face of severe trade‐offs with society and the biosphere, we conclude that large‐scale tCDR is not a viable alternative to aggressive emissions reduction. However, we argue that tCDR might serve as a valuable “supporting actor” for strong mitigation if sustainable schemes are established immediately

Enhanced clay formation key in sustaining the Middle Eocene Climatic Optimum

The Middle Eocene Climatic Optimum (around 40 million years ago) was a roughly 400,000-year-long global warming phase associated with an increase in atmospheric CO2 concentrations and deep-ocean acidifcation that interrupted the Eocene’s long-term cooling trend. The unusually long duration, compared with early Eocene global warming phases, is puzzling as temperature-dependent silicate weathering should have provided a negative feedback, drawing down CO2 over this timescale. Here we investigate silicate weathering during this climate warming event by measuring lithium isotope ratios (reported as δ7 Li), which are a tracer for silicate weathering processes, from a suite of open-ocean carbonate-rich sediments. We fnd a positive δ7 Li excursion—the only one identifed for a warming event so far —of ~3‰. Box model simulations support this signal to refect a global shift from congruent weathering, with secondary mineral dissolution, to incongruent weathering, with secondary mineral formation. We surmise that, before the climatic optimum, there was considerable soil shielding of the continents. An increase in continental volcanism initiated the warming event, but it was sustained by an increase in clay formation, which sequestered carbonate-forming cations, short-circuiting the carbonate–silicate cycle. Clay mineral dynamics may play an important role in the carbon cycle for climatic events occurring over intermediate (i.e., 100,000 year) timeframes