scholarly journals Early warning signals of tipping points in periodically forced systems

2016 ◽  
Vol 7 (2) ◽  
pp. 313-326 ◽  
Author(s):  
Mark S. Williamson ◽  
Sebastian Bathiany ◽  
Timothy M. Lenton
Keyword(s):  
Sea Ice ◽  
Early Warning ◽  
Tipping Point ◽  
Arctic Sea Ice ◽  
The Arctic ◽  
System Response ◽  
Tipping Points ◽  
Warning Signals ◽  
Early Warning Signals ◽  
Arctic Sea

Abstract. 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.

scholarly journals Early warning signals of tipping points in periodically forced systems

2015 ◽  
Vol 6 (2) ◽  
pp. 2243-2272 ◽  
Author(s):  
M. S. Williamson ◽  
S. Bathiany ◽  
T. M. Lenton
Keyword(s):  
Sea Ice ◽  
Early Warning ◽  
Tipping Point ◽  
Arctic Sea Ice ◽  
The Arctic ◽  
System Response ◽  
Tipping Points ◽  
Warning Signals ◽  
Early Warning Signals ◽  
Arctic Sea

Abstract. The prospect of finding generic early warning signals of an approaching tipping point in a complex system has generated much recent interest. 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 find alternative early warning signals of tipping points due to local bifurcations in systems subjected to periodic forcing whose time scale 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. We show that the phase lag and amplification of the system response provide early warning signals, based on a linear dynamics approximation. Furthermore, the power spectrum of the system's time series reveals the generation of harmonics of the forcing period, the size of which are proportional to how nonlinear the system's response is becoming with nonlinear effects becoming more prominent closer to a bifurcation. We apply these indicators 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.

scholarly journals A recent tipping point in the Arctic sea-ice cover: abrupt and persistent increase in the seasonal cycle since 2007

2013 ◽  
Vol 7 (1) ◽  
pp. 275-286 ◽  
Author(s):  
V. N. Livina ◽  
T. M. Lenton
Keyword(s):  
Sea Ice ◽  
Satellite Data ◽  
Early Warning ◽  
Seasonal Cycle ◽  
Ice Cover ◽  
Tipping Point ◽  
Arctic Sea Ice ◽  
The Arctic ◽  
Series Data ◽  
Arctic Sea

Abstract. There is ongoing debate over whether Arctic sea ice has already passed a "tipping point", or whether it will do so in the future. Several recent studies argue that the loss of summer sea ice does not involve an irreversible bifurcation, because it is highly reversible in models. However, a broader definition of a "tipping point" also includes other abrupt, non-linear changes that are neither bifurcations nor necessarily irreversible. Examination of satellite data for Arctic sea-ice area reveals an abrupt increase in the amplitude of seasonal variability in 2007 that has persisted since then. We identified this abrupt transition using recently developed methods that can detect multi-modality in time-series data and sometimes forewarn of bifurcations. When removing the mean seasonal cycle (up to 2008) from the satellite data, the residual sea-ice fluctuations switch from uni-modal to multi-modal behaviour around 2007. We originally interpreted this as a bifurcation in which a new lower ice cover attractor appears in deseasonalised fluctuations and is sampled in every summer–autumn from 2007 onwards. However, this interpretation is clearly sensitive to how the seasonal cycle is removed from the raw data, and to the presence of continental land masses restricting winter–spring ice fluctuations. Furthermore, there was no robust early warning signal of critical slowing down prior to the hypothesized bifurcation. Early warning indicators do however show destabilization of the summer–autumn sea-ice cover since 2007. Thus, the bifurcation hypothesis lacks consistent support, but there was an abrupt and persistent increase in the amplitude of the seasonal cycle of Arctic sea-ice cover in 2007, which we describe as a (non-bifurcation) "tipping point". Our statistical methods detect this "tipping point" and its time of onset. We discuss potential geophysical mechanisms behind it, which should be the subject of further work with process-based models.

The Thinning of Arctic Sea Ice, 1988–2003: Have We Passed a Tipping Point?

2005 ◽  
Vol 18 (22) ◽  
pp. 4879-4894 ◽  
Author(s):  
R. W. Lindsay ◽  
J. Zhang
Keyword(s):  
Sea Ice ◽  
Open Water ◽  
Ocean Model ◽  
Tipping Point ◽  
Arctic Sea Ice ◽  
The Arctic ◽  
First Year ◽  
Positive Feedbacks ◽  
Cooling Period ◽  
Arctic Sea

Abstract Recent observations of summer Arctic sea ice over the satellite era show that record or near-record lows for the ice extent occurred in the years 2002–05. To determine the physical processes contributing to these changes in the Arctic pack ice, model results from a regional coupled ice–ocean model have been analyzed. Since 1988 the thickness of the simulated basinwide ice thinned by 1.31 m or 43%. The thinning is greatest along the coast in the sector from the Chukchi Sea to the Beaufort Sea to Greenland. It is hypothesized that the thinning since 1988 is due to preconditioning, a trigger, and positive feedbacks: 1) the fall, winter, and spring air temperatures over the Arctic Ocean have gradually increased over the last 50 yr, leading to reduced thickness of first-year ice at the start of summer; 2) a temporary shift, starting in 1989, of two principal climate indexes (the Arctic Oscillation and Pacific Decadal Oscillation) caused a flushing of some of the older, thicker ice out of the basin and an increase in the summer open water extent; and 3) the increasing amounts of summer open water allow for increasing absorption of solar radiation, which melts the ice, warms the water, and promotes creation of thinner first-year ice, ice that often entirely melts by the end of the subsequent summer. Internal thermodynamic changes related to the positive ice–albedo feedback, not external forcing, dominate the thinning processes over the last 16 yr. This feedback continues to drive the thinning after the climate indexes return to near-normal conditions in the late 1990s. The late 1980s and early 1990s could be considered a tipping point during which the ice–ocean system began to enter a new era of thinning ice and increasing summer open water because of positive feedbacks. It remains to be seen if this era will persist or if a sustained cooling period can reverse the processes.

scholarly journals Deep learning for early warning signals of regime shifts

2021 ◽  
Author(s):  
Thomas Bury ◽  
Raman Sujith ◽  
Induja Pavithran ◽  
Marten Scheffer ◽  
Timothy Lenton ◽  
...  
Keyword(s):  
Deep Learning ◽  
Early Warning ◽  
Normal Forms ◽  
Learning Algorithm ◽  
Tipping Point ◽  
Regime Shifts ◽  
Tipping Points ◽  
Warning Signals ◽  
Early Warning Signals ◽  
Deep Learning Algorithm

Many natural systems exhibit regime shifts where slowly changing environmental conditions suddenly shift the system to a new and sometimes very different state. As the tipping point is approached, the dynamics of complex and varied systems all simplify down to a small number of possible 'normal forms' that determine how the new regime will look. Indicators such as increasing lag-1 autocorrelation and variance provide generic early warning signals (EWS) by detecting how dynamics slow down near the tipping point. But they do not indicate what type of new regime will emerge. Here we develop a deep learning algorithm that can detect EWS in systems it was not explicitly trained on, by exploiting information about normal forms and scaling behaviour of dynamics near tipping points that are common to many dynamical systems. The algorithm detects EWS in 268 empirical and model time series from ecology, thermoacoustics, climatology, and epidemiology with much greater sensitivity and specificity than generic EWS. It can also predict the normal form that will characterize the oncoming regime shift. Such approaches can help humans better manage regime shifts. The algorithm also illustrates how a universe of possible models can be mined to recognize naturally-occurring tipping points.

scholarly journals Deep learning for early warning signals of tipping points

2021 ◽  
Vol 118 (39) ◽  
pp. e2106140118 ◽  
Author(s):  
Thomas M. Bury ◽  
R. I. Sujith ◽  
Induja Pavithran ◽  
Marten Scheffer ◽  
Timothy M. Lenton ◽  
...  
Keyword(s):  
Deep Learning ◽  
Early Warning ◽  
Normal Forms ◽  
Learning Algorithm ◽  
Tipping Point ◽  
State Transitions ◽  
Tipping Points ◽  
Warning Signals ◽  
Early Warning Signals ◽  
Deep Learning Algorithm

Many natural systems exhibit tipping points where slowly changing environmental conditions spark a sudden shift to a new and sometimes very different state. As the tipping point is approached, the dynamics of complex and varied systems simplify down to a limited number of possible “normal forms” that determine qualitative aspects of the new state that lies beyond the tipping point, such as whether it will oscillate or be stable. In several of those forms, indicators like increasing lag-1 autocorrelation and variance provide generic early warning signals (EWS) of the tipping point by detecting how dynamics slow down near the transition. But they do not predict the nature of the new state. Here we develop a deep learning algorithm that provides EWS in systems it was not explicitly trained on, by exploiting information about normal forms and scaling behavior of dynamics near tipping points that are common to many dynamical systems. The algorithm provides EWS in 268 empirical and model time series from ecology, thermoacoustics, climatology, and epidemiology with much greater sensitivity and specificity than generic EWS. It can also predict the normal form that characterizes the oncoming tipping point, thus providing qualitative information on certain aspects of the new state. Such approaches can help humans better prepare for, or avoid, undesirable state transitions. The algorithm also illustrates how a universe of possible models can be mined to recognize naturally occurring tipping points.

Prévoir les variations saisonnières de la glace de mer arctique et leurs impacts sur le climat

2020 ◽  
pp. 024
Author(s):  
Rym Msadek ◽  
Gilles Garric ◽  
Sara Fleury ◽  
Florent Garnier ◽  
Lauriane Batté ◽  
...  
Keyword(s):  
Sea Ice ◽  
Arctic Region ◽  
Arctic Sea Ice ◽  
Climate Impacts ◽  
The Arctic ◽  
Recent Effort ◽  
Sea Ice Thickness ◽  
Arctic Sea ◽  
Ice Conditions ◽  
Upper Level

L'Arctique est la région du globe qui s'est réchauffée le plus vite au cours des trente dernières années, avec une augmentation de la température de surface environ deux fois plus rapide que pour la moyenne globale. Le déclin de la banquise arctique observé depuis le début de l'ère satellitaire et attribué principalement à l'augmentation de la concentration des gaz à effet de serre aurait joué un rôle important dans cette amplification des températures au pôle. Cette fonte importante des glaces arctiques, qui devrait s'accélérer dans les décennies à venir, pourrait modifier les vents en haute altitude et potentiellement avoir un impact sur le climat des moyennes latitudes. L'étendue de la banquise arctique varie considérablement d'une saison à l'autre, d'une année à l'autre, d'une décennie à l'autre. Améliorer notre capacité à prévoir ces variations nécessite de comprendre, observer et modéliser les interactions entre la banquise et les autres composantes du système Terre, telles que l'océan, l'atmosphère ou la biosphère, à différentes échelles de temps. La réalisation de prévisions saisonnières de la banquise arctique est très récente comparée aux prévisions du temps ou aux prévisions saisonnières de paramètres météorologiques (température, précipitation). Les résultats ayant émergé au cours des dix dernières années mettent en évidence l'importance des observations de l'épaisseur de la glace de mer pour prévoir l'évolution de la banquise estivale plusieurs mois à l'avance. Surface temperatures over the Arctic region have been increasing twice as fast as global mean temperatures, a phenomenon known as arctic amplification. One main contributor to this polar warming is the large decline of Arctic sea ice observed since the beginning of satellite observations, which has been attributed to the increase of greenhouse gases. The acceleration of Arctic sea ice loss that is projected for the coming decades could modify the upper level atmospheric circulation yielding climate impacts up to the mid-latitudes. There is considerable variability in the spatial extent of ice cover on seasonal, interannual and decadal time scales. Better understanding, observing and modelling the interactions between sea ice and the other components of the climate system is key for improved predictions of Arctic sea ice in the future. Running operational-like seasonal predictions of Arctic sea ice is a quite recent effort compared to weather predictions or seasonal predictions of atmospheric fields like temperature or precipitation. Recent results stress the importance of sea ice thickness observations to improve seasonal predictions of Arctic sea ice conditions during summer.

scholarly journals Retrieval of Snow Depth over Arctic Sea Ice Using a Deep Neural Network

2019 ◽  
Vol 11 (23) ◽  
pp. 2864 ◽  
Author(s):  
Jiping Liu ◽  
Yuanyuan Zhang ◽  
Xiao Cheng ◽  
Yongyun Hu
Keyword(s):  
Neural Network ◽  
Sea Ice ◽  
Snow Depth ◽  
Deep Neural Network ◽  
Arctic Basin ◽  
Temporal Variations ◽  
Arctic Sea Ice ◽  
The Arctic ◽  
Sea Ice Thickness ◽  
Arctic Sea

The accurate knowledge of spatial and temporal variations of snow depth over sea ice in the Arctic basin is important for understanding the Arctic energy budget and retrieving sea ice thickness from satellite altimetry. In this study, we develop and validate a new method for retrieving snow depth over Arctic sea ice from brightness temperatures at different frequencies measured by passive microwave radiometers. We construct an ensemble-based deep neural network and use snow depth measured by sea ice mass balance buoys to train the network. First, the accuracy of the retrieved snow depth is validated with observations. The results show the derived snow depth is in good agreement with the observations, in terms of correlation, bias, root mean square error, and probability distribution. Our ensemble-based deep neural network can be used to extend the snow depth retrieval from first-year sea ice (FYI) to multi-year sea ice (MYI), as well as during the melting period. Second, the consistency and discrepancy of snow depth in the Arctic basin between our retrieval using the ensemble-based deep neural network and two other available retrievals using the empirical regression are examined. The results suggest that our snow depth retrieval outperforms these data sets.

scholarly journals Observation-based selection of climate models projects Arctic ice-free summers around 2035

2021 ◽  
Vol 2 (1) ◽  
Author(s):  
David Docquier ◽  
Torben Koenigk
Keyword(s):  
Model Selection ◽  
Sea Ice ◽  
Climate Models ◽  
Global Climate ◽  
Coupled Model ◽  
Arctic Sea Ice ◽  
Global Climate Models ◽  
The Arctic ◽  
Arctic Sea ◽  
Area And Volume

AbstractArctic sea ice has been retreating at an accelerating pace over the past decades. Model projections show that the Arctic Ocean could be almost ice free in summer by the middle of this century. However, the uncertainties related to these projections are relatively large. Here we use 33 global climate models from the Coupled Model Intercomparison Project 6 (CMIP6) and select models that best capture the observed Arctic sea-ice area and volume and northward ocean heat transport to refine model projections of Arctic sea ice. This model selection leads to lower Arctic sea-ice area and volume relative to the multi-model mean without model selection and summer ice-free conditions could occur as early as around 2035. These results highlight a potential underestimation of future Arctic sea-ice loss when including all CMIP6 models.

scholarly journals Polar cod in jeopardy under the retreating Arctic sea ice

2019 ◽  
Vol 2 (1) ◽  
Author(s):  
Mats Brockstedt Olsen Huserbråten ◽  
Elena Eriksen ◽  
Harald Gjøsæter ◽  
Frode Vikebø
Keyword(s):  
Sea Ice ◽  
Barents Sea ◽  
Keystone Species ◽  
Ice Cover ◽  
Arctic Sea Ice ◽  
Biophysical Model ◽  
The Arctic ◽  
Polar Cod ◽  
Arctic Sea ◽  
Shelf Sea

Abstract The Arctic amplification of global warming is causing the Arctic-Atlantic ice edge to retreat at unprecedented rates. Here we show how variability and change in sea ice cover in the Barents Sea, the largest shelf sea of the Arctic, affect the population dynamics of a keystone species of the ice-associated food web, the polar cod (Boreogadus saida). The data-driven biophysical model of polar cod early life stages assembled here predicts a strong mechanistic link between survival and variation in ice cover and temperature, suggesting imminent recruitment collapse should the observed ice-reduction and heating continue. Backtracking of drifting eggs and larvae from observations also demonstrates a northward retreat of one of two clearly defined spawning assemblages, possibly in response to warming. With annual to decadal ice-predictions under development the mechanistic physical-biological links presented here represent a powerful tool for making long-term predictions for the propagation of polar cod stocks.

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