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Nonlinear Dynamics and Tipping Points in the Earth System

The dynamics of the Earth system and its components is highly nonlinear. In particular, several subsystems have been suggested to react abruptly at critical levels of anthropogenic forcing. Well-known examples of such Tipping Elements include the Atlantic Meridional Overturning Circulation, the polar ice sheets and sea ice, tropical and boreal forests, as well as the Asian monsoon systems. Interactions between the different Tipping Elements may either have stabilizing or destabilizing effects on the other subsystems, potentially leading to cascades of abrupt transitions. The critical forcing levels at which abrupt transitions occur have recently been associated with Tipping Points.

It is paramount to determine the critical forcing levels (and the associated uncertainties) beyond which the systems in question will abruptly change their state, with potentially devastating climatic, ecological, and societal impacts. For this purpose, we need to substantially enhance our understanding of the dynamics of the Tipping Elements and their interactions, on the basis of paleoclimatic evidence, present-day observations, and models spanning the entire hierarchy of complexity. Moreover, to be able to mitigate - or prepare for - potential future transitions, early warning signals have to be identified and monitored in both observations and models.

This multidisciplinary session invites contributions that address Tipping Points in the Earth system from the different perspectives of all relevant disciplines, including

- the mathematical theory of abrupt transitions in (random) dynamical systems,
- paleoclimatic studies of past abrupt transitions,
- data-driven and process-based modelling of past and future transitions,
- early-warning signals
- the implications of abrupt transitions for Climate sensitivity and response,
- ecological and societal impacts, as well as
- decision theory in the presence of uncertain Tipping Point estimates

Co-organized by CL4/CR7/OS1
Convener: Niklas BoersECSECS | Co-conveners: Hannah ChristensenECSECS, Peter Ditlevsen, Christian Franzke, Anna von der Heydt, Timothy Lenton , Marisa Montoya, Paul Williams, Naiming Yuan
| Mon, 23 May, 15:10–18:30 (CEST)
Room 0.94/95, Tue, 24 May, 08:30–11:50 (CEST)
Room 0.94/95

Mon, 23 May, 15:10–16:40

Chairpersons: Anna von der Heydt, Marisa Montoya

Michael Ghil

The dynamics of systems with time-dependent forcing or coefficients has become a matter of considerable interest in the last couple of decades in general and in the last dozen years or so in the climate sciences in particular (Ghil, 2019; Ghil & Lucarini, 2020; Ghil, 2021; Tel et al., 2021; and references therein). We shall provide a general introduction to the topic and illustrate it with several paleoclimate-related examples (Crucifix, 2012; Riechers et al., 2022; Rousseau et al., 2022). Perspectives for further applications of the concepts and methods of the theory of pullback and random attractors and of their tipping points to paleoclimate will also be provided.


  • Crucifix, M.: Oscillators and relaxation phenomena in Pleistocene climate theory, PTRSA, 370, 1140–1165, 2012.
  • Ghil, M., 2019: A century of nonlinearity in the geosciences, Earth & Space Science, 6, 1007–1042, doi: 1029/2019EA000599.
  • Ghil, M., 2020: Review article: Hilbert problems for the climate sciences in the 21st century – 20 years later, Nonlin. Processes Geophys., 27, 429–451, https://doi.org/10.5194/npg-27-429-2020.
  • Ghil, M., and V. Lucarini, 2020: The physics of climate variability and climate change, Mod. Phys., 92(3), 035002, doi: 10.1103/RevModPhys.92.035002.
  • Riechers, K., T. Mitsui, N. Boers, and M. Ghil, 2022: Orbital insolation variations, intrinsic climate variability, and Quaternary glaciations, Clim. Past Discuss. [preprint], https://doi.org/10.5194/cp-2021-136, in review.
  • Rousseau, D.-D., W. Bagnewski, and M. Ghil, 2021: Abrupt climate changes and the astronomical theory: are they related?, Clim. Past, accepted, doi: 10.5194/cp-2021-103 .
  • Tél, T., Bódai, T., Drótos, G., Haszpra, T., Herein, M., Kaszás, B. and Vincze, M., 2020. The theory of parallel climate realizations. Journal of Statistical Physics179(5), 1496–1530.

How to cite: Ghil, M.: Nonautonomous dynamics and its applications to paleoclimate, EGU General Assembly 2022, Vienna, Austria, 23–27 May 2022, EGU22-10128, https://doi.org/10.5194/egusphere-egu22-10128, 2022.

Anne Willem Omta et al.

Glacial-interglacial cycles constitute large natural variations in Earth's climate. The Mid-Pleistocene Transition (MPT) marks a shift of the dominant periodicity of these climate cycles from ~40 to ~100 kyr. Ramping with frequency locking is a promising mechanism to explain the MPT, combining an increase in the internal period with lockings to an external forcing. We identify the strength of positive feedbacks as a key parameter to induce increases in the internal period and allow ramping with frequency locking. Using the calcifier-alkalinity model, we simulate changes in periodicity similar to the Mid-Pleistocene Transition through this mechanism. However, the periodicity shift occurs up to 10 Million years after the change in the feedback strength. This result puts into question the assumption that the cause for the MPT must have operated around the same time as the observed periodicity shift.

How to cite: Omta, A. W., Shackleton, J., Follows, M., and Thomas, P.: The Mid-Pleistocene Transition: A delayed response to an increasing positive feedback?, EGU General Assembly 2022, Vienna, Austria, 23–27 May 2022, EGU22-1514, https://doi.org/10.5194/egusphere-egu22-1514, 2022.

Denis-Didier Rousseau et al.

The Earth’s climate has experienced numerous abrupt and critical transitions during its long history. Such transitions are evidenced in precise, high-resolution records at different timescales. This type of evidence suggests the possibility of identifying a hierarchy of past critical events, which would yield a more complex perspective on climatic history of the than the classical saddle-node two-dimension representation of tipping points. Such a context allows defining a tipping, or dynamical, landscape (Lucarini and Bódai, 2020), similar to the epigenetic landscape of Waddington (1957).

To illustrate a richer structure of critical transitions, we have analyzed 3 key high-resolution datasets covering the past 66 Ma and provided evidences of abrupt transitions detected with the augmented Kolmogorov-Smirnov test and a recurrence analysis (Bagniewski et al., 2021). These time series are the CENOGRID benthic d18O and d13C (Westerhold et al., 2020), the U1308 benthic d18O, d13C and the d18bulk carbonate (Hodell and Channell, 2016), and the NGRIP d18O (Rasmussen et al., 2014) records. The aim was to examine objectively the observed visual evidence of abrupt transitions and to identify among them the key thresholds indicating regime changes that differentiate among major clusters of variability. This identification is followed by establishing a hierarchy in the observed thresholds organized through a domino-like cascade of abrupt transitions that shaped the Earth’s climate system over the past 66 Ma.

This study is supported by the H2020-funded Tipping Points in the Earth System (TiPES) project.


Bagniewski, W., Ghil, M., and Rousseau, D. D.: Automatic detection of abrupt transitions in paleoclimate records, Chaos, 31, https://doi.org/10.1063/5.0062543, 2021.

Hodell, D. A. and Channell, J. E. T.: Mode transitions in Northern Hemisphere glaciation: co-evolution of millennial and orbital variability in Quaternary climate, Clim. Past, 12, 1805–1828, https://doi.org/10.5194/cp-12-1805-2016, 2016.

Lucarini, V. and Bódai, T.: Global stability properties of the climate: Melancholia states, invariant measures, and phase transitions, Nonlinearity, 33, R59–R92, https://doi.org/10.1088/1361-6544/ab86cc, 2020.

Rasmussen, S. O., Bigler, M., Blockley, S. P., et al.: A stratigraphic framework for abrupt climatic changes during the Last Glacial period based on three synchronized Greenland ice-core records: refining and extending the INTIMATE event stratigraphy, Quat. Sci. Rev., 106, 14–28, https://doi.org/10.1016/j.quascirev.2014.09.007, 2014.

Waddington, C. H.: The strategy of the genes., Allen & Unwin., London, 1957.

Westerhold, T., Marwan, N., Drury, A. J., et al.: An astronomically dated record of Earth’s climate and its predictability over the last 66 million years, Science, 369, 1383-+, https://doi.org/10.1126/science.aba6853, 2020.

How to cite: Rousseau, D.-D., Lucarini, V., Bagniewski, W., and Ghil, M.: Cascade of abrupt transitions in past climates, EGU General Assembly 2022, Vienna, Austria, 23–27 May 2022, EGU22-2396, https://doi.org/10.5194/egusphere-egu22-2396, 2022.

Shruti Setty et al.

The Paleocene-Eocene Thermal Maximum (PETM; 56 Ma) and Eocene Thermal Maximum 2 and 3 (ETM2; 54.06 Ma and ETM3; 52.87 Ma) were three of a series of abrupt climate and carbon cycle perturbations, characterized by massive carbon input into the ocean-atmosphere system and strong global warming. These abrupt events, termed hyperthermals, potentially represent ‘tipping points’ at moments in time when the resilience of the system was low and reinforced by strong internal feedbacks, such as the catastrophic release of carbon from submarine methane hydrates. Alternatively, external mechanisms such as volcanism may have played a pronounced external role during the PETM. Here, we evaluate if the hyperthermals indeed resulted from reduced Earth System resilience and tipping point behaviour through the mathematical analyses of climate and carbon cycle indicators, namely, oxygen and stable carbon isotope ratios of deep ocean foraminifer calcite, across the late Paleocene and early Eocene. Our combined analysis using Dynamic Indicators of Resilience (DIORs) and Convergent Cross Mapping (CCM) reveals a loss of resilience and an increase in the causal interaction between the carbon cycle and climate towards the PETM, ETM2, and ETM3. A novel, windowed CCM approach indicates a tight coupling between carbon and climate across the early Eocene, further supporting dominant climate forcing on carbon cycle dynamics. This indicates that the internal rather than external mechanisms were responsible for the hyperthermals, suggesting a secondary role for endogenic processes such as volcanism. Furthermore, the CCM analysis in conjunction with the absence of major positive feedbacks such as the presence of polar ice caps during early Eocene could be employed to stipulate that these hyperthermal events may be caused by the increase in coupling between the carbon cycle and climate systems, eventually pushing both systems towards a tipping point through increasing positive feedbacks.

How to cite: Setty, S., Cramwinckel, M., Leemput, I. V. D., Nes, E. H. V., Lourens, L. J., Sluijs, A., and Scheffer, M.: Loss of Earth System Resilience during Early Eocene Global Warming Events, EGU General Assembly 2022, Vienna, Austria, 23–27 May 2022, EGU22-10628, https://doi.org/10.5194/egusphere-egu22-10628, 2022.

Yvan Romé et al.

Millennial-scale variability has been extensively observed across the last glacial period records (115 to 12 thousand years ago) but reproducing it on general circulation models remains a challenge. In recent years, a growing number of climate models have reported simulations with oscillating behaviours comparable to typical abrupt climate changes, although often relying on unrealistic forcing fields and/or boundary conditions. This may become an issue when trying to review the mechanisms at stake because of glacial climates’ sensitivity to these parameters, notably ice sheets geometry and greenhouse gases concentration.

With the addition of snapshots of the early last deglaciation meltwater history over a last glacial maximum (~21 thousand years ago) equilibrium simulation, we obtained different regimes of climate variability, including oscillations that provides the perfect framework for studying abrupt climate changes dynamics in a glacial background. The oscillations consist of shifts between cold modes with a weak to almost collapsed Atlantic Meridional Ocean Circulation (AMOC) and warmer and stronger AMOC modes, with large reorganisation of the deep-water formation sites, surface ocean and atmospheric circulations. The phenomenon has a periodicity of roughly every 1500 years and can be linked to changes of about 10°C in Greenland. This new set of simulation suggests an intricate large-scale coupling between ice, ocean, and atmosphere in the North Atlantic when meltwater is discharged to the North Atlantic.

Most attempts at theorising millennial-scale variability have involved vast transfers of salt between the subtropical and subpolar gyres, often referred to as the salt oscillator mechanism, that in turn controlled the intensity of the north Atlantic current. We believe that the salt oscillator is in fact part of a larger harmonic motion spanning through all components of the climate system and that can enter into resonance under the specific boundary conditions and/or forcing. Illustrated by the mapping of the main salinity and heat fluxes on the oscillating simulations, we propose a new interpretation of the salt oscillator that includes the stochastic resonance phenomenon as well as the effect of meltwater forcing.

How to cite: Romé, Y., Ivanovic, R., and Gregoire, L.: Mechanisms behind climate oscillations in last glacial maximum simulations, EGU General Assembly 2022, Vienna, Austria, 23–27 May 2022, EGU22-2784, https://doi.org/10.5194/egusphere-egu22-2784, 2022.

Kolja Kypke and Peter Ditlevsen

The abrupt transitions in the last glacial period between cold stadial and warmer interstadial climate states found in Greenlandic ice-core records, known as Dansgaard-Oeschger (D-O) events, are a rich topic of study not only due to their potential similarities in time scales and mechanisms to present and near-future climate transitions but also since their underlying physical mechanisms are not fully understood. The dynamics of the climate can be described by a Langevin equation dx = −∂U/∂x dt + η(t) where the potential U(x) has a bimodal distribution to represent the stable stadial and interstadial states and the stochastic process η(t) is usually realized as a Gaussian white noise process that causes jumps between these two states. From the steady-state of the Fokker-Planck equation associated with this Langevin equation, the potential U(x) can be determined from the probability distribution of the ice-core record time series. Thus this minimal model simulates time series with statistics similar to those of the original ice-core record. Novel to this study, we introduce a multiplicative noise term η(t, x) to represent the different statistical properties of the noise in the stadial and interstadial periods. The difference between the Itô and the Stratonovich integration of the Langevin equation with multiplicative noise results in slight differences in the attribution of the drift and diffusion terms for a transformed variable. This is illustrated by performing both.

How to cite: Kypke, K. and Ditlevsen, P.: A minimal SDE model of D-O events with multiplicative noise, EGU General Assembly 2022, Vienna, Austria, 23–27 May 2022, EGU22-3973, https://doi.org/10.5194/egusphere-egu22-3973, 2022.

Jade Ajagun-Brauns and Peter Ditlevsen

A new simple approach inspired by MacAyeal (1979) to explain the time-asymmetric ‘saw-toothed’ shape and 100,000-year quasi-period of glacial-interglacial cycles since the Middle Pleistocene Transition, is presented. Using a simple model with fast-slow dynamics, the global ice volume is taken to be a function of two independently varying parameters, the solar insolation and ‘alpha’, a secondary control parameter, the study of which is the focus this research. The steady state of the model is a partially folded surface in three-dimensional space where insolation, ‘alpha’, and global ice volume are orthogonal axes. The pleated surface allows for the gradual increase and sudden decrease in ice volume that is observed in the paleoclimate record. To derive a time series of global ice volume, the Euler integration method is used, producing a time series which replicates the ‘saw-toothed’ pattern of glacial cycles in the late Pleistocene. The second control parameter, ‘alpha’, is proposed to be related to internal dynamics of the climate system, such as ice sheet dynamics.



D. R.  MacAyeal, ‘A Catastrophe Model of the Paleoclimate Record’ , Journal of Glaciology , Volume 24 , Issue 90 , 1979 , pp. 245 – 257.

How to cite: Ajagun-Brauns, J. and Ditlevsen, P.: A fast-slow model for glacial cycles since the Mid-Pleistocene Transition, EGU General Assembly 2022, Vienna, Austria, 23–27 May 2022, EGU22-5997, https://doi.org/10.5194/egusphere-egu22-5997, 2022.

Michael Dr. Bujatti-Narbeshuber

Confirmation exists for the 1997 revolutionary date of 12.850 cal yr BP established for the Laacher See Eruption (LSE) and introduced to encourage US-research on the P/H-KISS impact with LSE as isochrone and impact volcanism proxy (Bujatti-Narbeshuber, 1997). Bayesian analysis by Wolbach et al. (2018) of 157 dated records of the YD-impact hypothesis of Firestone et al. (2007) confirms impact with 2.854 ± 0.056 ka BP. This now allows to introduce the much larger P/H-KISS paleoceanographic transition scenario relating also to Holocene up to the present global climate change. The Holocene era, because of the thermohaline damped flow scenario, is herein considered as permanent end of the ice age, suggested here as the climatic consequence of an ocean topography and threshold change. Decoded cave art navigation world maps with Pleistocene paleoceanography content from Altamira , La Pasiega and El Castillo document in each one of the three maps specific AMOC stable states for interstadial/ full stadial/ stadial paleoclimate. Each map-thermohaline stable state is differently relating to a geomorphological boundary condition that is the subaerial surface Topography of a large Mid Atlantic Plateau (MAP)-Island. It is modelled in the P/H-KISS scenario as primary Pleistocene thermohaline phase 0 geomorphological threshold. As physical boundary condition it is in interaction with the thermohaline gulfstream current (above /below/at threshold). This results in the 3 distinct AMOC equilibrium stages of interstadial/ full stadial /stadial, as Pleistocene criticality interconnected by their respective further transition thresholds. When the primary  geomorphological threshold is removed the result is the Holocene damped flow, a transition continuum of thermohaline phases 1, 2, 3. Geomorphological proof is first the MAP-Island, invariably shown on all three maps. Furthermore the MAP-Island is identified by its characteristic topography on decorated columns in Göbekli Tepe as a highly abstract island symbol with deeper political-territorial meanings. With paleo-astronomical precession dating on Pillar 43, the LSE 12.850 cal yr BP date was reproduced and the YD (P/H-KISS) impact series from comet fragments in the Taurid stream were decoded by M. Sweatman (2019).  The symbol sequence on Pillar 18, revealed here for the first time, is the (HI-T) = MAP-Island-Dual 90°-Transition-Tsunami Code of the two step Mid Atlantic Ridge MAR & MAP- Island isostatic submersion by the Taurid stream Koefels-comet oceanic-impact fragments: Paleoclimatology thus confirms and now extends the D. Paillard (1998) three equilibria ocean-box-climate-model with 3 thresholds for 3 transitions between the 3 thermohaline stable states of the ice age to the larger P/H-KISS transition scenario of paleo-climate change. It states that the above 3 AMOC states are exclusively based on the existence of the MAP-Island threshold. Isostatic MAR & MAP-Submergence brings their ice age ending collapse into the broad continuum of the Global warming Threshold Triad with thermohaline damped flow in a very long lasting Holocene interstadial.


*) Bujatti-Narbeshuber, M. - Pleistocene/Holocene (P/H) boundary oceanic Koefels-comet Impact Series Scenario (KISS) of 12.850 yr BP Global-warming Threshold Triad (GTT). -Climates: Past, Present and Future; Second European Palaeontological Congress Abstracts edited by D.K. Ferguson & H.A. Kollmann; Vienna, 1997.


How to cite: Dr. Bujatti-Narbeshuber, M.: Pleistocene/Holocene (P/H) boundary oceanic Koefels-comet Impact Series Scenario (KISS) of 12.850 yr BP Global-warming Threshold Triad (GTT)-Part II *) , EGU General Assembly 2022, Vienna, Austria, 23–27 May 2022, EGU22-8412, https://doi.org/10.5194/egusphere-egu22-8412, 2022.

Vanessa Skiba et al.

Millennial-scale climate variability, especially abrupt stadial-interstadial transitions, are a prominent feature of the last glacial as recorded in Greenland ice core records (Dansgaard-Oeschger events). Event abruptness and presence of statistical early warning signals before these transitions indicate that they involve repeated crossing of a tipping point of the climate system. However, only little information is available for periods before the last glacial period as Greenland ice cores and many other high-resolution records do not extent beyond the last glacial cycle. Given the lack of understanding of the triggering mechanism responsible for glacial millennial-scale variability with palaeoclimate data from the last glacial, it is essential to investigate this phenomenon during earlier glacial periods.

Here, we present a new highly resolved, precisely U-Th-dated speleothem oxygen isotope record from the Northern European Alps, a region which has been previously shown to resemble the glacial millennial-scale climate variability obtained from Greenland ice core records very well. Our new data covers the time interval from the ante-penultimate glacial to the penultimate glacial (MIS8-MIS6) with a high degree of replication. For both glacial periods, we find phases of pronounced millennial-scale variability but also several, ~10 ka long phases with the climate system being exclusively in stadial conditions. We compare our data with conceptual model results and investigate the occurrence and absence of abrupt climate transitions of the last 300,000 a.

How to cite: Skiba, V., Trüssel, M., Plessen, B., Spötl, C., Eichstädter, R., Schröder-Ritzrau, A., Braun, T., Mitsui, T., Frank, N., Boers, N., Marwan, N., and Fohlmeister, J.: Abrupt climate events recorded in speleothems from the ante penultimate glacial, EGU General Assembly 2022, Vienna, Austria, 23–27 May 2022, EGU22-11671, https://doi.org/10.5194/egusphere-egu22-11671, 2022.

Eirik Myrvoll-Nilsen et al.

Layer-counted paleoclimatic proxy records have non-negligible uncertainty arising from the dating process. Knowledge of this uncertainty is important for a rigorous propagation to further analyses; for example for identification and dating of abrupt transitions in climate or to provide a complete uncertainty quantification of early warning signals. This dating uncertainty can be quantified by assuming a probabilistic model for the age-depth relationship. We assume that the number of counted layers per unit of depth can be described using a Bayesian regression model with residuals following an autoregressive process. By synchronizing the chronologies with other archives one can constrain the uncertainties and correct potential biases in the dating process. This is done by matching the chronologies to tie-points obtained by analyzing different archives covering the same period in time. In practice, tie-points can be associated with a significant amount of uncertainty which also needs to be accounted for. We present a theoretically consistent approach which, under certain assumptions, allows for efficient sampling from synchronized age-depth models that match the tie-points under known uncertainty distributions. The model and associated methodology has been implemented into an R-package. 

How to cite: Myrvoll-Nilsen, E., Riechers, K., and Boers, N.: Synchronization of layer-counted archives using a statistical age-depth model, EGU General Assembly 2022, Vienna, Austria, 23–27 May 2022, EGU22-9504, https://doi.org/10.5194/egusphere-egu22-9504, 2022.

Keno Riechers et al.

Multiple proxy records from Greenland ice cores exhibit a series of concomitant abrupt climatic shifts during the last glacial. These so-called Dansgaard–Oeschger (DO) events comprise, among others, warming over Greenland, a sudden retreat of North Atlantic and Nordic Seas’ sea ice, and an atmospheric reorganisation of hemispheric extent. Typically DO events are followed by a phase of moderate cooling, before the climate abruptly transition back to its pre-event state. While the physics behind these dynamics are still subject to a vibrant debate, the idea that at least one of the involved climatic subsystems features bistability is widely accepted.

We assess the stability of Greenland temperatures and the Northern Hemisphere atmospheric circulation represented by δ¹⁸O and dust concentration records from the NGRIP ice core, respectively. We investigate the 27-59 ky b2k period of the combined record which covers 12 major DO events at high temporal resolution. Regarding the data as the realisation of a stochastic process we reconstruct the corresponding drift and diffusion by computing the Kramers–Moyal (KM) coefficients. In contrast to previous studies, we find the drift of the δ¹⁸O to be monostable, while analysis of the dust record yields a bistable drift. Furthermore, we find a non-vanishing 4th-order KM coefficient for the δ¹⁸O, which indicates that the δ¹⁸O time series cannot be considered a standard type Langevin process. In a second step, we treat the joint (δ¹⁸O , dust) time series as a two dimensional stochastic process and compute the corresponding coefficients of the two dimensional KM expansion. This reveals the position of the fixed point of δ¹⁸O to be controlled by the value of the dust. In turn, the drift of the dust undergoes an imperfect supercritical pitchfork bifurcation when transitioning from low to high δ¹⁸O values.

How to cite: Riechers, K., Rydin, L., Hassanibesheli, F., Witthaut, D., Lind, P., and Boers, N.: Data-driven Reconstruction of Last Glacials' Climate Dynamics Suggests Monostable Greenland Temperatures and a Bistable Northern Hemisphere Atmosphere, EGU General Assembly 2022, Vienna, Austria, 23–27 May 2022, EGU22-13023, https://doi.org/10.5194/egusphere-egu22-13023, 2022.

Witold Bagniewski et al.

Paleoclimate proxy records contain abrupt transitions that may represent former instances of the climate system crossing a tipping point (TP). Properly identifying these TPs in the Earth’s past helps determine critical thresholds in present-day climate and better understand the climate system’s underlying bifurcation mechanisms.

Information contained in paleoclimate proxy records is often ambiguous because of the complexity of the system, which includes both deterministic and stochastic processes. Furthermore, paleoclimate time series differ in their time spans and periodicities, and often have high levels of noise and a nonuniform resolution. These combined sources of uncertainty highlight the need for using advanced statistical methods for robustly identifying and comparing TPs.

A recently developed method that uses an augmented Kolmogorov-Smirnov test has been shown to be highly effective for transition detection in different types of records. Here, we apply this method to a set of high-quality paleoproxy records exhibiting centennial-to millennial-scale variability that have been compiled in the PaleoJump database. We thereby detect previously unrecognized transitions in these records and identify potential TPs. Furthermore, we investigate regime changes with recurrence analysis and spectral analysis.

This study is supported by the H2020-funded Tipping Points in the Earth System (TiPES) project.

How to cite: Bagniewski, W., Ghil, M., and Rousseau, D.-D.: Paleoclimatic tipping points and abrupt transitions: An application of advanced time series analysis methods, EGU General Assembly 2022, Vienna, Austria, 23–27 May 2022, EGU22-12501, https://doi.org/10.5194/egusphere-egu22-12501, 2022.


Mon, 23 May, 17:00–18:30

Chairpersons: Niklas Boers, Timothy Lenton

Marina Martinez Montero et al.

In the context of climate change, the word "commitment" was originally used to denote how much extra warming is to be expected eventually given a certain fixed concentration of CO2. The notion has evolved and now it is customary to encounter terms such as "constant emissions commitment", "sea level rise commitment" and "zero emissions commitment". All these notions refer to how much change with respect to the current climate state is expected at a given point in the future considering our current climate state and specified future anthropogenic emissions.

Here, we propose thinking about commitment as available options for future action that will allow future decision makers to avoid harmful futures. The definition requires the identification of unwanted outcomes e.g., too high temperature or too fast sea level rise and the specification of a range of possible future anthropogenic emission/intervention scenarios. Given an initial climate state, the measure of commitment is based on the diagnosis of which of those emission/intervention scenarios yield futures safe from the unwanted outcomes. This new definition of commitment explicitly captures the notion of legacy: It measures the range of options that the next generations have at their disposal to avoid harmful futures.

We illustrate the definition and methodology with a simple model featuring ice sheet tipping points and ocean carbonate chemical balance. After having introduced the model, we specify the considered future anthropogenic emission/intervention options available, along with the considered unwanted outcomes. We show how the safe options available for future generations would change in time if we were to follow some of the most standard emission scenarios used in the literature.

How to cite: Martinez Montero, M., Crucifix, M., Botta, N., and Brede, N.: Commitment as Lost Opportunities, EGU General Assembly 2022, Vienna, Austria, 23–27 May 2022, EGU22-5928, https://doi.org/10.5194/egusphere-egu22-5928, 2022.

Guido Vettoretti et al.

Recent observationally based studies indicate that the Atlantic Meridional Overturning Circulation (AMOC) and the Greenland Ice Sheet (GIS) may be approaching critical thresholds or tipping points, although the timing is uncertain. The connection between both Greenland meltwater fluxes and anthropogenic greenhouse gas emissions and their impact on the future state of the AMOC is also uncertain. Here we investigate the role of ocean vertical mixing within the interior and surface boundary layer (the K-Profile Parameterization (KPP)) on past millennial scale climate variability in a coupled climate model. Previous studies have demonstrated a sensitivity of the period of millennial scale ice age oscillations to the KPP scheme. Here we show that small changes in the profiles of vertical mixing under ice age boundary conditions can drive the AMOC through a Hopf bifurcation and result in the appearance of millennial-scale AMOC oscillations. This has implications on whether changes in tidal energy dissipation in the coastal and deep ocean are important for modelling past climate variability. More importantly, the same changes in ocean vertical mixing can impact the stability and hysteresis behaviour of the modern AMOC under freshwater input to the North Atlantic as well as leading to abrupt transitions in AMOC strength under a doubling of carbon dioxide concentrations in the atmosphere. We show how understanding the sensitivity of the AMOC to ocean vertical mixing parameterizations used in coupled Earth System models may be important for constraining future climate tipping points.

How to cite: Vettoretti, G., Jochum, M., and Ditlevsen, P.: Modelling Abrupt Transitions in Past Ocean Circulation to Constrain Future Tipping Points, EGU General Assembly 2022, Vienna, Austria, 23–27 May 2022, EGU22-1988, https://doi.org/10.5194/egusphere-egu22-1988, 2022.

Javier Blasco et al.

Since the pre-industrial era, global sea level has been rising along with greenhouse gas emissions. Part of the contribution to this sea-level change is the mass lost from continental ice sheets, i.e. the Greenland (GrIS) and Antarctic (AIS) ice sheets, which are shrinking at an accelerated rate. However, how they will respond to future warming is highly uncertain due to our lack of knowledge and associated uncertainty in modelling several physical processes, as well as in warming projections. A way to gain insight into future projections is to study past warm periods that are, to some extent, comparable to the present day (PD) in terms of external forcing. The mid-Pliocene warm period (mPWP, 3.3-3.0 million years ago) offers an ideal benchmark, as it is the most recent period with CO2 levels comparable to PD (350-450 ppmv), showing global mean temperatures 2.5-4.0 degrees higher. Eustatic sea-level reconstructions from that period estimate a sea level 15-20 meters higher than PD, implying ice sheets were much smaller in size. The GrIS was starting to form and the AIS was most likely constrained to land-based regions. The Pliocene Model Intercomparison Project, Phase 2 (PlioMIP2) has brought together over 15 climate outputs from 11 General Circulation models from different institutions. These models have simulated mPWP conditions under 400 ppmv of CO2 concentration over a topography generated from an updated bedrock configuration for that time period. Here we use these model outputs to force offline a higher-order ice sheet model for the Antarctic and Greenland domain. Our aim is to investigate how polar continental ice sheets respond to these different climatic fields to pinpoint their most significant climatic and topographical discrepancies. In addition, several sources of structural dependence, from different dynamic states (i.e. basal friction laws) to different initial boundary conditions (starting from no ice-sheet to the PD configuration) are investigated in this modelling framework to create a comprehensive output database for statistical analysis.

How to cite: Blasco, J., Tabone, I., Moreno-Parada, D., Alvarez-Solas, J., Robinson, A., and Montoya, M.: The Antarctic and Greenland response to PlioMIP2 mPWP climatic fields, EGU General Assembly 2022, Vienna, Austria, 23–27 May 2022, EGU22-9322, https://doi.org/10.5194/egusphere-egu22-9322, 2022.

David Armstrong McKay et al.

Climate tipping points occur when change in a part of the climate system becomes self-perpetuating beyond a forcing threshold, leading to abrupt and/or irreversible impacts. Synthesizing paleoclimate, observational, and model-based studies, we provide a revised shortlist of global ‘core’ tipping elements and regional ‘impact’ tipping elements and their temperature thresholds. Current global warming of ~1.1°C above pre-industrial already lies within the lower end of some tipping point uncertainty ranges. Several more tipping points may be triggered in the Paris Agreement range of 1.5-2°C global warming, with many more likely at the 2-3°C of warming expected on current policy trajectories. In further work we use these estimates to test the potential for and impact of tipping cascades in response to global warming scenarios using a stylised model. This strengthens the evidence base for urgent action to mitigate climate change and to develop improved tipping point risk assessment, early warning capability, and adaptation strategies.

Preprint: https://doi.org/10.1002/essoar.10509769.1

How to cite: Armstrong McKay, D., Staal, A., Abrams, J., Winkelmann, R., Sakschewski, B., Loriani, S., Fetzer, I., Cornell, S., Rockström, J., and Lenton, T.: Updated assessment suggests >1.5°C global warming could trigger multiple climate tipping points, EGU General Assembly 2022, Vienna, Austria, 23–27 May 2022, EGU22-12438, https://doi.org/10.5194/egusphere-egu22-12438, 2022.

Victor Couplet and Michel Crucifix

The 'hothouse narrative' states that tipping cascades could lead humanity to a binary choice between a 'governed Earth' and a 'hothouse' with no midway alternative. To investigate this scenario, we construct a toy model of interacting tipping elements and ask the following questions: Given a continuous family of emission scenarios, are there discontinuities in the family of responses, as suggested by the 'hothouse narrative'? How realistic is this given knowledge provided by climate simulations and paleo-climate evidence? The relatively low complexity of our model allows us to easily run it for several thousand years and a large range of emissions scenarios, helping us highlight the fundamental role of the different time scales involved in answering our questions. On the one hand, we find that the near-linear relationship predicted by GCMs between global temperature and GHG emissions for the next century can break up at millennial time scales due to cascades involving slower tipping elements such as the ice sheets. This translates as a discontinuity in the family of responses of our model. On the other hand, we find that different emissions scenarios respecting the same carbon budget could potentially lead to different tipping cascades and thus qualitatively different outcomes.

How to cite: Couplet, V. and Crucifix, M.: Investigating the 'Hothouse narrative' with dynamical systems, EGU General Assembly 2022, Vienna, Austria, 23–27 May 2022, EGU22-5197, https://doi.org/10.5194/egusphere-egu22-5197, 2022.

Jan Swierczek-Jereczek et al.

Given large regions of ice grounded below sea level associated with a retrograde bedrock, the West Antarctic Ice Sheet (WAIS) is believed to be a tipping element whose tipping point could be reached within this century under high emission scenarios. As the WAIS represents the largest and most uncertain source of future sea-level rise, characterising its stability is crucial for defining safe emission pathways and protecting livelihoods in coastal regions. In the present work, we investigate its potential to undergo an abrupt change due to a fold bifurcation. To this end, we use a high-order ice sheet model with 16km spatial resolution. Rather than applying a fixed forcing rate as in previous studies, we apply a forcing scheme that adaptively increases the local temperature while keeping the system near equilibrium, which allows us to obtain a rigorous value for the bifurcation tipping point. More importantly, we show how this threshold can become relevant for much lower warming levels than expected - even within the bounds of relatively conservative emission scenarios. Subsequently, we explain the underlying mechanisms leading the marine ice-sheet instability to possibly arise earlier than suggested by the bifurcation study. We finally question whether the tipping point of the WAIS can be understood as a fixed temperature value and if not, by which information it should be extended to provide an early warning signal.

How to cite: Swierczek-Jereczek, J., Montoya, M., Robinson, A., Alvarez-Solas, J., and Blasco, J.: Is West-Antarctica’s Tipping Point a Fixed Value?, EGU General Assembly 2022, Vienna, Austria, 23–27 May 2022, EGU22-8753, https://doi.org/10.5194/egusphere-egu22-8753, 2022.

Nils Bochow

The rise of the global sea-level due to the melting of the Greenland ice-sheet poses one of the biggest threats to human society in the 21st century (IPCC, 2021). The Greenland ice sheet has been hypothesized to exhibit multiple stable states with tipping point behavior when crossing specific thresholds of the global mean temperature (Robinson et al., 2012). In regards to the desultory efforts to reduce the global emissions it becomes more and more unlikely to reach the 1.5°C goal by the end of the century and a crossing of the tipping threshold for the Greenland ice sheet becomes inevitable. First early-warning signals of a possible transition have already been found (Boers&Rypdal, 2021). However, it is known that a short-term overshooting of a critical threshold is possible without prompting a change of the system state (Ritchie et al., 2021). Using a complex ice sheet model, we investigate the effects of different carbon-capture scenarios after crossing the tipping threshold for the Greenland ice sheet. We are able to sketch a stability diagram for a number of emission scenarios and show that temporarily overshooting the temperature threshold for Greenland might be quasi-irreversible for some of the emission scenarios.

IPCC, 2021: Summary for Policymakers. In: Climate Change 2021: The Physical Science Basis. Contribution of
Working Group I to the Sixth Assessment Report of the Intergovernmental Panel on Climate Change [Masson-
Delmotte, V., P. Zhai, A. Pirani, S.L. Connors, C. Péan, S. Berger, N. Caud, Y. Chen, L. Goldfarb, M.I. Gomis, M.
Huang, K. Leitzell, E. Lonnoy, J.B.R. Matthews, T.K. Maycock, T. Waterfield, O. Yelekçi, R. Yu, and B. Zhou (eds.)].
Cambridge University Press. In Press.

Robinson, A., Calov, R. & Ganopolski, A. Multistability and critical thresholds of the Greenland ice sheet. Nature Clim Change 2, 429–432 (2012).

Boers, N. & Rypdal, M. Critical slowing down suggests that the western Greenland Ice Sheet is close to a tipping point. PNAS 118, (2021).

Ritchie, P. D. L., Clarke, J. J., Cox, P. M. & Huntingford, C. Overshooting tipping point thresholds in a changing climate. Nature 592, 517–523 (2021).

How to cite: Bochow, N.: Overshooting the tipping point threshold for the Greenland ice-sheet using a complex ice-sheet model, EGU General Assembly 2022, Vienna, Austria, 23–27 May 2022, EGU22-2353, https://doi.org/10.5194/egusphere-egu22-2353, 2022.

Richard Wood

Many generations of climate general circulation models (GCMs) have suggested that a radical reorganisation (tipping) of the Atlantic Meridional Overturning Circulation is unlikely in the 21st Century in response to the greenhouse gas emissions pathways considered by the Intergovernmental Panel on Climate Change (IPCC). Yet some studies suggest that GCMs as a class may represent an AMOC that is biased towards excessive stability. If this is the case then simply looking at AMOC response in the ensemble of current GCMs may give a misleading picture of the possible future pathways of the AMOC.

In this study we use a simple coupled climate model, including both the thermal and water cycle responses to greenhouse gas increase, to explore beyond the range of the current ensemble of ‘best estimate’ GCMs. What would the climate system need to look like in order for AMOC tipping to be a plausible outcome? We find that tipping behaviour would require key parameters controlling the response of the hydrological cycle to surface warming to be towards the edge of plausible ranges.

While AMOC tipping remains a ‘High Impact, Low Likelihood’ outcome, our results extend current knowledge by showing how AMOC tipping could occur in response to greenhouse gas forcing (as opposed to the common idealisation of ‘water hosing’ experiments). The results also show how monitoring key parameters of the climate system may over time allow the possibility of tipping to be more confidently assessed.

How to cite: Wood, R.: Climate storylines for AMOC tipping in response to increasing greenhouse gases, EGU General Assembly 2022, Vienna, Austria, 23–27 May 2022, EGU22-13181, https://doi.org/10.5194/egusphere-egu22-13181, 2022.

Lana Blaschke et al.

The Atlantic Meridional Overturning Circulation (AMOC) is a vital part of the global climate that has been suggested to exhibit bi-stability. A collapse from its current strong state to the weak one would have significant consequences for the climate system. Early-warning signals (EWS) for such a transition have recently been found in observational fingerprints for the AMOC.

Some uncertainty in our understanding of the AMOC and its recent evolution is due to the varying quality of its representation in state-of-the-art models. In this work we examine the historical AMOC simulations in the 6th Coupled Model Intercomparison Project (CMIP6) by analyzing the AMOC strength in the models both directly and through the sea-surface temperature fingerprint. As well as examining the evolution of these AMOC time-series in the models, we calculate their associated EWS and use these to evaluate the models in terms of their representation of the AMOC.

How to cite: Blaschke, L., Ben-Yami, M., Boers, N., and Nian, D.: AMOC Early-Warning Signals in CMIP6, EGU General Assembly 2022, Vienna, Austria, 23–27 May 2022, EGU22-5999, https://doi.org/10.5194/egusphere-egu22-5999, 2022.

Johannes Lohmann

Several climate sub-systems are believed to be at risk of undergoing abrupt, irreversible changes as a tipping point (TP) in Greenhouse gas concentrations is reached. Since the current generation of climate models is likely not accurate enough to reliably predict TPs, a hope is to anticipate them from observations via early-warning signals (EWS). EWS have been designed to identify generic changes in variability that occur before a well-defined TP is crossed.

Such well-defined, singular TPs are believed to arise from a single dominant positive feedback that destabilizes the system. However, one may ask whether the large number of spatio-temporal scales in the climate system, and associated second-order feedbacks, could not lead to a variety of more subtle, but discontinuous reorganizations of the spatial climate pattern before the eventual catastrophic tipping. Such intermediate TPs could hinder predictability and mask EWS.

We performed simulations with a global ocean model that shows a TP of the Atlantic meridional overturning circulation (AMOC) due to freshening of the surface waters resulting from increased ice melt. Using a large ensemble of equilibrium simulations, we map out the stability landscape of the ocean circulation in high detail. While in a classical hysteresis experiment only one regime of bistability is found, by very slow increases in forcing we observe an abundance of discontinuous, qualitative changes in the AMOC variability. These are used to initialize smaller-scale hysteresis experiments that reveal a variety of multistable regimes with at least 4 coexisting alternative attractors.

We argue that due to chaotic dynamics, non-autonomous instabilities, and complex geometries of the basins of attraction, the realized path to tipping can be highly sensitive to initial conditions and the trajectory of the control parameter. Further, we discuss the degree to which the equilibrium dynamics are reflected in the transient dynamics for different rates of forcing. The results have implications regarding the expected abruptness of TPs, as well as their predictability and the design of EWS.

How to cite: Lohmann, J.: Abundant multistability and intermediate tipping points in a global ocean model, EGU General Assembly 2022, Vienna, Austria, 23–27 May 2022, EGU22-4470, https://doi.org/10.5194/egusphere-egu22-4470, 2022.

Anna Poltronieri et al.

Every year, the area of the Arctic sea-ice decreases in the boreal spring and summer and reaches its yearly minimum in the early autumn. The continuous satellite-based time series shows that the September area has decreased from 4.5 x 106 km2 in 1979, to 2.8 x 106 km2 in 2020. The decline has been approximately linear in global mean surface temperature, with a rate of loss of 2.7 x 106 km2 per degree C of global warming.

In the CMIP6 ensemble, however, we find that the majority of the models that reach an Arctic sea-ice free state in the SSP585 runs show an accelerated loss of sea-ice for the last degree of warming compared to the second last degree of warming, which implies an increased sensitivity of the sea-ice to temperature changes. 

Both in the observational and CMIP6 data, we find that the decline in September sea-ice area is approximately proportional to the area north of which the zonal average temperature in spring and summer is lower than a critical threshold Tc. The Arctic amplification implies that the zonally averaged temperatures increase relative to the global temperatures, and with rates increasing with latitude. Linear extrapolation of the zonally averaged temperatures predicts that, with further warming, the September sea-ice area will depend non-linearly on global temperature, the sensitivity will increase and the September sea-ice area may become less that 1 x 106 km2 for global warming between 0.5 and 1.4oC above the current temperature. 

As a result of accelerated sea-ice loss, the average evolution of the sea-ice area among the CMIP6 models before the complete loss of the summer sea-ice shows an increase in the year-to-year fluctuations in minimum ice cover in the next decade. This implies exceptional accumulation of extreme events with very low or no sea-ice at all even before the final loss of the sea-ice. Likewise, an apparent short-term recovery of the sea-ice loss might be observable due to the increasing fluctuations. 

How to cite: Poltronieri, A., Bochow, N., and Rypdal, M.: Arctic summer sea-ice loss will accelerate in coming decades, EGU General Assembly 2022, Vienna, Austria, 23–27 May 2022, EGU22-5725, https://doi.org/10.5194/egusphere-egu22-5725, 2022.

Da Nian et al.

The Amazon rainforest has a major contribution to the bio-geochemical functioning of the Earth system and has been projected to be at risk of large-scale, potentially irreversible, dieback to a savanna state. Measuring the resilience of the Amazon rainforest empirically is critical to helping us understand the magnitude and frequency of disturbances that the rainforest can still recover from. Different means to quantify resilience in practice have been proposed. Here we determine the Amazon rainforest resilience based on a space-for-time replacement, and then estimating the average residence time in the forest state. This 'global' notion of resilience is different from local measures based on variance or autocorrelation and thus provides complementary information. We study the dependence of the exit-time-base resilience on total rainfall and, in order to study the evolution of the Amazon rainforest, we also estimate changes in their resilience over the years.

How to cite: Nian, D., Blaschke, L., Zheng, Y., and Boers, N.: Measuring Amazon rainforest resilience from remotely sensed data, EGU General Assembly 2022, Vienna, Austria, 23–27 May 2022, EGU22-9340, https://doi.org/10.5194/egusphere-egu22-9340, 2022.


Tue, 24 May, 08:30–10:00

Chairpersons: Peter Ditlevsen, Paul Williams

Corentin Herbert

The potential impact of tipping points for climate dynamics is now widely recognized. Furthermore, paleoclimate records suggest that abrupt climate changes have indeed occurred in Earth’s past, potentially on timescales which do not exceed a decade. Several tipping elements, involving various components of the climate system, such as the ocean circulation, sea-ice, continental ice sheets, vegetation, and their couplings, have been suggested. Yet, it remains virtually unknown whether the large-scale atmospheric circulation, the component of the climate system with shortest response time, may undergo bifurcations that could trigger abrupt climate change.

    In this talk I will discuss the possibility of abrupt transitions of the large-scale circulation in the tropics. Specifically, I will consider potential reversals of the mean zonal winds, from the weak easterlies observed in current climate to a "superrotation" state with prevailing westerly winds. The superrotating state exhibits a strongly reduced Hadley circulation.
    I will discuss positive feedback mechanisms and their relevance for the Earth across a hierarchy of models of increasing complexity. A low-dimensional model based on Rossby wave resonance exhibits bistability, and provides a simple criterion for the region of parameter space where this regime exists. We then study the nature of the transition to superrotation in a dry dynamical core, forced in an idealized manner. The main result is that there exists a parameter regime where the dry primitive equations support two coexisting states, with and without an equatorial jet. We will discuss the role of parameters such as the meridional temperature gradient and the boundary layer friction on the existence of this bifurcation.

How to cite: Herbert, C.: Bistability and hysteresis of the large-scale tropical circulation in idealized GCM simulations, EGU General Assembly 2022, Vienna, Austria, 23–27 May 2022, EGU22-6519, https://doi.org/10.5194/egusphere-egu22-6519, 2022.

René van Westen and Henk Dijkstra

The quasi-geostrophic wind-driven double-gyre ocean circulation in a midlatitude rectangular basin is a multi-stable system. Under time-independent forcing, the number of steady states is controlled by the Reynolds number. For a specific range of Reynolds numbers, at least two stable steady states exist. In the quasi-geostrophic model, sub-grid scale processes are usually heavily parameterised, either by deterministic or stochastic representation. In the stochastic case, noise-induced transitions between the steady states may occur.

A standard method to determine transition rates between different steady states is a Monte Carlo approach. One obtains sufficient independent realisations of the model and simply counts the number of transitions. However, this Monte Carlo approach is not well-suited for high-dimensional systems such as the quasi-geostrophic wind-driven ocean circulation. Moreover, when transition probabilities are rare, one needs long integration times or a large number of realisations.

Here we propose a new method to determine transition rates between steady states, by using Dynamically Orthogonal (DO) field theory. The stochastic dynamical system is decomposed using a Karhunen-Loéve expansion and separate problems arise for the ensemble mean state and the so-called time-dependent DO modes. Each DO mode has a specific probability density function, which represents the probability in that direction of phase space. In the case of two steady states, at least one of the DO modes has a bimodal distribution. We analyse transition probabilities using this specific DO mode, which is more efficient compared to the ordinary Monte Carlo approach. We will present the general method and show results for transition probabilities in the quasi-geostrophic wind-driven double-gyre ocean circulation.

How to cite: van Westen, R. and Dijkstra, H.: Transition Probabilities of Wind-driven Ocean Flows, EGU General Assembly 2022, Vienna, Austria, 23–27 May 2022, EGU22-5268, https://doi.org/10.5194/egusphere-egu22-5268, 2022.

Lilian Vanderveken and Michel Crucifix

Spatial organization is a well-known feature of vegetation in semi-arid regions. This phenomenon appears in various parts of the world where water is the limiting factor for plants growing. Those patterns can be reproduced by using reaction-diffusion equations. Rietkerk developed a vegetation patterns model where the joint effects of a local reaction and diffusion create heterogeneous solutions.

The existence of those solutions expands the range of precipitation conditions under which vegetation can prevail. The complete region in the bifurcation diagram where such stable patterns exist is called the Busse balloon.

To our knowledge, no full investigation of the Busse balloon in Rietkerk’s model is available. Here we address this gap and dissect this Busse balloon by analysing the patterned solution branches of the bifurcation diagram.

For a given domain length, those branches can be computed starting from the different zero modes at the edge of the Turing zone around the branch of homogeneous solutions. Then, we use a Newton-Raphson method to track each branch for precipitation changes. Two types of branches appear. What we call the main branches have a roughly constant wavenumber along the branch. What we call the “mixed state branches” originate at the transition between stability and instability along one main branch. The corresponding solutions appear as mixing the solutions of two main branches, which is why we call them that way. However, we show that the latter plays a minor role in the dynamics of the system.

The awareness of the various patterned branch sheds new light on the dynamics of wavenumber switching or R-tipping for patterned systems. More generally, this work gives new insights into the behaviour of patterned systems under changing environment.

How to cite: Vanderveken, L. and Crucifix, M.: Bifurcation diagram for vegetation patterns model: old ways for new insight, EGU General Assembly 2022, Vienna, Austria, 23–27 May 2022, EGU22-7531, https://doi.org/10.5194/egusphere-egu22-7531, 2022.

Taylor Smith et al.

It is theorized that the resilience of natural ecosystems – their ability to resist and recover from external perturbations – can be estimated from their natural variability. We test this hypothesis using a global set of recovery rates from large disturbances derived from satellite vegetation data, and find that the expected theoretical relationships between these empirical recovery rates and the lag-1 autocorrelation and variance indeed hold approximately. The spatial pattern of global vegetation resilience reveals a strong link to both precipitation availability and variability, implying that water plays a first-order role in controlling the resilience of global vegetation.

The resilience of vegetation is not, however, static – global changes in temperature, precipitation, and anthropogenic influence will all impact the ability of ecosystems to adapt to and recover from disturbances. We investigate the global spatial and temporal patterns of changes in resilience using the empirically confirmed metrics – lag-1 autocorrelation and variance – and find spatially heterogeneous long-term (1980s-) trends; recent trends (2000s-) in vegetation resilience are strongly negative across land-cover types and climate zones.

How to cite: Smith, T., Boers, N., and Traxl, D.: Global-scale Changes in Vegetation Resilience Mapped with Satellite Data, EGU General Assembly 2022, Vienna, Austria, 23–27 May 2022, EGU22-7029, https://doi.org/10.5194/egusphere-egu22-7029, 2022.

Valentin Wendling et al.

River runoff and climate data existing from 1950 to present time in West Africa are analyzed over a climatic gradient from the Sahel (semi-arid) to the Gulf of Guinea (humid). The region experienced a severe drought in the 70s-90s, with strong impact on the vegetation, soils and populations. We show that the hydrological regime in the Sahel has shifted: the runoff increased significantly between pre- and post-drought periods and is still increasing. In the Guinean region, instead, no shift is observed.

This suggests that a tipping point could have been passed, triggered by climate and/or land use change. In order to explore this hypothesis, we developed a System Dynamics model representing feedbacks between soil, vegetation and flow connectivity of hillslopes, channels and aquifers. Model runs were initialized in 1950 with maps of land use/land cover, and fed with observed rainfall (climate external forcing).

The modeling results accurately represent the observed evolution of the hydrological regime on the watersheds monitored since the 50s (ranging from 1 to 50000 km²). The model revealed that alternative stable states can exist for the climatic conditions of the study period. From the model runs, we showed that the drought triggered the crossing of a tipping point (rainfall threshold), which explains the regime shift. We identified domains within the watersheds where tipping occurred at small scale, leading to larger scale shifts. This result supports that tipping points exist in semi-arid systems where ecohydrology plays a major role. This approach seems well suited to identify areas of high risk of irreversible hydrological regime shifts under different climate and land-use scenarios.

How to cite: Wendling, V., Peugeot, C., Grippa, M., Kergoat, L., Mougin, E., Hiernaux, P., Rouché, N., Panthou, G., Rajot, J.-L., Pierre, C., Mora, O., Garcia-Mayor, A., Ba, A., Lawin, E., Bouzou-Moussa, I., Demarty, J., Etchanchu, J., Hector, B., Galle, S., and Lebel, T. and the TipHyc Project: Tipping points in hydrology: observed regional regime shift and System Dynamics modeling, EGU General Assembly 2022, Vienna, Austria, 23–27 May 2022, EGU22-5433, https://doi.org/10.5194/egusphere-egu22-5433, 2022.

Gisela Daniela Charó et al.

The topology of the branched manifold associated with the Lorenz model’s random attractor (LORA) evolves in time. LORA’s time-evolving branched manifold robustly supports the point cloud associated with the system’s invariant measure at each instant in time. 

This manifold undergoes not only continuous deformations — with branches that bend, stretch or compress — but also discontinuous deformations, with branches that intersect at discrete times. These discontinuities in the system's invariant measure manifest themselves in the decrease or increase of the number of 1-holes, thus producing abrupt changes in the branched manifold’s topology.

Topological tipping points (TTPs) are defined as abrupt changes in the topology of a random attractor’s branched manifold. Branched Manifold Analysis through Homologies
(BraMAH) is a robust method that allows one to detect these fundamental changes. 
The existence of such TTPs is being confirmed by careful statistical analysis of LORA’s time-evolving branched manifold, following up on Charó et al. (Chaos, 2021, doi:10.1063/5.0059461). Research is being pursued on early warning signals for these TTPs, concentrating on local fluctuations in the system’s invariant measure.

How to cite: Charó, G. D., Ghil, M., and Sciamarella, D.: Early warning signals for topological tipping points, EGU General Assembly 2022, Vienna, Austria, 23–27 May 2022, EGU22-12686, https://doi.org/10.5194/egusphere-egu22-12686, 2022.

Valérian Jacques-Dumas et al.

The Atlantic Meridional Overturning Circulation (AMOC) transports warm, saline water towards the northern North Atlantic, contributing substantially to the meridional heat transport in the climate system. Measurements of the Atlantic freshwater divergence show that it may be in a bistable state and hence subject to collapsing under anthropogenic forcing. We aim at computing the probability of such a transition. We focus on timescales of the century and on temporary collapses of the AMOC. Using simulated data from an idealized stochastic AMOC model, where forcing and white noise are applied via a surface freshwater flux, we compute the transition probabilities versus noise and forcing amplitudes.

Such transitions are very rare and simulating long-enough trajectories in order to gather sufficient statistics is too expensive. Conversely, rare-events algorithms like TAMS (Trajectory-Adaptive Multilevel Sampling) encourage the transition without changing the statistics. In TAMS, N trajectories are simulated and evaluated with a score function; the poorest-performing trajectories are discarded, and the best ones are re-simulated.

The optimal score function is the committor function, defined as the probability that a trajectory reaches a zone A of the phase space before another zone B. Its exact computation is in general difficult and time-consuming. In this presentation, we compare data-driven methods to estimate the committor. Firstly, the Analogues Markov Chain method computes it from the transition matrix of a long re-simulated trajectory. The K-Nearest Neighbours method relies on an existing pool of states where the committor function is already known to estimate it everywhere. Finally, the Dynamical Modes Decomposition method is based on a Galerkin approximation of the Koopman operator. The latter is the most efficient one for the AMOC model when using adaptive dimensionality reduction of the phase space.

How to cite: Jacques-Dumas, V., Dijkstra, H., and van Westen, R.: Data-driven estimation of the committor function for an idealised AMOC model, EGU General Assembly 2022, Vienna, Austria, 23–27 May 2022, EGU22-2689, https://doi.org/10.5194/egusphere-egu22-2689, 2022.

Noemie Ehstand et al.

Functional networks are powerful tools to study statistical interdependency structures in extended systems. They have been used to get insights into the structure and dynamics of complex systems in various areas of science. In particular, several studies have suggested the use of precursors based on percolation transitions in correlation networks to forecast El Niño events.

Our aim is to provide a better understanding of the potential of such percolation precursors for the prediction of episodic events in generic systems presenting chaotic oscillations. To this end, we study the behavior of the precursors in a spatially extended stochastic Vallis model, an asymmetric Lorenz-63 type model for the El Niño-Southern Oscillation (ENSO). Our results demonstrate the ability of the largest connected component of the network to anticipate abrupt changes associated with the system's oscillatory dynamics.

This research was conducted as part of the CAFE Innovative Training Network (http://www.cafes2se-itn.eu/) which has received funding from the European Union’s Horizon 2020 research and innovation programme under the Marie Skłodowska-Curie grant agreement No. 813844.

How to cite: Ehstand, N., Donner, R. V., López, C., and Hernández-García, E.: Using complex networks to predict abrupt changes in oscillatory systems, EGU General Assembly 2022, Vienna, Austria, 23–27 May 2022, EGU22-9237, https://doi.org/10.5194/egusphere-egu22-9237, 2022.

Joseph Clarke et al.

Tipping points in the Earth System could present challenges for society and ecosystems. The existence of tipping points also provides a major challenge for science, as the global warming thresholds at which they are triggered is highly uncertain. A theory of `Early Warning Signals' has been developed to 
warn of approaching tipping points. Although this theory uses generic features of a system approaching a Tipping Point, the conventional application of it relies on an implicit assumption that the system experiences white noise forcing. In the Earth system, this assumption is frequently invalid.
Here, we extend the theory of early warning signals to a system additively forced by an autocorrelated process. We do this by considering the spectral properties of both the system and also of the forcing.  We test our method on a simple dynamical system, before applying our method to a particular example from the Earth System: Amazon rainforest dieback. Using our new approach, we successfully forewarn of modelled rainforest collapse in a state-of-the-art CMIP6 Earth System Model.

How to cite: Clarke, J., Huntingford, C., Ritchie, P., and Cox, P.: Early Warning Signals For Climate Tipping Points: Beyond White Noise, EGU General Assembly 2022, Vienna, Austria, 23–27 May 2022, EGU22-10031, https://doi.org/10.5194/egusphere-egu22-10031, 2022.

Peter Ditlevsen

The warning of tipping to an undesired state in a complex system, such as the climate, when a control parameter slowly approaching a critical value ($\lambda(t) \rightarrow \lambda_0$) relies on detecting early warning signals (EWS) in observations of the system. The primary EWS are increase in variance, due to loss of resilience, and increased autocorrelation due to critical slow down. They are statistical in nature, which implies that the reliability and statistical significance of the detection depends on the sample size in observations and the magnitude of the change away from the base value prior to the approach to the tipping point. Thus the possibility of providing useful early warning depends on the relative magnitude of several interdependent time scales in the problem. These are (a) the time before the critical value $\lambda_c$ is reached, (b) the (inverse) rate of approach to the bifurcation point (c) The size of the time window required to detect a significant change in the EWS and finally, (d) The escape time for noise-induced transition (prior to the bifurcation). Here we investigate under which conditions early warning of tipping can be provided. 

How to cite: Ditlevsen, P.: Conditions for detecting early warning of tipping., EGU General Assembly 2022, Vienna, Austria, 23–27 May 2022, EGU22-5500, https://doi.org/10.5194/egusphere-egu22-5500, 2022.

Peter Ashwin et al.

One of the key problems in climate science is to understand the asymptotic behaviour of a climate model, such as Equilibrium Climate Sensitivity (ECS), from finite time computations of transients of a model that may be complex and realistic. Typically, this is done by fitting to some simpler model and then extrapolating to an asymptotic state. But how do transients behave in the presence of tipping points? More precisely, how much warning can one get of an approaching tipping point? In this work we highlight an illustrative example showing how a good fit of a transient to a simpler model does not necessarily guarantee a good extrapolation, and discuss some other implicit assumptions that may arise when estimating quantities such as ECS.

How to cite: Ashwin, P., Bastiaansen, R., and von der Heydt, A.: Fitting and extrapolation of transient behaviour in the presence of tipping points, EGU General Assembly 2022, Vienna, Austria, 23–27 May 2022, EGU22-12053, https://doi.org/10.5194/egusphere-egu22-12053, 2022.


Tue, 24 May, 10:20–11:50

Chairpersons: Christian Franzke, Hannah Christensen, Naiming Yuan

Josef Ludescher et al.

The El Niño Southern Oscillation (ENSO) is the most important driver of interannual global climate variability and affects weather and climate in large parts of the world. Recently, we have developed a dynamical network approach for predicting the onset of El Niño events well before the spring predictability barrier. In the regarded climate network, the nodes are grid points in the Pacific, and the strengths of the links (teleconnections) between them are characterized by the cross-correlations of the atmospheric surface temperatures at the grid points. In the year before an El Niño event, the links between the eastern equatorial Pacific and the rest of the Pacific tend to strengthen such that the average link strength exceeds a certain threshold. This feature can be used to predict the onset of an El Niño with 73% probability and its absence with 90% probability. The p-value of the hindcasting and forecasting phase (1981-2021) for this performance based on random guessing with the climatological average is 4.6*10-5.

To assess whether this predictive feature is also present in coupled general circulation models, we apply our algorithm to historical and control runs of CMIP5 and CMIP6. We find that the predictive performance present in observational data is absent or very low in GCMs. The lack of this feature may explain the difficulties of GCMs to overcome the spring barrier.

How to cite: Ludescher, J., Bunde, A., and Schellnhuber, H. J.: El Niño forecasting by climate networks: comparison of the forecasting performance in observational data and in historical and controls runs of CMIP5 and CMIP6, EGU General Assembly 2022, Vienna, Austria, 23–27 May 2022, EGU22-6329, https://doi.org/10.5194/egusphere-egu22-6329, 2022.

Chiara Cecilia Maiocchi et al.

Unstable periodic orbits (UPOs) are a valuable tool for studying chaotic dynamical systems, as they allow one to distill their dynamical structure. We consider here the Lorenz 1963 model with the classic parameters' value. We investigate how a chaotic orbit can be approximated using a complete set of UPOs up to symbolic dynamics' period 14. At each instant, we rank the UPOs according to their proximity to the position of the orbit in the phase space. We study this process from two different perspectives. First, we find that longer period UPOs overwhelmingly provide the best local approximation to the trajectory. Second, we construct a finite-state Markov chain by studying the scattering of the orbit between the neighbourhood of the various UPOs. Each UPO and its neighbourhood are taken as a possible state of the system. Through the analysis of the subdominant eigenvectors of the corresponding stochastic matrix we provide a different interpretation of the mixing processes occurring in the system by taking advantage of the concept of quasi-invariant sets.

How to cite: Maiocchi, C. C., Lucarini, V., and Gritsun, A.: Decomposing the Dynamics of the Lorenz 1963 model using Unstable Periodic Orbits: Averages, Transitions, and Quasi-Invariant Sets, EGU General Assembly 2022, Vienna, Austria, 23–27 May 2022, EGU22-1171, https://doi.org/10.5194/egusphere-egu22-1171, 2022.

Paul Pruzina et al.

One of the most fascinating, and surprising, aspects of stratified turbulence is the spontaneous formation of density staircases, consisting of layers with nearly constant density, separated by interfaces with large density gradients. Within a staircase, there are two key lengthscales: the layer depth, and the interface thickness. Density staircases appear in regions of the ocean where the overall stratification is stable, and can be induced experimentally by stirring a fluid with a stable salt gradient. Staircases also appear as a result of double diffusive convection, in both oceanic and astrophysical contexts. Turbulent transport through staircases is enhanced compared to non-layered regions, so understanding their dynamics is crucial for modelling salt and heat transport.

Progress has been made numerically and experimentally, but the fundamental aspects of the problem are not yet fully understood. One leading theory is the Phillips Effect: layering occurs due to the dependence of the turbulent density flux on the density gradient. If the flux is a decreasing function of the gradient for a finite range of gradients, then negative diffusion causes perturbations to grow into systems of layers and interfaces.

An important extension of the Phillips theory is by Balmforth, Llewellyn-Smith and Young [J. Fluid Mech., 335:329-358, 1998], who developed a k-ε style model of stirred stratified flow in terms of horizontally averaged energy and buoyancy fields. These fields obey turbulent diffusion equations, with fluxes depending on a mixing length. The parameterisation of this lengthscale is key to the model, as it must pick out both layer and interface scales. This phenomonological model parameterises terms based on dimensional arguments, and neglects diffusion for simplicity. This model produces clear density staircases, which undergo mergers where two interfaces combine to form one. Layers take up the interior of the domain, while edge regions on either side expand inwards at a rate of t1/2 , removing layers from the outside in. Eventually the edge regions fill the entire domain, so the long time behaviour of the layers cannot be seen.

We present a similar model for stirred stratified layering derived directly from the Boussinesq equations, including molecular and viscous diffusion, so the model can be tailored to specific conditions to make realistic predictions. We show that the layered  region can evolve indefinitely through mergers, by taking fixed-buoyancy boundary conditions to prevent the expansion of the edge regions. We investigate the effects of diffusion on layer formation and evolution, finding that it acts to stabilise the system, both by decreasing the range of buoyancy gradients that are susceptible to the layering instability, and by decreasing the growth rates of perturbations. The lengthscale of the instability also increases, with larger viscosities and diffusivities producing deeper layers with less sharp interfaces.

This model can be used as a more general framework for layering phenomena. Extending to equations for energy, temperature and salinity can model double diffusive layering. More general parameterisations for the fluxes allow it to be adapted to other settings, including potential vorticity staircases in atmospheres and E×B staircases in plasmas.

How to cite: Pruzina, P., Hughes, D., and Pegler, S.: Nonlinear Multiscale Modelling of Layering in Turbulent Stratified Fluids, EGU General Assembly 2022, Vienna, Austria, 23–27 May 2022, EGU22-269, https://doi.org/10.5194/egusphere-egu22-269, 2022.

Josef Schröttle and Nili Harnik

We run a moist shallow water model with stochastic mesoscale forcing, to simulate the effects of mesoscale forcing on exciting large-scale flow structures. In previous work, we showed how the mesoscale forcing excites a classical -5/3 eddy kinetic energy upscale cascade to planetary scales where the linear tropical modes such as Rossby, Yanai, Intertial Gravity, and Kelvin waves form. In this work, we focus on the arising zonal mean flow.

We present results from ensembles of a few hundred simulations indicating multiple-equilibria in the tropical flow, once latent heat release passes a certain threshold in the first 1000 days. Runs up to one hundred thousand days confirm these results and show abrupt transitions in the dry and moist shallow-water turbulence lasting several thousand days. We will discuss the transient nature of the mean flow and suggest a possible new mechanism for the transition of the wind at the equator to super-rotation in a moist environment.

How to cite: Schröttle, J. and Harnik, N.: Spontaneous transitions between sub- and superrotation in dry and moist shallow-water turbulence on the sphere, EGU General Assembly 2022, Vienna, Austria, 23–27 May 2022, EGU22-1307, https://doi.org/10.5194/egusphere-egu22-1307, 2022.

Christian Franzke and Qiyun Ma

Heat waves result from large-scale stationary waves and have major impacts on the economy and mortality. However, the dynamical processes leading to and maintaining heat waves are still not well understood. Here we use a nonlinear stationary wave model (NSWM) to examine the role played by anomalous stationary waves and how they are forced during heat waves. We will discuss heat waves in Europe and Asia. We show that the NSWM can successfully reproduce the main features of the observed anomalous stationary waves in the upper troposphere. Our results indicate that the dynamics of heat waves are nonlinear, and transient momentum fluxes are the primary drivers of the observed anomalous stationary waves. We will also discuss the role of anomalous SSTs in influencing heat waves.

How to cite: Franzke, C. and Ma, Q.: The role of transient eddies and diabatic heating in the maintenance of heat waves: a nonlinear quasi-stationary wave perspective, EGU General Assembly 2022, Vienna, Austria, 23–27 May 2022, EGU22-1571, https://doi.org/10.5194/egusphere-egu22-1571, 2022.

Melanie Kobras et al.

Eddy saturation describes the nonlinear mechanism in geophysical flows whereby, when average conditions are considered, direct forcing of the zonal flow increases the eddy kinetic energy, while the energy associated with the zonal flow does not increase. We present a minimal baroclinic model that exhibits complete eddy saturation. Starting from Phillips’ classical quasi-geostrophic two-level model on the beta channel of the mid-latitudes, we derive a reduced order model comprising of six ordinary differential equations including parameterised eddies. This model features two physically realisable steady state solutions, one a purely zonal flow and one where, additionally, finite eddy motions are present. As the baroclinic forcing in the form of diabatic heating is increased, the zonal solution loses stability and the eddy solution becomes attracting. After this bifurcation, the zonal components of the solution are independent of the baroclinic forcing, and the excess of heat in the low latitudes is efficiently transported northwards by finite eddies, in the spirit of baroclinic adjustment.

How to cite: Kobras, M., Ambaum, M. H. P., and Lucarini, V.: Eddy saturation in a reduced two-level model of the atmosphere, EGU General Assembly 2022, Vienna, Austria, 23–27 May 2022, EGU22-230, https://doi.org/10.5194/egusphere-egu22-230, 2022.

Robin Noyelle et al.

On a synoptic time scale, the northern mid-latitudes weather is dominated by the influence of the eddy-driven jet stream and its variability. The usually zonal jet can become mostly meridional during so-called blocking events, increasing the persistence of cyclonic and anticyclonic structures and therefore triggering extremes of temperature or precipitations. During those events, the jet takes unusual latitudinal positions, either northerly or southerly of its mean position. Previous research proposed theoretically derived 1D models of the jet stream to represent the dynamics of such events. Here, we take a data-driven approach using ERA5 reanalysis data over the period 1979-2019 to investigate the variability of the eddy-driven jet latitudinal position and wind speed variability. We show that shifts of the jet latitudinal position occur on a daily time scale and are preceded by a strong decrease of the jet zonal wind speed 2-3 days prior to the shift. We also show that the dynamics of the jet zonal wind speed can be modelled by a non-linear oscillator with stochastic perturbations. We combine those two results to propose a simple 1D model capable of representing the statistics and dynamics of blocking events of the eddy-driven jet stream. The model is based on two stochastic coupled non-linear lattices representing the jet latitudinal position and zonal wind speed. Our model is able to reproduce temporal and spatial characteristics of the jet and we highlight a potential link between the propagation of solitary waves along the jet and the occurrence of blocking events.

How to cite: Noyelle, R., Faranda, D., and Yiou, P.: Modeling the Northern eddy-driven jet stream position and wind speed variability with stochastic coupled non-linear lattices, EGU General Assembly 2022, Vienna, Austria, 23–27 May 2022, EGU22-1250, https://doi.org/10.5194/egusphere-egu22-1250, 2022.

Mari Eggen et al.

This study suggests a stochastic model for time series of daily zonal (circumpolar) mean stratospheric temperature at a given pressure level. It can be seen as an extension of previous studies which have developed stochastic models for surface temperatures. The proposed model is a combination of a deterministic seasonality function and a Lévy-driven multidimensional Ornstein–Uhlenbeck process, which is a mean-reverting stochastic process. More specifically, the deseasonalized temperature model is an order 4 continuous-time autoregressive model, meaning that the stratospheric temperature is modeled to be directly dependent on the temperature over four preceding days, while the model’s longer-range memory stems from its recursive nature. This study is based on temperature data from the European Centre for Medium-Range Weather Forecasts ERA-Interim reanalysis model product. The residuals of the autoregressive model are well represented by normal inverse Gaussian-distributed random variables scaled with a time-dependent volatility function. A monthly variability in speed of mean reversion of stratospheric temperature is found, hence suggesting a generalization of the fourth-order continuous-time autoregressive model. A stochastic stratospheric temperature model, as proposed in this paper, can be used in geophysical analyses to improve the understanding of stratospheric dynamics. In particular, such characterizations of stratospheric temperature may be a step towards greater insight in modeling and prediction of large-scale middle atmospheric events, such as sudden stratospheric warming. Through stratosphere–troposphere coupling, the stratosphere is hence a source of extended tropospheric predictability at weekly to monthly timescales, which is of great importance in several societal and industry sectors.

How to cite: Eggen, M., Rognlien Dahl, K., Näsholm, S. P., and Mæland, S.: Stochastic Modeling of Stratospheric Temperature, EGU General Assembly 2022, Vienna, Austria, 23–27 May 2022, EGU22-8745, https://doi.org/10.5194/egusphere-egu22-8745, 2022.

Alexander Feigin et al.
Stéphane Vannitsem and X. San Liang

The directional dependencies of different climate indices are explored using the Liang-Kleeman information flow in order to disentangle the influence of certain regions over the globe on the development of low-frequency variability of others. Seven key indices (the sea-surface temperature in El-Niño 3.4 region, the Atlantic Multidecadal Oscillation, the North Atlantic Oscillation, the North Pacific America pattern, the Arctic Oscillation, the Pacifid Decadal Oscillation, the Tropical North Atlantic index), together with three local time series located in Western Europe (Belgium), are selected. The analysis is performed on time scales from a month to 5 years by using a sliding window as filtering procedure.

A few key new results on the remote influence emerge: (i) The Arctic Oscillation plays a key role at short time (monthly) scales on the dynamics of the North Pacific and North Atlantic; (ii) the North Atlantic Oscillation is playing a global role at long time scales (several years); (iii) the Pacific Decadal Oscillation is indeed slaved to other influences; (iv) the local observables over Western Europe influence the variability on the ocean basins on long time scales. These results further illustrate the power of the Liang-Kleeman information flow in disentangling the dynamical dependencies.

How to cite: Vannitsem, S. and Liang, X. S.: Dynamical dependencies at monthly and interannual time scales in the Climate system: Study of the North Pacific and Atlantic regions, EGU General Assembly 2022, Vienna, Austria, 23–27 May 2022, EGU22-1994, https://doi.org/10.5194/egusphere-egu22-1994, 2022.

Mart Ratas and Peter Jan van Leeuwen
Knowledge on how information flows in complex Earth system models would be of great benefit for our understanding of the system Earth and its components. In principle the Kolmogorov or Fokker-Planck equation can be used to estimate the evolution of the probability density. However, this is not very practical since this equation can only be solved in very low dimensional systems. Because of that, mutual information and information flow have been used to infer information in complex systems. This usually involves integration over all state variables, which is generally numerically too expensive. Here we introduce an exact but much simpler way to find how information flows in numerical solutions that only involves integrations over the local state variables. It allows to infer both magnitude and direction of the information flow. The method is based on ensemble integrations of the system, but because the calculations are local the ensemble size can remain small, of  O(100). 
In this talk we will explain the methodology and demonstrate its use on the highly nonlinear Kumamoto-Sivashinsky model using a range of model sizes and exploring both 1-dimensional and multi-dimensional configurations. 

How to cite: Ratas, M. and van Leeuwen, P. J.: Information flow in complex high-dimensional systems, EGU General Assembly 2022, Vienna, Austria, 23–27 May 2022, EGU22-7496, https://doi.org/10.5194/egusphere-egu22-7496, 2022.