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.

References

• 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 Physics, 179(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.

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.

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.

References

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.

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.

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.

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.

Reference

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.

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.

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 4^th-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.

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.

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.

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.

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.

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.

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 T_c. 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 1.4^oC 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.

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.

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.

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.

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.

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.

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.

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.

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.

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.

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.

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.

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.

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.

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.

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.

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.