Early Warning Signs for Abrupt Transitions

Please note: This page is only available in English because the workshop will be held entirely in English. 

The workshop "Early Warning Signs for Abrupt Transitions" is organized by Peter Ashwin, University of Exeter, Niklas Boers, Technical University of Munich and Potsdam Institute for Climate Impact Research, and Kerstin Lux, Technical University of Munich. It will take place as an online event under the EU Horizon 2020 funded project "TiPES – Tipping Points in the Earth System". Also, non-TiPES members are invited to participate. Please register below.


Several subsystems of the earth might undergo abrupt transitions under sustained global warming. Predicting such a tipping event is a very complex task, and the detection of Early Warning Signs (EWS) is an active field of research.

Despite their importance in predicting abrupt transitions, their extraction from data is a challenging task. False positives, i.e. the increase in variance or lag-1 autocorrelation that is not followed by an abrupt transition, reduce the predictive power of such statistical precursor signs. Promising recent results on alternative indicators will be presented and discussed.

Furthermore, many previous results on EWS assume that the underlying noise follows a Brownian Motion. However, it might well be that there is a non-negligible time-correlation structure within the noise in the data. We will discuss how the type of noise affects the EWS.

We would like to present recent results on Early Warning Signs and discuss challenges in advancing the theory and application of EWS.


October 13, 2021, 1-5 pm CEST




Dr. Kerstin Lux

Technical University of Munich
Department of Mathematics

kerstin.lux (at) tum.de

Speakers include

Abstracts for talks

Towards a resilience sensing system for the biosphere (Tim Lenton)

We are in a climate and ecological emergency, where dangerous anthropogenic interference with the biosphere is risking abrupt and/or irreversible changes. To make it easier to see where things are going wrong, and to see where deliberate interventions are making things better, we propose a biosphere resilience sensing system, utilizing the generic mathematical behavior of complex systems: Loss of resilience corresponds to slower recovery from (and a larger response to) perturbations, gain of resilience equates to faster (and smaller) responses to perturbations. Such behavior can be monitored both in time (as described) and across space. We focus here on the potential for satellite remote sensing to provide global spatial coverage and high temporal resolution resilience sensing, particularly of the terrestrial biosphere.

Critical Slowing down in reconstructions of Greenland Ice Sheet Melt Rates and the strength of the AMOC (Niklas Boers)

Several subsystems of the Earth have been suggested to exhibit the potential to abruptly transition to alternative states. A formalism that might be suitable to describe such events is that of dynamical systems and especially bifurcation theory. Considering abrupt regime shifts of climate subsystems as bifurcation-induced transitions suggests they might be preceded by critical slowing down, which could be used as an early-warning signal. Here I show that critical slowing down can be detected in 1) height reconstructions from the central-western part of the Greenland ice sheet and 2) in sea-surface temperature and salinity based fingerprints of the Atlantic Meridional Overturning Circulation. 

Arctic summer sea-ice loss will accelerate in coming decades (Anna Poltronieri)

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.  

In the CMIP6 ensemble, we find that the majority of the models that reach an Arctic sea-ice free state in the SSP585 runs shows 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.  

As a result of accelerated sea-ice loss, the average evolution of the sea-ice area among the CMIP6 models before the loss of the summer sea-ice shows an increase in the year-to-year fluctuations in minimum ice cover in the next decade.

Pronounced loss of Amazon rainforest resilience since the early 2000s (Chris Boulton)

The resilience of the Amazon rainforest to climate and land-use change is crucial for biodiversity, regional climate, and the global carbon cycle. Deforestation and climate change, via increasing dry-season length and drought frequency, may already have pushed the Amazon close to a critical threshold of rainforest dieback. Here we quantify changes of Amazon resilience by applying established indicators (measuring lag-1 autocorrelation) to remotely sensed vegetation data with focus on vegetation optical depth (1991-2016). We find that more than ¾ of the Amazon rainforest has been losing resilience since the early 2000s, consistent with the approach to a critical transition. Resilience is being lost faster in regions with less rainfall, and in parts of the rainforest that are closer to human activity. We provide direct empirical evidence that the Amazon rainforest is losing stability, risking dieback with profound implications for biodiversity, carbon storage and climate change at a global scale. 

Early Warning Signs for Systems driven by Time-Correlated Noise Processes (Kerstin Lux)

Some subsystems of the Earth have been identified to be at risk of undergoing critical transitions.

From the theory of stochastic fast-slow systems [1], it is known that approaching such a tipping point goes along with an increase of variance and/or autocorrelation fluctuations if the noise term is represented by a Brownian motion. However, it is well-known that noise present in many climate systems shows time-correlation.

Therefore, in this talk, I will address Early Warning Signs (EWS) for stochastic fast-slow systems driven by colored noise, fractional Brownian motion and the Rosenblatt process [2]. Our results show that, for colored noise, there is no variance increase at all, so the type of noise can make us "blind" for tipping.

[1] C. Kuehn. A Mathematical Framework for Critical Transitions: Normal Forms, Variance and Applications. J. Nonlinear Sci., 23(3):457–510, 2013.

[2] C. Kuehn, K. Lux, and A. Neamtu. Warning Signs for Non-Markovian Bifurcations: Color Blindness and Scaling Laws. arXiv:2106.08374, pages 1–14, 2021.

Abstracts for posters

 The coupled Amazon vegetation-atmosphere system approaches a critical transition (Nils Bochow, UiT)

The Amazon rainforest is threatened by land use change and increasing drought and fire frequency. Studies suggest a sudden dieback of the entire rainforest after partial forest loss, but the critical threshold and underlying mechanisms remain uncertain. Here we employ a non-linear model of the moisture transport and recycling across the Amazon Basin to identify several precursor signals for a critical transition in the coupled atmosphere-vegetation dynamics. The model reproduces key features of these dynamics and allows to identify changes in the hydrological cycle and classical statistical indicators as precursor signals for a critical transition. We reveal characteristic changes in hydrological reanalysis data that are consistent with the identified precursor signals. In accordance with our model results, we attribute these signals to forest loss due to deforestation, droughts, and fires. Our results suggest that continuing deforestation and degradation in the eastern Amazon could tip the entire rainforest into a savanna state.

Evaluating the performance of EWS: a verification analysis on COVID-19 epidemic data (Daniele Proverbio, University of Luxembourg)

To extend the toolkit of alerting indicators against the emergence of infectious diseases, recent studies have suggested the use of generic early warning signals (EWS) from the theory of dynamical systems. However, it is still debated whether they are generically applicable or potentially sensitive to some dynamical characteristics such as system noise and rates of approach to critical parameter values. In addition, testing on empirical data has so far been limited, so verifying EWS performance remains a challenge.  

In this study, we tackle this question by analyzing common EWS, such as increasing variance and autocorrelation, next to the emergence of COVID-19 outbreaks. We illustrate that these EWS might be successful in detecting disease emergence if some basic assumptions are satisfied: a slow forcing through the transitions and not-fat-tailed noise. Different detrending methods might further improve the performance. In uncertain cases, noise properties or commensurable time scales may obscure the expected early warning signals.  

Overall, our results suggest that EWS can be useful for active monitoring of epidemic dynamics, but that their performance is sensitive to certain features of the underlying dynamics. Our findings thus pave a connection between theoretical and empirical studies, constituting a further step towards the application and interpretation of EWS indicators for informing public health policies.

Early Warning Signals for Tipping in the Presence of Coloured Noise (Joseph Clarke, Univserity of Exeter)

Given the significant impacts likely to be caused by an Earth System Tipping Element crossing a critical threshold it is important to have some early warning of an approaching threshold. Typically, it is assumed that the tipping element is forced by a white noise process. In this case, the variance and autocorrelation should increase as the threshold is approached. However, in the Earth system the forcing is often not white but red and in this case we do not see an increase in the variance (see Kerstin Lux's talk!). We identify a potential Early warning signal by examining the spectral properties of both the system and the forcing.