arXiv subjects

Johannes Lohmann

Publications and source records attributed to Johannes Lohmann.

8 recordsLinked to original sources

arXiv2026

Predicting tipping points: The many shades of non-equilibrium and catch-22s of early-warning

The potential of crossing climate tipping points (TP) has reached the attention of many researchers and the general public. On the one hand, the basis for this concern is strengthening, with simulations showing that abrupt transitions might occur even for moderate emission scenarios. On the other hand, our understanding of what constitutes such transitions mathematically is becoming more nuanced. This leads to challenges for the fidelity of early-warning signals (EWS), which accompany bifurcations in systems that closely track a slowly changing steady state. Different kinds of out-of-equilibrium dynamics in a rapidly changing climate, as well as chaos, blur the critical tipping threshold and imply limits in predictability. Using EWS to detect loss of local stability from data requires careful evaluation in the high-dimensional system, and may have limited predictive power in a highly multistable climate, where there is more than a single, well-known alternative state. This calls for new methods using non-equilibrium statistical mechanics and dynamical systems to efficiently probe the global stability properties of climate models and observations.

physics.ao-ph↗

arXiv2026

On early-warning of full versus partial Atlantic overturning circulation collapse

Climate models indicate a significant slowdown of the Atlantic Meridional Overturning Circulation (AMOC) in the future, and some suggest it may collapse irreversibly to a substantially weakened state. The global warming threshold where this may happen is highly uncertain. An alternative to model-based threshold estimation are early-warning signals (EWS) in AMOC fingerprints, which can predict destabilization of a steady state (a saddle-node bifurcation) from generic changes in statistical properties. But an AMOC collapse may be a sequence of partial weakenings with shutdown of deep water formation in distinct regions. A conceptual model featuring sequential tipping points in two such regions is presented. Since the system only follows the expected saddle-node normal form when very close to each tipping point, a variety of trends in EWS are seen for different observables. This makes it hard to determine what type of collapse (partial or full) will follow, and when it will happen.

physics.ao-ph↗

arXiv2026

Alternate states and intermingledness in complex high-dimensional systems

Many natural systems posses, and can transition between, multiple alternative states. For example, a climate ``tipping element'' is a climate component that can transition to an alternative steady state due to an external perturbation such as global warming. Despite the potential impact, existence of alternate states in realistic, complex simulations (e.g. climate models) remain poorly understood. Arguably a reason for this is the lack of applicable methodology that explicitly targets finite yet high-dimensional datasets. In this work we utilize recent progress in computational nonlinear dynamics to formulate a workflow that analyses potentially multi-state simulation data and decides algorithmically what are the alternate states contained within, if any are clearly distinguishable. The framework undergoes an optimization routine that showcases which observables in the data best differentiate the alternate states, and which ones do not differentiate at all, which could be used to guide monitoring and early-warning for multistable components in climate or ecosystems. Finally, once the alternate states have been found, we define an indicator called ``intermingledness''. It quantifies differences and similarities between alternate states, as well as for their basins of attraction (if applicable), across various diagnostic variables. We analyse and present results using three diverse climate datasets: Atlantic ocean circulation, atmospheric midlatitude flow, and habitability of exoplanets. The method is not exclusive to climatic data, but applicable to a variety of cases, including complex networks such as power grids or biological networks. We also provide easy-to-use open source code for applying the workflow to new data.

physics.ao-ph↗

arXiv2025

Choosing observables that capture critical slowing down before tipping points: A Fokker-Planck operator approach

Tipping points (TP) are abrupt transitions between metastable states in complex systems, most often described by a bifurcation or crisis of a multistable system induced by a slowly changing control parameter. An avenue for predicting TPs in real-world systems is critical slowing down (CSD), which is a decrease in the relaxation rate after perturbations prior to a TP that can be measured by statistical early warning signals (EWS) in the autocovariance of observational time series. In high-dimensional systems, we cannot expect a priori chosen scalar observables to show significant EWS, and some may even show an opposite signal. Thus, to avoid false negative or positive early warnings, it is desirable to monitor fluctuations only in observables that are designed to capture CSD. Here we propose that a natural observable for this purpose can be obtained by a data-driven approximation of the first non-trivial eigenfunction of the backward Fokker-Planck (or Kolmogorov) operator, using the diffusion map algorithm.

nlin.CD↗

arXiv2025

Direct test for critical slowing down before Dansgaard-Oeschger events via the volcanic climate response

It is tested whether past abrupt climate changes support the validity of statistical early-warning signals (EWS) as predictor of future climate tipping points. EWS are expected increases in amplitude and correlation of fluctuations driven by noise. This is a symptom of critical slowing down (CSD), where a system's recovery from an external perturbation becomes slower as a tipping point (represented by a bifurcation) is approached. EWS are a simple, indirect measure of CSD, but subject to assumptions on the noise process and measurement stationarity that are hard to verify. In this work the existence of CSD before the Dansgaard-Oeschger (DO) events of the last glacial period is directly tested by inferring the climate's recovery from large volcanic eruptions. By averaging over hundreds of eruptions, a well-defined, stationary perturbation is constructed and the average climate response is measured by eight ice core proxies. As the abrupt DO warming transitions are approached, the climate response to eruptions remains the same, indicating no CSD. For the abrupt DO cooling transitions, however, some key proxies show evidence of larger climate response and slower recovery as the transitions are approached. By comparison, almost all proxies show statistical EWS before cooling and warming transitions, but with only weak confidence for the warming transitions. There is thus qualitative agreement of CSD and EWS, in that the evidence for bifurcation precursors is larger for the cooling transitions. However, the discrepancy that many proxies show EWS but no direct CSD (and vice versa) highlights that statistical EWS in individual observables need to be interpreted with care.

physics.ao-ph↗

arXiv2025

The role of edge states for early-warning of tipping points

Tipping points (TP) are often described as low-dimensional bifurcations, and are associated with early-warning signals (EWS) due to critical slowing down (CSD). CSD is an increase in amplitude and correlation of noise-induced fluctuations away from a reference attractor as the TP is approached. But for high-dimensional systems it is not obvious which variables or observables would display the critical dynamics and carry CSD. Many variables may display no CSD, or show changes in variability not related to a TP. It is thus helpful to identify beforehand which observables are relevant for a given TP. Here we propose this may be achieved by knowledge of an unstable edge state that separates the reference from an alternative attractor that remains after the TP. This is because stochastic fluctuations away from the reference attractor are preferentially directed towards the edge state along a most likely path (the instanton). As the TP is approached the edge state and reference attractor typically become closer, and the fluctuations can evolve further along the instanton. This can be exploited to find observables with substantial CSD, which we demonstrate using conceptual dynamical systems models and climate model simulations of a collapse of the Atlantic Meridional Overturning Circulation (AMOC).

nlin.CD↗

arXiv2024

Melancholia States of the Atlantic Meridional Overturning Circulation

The Atlantic Meridional Overturning Circulation (AMOC) is a much studied component of the climate system, because its suspected multistability is associated with tipping behaviour yielding potentially large regional and global climatic impacts. In this paper we investigate the global stability properties of the system using an ocean general circulation model. We construct an unstable AMOC state, i.e., an unstable solution of the flow that resides between the stable regimes of a vigorous and collapsed AMOC. Such a solution, also known as a Melancholia or edge state, is a dynamical saddle embedded in the boundary separating the competing basins of attraction. It is physically relevant since it lies on the most probable path of a noise-induced transition between the two stable regimes, and because tipping occurs when one of the attractors and the Melancholia state collide. Its properties may thus give hints towards physical mechanisms and predictability of the critical transition. We find that while the AMOC Melancholia state as viewed from its upper ocean properties lies between the vigorous and collapsed regimes, it is characterized by an Atlantic deep ocean that is fresher and colder compared to both stable regimes. The Melancholia state has higher dynamic enthalpy than either stable state, representing a state of higher potential energy that is in good agreement with the dynamical landscape view on metastability.

physics.ao-ph↗

arXiv2023

Multistability and Intermediate Tipping of the Atlantic Ocean Circulation

Tipping points (TP) in climate sub-systems are usually thought to occur at a well-defined, critical forcing parameter threshold, via destabilization of the system state by a single, dominant positive feedback. However, coupling to other sub-systems, additional feedbacks, and spatial heterogeneity may promote further small-amplitude, abrupt reorganizations of geophysical flows at forcing levels lower than the critical threshold. Using a primitive-equation ocean model we simulate a collapse of the Atlantic Meridional Overturning Circulation (AMOC) due to increasing glacial melt. Considerably prior to the collapse, various abrupt, qualitative changes in AMOC variability occur. These intermediate tipping points (ITP) are transitions between multiple stable circulation states. Using 2.75 million years of model simulations, we uncover a very rugged stability landscape featuring parameter regions of up to nine coexisting stable states. The path to an AMOC collapse via a sequence of ITPs depends on the rate of change of the meltwater input. This challenges our ability to predict and define safe limits for TPs.

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