Dynamics of tipping cascades on complex networks

Abstract

Tipping points occur in diverse systems in various disciplines such as ecology, climate science, economy, and engineering. Tipping points are critical thresholds in system parameters or state variables at which a tiny perturbation can lead to a qualitative change of the system. Many systems with tipping points can be modeled as networks of coupled multistable subsystems, e.g., coupled patches of vegetation, connected lakes, interacting climate tipping elements, and multiscale infrastructure systems. In such networks, tipping events in one subsystem are able to induce tipping cascades via domino effects. Here, we investigate the effects of network topology on the occurrence of such cascades. Numerical cascade simulations with a conceptual dynamical model for tipping points are conducted on Erdős-Rényi, Watts-Strogatz, and Barabási-Albert networks. Additionally, we generate more realistic networks using data from moisture-recycling simulations of the Amazon rainforest and compare the results to those obtained for the model networks. We furthermore use a directed configuration model and a stochastic block model which preserve certain topological properties of the Amazon network to understand which of these properties are responsible for its increased vulnerability. We find that clustering and spatial organization increase the vulnerability of networks and can lead to tipping of the whole network. These results could be useful to evaluate which systems are vulnerable or robust due to their network topology and might help us to design or manage systems accordingly.

High-resolution global atmospheric moisture connections from evaporation to precipitation

“…No independent observations exist to validate the sourceto-sink relations in our database directly. Some studies validate moisture recycling using tracers in atmospheric models or stable water isotope measurements (Koster et al, 1993;Kurita and Yamada, 2008). However, tracers in atmospheric models are still very much dependent on model physics, especially the treatment of the vertical transport of moisture (see .…”

Interacting tipping elements increase risk of climate domino effects under global warming

“…where x i indicates the state of a certain tipping element, c i is the critical parameter and τ i the typical tipping time scale with i = {Greenland Ice Sheet, West Antarctic Ice Sheet, AMOC, ENSO, Amazon rainforest}. This equation has been investigated in different network types and widely been applied to systems in ecology, economics, political and medical frameworks (Krönke, 2019;Brummitt, 2015;Abraham, 1991). While the first term (Individual dynamics term) indicates the dynamical properties of each tipping element, the second term (Coupling term) describes the connections of each tipping element to the other elements ( Fig.…”

Network dynamics of drought-induced tipping cascades in the Amazon rainforest

“…The state x j must be divided by 2 since the distance from minimum to maximum state is 2. Similar forms of the network and the differential equation have already been used in earlier studies in the literature, but in a way more simplified form compared to this work 62,38 .…”

“…To account for possible spatial variability in the adaptation levels, we construct an ensemble of size 100 for each investigated year. We construct this moisture recycling network using output from Lagrangian atmospheric moisture tracking simulations and a global hydrological model (see methods) 29,30,38 .…”