Many climate subsystems are thought to be susceptible to tipping—and some might be close to a tipping point. The general belief and intuition, based on simple conceptual models of tipping elements, is that tipping leads to reorganization of the full (sub)system. Here, we explore tipping in conceptual, but spatially extended and spatially heterogenous models. These are extensions of conceptual models taken from all sorts of climate system components on multiple spatial scales. By analysis of the bifurcation structure of such systems, special stable equilibrium states are revealed: coexistence states with part of the spatial domain in one state, and part in another, with a spatial interface between these regions. These coexistence states critically depend on the size and the spatial heterogeneity of the (sub)system. In particular, in these systems the crossing of a tipping point not necessarily leads to a full reorganization of the system. Instead, it might lead to a reorganization of only part of the spatial domain, limiting the impact of these events on the system’s functioning.https://iopscience.iop.org/article/10.1088/1748-9326/ac59a8
Many Earth system components and ecosystems have been shown to exhibit tipping [1–5]: when a tiny change in environmental conditions or parameters leads to a critical shift towards an alternative state that might have completely different functioning. For instance, the Amazonian rainforest that might disappear [6, 7], desertification [8, 9], a restructuring of the Atlantic meridional overturning circulation [10, 11], collapses of ice sheets [12–14], turbidity in shallow lakes , amongst many others. Even on a planetary scale, tipping might have happened , and is hypothesised to be possible in the (near) future [17–19].
Typically, tipping is illustrated and explained using simple, conceptual low-dimensional models, that have two alternative states and that can tip between them as climatic conditions change [1–3, 20]. In more complex, more detailed high-dimensional models and in real-life data tipping is, however, often not as clear and pronounced [4, 5, 21]. Tipping from one state to a completely differently structured state is hardly ever observed. Instead, partial restructurings occur more often. For instance, (large) parts of an ice sheet melt, instead of the whole sheet melting in one single tipping event .
This suggests that low- and high-dimensional models behave differently. It could be that high-dimensional models are tuned for stability too much, suppressing tipping behaviour . It could also be that the low-dimensional models are too restrictive in the number of physical processes, thereby exaggerating tipping behaviour [24, 25]. At least, the most simple models really only allow for two alternative states and nothing more. Adding complexity to these leads to more response options for the system, which might lead to less severe tipping events. For instance, adding more boxes to a box model [26, 27], or incorporating spatial effects [21, 25].
In this paper, we investigate the behaviour of conceptual models when spatial effects are incorporated: spatial transport and spatial heterogeneity. This setting has received only little attention in the literature [21, 28] and a thorough theoretical understanding of such systems is still lacking, despite their omnipresence . In such models additional stable states called co-existence states can emerge, in which part of the domain resides in one state and the rest in another state, with a spatial interface separating these regions [21, 24]—see figure 1 for real-life examples. Consequently, in these systems transitions can occur in which only in part of the spatial domain the system changes state, providing a more subtle, fragmented tipping pathway.
The rest of this paper is structured as follows. In section 2, we first review the classic theory of coexistence states in spatially homogeneous (gradient) systems. Subsequently, we detail how this theory changes in a spatially heterogeneous setting. We focus on the possibility of new equilibrium coexistence states and the different bifurcation diagrams these systems can have depending on the spatial heterogeneity. Then, in section 3, we illustrate the potential widespread relevance of coexistence states using several examples of climate subsystems on different spatial scales. For this, we use a variety of conceptual models, that have been proposed before in the literature, or spatially extended versions thereof. Finally, we end with a discussion in section 4.
Climate tipping might not always be disastrous
UNIVERSITY OF COPENHAGEN – FACULTY OF SCIENCE
The consequences of crossing a tipping point might often be much more subtle and less severe than generally assumed. That is the conclusion of a mathematical analysis of tipping in large, spatially heterogeneous systems, which natural systems like ice sheets, lakes, and forests often are. The study by dr. Robbin Bastiaansen et al. from Utrecht University, The Netherlands is published in Environmental Research Letters.
In most scientific works on tipping points in the Earth system, as well as in public discussions, it is often assumed that tipping leads to catastrophic and irreversible changes for the whole system. But in the paper, titled Fragmented tipping in a spatially heterogeneous world, it is argued that such a view is based on too simplistic modelling.
The real world is heterogeneous
The authors reveal that when spatial heterogeneity is added to the simulations, the severity of hitting a tipping point seems to strongly depend on the spatial size and heterogeneity of the system. This means that in large, heterogeneous, systems tipping might often instead lead to minor, stepwise, and even reversible changes. Many climate sub-systems, such as ocean current systems, ice sheets, and large biotopes like rain forests, are indeed large and spatially heterogeneous.
The finding can be illustrated with a pair of lakes of different sizes. In a small pond, there is only little variation (little heterogeneity) within the system and consequently, nutrient pollution can induce tipping in which excessive growth of algae makes the full pond turbid. In a larger lake, however, tipping might not involve the whole lake. Parts of the lake might avoid turbidity because of the sheer size of the system which makes it more heterogeneous.
Passing a tipping point is, therefore, less critical in the large lake than in the small one. Indeed, the heterogeneity also makes tipping more easily reversible in the large system. In small lakes, restoration via an improvement of the nutrient balance is often very difficult as the system is trapped in a turbid state. In larger lakes, however, even the removal of small amounts of nutrients can immediately lead to an expansion of the clear parts of the lake.
Moreover, because species may survive in the clear parts of the lake and later reinhabit the turbid areas as they once again might clear up, also the impact of tipping on the ecosystem can be much less severe if parts of the system maintain their original state.
Generally, the study from Bastiaansen et al. informs us that what comes after the crossing of a climate tipping point is still very much an open question. The study, however, does not make Bastiaansen think we should simply relax about climate tipping.
”I am still worried about tipping points. Because I can imagine critical things might happen especially as climate change persists. But I am not as worried that once we cross a tipping point, everything is going to hell immediately. I think it is going to be much more subtle than the kind of narrative that has been painted in some papers about planetary boundaries: that once we cross over one tipping point everything just collapses simultaneously. I don’t think that is the case,” concludes Robbin Bastiaansen.
The TiPES project is an EU Horizon 2020 interdisciplinary climate science project on tipping points in the Earth system. 18 partner institutions work together in more than 10 countries. TiPES is coordinated and led by The Niels Bohr Institute at the University of Copenhagen, Denmark and the Potsdam Institute for Climate Impact Research, Germany. The TiPES project has received funding from the European Horizon 2020 research and innovation program, grant agreement number 820970.
Environmental Research Letters
METHOD OF RESEARCH
Fragmented tipping in a spatially heterogeneous world
ARTICLE PUBLICATION DATE