Paper: Fragmented tipping in a spatially heterogeneous world
Abstract
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
Introduction
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 [15], amongst many others. Even on a planetary scale, tipping might have happened [16], 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 [22].
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 [23]. 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 [29]. 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.
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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.
Press release.
Climate tipping might not always be disastrous
Crossing a tipping point may lead to many other situations than the generally assumed catastrophic outcome
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.
Still worried
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.
JOURNAL
Environmental Research Letters
DOI
METHOD OF RESEARCH
Computational simulation/modeling
ARTICLE TITLE
Fragmented tipping in a spatially heterogeneous world
ARTICLE PUBLICATION DATE
11-Mar-2022
Tipping Point? Like where the earth has gone into and out of glacial cycles in this Ice Age we have been for the last few million years? With sea levels 30 to 40 meters higher and 150 meters lower? And some pretentious fool is going to model tipping points, like you know, the earth is going to turn into a fireball hell unless you keep funding me?
More like the tipping point when too many people crowd along one side of an island. You can’t trust those darned things.
When I posted a reference to this, suddenly everyone was defending this idiotic stance. Very odd.
Classic!
Most things that tip, later on, tip back again, or are replaced by something else that does tip back again. These are the usual cycles of nature.
I reach a tipping point every time my wife and I dine in a restaurant. Some of those points are bigger than others…
This is another paper that can be added to the ever-expanding folder labeled –
Disappearing Up Our Collective Anus With Models
Actually, disagree. I went and read the paper before commenting (below). It is a good paper. The problem is their opening paragraph, since none of what they do relates to climate despite their (to get published?) claims otherwise.
Good on you Rud.
Eric Worrall reads The Guardian for us, and you wade through turgid text like this paper.
Above & beyond the call of duty by both of you.
I didn’t get past –
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.
The paper reads better with “environmental subsystems” instead of “climate subsystems” in a dozen of the 13 places that the word “climate” is used. I think you’re right, maybe it was a global “cut and paste” to meet reviewers’ publication suggestions. Anyway, nothing like the word “Laplacian” to wake up dormant brain cells…..
I feel better already.
I went and read the paper and looked at the underlying mathematics. Although the math is solid and I like their conclusions, I unfortunately don’t think they apply much to climate—starting with their definition of a tipping point: “a region of parameter space in which there is bistability (states A and B) with saddle node bifurcations between high A and high B”. It is fairly easy to model such systems mathematically, and they do both generally and in four detailed examples. The eutrafication of a pond versus a large shallow lake is their post example, and also good math (I once upon a time for a math modeling class in college did something similar for Lake Erie—big old mess of partial differential equations). Their photo illustration is Lake St. Clair.
But that good example and image is NOT climate relevant. And the climate related high A high B bifurcation (transition) between glacial/interglacial takes about 15,000 years based on the two most recent interglacials, Eemian and Holocene. That truth is NOT an alarmist ‘climate tipping point’.
Their first 5 footnotes purport to show climate tipping points. I offer two of these footnote as intellectually dishonest examples, both from PNAS. The first paper title is ‘Catalog of abrupt shifts in IPCC climate models’. Climate models are NOT climate. The second is ‘Tipping elements in Earth climate systems’, senior author alarmist and Papal advisor Schellnhuber of PIK. Nuff said.
Essay Tipping Points in ebook Blowing Smoke went thru all of the usual alarmist climate tipping suspects, and debunked them all. Essay Shell Games showed two instances of academic misconduct concerning ‘ocean acidification’ tipping, as well as an example of IPCC AR4 ‘science’ being just WRONG (oceans are buffered so cannot pH ‘tip’). And essay ‘By land or by sea’ exposed academic misconduct concerning the sea level rise Eemian ‘tipping point’. It took 3000 years to reach the Eemian highstand about 6.5 meters above today. That is a SLR rate of just under (6500/3000) 2.2mm/year, just like now.
I wonder if gold was used as a currency back then.
I still don’t care much for the alarmist term ‘tipping point’ which is nothing of the sort, despite their goalpost-moving efforts with definitions of words to make things sound as terrifying as possible. It’s a ‘change’ – things change all the time it’s the only constant! I realise that our species doesn’t like any change and some, like climate alarmists, downright fear it but if you properly understand how and why things change it is easier to cope with.
I think that is too limiting. The Triple-Point of water is a location on a phase diagram where solid, liquid, and vapor co-exist, and a slight change in temperature and/or pressure can cause the water to change to just one phase. However, physical chemists don’t use the visually rich imagery of the Leaning Tower of Pisa. Instead, they talk about “shifting,” “transitioning,” or “becoming.”
Whether the mathematics of the paper is good or not, I think that they are attempting to legitimize a phrase that is best used to describe a physical object with a center of mass, subject to a force that moves that center of mass beyond the base supporting the object.
How many papers deal with beneficial tipping points, compared to horrible tipping points?
How are tipping points not just ordinary, normal changes in weather or climate?
Should they suddenly require attention, funding, policies because mathematics has uncovered attractors and some form of chaos?
More bandwagon science. Downplay it.
Ask who on earth keeps supplying chunks of your taxes to a bloated academia drifting ever further from the real world. Geoff S
I feel somewhat cheated that tipping point doesn’t necessarily mean catastrophe.
I think some think, global warming could green the Sahara Desert-
that seems to me a beneficial tipping points
Like re-greening if the Sahara from CO2 you mean? I’d like to see how they will spin that into a disaster. “A requiem for barren sand”.
The only things that don’t tip are Canadians.
Yah, but… ya can tip cows.
Nah – you’re confusing them with Kiwis.
Wrong, Canadians tip, Brits don’t.
Oi!
Don’t stereotype.
Paper covers ocean circulation but not ecosystems, just lakes, grasslands, savannas and tropical forests which maybe simpler, at least in their analysis. Lakes are simpler, but not all turbidity is algae related as they consider. There are a lot of ocean, usually more estuarine, models which have not proven very predictive despite heavy investing. This thorough review (open access), for example, traces history and problems. (Ganju, N.K., and 13 other authors. 2016. Progress and challenges in coupled hydrodynamic-ecological estuarine modeling. Estuaries Coasts 39(2):311–332. https://doi.org/10.1007/s12237-015-0011-y
There are many examples of marine mass mortalities, most catastrophic in the local sense, where return to ‘normal’ is time related [(logistic) growth rate] which they have. Freezes as we just had in Texas historically take 2-3 years and based on the scarcity of predatory birds on the mainland after 13 months suggests the same. They do end with ‘more resilient’ for climate subsystems.
They talk about the “reversibility of tipping if changes can be undone.” Seems to imply that once humans, or their effects, are gone.
“Tipping Point” is one of the most overused phrases of the 21st century, largely because climate alarmists want to scare the public with imagery of a tall tree or building falling to the ground.
It is applied generally to sudden and not easily reversed changes in a system. Water going through a phase change from, say ice to water, would be an example of such a so-called tipping point. However, there is a long and appropriate use of such words as “transition” or “transformation” to describe such rapid phase changes, in contrast to “evolution” or “modification.”
“Tipping Point” is just another example of alarmists trying to manipulate the dialog by inappropriately using pejorative words, when there are other words that are more descriptive and appropriate.
A scientist chooses words carefully to describe a phenomenon objectively; a lawyer chooses words that will appeal to the emotions of jurors with the intent of manipulating them. “Tipping Point” is a lawyer phrase!
We are in the middle of a “tip” from 2 km. thick ice to boreal forests, tundra, and reduced sea ice extent.
Perhaps increasing CO2 will tip the world out the glacial cycles back into the warm ocean state.
Which is a good thing, isn’t it?
And the PETM is still 15 degrees away. (See Scotese)
If Rud says the paper is basically sound, I won’t argue with that.
I don’t think the term “tipping points” is very helpful, either. Generally up to now the climate alarmist narrative – and the skeptical narrative for that matter – have denied chaos and nonlinear/emergent dynamics, preferring the familiar safety of Linearland. However use of the term “tipping point” represents an opportunistic snatch at one element of chaotic dynamics – a catastrophic regime or attractor change – and using it as a jump-scare to spice up alarmism. Now we don’t have to wait for a linear ramp up to disaster. Climate’s “dies irae-dies illa” can descend from heaven any day.
However tipping points alone do not represent nonlinear-emergent theory any more than mushy peas alone represent the glorious edifice of British cuisine. They’re just a cherry.
For instance, chaotic dynamics are just as likely to act for stability and resist change in climate and biosphere, as they are to precipitate a sudden catastrophe. Emergent thermal homeostasis is a well established chaos-related phenomenon that has been reviewed here by Willis Eschenbach:
https://wattsupwiththat.com/2013/02/07/emergent-climate-phenomena/
Chaos-emergent theory can also make a critical contribution to climate attribution. Accepting the reality of nonlinear dynamics, emergent (entropy-exporting) pattern and an attractor landscape, more or less destroys the argumentum ad ignorantum much loved in climate alarmism, that claims “this change must be from CO2 because we can’t see what else it could possibly be”. What you allow yourself to see restricted to Linearland alone is a very small rather exceptional slice of the real world. For instance emergent chaotic oscillations give rise to phenomena such as the Pacific Decadal Oscillation (PDO), the Atlantic Multidecadal Oscillation (AMO) and other such ocean driven oscillatory systems. They can cause decadal and longer scale climate developments and oscillations that are often claimed to represent purely anthropogenic “climate change”
Further thoughts along these lines can be found here:
https://ptolemy2.wordpress.com/2021/11/13/climate-pandemonium/
Is climate tipping a myth like cow topping?
No, it’s more like cow tipping. And cow topping sounds like a Rule 34 meme.
ROFLMAO TILT
And check out the new restaurant I found.
https://www.google.com/amp/s/www.zomato.com/mumbai/rule-34-kandivali-west/menu%3famp=1
Rule 34 menu
The “tipping point” argument seems like a fundamental misunderstanding of the nature of systems. The climate is not a light switch: on, off. It is a really complex system with hundreds of interacting, dynamic inputs. And as a rule complex systems with large numbers of variables don’t “flip” because a single variable of median importance changes in value by 30-something percent.
Did they miss any trendy jargon at all in this paper and its intro?