Uh…no comment~cr
Theoretical progress in climate science indicates algebraic topology applied to reduced climate models might help predict if and when the Earth system will tip
UNIVERSITY OF COPENHAGEN – FACULTY OF SCIENCE
CREDIT: TIPES/HP
The Earth’s climate system seems to have shifted abruptly between colder and warmer modes in the past. Do we risk the same today from anthropogenic climate change? Frankly, climate models cannot answer that question yet. But a result in the journal Chaos by Gisela D. Charó, Mickaël D. Chekroun, Denisse Sciamarella and Michael Ghil suggests a way to resolve the matter. Analyzing a model that combines the two leading theories for climate change with algebraic topology tools, the authors show that the climate system indeed progresses through abrupt transitions, also known as tipping points. These tools are applicable to reduced climate models and they well might help assess whether the Earth’s climate system on a whole is about to tip due to global warming. The work is part of the TiPES project, a European science collaboration on tipping points in the Earth system.
How does the climate evolve?
”It is one of the truly unsolved mysteries about the climate sciences, that we are trying to get at,” explains Michael Ghil, École Normale Supérieure, Paris, France.
There have been essentially two complementary views of what makes climate evolve. One is the deterministically chaotic view of Edward Lorenz. This is the chaos theory that is widely known through the idea that a butterfly flapping its wings on one continent can be the origin of a raging storm on another continent.
The other view is that of Klaus Hasselmann, the recent Nobel Prize winner, who said the climate system is stochastic and everything fluctuates but regresses to the mean.
The combination looks strange
”We have earlier, in 2008, brought these two theories together and shown that things get a lot more interesting if you have both deterministic chaos and stochastic perturbations,” says Michael Ghil.
The result from 2008, a so-called random attractor, can be seen in a video here, https://vimeo.com/240039610.
This random attractor changes with time. The shape it takes at a given instant, called a snapshot, determines where the climate system is most likely to be. It has not been clear, however, how to interpret the random attractor’s changes in time. What does its changing path mean for our understanding of the climate? Algebraic topology now helps with that.
Abrupt changes
Algebraic topology is quite abstract but its results are easy to understand. If two systems’ geometric objects are qualitatively similar, they contain the same number of holes.
The analysis in Chaos of the climate’s random attractor reveals that, over time, holes appear and disappear. This means the system shifts between different regimes. The transitions seem to be instantaneous. And because the analysis in effect reveals changes in the most fundamental properties of the physical system being analysed, the results suggest that the nature of Earth’s climate indeed is to evolve through abrupt transitions – commonly known as tipping points.
Early warning
The method might have implications for predicting an eventual tipping of the climate system. Today, such a tipping of the entire climate system is much too complicated an occurrence to establish an early warning system for. However, algebraic topology could be the answer.
”This is a fairly robust method of establishing critical conditions in very complex situations. So I think that it should be possible to use these tools in order to really foreshadow transitions in a system that is as complex as the climate system,” says Michael Ghil.
Success in carrying out this program, however, will depend on whether climate models can be reduced to manageable sizes for analysis with the algebraic topology tools used in this work.
Contributors to this work.
Gisela D. Charó, CONICET – Universidad de Buenos Aires (UBA), Argentina; and the CNRS – IRD – CONICET – UBA. Institut Franco-Argentin d’Études sur le Climat et ses Impacts, Argentina. Mickaël D. Chekroun, the Weizmann Institute of Science, Rehovot, Israel. Denisse Sciamarella, CNRS – Centre National de la Recherche Scientifique, Paris, France, and CNRS – IRD – CONICET – UBA. Institut Franco-Argentin d’Études sur le Climat et ses Impacts, CABA, Argentina. Michael Ghil, Geosciences Department and Laboratoire de Météorologie Dynamique (CNRS and IPSL), École Normale Supérieure and PSL University, Paris, France, and Department of Atmospheric & Oceanic Sciences, University of California, Los Angeles, California, USA.
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
Chaos An Interdisciplinary Journal of Nonlinear Science
DOI
METHOD OF RESEARCH
Computational simulation/modeling
SUBJECT OF RESEARCH
Not applicable
ARTICLE TITLE
Noise-driven topological changes in chaotic dynamics
ARTICLE PUBLICATION DATE
12-Oct-2021
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The most overused word-pairing of the 21st century!
I fully accept the tipping point model both in theory and practice. In theory a two energy state model with an energy barrier between the two states is understandable. Anyone who wears contact lenses knows there is a right way and wrong way for them to be and there is a small energy push needed to turn contacts the from the wrong way to the right way so as to feel comfortable on the eye. In practice we know the earth system has oscillated between cold glacial conditions and warmer interglacial for several hundred thousand years and the transitions appear to be those tipping points which we don’t fully understand.
We also know with certainty that my Jeep did not cause those tipping points. Applying theory of tipping points to demonstrably useless climate models is clearly a work that belongs to chaos theory. I don’t intend that as complement.
Also I don’t need Herculean math skills to know that the forces involve in a butterfly flapping it’s wings can never, in the known universe, be causative of a hurricane. The idiot who tracks the series of events beginning with butterfly flying and ends with a hurricane, and then concludes the former caused the latter has a problem with thinking.
The butterfly effect is a misnomer. Chaos is a math property exhibited by certain nonlinear equations. Infinitesimal differences in initial conditions quickly lead to divergent behavior. No butterflies are involved. The proper language is extreme sensitivity to initial conditions.
True, but is only one manifestation. Others include bifurcations (see my peer reviewed paper on same in a manufacturing setting in Journal of Strategy, if I recall correctly 1991) and strange attractors in N-1 Lorenz space. An example of bifurcation between strange attractors is ice ages alternating with warm periods. What we don’t know is why the ice period shifted from about 40ky to about 100ky about 1000ky ago.
I agree but as it is commonly used the implication that a very tiny force or action can lead to a massively energetic action is often made simply with the observation of one following the other.
Ah… the solution! When all the existing models don’t work, cobble up another BS model combining all previous BS models.
My nephew has a recent PhD in mathematics from LSU. His specialty is algebraic topology. So I called and asked him if it could be applied to the output of mathematically chaotic climate models to predict shifts between their strange attractors. His emphatic answer was no. Nuff said.
Guess I do not have to look at the article. Of course the authors likely disagree. I still want to know what a hole in an attractor looks like? Is it a place the system trajectories do not go? Or do they go in and disappear? Are we in danger of hitting a hole? That would be worse than a tipping point! Can we get tipped into a hole? Just kidding but still wondering about them holes. Maybe your nephew could look at the paper.
He did not want to waste his time—I tried.
IMHO, a hole in an attractor is actually a hole in the paper and it’s premises. Attractors are like gravity wells. They have a bottom, but the bottom cannot be a hole.
Regards
The last major perturbation of the climate was the closure of the Isthmus of Panama some 3.5 million years ago. That stopped the circulation of a global current and more or less split the equatorial circulation into Atlantic and Pacific. The split appears to have caused the newest ice ages, and several greatly different weather effects- the el Nino-la Nina circulation, redirection of the Gulf Stream and the formation of a cold counter current, a huge change in the South American fauna due to the infiltration of North American species and more.
While it may eventually be possible to predict the climate behavior many mathematician/scientists have pointed out how difficult the idea is. The primary limitation is computing power. Digital computers have serious limitations since it is very difficult to solve differential equations on them. Due to digital limits, differential equations have to be solved by procedures. But the procedures are limited in accuracy by the same limits in the machine. Over the millions of repetitive calculations the error in the results can balloon out of control.
Other limitations, specifically the smallest difference the computer can generate is still to big to make useful modelling calculations, particularly since all the calculations build up errors as the calculations interact with each other. Perhaps quantum computing will solve the problem some day. Until it does, the machine error, the machine epsilon, will continue to limit digital computers for climate models.
The other major problem is with the climate models themselves. The climate responds, such as a droplet forming, at tiny levels. When a drop of water hits the ocean surface it makes a vortex that can take some seconds to die out while its energy is spreading out. Both the droplet formation and its dissolution are both the source and the generation of the storm’s power.
Until the calculation problem is solved it won’t be possible to calculate useful results. They can’t just be lumped into averages because the effects don’t act on averages. For example, how does one determine the behavior of clouds on a rainy day. Which one is going to rapidly grow and generate a tornado. What limits an incipient tornado from dropping down and devastating a town or simply lets it fold back into the storm?
If it is chaotic no amount of computing power will make it predictable because we cannot know the state of the system to the degree needed to rule out the sensitivity that makes it unpredictable.
I would think the last perturbation of the climate was coming out of the last ice age, which is very recent.
See my post here some years ago for illustrations of your basic points. Titled, “The Trouble with Climate Models”. The present climate model computational intractability (thanks to the CFL constraint on numeric solutions to PDEs) is 6-7 Orders of Magnitude!
90% of the last 10 to 15 thousand years was at a minimum 1 to 3C warmer than today, and no tipping points were hit.
Anyone who believes a few tenths of a degree is going to kill us all is delusional.
We know they are. Examples: Mann thinks he is a scientist, and Kerry thinks he thinks.
The only possible tipping point is towards a colder climate.
A European science collaboration on tipping points in the Earth system found that the tipping points MIGHT be predicted. What a nice result. May their lunch plates be always full.
Eventually, after much improvement, the models might be able to predict the positions of chicken entrails on a table.
“Theoretical progress in imaginary climate science indicates algebraic topology misapplied to reduced imaginary climate models”
This one sentence is filled with specious assumptions surrounded by sophistry words.
e.g., how does one theory progress? Any change makes it a new theory.
Or, how does theoretical anything progress?
Theoretical basically means hypothetical. If theoretical happens to relate to reality, it loses that bit of theoretical. Theoretical undergoes a irrational change remains firmly theoretical. That is, theoretical does not “progress”. That pure sophistry.
Eventually, it begs the question exactly why do algebraic functions relate to inaccurate climate models in any predictive sense?
I think Niels Bohr is spinning in his grave at the abuse, by reference, of his name.
Only 2 things wrong with this paper: 1) Tipping points, 2) models. Need I say more?