## Tipping Points in Climate Systems

If you’ve just recently gotten a PhD, you can get paid to spend a week this summer studying tipping points in climate systems!

They’re having a program on this at ICERM: the Institute for Computational and Experimental Research in Mathematics, in Providence, Rhode Island. It’s happening from July 15th to 19th, 2013. But you have to apply soon, by the 15th of March!

For details, see below. But first, a word about tipping points… in case you haven’t thought about them much.

### Tipping Points

A tipping point occurs when adjusting some parameter of a system causes it to transition abruptly to a new state. The term refers to a well-known example: as you push more and more on a glass of water, it gradually leans over further until you reach the point where it suddenly falls over. Another familiar example is pushing on a light switch until it ‘flips’ and the light turns on.

In the Earth’s climate, a number of tipping points could cause abrupt climate change:

(Click to enlarge.) They include:

• Loss of Arctic sea ice.
• Melting of the Greenland ice sheet.
• Melting of the West Antarctic ice sheet.
• Permafrost and tundra loss, leading to the release of methane.
• Boreal forest dieback.
• Amazon rainforest dieback
• West African monsoon shift.
• Indian monsoon chaotic multistability.
• Change in El Niño amplitude or frequency.
• Change in formation of Atlantic deep water.
• Change in the formation of Antarctic bottom water.

• T. M. Lenton, H. Held, E. Kriegler, J. W. Hall, W. Lucht, S. Rahmstorf, and H. J. Schellnhuber, Tipping elements in the Earth’s climate system, Proceedings of the National Academy of Sciences 105 (2008), 1786–1793.

Mathematicians are getting interested in how to predict when we’ll hit a tipping point:

• Peter Ashwin, Sebastian Wieczorek and Renato Vitolo, Tipping points in open systems: bifurcation, noise-induced and rate-dependent examples in the climate system, Phil. Trans. Roy. Soc. A 370 (2012), 1166–1184.

Abstract: Tipping points associated with bifurcations (B-tipping) or induced by noise (N-tipping) are recognized mechanisms that may potentially lead to sudden climate change. We focus here a novel class of tipping points, where a sufficiently rapid change to an input or parameter of a system may cause the system to “tip” or move away from a branch of attractors. Such rate-dependent tipping, or R-tipping, need not be associated with either bifurcations or noise. We present an example of all three types of tipping in a simple global energy balance model of the climate system, illustrating the possibility of dangerous rates of change even in the absence of noise and of bifurcations in the underlying quasi-static system.

We can test out these theories using actual data:

• J. Thompson and J. Sieber, Predicting climate tipping points as a noisy bifurcation: a review, International Journal of Chaos and Bifurcation 21 (2011), 399–423.

Abstract: There is currently much interest in examining climatic tipping points, to see if it is feasible to predict them in advance. Using techniques from bifurcation theory, recent work looks for a slowing down of the intrinsic transient responses, which is predicted to occur before an instability is encountered. This is done, for example, by determining the short-term auto-correlation coefﬁcient ARC in a sliding window of the time series: this stability coefﬁcient should increase to unity at tipping. Such studies have been made both on climatic computer models and on real paleoclimate data preceding ancient tipping events. The latter employ re-constituted time-series provided by ice cores, sediments, etc, and seek to establish whether the actual tipping could have been accurately predicted in advance. One such example is the end of the Younger Dryas event, about 11,500 years ago, when the Arctic warmed by 7 C in 50 years. A second gives an excellent prediction for the end of ’greenhouse’ Earth about 34 million years ago when the climate tipped from a tropical state into an icehouse state, using data from tropical Paciﬁc sediment cores. This prediction science is very young, but some encouraging results are already being obtained. Future analyses will clearly need to embrace both real data from improved monitoring instruments, and simulation data generated from increasingly sophisticated predictive models.

The next paper is interesting because it studies tipping points experimentally by manipulating a lake. Doing this lets us study another important question: when can you push a system back to its original state after it’s already tipped?

• S. R. Carpenter, J. J. Cole, M. L. Pace, R. Batt, W. A. Brock, T. Cline, J. Coloso, J. R. Hodgson, J. F. Kitchell, D. A. Seekell, L. Smith, and B. Weidel, Early warnings of regime shifts: a whole-ecosystem experiment, Nature 332 (2011), 1079–1082.

Abstract: Catastrophic ecological regime shifts may be announced in advance by statistical early-warning signals such as slowing return rates from perturbation and rising variance. The theoretical background for these indicators is rich but real-world tests are rare, especially for whole ecosystems. We tested the hypothesis that these statistics would be early-warning signals for an experimentally induced regime shift in an aquatic food web. We gradually added top predators to a lake over three years to destabilize its food web. An adjacent lake was monitored simultaneously as a reference ecosystem. Warning signals of a regime shift were evident in the manipulated lake during reorganization of the food web more than a year before the food web transition was complete, corroborating theory for leading indicators of ecological regime shifts.

### IdeaLab program

If you’re seriously interested in this stuff, and you recently got a PhD, you should apply to IdeaLab 2013, which is a program happening at ICERM from the 15th to the 19th of July, 2013. Here’s the deal:

The Idea-Lab invites 20 early career researchers (postdoctoral candidates and assistant professors) to ICERM for a week during the summer. The program will start with brief participant presentations on their research interests in order to build a common understanding of the breadth and depth of expertise. Throughout the week, organizers or visiting researchers will give comprehensive overviews of their research topics. Organizers will create smaller teams of participants who will discuss, in depth, these research questions, obstacles, and possible solutions. At the end of the week, the teams will prepare presentations on the problems at hand and ideas for solutions. These will be shared with a broad audience including invited program officers from funding agencies.

Two Research Project Topics:

• Tipping Points in Climate Systems (MPE2013 program)

• Towards Efficient Homomorphic Encryption

IdeaLab Funding Includes:

• Travel support

• Six nights accommodations

• Meal allowance

The Application Process:

IdeaLab applicants should be at an early stage of their post-PhD career. Applications for the 2013 IdeaLab are being accepted through MathPrograms.org.

Application materials will be reviewed beginning March 15, 2013.

### 17 Responses to Tipping Points in Climate Systems

1. Curtis Faith says:

Very nice John. Some very interesting implications for economic stability too

2. Arrow says:

Seems like a pretty one sided list, where are all the tipping points which would offer us a net benefit?

For example:
1. Breaking of the glacial-interglacial cycle. Unlike potential 2-3 degrees of global warming another glaciacion would really decimate humanity. The benefits of breaking this cycle alone would outweigh all the negative consequences of all the tipping points you mentioned combined.

2. Greening of Sahara (and perhaps other deserts). It’s even mentioned in the link you mentioned.

3. Restoring Greenland to it’s proper green state.

4. Opening of the northwest passage.

and so on.

• John Baez says:

I thought you said warming had stopped! And now you’re talking about ‘breaking off the glacial-interglacial cycle’!

There’s a certain multi-pronged philosophy about climate change which I’ve never understood, which goes something like this:

1) Global warming is a myth.
2) But if it’s not, it stopped a while ago.
3) But if it didn’t, it will stop soon.
4) But if it doesn’t, it’s not actually bad.
5) But if it is, at least it’s not human-caused.
6) But if it is, it’s too late to do anything about it.

It’s true that people focus more on ‘bad’ tipping points than ‘good’ ones. Luckily the math and physics of tipping points doesn’t really care what we think is ‘bad’ and what we think is ‘good’.

• Arrow says:

Well if we are talking about potential tipping points I think both good and bad ones should be represented, whether global warming is a threat or not.

Also the role of a skeptic is to question all the assumptions of the theory. But to clarify my stance:

1) There is a small warming trend in the global mean temperature of the last century. It did slow down in the last 15 years despite CO2 continualy increasing.

2) The complexity of global climate and limitations of scientific method make it is impossible to say how much of this warming is attributable to man-made emissions. Maybe most of it, maybe only a little. Current long term climate models are completely inadequate and unreliable.

3) Even assuming the warming will continue into the future it will have both beneficial and harmful effects. Though if it does avert another ice age the beneficial effects will outweigh the harmful ones by far.

4) Even if you wanted to do so, there is absolutely no realistic way to halt CO2 emissions (other then another world war leading to population collapse which is also unlikely atm). As long as cheap fossil fuels are available they will be consumed.

• You forgot a contained thermonuclear war, that might also slow it down for a while, even without halting CO2 …

Anyway, more seriously speaking, geoengineering is probably a good option.

• John Baez says:

Arrow wrote:

Well if we are talking about potential tipping points I think both good and bad ones should be represented, whether global warming is a threat or not.

I agree with you here. As you know, some people tend to focus on big bad things that might happen in the future, while others tend to focus on big good things. It’s very hard to get anyone to behave in a ‘neutral’ way here (or even to define exactly what ‘neutral’ means).

But there’s also a real sense in which sudden large changes in the Earth’s ecosystem are inherently likely to be bad at first and only slowly reveal their good side. The reason is that people and other organisms are adapted to the current situation.

For example, if Greenland were to suddenly warm up and melt, it would take at least a few decades and perhaps longer for plants to form rich organic soil there, allowing people to farm there. Eventually it would be a nice place to live. But we’d feel the bad effects right away: there would be a global sea level rise of about 7 meters, which would inundate most of the world’s coastal cities.

If the change were very slow, we’d have more time to move our cities, and readapt in other ways. And quite generally, slow changes in the Earth’s climate are easier to handle than rapid ones.

1) There is a small warming trend in the global mean temperature of the last century. It did slow down in the last 15 years despite CO2 continually increasing.

2) The complexity of global climate and limitations of scientific method make it is impossible to say how much of this warming is attributable to man-made emissions. Maybe most of it, maybe only a little. Current long term climate models are completely inadequate and unreliable.

It’s nice to see this list all in one place. To me it resembles a multi-layered legal defense more than what I’d call science: “my client had no motive to commit the crime, and even if he did he wasn’t there, and even if he was he didn’t have that gun… and even if he did, the shooting was in self-defense.” But I can see a certain kind of logic to it.

Let me just fire off some instant reactions. Obviously each one of the topics requires a lot of analysis, which can’t be done adequately in blog comments. But here’s what I think:

There is an amazingly rapid sky-rocketing of CO2 concentrations in the last century, unprecedented within the last 800,000 years. Very simple robust physics shows that this is making the Earth warm up, and if it continues, the Earth will warm up more, at a very rapid pace by geological standards.

(Click for details.)

It’s not impossible to determine how much of the observed global warming is due to this effect—not if we don’t demand several decimal points of accuracy. It’s a challenging problem, but not beyond human powers. We’ve got a lot of smart people working on it, so our understanding is converging to the truth. It’s likely that a doubling of CO2 will cause somewhere between 1.5 and 4.5 °C of warming, and our estimates of this will keep getting better.

3) Even assuming the warming will continue into the future it will have both beneficial and harmful effects. Though if it does avert another ice age the beneficial effects will outweigh the harmful ones by far.

We’ve probably already put enough CO2 to significantly postpone the next glacial cycle:

• Andrew Revkin, The next Ice Age and the Anthropocene, Dot Earth, 8 January 2012.

The Milankovich cycles are gentle enough for the next 100,000 years that we’re probably okay for that long, given what we’ve done so far. If we want to avert later glacial cycles, the easiest way is to save some fossil fuels and burn them later as needed.

4) Even if you wanted to do so, there is absolutely no realistic way to halt CO2 emissions (other then another world war leading to population collapse which is also unlikely atm). As long as cheap fossil fuels are available they will be consumed.

This is certainly possible, and this is what I’m scared of.

There are spots of hope. US carbon emissions have hit a 20-year low. California has started a cap-and-trade system, to live up to a law requiring that greenhouse gas emissions be cut to 1990 levels by 2020 and 80% below 1990 levels by 2050. China is considering a carbon tax. And so on. But it’s a tough battle and we could very easily lose it. I’m expecting it to be touch-and-go for the next few decades at least.

• Arrow says:

I am not demanding many decimal places but stating that the climate sensitivity is most likely between 1.5C and 4.5C per CO2 doubling is almost equivalent to my statement above that it is impossible to tell if our emissions are responsible for most of the warming or only a small fraction of it.

During the last 100 years CO2 increased from 300ppm to 385ppm, so 85ppm or 28% of the doubling. Assuming sensitivity of 1.5C per doubling gives us 0.42C, assuming sensitivity of 4.5C gives us 1.27C, the actual temperature increase in this period was 1C.

And this is only the most likely range, the real sensitivity could still turn out to be outside of it, published estimates have been all over the place and pretty contradictory considering reported confidence:
http://wattsupwiththat.files.wordpress.com/2012/10/climate-sensitivity-estimates.png?w=640&h=323

Data from these graphs:

http://en.wikipedia.org/wiki/File:Global_Temperature_Anomaly_1880-2012.svg

• John Baez says:

Arrow wrote:

I am not demanding many decimal places but stating that the climate sensitivity is most likely between 1.5C and 4.5C per CO2 doubling is almost equivalent to my statement above that it is impossible to tell if our emissions are responsible for most of the warming or only a small fraction of it.

You made a math mistake (see my next comment), so where you said “small fraction” you should have said “half”.

But I made a mistake too: my statement was out of date. In 2001, the IPCC Third Assessment Report judged that the climate sensitivity was likely to be between 1.5 °C and 4.5 °C. In 2007, the Fourth Assessment Report said the climate sensitivity is

likely to be in the range 2 to 4.5 °C with a best estimate of about 3 °C, and is very unlikely to be less than 1.5 °C. Values substantially higher than 4.5 °C cannot be excluded, but agreement of models with observations is not as good for those values

In the earlier report, “likely” was not defined. In the more recent report, “likely” means “greater than 66% chance of being correct”, while “very unlikely” means “less than a 10% chance of being correct”.

A lot of work has been put into ruling out very high climate sensitivities. As time passes, we’ll continue to narrow down the estimate.

Second of all, you shouldn’t neglect the possibility that CO2 is responsible for more than 100% of the observed warming. In fact there’s a growing consensus that this is the case:

The point is that human sulfur dioxide (SO2) emissions have a cooling effect, while greenhouse gases (GHG) have a warming effect. So, it seems roughly 100–170% of global warming is due to our greenhouse gases, mainly CO2. Click the figure for more details.

Third, we can see that rapid human-caused warming is overcoming a long-term cooling trend:

Again, click for details.

Third, even if you believe in the low-end figure of 1.5 °C of warming for each doubling of CO2, you should be scared, since you say that humans will burn all the easily available carbon. So far, through the course of history, humans have put about 567 gigatonnes of carbon into the atmosphere. But the remaining proven reserves of carbon total about 2800 gigatonnes. We can estimate what the effects would be, and they’re not pretty.

For example: so far we’re following the scenario where we don’t limit carbon emissions and we hit 1000 ppm of CO2 by 2100. It doesn’t take anything close to burning all available carbon to do this! This would mean about 1.8 doublings from the pre-industrial value of 280 ppm. With the ultra-optimistic figure of 1.5 °C climate sensitivity, that gives 2.8 °C warming. But with the best-guess figure of 2 °C climate sensitivity, that’s 3.7 °C warming.

If you look at the climate history graph again, you’ll see that even 2.8°C warming between the industrial revolution and 2100 would be an astounding event. It would blast right through the roof here:

• John Baez says:

Arrow wrote:

During the last 100 years CO2 increased from 300ppm to 385ppm, so 85ppm or 28% of the doubling. Assuming sensitivity of 1.5C per doubling gives us 0.42C, assuming sensitivity of 4.5C gives us 1.27C, the actual temperature increase in this period was 1C.

There’s a math mistake here. The idea of climate sensitivity is that temperature increases logarithmically with CO2 concentration. The climate sensitivity is the temperature increase per doubling of CO2. But to see ‘what fraction of a doubling’ we get by going from 300 ppm to 385 ppm, here’s what we do.

First we take the ratio

$385/300 = 1.28 \dots$

Then we take its logarithm using base 2:

$\log_2(1.28) = \ln(1.28)/\ln(2) = 0.36$

So, we get 0.36 of a doubling, not 0.28 as you said.

If the climate sensitivity is 1.5 °C per doubling, that gives 0.54 °C. If the climate sensitivity is 4.5 °C per doubling, that gives 1.62 °C.

If the temperature actually went up 1 °C during the last 100 years, and all the temperature increase were due to CO2, this would correspond to a climate sensitivity during 2.8 °C per doubling.

• Arrow says:

OK, thanks for the correction, I missed that.

So the value of 1.5C would make our emissions account for a bit more then half the warming. Still we don’t really know what the actual sensitivity is. Personally I don’t find IPCC likelyhood estimates trustworthy (how did they come up with them anyway? Also “better then 66%” is only somewhat better then a coin toss).

Yes, the sensitivity could also be pretty high with the warming being masked by other factors but again there is simply no way to tell if this is the case. Appeals to a growing consensus are not convincing to me.

As for the burning of the remaining fossil fuels I don’t see why we should be scared – another 1.8 °C of warming by 2100 seems entirely managable and even an extra 2.7 wouldn’t be a catastrophe. Sure there would be winners and losers (as always) but humanity could certainly adopt. I would be way more scared if we were to run out of cheap fossil fuels soon. That would immediately result in a steep decline in living standards for me and almost everyone else and likely destabilise large regions of the planet.

• John Baez says:

Arrow wrote:

how did they come up with them anyway?

Since all this information is free online, this is something you can easily read about.

Appeals to a growing consensus are not convincing to me.

Again, I gave you a link that takes you to the actual papers. You need to read this stuff to assess it. It’s cheap and easy to be skeptical without looking at the evidence.

As for the burning of the remaining fossil fuels I don’t see why we should be scared – another 1.8 °C of warming by 2100 seems entirely managable and even an extra 2.7 wouldn’t be a catastrophe.

You give no evidence for this shockingly optimistic claim. And don’t forget, assuming a warming of just 2.7°C involves another optimistic assumption: that the climate sensitivity is at the low end of the likely range. As I said, 3.8 °C is a middle-of-the-road estimate. Stacking optimism on optimism tends to end badly.

• Forget about exact climate sensitivity. planet3.org has 2 nice graphs based on the latest hockey stick quoted by John: An “alarmist graph” and a “lukewarmers’ graph”:

Given that this change still takes us well outside the experience of humanity in range, and well outside the normal experience of the biosphere in rapidity, such an outcome offers no grounds for complacency. And the data themselves plainly argue against a sensitivity smaller than that.

http://planet3.org/2013/03/08/why-equilibrium-sensitivity-is-not-policy-relevant/

• Arrow says:

John: “Since all this information is free online, this is something you can easily read about.”
Is it? The section you linked to has nothing relevant although the summary of it is notable “a set of model metrics that might be used to narrow the range of plausible climate change feedbacks and climate sensitivity has yet to be developed”.

However the Box 1.1 in section 1 has among others the following to say about likelyhood estimates: “Structural uncertainties are generally described by giving the authors’ collective judgment of their confidence in the correctness of a result.”
http://www.ipcc.ch/publications_and_data/ar4/wg1/en/ch1s1-6.html
So basically the authors state how confident they are in their results… How objective do you think are such self-assesments? The permanently inflated reaction yields in chemistry come to mind, and in chemistry, unlike in climate science, there is a pretty straightforward way to experimentally verify such claims.

The confidence values of various sensitivity estimates I already linked to are a good illustration of how well such self-assesments agree with each other (they don’t). Averaging diverging guesstimates doesn’t improve our knowledge, it’s the emperor of China’s nose fallacy.
http://wattsupwiththat.files.wordpress.com/2012/10/climate-sensitivity-estimates.png?w=640&h=323

John: “Again, I gave you a link that takes you to the actual papers. You need to read this stuff to assess it. It’s cheap and easy to be skeptical without looking at the evidence.”

The relevant part of your link is this: “However, because aerosols have a number of different effects (including directly by blocking sunlight, and indirectly by seeding clouds, which both block sunlight and increase the greenhouse effect), the magnitude of their cooling effect is one of the biggest remaining uncertainties in climate science.”

And in any case all those papers you mention are based on simplistic climate models which have yet to prove they can simulate anything properly. To me such evidence is worthless. The physics is fine, but knowing the relevant physics doesn’t mean we can reliably simulate global climate just as knowing the relevant physics is not enough to reliably simulate living cells or even folding of single proteins!.

• John Baez says:

Arrow wrote:

The section you linked to has nothing relevant…

The section I linked to is the introduction to chapter 8.6, “Climate Sensitivity and Feedbacks”, in the IPCC Fourth Assessment Report: Climate Change 2007. You were wondering how the IPCC came up with estimates of climate sensitivity. Reading this chapter—not just the introduction—would be the way to find out.

I wrote:

Second of all, you shouldn’t neglect the possibility that CO2 is responsible for more than 100% of the observed warming. In fact there’s a growing consensus that this is the case:

The point is that human sulfur dioxide (SO2) emissions have a cooling effect, while greenhouse gases (GHG) have a warming effect. So, it seems roughly 100–170% of global warming is due to our greenhouse gases, mainly CO2. Click the figure for more details.

Arrow wrote:

Appeals to a growing consensus are not convincing to me.

and then:

The relevant part of your link is this: “However, because aerosols have a number of different effects (including directly by blocking sunlight, and indirectly by seeding clouds, which both block sunlight and increase the greenhouse effect), the magnitude of their cooling effect is one of the biggest remaining uncertainties in climate science.”

That’s nothing new: that’s the reason people estimate the climate sensitivity as lying between 1.5 °C and 4.5 ° C, instead of giving a more narrow range of figures. If I were claiming climate sensitivity were accurately known, you’d be right to bring that up. But I didn’t: I was just claiming that there’s a growing consensus that greenhouse gases contribute more than 100% of the observed global warming, while other factors, such as SO2 and other aerosols, bring this down to the observed figure. This is compatible with the current uncertainty in climate sensitivity.

The relevant part of my link was actually the discussion of the papers on this subject.

Your new comment raises even more issues, but I don’t have time to respond to all of them right now. It would be great if you could dig down to the actual science, and focus in on one issue at a time, instead of making rapid-fire criticisms in many directions at once. We could make a lot more progress understanding the subject that way.

• Arrow says:

I see you misunderstood me, when I wondered “how did they come up with that?” I meant how IPCC managed to turn numerous contradictory sensitivity estimates reported in the literature into the likelihoods they quote for particular sensitivity ranges. For example how did they come up with the 66% number you quoted for climate sensitivity being in 2-4.5C range. Hence my followup but I did manage to find the answer to that question in the report.

Anyway if we were to focus on one issue then by far the most fundamental disagreement we have is about climate models. As I said many times before, I consider all global climate models to be simplistic, inadequate and completely unreliable. This immediately invalidates most of the climate science which is based on them. I find both arguments from authority and from consensus completely empty and unpersuasive, the only thing that matters to me is empirical evidence.

To change my opinion about climate models I would have to see numerous long term (many decades) climate predictions based on them turn out to be correct. I doubt it will happen during my lifetime.

You seem to believe climate models and their predictions are trustworthy. What I would like to know is what makes you think so? And to be sure, neither the fact that many very smart people try their best to make them correct nor the fact that models are based on correct physics count. Biology is the best proof of that if you needed one. Neither very smart people nor the correct physics count for much when it comes to modelling the complexity of life, and I am sure the same holds for climate. The only difference is that in the case of life experiments make our ignorance immediately obvious to us.

• John Baez says:

I’ll reply to your question in a little while… busy preparing final exams!

3. […] 2013/03/04: JCBaez: Tipping Points in Climate Systems […]

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