This Week’s Finds (Week 308)

Last week we met the El Niño-Southern Oscillation, or ENSO. I like to explain things as I learn about them. So, often I look back and find my explanations naive. But this time it took less than a week!

What did it was reading this:

• J. D. Neelin, D. S. Battisti, A. C. Hirst et al., ENSO theory, J. Geophys. Res. 103 (1998), 14261-14290.

I wouldn’t recommend this to the faint of heart. It’s a bit terrifying. It’s well-written, but it tells the long and tangled tale of how theories of the ENSO phenomenon evolved from 1969 to 1998 — a period that saw much progress, but did not end with a neat, clean understanding of this phenomenon. It’s packed with hundreds of references, and sprinkled with somewhat intimidating remarks like:

The Fourier-decomposed longitude and time dependence of these eigensolutions obey dispersion relations familiar to every physical oceanographer…

Nonetheless I found it fascinating — so, I’ll pick off one small idea and explain it now.

As I’m sure you’ve heard, climate science involves some extremely complicated models: some of the most complex known to science. But it also involves models of lesser complexity, like the "box model" explained by Nathan Urban in "week304". And it also involves some extremely simple models that are designed to isolate some interesting phenomena and display them in their Platonic ideal form, stripped of all distractions.

Because of their simplicity, these models are great for mathematicians to think about: we can even prove theorems about them! And simplicity goes along with generality, so the simplest models of all tend to be applicable — in a rough way — not just to the Earth’s climate, but to a vast number of systems. They are, one might say, general possibilities of behavior.

Of course, we can’t expect simple models to describe complicated real-world situations very accurately. That’s not what they’re good for. So, even calling them "models" could be a bit misleading. It might be better to call them "patterns": patterns that can help organize our thinking about complex systems.

There’s a nice mathematical theory of these patterns… indeed, several such theories. But instead of taking a top-down approach, which gets a bit abstract, I’d rather tell you about some examples, which I can illustrate using pictures. But I didn’t make these pictures. They were created by Tim van Beek as part of the Azimuth Code Project. The Azimuth Code Project is a way for programmers to help save the planet. More about that later, at the end of this article.

As we saw last time, the ENSO cycle relies crucially on interactions between the ocean and atmosphere. In some models, we can artificially adjust the strength of these interactions, and we find something interesting. If we set the interaction strength to less than a certain amount, the Pacific Ocean will settle down to a stable equilibrium state. But when we turn it up past that point, we instead see periodic oscillations! Instead of a stable equilibrium state where nothing happens, we have a stable cycle.

This pattern, or at least one pattern of this sort, is called the "Hopf bifurcation". There are various differential equations that exhibit a Hopf bifurcation, but here’s my favorite:

Here and are functions of time, , so these equations describe a point moving around on the plane. It’s easier to see what’s going on in polar coordinates:

The angle goes around at a constant rate while the radius does something more interesting. When , you can see that any solution spirals in towards the origin! Or, if it starts at the origin, it stays there. So, we call the origin a "stable equilibrium".

Here’s a typical solution for , drawn as a curve in the plane. As time passes, the solution spirals in towards the origin:

The equations are more interesting for . Then whenever

This has two solutions, and . Since is a solution, the origin is still an equilibrium. But now it’s not stable: if is between and , we’ll have , so our solution will spiral out, away from the origin and towards the circle . So, we say the origin is an "unstable equilibrium". On the other hand, if starts out bigger than , our solution will spiral in towards that circle.

Here’s a picture of two solutions for :

The red solution starts near the origin and spirals out towards the circle . The green solution starts outside this circle and spirals in towards it, soon becoming indistinguishable from the circle itself. So, this equation describes a system where and quickly settle down to a periodic oscillating behavior.

Since solutions that start anywhere near the circle will keep going round and round getting closer to this circle, it’s called a "stable limit cycle".

This is what the Hopf bifurcation is all about! We’ve got a dynamical system that depends on a parameter, and as we change this parameter, a stable fixed point become unstable, and a stable limit cycle forms around it.

This isn’t quite a mathematical definition yet, but it’s close enough for now. If you want something a bit more precise, try:

• Yuri A. Kuznetsov, Andronov-Hopf bifurcation, Scholarpedia, 2006.

Now, clearly the Hopf bifurcation idea is too simple for describing real-world weather cycles like the ENSO. In the Hopf bifurcation, our system settles down into an orbit very close to the limit cycle, which is perfectly periodic. The ENSO cycle is only roughly periodic:

The time between El Niños varies between 3 and 7 years, averaging around 4 years. There can also be two El Niños without an intervening La Niña, or vice versa. One can try to explain this in various ways.

One very simple, general idea to add random noise to whatever differential equation we were using to model the ENSO cycle, obtaining a so-called stochastic differential equation: a differential equation describing a random process. Richard Kleeman discusses this idea in Tim Palmer’s book:

• Richard Kleeman, Stochastic theories for the irregularity of ENSO, in Stochastic Physics and Climate Modelling, eds. Tim Palmer and Paul Williams, Cambridge U. Press, Cambridge, 2010, pp. 248-265.

Kleeman mentions three general theories for the irregularity of the ENSO. They all involve the idea of separating the weather into "modes" — roughly speaking, different ways that things can oscillate. Some modes are slow and some are fast. The ENSO cycle is defined by the behavior of certain slow modes, but of course these interact with the fast modes. So, there are various options:

1. Perhaps the relevant slow modes interact with each other in a chaotic way.
2. Perhaps the relevant slow modes interact with each other in a non-chaotic way, but also interact with chaotic fast modes, which inject noise into what would otherwise be simple periodic behavior.
3. Perhaps the relevant slow modes interact with each other in a chaotic way, and also interact in a significant way with chaotic fast modes.

Kleeman reviews work on the first option but focuses on the second. The third option is the most complicated, so the pessimist in me suspects that’s what’s really going on. Still, it’s good to start by studying simple models!

How can we get a simple model that illustrates the second option? Simple: take the model we just saw, and add some noise! This idea is discussed in detail here:

• H. A. Dijkstra, L. M. Frankcombe and A.S von der Heydt, The Atlantic Multidecadal Oscillation: a stochastic dynamical systems view, in Stochastic Physics and Climate Modelling, eds. Tim Palmer and Paul Williams, Cambridge U. Press, Cambridge, 2010, pp. 287-306.

This paper is not about the ENSO cycle, but another one, which is often nicknamed the AMO. I would love to talk about it — but not now. Let me just show you the equations for a Hopf bifurcation with noise:

They’re the same as before, but with some new extra terms at the end: that’s the noise.

This could easily get a bit technical, but I don’t want it to. So, I’ll just say some buzzwords and let you click on the links if you want more detail. and are two independent Wiener processes, so they describe Brownian motion in the and coordinates. When we differentiate a Wiener process we get white noise. So, we’re adding some amount of white noise to the equations we had before, and the number says precisely how much. That means that and are no longer specific functions of time: they’re random functions, also known as stochastic processes.

If this were a math course, I’d feel obliged to precisely define all the terms I just dropped on you. But it’s not, so I’ll just show you some pictures!

If and , here are some typical solutions:

They look similar to the solutions we saw before for , but now they have some random wiggles added on.

(You may be wondering what this picture really shows. After all, I said the solutions were random functions of time, not specific functions. But it’s tough to draw a "random function". So, to get one of the curves shown above, what Tim did is randomly choose a function according to some rule for computing probabilities, and draw that.)

If we turn up the noise, our solutions get more wiggly. If and , they look like this:

In these examples, , so we would have a limit cycle if there weren’t any noise — and you can see that even with noise, the solutions approximately tend towards the limit cycle. So, we can use an equation of this sort to describe systems that oscillate, but in a somewhat random way.

But now comes the really interesting part! Suppose . Then we’ve seen that without noise, there’s no limit cycle: any solution quickly spirals in towards the origin. But with noise, something a bit different happens. If and we get a picture like this:

We get irregular oscillations even though there’s no limit cycle! Roughly speaking, the noise keeps knocking the solution away from the stable fixed point at , so it keeps going round and round, but in an irregular way. It may seem to be spiralling in, but if we waited a bit longer it would get kicked out again.

This is a lot easier to see if we plot just as a function of . Then we can run our solution for a longer time without the picture becoming a horrible mess:

If you compare this with the ENSO cycle, you’ll see they look roughly similar:

That’s nice. Of course it doesn’t prove that a model based on a Hopf bifurcation plus noise is "right" — indeed, we don’t really have a model until we’ve chosen variables for both and . But it suggests that a model of this sort could be worth studying.

If you want to see how the Hopf bifurcation plus noise is applied to climate cycles, I suggest starting with the paper by Dijkstra, Frankcombe and von der Heydt. If you want to see it applied to the El Niño-Southern Oscillation, start with Section 6.3 of the ENSO theory paper, and then dig into the many references. Here it seems a model with may work best. If so, noise is not required to keep the ENSO cycle going, but it makes the cycle irregular.

To a mathematician like me, what’s really interesting is how the addition of noise "smooths out" the Hopf bifurcation. When there’s no noise, the qualitative behavior of solutions jumps drastically at . For we have a stable equilibrium, while for we have a stable limit cycle. But in the presence of noise, we get irregular cycles not only for but also . This is not really surprising, but it suggests a bunch of questions. Such as: what are some quantities we can use to describe the behavior of "irregular cycles", and how do these quantities change as a function of and ?

You’ll see some answers to this question in Dijkstra, Frankcombe and von der Heydt’s paper. However, if you’re a mathematician, you’ll instantly think of dozens more questions — like, how can I prove what these guys are saying?

If you make any progress, let me know. If you don’t know where to start, you might try the Dijkstra et al. paper, and then learn a bit about the Hopf bifurcation, stochastic processes, and stochastic differential equations:

• John Guckenheimer and Philip Holmes, Nonlinear Oscillations, Dynamical Systems and Bifurcations of Vector Fields, Springer, Berlin, 1983.

• Zdzisław Brzeźniak and Tomasz Zastawniak, Basic Stochastic Processes: A Course Through Exercises, Springer, Berlin, 1999.

• Bernt Øksendal, Stochastic Differential Equations: An Introduction with Applications, 6th edition, Springer, Berlin, 2003.

Now, about the Azimuth Code Project. Tim van Beek started it just recently, but the Azimuth Project seems to be attracting people who can program, so I have high hopes for it. Tim wrote:

My main objectives to start the Azimuth Code Project were:

• to have a central repository for the code used for simulations or data analysis on the Azimuth Project,

• to have an online free access repository and make all software open source, to enable anyone to use the software, for example to reproduce the results on the Azimuth Project. Also to show by example that this can and should be done for every scientific publication.

Of less importance is:

• to implement the software with an eye to software engineering principles.

This less important because the world of numerical high performance computing differs significantly from the rest of the software industry: it has special requirements and it is not clear at all which paradigms that are useful for the rest will turn out to be useful here. Nevertheless I’m confident that parts of the scientific community will profit from a closer interaction with software engineering.

So, if you like programming, I hope you’ll chat with us and consider joining in! Our next projects involve limit cycles in predator-prey models, stochastic resonance in some theories of the ice ages, and delay differential equations in ENSO models.

And in case you’re wondering, the code used for the pictures above is a simple implementation in Java of the Euler scheme, using random number generating algorithms from Numerical Recipes. Pictures were generated with gnuplot.

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There are two ways of constructing a software design. One way is to make it so simple that there are obviously no deficiencies. And the other way is to make it so complicated that there are no obvious deficiencies. – C.A.R. Hoare

Adapting to a Hotter Earth

Over on the Azimuth Forum, Staffan Liljegren pointed out a good article in The Economist:

• Facing the consequences, The Economist, 25 November 2010.

I’m going to quote the beginning, and hope that lures you into reading the rest. This is important stuff!

Adapting to climate change

Facing the consequences

Global action is not going to stop climate change. The world needs to look harder at how to live with it.

ON NOVEMBER 29th representatives of countries from around the world will gather in Cancún, Mexico, for the first high-level climate talks since those in Copenhagen last December. The organisers hope the meeting in Mexico, unlike the one in Denmark, will be unshowy but solid, leading to decisions about finance, forestry and technology transfer that will leave the world better placed to do something about global warming. Incremental progress is possible, but continued deadlock is likelier. What is out of reach, as at Copenhagen, is agreement on a plausible programme for keeping climate change in check.

The world warmed by about 0.7°C in the 20th century. Every year in this century has been warmer than all but one in the last (1998, since you ask). If carbon-dioxide levels were magically to stabilise where they are now (almost 390 parts per million, 40% more than before the industrial revolution) the world would probably warm by a further half a degree or so as the ocean, which is slow to change its temperature, caught up. But CO₂ levels continue to rise. Despite 20 years of climate negotiation, the world is still on an emissions trajectory that fits pretty easily into the “business as usual” scenarios drawn up by the Intergovernmental Panel on Climate Change (IPCC).

The Copenhagen accord, a non-binding document which was the best that could be salvaged from the summit, talks of trying to keep the world less than 2°C warmer than in pre-industrial times—a level that is rather arbitrarily seen as the threshold for danger. Many countries have, in signing the accord, promised actions that will or should reduce carbon emissions. In the World Energy Outlook, recently published by the International Energy Agency, an assessment of these promises forms the basis of a “new policies scenario” for the next 25 years (see chart 1). According to the IEA, the scenario puts the world on course to warm by 3.5°C by 2100. For comparison, the difference in global mean temperature between the pre-industrial age and the ice ages was about 6°C.

The IEA also looked at what it might take to hit a two-degree target; the answer, says the agency’s chief economist, Fatih Birol, is “too good to be believed”. Every signatory of the Copenhagen accord would have to hit the top of its range of commitments. That would provide a worldwide rate of decarbonisation (reduction in carbon emitted per unit of GDP) twice as large in the decade to come as in the one just past: 2.8% a year, not 1.4%. Mr Birol notes that the highest annual rate on record is 2.5%, in the wake of the first oil shock.

But for the two-degree scenario 2.8% is just the beginning; from 2020 to 2035 the rate of decarbonisation needs to double again, to 5.5%. Though they are unwilling to say it in public, the sheer improbability of such success has led many climate scientists, campaigners and policymakers to conclude that, in the words of Bob Watson, once the head of the IPCC and now the chief scientist at Britain’s Department for Environment, Food and Rural Affairs, “Two degrees is a wishful dream.”

The fight to limit global warming to easily tolerated levels is thus over. Analysts who have long worked on adaptation to climate change—finding ways to live with scarcer water, higher peak temperatures, higher sea levels and weather patterns at odds with those under which today’s settled patterns of farming developed—are starting to see their day in the uncomfortably hot sun. That such measures cannot protect everyone from all harm that climate change may bring does not mean that they should be ignored. On the contrary, they are sorely needed.

For more see:

• World Energy Outlook 2010, Azimuth Project.

This Week’s Finds (Week 307)

I’d like to take a break from interviews and explain some stuff I’m learning about. I’m eager to tell you about some papers in the book Tim Palmer helped edit, Stochastic Physics and Climate Modelling. But those papers are highly theoretical, and theories aren’t very interesting until you know what they’re theories of. So today I’ll talk about "El Niño", which is part of a very interesting climate cycle. Next time I’ll get into more of the math.

I hadn’t originally planned to get into so much detail on the El Niño, but this cycle is a big deal in southern California. In the city of Riverside, where I live, it’s very dry. There is a small river, but it’s just a trickle of water most of the time: there’s a lot less "river" than "side". It almost never rains between March and December. Sometimes, during a "La Niña", it doesn’t even rain in the winter! But then sometimes we have an "El Niño" and get huge floods in the winter. At this point, the tiny stream that gives Riverside its name swells to a huge raging torrent. The difference is very dramatic.

So, I’ve always wanted to understand how the El Niño cycle works — but whenever I tried to read an explanation, I couldn’t follow it!

I finally broke that mental block when I read some stuff on William Kessler‘s website. He’s an expert on the El Niño phenomenon who works at the Pacific Marine Environmental Laboratory. One thing I like about his explanations is that he says what we do know about the El Niño, and also what we don’t know. We don’t know what triggers it!

In fact, Kessler says the El Niño would make a great research topic for a smart young scientist. In an email to me, which he has allowed me to quote, he said:

We understand lots of details but the big picture remains mysterious. And I enjoyed your interview with Tim Palmer because it brought out a lot of the sources of uncertainty in present-generation climate modeling. However, with El Niño, the mystery is beyond Tim’s discussion of the difficulties of climate modeling. We do not know whether the tropical climate system on El Niño timescales is stable (in which case El Niño needs an external trigger, of which there are many candidates) or unstable. In the 80s and 90s we developed simple "toy" models that convinced the community that the system was unstable and El Niño could be expected to arise naturally within the tropical climate system. Now that is in doubt, and we are faced with a fundamental uncertainty about the very nature of the beast. Since none of us old farts has any new ideas (I just came back from a conference that reviewed this stuff), this is a fruitful field for a smart young person.

So, I hope some smart young person reads this and dives into working on El Niño!

But let’s start at the beginning. Why did I have so much trouble understanding explanations of the El Niño? Well, first of all, I’m an old fart. Second, most people are bad at explaining stuff: they skip steps, use jargon they haven’t defined, and so on. But third, climate cycles are hard to explain. There’s a lot about them we don’t understand — as Kessler’s email points out. And they also involve a kind of "cyclic causality" that’s a bit tough to mentally process.

At least where I come from, people find it easy to understand linear chains of causality, like "A causes B, which causes C". For example: why is the king’s throne made of gold? Because the king told his minister "I want a throne of gold!" And the minister told the servant, "Make a throne of gold!" And the servant made the king a throne of gold.

Now that’s what I call an explanation! It’s incredibly satisfying, at least if you don’t wonder why the king wanted a throne of gold in the first place. It’s easy to remember, because it sounds like a story. We hear a lot of stories like this when we’re children, so we’re used to them. My example sounds like the beginning of a fairy tale, where the action is initiated by a "prime mover": the decree of a king.

There’s something a bit trickier about cyclic causality, like "A causes B, which causes C, which causes A." It may sound like a sneaky trick: we consider "circular reasoning" a bad thing. Sometimes it is a sneaky trick. But sometimes this is how things really work!

Why does big business have such influence in American politics? Because big business hires lots of lobbyists, who talk to the politicians, and even give them money. Why are they allowed to do this? Because big business has such influence in American politics. That’s an example of a "vicious circle". You might like to cut it off — but like a snake holding its tail in its mouth, it’s hard to know where to start.

Of course, not all circles are "vicious". Many are "virtuous".

But the really tricky thing is how a circle can sometimes reverse direction. In academia we worry about this a lot: we say a university can either "ratchet up" or "ratchet down". A good university attracts good students and good professors, who bring in more grant money, and all this makes it even better… while a bad university tends to get even worse, for all the same reasons. But sometimes a good university goes bad, or vice versa. Explaining that transition can be hard.

It’s also hard to explain why a La Niña switches to an El Niño, or vice versa. Indeed, it seems scientists still don’t understand this. They have some models that simulate this process, but there are still lots of mysteries. And even if they get models that work perfectly, they still may not be able to tell a good story about it. Wind and water are ultimately described by partial differential equations, not fairy tales.

But anyway, let me tell you a story about how it works. I’m just learning this stuff, so take it with a grain of salt…

The "El Niño/Southern Oscillation" or "ENSO" is the largest form of variability in the Earth’s climate on times scales greater than a year and less than a decade. It occurs across the tropical Pacific Ocean every 3 to 7 years, and on average every 4 years. It can cause extreme weather such as floods and droughts in many regions of the world. Countries dependent on agriculture and fishing, especially those bordering the Pacific Ocean, are the most affected.

And here’s a cute little animation of it produced by the Australian Bureau of Meteorology:

Let me tell you first about La Niña, and then El Niño. If you keep glancing back at this little animation, I promise you can understand everything I’ll say.

Winds called trade winds blow west across the tropical Pacific. During La Niña years, water at the ocean’s surface moves west with these winds, warming up in the sunlight as it goes. So, warm water collects at the ocean’s surface in the western Pacific. This creates more clouds and rainstorms in Asia. Meanwhile, since surface water is being dragged west by the wind, cold water from below gets pulled up to take its place in the eastern Pacific, off the coast of South America.

I hope this makes sense so far. But there’s another aspect to the story. Because the ocean’s surface is warmer in the western Pacific, it heats the air and makes it rise. So, wind blows west to fill the "gap" left by rising air. This strengthens the westward-blowing trade winds.

So, it’s a kind of feedback loop: the oceans being warmer in the western Pacific helps the trade winds blow west, and that makes the western oceans even warmer.

Get it? This should all make sense so far, except for one thing. There’s one big question, and I hope you’re asking it. Namely:

Why do the trade winds blow west?

If I don’t answer this, my story so far would work just as well if I switched the words "west" and "east". That wouldn’t necessarily mean my story was wrong. It might just mean that there were two equally good options: a La Niña phase where the trade winds blow west, and another phase — say, El Niño — where they blow east! From everything I’ve said so far, the world could be permanently stuck in one of these phases. Or, maybe it could randomly flip between these two phases for some reason.

Something roughly like this last choice is actually true. But it’s not so simple: there’s not a complete symmetry between west and east.

Why not? Mainly because the Earth is turning to the east.

Air near the equator warms up and rises, so new air from more northern or southern regions moves in to take its place. But because the Earth is fatter at the equator, the equator is moving faster to the east. So, the new air from other places is moving less quickly by comparison… so as seen by someone standing on the equator, it blows west. This is an example of the Coriolis effect:

By the way: in case this stuff wasn’t tricky enough already, a wind that blows to the west is called an easterly, because it blows from the east! That’s what happens when you put sailors in charge of scientific terminology. So the westward-blowing trade winds are called "northeasterly trades" and "southeasterly trades" in the picture above. But don’t let that confuse you.

(I also tend to think of Asia as the "Far East" and California as the "West Coast", so I always need to keep reminding myself that Asia is in the west Pacific, while California is in the east Pacific. But don’t let that confuse you either! Just repeat after me until it makes perfect sense: "The easterlies blow west from West Coast to Far East".)

Okay: silly terminology aside, I hope everything makes perfect sense so far. The trade winds have a good intrinsic reason to blow west, but in the La Niña phase they’re also part of a feedback loop where they make the western Pacific warmer… which in turn helps the trade winds blow west.

But then comes an El Niño! Now for some reason the westward winds weaken. This lets the built-up warm water in the western Pacific slosh back east. And with weaker westward winds, less cold water is pulled up to the surface in the east. So, the eastern Pacific warms up. This makes for more clouds and rain in the eastern Pacific — that’s when we get floods in Southern California. And with the ocean warmer in the eastern Pacific, hot air rises there, which tends to counteract the westward winds even more!

In other words, all the feedbacks reverse themselves.

But note: the trade winds never mainly blow east. During an El Niño they still blow west, just a bit less. So, the climate is not flip-flopping between two symmetrical alternatives. It’s flip-flopping between two asymmetrical alternatives.

I hope all this makes sense… except for one thing. There’s another big question, and I hope you’re asking it. Namely:

Why do the westward trade winds weaken?

We could also ask the same question about the start of the La Niña phase: why do the westward trade winds get stronger?

The short answer is that nobody knows. Or at least there’s no one story that everyone agrees on. There are actually several stories… and perhaps more than one of them is true. But now let me just show you the data:

The top graph shows variations in the water temperature of the tropical Eastern Pacific ocean. When it’s hot we have El Niños: those are the red hills in the top graph. The blue valleys are La Niñas. Note that it’s possible to have two El Niños in a row without an intervening La Niña, or vice versa!

The bottom graph shows the "Southern Oscillation Index" or "SOI". This is the air pressure in Tahiti minus the air pressure in Darwin, Australia. You can see those locations here:

So, when the SOI is high, the air pressure is higher in the east Pacific than in the west Pacific. This is what we expect in an La Niña: that’s why the westward trade winds are strong then! Conversely, the SOI is low in the El Niño phase. This variation in the SOI is called the Southern Oscillation.

If you look at the graphs above, you’ll see how one looks almost like an upside-down version of the other. So, El Niño/La Niña cycle is tightly linked to the Southern Oscillation.

Another thing you’ll see from is that ENSO cycle is far from perfectly periodic! Here’s a graph of the Southern Oscillation Index going back a lot further:

This graph was made by William Kessler. His explanations of the ENSO cycle are the first ones I really understood:

• William Kessler, What is El Niño and how does it relate to the usual situation in the tropical Pacific?
• William Kessler, El Niño: How it works, how we observe it.

My own explanation here is a slow-motion, watered-down version of his. Any mistakes are, of course, mine. To conclude, I want to quote his discussion of theories about why an El Niño starts, and why it ends. As you’ll see, this part is a bit more technical. It involves three concepts I haven’t explained yet:

• The "thermocline" is the border between the warmer surface water in the ocean and the cold deep water, 100 to 200 meters below the surface. During the La Niña phase, warm water is blown to the western Pacific, and cold water is pulled up to the surface of the eastern Pacific. So, the thermocline is deeper in the west than the east:
  
  
  

  When an El Niño occurs, the thermocline flattens out:

  
  
  
  
  
  

• "Oceanic Rossby waves" are very low-frequency waves in the ocean’s surface and thermocline. At the ocean’s surface they are only 5 centimeters high, but hundreds of kilometers across. They move at about 10 centimeters/second, requiring months to years to cross the ocean! The surface waves are mirrored by waves in the thermocline, which are much larger, 10-50 meters in height. When the surface goes up, the thermocline goes down.
• The "Madden-Julian Oscillation" or "MJO" is the largest form of variability in the tropical atmosphere on time scales of 30-90 days. It’s a pulse that moves east across the Indian Ocean and Pacific ocean at 4-8 meters/second. It manifests itself as patches of anomalously high rainfall and also anomalously low rainfall. Strong Madden-Julian Oscillations are often seen 6-12 months before an El Niño starts.

With this bit of background, let’s read what Kessler wrote:

There are two main theories at present. The first is that the event is initiated by the reflection from the western boundary of the Pacific of an oceanic Rossby wave (type of low-frequency planetary wave that moves only west). The reflected wave is supposed to lower the thermocline in the west-central Pacific and thereby warm the SST [sea surface temperature] by reducing the efficiency of upwelling to cool the surface. Then that makes winds blow towards the (slightly) warmer water and really start the event. The nice part about this theory is that the Rossby waves can be observed for months before the reflection, which implies that El Niño is predictable.

The other idea is that the trigger is essentially random. The tropical convection (organized largescale thunderstorm activity) in the rising air tends to occur in bursts that last for about a month, and these bursts propagate out of the Indian Ocean (known as the Madden-Julian Oscillation). Since the storms are geostrophic (rotating according to the turning of the earth, which means they rotate clockwise in the southern hemisphere and counter-clockwise in the north), storm winds on the equator always blow towards the east. If the storms are strong enough, or last long enough, then those eastward winds may be enought to start the sloshing. But specific Madden-Julian Oscillation events are not predictable much in advance (just as specific weather events are not predictable in advance), and so to the extent that this is the main element, then El Niño will not be predictable.

In my opinion both these two processes can be important in different El Niños. Some models that did not have the MJO storms were successful in predicting the events of 1986-87 and 1991-92. That suggests that the Rossby wave part was a main influence at that time. But those same models have failed to predict the events since then, and the westerlies have appeared to come from nowhere. It is also quite possible that these two general sets of ideas are incomplete, and that there are other causes entirely. The fact that we have very intermittent skill at predicting the major turns of the ENSO cycle (as opposed to the very good forecasts that can be made once an event has begun) suggests that there remain important elements that are await explanation.

Next time I’ll talk a bit about mathematical models of the ENSO and another climate cycle — but please keep in mind that these cycles are still far from fully understood!

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To hate is to study, to study is to understand, to understand is to appreciate, to appreciate is to love. So maybe I’ll end up loving your theory. – John Archibald Wheeler

Cancún

What happened at the United Nations Climate Change Conference in Cancún this year? I’m trying to figure that out, and I could use your help.

But if you’re just as confused as I am, this is an easy place to start:

• Climate talks wrap with hope for developing nations, Weekend Edition Saturday, National Public Radio.

Here’s what I’ve learned so far.

The good news is, first, that the negotiations didn’t completely collapse. That was a real fear.

Second, 190 countries agreed to start a Green Climate Fund to raise and disburse $100 billion per year to help developing countries deal with climate change… starting in 2020.

A good idea, but maybe too late. The World Bank estimates that the cost of adapting to a world that’s 2 °C warmer by 2050 will be about $75-100 billion per year. The International Energy Agency estimates that the cost of supporting clean energy technology in developing countries is $110 billion per year if we’re going to keep the temperature rise below 2 °C. But these organizations say we need to start now, not a decade from now!

And how to raise the money? The Prime Minister of Norway, Jens Stoltenberg, leads the UN committee that’s supposed to answer this question. He told the BBC that the best approach would be a price on carbon that begins to reflect the damage it does:

Carbon pricing has a double climate effect — it’s a huge source for revenue, but also gives the right incentives for reducing emissions by making it expensive to pollute. The more ambitious we are, the higher the price will be – so there’s a very close link between the ceiling we set for emissions and the price. We estimate that we need a price of about $20/25 per tonne to mobilise the $100bn.

Third, our leaders made some steps towards saving the world’s forests. Every year, forests equal to the area of England get cut down. T This has got to stop, for all sorts of reasons. For one thing, it causes 20% of the world’s greenhouse gas emissions — about the same as transportation worldwide!

Cancun set up a framework called REDD+, which stands for Reducing Emissions from Deforestation and Degrading Emissions, with the cute little + standing for broader ecosystem conservation. This is supposed to create incentives to keep forests standing. But there’s a lot of work left. For example, while a $4.1 billion start-up fund is already in place, there’s no long-term plan for financing REDD+ yet.

The bad news? Well, the main bad news is that there’s still a gap between what countries have pledged to do to reduce carbon emissions, and what they’d need to do to keep the expected rise in temperature below 2 °C — or if you want a clearer goal, keeping CO₂ concentrations below 450 parts per million.

But it’s not as bad as you might think… at least if you believe this chart put out by the Center for American Progress. They say:

We found that even prior to the Copenhagen climate summit, if all parties did everything they claimed they would do at the time, the world was only five gigatons of annual emissions shy of the estimated 17 gigatons of carbon dioxide or CO₂ equivalent annual reductions needed to put us on a reasonable 2°C pathway. Since three gigatons of the projected reductions came from the economic downturn and improved projections on deforestation and peat emissions, the actual pledges of countries for additional reductions were slightly less than two-thirds of what was needed. But they were still not sufficient for the 2°C target.

and then:

After the Copenhagen Accord was finalized at the December 2009 climate summit, a January 2010 deadline was established for countries to submit pledges for actions by 2020 consistent with the accord’s 2°C goal. Two breakdowns of the pledges in February, and later in March, by Project Catalyst estimated that the five-gigaton gap had shrunk somewhat and more pledges had come in from developing countries. Part of the reason that pledges increased from developing countries was that the Copenhagen Accord had finally made a significant step forward on establishing a system of cooperation between developed and developing countries that had a chance at providing incentives for additional reductions.

And now, they say, the gap is down to 4 gigatons per year. This chart details it… click to make it bigger:

That 4-gigaton gap doesn’t sound so bad. But of course, this estimate assumes that pledges translate into reality!

So, the fingernail-biting saga of our planet continues…

This Week’s Finds (Week 306)

This week I’ll interview another physicist who successfully made the transition from gravity to climate science: Tim Palmer.

JB: I hear you are starting to build a climate science research group at Oxford.  What led you to this point? What are your goals?

TP: I started my research career at Oxford University, doing a PhD in general relativity theory under the cosmologist Dennis Sciama (himself a student of Paul Dirac). Then I switched gear and have spent most of my career working on the dynamics and predictability of weather and climate, mostly working in national and international meteorological and climatological institutes. Now I’m back in Oxford as a Royal Society Research Professor in climate physics. Oxford has a lot of climate-related activities going on, both in basic science and in impact and policy issues. I want to develop activities in climate physics. Oxford has wonderful Physics and Mathematics Departments and I am keen to try to exploit human resources from these areas where possible.

The general area which interests me is in the area of uncertainty in climate prediction; finding ways to estimate uncertainty reliably and, of course, to reduce uncertainty. Over the years I have helped develop new techniques to predict uncertainty in weather forecasts. Because climate is a nonlinear system, the growth of initial uncertainty is flow dependent. Some days when the system is in a relatively stable part of state space, accurate weather predictions can be made a week or more ahead of time. In other more unstable situations, predictability is limited to a couple of days. Ensemble weather forecast techniques help estimate such flow dependent predictability, and this has enormous practical relevance.

How to estimate uncertainty in climate predictions is much more tricky than for weather prediction. There is, of course, the human element: how much we reduce greenhouse gas emissions will impact on future climate. But leaving this aside, there is the difficult issue of how to estimate the accuracy of the underlying computer models we use to predict climate.

To say a bit more about this, the problem is to do with how well climate models simulate the natural processes which amplify the anthropogenic increases in greenhouse gases (notably carbon dioxide). A key aspect of this amplification process is associated with the role of water in climate. For example, water vapour is itself a powerful greenhouse gas. If we were to assume that the relative humidity of the atmosphere (the percentage of the amount of water vapour at which the air would be saturated) was constant as the atmosphere warms under anthropogenic climate change, then humidity would amplify the climate change by a factor of two or more. On top of this, clouds — i.e. water in its liquid rather than gaseous form — have the potential to further amplify climate change (or indeed decrease it depending on the type or structure of the clouds). Finally, water in its solid phase can also be a significant amplifier of climate change. For example, sea ice reflects sunlight back to space. However as sea ice melts, e.g. in the Arctic, the underlying water absorbs more of the sunlight than before, again amplifying the underlying climate change signal.

We can approach these problems in two ways. Firstly we can use simplified mathematical models in which plausible assumptions (like the constant relative humidity one) are made to make the mathematics tractable. Secondly, we can try to simulate climate ab initio using the basic laws of physics (here, mostly, but not exclusively, the laws of classical physics). If we are to have confidence in climate predictions, this ab initio approach has to be pursued. However, unlike, say temperature in the atmosphere, water vapour and cloud liquid water have more of a fractal distribution, with both large and small scales. We cannot simulate accurately the small scales in a global climate model with fixed (say 100km) grid, and this, perhaps more than anything, is the source of uncertainty in climate predictions.

This is not just a theoretical problem (although there is some interesting mathematics involved, e.g. of multifractal distribution theory and so on). In the coming years, governments will be looking to spend billions on new infrastructure for society to adapt to climate change: more reservoirs, better flood defences, bigger storm sewers etc etc. It is obviously important that this money is spent wisely. Hence we need to have some quantitative and reliable estimate of certainty that in regions where more reservoirs are to be built, the climate really will get drier and so on.

There is another reason for developing quantitative methods for estimating uncertainty: climate geoengineering. If we spray aerosols in the stratosphere, or whiten clouds by spraying sea salt into them, we need to be sure we are not doing something terrible to our climate, like shutting off the monsoons, or decreasing rainfall over Amazonia (which might then make the rainforest a source of carbon for the atmosphere rather than a sink). Reliable estimates of uncertainty of regional impacts of geoengineering are going to be essential in the future.

My goals? To bring quantitative methods from physics and maths into climate decision making.  One area that particularly interests me is the application of nonlinear stochastic-dynamic techniques to represent unresolved scales of motion in the ab initio models. If you are interested to learn more about this, please see this book:

• Tim Palmer and Paul Williams, editors, Stochastic Physics and Climate Modelling, Cambridge U. Press, Cambridge, 2010.

JB: Thanks! I’ve been reading that book. I’ll talk about it next time on This Week’s Finds.

Suppose you were advising a college student who wanted to do something that would really make a difference when it comes to the world’s environmental problems.  What would you tell them?

TP: Well although this sounds a bit of a cliché, it’s important first and foremost to enjoy and be excited by what you are doing. If you have a burning ambition to work on some area of science without apparent application or use, but feel guilty because it’s not helping to save the planet, then stop feeling guilty and get on with fulfilling your dreams. If you work in some difficult area of science and achieve something significant, then this will give you a feeling of confidence that is impossible to be taught. Feeling confident in one’s abilities will make any subsequent move into new areas of activity, perhaps related to the environment, that much easier. If you demonstrate that confidence at interview, moving fields, even late in life, won’t be so difficult.

In my own case, I did a PhD in general relativity theory, and having achieved this goal (after a bleak period in the middle where nothing much seemed to be working out), I did sort of think to myself: if I can add to the pool of knowledge in this, traditionally difficult area of theoretical physics, I can pretty much tackle anything in science. I realize that sounds rather arrogant, and of course life is never as easy as that in practice.

JB: What if you were advising a mathematician or physicist who was already well underway in their career?  I know lots of such people who would like to do something "good for the planet", but feel that they’re already specialized in other areas, and find it hard to switch gears.  In fact I might as well admit it — I’m such a person myself!

TP: Talk to the experts in the field. Face to face. As many as possible. Ask them how your expertise can be put to use. Get them to advise you on key meetings you should try to attend.

JB: Okay.  You’re an expert in the field, so I’ll start with you.  How can my expertise be put to use?  What are some meetings that I should try to attend?

TP: The American Geophysical Union and the European Geophysical Union have big multi-session conferences each year which include mathematicians with an interest in climate. On top of this, mathematical science institutes are increasingly holding meetings to engage mathematicians and climate scientists. For example, the Isaac Newton Institute at Cambridge University is holding a six-month programme on climate and mathematics. I will be there for part of this programme. There have been similar programmes in the US and in Germany very recently.

Of course, as well as going to meetings, or perhaps before going to them, there is the small matter of some reading material. Can I strongly recommend the Working Group One report of the latest IPCC climate change assessments? WG1 is tasked with summarizing the physical science underlying climate change. Start with the WG1 Summary for Policymakers from the Fourth Assessment Report:

• Intergovernmental Panel on Climate Change, Climate Change 2007: The Physical Science Basis, Summary for Policymakers.

and, if you are still interested, tackle the main WG1 report:

• Intergovernmental Panel on Climate Change, Climate Change 2007: The Physical Science Basis, Cambridge U. Press, Cambridge, 2007.

There is a feeling that since the various so-called "Climategate" scandals, in which IPCC were implicated, climate scientists need to be more open about uncertainties in climate predictions and climate prediction models. But in truth, these uncertainties have always been openly discussed in the WG1 reports. These reports are absolutely not the alarmist documents many seem to think, and, I would say, give an extremely balanced picture of the science. The latest report dates from 2007.

JB: I’ve been slowly learning what’s in this report, thanks in part to Nathan Urban, whom I interviewed in previous issues of This Week’s Finds. I’ll have to keep at it.

You told me that there’s a big difference between the "butterfly effect" in chaotic systems with a few degrees of freedom, such as the Lorenz attractor shown above, and the "real butterfly effect" in systems with infinitely many degrees of freedom, like the Navier-Stokes equations, the basic equations describing fluid flow. What’s the main difference?

TP: Everyone knows, or at least think they know, what the butterfly effect is: the exponential growth of small initial uncertainties in chaotic systems, like the Lorenz system, after whom the butterfly effect was named by James Gleick in his excellent popular book:

• James Gleick, Chaos: Making a New Science, Penguin, London, 1998.

But in truth, this is not the butterfly effect as Lorenz had meant it (I knew Ed Lorenz quite well). If you think about it, the possible effect of a flap of a butterfly’s wings on the weather some days later, involves not only an increase in the amplitude of the uncertainty, but also the scale. If we think of a turbulent system like the atmosphere, comprising a continuum of scales, its evolution is described by partial differential equations, not a low order set of ordinary differential equations. Each scale can be thought of as having its own characteristic dominant Lyapunov exponent, and these scales interact nonlinearly.

If we want to estimate the time for a flap of a butterfly’s wings to influence a large scale weather system, we can imagine summing up all the Lyapunov timescales associated with all the scales from the small scales to the large scales. If this sum diverges, then very good, we can say it will take a very long time for a small scale error or uncertainty to influence a large-scale system. But alas, simple scaling arguments suggest that there may be situations (in 3 dimensional turbulence) where this sum converges. Normally, we thinking of convergence as a good thing, but in this case it means that the small scale uncertainty, no matter how small scale it is, can affect the accuracy of the large scale prediction… in finite time. This is quite different to the conventional butterfly effect in low order chaos, where arbitrarily long predictions can be made by reducing initial uncertainty to sufficiently small levels.

JB: What are the practical implications of this difference?

TP: Climate models are finite truncations of the underlying partial differential equations of climate. A crucial question is: how do solutions converge as the truncation gets better and better?  More practically, how many floating point operations per second (flops) does my computer need to have, in order that I can simulate the large-scale components of climate accurately. Teraflops, petaflops, exaflops? Is there an irreducible uncertainty in our ability to simulate climate no matter how many flops we have? Because of the "real" butterfly effect, we simply don’t know. This has real practical implications.

JB: Nobody has proved existence and uniqueness for solutions of the Navier-Stokes equations. Indeed Clay Mathematics Institute is offering a million-dollar prize for settling this question. But meteorologists use these equations to predict the weather with some success.  To mathematicians that might seem a bit strange.  What do you think is going on here?

TP: Actually, for certain simplifications to the Navier-Stokes equations, such as making them hydrostatic (which damps acoustic waves) then existence and uniqueness can be proven. And for weather forecasting we can get away with the hydrostatic approximation for most applications. But in general existence and uniqueness haven’t been proven. The "real" butterfly effect is linked to this. Well obviously the Intergovernmental Panel on Climate Change can’t wait for the mathematicians to solve this problem, but as I tried to suggest above, I don’t think the problem is just an arcane mathematical conundrum, but rather may help us understand better what is possible to predict about climate change and what not.

JB:  Of course, meteorologists are really using a cleverly discretized version of the Navier-Stokes equations to predict the weather. Something vaguely similar happens in quantum field theory: we can use "lattice QCD" to compute the mass of the proton to reasonable accuracy, but nobody knows for sure if QCD makes sense in the continuum.  Indeed, there’s another million-dollar Clay Prize waiting for the person who can figure that out.   Could it be that sometimes a discrete approximation to a continuum theory does a pretty good job even if the continuum theory fundamentally doesn’t make sense?

TP: There you are! Spend a few years working on the continuum limit of lattice QCD and you may end up advising government on the likelihood of unexpected consequences on regional climate arising from some geoengineering proposal! The idea that two so apparently different fields could have elements in common is something bureaucrats find it hard to get their heads round.  We at the sharp end in science need to find ways of making it easier for scientists to move fields (even on a temporary basis) should they want to.

This reminds me of a story. When I was finishing my PhD, my supervisor, Dennis Sciama announced one day that the process of Hawking radiation, from black holes, could be understood using the Principle of Maximum Entropy Production in non-equilibrium thermodynamics. I had never heard of this Principle before, no doubt a gap in my physics education. However, a couple of weeks later, I was talking to a colleague of a colleague who was a climatologist, and he was telling me about a recent paper that purported to show that many of the properties of our climate system could be deduced from the Principle of Maximum Entropy Production. That there might be such a link between black hole theory and climate physics, was one reason that I thought changing fields might not be so difficult after all.

JB: To what extent is the problem of predicting climate insulated from the problems of predicting weather?  I bet this is a hard question, but it seems important.  What do people know about this?

TP: John Von Neumann was an important figure in meteorology (as well, for example, as in quantum theory). He oversaw a project at Princeton just after the Second World War, to develop a numerical weather prediction model based on a discretised version of the Navier-Stokes equations. It was one of the early applications of digital computers. Some years later, the first long-term climate models were developed based on these weather prediction models. But then the two areas of work diverged. People doing climate modelling needed to represent lots of physical processes: the oceans, the cryosphere, the biosphere etc, whereas weather prediction tended to focus on getting better and better discretised representations of the Navier-Stokes equations.

One rationale for this separation was that weather forecasting is an initial value problem whereas climate is a "forced" problem (e.g. how does climate change with a specified increase in carbon dioxide?). Hence, for example, climate people didn’t need to agonise over getting ultra accurate estimates of the initial conditions for their climate forecasts.

But the two communities are converging again. We realise there are lots of synergies between short term weather prediction and climate prediction. Let me give you one very simple example. Whether anthropogenic climate change is going to be catastrophic to society, or is something we will be able to adapt to without too many major problems, we need to understand, as mentioned above, how clouds interact with increasing levels of carbon dioxide. Clouds cannot be represented explicitly in climate models because they occur on scales that can’t be resolved due to computational constraints. So they have to be represented by simplified "parametrisations". We can test these parametrisations in weather forecast models. To put it crudely (to be honest too crudely) if the cloud parametrisations (and corresponding representations of water vapour) are systematically wrong, then the forecasts of tomorrow’s daily maximum temperature will also be systematically wrong.

To give another example, I myself for a number of years have been developing stochastic methods to represent truncation uncertainty in weather prediction models. I am now trying to apply these methods in climate prediction. The ability to test the skill of these stochastic schemes in weather prediction mode is crucial to having confidence in them in climate prediction mode. There are lots of other examples of where a synergy between the two areas is important.

JB: When we met recently, you mentioned that there are currently no high-end supercomputers dedicated to climate issues.  That seems a bit odd.  What sort of resources are there?  And how computationally intensive are the simulations people are doing now?

TP: By "high end" I mean very high end: that is, machines in the petaflop range of performance. If one takes the view that climate change is one of the gravest threats to society, then throwing all the resources that science and technology allows, to try to quantify exactly how grave this threat really is, seems quite sensible to me. On top of that, if we are to spend billions (dollars, pounds, euros etc.) on new technology to adapt to climate change, we had better make sure we are spending the money wisely — no point building new reservoirs if climate change will make your region wetter. So the predictions that it will get drier in such a such a place better be right. Finally, if we are to ever take these geoengineering proposals seriously we’d better be sure we understand the regional consequences. We don’t want to end up shutting off the monsoons! Reliable climate predictions really are essential.

I would say that there is no more computationally complex problem in science than climate prediction. There are two key modes of instability in the atmosphere, the convective instabilites (thunderstorms) with scales of kilometers and what are called baroclinic instabilities (midlatitude weather systems) with scales of thousands of kilometers. Simulating these two instabilities, and their mutual global interactions, is beyond the capability of current global climate models because of computational constraints. On top of this, climate models try to represent not only the physics of climate (including the oceans and the cryosphere), but the chemistry and biology too. That introduces considerable computational complexity in addition to the complexity caused by the multi-scale nature of climate.

By and large individual countries don’t have the financial resources (or at least they claim they don’t!) to fund such high end machines dedicated to climate. And the current economic crisis is not helping! On top of which, for reasons discussed above in relation to the "real" butterfly effect, I can’t go to government and say: "Give me a 100 petaflop machine and I will absolutely definitely be able to reduce uncertainty in forecasts climate change by a factor of 10". In my view, the way forward may be to think about internationally funded supercomputing. So, just as we have internationally funded infrastructure in particle physics, astronomy, so too in climate prediction. Why not?

Actually, very recently the NSF in the US gave a consortium of climate scientists from the US, Europe and Japan, a few months of dedicated time on a top-end Cray XT4 computer called Athena. Athena wasn’t quite in the petaflop range, but not too far off, and using this dedicated time, we produced some fantastic results, otherwise unachievable, showing what the international community could achieve, given the computational resources. Results from the Athena project are currently being written up — they demonstrate what can be done where there is a will from the funding agencies.

JB: In a Guardian article on human-caused climate change you were quoted as saying "There might be a 50% risk of widespread problems or possibly only 1%.  Frankly, I would have said a risk of 1% was sufficient for us to take the problem seriously enough to start thinking about reducing emissions."

It’s hard to argue with that, but starting to think about reducing emissions is vastly less costly than actually reducing them.  What would you say to someone who replied, "If the risk is possibly just 1%, it’s premature to take action — we need more research first"?

TP: The implication of your question is that a 1% risk is just too small to worry about or do anything about. But suppose the next time you checked in to fly to Europe, and they said at the desk that there was a 1% chance that volcanic ash would cause the aircraft engines to fail mid flight, leading the plane to crash, killing all on board. Would you fly? I doubt it!

My real point is that in assessing whether emissions cuts are too expensive, given the uncertainty in climate predictions, we need to assess how much we value things like the Amazon rainforest, or of (preventing the destruction of) countries like Bangladesh or the African Sahel. If we estimate the damage caused by dangerous climate change — let’s say associated with a 4 °C or greater global warming — to be at least 100 times the cost of taking mitigating action, then it is worth taking this action even if the probability of dangerous climate change was just 1%. But of course, according to the latest predictions, the probability of realizing such dangerous climate changes is much nearer 50%. So in reality, it is worth cutting emissions if the value you place on current climate is comparable or greater than the cost of cutting emissions.

Summarising, there are two key points here. Firstly, rational decisions can be made in the light of uncertain scientific input. Secondly, whilst we do certainly need more research, that should not itself be used as a reason for inaction.

Thanks, John, for allowing me the opportunity to express some views about climate physics on your web site.

JB: Thank you!

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The most important questions of life are, for the most part, really only problems of probability. – Pierre Simon, Marquis de Laplace

The Azolla Event

My friend Bruce Smith just pointed out something I’d never heard of:

• Azolla event, Wikipedia.

As you may recall, the dinosaurs were wiped out by an asteroid about 65 million years ago. Then came the Cenozoic Era: first the Paleocene, then the Eocene, and so on. Back in those days, the Earth was very warm compared to now:

Paleontologists call the peak of high temperatures the “Eocene optimum”. Back then, it was about 12 °C warmer on average. The polar regions were much warmer than today, perhaps as mild as the modern-day Pacific Northwest. In fact, giant turtles and alligators thrived north of the Arctic circle!

(“Optimum?” Yes: as if the arguments over global warming weren’t confusing enough already, paleontologists use the term “optimum” for any peak of high temperatures. I think that’s a bit silly. If you were a turtle north of the Arctic circle, it was indeed jolly optimal. But what matters now is not that certain temperature levels are inherently good or bad, but that the temperature is increasing too fast for life to easily adapt.)

Why did it get colder? This is a fascinating and important puzzle. And here’s one puzzle piece I’d never heard about. I don’t know how widely accepted this story is, but here’s how it goes:

In the early Eocene, the Arctic Ocean was almost entirely surrounded by land:

A surface layer of less salty water formed from inflowing rivers, and around 49 million years ago, vast blooms of freshwater fern Azolla began to grow in the Arctic Ocean. Apparently this stuff grows like crazy. And as bits of it died, it sank to the sea floor. This went on for about 800,000 years, and formed a layer 8 up to meters thick. And some scientists speculate that this process sucked up enough carbon dioxide to significantly chill the planet. Some say CO₂ concentrations fell from 3500 ppm in the early Eocene to 650 ppm at around the time of this event!

I don’t understand much about this — I just wanted to mention it. After all, right now people are thinking about fertilizing the ocean to artificially create blooms of phytoplankton that’ll soak up CO₂ and fall to the ocean floor. But if you want to read a well-informed blog article on this topic, try:

• Ole Nielsen, The Azolla event (dramatic bloom 49 million years ago).

By the way, there’s a nice graph of carbon dioxide concentrations here… inferred from boron isotope measurements:

• P. N. Pearson and M. R. Palmer, Atmospheric carbon dioxide concentrations over the past 60 million years, Nature 406 (6797): 695–699.

Our Future

I want to start talking about plans for cutting back carbon emissions, and some scenarios for what may happen, depending on what we do. We’ve got to figure this stuff out!

You’ve probably heard of 350.org, the grassroots organization that’s trying to cut CO₂ levels from their current level of about 390 parts per million back down to 350. That’s a noble goal. However, even stabilizing at some much higher level will require a massive effort, given how long CO₂ stays in the atmosphere:

In a famous 2004 paper, Pacala and Socolow estimated that in a “business-as-usual” scenario, carbon emissions would rise to 14 gigatons per year by 2054… while to keep CO₂ below 500 ppm, they’d need to be held to 7 gigatons/year.

Alas, we’ve already gone up to 8 gigatons of carbon per year! How can we possibly keep things from getting much worse? Pacala and Socolow listed 15 measures, each of which could cut 1 gigaton of carbon per year:

(Click for a bigger image.)

Each one of these measures is big. For example, if you like nuclear power: build 700 gigawatts of nuclear power plants, doubling what we have now. But if you prefer wind: build turbines with 2000 gigawatts of peak capacity, multiplying by 50 what we have now. Or: build photovoltaic solar power plants with 2000 gigawatts of peak capacity, multiplying by 700 what we have now!

Now imagine doing lots of these things…

What if we do nothing? Some MIT scientists estimate that in a business-as-usual scenario, by 2095 there will be about 890 parts per million of CO₂ in the atmosphere, and a 90% chance of a temperature increase between 3.5 and 7.3 degrees Celsius. Pick your scenario! The Stern Review on the Economics of Climate Change has a chart of the choices:

(Again, click for a bigger image.)

Of course the Stern Review has its detractors. I’m not claiming any of these issues are settled: I’m just trying to get the discussion started here. In the weeks to come, I want to go through plans and assessments in more detail, to compare them and try to find the truth.

Here are some assessments and projections I want us to discuss:

• International Panel on Climate Change Fourth Assessment Report, Climate Change 2007.

• The Dutch Government, Assessing an IPCC Assessment.

• The Copenhagen Diagnosis. Summary on the Azimuth Project.

• National Research Council, Climate Stabilization Targets: Emissions, Concentrations, and Impacts over Decades to Millennia. Summary on the Azimuth Project

• K. Anderson and A. Bows, Reframing the climate change challenge in light of post-2000 emission trends. Summary on the Azimuth Project.

• William D. Norhaus, A Question of Balance: Weighing the Options on Global Warming Policies.

• The Stern Review on the Economics of Climate Change.

And here are some “plans of action”:

• The Kyoto Protocol.

• World Nuclear Association, Nuclear Century Outlook. Summary and critique on the Azimuth Project.

• Mark Z. Jacobson and Mark A. Delucchi, A path to sustainable energy: how to get all energy from wind, water and solar power by 2030. Summary and critique on the Azimuth Project.

• Joe Romm, How the world can (and will) stabilize at 350 to 450 ppm: The full global warming solution. Summary on the Azimuth Project.

• Robert Pacala and Stephen Socolow, Stabilization wedges: solving the climate problem for the next 50 years with current technologies. Summary on the Azimuth Project

• New Economics Foundation, The Great Transition: A Tale of How it Turned Out Right. Summary on the Azimuth Project.

• The Union of Concerned Scientists, Climate 2030: A National Blueprint for a Clean Energy Economy.

• The Scottish Government, Renewables Action Plan.

• Bjorn Lømborg and the Copenhagen Business School, Smart Solutions to Climate Change.

As you can see, there’s already a bit about some of these on the Azimuth Project. I want more.

What are the most important things I’m missing on this list? I want broad assessments and projections of the world-wide situation on carbon emissions and energy, and even better, global plans of action. I want us to go through these, compare them, and try to understand where we stand.