The Atmospheric Physics Behind Net Zero

- Well, good evening, everybody. Thank you very much. Welcome to the second Gresham lecture on net zero. I'm Myles Allen, the Frank Jackson Professor of the Environment at Gresham College, and I'm also a professor at the University of Oxford, and today I'm talking to you about the atmospheric physics behind net zero. At the beginning of the last lecture, I talked to you about how different ways in which climate, in which science in general makes progress by chance, by design, by just changing the subject, and in this one, I'm going to talk a little bit about how occasionally science doesn't make progress for interesting reasons. We sort of get stuck for a bit, and there's a couple of instances of how we've got stuck in the history of net zero, which I'll be talking about today. A lot of this history goes back a long way, all the way back to the 19th century. Joseph Fourier, familiar to mathematicians as the person behind Fourier transforms, Eunice Foote, less well known, but I'll talk about her in a minute, and John Tyndall, these were thinkers in the early to mid 19th century who were fascinated by the fact that there was an invisible light out there, infrared light that you couldn't see but which behaved in the same way as visible light, and they were fascinated by this phenomenon. Joseph Fourier speculated without any evidence whatsoever, it's interesting how he sort of came up with the idea, that it was actually gases in the atmosphere that were responsible for keeping the Earth warm,'cause they were able to work out the temperature the planet would be if we had no atmosphere, and hence is credited with having sort of come up with the greenhouse effect originally. Eunice Foote was an American woman who presented a paper of circumstances affecting the heat of the sun's rays, which was the first empirical demonstration of the fact that different gases have a different impact on temperature, and she showed that carbon dioxide in particular was particularly effective at keeping things warm. Interestingly, I'm afraid I don't have a picture of her. We don't have a picture of her says something about 19th century science, doesn't it? And also, she never got to read her paper. Her husband had to read it for her to the American Chemical Society. Fortunately, things have moved on, but we can also bicker a little bit about whether she demonstrated the greenhouse vapor. She definitely demonstrated a different impact of carbon dioxide and water vapor compared to, say, dry air in affecting the heat of the sun's rays. But the man who just a few years later, because of, there was no internet back then, so he can't have known of Eunice Foote's experiments, an Irishman called John Tyndall on the right here was the first to really demonstrate how gases affect infrared light. And he did a number of really elegant experiments and left us some beautiful drawings of his experiments, including this one in which, if you look on the right here, you can see it's labeled C on the diagram, there's a block of metal or something which is being heated by a gas flame underneath it. And the heat, the infrared light from that hot body is going through that long pipe and being measured by that thermopile, the two sort of cones at the other end, and he's passing gases through the pipe to see what the gases did to the passage of the infrared light. And what he was able to show with this very ingenious experiment was that even if you could see through the gas perfectly well with your eyes, for the infrared light, it made a huge difference what gases he put into the pipe, and in particular, he showed that carbon dioxide was a very effective blocker of infrared light. And it was then his experiments that were taken up by another 19th century scientist, this time a Swede, Svante Arrhenius, who actually gave the first quantitative account of the impact of increasing carbon dioxide on global temperatures. So Arrhenius, and this is a quote, well, his paper was in German, but this is a quote from his paper."Any doubling of the percentage of carbon dioxide in the air would raise the earth's temperature by four degrees, and if the carbon dioxide were increased fourfold, it would increase temperature by eight degrees." It almost reads like a sentence out of a modern climate science paper. This was 1898, so it's extraordinary how long ago we've understood this. Interestingly, Arrhenius thought this would take 1,000 years or so, 'cause of course he couldn't possibly anticipate that coal, oil, and gas use would explode. I mean, oil and gas use wasn't really a thing back then. Coal was the fuel of the time. And he thought it might take 1,000 years to happen. He also, being a Swede, thought it'd be a good thing, interestingly. So again, attitudes have changed. But what's really interesting from the point of view of the science is that unfortunately Arrhenius didn't really get to bask in the glory of his discovery or his, for very long, because another Swede, an even more famous Swede, intervened, Angstrom, someone who'd be very well known to any chemist. He actually has a unit named after him, the Angstrom. And what Angstrom did was he was very skeptical about Arrhenius's ideas about carbon dioxide and climate, so he repeated Tyndall's experiment, and he worked out that between him and space was about two meters of carbon dioxide. If you took all the carbon dioxide in the atmosphere and brought it down to the surface, so you had pure carbon dioxide and no carbon dioxide beyond, it's about two meters before you make a note. It's about three meters now. There you go. Stuff's been happening since then. But back then, so two meters. And he also knew that it did, I mean, you know, they understood the absorption of infrared light in gases quite well by this stage, and he understood it didn't really matter how long the path was. What mattered with the amount of stuff in the way. If that sounds implausible to you, I hope you'll forgive this particular analogy, but I find it does work. If you pee in a bucket, the color looking down through the bucket doesn't depend on the amount of water in the bucket. Now, you can all go and try this out at home if you don't believe me.(audience laughs) Don't try it out here, but some, but it's true, so in other words, it's sort of the equivalent. He's bringing the carbon dioxide in, you know, all the way down to the surface, and then checking to see, okay, how much carbon, how much infrared light is it actually absorbing? And what he found was that when he took the sort of right amount of carbon dioxide, the amount between us and space, it's, well, it's 0.04% now. It was 0.03, less than 0.03% back then. And he found that none of the infrared line got through. And if he doubled it, still none of it got through. So he said, "Well, there you go." And if you added water vapor, even less of it got through. I mean, it's a tiny amount got through, and with the water vapor in as well, it made no difference whatsoever. So he then published a paper saying, "Well, Arrhenius was obviously wrong, interesting idea, but actually all of the infrared light gets absorbed by the carbon dioxide, so adding more carbon dioxide can't possibly make any difference," so the CO2 theory is rubbish." Sounds very plausible. In fact, it was completely successful as a debunk of Arrhenius's theory. For 50 years, people forgot all about it. So poor old Arrhenius went to his grave with no idea that he'd actually discovered something important. And actually more, sort of personally, this is important to me because every now and then a physicist somewhere in the world sort of rediscovers Angstrom's argument and writes me an angry email saying, "Climate scientists are all incompetent. You obviously haven't thought about band saturation, and so, you know, global warming is not caused by rising carbon dioxide." And it's sort of understandable that people have this confusion, because if we go to, you know, apologies to "Encyclopaedia Britannica," but they're supposed to get things right. I mean, and this is not an uncommon picture out there. This is sort of the standard schoolbook picture we have of how the greenhouse effect works, and what it implies is that the infrared opacity of the atmosphere, sort of the amount of infrared light that gets through the atmosphere to space, somehow determines the Earth's surface temperature. I mean, Angstrom couldn't do this, but we can now. If we look at the planet in the infrared from space, what's impressive, well, it's a tremendously impressive movie. You can see the daily cycle of cloudiness over somewhere. You can see the swirls of weather motions in the atmosphere and so on. But what you can't see is the surface. Angstrom was right. The atmosphere is completely opaque as far as, you know, for all practical purposes, the atmosphere is opaque in the infrared. So at this point, when I'm giving this lecture to students, some of them will start sort of shifting in their seats and wondering if I'm sponsored by a major oil corporation.(audience laughs) But I'm now going to tell you before you leave or sort of switch off and decide that we don't, global warming's not a thing, I'm now going to tell you how it actually does work because it's not that much more complicated. We just have to think about the way carbon dioxide works in the atmosphere, the way the atmosphere works as well underneath the carbon, you know, holding the carbon dioxide. Carbon dioxide's well mixed through the atmosphere. If you put carbon dioxide into the atmosphere, it's mixed, the proportion of air that is carbon dioxide is the same wherever you are, whatever altitude you're at. So if I just take a chunk of atmosphere, a square column, and I represent carbon dioxide molecules by these colored balls where the temperature of the molecules is indicated by the color, and the absorption density, which is pretty close to the density, but it just varies a little bit faster, that's a sort of, kind of a detail, is indicated by the density, okay? So you can see what I'm driving at here. Before I go any further, the depth of the atmosphere is many kilometers, so these colored balls are sort of hundreds of meters across. I made this graphic to give a presentation to a San Francisco court,'cause I was tasked with explaining how the greenhouse effect works to the court, and afterwards, Rush Limbaugh, a very strong-willed radio host in America, got very angry about the fact that I was a typical climate scientist exaggerating the problem, making out these molecules are much bigger than they are.(audience laughs) So I should warn you, molecules are not to scale. I'm showing you what they do. Here we are, temperature and density of carbon dioxide molecules both decrease with height. So if we look from the side, you can see that progression as you go up through the atmosphere. It gets colder, we all know why it gets colder, with height. You've all experienced that if you've climbed a mountain. Roughly sort of six degrees or so per kilometer, as you climb the mountain, air gets colder. And the density likewise,'cause air is sitting under its own weight. So as you go up through the atmosphere, the density falls off as well. Now, imagine what's going to happen if you look down at this sort of ball pit from above. Well, here's the actual view. You can see you see a, you can see a bunch of colors. What you don't see are those bright reds at the surface. You can't see through the atmosphere. Angstrom was right, okay? What you see is the average color of the balls that you can see, obviously enough, okay? So you can only see some of the way into the atmosphere, and that determines, if we sort of flip that around, each of these balls represents a temperature. They're all releasing energy. The hot ones are releasing energy faster than the cold ones. So the average rate at which the Earth is sending energy back out into space is determined by the average temperature or the average color of the balls you can see from space. So far so good. Now, what's going to happen, so there's the rate of energy emitted to space depends on the average temperature of the molecules that you can see from above. So as we increase CO2, what happens? Well, I've just doubled the density of CO2 molecules everywhere, and I can't see as deep into my ball pit because there's more CO2. So what that does is it forces energy to escape from a higher altitude, because, and you can see immediately, it means that the molecules you can see from space are colder, so they're not releasing as much energy. So that mean higher air is colder, and so it's radiating less energy back out into space. So as we double CO2, we reduce the amount of energy going back out into space. The same energy in, less energy out, global warming. This story has not mentioned the amount of infrared light going all the way through the atmosphere in either direction, okay? So Angstrom was wrong. You can ask at the end. If you haven't, well, and you can either ask or tell me at the end why Angstrom's experiment was wrong, So that's a little challenge to you to think about through the rest of the... So we have an imbalance. Same energy coming in, less energy going out. The system has to warm up, because energy is accumulating in the climate system. How much it warms up, we'll come on to that. But it has to warm up a bit. And here it is warming up, to restore the balance, to make it the same color as it was before. So the whole atmosphere warms up. We've restored that color there to what it was in the original states, the average color. They're different balls, different altitudes. You're not seeing as deep into the atmosphere, but you've warmed it all up, so you're seeing on average the same temperature molecules as you saw before. And even better from the point of view of explaining Arrhenius's observations, if you double it again, you actually get the same reduction in temperature, adding even more balls here. So we've explained two things that Arrhenius posited. One was that increasing CO2 would increase global temperature and also that every doubling of CO2, even though it would take twice as much extra CO2 in the atmosphere to achieve that doubling, every doubling would have actually about the same impact on the global energy budget as the last one. If this has all seemed a bit bemusing, don't panic. This is really well-understood science. I just wanted to stress this here'cause I think it's quite an interesting story about how a very, Angstrom was a Nobel Prize winner, very eminent scientist could basically, he parked the whole CO2 theory for 50 years with that elegant experiment that just missed out what was really crucial, okay, I'll sort of give you a hint here, what was really crucial for understanding the greenhouse effect, which is the interplay between temperature and density through the atmosphere. So, but even if you found this, you know, a little bit confusing, you don't need to worry about it because we've actually seen the impact of rising greenhouse gases from space. And this is an observation that I sort of, it's a beautiful observation, mostly because of the ingenuity of the scientists in the sort of late 1960s. They flew an infrared spectrometer, which if you sort of, that's a really delicate, complicated instrument that you would normally require a lab to operate. And they flew an infrared spectrometer on a spacecraft in 1970, which is an extraordinary achievement, and they got a spectrum of infrared light. So that's a measure of how much infrared light was emerging depending on the color, the color or the wavelengths of the infrared. And then 25-odd years later, 27 years later, it so happens the Japanese space agency flew a similar instrument. They didn't do it deliberately, just so, but John Harries and his coworkers, Helen Brindley, noticed that it was the same observation had been made separated by 27 years, and it was separated also by over 30 or 40 parts per million of carbon dioxide. So carbon dioxide had gone up in the interim as had methane, CFCs, and so on. So they were able to compare these two spectra, correct it for the fact that the temperature was a bit different in the second period, and see the reduction in outgoing energy that resulted from the greenhouse gases in the atmosphere. So it's not a theory. We can see the impact of extra greenhouse gases on outgoing energy in precisely the wavelengths of light, the color of infrared light that we expect to see because of our understanding of the properties of these gases. So, you know, I've told you sort of kind of how it works and why we're very confident in this part of the story that as you increase carbon dioxide concentrations, it's trapping energy in the system. It's slowing down the rate at which energy escapes to space, creating an imbalance between incoming energy from the sun and outgoing energy to space and thereby driving some global warming. I emphasize some because we don't yet know, so in from this explanation, the scientific community has made some progress on this, but this explanation alone doesn't tell you how much global warming. And to understand the response, we need a model. And this headline really annoyed me when I saw it."Yale 360," actually, it's a great website. It's got loads of really good information on it. But this article irritated me, because you don't, trusting a climate model, you trust your priest or your partner. You don't trust a climate model. It's the wrong phrase to apply to a model. A model is a set of equations. It may require a computer to solve them, but that's all it is. And it doesn't always even need a computer to solve them. We can solve equations using fluids and pipes. So I'm now going to introduce you to a little model, a climate model, which we'll be seeing more of during these lectures. And shall we cut to the view of the demo now? Thank you. Somebody's coming over to help that out. So with apologies to the people at front for the gentle whine, but I shall step away from it so that you don't get, hopefully it doesn't pick up too badly on the microphone. But what this represents, this is a way of solving equations. It's a model, but it's not using a computer. It's using, yes, it is using a computer to drive it, okay? But the actual, the calculations themselves are being done by the flow of the fluid in the pipes, because you've got a better intuition probably of how fluid flows through pipes than you have about how energy flows through the global atmosphere. So we'll start at the top here. This is a sort of, this is a simulation of our global climate system. The red stuff, which you can see dripping in, is energy. And so the flow of energy coming in, this is the energy flowing in from the sun, warming our planet. And down the bottom here,(fluid bubbling)(machine whirring) yes, it's going down, not up, but you know, we can't have everything, okay? This is energy flowing back out into space. Can I ask you to ignore the cylinder over on the right-hand side. We were discussing beforehand whether to put some sort of drape, some sort of cloth over it or something for the big reveal in the next lecture. But we'll talk about the cylinder over on the right-hand side. It's got a cork in it. It's not doing anything. Trust me, it's not doing anything, okay? So just ignore it. So we have a balance between energy coming in from the sun and energy flowing out into space, and this balance sets the planetary temperature, which is the level of fluid in this pipe. If we cranked up the power of the sun and we had the same processes controlling energy going back out into space, you can imagine the Earth's going to have to get a lot warmer. I'm going to make one slight modification of this model in order to be able to sort of do experiments with it, which is that this natural flow, which I'm showing you here, is about 240 watts per square meter. That's two, you know, 240 watts every square meter of the Earth's surface, two old-fashioned incandescent light bulbs beating down all the time, flowing in, flowing out. Compare that to the kind of changes that greenhouse gases have had. The greenhouse effect today is about 2.5 to 3 watts per square meters, so 1% or so of that natural flow. So I'd need a sort of fire hose blowing in, okay, to represent the full natural flow. And then, so I'm going to say, well, most of it doesn't change. We're only going to focus on the things that change. So I'm going to say instead of the total energy coming in from the sun, I'm going to talk about the net extra energy flow in, and that could be driven by two kinds of things. A little bit of an increase in the power output of the sun, for example, that would increase the net energy flow in. But because it's the net energy flow in, it could also be increased by more greenhouse gases reducing the energy flow out, yeah? It has the same impact, reduce energy flow out, extra energy in, the net, the impact on the net energy flow in is the same. And so I also have to take that off and say this is the net energy flow back out into space. So this is the extra energy I'm putting in, extra energy when we're sort of departing from equilibrium. And this, instead of being the total planetary temperature, sort of total temperature of the planet is about 200 and, well, it's about 300 degrees. You may think that sounds hot, doesn't it? But that's in total energy units, which are in Kelvin. And we can talk afterwards about what that means if you're interested, but I digress. So this is now, back in sort of centigrade, this is the change in planetary temperature, so changes from that pre-industrial equilibrium state. So just to sort of, so to avoid having to come equipped with a fire hose, we're showing you just small changes about the background states, well, small in the context of the planet, energy flows through the planet as a whole, still substantial in terms of impact on humanity. So what happens if we increase the speed of the pump? Well, I mean, intuitively, you know, you know what's going to happen, but I'm going to do it for you anyway. So I've doubled the speed of the pump.(pump whirring) Mm-hmm. Is it all doing what you expected it to do? I hope so. Actually. I quite often ask a class,"What do you think it's going to do?" And people say, "It's going to overflow." I say, "Well, of course if I overdid it, it would overflow." But it's stopped rising now, hasn't it, yeah? Because now the extra flow in from, at the top is being balanced by the extra flow being driven out by the extra pressure in the pipe. And that corresponds to warmer temperatures in the planet forcing energy back out into space faster than they did before. Now, if I do it again, I'll increase the energy. I'll double the carbon dioxide again. So I'll increase the net energy flow in, and here we are.(pump chugging) So notice we get about the same amount of warming every extra energy flow, every unit increase in the energy flow. Just as a warning, in case you're disappointed when you try this at home, it's really, if I was to use water for this, by the way, I should've prefaced this with, and apologies, guys, for forgetting to mention this, this brilliant contraption was built by Benedict Pery of Oxford physics and Toby Rowles of Durham physics, and they had to think very hard about designing it to make sure it actually did solve the equations we wanted it to solve. And in fact, when I first came up with the idea, I thought, "Well, we'll just use water." And if you try it at home and just use water, you won't find that, you know, extra, double the speed of the pump you get twice as high because water goes turbulent, and turbulence is a mess, turbulence is hard. So this fluid, so if you use olive oil or something like that, it'll be fine, okay? So it's a little bit viscous. So the fluid we're using here is a little bit viscous, stops it going turbulent, stops it getting difficult. As soon as it goes turbulent, life gets difficult. That's a general rule of fluid mechanics. Right, so we've captured the idea that as you increase the net energy into the climate system by increasing greenhouse gases, you require the Earth's surface temperature to increase in order to drive that energy out again to restore the balance between incoming and outgoing energy. So far so good. But with this system, we were able to do a, we were able to do a little test to, if I just restore it to its original, we were able to do a little test of, you know, we raised the pump level a little bit, and then we knew how much, and then we were able to predict how much we'd need to raise the pump level again in order to go, in order to raise it, how much it would raise the water level, the fluid level the second time. Interestingly, when scientists were first thinking about the climate problem, they were more in this situation. They could see it was fluctuating. They could see how it worked. But they hadn't actually turned, well, we humanity hadn't actually dialed up the knob yet. So if you had to do that, now with this simple system, you know, we understand fluid flowing in pipes pretty well. If you knew the viscosity of the fluid, if you knew the diameter of that pipe and so on, you'd be able to predict what would happen. But of course with the climate system, there's a lot of processes involved. So how can we predict before it happens? You know, once we've done it once, we could predict what would happen if we did it again, no problem. But how could we predict how much that would go up when we're in this situation before anything's happened at all? And that comes back to the modeling. So I think I'll go back to the PowerPoint now. So that'll switch off the annoying noise. So remember this, and say a little thank you to Toby Rowles and Ben Pery for their amazing craftsmanship that it actually worked on the day. And we will now switch it off. But you'll see plenty more of it. And if you're wondering what's this and why has it got a cork in it, all will be revealed in the ocean's lecture, yes, that's a hint, in January. So you don't need to trust climate models. This is a model. It's a plastic tube. F is the extra flow we're putting in, h is the increased water depth, k is the openness of the outlet pipe, the sort of willingness of the outlet pipe to let fluid through it, which of course depends on the syrupiness of the fluid you're putting in and so on. And we put these things together, and it's sort of fairly obvious, isn't it? The faster, the bigger the F, the higher the h, the more the fluid level in the pipe will raise. So that's a model. This is a model, the Earth's climate system in equilibrium. Notice it's really very similar. And this is the point. This system of fluid in pipes is solving the same equations. Equations are not things that mathematicians dream up to annoy people at school, although many people feel that's the case. They're actually what nature uses to govern our universe. And this is the equation, or approximately the equation, that governs our climate system in equilibrium. F now is that net additional energy flowing into the climate system, which might be due to a dialing up of the power out of the sun on the one hand or a dialing up of greenhouse gas levels throttling outgoing energy to space, both of which cause a net energy into the climate system. So less energy out is the same as more energy in. T, big capital T, always refers to global average temperature, but now it refers to the increase in global average temperature above pre-industrial, so not an absolute temperature but a change in temperature above pre-industrial, what people refer to as the level of global warming. And lambda here is the sensitivity parameter. It's like k, it's something that it's quite hard to go out and measure. It's just what determines the relationship between F and between the forcing, well, F, the forcing, and T, the temperature. A very important quantity that people talked about for years, and remember I said at the beginning of the lecture I was going to talk about scientific cul-de-sacs a little bit in this lecture, and my personal view is our focus, the climate science community's focus on the equilibrium climate sensitivity was a bit of a cul-de-sac. But when we started thinking about the climate problem, this is the way we thought about it. We knew that as you increase the flow of energy into the climate system, temperatures would have to respond. And we asked, "Well, how much warming would we need to restore the balance between incoming and outgoing energy?" Very simple question to ask. And in particular, people asked this specific question, if we were to double carbon dioxide concentrations, how much warming would we need to restore the balance between incoming and outgoing energy? That's what's called the equilibrium climate sensitivity, and it's exactly the same equation. I've just sort of added these little suffixes here to say this is the special case where you haven't just done any old extra flow of energy in, but you've specifically doubled carbon dioxide. So it's a sort of a standard experiment that people might think of doing, either, well, you can do it with a climate model. We can't actually do it with the real world. Well, we're sort of in the process of doing something like it with the real world, but we aren't in a position with the real world crucially to do what we can do with a climate model, which is to double carbon dioxide and then leave it indefinitely to see what it does. I mean, I suppose we could leave the world. No, okay, nevermind, we'll get lost in the philosophy that, but anyway, and again, lambda here is the sensitivity parameter again, and lambda depends on lots of very uncertain processes in, it depends on water vapor in the atmosphere. It depends on clouds. It depends on melting of snow, how fast sea ice retreats, how the rate of temperature change through the atmosphere adjusts and so on. I could spend a whole lecture talking about what determines lambda, but all you really need to know is the various things that determine lambda are, (coughs) excuse me, are uncertain, so it's uncertain. It's something we're not sure what it is. And back in 1979, Jules Charney chaired a board, a panel of the National Academy of Sciences in the US that estimated a range for this climate sensitivity parameter. This is the thing which Svante Arrhenius said it was about four degrees, remember? Well, these guys, they looked at Arrhenius's reasoning, and they thought that that was probably a bit over the top. They actually, well, they didn't really have much, that much quantitative support to it. What they had was a couple now of actual numerical simulations of the Earth's climate in which they could double carbon dioxide. So they're in the sort of position we were in. I'm not going to switch it on again, 'cause annoying noise, but they were in the position we were in where they hadn't actually done anything to the system itself, and it was sort of wobbling about, but they were using computer simulations of the Earth's climate to try and work out what might happen if we were to double carbon dioxide, and they came up with this range. And it's important to recognize this was an entirely model-based prediction. The blue there shows, you know, these are monthly temperatures since 1850. This is the modern record, so it's, I don't know exactly what the record was like when Jules Charney was looking at it, but the important point was, you know, it wouldn't have been better than this, because it was, we're talking 40 years ago. So, you know, there was no way they hadn't, they weren't observing a global warming at the time. In fact, if anything, temperatures had been pretty stable for the past 20 or 30 years. There is a sort of myth out there that the scientific community was predicting a global ice age in the '70s. It's very hard to find the foundation for this. I mean, there were, you know, every time the weather got cold in the 1970s, a newspaper ran an article saying we're going to get a new ice age. But that's just 'cause that's what newspapers like to do. It's very hard to find actual scientific articles predicting a new ice age back then. But what was very clear to the scientific community was they knew what was happening to carbon dioxide, and they predicted that a likely outcome of that would be a global warming. I actually remember when I was a graduate student in, I mean, you know, so I was a graduate student sort of around here, and I remember a, one of the first lectures I went to, a very eminent professor in Oxford was sort of chatting about this record. And I remember him saying,"Yeah, it's interesting, isn't it, how they always predict the warming right after the end of the data" in a sort of slightly sort of,"Ah, we're cleverer than that" sort of tone of voice. Anyway, obviously were no longer in that situation, but it wasn't, you know, back then global warming was something that, you know, attention-seekers and geographers did, whereas, you know, hardcore physicists did weather and, you know, El Nino and sort of interesting climate variability and that sort of thing. But that, of course, has changed. But you know, back then, the likes of Charney were in a position where, as we were there, that if they were going to make a prediction of global warming, it had to be model based because they weren't, they didn't have any data to help them. And they just had two models, and basically the 1.5 to 4.5 range they gave was based on the fact that the two models they had, one of them had a climate sensitivity of two, the other one had a climate sensitivity of four. They thought, "Well, it's a bit silly just to give the range, so we'll add half a degree on either end." I believe, I talked to Carl Wunsch about it, that was kind of the level it was at. That was what, you know. So can we do better than that? Well, we, you know, fast-forward 25 years or so, and the sort of, if you like, the sort of reductio ad absurdum of the whole enterprise of the scientific community trying to work out, use climate models to pin down the climate sensitivity was an experiment we led from Oxford back in the mid 2000s called climateprediction.net, and some of you may have actually participated in this experiment, we generated, yeah, thanks, we generated versions of a climate model, distributed them all over the world. So people were running these models all over the place. There was one even being run at the South Pole, and they all doubled CO2 and sent us their results back to see what warming they got. And what was really interesting was that they got this sort of distribution. These are the first results we got from the experiment, and they got this distribution of simulated climate sensitivity. So remember, this was 1.5 to 4.5 degrees. That was Jules Charney's range. Arrhenius's estimate was four degrees. So lot of support for Jules Charney's range, but this interesting sort of tale of possible warming going out to some ridiculously high numbers, which caused a certain amount of consternation at the time because it showed how difficult it would be to pin down the risk of high climate sensitivity or high level of warming if we were to stabilize greenhouse gas concentrations at any particular level. And it's interesting that the latest generation of models over here on the right aren't really helping either. I mean, they're not going up to 10 degrees, but they are up at sort of six degrees or so, the highest sensitivities in the models, and you know, well above the upper end of the range that most people think is plausible. So this equilibrium climate response is uncertain, okay? But lots of things are uncertain. The real problem with the equilibrium climate sensitivity is not that it's uncertain, but that it's contestable, that it's difficult to get everybody to agree on the uncertainty in the equilibrium climate sensitivity. And this brings us to a really interesting problem in probability theory, which I'm going to, there's not that many problems in maths that, you know, we can understand unless we're sort of pro mathematicians, but this is one of them. And so suppose you're driving a car with a dodgy speedometer, and you know, okay, so distance equals speed times journey-time. You're familiar with that. So you've got 40 miles to go. You know the distance you've got to travel. The speedo says your speed's somewhere between 20 and 40 miles per hour. I did this last night, so I really hope I haven't made a mistake in the maths. Anyway, so the journey will take between one and two hours. So far so good. You're meant to arrive in 1 1/2 hours. What are the chances that you're going to be late? Who'd like to answer the question? Someone be brave. By the way, I'm willing to accept either of the obvious answers, and I've got both of them covered up. So go for it. You can't go wrong.- [Audience Member] 30.- 30.(audience member speaking faintly) You're meant to, you're going to arrive, the journey will take between one and two hours. You're going to be late if you're more than, you're meant to arrive in 1 1/2 hours. What are the chances you're going to be late? Somebody said 50%, okay. Does anybody want, do I have any other offers?- [Audience Member] 37 1/2%, assuming it's a uniform distribution (speaking faintly).- Okay, so someone's concentrating. If you assume all arrival times in the range are equally likely, yes, 50%. If you assume all speeds in the range are equally likely, 33%, yeah, more or less. No, no, no, no, you're good, you're good, you're good. So which is correct? All you're told is it's a rubbish speedometer. If it says 30, it could be anywhere between 20 and 40. If that's all you're told, which of these is correct? And by the way, I'm not going to tell you the answer to that question because I don't know what it is, okay? Well, some people argue that there is an answer. Let me just show you, it gets even more interesting if we talk about smaller probabilities. So suppose instead of you'll be late, you'll get fired if you arrive in more than 1.9 hours, okay? So what are the odds you're going to get fired? This is a really bad outcome. Well, if you assume all arrival times are equally likely, 10%,'cause between one hour and two hours, 1.9, 10%, yeah, the margin, okay? If you assume all speeds are equally likely, I won't force you to do this one, but it's about 5%, 5.2%, okay? So factor of two difference in probability just based on what you assume your ignorance means, okay? Now, let's think of another problem which may seem slightly more relevant to this lecture. Today's level of energy imbalance due to human activity is, depending on exactly where you measure it from, roughly 2.8 watts per square meter. Just rearranging those equations from before, I'll call it Fnow. That's the extra energy flowing into the climate system as a result of past increases in greenhouse gas concentrations and other forms of anthropogenic pollution in the atmosphere. So if we were to stop the atmosphere changing and hold it at today's concentrations of everything forever, how much warming would we get? Well, that's going to depend on this equilibrium climate sensitivity. So suppose the equilibrium climate sensitivity is 1.5 to 4.5 degrees, and suppose the extra energy flow from a doubling of CO2 is 3.7 watts per meter squared, what are the odds of this equilibrium warming with today's concentrations of greenhouse gases alone? And by the way, these are sort of illustrative examples. So you can do the maths in your head, which I'm sure you're all doing right now, that these are not the actual sort of canonical distributions people accept at the moment. So all, if we assume all values of lambda, of the sensitivity parameter equally likely, we get 7% risk of temperatures going above three degrees. If we assume all values of the climate sensitivity, the warming due to doubling CO2 are equally likely, you won't have done all the maths in your head, but what are you expecting here? Is that going to be a higher number or a lower number? Did somebody say higher? I'm going to pretend you did, well done, okay? So again, a factor of two difference in the risk just arising from what you assume your ignorance looks like. Now, so this is the problem with this equilibrium response. It's not just that it's uncertain. Lots of things are uncertain. We deal with uncertainty all the time. It's the uncertainty in climate sensitivity itself is contestable because the answer seems to depend on sort of subjective decisions about how you set the problem up. What's even worse is it's even contested whether it's contestable. So there are people out there who say,"No, it's not contestable. You have to use this system," okay? And for example, a big school of statistics says, "Yes, this was all solved by Edwin Jaynes in 1970," except that Jaynes's solution has been contested by a paper published by Alon Drury in 2015. Not many bits of maths we can sort of get our minds around more or less are contested by papers published in the past decade. This is out there. This is still being argued over. So the argument continues. Over on the right here, that sort of 2.6 to 4.1, that's the sort of canonical range of climate sensitivity in the most recent Intergovernmental Panel on Climate Change, and it came out of a big study which was initiated in a meeting in a castle in Bavaria. They gathered together all the scientists who'd been thinking about climate sensitivity. It was the Max Planck Institute gathered, and I was in on the original meeting, and it was a very interesting meeting. We all talked about the different lines of evidence, and then a team from the meeting went off to develop this paper, Sherwood, et al., which was the outcome. I wasn't involved in the paper, I guess because the last thing you want on an author team for a paper is somebody who just sits in the corner and says,"This is all pointless. I don't care." So, but that is my view on the climate sensitivity. I think it's a daft question. And of course as recently as a couple of months ago, a new estimate using identical data has emerged, but just different statistical methods and statistical assumptions, which gives us a very different range. So it's difficult to estimate this long-term equilibrium warming of the climate system, even when we take into account additional information from that which is just given us by our climate models. Why does this matter? Well, back in 1992, not long after, well, a decade, 13 years after the Charney report, but at a time when the only experiments we could do with climate models was double CO2 and see how much they warmed up, the Rio Convention was written, and that contained this crucial line that the parties were aiming for stabilization of greenhouse gas concentrations in the atmosphere at a level that would prevent dangerous anthropogenic interference in the climate system. And so immediately the scientific community thought,"Well, we've clearly got to work out what that level is," which meant we had to work out the climate sensitivity. Fortunately, it turns out we don't, and this is the change of the subject that we will be going through in the next two Gresham lectures. But unfortunately, like the thing from the crypt, it's coming back to haunt us even today. So the equilibrium climate sensitivity, this very-long-term equilibrium response, only matters if we actually stabilize atmospheric concentrations of greenhouse gases and allow the climate to re-equilibrate, which takes many, many centuries. The breakthrough in the late 2000s, which led us to net zero, was the realization that we can actually stop the warming well before restoring climate equilibrium if we reduce anthropogenic emissions to net zero. Unfortunately, there's a catch. That assumption was we were talking about anthropogenic emissions, assuming that carbon dioxide that was taken up by plants or oceans would just count as natural uptake, even if it was being taken up faster as a result of the fact there was more carbon dioxide in the atmosphere. We'll come back to this in the carbon cycle lecture, but a worrying development is that people, I guess rather naively, when we published those papers, we thought people would be grateful to nature for carbon that was being taken up by trees growing faster and just regard it as something natural that was happening. But of course those trees belong to somebody or they belong to a country, and now those countries want to take credit for that carbon uptake. And suddenly everybody wants to say that any carbon taken up by anything anywhere is a negative emission and sell it on the offset markets. And if we carry on burning fossil fuels and just buying offsets with these natural absorptions being counted as a negative emission, we're right back to where we started, because then net zero only means stabilizing concentrations in the atmosphere, and it's very hard to predict when temperatures would stop rising if we were to do that. So I just mention this at the end because it's not often that a basic problem of probability theory, by the way, it's called Bertrand's paradox that I've been talking about here, actually has an impact on global climate policy. And it even has an impact when you decide whether or not to check that box next time you take an air flight. It's a good idea, why not do it, but just remember it's not really compensating for your emissions. So that's what we've tried to cover in this lecture, how rising carbon dioxide concentrations cause global warming, how they actually cause global warming as opposed to the schoolbook picture, why the equilibrium climate sensitivity is so hotly contested. And that was the sort of paradigmatic view of climate science and what we were trying to do before net zero. So this was the problem we faced in the 2000s and why we moved, changed the subject to net zero. And then finally this point about how even, you know, quite fundamental thorny issues in probability theory can actually have big global implications, thank you.(audience applauding)- Thanks so much, Professor Allen, for such a fascinating lecture. I've got a couple of questions from online before we're going to go to the room. So the first question is,"Do you think the climate sensitivity problem held up climate policy?"- I think it fed into the way the Rio Convention, it's an interesting feedback. It fed into the way the Rio Convention was framed, which fed into this A-level, and you know, if that's in the convention, this is an important international document, so of course we all ran around trying to solve it. And yes, so I think it, yeah, I think it did, it did hold things up. It certainly in my view wasted a lot of scientists' time. I should say I have colleagues who get very angry when I say that trying to pin down the climate sensitivity was a waste of time. I mean, 'cause they're, "No, no, we're going to keep trying." I said, "Well, yeah, you can search for the holy grail if you want to, but hmm, you know, it may not be that useful when you find it," anyway.- "Here in 2021, the world's largest direct air carbon removal plant opened in Iceland. According to some calculations, it will capture about three seconds worth of each year's global CO2 emissions. Is carbon capture going to get us to net zero?"- It'll have to, but that's the topic of the last Gresham lecture of this year. So please come to the final Gresham lecture of this cycle where we talk about how we actually achieve net zero. Apologies to that questioner.- [Audience Member] How did Arrhenius come up with this number? Did he know, was it a guess, or did he-- I think it was, he was quite lucky. Yeah, a number of things in his calculation. So he didn't do it using this sort of colored balls in the atmosphere argument, but he did know that, he did take into account changing temperature in the atmosphere. And by the way, I should've said, does anybody want to answer the question about Angstrom before we go any further? What was wrong with Angstrom's experiment?- There's someone-- Far away, there's somebody at the back. Did you want to answer Angstrom's experiment? Is that okay?- [Audience Member] Is it to do with speed of the molecules as the temperature increases? So the CO2 molecules are moving less distance (indistinct)?- [Moderator] Could you repeat, please?- Is the, yes, so the suggestion was that it was to do with the speed of the molecules and effectively the sort of path length between collisions of molecules. That actually does affect the speed with which the absorption density of CO2 varies with height, but it's kind of a more subtle effect. No, the big thing that Angstrom got wrong was the temperature of the gas in the pipe was the same, whereas in the atmosphere it cools off by, you know, between the surface, 300, you know, 300 Kelvin, sorry, in familiar units, 15 or so degrees at the surface down to minus 70 or so up at the tropopause. So we have this huge gradient of temperature in the atmosphere, which of course Angstrom didn't have in his pipe. If the atmosphere was all the same temperature, it's true, Angstrom would be right. It wouldn't make any difference to add more CO2 to it, because if you think about those colored balls, if they were all the same temperature, if they were all the same color, doubling the concentration wouldn't change the color as you perceive it from the top. It'd be just the same color because they were all the same colors to start with. So that's what, that's the crucial thing Angstrom got wrong was that he did this elegant experiment, but he left out a crucial ingredient which worked in the real world.- [Audience Member] And sorry, yeah, is it true to say that the relationship between the extra CO2 amount and the rising temperature is far from smooth because of tipping points like methane released from melting permafrost or melting ice and things like that? Or are they relatively small effects in the grand scheme?- I mean, if I just, so far, it's been sort of depressingly predictable, if you like. And this is of course one of the concerns is that will the climate sort of operate in a sort of a jump thing, like a bad vehicle sort of lurching forwards and so on? But most of the models we have, at least for sort of low levels of warming, warm up fairly predictably up to sort of two or three degrees. Beyond that, I think it's kind of, beyond that, there'd be dragons, yeah? I mean, I wouldn't want to give too many assurances. But that's what the model, we've not been there. We've not tried this experiment on the real world before. So we don't know.- Professor Allen, we have one more from online, which I'm going to ask you now."Why does carbon dioxide not act equally as two-way insulation?"- Well, it does in the sense that it absorbs energy, depending on, I'm not quite sure what you mean by two-way, but it does absorb energy going up in the same way it absorbs energy going down, but crucially, there's much more energy going up because the surface is much warmer than space. Space is really cold, four degrees Kelvin, so minus 269 Centigrade. So, you know, that's why most of the energy that a carbon dioxide molecule encounters as it sort of wanders around through the atmosphere is coming up from below. If you're meaning that the, why doesn't carbon dioxide not interact with visible light, that's actually, why does it prefer to interact with infrared light, not visible light? That's actually a really interesting question. I mean, hmm, and really to answer that, you sort of get to the point in the road where you, the sort of signs say you can't really go further without quantum mechanics. But I mean, just to give you an idea, the carbon dioxide molecules, because it's a three molecule, it's a three-atom molecule, so it can bend in all kinds of ways, and it's sort of relatively floppy compared to, say, an oxygen or nitrogen molecule, which can only really do sort of one thing. So that's why carbon dioxide can, if you like, resonate to lower frequency, at lower frequencies than an oxygen or nitrogen molecule can, which is why, if you imagine a floppy guitar string, a loose guitar string gives a deeper, longer, a deeper and lower frequency note than a tight guitar string, yeah? So an oxygen or nitrogen molecule is like a tight guitar string. It can only do really high frequencies, visible light. It can only, well, it doesn't even interact with visible light. It interacts with ultraviolet, that's about it. It doesn't really interact with very much at all. Whereas the carbon dioxide molecule, it's floppier, so it can resonate at these lower frequencies that are associated with infrared light. So that's the big difference between carbon, but interestingly, if you shine visible light at a carbon dioxide molecule, that barely notices because the light is too, the frequency is too high.- Professor Allen, thank you so much. I'm afraid that's all the time we have for questions now, but please do come and ask any further questions to Professor Allen in person. I'm going to remind you about the date of his next lecture, which is, it's the Ocean Physics Behind Net Zero on the 31st of January. And I believe that's going to be here, but do check our website.- And that is when we uncork the ocean.(audience laughs)- Thank you very much.(audience applauding)